Production of

Calcium Magnesium Acetate (CMA)

from Dilute Aqueous Solutions

of Acetic Acid

by

Daniel B. Leineweber

A thesis submitted in partial fulfillment of

the requirements for the degree of

Master of Science

(Chemical Engineering)

at the

University of Wisconsin-Madison

December 25, 2002

Abstract

Calcium Magnesium Acetate (CMA) can be used as a biodegradable non-

corrosive deicing salt, and has already been selected by the U.S. Federal

Highway Administration as the road salt to replace sodium chloride. Another

potential use for CMA is as an additive to coal combustion, where it acts as a

catalyst and sulfur remover. Hence CMA is likely to become a bulk chemical

used in multi-million ton quantities in the future.

In order to reduce the high production cost associated with conventional

processes, fermentation has been proposed as an advantageous route for CMA

production. The bioconversion of low-grade biomass yields acetic acid which

is then reacted with dolime or dolomite to make CMA. This can be done

directly by addition of dolime or dolomite to the fermentor, neutralizing the

acid and thus helping to avoid product inhibition of the organisms. However,

producing a stoichiometric solution of CMA in this manner is complicated by

the different reactivities and solubilities of the various corresponding calcium

and magnesium compounds, particularly in dilute acetic acid solutions such

as those present in the context of fermentation.

The main objective of this study is to gain a better understanding of the

thermodynamics and kinetics of the various reactions involved in the pro-

duction of CMA and to find ways to control the composition of the product.

Equilibrium models are examined both theoretically and experimentally to

obtain some information about thermodynamic limitations, and a dynamic

model is developed for a hypothetic continuous fermentation process to give

at least a qualitative idea of the kinetic features. A more practical approach

is made to specifically address the problem of composition control—it is

shown that a stationary solids phase allows producing a stoichiometric so-

i

lution of CMA, and, more generally, that it is possible to achieve a wide

range of other product compositions if desired. Feasibility is confirmed by an

experimental continuous dissolution process, and the performance of three

different neutralizer materials is compared: type S dolime and selectively

calcined dolomite are both found to be adequate choices for future applica-

tions; however, the use of uncalcined dolomite is not recommended due to

its very low reactivity. Selectively calcined dolomite provides the option of

producing a high-magnesium CMA with a calcium to magnesium mole ra-

tio of 2:3, which might be suitable for crystallization as a double salt; this

finding makes the almost unknown selectively calcined material particularly

interesting. The preliminary design of a process for the production of CMA

from wood hydrolyzate (waste sugars) and selectively calcined dolomite is

presented, and an economic analysis shows that this new process compares

well to previously proposed ones.

ii

Acknowledgements

Many individuals and institutions have contributed either directly or indi-

rectly to this study; I should like to mention some of them by name:

Professor D. C. Cameron deserves credit for his idea to investigate the

problem of composition control in the context of CMA fermentation processes

and to look at CMA production from the viewpoint of aquatic chemistry—

nobody had ever done this before. By asking the right questions he helped

me to determine the direction of my research; as my major professor he also

read and commented on several draft versions of my thesis.

Professor R. E. Swaney, who has worked with me on this project as a

co-advisor, spent hours discussing problems related to process design and

economics, and he has given me many useful suggestions. It also was a

valuable experience for me to be a teaching assistant in his ChE 450 Process

Design course—as a matter of fact, this course even inspired my idea of

examining CMA as a possible new byproduct of the pulp and paper industry.

The Department of Chemical Engineering here at UW-Madison has al-

ways provided a friendly atmosphere and a great environment for doing re-

search. They have also supported me financially during summer and fall 1992

by offering me a combined teaching/research assistantship, when it turned

out that it was not possible to get funding from other sources. All this help

iii

and support is greatly appreciated.

Several Undergraduate Students have worked with me on experiments

during their ChE 424 Summer Lab, and D. Kotowsky has helped me with

the preparation of selectively calcined dolomite during the fall semester.

Last but not least I also want to thank my parents in Germany for their

continuous support and my girl friend Elizabeth for her patience and love.

iv

Contents

1 CMA and Its Applications 1

1.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Properties of CMA . . . . . . . . . . . . . . . . . . . . . . . . 5

2 The Production of CMA 10

2.1 Raw Materials and Reactions . . . . . . . . . . . . . . . . . . 10

2.2 Production Routes and Costs . . . . . . . . . . . . . . . . . . 15

2.3 In-Fermentor Production of CMA . . . . . . . . . . . . . . . . 19

2.3.1 Process and Organism . . . . . . . . . . . . . . . . . . 19

2.3.2 Encountered Problems . . . . . . . . . . . . . . . . . . 29

3 Equilibrium Models 32

3.1 Nonideal Effects in Aquatic Solutions . . . . . . . . . . . . . . 33

3.2 The Hydroxide System . . . . . . . . . . . . . . . . . . . . . . 37

3.3 The Carbonate System . . . . . . . . . . . . . . . . . . . . . . 49

4 The Dynamic Approach 59

4.1 Heterogenous Reactions . . . . . . . . . . . . . . . . . . . . . 61

4.2 Kinetics of Dissolution . . . . . . . . . . . . . . . . . . . . . . 66

v

4.2.1 Carbonates: Calcite, Magnesite, Dolomite . . . . . . . 67

4.2.2 Oxide Minerals: CaO, MgO . . . . . . . . . . . . . . . 83

4.3 The Dynamic Model and Its Limitations . . . . . . . . . . . . 89

4.3.1 Outline of the Process Model . . . . . . . . . . . . . . 90

4.3.2 Model Uncertainties and Conclusions . . . . . . . . . . 105

5 Process Design Considerations 107

5.1 How to Solve the Mole Ratio Problem . . . . . . . . . . . . . 109

5.1.1 Stationary Solids Phase . . . . . . . . . . . . . . . . . 109

5.1.2 Experimental Realization . . . . . . . . . . . . . . . . . 115

5.2 Preliminary Plant Design . . . . . . . . . . . . . . . . . . . . . 129

5.2.1 Process Description and Flowsheet . . . . . . . . . . . 130

5.2.2 Economic Analysis and Discussion . . . . . . . . . . . 140

6 Analysis of Results 144

6.1 Results and Conclusions . . . . . . . . . . . . . . . . . . . . . 144

6.2 Future Work and Recommendations . . . . . . . . . . . . . . . 149

A Original ICP Data 151

A.1 Equilibrium Experiments (Chapter 3) . . . . . . . . . . . . . 151

A.2 CMA Production (Section 5.1.2) . . . . . . . . . . . . . . . . 153

B Lime and Limestone Analyses 157

B.1 Type S Dolomitic Hydrated Lime . . . . . . . . . . . . . . . . 157

B.2 Dolomitic Limestone . . . . . . . . . . . . . . . . . . . . . . . 159

C Equipment List (Section 5.1.2) 160

vi

List of Tables

1.1 Properties of CaAc2 and MgAc2 . . . . . . . . . . . . . . . . . 6

2.1 Inhibition of C. thermoaceticum by CMA . . . . . . . . . . . . 25

2.2 Dependence of product inhibition on pH . . . . . . . . . . . . 27

3.1 Tableau of the hydroxide system . . . . . . . . . . . . . . . . . 40

3.2 Equilibrium speciation for the hydroxide system . . . . . . . . 42

3.3 Tableau of the carbonate system . . . . . . . . . . . . . . . . . 51

3.4 Equilibrium speciation for the carbonate system . . . . . . . . 53

4.1 Rate constants for calcite and magnesite . . . . . . . . . . . . 70

4.2 Rate constants for dolomite . . . . . . . . . . . . . . . . . . . 79

4.3 Summary of carbonate and oxide dissolution rates . . . . . . . 89

4.4 Tableau of the liquid phase equilibrium model . . . . . . . . . 96

5.1 Capital requirement for CMA plant . . . . . . . . . . . . . . . 141

5.2 Annual operating cost for CMA plant . . . . . . . . . . . . . . 142

A.1 ICP results for equilibrium experiments . . . . . . . . . . . . . 152

A.2 ICP results for CMA from type S dolime . . . . . . . . . . . . 154

A.3 ICP results for CMA from selectively calcined dolomite . . . . 155

vii

A.4 Concentrations of impurities . . . . . . . . . . . . . . . . . . . 156

B.1 Sieve analysis of type S dolime . . . . . . . . . . . . . . . . . . 158

B.2 Chemical analysis of type S dolime . . . . . . . . . . . . . . . 158

viii

List of Figures

1.1 Phase diagram for CaAc2 – H2O . . . . . . . . . . . . . . . . . 8

1.2 Phase diagram for MgAc2 – H2O . . . . . . . . . . . . . . . . 9

2.1 In-fermentor production of CMA (batch process) . . . . . . . . 28

3.1 Titration of hydroxides—solid species . . . . . . . . . . . . . . 46

3.2 Titration of hydroxides—soluble species . . . . . . . . . . . . . 47

3.3 Titration of carbonates—solid species . . . . . . . . . . . . . . 55

3.4 Titration of carbonates—soluble species . . . . . . . . . . . . 56

4.1 Concentration profiles for heterogenous reactions . . . . . . . . 62

4.2 Surface reaction and mass transfer . . . . . . . . . . . . . . . 65

4.3 Calcite dissolution—dominance of reaction mechanisms . . . . 72

4.4 Carbonate dissolution rates vs. pH . . . . . . . . . . . . . . . 78

4.5 Magnesium oxide dissolution rates vs. pH . . . . . . . . . . . . 88

4.6 Overall structure of model system . . . . . . . . . . . . . . . . 91

5.1 Setup of experimental system . . . . . . . . . . . . . . . . . . 116

5.2 Production of CMA from type S dolime . . . . . . . . . . . . . 120

5.3 Production of CMA from selectively calcined dolomite . . . . 123

5.4 Ideal mole ratio curves . . . . . . . . . . . . . . . . . . . . . . 127

ix

5.5 Block flow diagram of acetic acid pulping . . . . . . . . . . . . 131

5.6 Mass balance for production of 1:1 CMA . . . . . . . . . . . . 134

5.7 Mass balance for production of 2:3 CMA . . . . . . . . . . . . 136

5.8 Process flow diagram for CMA production . . . . . . . . . . . 137

x

Notation

Dimensions are given in terms of mass (M), length (L), time (t), temperature

(T ), and amount of substance (N).

Latin Letters

A area, L2

A constant in Debye-Huckel formula, L3/2N−1/2

A constant in Davies’ formula, dimensionless

a adjustable size parameter in Debye-Huckel formula, L

Ai molar activity of species i, NL−3

Ai effective surface area for species i, L2

B constant in Debye-Huckel formula, L1/2N−1/2

b constant in Davies’ formula, dimensionless

C molar concentration in bulk solution, NL−3

C(s) molar concentration at surface layer, NL−3

Ceq equilibrium concentration, NL−3

C(s)eq equilibrium concentration at surface layer, NL−3

Ci molar concentration of species i, NL−3

D coefficient of diffusion, L2t−1

xi

D dilution rate, t−1

G Gibbs free energy, ML2t−2

∆G molar free energy change of reaction, ML2t−2N−1

∆G0 standard free energy change of reaction, ML2t−2N−1

F volumetric flow rate, L3t−1

I ionic strength, NL−3

J molar flux, Nt−1L−2

JC molar flux due to surface reaction, Nt−1L−2

JT molar flux due to transport process, Nt−1L−2

K equilibrium constant, dimension varies

Kc concentration equilibrium constant, dimension varies

Ksp solubility product, dimension varies

ki rate constant of chemical reaction i, dimension varies

kC rate constant of heterogenous chemical reaction, dimension varies

kT mass transport coefficient, Lt−1

M molar mean molecular weight, MN−1

Mi molecular weight of species i, MN−1

N amount of substance, N

Ni amount of species i, N

Nx amount of biomass, N

n empirical reaction order, dimensionless

P pressure, ML−1t−2

Pi partial pressure of component i, ML−1t−2

Q reaction quotient, dimension varies

R gas constant, ML2t−2T−1N−1

R net rate of heterogenous reaction, Nt−1L−2

xii

Rf forward rate of heterogenous reaction, Nt−1L−2

Rb backward rate of heterogenous reaction, Nt−1L−2

Si symbol for species i, dimensionless

T absolute temperature, T

TOT total (analytical) concentration, NL−3

t time, t

V volume, L3

xi mole fraction of species i, dimensionless

z rectangular coordinate, L

zi charge number of species i, dimensionless

Greek Letters

αP growth related constant for product formation, dimensionless

αS growth related constant for substrate uptake, dimensionless

βP non-growth related constant for product formation, t−1

βS non-growth related constant for substrate uptake, t−1

δ thickness of diffusion layer (Nernst theory), L

γi activity coefficient of species i, dimensionless

µ growth rate, t−1

µi chemical potential of species i, ML2t−2N−1

µ0i standard free energy of species i, ML−2t−2N−1

νi stoichiometric coefficient of species i, dimensionless

ξi mass fraction of species i, dimensionless

xiii

Subscripts and Superscrips

(aq) aqueous

b backward

C chemical reaction

dol dolomite

eq equilibrium

f feed

f forward

(g) gaseous

P product

S substrate

(s) solid

(s) surface layer

sp solubility product

T transport process

T total (analytical)

x biomass

xiv

Chapter 1

CMA and Its Applications

1.1 Historical Background

Sodium chloride (rock salt) has been used as a deicing agent on roads and

highways in the United States since the 1930s. Because of its effectiveness

over a wide range of temperatures, easy application, and low cost it quickly

became the most common road deicer. The annual consumption of salt for

highway deicing in the U.S. increased from approximately 4 million tons in

the early 1960s to a peak value of 12 million tons by the late 1970s. Cur-

rently about 10 million tons are spread on the roadways every year [Cho91].

Only at very low temperatures calcium chloride—which is significantly more

expensive—is used instead (about 0.3 million tons per year) because it has a

lower eutectic temperature than sodium chloride.

Dumping these huge amounts of salt on the roadways caused serious

corrosion problems, and also a lot of environmental damage. The major

drawbacks are

1

2

• bridge-deck deterioration caused by corroding reinforcing bars,

• corrosion of vehicle chassis,

• pollution of soil, groundwater, and aquatic habitats by sodium and

chloride ions in runoff,

• damage to roadside vegetation.

There is also concern about possible effects on human health caused by high

levels of sodium in drinking water. It has been estimated that the total annual

damage resulting from the use of sodium chloride as road deicer is at least

15 times the cost for purchase and application of the salt [Cho91]. However,

these economic losses must be related to the benefits of road salting like

reduced number of accidents, or reduced business losses due to transportation

delays—economically the benefits still outweigh the losses. Hence it pays to

keep highways snow- and ice-free in winter, but it would pay even more if

this could be done without the adverse effects.

In the early 1970s an extensive research program was initiated by the

Federal Highway Administration (FHWA) in order to investigate the effects

of road salt and find ways to minimize the damage. As a result many im-

provements were made to bridge construction, e.g. sealed concrete bridge

decks, epoxy-coated reinforcing bars, and cathodic protection, which are ex-

pected to slow down bridge deterioration considerably. Measures to reduce

the amount of salt needed for the desired melting effect were also successfully

implemented, mainly through improved application techniques that made it

possible to get the salt to the proper location in the proper amount and

to keep it there. But all of this could not really solve the problems associ-

3

ated with the use of sodium chloride, thus a search for alternative deicing

chemicals was begun.

In 1976 the FHWA awarded a contract for the study of alternative de-

icers to Bjorksten Research Laboratories, Inc. in Madison, WI. This study

was conducted by Dunn and Schenk who became the “inventors” of CMA

[Dun80]. Starting from the periodic table they first eliminated all chemical

elements that were radioactive, toxic or expensive, and by considering deicing

properties, corrosivity, etc. of the compounds that could be made from the

remaining ones they were able to eliminate several more candidates. Only

nine elements were left as possible constituents of new deicing chemicals:

H, C, N, O, Na, Mg, P, K, and Ca. Compounds containing these elements

were grouped in organic compounds, inorganic salts, and mixed salts (con-

sisting of an inorganic and an organic component), and solubility, eutectic

temperature, solution pH, and estimated cost were evaluated for each com-

pound. From the continued elimination process finally two candidate deicers

remained, methanol and calcium magnesium acetate. Both were studied

extensively in lab and field experiments to assess their deicing properties,

potential corrosive effects, and toxicity. Later methanol was also eliminated

because of its flammability, solvent nature, and poor persistency on road

surfaces, thus leaving only CMA for further consideration.

At this point the FHWA and the state highway agencies directed their

efforts towards a comprehensive project for the complete evaluation of CMA.

Numerous institutions were involved in those studies1 made during the 1980s.

General characteristics and deicing properties of CMA were determined, its

practical application was tested in several field trials, production methods

1For a list of references, see [Cho91].

4

were developed, and potential environmental effects were evaluated. It was

found that compared to sodium chloride CMA is

• almost as effective as an deicer and can be applied using the same

equipment,2

• less corrosive to steel and other highway-related metals,

• less damaging to concrete (scaling occurred only for CMA solutions

below pH 7 containing traces of free acetic acid),

• less harmful to soil, groundwater, human health, plant and animal life,

• but unfortunately much more expensive (currently CMA costs 10–

20 times as much as rock salt).

CMA is expected to be environmentally safe: the acetate part is biodegradable

and calcium and magnesium ions are biocompatible, since they are already

present in large amounts in most natural soils. Oxidation of calcium mag-

nesium acetate by soil microorganisms would generate calcium magnesium

carbonates which are non-toxic and could even improve soil quality in some

cases. One minor concern is a possible increase in biological oxygen demand

(BOD) when CMA is flushed into natural waters, but this is not likely to

cause damage because the run-off occurs when temperatures are low and

biological systems function slowly.

Hence this new deicer is in fact quite promising—it has almost ideal

characteristics, the only remaining problem being its high production cost.

The FHWA ended their involvement in CMA research in 1989, but industry,

2The amount of CMA required for the same deicing effect is slightly higher, and there

may be problems with clumping due to the hydroscopic nature of the material.

5

universities, and states are continuing to search for economically feasible ways

of manufacturing CMA, and to further improve the deicing and handling

properties of the material.

Still another potential application for CMA has been proposed recently

[Wis91, Chapters 9–14]: it can be used as an additive to coal combustion,

where it catalyzes the combustion and at the same time acts as a “sulfur

grabber”, forming solid calcium sulfate and thus substantially reducing sulfur

dioxide in the stack gases. The coal merely has to be impregnated with a

CMA solution before combustion. Used in this manner, CMA would help to

prevent acid rain, and would also enhance the efficiency of coal-fired boilers.3

In conclusion, CMA is a very interesting new chemical for environmental

applications—both of its proposed major uses can be expected to have a

large positive impact on the environment.

1.2 Properties of CMA

Usually dry CMA is considered to be a physical mixture of calcium acetate

CaAc2·H2O and magnesium acetate MgAc2·4H2O, both in their stable hy-

drated form as the monohydrate and tetrahydrate, respectively.4 Therefore

it should be possible to produce CMA with an arbitrary mole ratio of Ca:Mg.

Experiments have shown that under conditions of slow crystallization CaAc2

and MgAc2 in fact crystallize separately, while fast crystallization may pro-

duce a double salt with a low Ca:Mg ratio of about 1:3 [Mar85]. A process

for the manufacture of a double salt with empirical formula CaxMgyAc2(x+y)

3It might be preferable to use calcium acetate instead of CMA in this application, since

the magnesium does not react.

4Ac− is widely used as a shorthand notation for the acetate ion CH3COO−.

6

Table 1.1: Properties of CaAc2 and MgAc2; solubilities from [Lin65], allother properties from [Mer83].

Calcium Acetate Magnesium Acetate

formula Ca(CH3COO)2 Mg(CH3COO)2

molecualar weight 158.17g/mol 142.40g/mol

mass fractions O 40.46%C 30.37%Ca 25.34%H 3.82%

O 44.94%C 33.73%Mg 17.08%H 4.25%

stable form (25◦C) monohydrate tetrahydrate

density 1.50g/cm3 (anhydrate) 1.45g/cm3 (tetrahydrate)

solubility (25◦C) 34.2g CaAc2/100g H2O 65.6g MgAc2/100g H2O(55◦C) 32.8g CaAc2/100g H2O 97.9g MgAc2/100g H2O

melting point (decomposes at 160◦C) about 80◦C

prior uses in leather manufacture none reportedin lubricants

as food stabilizeras corrosion inhibitor

where x = 3 to 4 and y = 7 to 6 has been patented [Tod90], and is currently

used by Chevron Chemical Co. for commercial production of CMA.

Table 1.1 shows some properties of the individual acetate salts. Both

CaAc2 and MgAc2 have a high solubility in water—a necessary condition for

effective freezing point depression and good deicing performance. Note that

the solubility of CaAc2 decreases with increasing temperature, while MgAc2

has a positive temperature coefficient of solubility. The eutectic tempera-

7

tures with water as reported by [Dun80] are −15◦C for CaAc2 and −30◦C

for MgAc2 compared to −21.1◦C for NaCl; the corresponding phase diagrams

are shown in Figures 1.1 and 1.2. From this data one should expect bet-

ter deicing properties for high-magnesium CMA or even consider the use of

pure magnesium acetate. In fact the evaluation of eutectic data for CMA

solutions of various Ca:Mg mole ratios revealed that optimum freezing point

depression was obtained for a Ca:Mg ratio of 3:7 over a wide range of CMA

concentrations. However, under field conditions this 3:7 CMA tended to be

much slower in its ice melting rate than the originally proposed 1:1 CMA, so

finally the 1:1 ratio was recommended again as the optimum deicer composi-

tion [Sch91]. This last remark may not apply to the double salt mentioned

above—[Tod90] claim for their CMA unique properties that are not com-

parable to those of a physical mixture with the same composition.

Probably as important as the chemical composition is the physical form

of the deicer. As Gancy points out [Gan84a, Gan84b], dense and course

particles are required for effective ice removal, because it is sufficient to just

break up the ice layer by “drilling holes” down to the pavement and weak-

ening the pavement-ice interface. The ice layer then fractures and is finally

cleared away by the ongoing traffic. Hence it would be an enormous waste

of deicer material to use a fine powder or a brine in an attempt to melt all

the ice on the road surface. The most preferred physical form for a CMA

deicer is the hard, coarse, and non-friable flake which can be produced from

wet CMA using a drum pelletizer or similar equipment.

8

−40

−30

−20

−10

0

10

0 10 20 30 40 50

temp.

(◦C)

CaAc2 conc. (wt%)

I

II

III

CaAc2 – H2O liquidusmeasured data 3

3

33

33

33

3

CaAc2 – H2O eutectic linemeasured data 2

2 222 2

2

NaCl – H2O eutectic +

+

Figure 1.1: Phase diagram for CaAc2 – H2O. In region I there is only liquidCaAc2 solution present, in region II there is water ice and liquid CaAc2 solu-tion, and in region III there are two solid phases, water ice and CaAc2·2H2O.Eutectic of NaCl – H2O included for comparison. Adapted from [Dun80].

9

−40

−30

−20

−10

0

10

0 10 20 30 40 50

temp.

(◦C)

MgAc2 conc. (wt%)

I

II

III

MgAc2 – H2O liquidusmeasured data 3

3

3

3

3

3

3

MgAc2 – H2O eutectic linemeasured data 2

2

2

2 2

2

NaCl – H2O eutectic +

+

Figure 1.2: Phase diagram for MgAc2 – H2O. In region I there is onlyliquid MgAc2 solution present, in region II there is water ice and liquidMgAc2 solution, and in region III there are two solid phases, water ice andMgAc2·4H2O. Eutectic of NaCl – H2O included for comparison. Adaptedfrom [Dun80].

Chapter 2

The Production of CMA

2.1 Raw Materials and Reactions

CMA is produced by neutralization of acetic acid with either dolomitic lime-

stone, mainly consisting of calcium and magnesium carbonates, or with its

burned and hydrated form called dolomitic lime, which is mainly calcium

and magnesium hydroxide. Some important properties of these raw materi-

als shall be discussed at this point.

Acetic acid, formula CH3COOH, is a flammable, colorless liquid with a

characteristic sharp odor; it solidifies at 16.7◦C, thus its pure form is

called glacial acetic acid. In aquatic solutions it is weakly dissociated

(pKa = 4.76); at concentrations of 1.0 M, 0.1 M, and 0.01 M the result-

ing pH is 2.4, 2.9, and 3.4, respectively [Mer83]. Many metals, as well

as their oxides and carbonates, dissolve in aqueous solutions of acetic

acid to give simple salts. The reactions are considerably slower than

those of hydrochloric acid or sulfuric acid, but the rate is still higher

10

11

than with most other organic acids [Wag78]. Vinegar, a dilute aque-

ous solution of acetic acid (approximately 5%), has been used as a food

acidulant and preservative for thousands of years. Today acetic acid

is also widely used in the chemical industry as a solvent and as a raw

material for many organic syntheses, e.g. the manufacture of vinyl ac-

etate and cellulose acetate. The acetic acid production capacity in the

United States was 1.6 million tons in 1990, while only about 1.1 million

tons were actually consumed [Bus90]. At the present time the main

production routes for acetic acid are liquid-phase oxidation of n-butane,

and methanol carbonylation, both with feedstocks derived from natu-

ral gas or petroleum [Bus90, Wag78]. Alternative processes include

the destructive distillation of wood, and the fermentation of ethanol or

sugars, but except for the production of vinegar which is still made by

fermentation, these routes were considered no longer competitive when

cheap feedstocks based on natural gas and petroleum were introduced

following World War II. However, more recently there is again a grow-

ing interest in producing acetic acid from renewable biomass sources

like corn or even organic wastes, and much research has been done in

this field [Bus90, Gho85, Sch82b,Wan78]. The price1 for synthetic

glacial acetic acid was between $ 500 and $ 600 per ton in 1990.

Dolomitic limestone is generally understood to contain at least 20 wt%

and up to 44 wt% of MgCO3, it may consist of the carbonate minerals

dolomite, calcite, aragonite, and magnesite in varying relative amounts

along with impurities like silica or alumina. Dolomite is the double

carbonate CaMg(CO3)2, calcite and aragonite are two different crys-

1All product prices and costs are given per (US) ton; 1 ton = 2000 lb = 907.18 kg.

12

talline forms of CaCO3, and magnesite refers to MgCO3. Normally a

magnesium-rich dolomitic limestone (40–44 wt% of MgCO3) is more or

less pure dolomite and therefore has a Ca:Mg mole ratio of approxi-

mately 1:1. Dolomitic stones with 20–40 wt% MgCO3 contain also a

considerable amount of calcite. Since calcite is the main constituent

of high-calcium limestone, calcite and dolomite are by far the most

abundant carbonates of calcium and magnesium. Both aragonite and

magnesite occur in small amounts together with the other carbonate

minerals, but their pure forms are rare and expensive. For the produc-

tion of a 1:1 CMA, dolomite seems to be most suitable, because it has

the required mole ratio. Other dolomitic limestones could be used as

well if a higher calcium content in the product is acceptable. Dolomitic

limestone currently sells for about $ 16 per ton.

Dolomitic lime is produced from dolomitic limestone by calcining , i.e.,

heating the stone to a temperature between 900 and 1100◦C in a kiln.

The carbonates are transformed into oxides, and CO2 is released. Lime-

stone particle size, temperature, and calcination time are important

factors determining the quality of the product. Ideally, the particles do

not change in size and form during calcination; they just loose weight

and become more and more porous. A lime particle is said to be un-

derburned, when it still has an unreacted core of carbonate, and it is

overburned, when it has lost its porous structure through sintering.

The limestone fed into the kiln should be of uniform size, since par-

ticles smaller than average tend to be overburned, while larger lumps

are often underburned. The reactivity of the lime with water decreases

with increasing degree of sintering. For most applications, a highly

13

reactive product is desired, and hence overburning of the lime has to

be avoided. However, the so-called dead burned dolomite (sintered at

very high temperatures) is used as a basic refractory. The thermal de-

composition of dolomite is assumed to be a two step process: at low

temperatures (600–725◦C) magnesium oxide and calcite are formed,

and only above 800–900◦C the calcite is decomposed to calcium oxide.

This has two implications:

1. The MgO in fully calcined dolomitic lime is often hardburned and

unreactive, because the sintering of MgO starts at lower temper-

atures than that of CaO.

2. It is possible to produce selectively calcined dolomite CaCO3 ·MgO

by calcining at low temperature. The MgO produced has a very

low degree of sintering; therefore, it is chemically more reactive.

Although this product seems to have some interesting properties

(and could actually be produced with less energy than required

for fully calcined lime) it has never been produced on a large scale

[Bol22, Boy80, Sha22, Sta53].

In most applications the lime is reacted with water in a process called

slaking before use. The reaction of CaO with water is highly exother-

mic and proceeds very fast as long as the lime is not hardburned; CaO

is almost completely transformed into Ca(OH)2. However, under nor-

mal conditions the MgO does not hydrate equally well, since its lower

reactivity tends to be further decreased by overburning. Thus normal

hydrated lime (type N) is comprised of mainly Ca(OH)2 · MgO, and

only small amounts of Mg(OH)2, but it is possible to obtain a fully

14

hydrated product by applying high pressure and temperature during

slaking. This specially treated lime is called type S dolime. Depending

on the amount of water used in the process, either a dry hydrate, a

putty, a slurry, or a liquid (“milk of lime”) result. In the context of

CMA production mainly the use of type N dolomitic lime (obtained

from dolomitic quicklime by “normal” slaking) has been proposed, for

instance by [Mar85], but type S dolomitic lime is more suitable,2 and

selectively calcined dolomite could also have some potential. The mar-

ket price for type S dolime is about $ 67 per ton, for unslaked dolomitic

quicklime about $ 57 per ton. If produced on a large scale, selectively

calcined dolomite could actually be cheaper than quicklime.

Limestone as well as lime reacts with aqueous solutions of acetic acid to

form the desired acetate salts. The governing neutralization reactions for

dolomite, calcite and magnesite are

CaMg(CO3)2 + 4HAc = CaAc2 +MgAc2 + 2CO2 + 2H2O (2.1)

CaCO3 + 2HAc = CaAc2 + CO2 +H2O (2.2)

MgCO3 + 2HAc = MgAc2 + CO2 +H2O, (2.3)

and for the hydroxides

Ca(OH)2 + 2HAc = CaAc2 + 2H2O (2.4)

Mg(OH)2 + 2HAc = MgAc2 + 2H2O. (2.5)

As will be seen later, equilibria and kinetics of these reactions are highly

dependent on pH and tend to be quite different for calcium and magnesium,

2According to a personal communication with Dunn, the type N material suffers from

the low reactivity of the hard-burned magnesium component.

15

respectively. Generally the hydroxides react much faster with acetic acid

than the carbonates.

2.2 Production Routes and Costs

Various kinds of processes have been proposed for the manufacture of CMA,

but only some of them have been actually tested at a pilot plant level. CMA

has not yet been produced on a large scale, and almost all patented and

commercially used processes start from purchased acetic acid as raw material.

Depending on the source of acetic acid, the processes can be grouped into

three basic categories:

Conventional Processes use glacial or concentrated acetic acid which may

be derived from either petroleum or natural gas. Acetic acid produced

in this manner is quite expensive although large scale processes are well

established, because big amounts of valuable raw materials are utilized.

Since acetic acid cost is the key factor determining the cost of the final

product (the weight fraction of acetate in CMA is almost 80%), little

margin is left for improvements that would substantially lower the price

at which CMA can be produced.

The ways of reacting acetic acid with dolime or dolomite to make CMA,

and the subsequent steps necessary to get a dry product in the form

of flakes or pellets have been extensively studied, and many of them

are patented [Gan83, Gan84a, Gan84b, Gan86, Gan87b, Tod90,

Rip86]. Chevron Chemical Co. began commercial production of their

CMA-deicer ICE-B-GONTM in 1985, and they are now one of the main

producers of CMA. The selling price for ICE-B-GONTM was $ 657

16

per ton in 1989; it has been estimated that on a large production scale

a price between $ 400 and $ 450 per ton could possibly be reached—still

too much to really consider complete replacement of sodium chloride

by CMA, since rock salt is available for between $ 25 and $ 50 per ton.

In order to obtain an affordable deicing product it has been suggested

to produce CMA-coated sand or substitute part of the acetate by cheap

chloride [Gan87a].

Fermentation Processes use a feedstock of glucose, corn, or low-grade

biomass (e.g. organic municipal waste) which is converted to acetic acid

by microorganisms like Clostridium thermoaceticum. Depending on

the raw material, a pretreatment may be required before fermentation.

Basically three different routes can be followed for CMA production:

• The acetic acid is extracted from the fermentation broth using

a liquid-ion exchanger and then reacted with dolime [Tra90,

Wis88, Yan92]. The advantages of this approach are that it

would allow continuous operation and would yield a CMA so-

lution at relatively high concentration; potential problems are

the high cost of exchanger-materials and the fact that efficient

extraction requires an acidic pH (only the undissociated acid is

extracted)—therefore, either the fermentation must be done with-

out pH control3 which greatly reduces the production rate and

attainable concentration of acetic acid, or the broth must be acid-

ified before extraction, thus adding another costly step to the pro-

cess and generating a salt solution which has to be disposed of as

3A strain of C. thermoaceticum capable of growth and acetic acid production at pH 4.5

has actually been isolated, but productivity and growth rate were low [Sch82a].

17

a waste stream. It has been proposed to integrate the fermen-

tation and the extraction process to remove the acid from the

reactor while it is being produced in order to avoid or at least re-

duce product inhibition of the organisms, but much more work is

needed before it is possible to assess the viability of such a process.

• CMA is produced directly in the fermentor by controlled addition

of dolime or dolomite to the broth, so that the pH remains in a

favourable range for the organisms during fermentation [Hud88,

Mar85, Wie91]. Batch fermentation as well as continuous pro-

cesses can be used; however, to date significantly higher final

product concentrations were obtained through batch fermenta-

tion. The advantages of this route are higher acetic acid produc-

tion rates (because of pH control) and probably lower capital in-

vestment, since smaller equipment can be used. Among the prob-

lems are the difficulties to produce a stoichiometric CMA solution

from dilute acetic acid at a near-neutral pH, and the inhibition of

the organisms at higher CMA concentrations. The latter restricts

CMA concentrations in the broth to about 5 wt% with currently

available organisms, hence energy requirements for product recov-

ery are relatively high.

• Another interesting route has been described in an early U.S. Pat-

ent dating back to 1932 [Car32]—decades before anyone was talk-

ing about CMA and its potential use as a deicer chemical: During

fermentation the pH is controlled using ammonia, thus producing

a dilute aqueous solution of ammonium acetate. The broth is fil-

tered, and lime (or another nonvolatile base) is added which gives

18

calcium acetate (or some other acetate salt) and easily decom-

posable ammonium compounds like ammonium hydroxide. This

solution is first sent into a scrubbing column to recover the ex-

pensive ammonia and then through a multi-effect evaporator and

dryer, where the water is boiled away and a dry acetate salt is

obtained as final product. In the scrubbing tower, the broth is

contacted with the vapor from the first effect of the evaporator;

the vapor leaving the top of the scrubbing tower serves as the

heating medium in the second effect. It contains about 96% of

the ammonia which can be directly recycled back to the fermen-

tor for reuse as neutralizer.

Cost estimates for fermentation processes range from about $ 260 to

$ 500 per ton, depending on the feedstock, organism, and process scale.

There is still much research under way to find better organisms [Hud88]

or improve existing ones [Lju85, Par90, Wis91] in order to achieve

higher production rates and higher product concentrations.

Alkaline Fusion Processes involve heating cellulosic waste materials in an

excess of alkali to a temperature above 200◦C; an exothermic reaction

then converts the cellulose to acetate (up to 30%), methanol, acetone,

carbonate, and oxalate. Processes of this kind have been already de-

scribed 100 years ago [Cro92], and lab experiments have shown that

they can be easily adapted for CMA production [Dun80], but it has

to be mentioned that the acetate yield is significantly lower for earth

alkaline metals like calcium and magnesium than for alkaline metals

like sodium. There is a patent on an alkaline fusion process for CMA

19

manufacture [San84], but recently there seems to be little interest in

developing this route further, although it might be very promising—

[Dun80] estimated the cost being as low as $ 100 per ton of unpurified

CMA if solid organic wastes were used as raw material.

Throughout the subsequent part of this work, focus will be on fermentation

processes only, and particularly in-fermentor production of CMA will be

considered. Hence a more detailed description of this specific route and of

some of the problems encountered in this context is required, which will be

given in the next section.

2.3 In-Fermentor Production of CMA

2.3.1 Process and Organism

It has been estimated that in-fermentor production of CMA is advantageous

compared to conventional processes, even when a high-cost corn feedstock is

used [Mar85]. The potential use of low-grade biomass like municipal wastes,

agricultural and forest residues, etc. instead of corn would result in further

significant cost reductions, and a selling price of about $ 260 per ton CMA

seems to be attainable [Hud88].

None of the proposed CMA fermentation processes uses the commercially

available technology for vinegar production, a two step process involving

two different organisms, where glucose is first converted anaerobically to

ethanol by Saccharomyces cerevisiae and then further metabolized to acetic

acid under aerobic conditions by Acetobacter aceti. A one step fermentation

with thermophilic homoacetogenic bacteria like Clostridium thermoaceticum

20

[Wan78] is preferred for several reasons:

1. The actual yields of acetic acid are often more than 85% (g acetic acid

per g glucose) for homoacetate fermentations, compared to only 50%

for the vinegar process.

2. Homoacetogenic bacteria are able to produce acetic acid not only from

C6 sugars like glucose, but also from some C5 sugars like xylose that

would represent a significant portion of the sugars produced by hydrol-

ysis of lignocellulosic feedstocks. In the vinegar process only glucose is

metabolized.

3. The homoacetate process is anaerobic, hence simpler equipment can

be used (no aeration, less agitation), and the total energy requirements

including product recovery are lower than in the vinegar process, if the

acetate concentration in the broth is at least 2 wt% [Gho85].

4. Since homoacetate fermentations are carried out at a fairly high tem-

perature level (about 60◦C), the growth of unwanted other organisms

is effectively suppressed. If sterilization is necessary at all, the related

cooling costs are reduced, and there may be other process advantages

like a positive effect on dissolution kinetics of the lime or limestone

introduced for neutralization.

For instance, glucose is converted to acetic acid by C. thermoaceticum with

a theoretical yield of 100% according to the reactions [Wie91]

C6H12O6 + 2H2O −→ 2CH3COOH+ 2CO2 + 8H+ + 8e− (2.6)

2CO2 + 8H+ + 8e− −→ CH3COOH+ 2H2O, (2.7)

21

or in sum,

C6H12O6 −→ 3CH3COOH. (2.8)

It is remarkable that this organism is able to synthesize acetic acid by fixation

of CO2. A similar overall reaction can be written for the metabolization of

xylose

2C5H10O5 −→ 5CH3COOH. (2.9)

Since acetic acid is the only fermentation product, a relatively “clean” solu-

tion of CMA could be obtained without need for expensive separation tech-

niques. If organic wastes containing cellulose and hemicellulose are to be used

as a feedstock, these materials must be transformed into a mixture of soluble

sugars by hydrolysis under mild conditions before they can be fermented.

Wang et al. found that C. thermoaceticum produces acetic acid not only

during growth, but also when cell growth ceases [Wan78]. They used the fol-

lowing model to describe the growth-related and non-growth-related aspects

of product formation,dNP

dt= (αPµ+ βP)Nx, (2.10)

where NP denotes the produced amount of acetic acid in moles, µ the spe-

cific growth rate, and Nx the total biomass in moles, based on the average

elemental composition of cells.4 Since for exponential growth

dNx

dt= µNx, (2.11)

equation (2.10) can be rewritten as

dNP

dt= αP

dNx

dt+ βPNx, (2.12)

4Often the composition CH1.8O0.5N0.16S0.0045P0.0055 is used for biomass, corresponding

to a molecular weight of 24.4 g mol−1 [Rie91].

22

i.e., the total acetic acid production rate depends linearly on both the biomass

growth rate and the amount of biomass already present; the corresponding

terms in equation (2.10) are often referred to as growth term andmaintenance

term. The linear relationship was found to be valid for specific growth rates in

the range of 0 to 0.15 h−1 with αP = 0.8 (mole acetic acid per mole cells) and

βP = 0.065 h−1 (mole acetic acid per mole cells per hour) at pH 7.0 [Wan78].

In a very similar manner, the substrate consumption can be modeled by the

expression

−dNS

dt= (αSµ+ βS)Nx, (2.13)

where NS denotes the amount of substrate consumed in moles, and the overall

yield of product on substrate (“actual” yield) is then given by

Y ovPS = −

dNP/dt

dNS/dt. (2.14)

A typical value for Y ovPS on a mole basis is 2.55 (mole acetic acid per mole glu-

cose), or, equivalently, 0.85 on a weight basis (g acetic acid per g glucose).5

From these results it can be concluded that growth is not absolutely re-

quired for acetic acid production—a high productivity could also be achieved

through high cell density at minimal growth using immobilized cells or cell

recycling.

Direct anaerobic digestion of cellulosic waste by a mixed culture of acid-

formers is another process that has been considered for CMA production

[Tra91, Tra90,Wis88]. The organisms are found in stable manure, pond

mud, and sewage sludge; some of them—called cellulolytic bacteria—are able

to hydrolyze cellulose or hemicellulose, while others depend on the solu-

ble sugars and alcohols provided by the metabolic activity of the former.

5This shows that it is very important to indicate on which basis the yield has been

calculated, although it is a dimensionless quantity.

23

The thermophilic homoacetogenic bacteria discussed above belong to the

second group of organisms and are therefore not capable of using cellulose

as a substrate. Acetic acid is only one of the organic acids produced by

the acid-formers, other products are formic, butyric, propionic, lactic, suc-

cinic, and isobutyric acids [Gho85]. Under normal conditions, these organic

acids are further metabolized to methane by another group of bacteria called

methanogens. Their growth must be suppressed in order to allow for accu-

mulation of acetic acid. Sewage sludge, woody biomass, and in principle, any

kind of organic waste can be directly used in this process, and since these

feedstocks are available in large amounts at a very low cost, or, in some

cases even a credit can be taken for the disposal of such waste materials,

anaerobic digestion seems to be economically quite attractive. On the other

hand, the deicer produced is not pure CMA, but rather a complex mixture

comprising the salts of different organic acids, and hence is likely to be less

effective. In addition, the acetic acid production rate is extremely low, and

the acetate concentration that has been obtained in experiments is also very

low, only about 0.8 wt%, although theoretically 3 wt% should be possible

[Tra91]. This makes product recovery by conventional methods like multi-

effect evaporation too expensive, and an extraction process as described in

the last section must be used. Therefore, anaerobic digestion does not seem

appropriate for in-fermentor production of CMA.

At the moment, batch fermentation appears the most economical, be-

cause it yields the highest final product concentration, and hence minimizes

subsequent drying requirements; however, it is possible to make consider-

able improvements to continuous processes with cell recycling or immobi-

lized cells—these continuous fermentations, when developed, will ultimately

24

be the preferred processes [Wie91]. Contiuous operation per se is advan-

tageous in many respects, but the main advantage is that the continuous

fermentation allows a much higher production rate per unit volume than the

batch process. Acetic acid production rates of up to 8 g l−1 h−1 were re-

ported for continuous processes, compared to less than 1 g l−1 h−1 for batch

fermentations [Bus90]. According to Schwartz and Keller, a productiv-

ity of 5 g l−1 h−1 should be achieved in commercial fermentations for acetic

acid production [Sch82b]. Hence in our context, a CMA production rate of

5 g l−1 h−1 shall be assumed; this corresponds to an acetic acid productivity

of about 4 g l−1 h−1 which should be attainable using a continuous process,

but probably can not be achieved with batch fermentation. A reasonably

concentrated solution of CMA would have 7 to 10 wt% or 75 to 111 g l−1

[Hud88, Mar85]. This target concentration requires microorganisms that

are acclimated to fairly high levels of calcium, magnesium, and acetate. “Nor-

mal” strains of C. thermoaceticum are strongly inhibited by their product

even at near-neutral pH and are also negatively affected by higher concentra-

tions of calcium and magnesium; this led Ljungdahl et al. to the conclusion

that the “properties of the wild type strains (. . . ) do not suggest success-

ful applications of these strains for industrial production of CMA or acetic

acid” [Lju85]. More recently, Parekh and Cheryan were able to isolate

an “improved” strain of C. thermoaceticum that could grow in the presence

of 70 g l−1 sodium acetate, 50 g l−1 magnesium chloride, and 20 g l−1 calcium

chloride at pH 6.8 [Par90]. From this data, the approximate tolerance levels

for acetate, magnesium, and calcium ions are 50 g l−1, 12 g l−1, and 7 g l−1,

respectively (under the conservative assumption that high concentrations of

sodium and chloride do not cause inhibition, i.e., without these additional

25

Table 2.1: Concentrations of calcium, magnesium, and acetate ions in differ-ent CMA solutions compared to the tolerance levels of C. thermoaceticum atpH 6.8. A 1:1 molar ratio of Ca:Mg was assumed for the three fictive CMAsolutions with total concentrations 50, 60, and 70 g l−1. Also included areexperimental results for a 1:3 CMA obtained by [Wie91] in batch fermen-tation at pH 6–6.8. The tolerance levels were calculated from the data of[Par90]. All concentrations are given in units g l−1.

Concentration ofCa2+ Mg2+ Ac− Total CMA

4.8 wt% CMA (1:1) 6.7 4.0 39.3 50.0

5.7 wt% CMA (1:1) 8.0 4.9 47.1 60.0

6.5 wt% CMA (1:1) 9.3 5.7 55.0 70.0

3.1 wt% CMA (1:3) 2.4 4.1 25.8 32.3(experimental)

tolerance levels 7 12 50

ions even higher levels of acetate, magnesium, and calcium might be toler-

ated). Calcium has a relatively high toxicity and would definitely be one of

the factors limiting the attainable concentration of CMA. As shown in Ta-

ble 2.1, it should be theoretically possible to obtain a CMA concentration of

at least 50 g l−1 using this improved strain; at 60 g l−1 the calcium tolerance

would be slightly exceeded, and at 70 g l−1 both calcium and acetate would

be limiting. For these calculations, a 1:1 molar ratio of Ca:Mg was assumed.

Experimentally, 32 g l−1 of a 1:3 CMA were obtained by Wiegel et al. in

their pH controlled batch fermentation [Wie91]. Thus it still is somewhat

optimistic—but not too unrealistic—to assume that it will be possible to at-

26

tain a CMA concentration of about 50 g l−1 (4.8 wt%) with currently available

strains of C. thermoaceticum. This assumption shall be used throughout the

rest of this study, although it falls short of the target concentration stated

above. Possibly, an organism might be genetically engineered that possesses

a higher tolerance to calcium and acetate in order to meet the target. It

has been also proposed to use halophilic organisms from the Dead Sea that

can naturally tolerate the conditions of highly concentrated ionic solutions,

in particular high levels of calcium ion; actually such organisms have been

successfully weaned from sodium chloride and encouraged to produce acetic

acid [Hud88]. But keeping in mind that it is quite difficult to obtain high

product concentrations with continuous processes, 7–10 wt% does not seem

to be a reasonable goal at the moment.

Different studies have shown that C. thermoaceticum is far more sensi-

tive to the undissociated acetic acid than the acetate ion [Sch82b,Wan84].

While acetate ion can be tolerated at concentrations of up to 48 g l−1, total

growth inhibition by undissociated acetic acid already occurs when its con-

centration is as low as 2.8 g l−1 [Wan84]. It is quite instructive to calculate

the maximum attainable total acetic acid concentration (undissociated acetic

acid plus acetate ion) as a function of pH by the Henderson-Hasselbalch

equation

log[Ac−]

[HAc]= pH− pKa (2.15)

and the mole balance

[HAc]T = [HAc] + [Ac−], (2.16)

assuming that neither of the two respective inhibitory concentrations for ac-

etate ion and undissociated acid may be exceeded. Then the maximum total

27

Table 2.2: Calculation of undissociated acetic acid concentration, acetate ionconcentration, and total acetic acid concentration at different values of pH;all concentrations are given in units g l−1.

pH Concentration ofHAc Ac− HAc plus Ac−

5.0 2.8 4.8 7.65.2 2.8 7.6 10.45.4 2.8 12.0 14.85.6 2.8 19.0 21.85.8 2.8 30.2 33.0

6.0 2.8 48.0 50.8

6.2 1.8 48.0 49.86.4 1.1 48.0 49.16.6 0.71 48.0 48.76.8 0.45 48.0 48.57.0 0.28 48.0 48.3

concentration at different values of pH is limited by the inhibitory concen-

tration which is reached first. The results presented in Table 2.2 show that

below pH 6, undissociated acetic acid is responsible for growth inhibition

since the tolerance level of 2.8 g l−1 is reached before attaining an acetate

ion concentration of 48 g l−1. Above pH 6, acetate ion is the limiting factor,

because now the inhibitory concentration of undissociated acetic acid is not

exceeded before acetate ion becomes inhibiting. From the data it also be-

comes obvious that only very low total concentrations of acetic acid can be

obtained at pH < 6. Therefore, the pH of the broth should be maintained

in the range of pH 6–7 during fermentation by controlled addition of lime or

limestone, and perhaps bubbling with CO2, in order to avoid serious inhibi-

28

fermentor(pH 6–6.8)

pH controlunit

-

?

6

¾

-

6

CO2

substrate CO2

dolimeslurry

Figure 2.1: Fed batch fermentation process for CMA production, pH is con-trolled by addition of a dolime slurry; process as used by [Wie91].

tion of HAc production. A simple pH-controlled fed batch process for CMA

production as the one used byWiegel et al. [Wie91] is shown in Figure 2.1,

a continuous process could be controlled in a similar way.

After completion of the fermentation, the pH of the broth must be ad-

justed to pH 8–9, because traces of free acetic acid in the product would

be damaging to concrete. This pH adjustment could be done by adding an

extra amount of lime, but the sluggish reaction makes it difficult to obtain

a uniform and stable product. For this reason, it has been suggested to use

a small amount of potassium hydroxide instead of lime for the “fine tuning”

[Gan84a]. At the same time, the desired 1:1 mole ratio of Ca:Mg should

be achieved in the solution. If there remain undissolved solids, they may or

may not be removed before drying the product. Remaining particles could

actually improve deicing properties, since they would enhance friction.

29

2.3.2 Encountered Problems

As already mentioned, some difficulties arise from the different solubilities

and reactivities of the various corresponding calcium and magnesium com-

pounds, particularly at near-neutral pH. Hence process control seems to be

quite complicated. Marynowski et al. describe these problems in the fol-

lowing way [Mar85, page 459–460]:

Dolomite is essentially insoluble in neutral or alkaline solu-

tions, and its rate of dissolution in well-agitated acid solutions is

a negative exponential function of the pH (i.e., each decrease of

one pH unit results in about a tenfold increase in the dissolution

rate for a given particle size of dolomite). We have found that

even finely pulverized (< 100 mesh) dolomite requires a pH < 6

before any CO2 evolution is observable and that a pH < 4 is

required for complete dissolution within approximately 1 hour.

Thus, if use of dolomite were to be considered for pH control in

a fermentation medium, we estimate that the fermentation or-

ganism would have to be able to survive and produce acetic acid

efficiently at a pH of about 5 or less. (. . . ).

Light-burned dolime is much more reactive than dolomite, and

we estimate that it may be useful for fermentation pH control at

pH values up to about 6. At higher pH, however, the reactivities

of CaO and MgO differ greatly; CaO continues to dissolve rapidly

up to pH > 12, whereas MgO becomes essentially inert at pH > 6.

Therefore, any attempt to use dolime for fermentation pH control

at pH > 6 would produce a solution of calcium acetate only, not

one of CMA.

30

These observations were obviously made on the basis of simple model sys-

tems and equilibrium calculations—“real” fermentation experiments showed

remarkably different results. As part of their CMA-project Wiegel et al.

produced 150 lb of CMA by fermentation [Wie91]. They grew C. ther-

moaceticum in fed batch fermentation on hydrolyzed corn starch with bub-

bling of CO2 through the medium; the temperature was maintained at about

60◦C; the pH was kept in the range of pH 6–6.8 by addition of a dolime

slurry during fermentation, and it was finally adjusted to about pH 8 using

an extra amount of dolime; the duration was 5–6 days. In contrast to the

results cited above they found [Wie91, page 384]:

One of the most interesting observations is that magnesium of

the dolime was preferentially solubilized over calcium. Thus, the

CMA produced was more a magnesium acetate than calcium ac-

etate. The ratio between the Mg/Ca was from 1.8 to as high

as 3.

For instance, they reported final soluble concentrations of 58.8 mM for cal-

cium and 168.0 mM for magnesium, while the total concentrations for these

elements were 142.09 mM and 179.25 mM, respectively. They did not check

the nature of the precipitates (e.g. hydroxide, carbonate, phosphate), and

they did not offer an explanation. Among the possible reasons for these dif-

ferences are temperature effects, the precipitation of calcium carbonate (due

to CO2 bubbling) or less significantly, the precipitation of calcium phosphate

(because the medium contained a certain amount of phosphate). It should

be also pointed out that the fermentation is necessarily a non-equilibrium

process and that ultimately a dynamic approach must be taken in order to

explain the process behaviour.

31

Although inconclusive regarding the details, the available literature clear-

ly indicates that one has to expect some problems with producing a stoichio-

metric solution of CMA in the context of fermentation. These problems are

less important if the neutralization reactions can be carried out using concen-

trated acetic acid at pH < 5, but still then the final pH adjustment remains

complicated [Gan84a]. As a basis to address these difficulties, a better un-

derstanding of the thermodynamics and kinetics of the various dissolution

reactions is required. In the next chapter, several simple equilibrium models

will be examined both theoretically and experimentally to find the thermody-

namic limitations. Then an attempt will be made to develop a more realistic

dynamic model that will allow process simulation and the design of a control

strategy.

Chapter 3

Equilibrium Models

The equilibrium of a closed chemical system is determined by its lowest

possible Gibbs free energy G. In this case, the free energy change ∆G of all

chemical reactions that can take place in the system has to be zero. If the

“recipe” of the system—i.e., its initial composition—is known, its equilibrium

composition at given temperature and pressure can be calculated; however,

this kind of calculation does not answer the question how fast the equilibrium

will be approached. Many reactions proceed very slowly, so that systems can

appear virtually stable although far from equilibrium.

There are two basic methods to calculate chemical equilibria: The first

technique directly minimizes the total Gibbs free energy as a function of

composition under the constraints of mass conservation for each independent

component; the second one consists of solving a set of nonlinear equations

provided by the mole balances and mass law equations, which is equivalent

to the condition of free energy minimum. For both methods, the complete

set of species present at equilibrium must be known. In addition, the min-

imization approach requires knowledge of the standard Gibbs free energy

32

33

for each species, while the so-called equilibrium constant method depends on

information about the independent reactions that take place in the system

and their equilibrium constants. Since stability constants are readily avail-

able for most complexes and solids of interest in aquatic systems [Mar89],

the second technique is used more frequently in this context.

“Small” chemical equilibrium problems can be solved by hand using a

methodology that allows to make significant simplifications to the original

set of nonlinear equations and also gives some insight on how the system

would behave under altered conditions [Mor83]. More complex problems

involving many different species and reactions must be solved numerically on

a computer; appropriate software for the study of aquatic systems has been

developed. Most of these programs use the Newton-Raphson algorithm

to solve the set of nonlinear equations for equilibrium composition. The

sophisticated ones like MINEQL [Mor72] can handle nonideality corrections

necessary for concentrated systems and can even find the correct set of solids

in cases where it is unknown which solid phases are present at equilibrium.

Since nonideal effects must be considered for the systems to be discussed, a

brief introduction to nonideality corrections is in place.

3.1 Nonideal Effects in Aquatic Solutions

In an ideal thermodynamic system the partial molar free energy or chemical

potential µi of a species i depends exclusively on the mole fraction xi of that

species

µi = µ0i +RT ln xi, (3.1)

34

the presence of other species has no effect on µi. The composition of aquatic

solutions is expressed in molar concentrations Ci (number of moles solute

per liter of solution) rather than on the mole fraction scale. It is possible to

rewrite (3.1) for molar concentrations

µi = µ0i +RT lnCi (3.2)

by incorporating an approximately constant conversion term in the standard

free energy µ0i . Thus standard free energies are strictly dependent on the

chosen concentration scale, each of which corresponds to a different standard

state. In real aquatic solutions equation (3.2) holds only for infinite dilution—

otherwise interactions of solute molecules or ions occur that influence the

chemical potential of a given soluble species. In order to account for these

nonideal effects, a correction factor γi, the so-called activity coefficient, is

introduced in (3.2), so that

µi = µ0i +RT ln γiCi. (3.3)

The product Ai = γiCi is called the activity of species i. It remains to

determine the activity coefficients γi, an important and extensively studied

problem in applied thermodynamics.

For dilute ionic solutions the Debye-Huckel theory provides the nec-

essary basis. In this theory only interactions due to long-range electrostatic

forces among ions are considered: attraction of ions of opposite charge and

repulsion of ions of like charge. As a result of these interactions the distribu-

tion of ions in solution is not uniform—in the vicinity of a positive ion there is

a greater probability to find negative ions than positive ions, and vice versa.

This separation of charges leads to local variations in the electrical potential

which effectively decrease the partial molar free energy of each ionic species.

35

By evaluation of the relevant electrostatic energy it is possible to determine

the activity coefficients, typically γi < 1 for ionic species. Uncharged solutes

are assumed to behave ideally, i.e. for neutral species γi = 1.

As a general measure for ionic concentration, the ionic strength I of the

solution is defined by

I =1

2

∑

i

z2iCi, (3.4)

where zi is the charge number and Ci the molar concentration of species i.

Then according to Debye-Huckel theory the activity coefficients are given

by [Mor83]

ln γi = −Az2i

I1/2

1 +BaI1/2(3.5)

in which the constants A and B depend on absolute temperature T and the

dielectric constant of the system, and a is an adjustable size parameter that

corresponds roughly to the radius of the hydrated ion. The dimensions of

A and B are chosen in a way that ln γi is dimensionless (I has dimensions

mole per liter). This formula can be used for ionic strengths up to 0.1 M; at

higher concentrations other nonideal effects come into play, and some of the

approximations on which (3.5) is based are no longer valid.

There have been several attemps to extend the applicability of the classic

Debye-Huckel formula (3.5) to higher ionic strength systems, and a variety

of empirical and semiempirical expressions have been proposed. One of the

simplest and most widely used expressions of that kind is Davies’ formula

given by

ln γi = −Az2i

(

I1/2

1 + I1/2− bI

)

(3.6)

where (for water at 25◦C) A = 1.17, b = 0.3, and I has to be “stripped”

of its dimensions mole per liter [Mor83, Dav62]. This equation is fairly

36

accurate in the range I = 0 to 0.7 M. For higher concentrated systems a

more sophisticated approach becomes necessary that accounts for specific

as well as unspecific ion interactions and also predicts the large increase in

activity coefficients beyond I = 0.7 M.

With the knowledge of activity coefficients, the effect of nonideality on

equilibrium is easily established. For a chemical reaction symbolized by

0 = ν1S1 + ν2S2 + ν3S3 + · · · (3.7)

where Si denotes species i and νi, the corresponding stoichiometric coefficient

(positive for products, negative for reactants), the molar free energy change

∆G is given by

∆G =∑

i

νiµi, (3.8)

or after substitution of equation (3.3) for µi

∆G =∑

i

νiµ0i +RT ln

(

∏

i

γνi

i Cνi

i

)

= ∆G0 +RT lnQ. (3.9)

The constant term ∆G0 is called the standard free energy change of the reac-

tion, and Q is the reaction quotient. At equilibrium, ∆G = 0 and therefore

Q = exp

(

−∆G0

RT

)

= K (3.10)

in which K denotes the equilibrium constant of reaction (3.7). In terms of

activities Ai = γiCi, this mass law equation can be written

∏

i

Aνi

i = K, (3.11)

37

but in most practical applications it is more convenient to deal with con-

centrations rather than activities. This leads to a second form of (3.11),

namely∏

i

Cνi

i = K∏

i

γ−νi

i , (3.12)

where the activity coefficients have been brought to the other side. The term

on the right side of (3.12)

Kc = K∏

i

γ−νi

i (3.13)

is called the concentration equilibrium constant of reaction (3.7). Hence mass

laws can be written in terms of concentrations even for concentrated systems

where the approximation that activities and concentrations are the same is

no longer valid, if the standard equilibrium constants K are corrected using

equation (3.13).

3.2 The Hydroxide System

As a very simplified model for CMA production, the neutralization of HAc

with Ca(OH)2 and Mg(OH)2 was examined. It was assumed that there is

no CO2 present in the system. First the equilibrium speciation for a closed

system containing HAc and an excess of both Ca(OH)2 and Mg(OH)2 was

calculated, i.e., neither of the two solids could dissolve completely. The initial

composition of the system was given by

38

Recipe 1:

• 0.5 M HAc

• 0.3 M Ca(OH)2(s)

• 0.3 M Mg(OH)2(s).

The problem was solved “almost” by hand using only a programmable pocket

calculator; essentially the same solution was obtained from the TITRATOR

software package which is available on MS-DOS machines [Cab87]. The

species considered to be present at equilibrium were H2O, H+, OH−, HAc,

Ac−, Ca2+, CaOH+, Ca(OH)2(s), CaAc+, Mg2+, MgOH+, Mg(OH)2(s), and

MgAc+. Among these species, the following independent reactions can be

written (equilibrium constants from [Mar89], at zero ionic strength and

25◦C):

H2O = H+ +OH−, logK = −14.0

HAc = H+ +Ac−, logK = −4.76

CaOH+ = Ca2+ +OH−, logK = −1.15

Ca(OH)2(s) = Ca2+ + 2OH−, logK = −5.19

CaAc+ = Ca2+ +Ac−, logK = −1.2

MgOH+ = Mg2+ +OH−, logK = −2.6

Mg(OH)2(s) = Mg2+ + 2OH−, logK = −11.1

MgAc+ = Mg2+ +Ac−, logK = −1.3

(3.14)

As principal components, the species H2O, H+, Ac−, Ca(OH)2, and Mg(OH)2

were chosen. The number of components (five) is in fact equal to the number

of species (thirteen) minus the number of independent reactions (eight) since

each reaction defines a stoichiometric relationship among species which allows

to express one of them as a formula of the others, i.e. for each species it is

39

possible to write a mass law involving only principal components by simple

rearrangement of the given independent reactions. The linear operations

necessary to obtain the desired form of mass laws may include adding two or

more reactions (their logK values have to be added, too) and changing the

direction of a reaction (what simply changes the sign of the corresponding

logK value).

All the information regarding the setup of the equilibrium problem can

be organized conveniently in form of a tableau which is shown in Table 3.1.

At the top of this tableau, the stoichiometric formulae of the species as a

function of the components are given along with the corresponding logK

(and also logKc) values, and at the bottom, stoichiometric coefficients and

total amounts are included for the chemicals used in the recipe. Hence each

row in the upper part corresponds to a mass law, and each column stands for

a mole balance. Water is completely omitted from the tableau although it is

chosen as a component, since its presence is understood in aquatic systems.

From the columns, the mole balances for the components are ([. . .] denoting

concentrations)

TOTH = [H+]− [OH−] + [HAc] + 2[Ca2+] + [CaOH+]

+ 2[CaAc+] + 2[Mg2+] + [MgOH+] + 2[MgAc+]

= [HAc]T = 0.5 M (3.15)

TOTAc = [HAc] + [Ac−] + [CaAc+] + [MgAc+]

= [HAc]T = 0.5 M (3.16)

TOTCa(OH)2 = [Ca2+] + [CaOH+] + [Ca(OH)2(s)] + [CaAc+]

= [Ca(OH)2(s)]T = 0.3 M (3.17)

TOTMg(OH)2 = [Mg2+] + [MgOH+] + [Mg(OH)2(s)] + [MgAc+]

40

Table 3.1: Tableau-representation of the hydroxide system (Recipe 1). Equi-librium constants at 25◦C; logK at zero ionic strength, logKc at I = 0.35 M.

Species H+ Ac− Ca(OH)2(s) Mg(OH)2(s) logK logKc

H+ 1OH− −1 −14.0 −13.7HAc 1 1 +4.76 +4.46Ac− 1Ca2+ 2 1 +22.81 +23.12CaOH+ 1 1 +9.96 +9.96

Ca(OH)2(s) 1CaAc+ 2 1 1 +24.01 +23.71Mg2+ 2 1 +16.9 +17.2MgOH+ 1 1 +5.5 +5.5

Mg(OH)2(s) 1MgAc+ 2 1 1 +18.2 +17.9

Recipe TOTX

HAc 1 1 0.5 MCa(OH)2(s) 1 0.3 MMg(OH)2(s) 1 0.3 M

41

= [Mg(OH)2(s)]T = 0.3 M (3.18)

and from the rows, the mass laws for the species are (assuming zero ionic

strength)

[OH−] = 10−14.0[H+]−1 (3.19)

[HAc] = 10+4.76[H+][Ac−] (3.20)

[Ca2+] = 10+22.81[H+]2 (3.21)

[CaOH+] = 10+9.96[H+] (3.22)

[CaAc+] = 10+24.01[H+]2[Ac−] (3.23)

[Mg2+] = 10+16.9[H+]2 (3.24)

[MgOH+] = 10+5.5[H+] (3.25)

[MgAc+] = 10+18.2[H+]2[Ac−] (3.26)

In general, these mass laws are valid for activities rather than concentrations,

but it is possible to retain the given convenient form at ionic strength greater

than zero by simply using the concentration equilibrium constantsKc defined

in equation (3.13) instead of the standard constantsK. The activities of solid

species are always fixed to one, hence they do not appear in (3.19)–(3.26).

To obtain a first rough estimation for the equilibrium composition, the

uncorrected mass laws (3.19)–(3.26) were substituted into the mole bal-

ances (3.15)–(3.18), resulting in four nonlinear equations for the component

concentrations [H+], [Ac−], [Ca(OH)2(s)], and [Mg(OH)2(s)]. It was possi-

ble to further eliminate [Ac−] from the TOTH balance (3.15) using equa-

tion (3.16); thus only one equation of one unknown had to be solved numeri-

cally, which could be easily done with the built-in equation solver of a pocket

calculator. The result is shown in Table 3.2 (first column). From this data

42

Table 3.2: Equilibrium speciation for the hydroxide system (Recipe 1). pHcorresponds to negative log of hydrogen ion activity rather than concentra-tion.

species Equilibrium Concentrations (M)I = 0 I = 0.35 experimental

H+ 8.32 · 10−13 9.07 · 10−13

pH 12.08 12.19 12.51

OH− 1.20 · 10−2 2.20 · 10−2

Ac− 0.293 0.352HAc 1.40 · 10−8 9.20 · 10−9

Ca2+ 4.47 · 10−2 0.108CaOH+ 7.59 · 10−3 8.27 · 10−3

CaAc+ 0.207 0.148

total soluble Ca 0.260 0.265 0.288

Ca(OH)2(s) 4.02 · 10−2 3.49 · 10−2

Mg2+ 5.51 · 10−8 1.30 · 10−7

MgOH+ 2.63 · 10−7 2.87 · 10−7

MgAc+ 3.21 · 10−7 2.30 · 10−7

total soluble Mg 6.39 · 10−7 6.47 · 10−7 7.67 · 10−5

Mg(OH)2(s) 0.3 0.3

43

the ionic strength I could be calculated: the value found was I = 0.35 M,

indicating a fairly concentrated solution.

For a more accurate result, ionic strength corrections were required. Ap-

proximated values for the activity coefficients γi at I = 0.35 M were obtained

from Davies’ formula (3.6), which gave γi = 0.70 and γi = 0.24 for ions hav-

ing single and double charge, respectively. Then the concentration equilib-

rium constants Kc could be determined according to (3.13); their log values

are given in Table 3.1. Using the corrected constants, a slightly different

equilibrium composition was found (Table 3.2, second column). The differ-

ences were smaller than expected, in particular for the total soluble calcium

and magnesium concentrations, both of which did not change significantly.

The resulting new ionic strength was I = 0.48 M, its increase was mainly

due to the increase of [Ca2+] (double charge!) at the expense of [CaAc+].

It was not necessary to make another iteration using I = 0.48 M, because

the activity coefficients have almost constant values in the range I = 0.3

to 0.7 M, so that no further significant changes were expected, taking into

account the restricted accuracy of such calculations.

In order to confirm the validity of these calculations, the equilibrium

composition for Recipe 1 was also determined experimentally. The system

was prepared from deionized water and reagent-grade HAc, Ca(OH)2, and

Mg(OH)2. Stirring and sparging with nitrogen were provided during equi-

libration; the pH of the solution was monitored. After approximately half

an hour the pH had stabilized, and it was assumed that the system had

reached equilibrium. The undissolved solids were removed by filtration, and

the sample solution was analyzed for total soluble calcium and magnesium by

inductively coupled plasma emission spectroscopy (ICP). It was found that

44

pH and total soluble calcium had been predicted with an error of less than

10%, but the concentration of magnesium had been grossly underestimated

by almost two orders of magnitude (see Table 3.2, third column1). One pos-

sible explanation for this significant deviation might be that the system had

not yet reached “true” equilibrium, i.e., the solution was still oversaturated

with respect to magnesium species.

Very similar values were obtained for industrial-grade type S dolime,

supplied by The Western Lime & Cement Co. in West Bend, Wisconsin:

pH 12.47, 0.258 M total soluble calcium, and 4.03 · 10−5 M total soluble

magnesium. Obviously the impurities2 did not have a strong influence on

the equilibrium speciation.

The theoretical as well as the experimental results show that in ac-

cordance with the observations by [Mar85], only a negligable amount of

Mg(OH)2(s) dissolved because of the high pH, and essentially a solution of

calcium acetate was produced, not one of CMA. However, it must be pointed

out that in the context of the proposed fermentation process a pH > 12 will

never be reached. This leads to the more important question what happens,

if there is no excess of Ca(OH)2(s) in the system, and the pH is allowed to

drop far enough for dissolution of Mg(OH)2(s).

An answer to this question was found by simulating a titration of calcium

and magnesium hydroxide with acetic acid, i.e., by determining the equilib-

rium composition depending on the total amount of acetic acid added to

the system. These calculations were made using the TITRATOR program.

Unfortunately it turned out that the available option of “automatic” ionic

1The original data on the ppm scale can be found in Appendix A.1.

2See Appendix B.1 for a chemical analysis of the lime.

45

strength corrections did not work properly, so zero ionic strength had to be

assumed. In order to restrict the error introduced at higher ionic strength,

only half the hydroxide concentrations of Recipe 1 were chosen according to

Recipe 2:

• 0–0.7 M HAc (titrant)

• 0.15 M Ca(OH)2(s)

• 0.15 M Mg(OH)2(s).

The results are visualized separately for solid species and total soluble con-

centrations in Figures 3.1 and 3.2; the equilibrium concentration of H+ has

been included in both diagrams. There are two interesting points, where

some of the concentrations change dramatically: one at TOTHAc = 0.3 M,

where just all Ca(OH)2(s) is dissolved, and another at TOTHAc = 0.6 M,

where also the last bit of Mg(OH)2(s) has disappeared. As long as there is

Ca(OH)2(s) present, a pH > 12 is maintained, and the solution phase con-

tains only traces of magnesium species. After Ca(OH)2(s) has disappeared,

the pH drops to a value of about pH 9–10 and again remains almost constant

while the dissolution of Mg(OH)2(s) takes place; finally it drops further to

the region of pH 4–6 (the pKa of HAc is 4.76, i.e. a pH of about this value

would be reached when the concentrations of acetate ion and undissociated

acetic acid become equal).

Several real titration experiments were performed with the individual

hydroxides and the mixed system according to Recipe 2. After each addition

of HAc, the pH was allowed to stabilize before a reading was taken and the

titration was continued. The time required for a stable pH reading was less

46

−14

−12

−10

−8

−6

−4

−2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

logC

TOTHAc

Ca(OH)2(s) ×

××××××××××

Mg(OH)2(s)

H+ 3

33333333333

33333333333

3

333

Figure 3.1: Titration of the hydroxide system (Recipe 2)—variation of solidspecies concentrations with TOTHAc.

47

−14

−12

−10

−8

−6

−4

−2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

logC

TOTHAc

total soluble Ca ×

××××××

××××××××××××××××××××

total soluble Mg

H+ 3

33333333333

33333333333

3

333

Figure 3.2: Titration of the hydroxide system (Recipe 2)—variation of totalsoluble calcium and magnesium concentrations with TOTHAc.

48

than 20 sec for Ca(OH)2, but as long as 10 min for Mg(OH)2, indicating that

Mg(OH)2 reacted significantly slower than Ca(OH)2. A good agreement was

found between the obtained experimental curves of pH versus TOTHAc and

the simulation results stated above: Ca(OH)2(s) dissolved at pH > 12 and

Mg(OH)2(s) at pH 9–10.

Therefore, no thermodynamic limitation should be expected for the dis-

solution reaction of Mg(OH)2(s) at any pH < 9, and the experiment showed

that although Mg(OH)2(s) dissolved slowly compared to Ca(OH)2(s) the dis-

solution rate was still considerable. This result is in contrast to the observa-

tion reported by [Mar85] that “MgO becomes essentially inert at pH > 6”.

Since [Mar85] used unslaked dolomitic lime CaO ·MgO rather than highly

hydrated (type S) dolime Ca(OH)2 ·Mg(OH)2, their problem was most likely

due to hard-burned (sintered) MgO with low reactivity, hence the exergonic

reaction

MgO(s)+H2O −→ Mg(OH)2(s)

proceeded very slowy at pH > 6. Apart from using type S dolime which is

more expensive than quicklime and normal hydrated lime, two other possi-

bilities to overcome this problem would be

• to dissolve MgO at pH < 6 as proposed by [Mar85], or

• to use selectively calcined dolomite (containing light-burned MgO with

high reactivity) which could actually be produced at lower cost than

quicklime and might have other advantages.

The last case represents an interesting combined carbonate-hydroxide system

and will be considered again in the context of a dynamic model after the

carbonate system has been examined.

49

3.3 The Carbonate System

Regardless wheter dolime, dolomite, or selectively calcined dolomite is used

for acetic acid neutralization in a real fermentation processs, carbonates

will always be present in the system since CO2 is an intermediate prod-

uct in homoacetate fermentations (and occasionally also provided by gas

bubbling). Thermodynamically the solids calcium hydroxide and calcium

carbonate cannot coexist in water at ambient partial pressure of CO2 which

is PCO2= 10−3.5 bar, because the exergonic reaction

CO2(g)+ Ca(OH)2(s) −→ CaCO3(s)+H2O (3.27)

must proceed to the right until Ca(OH)2(s) is exhausted if PCO2is fixed

[Mor83]. The same is true for the corresponding magnesium compounds;

again the reaction

CO2(g)+Mg(OH)2(s) −→ MgCO3(s)+H2O (3.28)

is exergonic at PCO2= 10−3.5 bar. Therefore, the hydroxide system discussed

in the previous section would be ultimately transformed into the carbonate

system if there is enough CO2 present. Both reactions (3.27) and (3.28) can

be applied also to the dry compounds—the hydroxides absorb CO2 from the

air and are gradually transformed to carbonates (a possible source of error

in experiments, when “old” chemicals are used).

The carbonate system was examined in the same way as the hydroxide

system; hence only a brief discussion is necessary. Again, the closed system

was defined by

50

Recipe 3:

• 0.5 M HAc

• 0.3 M CaCO3(s) (calcite)

• 0.3 M MgCO3(s) (magnesite)

• CO2(g) at fixed partial pressure PCO2= 10−3.5 bar,

having an excess of both calcium and magnesium carbonate. Now 21 species

had to be considered, 15 independent reactions among them could be written,

and hence 6 principal components had to be chosen. Species and components

can be found in Table 3.3, the independent reactions are

H2O = H+ +OH−, logK = −14.0

HAc = H+ +Ac−, logK = −4.76

CO2(g)+H2O = H2CO∗3, logK = −1.5

H2CO∗3 = H+ +HCO−

3 , logK = −6.3

HCO−3 = H+ + CO2−

3 , logK = −10.3

CaOH+ = Ca2+ +OH−, logK = −1.15

CaAc+ = Ca2+ +Ac−, logK = −1.2

CaHCO+3 = Ca2+ +HCO−

3 , logK = −1.26

CaCO3 = Ca2+ + CO2−3 , logK = −3.2

CaCO3(s) = Ca2+ + CO2−3 , logK = −8.35

MgOH+ = Mg2+ +OH−, logK = −2.6

MgAc+ = Mg2+ +Ac−, logK = −1.3

MgHCO+3 = Mg2+ +HCO−

3 , logK = −1.01

MgCO3 = Mg2+ + CO2−3 , logK = −3.4

MgCO3(s) = Mg2+ + CO2−3 , logK = −7.46,

(3.29)

51

Table 3.3: Tableau-representation of the carbonate system (Recipe 3). Equi-librium constants at 25◦C; logK at zero ionic strength, logKc at I = 0.33 M.

Species H+ Ac− CaCO3(s) MgCO3(s) CO2 logK logKc

H+ 1OH− −1 −14.0 −13.7HAc 1 1 +4.76 +4.46Ac− 1CO2(g) 1H2CO

∗3 1 −1.5 −1.5

HCO−3 −1 1 −7.8 −7.5

CO2−3 −2 1 −18.1 −17.2

Ca2+ 2 1 −1 +9.75 +10.06CaOH+ 1 1 −1 −3.1 −3.1CaAc+ 2 1 1 −1 +10.95 +10.65CaHCO+

3 1 1 +3.21 +3.21CaCO3 1 −5.15 −5.15CaCO3(s) 1Mg2+ 2 1 −1 +10.64 +10.95MgOH+ 1 1 −1 −0.76 −0.76MgAc+ 2 1 1 −1 +11.94 +11.64MgHCO+

3 1 1 +3.85 +3.85MgCO3 1 −4.06 −4.06MgCO3(s) 1

HAc 1 1 0.5 MCaCO3(s) 1 0.3 MMgCO3(s) 1 0.3 MCO2(g) 1 ?

52

where H2CO∗3 represents by convention H2CO3 + CO2(aq). The equilibrium

speciation was calculated using TITRATOR, first at zero ionic strength, then

at the resulting value I = 0.33 M (with activity coefficents γi = 0.7 for single

charged ions and γi = 0.25 for double charged ions); both compositions are

given in Table 3.4 together with the experimental result obtained for a system

that was prepared from deionized water and reagent-grade HAc, CaCO3, and

MgCO3.3 Again there were no great differences between the uncorrected and

the corrected total soluble concentrations of calcium and magnesium. This

time the equilibration of the real system took several hours (compared to half

an hour for the hydroxide system), indicating that the carbonates reacted

significantly slower than the hydroxides. The total concentration of soluble

magnesium species and the measured pH agree well with the predicted values,

but the total soluble calcium concentration was overestimated by a factor of

ten. There was no convincing explanation found for this deviation; maybe,

the powdered carbonates did not have the same thermodynamic properties

as calcite and magnesite.

In contrast to the hydroxides a considerable amount of both carbonates

dissolved, but now magnesium was preferentially solubilized over calcium

(about ten to hundred times as much magnesium as calcium), and the equi-

librium pH was much lower.

The simulated titration at zero ionic strength was carried out for the

system defined by

3The carbonates used in this experiment were in form of very fine powders, possibly

produced by precipitation, and hence their crystal structure was not necessarily that of

calcite and magnesite, respectively.

53

Table 3.4: Equilibrium speciation for the carbonate system (Recipe 3). pHcorresponds to hydrogen ion activity rather than concentration.

Species Equilibrium Concentrations (M)I = 0 I = 0.33 experimental

H+ 1.56 · 10−8 1.72 · 10−8

pH 7.81 7.91 8.22

OH− 6.42 · 10−7 1.16 · 10−6

Ac− 0.288 0.344HAc 2.58 · 10−4 1.71 · 10−4

H2CO∗3 1.00 · 10−5 1.00 · 10−5

HCO−3 3.22 · 10−4 5.80 · 10−4

CO2−3 1.03 · 10−6 6.72 · 10−6

Ca2+ 4.32 · 10−3 1.08 · 10−2

CaOH+ 3.91 · 10−8 4.33 · 10−8

CaAc+ 1.97 · 10−2 1.45 · 10−2

CaHCO+3 2.53 · 10−5 2.80 · 10−5

CaCO3 7.08 · 10−6 7.08 · 10−6

total soluble Ca 2.40 · 10−2 2.53 · 10−2 3.60 · 10−3

CaCO3(s) 0.276 0.275

Mg2+ 3.35 · 10−2 8.37 · 10−2

MgOH+ 8.57 · 10−6 9.47 · 10−6

MgAc+ 0.192 0.141MgHCO+

3 1.10 · 10−4 1.22 · 10−4

MgCO3 8.71 · 10−5 8.71 · 10−5

total soluble Mg 0.226 0.225 0.219

MgCO3(s) 7.39 · 10−2 7.49 · 10−2

54

Recipe 4:

• 0–0.7 M HAc (titrant)

• 0.15 M CaCO3(s) (calcite)

• 0.15 M MgCO3(s) (magnesite)

• CO2(g) at fixed partial pressure PCO2= 10−3.5 bar

using TITRATOR; Figures 3.3 and 3.4 show the resulting titration curves.

Initially the pH has a value of about pH 8, and it only slightly decreases while

MgCO3(s) and then CaCO3(s) dissolve. After both solids have disappeared, it

drops to the region of pH 4–6. There are no big concentration “jumps” at the

point TOTHAc = 0.3 M as was the case for the hydroxides—the reactivities

of MgCO3(s) and CaCO3(s) are different, but not very much. Because of the

slow reaction, no real titration experiment was performed; this would have

required an automated titrator.

An experiment using the double carbonate dolomite CaMg(CO3)2 instead

of a mixture of CaCO3 and MgCO3 showed quite different results: the reac-

tivity was much lower than for the system defined by Recipe 3 (the pH was

still below pH 6 after several hours of equilibration), and very surprisingly,

more calcium than magnesium was found in the filtered sample taken after

24 hours. The concentrations were 0.121 M and 0.0854 M for calcium and

magnesium, respectively. Again, an excess of base was used (about 0.6 M

dolomite), and the material was finely pulverized. It is difficult to find an

explanation for this strange behaviour; first of all, the system probably did

not reach true equilibrium, and perhaps the limestone contained not only

dolomite, but also some calcite which could possibly dissolve much faster

55

−14

−12

−10

−8

−6

−4

−2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

logC

TOTHAc

CaCO3(s) ×

××××××××××××××××××××××

MgCO3(s)

H+ 3

3

333333333333333333333

3

333

Figure 3.3: Titration of the carbonate system (Recipe 4)—variation of solidspecies concentrations with TOTHAc.

56

−14

−12

−10

−8

−6

−4

−2

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

logC

TOTHAc

total soluble Ca ×

×

××××××

×××××××××××

××××××××

total soluble Mg

H+ 3

3

333333333333333333333

3

333

Figure 3.4: Titration of the carbonate system (Recipe 4)—variation of totalsoluble calcium and magnesium concentrations with TOTHAc.

57

than dolomite. However, an analysis of the limestone itself showed that it

actually had just slightly more calcium than would be theoretically expected

for pure dolomite,4 and it is not sure whether or not the given explanation

is correct. If the use of dolomite as a neutralizer is considered in spite of its

low reactivity, this problem definitely has to be addressed again.

Another experiment was made in order to examine the influence of CO2

bubbling: a hydroxide system prepared according to Recipe 1 was bubbled

with CO2 instead of nitrogen. After about three hours the pH had stabi-

lized at a value of pH 6.48. The sample was filtered and stored for several

days in a closed tube before it could be analyzed. During this time a small

amount of precipitate formed, so that the solution had to be filtered again.

Unfortunately, no second pH reading was taken at the time of analysis. The

total soluble concentrations for calcium and magnesium were 4.65 · 10−3 M

and 0.278 M, respectively. These values agree quite well with the ones found

for the carbonate system, indicating that the hydroxides had been actually

transformed to carbonates. Both concentrations are significantly higher than

in the carbonate case discussed above; this is probably due to a higher con-

centration of CO2 and therefore a lower equilibrium pH, because the sample

was not equilibrated with air.

In the light of these results, the following explanation seems to be plau-

sible for the observation by [Wie91] that magnesium was preferentially sol-

ubilized during their CMA-fermentation: although they did not directly use

carbonates, it is very likely that carbonates were formed according to reac-

tions (3.27) and (3.28) or just through simple precipitation,5 thus leading to

4The results of this analysis can be found in Appendix B.2.5As a matter of fact, precipitated CaCO3 is normally produced by bubbling CO2

58

a combined hydroxide-carbonate system with somewhat intermediate char-

acteristics. However, it is not possible to apply the results of the equilibrium

case directly to the real fermentation system, since during the whole pro-

cess the solid calcium and magnesium phases are not in equilibrium with

the liquid phase. Therefore, the equilibrium models discussed so far must

be considered as “limiting cases” that can only give information about basic

thermodynamic properties (e.g. the equilibrium pH values of the dissolution

reactions), but not about the behaviour of real non-equilibrium processes. A

dynamic approach is necessary to obtain more realistic models; this approach

will be discussed in the following chapter.

through an aqueous suspension of Ca(OH)2 (milk of lime).

Chapter 4

The Dynamic Approach

Although lime and limestone neutralization is widely used in waste water

treatment, it is difficult to find conclusive models for the dissolution kinetics

in literature. Obviously in most applications to date a detailed model was not

required—the only thing one had to know was how many minutes or hours

it takes to neutralize a given acid solution using a certain type and amount

of neutralization agent. From this empirical data it can be concluded that in

general the calcium minerals react faster than the magnesium minerals, and

that the hydroxides have a higher reactivity than the carbonates [Boy80].

In the case of CMA production it definitely is necessary to study the

kinetics of the neutralization reactions, since not only “neutralizing capacity”

and “reaction time”, but also the composition of the resulting solution are

important. Therefore, an extensive literature search was performed using

computerized versions of Engineering Index and Chemical Abstracts. About

25 papers related to the following fields were found:

1. Kinetics of acid neutralization with lime or limestone; most of these

59

60

“engineering” papers dealt with the neutralization of sulfuric acid in

the context of acidic waste treatment (coal mine drainage, pickling

liquors) [Bar76, Bog85, Hoa45, Par65, Pea75].

2. Kinetics of heterogenous reactions in general [Bir52].

3. Calcite dissolution kinetics; many publications of detailed studies that

were made by geologists in order to understand the natural dissolu-

tion of carbonate rocks [Cho89, Com90a, Com90b, Plu76, Plu78,

Plu79, Ric83, Sjo76, Sjo84, Sua84, Ber74].

4. Dolomite and Magnesite dissolution kinetics [Bus82, Cho89, Sua84].

5. Dissolution kinetics of CaO and MgO [Cas91, Gor84, Mac71,

Seg78, Seg88, Ver69].

There was just one single publication found that specifically dealt with the

dissolution of limestone in acetic acid [Sua84], and nothing about the reac-

tion of acetic acid with lime. Probably some of the more general models could

be applied to the production of CMA, but difficulties are to be expected,

since these models were found using CO2-water systems in combination with

strong mineral acids like HCl or H2SO4. Hence it would be necessary to per-

form experiments in order to verify model structure and parameters. Most

likely the dynamic model will turn out to be a system of differential algebraic

equations (DAEs)—some differential equations describing the heterogenous

surface reactions combined with a set of algebraic equations (mole balances

and mass laws) which determine the speciation in the bulk fluid.

Another question is whether the design of the process can be based on

such a dynamic model which will necessarily involve large uncertainties (liter-

61

ature data on the dissolution rate of one specific compound at a given pH and

temperature may differ by an order of magnitude or more among different

sources). It may be possible to overcome this problem by a “clever” process

design that does not require exact knowledge of the dissolution kinetics.

4.1 Heterogenous Reactions

The dissolution of lime or limestone particles in an aquatic solution of acetic

acid is a heterogenous reaction—it occurs at the interface between two phases,

a solid and a solution. The rate of a heterogenous reaction is proportional to

the available surface area of the solid. In order to find the factors which may

control the rate it is helpful to decompose the whole process into a series of

five primary steps [Bir52]:

1. Transport of the reactants from the bulk solution to the interface.

2. Adsorption at the interface.

3. Reaction at the interface.

4. Desorption of the products.

5. Transport of the products from the interface to the bulk solution.

Of these, steps 1 and 5 are tranport processes, steps 2–4 are chemical pro-

cesses. Depending on which step is the slowest and therefore rate determin-

ing, the overall rate may be either

• transport controlled, if the rate of mass transfer to or from the solid

surface by diffusion and convection is very much slower than the rate

of chemical reaction at the interface,

62

6

Ceq

C

- z

b

c

a

solidboundarylayer

bulksolution

Figure 4.1: Concentration profiles near the interface for (a) transport con-trolled, (b) chemically controlled, and (c) intermediate-type heterogenousreactions.

• chemically controlled, if the surface reaction is much slower than either

of the transport processes, or

• of intermediate type (general case), if both rates are of the same order

of magnitude and hence the observed rate is determined by a function

of the two.

Figure 4.1 shows the corresponding concentration profiles near the interface

for a dissolution reaction involving only one solute and the solvent. In case

of a chemically controlled reaction the bulk concentration C of the solute

extends right to the surface, and there is no boundary layer. In both other

cases the concentration at the interface is not the same as in the bulk so-

lution; there must exist a boundary layer with a concentration gradient. If

the observed rate is transport controlled then equilibrium is established at

63

the interface, i.e., the surface concentration is equal to the equilibrium con-

centration Ceq. In the general case the surface concentration has some value

between C and Ceq.

The classical theory of heterogenous reactions was formulated byNernst

at the beginning of the century. He assumed that the chemical processes are

always much faster than the transport processes, that there is no concen-

tration gradient within the bulk solution in well-stirred systems, but the

concentration varies linearly with distance (measured normal to the surface)

in a thin boundary layer adhering to the solid surface, and that the thickness

of this layer is only a function of the stirring rate and geometry of the system,

but does not depend on the coefficient of diffusion of the solute, the viscos-

ity, and the temperature [Bir52]. In general, none of these assumptions is

justified, but the theory provided a useful approximation at least for many

transport controlled reactions. Consider a solid of surface area A being in

contact with a volume V of solution. Then it can be shown by Fick’s law

and a mass balance thatdC

dt= −

DA

V

dC

dz, (4.1)

where dC/dt is the rate of change of concentration in the bulk solution, dC/dz

is the concentration gradient normal to the surface and D is the coefficient of

diffusion of the solute. Assuming equilibrium at the interface and linearity,

the gradient can be written

dC

dz=

C − Ceq

δ, (4.2)

where Ceq is the equilibrium concentration and δ the thickness of the diffusion

layer; by substitution in (4.1),

dC

dt=

DA

V δ(Ceq − C). (4.3)

64

This is a very simple first order rate equation, but reasonable agreement was

found for many heterogenous reactions. Careful analyses have shown that

the values obtained for δ are too large to be interpreted as above, and that

the linearity assumption for the gradient is far from reality. As more and

more chemically controlled reactions were discovered, the need to generalize

from the transport-limited case was realized.

In order to extend the Nernst theory to reactions that are at least partly

controlled by surface reaction, the equilibrium assumption must be given up,

and an additional rate equation for the chemical reaction is required [Plu76].

The molar flux JT from the interface to the bulk solution can be expressed

as

JT = kT (C(s) − C), (4.4)

where C is again the bulk fluid concentration and C (s) is the concentration

at the outer edge of a very thin surface layer right at the interface, see Fig-

ure 4.2. The constant kT is the mass transport coefficient for the solute and

is determined by fluid properties and surface geometry. The concentration

difference C(s) − C acts as a driving force for the mass transport from the

interface to the bulk solution through the diffusion boundary layer. Equa-

tion (4.4) is a good approximation for relatively small fluxes and is valid only

if no homogenous reactions involving the solute occur within the boundary

layer. On the other hand, it is often possible to express the rate of surface

reaction by an empirical relation of the form

JC = kC(C(s)eq − C(s))n, (4.5)

where JC is the molar flux into the surface layer that results from the chemical

reaction characterized by rate constant kC and empirical order n, and C(s)eq

65

C(s) C

-JC

-JT

solid

diffusionboundarylayer

bulksolution

surfacelayer

Figure 4.2: Molar fluxes due to surface reaction and mass transfer for anintermediate-type heterogenous reaction.

denotes the equilibrium concentration at the interface. Since only a small

amount of mass can be accumulated in the thin surface layer, a steady state

is established almost instantaneously; the mass balance for the surface layer

forces JC = JT . Hence equations (4.4) and (4.5) may be combined as

J = kT (C(s) − C) = kC(C

(s)eq − C(s))n, (4.6)

where the subscripts of J have been dropped. Equation (4.6) applies to

the general intermediate case and allows to eliminate the unknown concen-

tration C(s). For a first order chemical reaction, n = 1, and C (s) can be

expressed as

C(s) =kT

kT + kCC +

kCkT + kC

C(s)eq , (4.7)

thus leading to the simple relation

J =kTkC

kT + kC(C(s)

eq − C). (4.8)

66

For kT À kC equation (4.8) reduces to

J = kC(C(s)eq − C), (4.9)

the limiting case of reaction control. Similarly, the transport controlled case

is obtained for kC À kT . The rate of change of concentration in the bulk

solution for dissolution from a surface of area A into a fluid of volume V is

related to the flux J bydC

dt=

A

VJ (4.10)

as long as no homogenous reactions with the solute occur in the bulk fluid.

This allows to write the rate equation

dC

dt=

A

V

kTkCkT + kC

(C(s)eq − C) (4.11)

for first order, intermediate-type reactions. In some cases, C may denote

not the bulk concentration of the dissolving species itself, but of some other

species in the system which reacts with the solid and is depleted, e.g., H+

for the dissolution of a metal in acid. However, it must be pointed out

that the equations discussed here can be applied only to very simple disso-

lution processes involving just one significant heterogenous reaction and no

homogenous reactions in the boundary layer or bulk solution. As will be seen

in the next section, surface processes involving more than one species, paral-

lel heterogenous reactions, and accompanying homogenous reactions actually

occur; the corresponding models are of course more complicated.

4.2 Kinetics of Dissolution

Various models for the dissolution of carbonates and oxides in acids can

be found in the literature; some of them shall be discussed briefly at this

67

point because of their relevance for CMA production. From these models,

approximate dissolution rates will be calculated for the range of pH 5–7 in

order to give an idea of the orders of magnitude to be expected. The two

classes of potential raw materials, carbonate minerals and oxide minerals,

are discussed separately. More detailed information about the dissolution of

carbonates is available than about that of oxides, especially in the higher pH

range.

4.2.1 Carbonates: Calcite, Magnesite, Dolomite

The dissolution and precipitation of carbonate minerals plays an important

role in natural systems, e.g. for the weathering of carbonate rocks, or the

composition of natural waters. Hence the study of mechanisms and kinetics of

these processes has been an area of interest particularly for geochemists, geol-

ogists, and soil scientists, and most of the publications are found in geological

journals. Calcite has been the most extensively and rigorously studied, but

it has been shown that other simple carbonates like magnesite have a similar

behaviour. Only the dissolution of dolomite as a two-component carbonate

seems to follow a different mechanism, but still the same methodology could

be applied to its study. First the findings for calcite will be discussed, and

then directly compared with the corresponding results for magnesite; finally

the different behaviour of dolomite will be addressed.

Studies of Calcite Dissolution

Soon it was realized that there exist different mechanisms for calcite disso-

lution depending on the pH regime, and the partial pressure of CO2. The

saturation of the bulk solution with respect to Ca2+ and CO2−3 has also an

68

important influence, since far from equilibrium the overall dissolution rate is

determined solely by the forward rate (the backward rate is neglegibly small),

while near equilibrium the forward and backward rate are of the same order

of magnitude. In some cases, experimental conditions may also play a role,

especially hydrodynamics and surface geometry of the system. For instance,

it has been shown only recently that the dissolution of calcite at pH < 4

is not necessarily transport controlled as supposed by most authors, but

rather limited by the rate of surface reaction under conditions of high mass

transport [Com90a].

The first comprehensive model of the dissolution process was the one de-

veloped by Plummer et al. [Plu78, Plu79]. In their experiments, they

used two different fractions of crushed and sized Iceland spar (estimated

surface area of the particles 44.5 cm2/g and 96.5 cm2/g, respectively) in a

well-stirred system at fixed PCO2(provided by bubbling with CO2, N2, or a

mixture of both) and constant temperature. A “pH-stat” method was used

to study dissolution far from equilibrium at low pH, while “free drift” experi-

ments were made to examine systems nearer equilibrium. In the overlapping

region of the two methods, the obtained results were in agreement.

During the pH-stat runs, a constant specified pH was maintained through

controlled addition of a standard HCl solution using an automated titrator;

the rate of addition of standard solution dVHCl/dt was recorded. Then the

rate of calcite dissolution R could be estimated from

R = 0.5CHCl

A

dVHCl

dt, (4.12)

where CHCl is the molarity of the standard HCl solution and A the surface

area of the solid particles. This relation is justified, because at constant

pH and PCO2the activities of H2CO

∗3, HCO

−3 , and CO

2−3 are constant in

69

solution. Hence for each mole of CaCO3 dissolved, two moles of hydrogen

ions are consumed, and one mole of CO2 leaves the system with the bubbled

gas phase; i.e., the rate of calcite dissolution is essentially half the rate of

“hydrogen ion addition”.

In case of the free drift runs, the pH was allowed to vary as the reaction

proceeded to near equilibrium at constant PCO2and temperature. Measure-

ment of the pH as a function of time provided a means to follow the reac-

tion, since the composition of the bulk solution at each point of time could

be calculated from pH and PCO2using an iterative algorithm (similar to the

algorithms discussed in Chapter 3). The rate of calcite dissolution had to be

computed stepwise from this data by means of a central difference formula.

By analysis of their pH-stat data, Plummer et al. found the following

empirical expression for the forward rate of dissolution

Rf = k1AH+ + k2AH2CO∗

3+ k3AH2O, (4.13)

where Ai is the activity of species i in the bulk fluid, and ki are rate con-

stants dependent on temperature. The dimensions used in [Plu78] are

M = mol l−1 = mmol cm−3 for the activities Ai, cm s−1 for the rate con-

stants ki, and hence mmol cm−2 s−1 for the rate Rf itself. Throughout this

section, another convention shall be adopted in order to make the models of

different authors better comparable and avoid confusion: all rates are mea-

sured in mol cm−2 s−1, activities have units of M = mol l−1, and first order

rate constants are assigned dimensions of mol cm−2 s−1 M−1 = l cm−2 s−1,

i.e., their numerical values differ from [Plu78] simply by a factor of 1000.

The temperature dependence of the rate constants at temperatures between

70

Table 4.1: Summary of empirical rate constants for the dissolution of cal-cite and magnesite; the corresponding rate expressions are given by equa-tions (4.19) and (4.29). First order constants k1, k2, k3 and second order con-stants k−3, k4 have dimensions of mol cm

−2 s−1 M−1 and mol cm−2 s−1 M−2,respectively.

Calcite Magnesite

[Cho89] [Plu78] [Cho89]

25◦C 25◦C 48◦C 25◦C

k1 = 8.9 · 10−5 k1 = 5.1 · 10

−5 k1 = 6.5 · 10−5 k1 = 2.5 · 10

−9

k2 = 5.0 · 10−8 k2 = 3.5 · 10

−8 k2 = 1.2 · 10−7 k2 = 6.0 · 10

−10

k3 = 6.5 · 10−11 k3 = 1.2 · 10

−10 k3 = 3.1 · 10−10 k3 = 4.5 · 10

−14

k−3 = 1.9 · 10−2 k4 = 2.6 · 10

−5 k4 = 1.3 · 10−4 k−3 = 4.5 · 10

−6

5◦C and 48◦C is given by the empirical expressions

log k1 = −2.802− 444/T (4.14)

log k2 = −0.16− 2177/T (4.15)

log k3 = −8.86− 317/T (5◦C to 25◦C) (4.16)

log k3 = −4.10− 1737/T (25◦C to 48◦C), (4.17)

where T is temperature in K and ki have been transformed to new units.

Values for ki at 25◦C and 48◦C are shown in Table 4.1.

Three regimes of pH and PCO2can be distinguished, where one of the

terms in equation (4.13) dominates both others:

1. At low pH, the rate is almost independent of PCO2and approximately

proportional to the bulk fluid activity of H+.

71

2. At moderate to high pH and high PCO2, the rate shows a linear depen-

dence on the bulk concentration of dissolved CO2.

3. At high pH and in near absence of CO2, the rate becomes independent

of both pH and PCO2and is approximately constant.

These regions in the pH,PCO2plane, as well as an area where the forward rate

depends significantly on more than one mechanism, are shown in Figure 4.3.

In addition, Rf was found to be dependent on the rate of stirring in regime 1,

but not in the other two regions. This led to the conclusion that the forward

rate is controlled by H+ transport at pH < 5, but essentially controlled by

surface reaction at high pH.

Data from the free drift experiments showed that the backward rate Rb

depends linearly on the activity product of Ca2+ and HCO−3 (Rb was calcu-

lated as the difference between the forward rate Rf and the observed rate R)

and hence could be described by

Rb = k4ACa2+AHCO−

3, (4.18)

where k4 (dimensions mol cm−2 s−1 M−2) was found to be a function not

only of temperature, but also of PCO2. From equations (4.13) and (4.18) it

follows that the net rate R is given by

R = Rf −Rb = k1AH+ + k2AH2CO∗

3+ k3AH2O − k4ACa2+AHCO−

3, (4.19)

which describes the whole range of experimental data in terms of individual

ion activities in the bulk fluid.

In order to derive a theoretical expression for k4, Plummer et al. devel-

oped a reaction mechanism model for calcite dissolution. They concluded

72

0

0.2

0.4

0.6

0.8

1

3 4 5 6 7 8 9 10

PCO2

(atm)

pH

H+

H2O

H2CO∗3

k1AH+ = k2AH2CO∗

3+ k3AH2O

k2AH2CO∗

3= k1AH+ + k3AH2O

k3AH2O = k1AH+ + k2AH2CO∗

3

Figure 4.3: The rate of forward reaction is dominated by one of the termsin equation (4.13) in the three regions labeled H+, H2CO

∗3, and H2O. Along

the lines, one term just balances the other two, and in the area enclosed theforward rate depends significantly on more than one mechanism. Adaptedfrom [Plu78].

73

that three parallel reactions occur on the surface,

CaCO3 +H+ = Ca2+ +HCO−

3 (4.20)

CaCO3 +H2CO3 = Ca2+ + 2HCO−3 (4.21)

CaCO3 +H2O = Ca2+ +HCO−3 +OH

−, (4.22)

and further assumed that reaction (4.20) is fast and therefore limited by

mass transport, while reactions (4.21) and (4.22) are much slower, and their

rates are chemically controlled. On basis of these assumptions, the surface

layer activities of H2CO3 and H2O are equal to the corresponding bulk fluid

activities, and the activities of all other species in the surface layer (including

H+) are determined by calcite and carbonate species equilibria. For instance,

A(s)H+ is given by the calcite saturation value at A

(s)H2CO3

= AH2CO3and may

be calculated using an equilibrium model. A formal kinetic analysis of the

reactions (4.20)–(4.22) leads to a rate expression that is equivalent to the

empirical equation (4.19), and defines the rate constant k4 as

k4 = k′4 + k′′4A(s)HCO−

3

+ k′′′4 A(s)OH− , (4.23)

where A(s)i are the surface layer activities of species i, and the new constants

k′4, k′′4 , and k′′′4 can be expressed in terms of the forward rate constants and

some equilibrium constants [Plu78, Plu79]. The agreement between the-

oretical and observed values of k4 was satisfactory over some range of CO2

partial pressures.

Plummer et al. had to make the crucial assumption that the partial

pressure of CO2 at the surface has the same value as in the bulk fluid (this is

equivalent to A(s)H2CO3

= AH2CO3since AH2CO3

is proportional to AH2CO∗

3which

in term depends linearly on PCO2by Henry’s law)—an assumption that

74

may not hold under certain conditions. In an attempt to verify their model

by comparison with several other studies in the literature, Plummer et al.

themselves found discrepancies of more than one order of magnitude, espe-

cially under conditions of low PCO2[Plu79]. More recently, the model has

been criticized by Compton and co-workers as conveying only limited mech-

anistic information, because the empirical rate expression (4.19) is based on

bulk fluid activities instead of surface layer activities, and the experimental

conditions do not allow a well-defined, calculable and controllable transport

of the reactants to the interface [Com90a, Com90b]. Although the model

seems to agree quite well with the original set of data, its applicability to

data obtained under different experimental conditions is strictly limited, in-

dicating that there must be a significant dependence upon specific properties

of the experimental method applied.

A completely different experimental approach was used in the study by

Compton et al. which has already been cited [Com90a, Com90b]. They

proposed a new strategy for studying surface reactions and applied their

sophisticated method to calcite dissolution: a calcite crystal forms part of

one wall of a rectangular flow cell, through which a standard HCl solution

is pumped under laminar flow conditions. Immediately downstream of the

crystal, an appropriate detector electrode is placed in the wall, measuring

either directly the concentration of Ca2+ or the remaining level of the reactant

H+ as a function of flow rate. This technique has several advantages, for

instance

• defined surface area and topography of the crystal,

• very high rates of mass transport possible,

75

• transport of the reactants to the interface and the products to the

detection system calculable and controllable because of defined flow,

• measurement of surface concentrations instead of bulk values,

• steady-state flow system, hence no chemostatic control necessary.

Two different pH regimes were examined: At pH < 4, the data was described

best by first-order heterogenous kinetics according to the rate law

R = k1[H+](s), (4.24)

where R is the dissolution rate with units mol cm−2 s−1, [H+](s) denotes the

surface concentration of H+ in M, and the rate constant was found to be

k1 = (4.3± 1.5) · 10−5 mol cm−2 s−1 M−1. Compton et al. were able to

avoid transport control during all their experiments, down to very low values

of pH. Under high pH conditions, i.e., at pH > 7, and in the near absence of

CO2, they chose the following rate law as that which best fits the observed

data

R = k − k′[Ca2+](s)[CO2−3 ]

(s), (4.25)

where R has the same units as above and k′ = k/Ksp with the solubility

product of calcium carbonate Ksp. Again, [Ca2+](s) and [CO2−

3 ](s) are sur-

face concentrations, and the zero order rate constant k is dependent upon

surface morphology (especially roughness). The value found for a surface of

Iceland spar, polished with a succession of grit sizes down to 0.25 µm, was

k = 9.5 · 10−11 mol cm−2 s−1. It can be shown that in the absence of CO2

and at pH > 7 Plummer’s rate expression (4.19) reduces to the same ki-

netic form as (4.25) under the assumption that dissolution ceases when the

calcite solubility product is reached [Com90b]. However, equation (4.25)

76

refers to surface concentrations rather than bulk phase quantities, and one

may conclude that it is more physically significant, i.e., closer related to the

“real” mechanism of surface reaction. On the other hand, model equations

like (4.19) are of great practical value, since in most practical cases the sur-

face concentrations can neither be measured nor calculated, and it is not

possible to eliminate the influence of transport processes.

Still another problem arises from the effect of impurities: it is known

that trace amounts of inhibitors (such as phosphate) can cause large changes

in rate without significantly altering the thermodynamic properties of the

system [Ber74, Plu79]. Unfortunately, there is no simple way of predicting

the total effect that an impurity or combination of impurities may have on the

rate of reaction, since theoretical models are not available to date. This shows

the difficulty in developing a useful general model of calcite dissolution—

very often a specific empirical relation for the system in question might be

preferred.

Comparative Study of Carbonate Dissolution

Another interesting publication that shall be discussed here is the compara-

tive study by Chou et al., who investigated the dissolution of various carbon-

ates (including calcite, magnesite, and dolomite) in standard HCl solutions

at 25◦C [Cho89]. They used a continuous fluidized bed reactor and samples

of relatively coarse particle size (0.3–0.4 mm for calcite, 0.05–0.1 mm for

magnesite, and 0.1–0.2 mm for dolomite). Surface area and composition of

the solid phase remained approximately unchanged during each dissolution

experiment. The reactor was operated at a constant flow rate of standard

input solution, and the composition of the output solution quickly reached a

77

steady state. The output solution was collected and analyzed for dissolved

species, and also the pH was measured. This allowed to determine the disso-

lution rate by multiplying the concentration of cations with the flow rate of

the output solution and dividing by the estimated surface area of the solid.

The partial pressure of CO2 could not be fixed at some arbitrary value like

in the experiments above, but it could be calculated from the measured data

(bulk fluid concentrations and pH). The experiments showed that both calcite

and magnesite have the same general rate dependence on pH, but the rate

of dissolution of magnesite is about three to four orders of magnitude lower

than that of calcite, see Figure 4.4. The authors proposed a reaction model

similar to that of Plummer et al. to describe their data on the dissolution

of one-component carbonates,

MCO3 +H+ = M2+ +HCO−

3 (4.26)

MCO3 +H2CO∗3 = M2+ + 2HCO−

3 (4.27)

MCO3 = M2+ + CO2−3 , (4.28)

where M represents either Ca or Mg. From these three reaction steps they

derived the rate expression

R = k1AH+ + k2AH2CO∗

3+ k3 − k−3AM2+ACO2−

3, (4.29)

where the contribution of the first two reactions to the backward rate has

already been omitted since it is not significant. The rate constants ki were

determined from the experimental results; their numerical values are given

in Table 4.1 for both calcite and magnesite.

For dolomite as a two-component carbonate, Chou et al. found the fol-

lowing empirical rate equation,

Rf = k1AnH+ + k2A

nH2CO∗

3

+ k3, (4.30)

78

−15

−14

−13

−12

−11

−10

−9

−8

−7

2 4 6 8 10

logR

pH

calcite ×

×

×××

××

××

××××××

×××

×××

magnesitedolomite 3

3

3

3

3

3333

33

333333

3

Figure 4.4: Dissolution rates vs. pH for calcite, dolomite, and magnesite;experimental data obtained with continuous fluidized bed reactor at 25◦C.Adapted from [Cho89].

79

Table 4.2: Summary of empirical rate constants for the dissolution ofdolomite; the corresponding expressions for forward and backward rate aregiven by equations (4.30) and (4.31), respectively. Forward rate constantsk1, k2, k3 have dimensions of mol cm

−2 s−1 M−n, backward rate constant k4

has dimensions of mol cm−2 s−1 M−1.

Dolomite

Ca0.498Mg0.502CO3 Ca0.509Mg0.489Fe0.002CO3

[Cho89] [Bus82]

25◦C 25◦C 55◦C

n = 0.75 n = 0.5 n = 0.6

k1 = 2.6 · 10−7 k1 = 4.1 · 10

−8 k1 = 2.5 · 10−7

k2 = 1.0 · 10−8 k2 = 1.3 · 10

−9 k2 = 2.0 · 10−9

k3 = 2.2 · 10−12 k3 = 5.0 · 10

−9 k3 = 2.5 · 10−11

k4 = 5.6 · 10−8 k4 = 2.0 · 10

−7

which only describes the forward rate. After a very short initial stage of

dissolution, calcium and magnesium are released stoichiometrically, i.e., in

a 1:1 mole ratio.1 An important difference in behaviour compared to the

other carbonates is that the reaction order n is a fractional number less than

one. The best fit of experimental data was obtained for n = 0.75 and the rate

constants given in Table 4.2. There is not yet a really convincing explanation

for the fractional order of reaction—Chou et al. assume that the formation

1Since initially Ca is released faster than Mg, the dolomite surface acquires a Ca:Mg

mole ratio that is smaller than that of the bulk solid. This affects only a few atomic layers

on the surface [Bus82].

80

of positively charged surface complexes due to H+ uptake causes electrostatic

interactions which in term may lead to the fact that the degree of protonation

of the surface increases only slightly with decreasing pH, i.e., the observed

reaction order is less than one. As shown in Figure 4.4, the dissolution rate

of dolomite is about one order of magnitude lower than the calcite rate, but

still two orders of magnitude higher than the magnesite rate.

Busenberg and Plummer used the same equation (4.30) to describe

their data on dolomite dissolution, but they found a reaction order of n = 0.5

at temperatures below 45◦C which increases at higher temperatures [Bus82].

They also identified one backward reaction with empirical rate

Rb = k4AHCO−

3, (4.31)

and they were able to show that this backward rate is significant even far

from equilibrium. This is one important reason for the very low net rate

of dissolution, particularly at pH > 6 as H+ attack becomes less dominant.

The dissolution reaction essentially stops quite far from equilibrium, and

the amount of time necessary to reach “true” equilibrium might be so large,

that this will never be observed in laboratory or nature. Rate constants for

the temperatures 25◦C and 55◦C can be found in Table 4.2, but it must

be pointed out that these constants are highly dependent on the source of

dolomite. Busenberg and Plummer studied eight different dolomite speci-

mens of both sedimentary and hydrothermal origin and found that the latter

dissolved significantly slower at least in the low temperature regime. The

rate constants given here refer to a microcrystalline sedimentary dolomite

from Wisconsin. There is also a significant increase in dissolution rate with

increasing temperature: dolomite dissolves five to ten times faster at 45–60◦C

than at 25◦C.

81

Acid Neutralization with Limestone

The use of crushed or powdered limestone to neutralize acidic wastes like coal

mine drainage and pickling liquors has been investigated by several workers

since limestone is the least expensive neutralizing agent available [Bar76,

Hoa45, Par65, Pea75]. There have been some difficulties in the practical

application of limestone neutralization, because

• the reaction rates of limestone are relatively low,

• the active limestone surface may be fouled by oil, grease, or sulfate and

phosphate precipitates, thereby disrupting dissolution,

• the equilibrium pH is too low to precipitate certain metal ions which

have to be removed from the waste water.

Out of these reasons, lime is more commonly used for the treatment of acidic

wastes. Nevertheless, limestone neutralization has been successfully applied,

especially in cases where the waste water does not contain too much sulfuric

acid. Parsons described design and installation of an upflow limestone

neutralization plant; after some simple modifications like increased flowrates

in the limestone bed and removal of fouling substances from the input stream,

satisfactory operation of the system was achieved [Par65].

Hoak et al. proposed a combined limestone-lime treatment of spent pick-

ling liquors: pulverized high-calcium limestone is used to raise the pH to

about pH 6 and precipitate part of the metals, then the treatment is com-

pleted with lime. Dolomitic limestones are practically useless for this purpose

due to their very low reactivity. As a rule of thumb, the rate of reaction with

pickle liquor was found to be inversely proportional to the percentage of mag-

82

nesium carbonate in the limestone, e.g., a limestone with 5 wt% MgCO3 has

only about 1/5 of the normal reaction rate [Hoa45].

Barton and Vatanatham presented a simple model for the kinetics

of limestone neutralization [Bar76]. They examined the dissolution rate of

calcite particles in 0.01 N sulfuric acid; the pH was allowed to drift freely.

Particles with almost uniform initial size were used, and a shrinking particle

model was applied to describe the change in surface area. All the reactions

in the bulk phase were assumed to be at equilibrium, and for the dissolution

rate the following expression—valid in the range between pH 2 and 6—was

found which is first order with respect to H+ concentration2

−dN

dt= Ak ([H+]− [H+]eq)

=6kMN

1/30

ρD0

N2/3 ([H+]− [H+]eq) . (4.32)

In this equation,

N = moles of solid CaCO3 at time t,

A = surface area of CaCO3(s) at time t,

k = rate constant,

[H+] = molar H+ concentration in bulk solution at time t,

[H+]eq = molar H+ concentration in bulk solution at equilibrium,

M = molecular weight of CaCO3(s),

N0 = moles of initial CaCO3(s),

ρ = density of CaCO3(s), and

D0 = initial particle diameter.

From their data at different temperatures, the authors concluded that the

dissolution rate was controlled by H+ diffusion rather than surface reaction

2The model equation is misprinted in the original paper.

83

in the given pH range. Since their dynamic model is not valid at pH > 6, it

cannot be applied to the production of CMA at near-neutral pH. The same

is true for the model proposed by Pearson et al., who examined the use

of crushed limestone for the treatment of coal mine drainage and derived

practical rules for the design of such neutralization processes [Pea75].

The only study that investigated the dissolution of calcite and dolomite

in acetic acid was done by Suarez andWood in the context of soil analysis

[Sua84]. They measured the buildup of CO2-pressure in a sealed reaction

vessel in order to determine calcite surface area and content in soil sam-

ples (surface area and total calcite were determined from maximum slope

of pressure vs. time and final pressure, respectively). A buffered solution

containing sodium acetate and acetic acid was used in these experiments;

therefore, the pH remained nearly constant at about pH 4.3 during the reac-

tion. Under these conditions, calcite dissolves approximately 70 times faster

than dolomite. This is but the only useful result since the publication con-

tains neither absolute rate data nor a theoretical model.

4.2.2 Oxide Minerals: CaO, MgO

Kinetics and mechanisms of the dissolution of metal oxides in aqueous me-

dia have been studied for several reasons—the reactivity of oxide surfaces in

solution is an interesting field of study and also has some practical implica-

tions, e.g. for the etching of metals, the extraction of ores, and the inhibition

of corrosion. Although quite a lot has been published in this field since the

1960s, it is difficult to find rate data or kinetic models for the higher pH

regime above pH 4. Therefore, it will be necessary to rely on rather crude

extrapolations, or to collect additional data.

84

An excellent review of oxide dissolution is provided by Segall et al.

[Seg88]. They use an approach based on solid state science, thus emphasiz-

ing the role of the solid and including solution properties as necessary. There

are three basic types of oxides,

• ionic oxides like CaO, MgO

• semiconducting oxides like CoO (p-type), ZnO (n-type)

• covalent oxides like Al2O3, SiO2,

with different mechanisms of dissolution. Other important factors deter-

mining reactivity are pretreatment (effect on surface and bulk defect sites),

surface structure, and surface alteration in solution. Only the ionic oxides—

particularly CaO and MgO—shall be discussed in further detail now. Com-

pared to the other types, these oxides dissolve very fast: the dissolution

rates at pH 1 and 30◦C (after the initial stage of acidic solution attack)

are 1.2 · 10−7 and 1.2 · 10−8 mol cm−2 s−1 for CaO and MgO, respectively

[Seg88]. It is believed that the dissolution process comprises the following

steps [Seg88]:

1. Restructuring of ionic surface upon initial contact with aqueous solu-

tion (produces a roughened surface structure with many defect sites).

2. Alteration of surface charge.

3. M2+ transfer to solution.

4. H+ transfer to O2− ion.

5. OH− (or H2O) transfer to solution.

85

Steps 1 and 2 are responsible for a significant alteration of reactivity that

occurs at the very beginning of the dissolution process (less than 5% of the

solid dissolved). After completion of this initial stage, the surface structure

remains nearly unchanged until about 75% of the solid are dissolved, and dis-

solution proceeds according to steps 3–5 only (“advanced stage”). However,

it should be pointed out that the reaction steps 3–5 given above are not the

only ones that have been proposed: for instance, Vermilyea assumed that

MgO first reacts with water to form a Mg(OH)2 layer on the surface and the

rate is controlled by dissolution of the Mg(OH)2 via steps 3 and 5 [Ver69].

MacDonald et al. supported the same view in their study [Mac71].

Depending on pH and saturation conditions, the observed dissolution rate

is controlled by either transport, surface reaction, or both. Three different ki-

netic regimes can be distinguished, which, in practice, often overlap [Seg88].

Regime I: At high product concentration approaching saturation, it is as-

sumed that the surface layer is in equilibrium with the solid, and the

rate is controlled by transport of either M2+ or OH− from the surface

layer to the bulk solution. The kinetics can be described by Nernst

theory.

Regime II: Transport control is found also in the extreme cases where the

dissolution rate is very high, or the concentration of a reactant is very

low. The first case occurs at rates greater than 5 · 10−8 mol cm−2 s−1,

e.g., with CaO dissolving at pH 1–2, and the diffusion of dissolved

species away from the surface is rate limiting. The second case can be

observed with ionic oxides at pH > 6; then the rate is controlled by

arrival of H+.

86

Regime III: In the intermediate pH regime (pH 2–6), the dissolution rate

is mainly reaction controlled, and it typically ranges between 10−9 and

10−12 mol cm−2 s−1. The activation energy in this regime is usually

greater than 65 kJ mol−1 (compared to only 15–20 kJ mol−1 for dif-

fusion control). However, the results of MacDonald et al., who in-

vestigated MgO dissolution in dilute sulfuric acid at pH 3–5 using a

rotating disc technique, demonstrate the existence of mixed kinetic

control, with transport control playing a more and more dominant role

at higher temperatures [Mac71].

These different kinetic regimes combined with the necessary distinction be-

tween initial and advanced stages of dissolution clearly complicated the in-

terpretation of experimental results, and, in fact, the available literature is

not very conclusive. There are several conflicting results reported for the dis-

solution of MgO, and it is hard to find anything at all about CaO dissolution

kinetics, since in this case experiments are further complicated by the very

high reactivity of CaO (which is about one order of magnitude higher than

that of MgO).

Briefly, the main results can be stated as follows: During the initial stage

of dissolution, both CaO and MgO show a significant rise in rate despite

decreasing pH under free drift conditions; this initial rise is steeper for CaO

than for MgO. The effect has been attributed to surface roughening due to

initial solution attack [Seg88, Seg78], but is still not very well understood

and shall not be discussed in further detail here. For the advanced dissolu-

tion regime of MgO, most authors found a linear relationship between the

logarithm of rate R and pH, but both the slopes (ranging from −0.5 to −1)

and the absolute values differ greatly [Seg88]. Figure 4.5 gives a good im-

87

pression of the variation in published rates for MgO at 20–25◦C for pH 2–6.

The advanced kinetics of CaO are reported to show similar features to MgO

but at rates about ten times greater [Seg88].

At the moment there seems to be no way to explain these apparent exper-

imental contradictions. Some of the difficulties may arise from uncertainties

in estimating the effective surface area (by gas absorption or geometrical

considerations), changes in particle size distribution during dissolution (es-

pecially in the case of powders), and the use of background electrolytes in

some of the experiments. Vermilyea found that certain substances act as

inhibitors (e.g. periodate) or accelerators (e.g. phosphate, acetate3) in the dis-

solution of magnesium hydroxide [Ver69]. Another possible effect that may

occur in technical applications of calcium hydroxide as neutralizing agent is

the precipitation of calcium sulfate (gypsum) on the surface of the calcium

hydroxide particles, if sulfuric acid is present in the solution. Even a very

thin film of gypsum has been shown to significantly decrease the dissolution

rate [Bog85].

From these results one must conclude that it is even more difficult to

develop a kinetic model for the dissolution of CaO and MgO than it was

for the carbonates. As already stated at the beginning of this section, it is

therefore necessary to rely on rather crude estimates for the dissolution rates

in the interesting pH range, and to verify these estimates through subsequent

experiments under “real” process conditions. Reasonable extrapolated values

for the rates at pH 6 would be 1 · 10−9 and 1 · 10−10 mol cm−2 s−1 for CaO

and MgO, respectively. These values may be compared to similar estimates

3This is particularly interesting, since both acetate and phosphate would be present in

a CMA fermentation.

88

−12

−11

−10

−9

−8

−7

1 2 3 4 5 6 7

logR

pH

MgO smoke crystals at 25◦Csized, sieved powder at 20◦C

rotating disk at 20◦Crotating disk at 20◦C

Figure 4.5: Summary of published dissolution rates vs. pH for MgO, in unitsmol cm−2 s−1. The data was collected from various sources by Segall etal.; diagram adapted from [Seg88].

89

Table 4.3: Summary of dissolution rates at 20–25◦C for carbonate mineralsand oxide minerals. The carbonate rates are based on the experimental dataof [Cho89], the values for CaO and MgO were chosen according to the datapresented in [Seg88], assuming a slope of −0.6 for logR vs. pH betweenpH 5 and 7. Rates are given in units of mol cm−2 s−1.

Mineral Dissolution Rate

pH 5 pH 6 pH 7

calcite 2 · 10−9 2 · 10−10 8 · 10−11

dolomite 9 · 10−11 2 · 10−11 1 · 10−11

magnesite 2 · 10−13 1 · 10−13 6 · 10−14

CaO 4 · 10−9 1 · 10−9 3 · 10−10

MgO 4 · 10−10 1 · 10−10 3 · 10−11

for the carbonate minerals. Table 4.3 gives a summary of dissolution rates at

pH 5, 6, and 7 for all the minerals discussed. The rates cover a range of almost

four orders of magnitude from the slowest dissolving mineral (magnesite) to

the fastest (CaO). It might be interesting to observe that the rates of calcite

and MgO are relatively high and of the same order of magnitude. Since such

a mixture can be easily prepared from dolomite by selective calcination, it

could have some potential as neutralizing agent in CMA production.

4.3 The Dynamic Model and Its Limitations

At this point, it is time to “put everything together”—most of the results

obtained so far will be used to develop a dynamic model of CMA production

90

in a continuous fermentor. A brief discussion of the model and its struc-

ture forms the main part of this section. Simplifying assumptions had to be

made where certain aspects of the process were unknown or quantitative de-

scriptions were not available. Other significant uncertainties were introduced

by the underlying models used to describe acetic acid production, dissolu-

tion kinetics, and liquid phase equilibrium speciation. Altogether, this led

to the conclusion that quantitative results obtained from this model must

be expected to carry only very limited information about the real process.

Therefore, the original plan to examine process dynamics and control by

simulation has been abandoned in favour of a more practical approach to

be presented in the next chapter. Nevertheless, the theoretical model allows

to gain some insight into the dynamic structure of the process, it helps to

identify important factors determining the process behaviour, it puts the pre-

viously obtained results into a new perspective, and it allows to draw some

qualitative conclusions for process design and control.

4.3.1 Outline of the Process Model

Overall System Structure

The continuous reactor containing fermentation broth (with dissolved sub-

strate and product), cells, and undissolved lime or limestone solids is modeled

as an open system with lumped parameters. Four phases shall be distin-

guished as shown in Figure 4.6:

1. The liquid phase comprises water and all dissolved species, but not

the suspended cells and particles. It may be characterized by the vol-

ume V and the total concentrations of dissolved substrate, calcium,

91

cells(µ, Nx)

solids phase

(Ni, Ai)

liquid phase

(V , CTS ,

CTCa, C

TMg, C

TAc)

gas phase(PCO2

)

R

µ

R

- -

µ

µ

ª

I

R

6

cell loss solids feed solids discharge

gas discharge

HAc S Ca, Mg, CO2

CO2

feed stream(F f , Cf

S )

product stream

(F , CTS ,

CTCa, C

TMg, C

TAc)

Figure 4.6: Overall structure of the model system with definition of phases,streams, and relevant dynamic variables.

92

magnesium, and acetate, which are denoted by CTS , C

TCa, C

TMg, and CT

Ac,

respectively. A feed stream with defined flow rate F f and substrate con-

centration CfS (all other concentrations zero) enters the liquid phase,

and a product stream characterized by F , CTS , C

TCa, C

TMg, and CT

Ac is

withdrawn. For our purposes, it shall be assumed that at any time

F = F f , i.e., the liquid volume V is a constant. The system is well

stirred, so that all concentrations are functions of time only.

2. The gas phase contains water and carbon dioxide. By maintaining a

constant pressure, the partial pressure of carbon dioxide, PCO2, can be

fixed (water at fermentation temperature of 60◦C has a vapor pressure

of about 0.2 bar). The exsolution of CO2 from the liquid phase is

assumed to be fast since the reactor is highly turbulent. Therefore,

H2CO∗3 in the liquid phase is in equilibrium with the gas phase at fixed

PCO2. Evolved gases are discharged. Bubbling with CO2 should be

avoided if possible, because a high PCO2decreases carbonate dissolution

rates and may even transform hydroxides into carbonates. Instead, an

inert purge gas like nitrogen may be used to further facilitate exsolution

of CO2.

3. The cells transform the substrate S, which may be glucose or xylose,

into acetic acid. For simplification, the substrate is assumed to be pure

glucose, and other components needed by the organism are neglected.4

The biomass is characterized by its amount Nx and its growth rate µ;

simple model equations are used for acetic acid production rate and

substrate uptake rate. Cell loss depends on the rate of cell lysis as well

4In reality, at least a source of nitrogen, sulfur, and phosphorus must be provided in

addition to the substrate for growth.

93

as on process characteristics like dilution rate D = F/V , cell immobi-

lization, or cell recycling. In a continuous fermentation, it is possible

to establish a steady state with constant Nx (growth equals cell loss).

4. The solids phase consists of the undissolved lime or limestone particles.

Three different cases will be considered,

• the use of dolomite CaMg(CO3)2,

• the use of selectively calcined dolomite CaCO3 ·MgO, and

• the use of type S dolime Ca(OH)2 ·Mg(OH)2.

Dissolution kinetics are described by the available empirical rate ex-

pressions, and in case of the carbonates also precipitation may occur

(“negative” dissolution rate, modeled by the same equations). How-

ever, the direct transformation of solid hydroxides into carbonates by

CO2 could not be described dynamically and is neglected. The solids

phase is characterized by the total amount Ni and the effective surface

area Ai for each of the solid species present. Fresh particles are fed to

the system to make up for the amount dissolved, and there may be also

a discharge of unreacted solids. The overall neutralization rate may be

controlled by changing the available effective surface area.

Although the pH of the liquid phase is an important variable which greatly

influences the dissolution rates and also affects the organism, it has not been

listed above as a relevant dynamic variable, because it will be shown that

the pH at each instance of time is determined by the variables CTCa, C

TMg, C

TAc,

and PCO2. The same is true for all other individual species concentrations in

the liquid phase. These dependencies shall be discussed next.

94

Liquid Phase Equilibrium Speciation

Homogenous ionic reactions in solution are very fast compared to dissolution

reactions and microbial product formation. Hence it can be assumed that

at each point of time all homogenous reactions in the liquid phase are at

equilibrium. In addition, dissolved CO2 shall be in equilibrium with the gas

phase as already stated above. No reaction shall occur between the dissolved

substrate (glucose) and any of the other species in solution.5 The presence of

glucose therefore does not have any influence on the ionic equilibrium and can

simply be neglected at this point. In order to find the liquid phase equilibrium

speciation, only a few modifications have to be made to the approach already

used in Section 3.3 for the carbonate system (see Table 3.3):

• The reactions involving solid species are omitted because solids are not

considered to be part of the equilibrium model any more (there is no

equilibrium between liquid and solid phase). This reduces the number

of species as well as the number of independent reactions by two.

• Although the number of principal components remains the same, now

other species must be chosen for CaCO3(s) and MgCO3(s), for instance

Ca2+ and Mg2+. Also Ac− may be replaced by HAc, resulting in the

list of components H2O, H+, HAc, Ca2+, Mg2+, and CO2(g).

• There is no longer a fixed “recipe”—instead, the total concentrations

of dissolved calcium, magnesium, and acetate are given as functions of

time (CTCa, C

TMg, and CT

Ac, respectively). Nevertheless, the equilibrium

5This is a potentially “dangerous” simplification which has not been checked thoroughly

because of time constraints. In fact, it is not unlikely that certain reactions may occur.

95

composition can be calculated at each point of time, in a similar manner

as it was done for the titration discussed in Chapter 3.

The species and their stoichiometric formulae in terms of the components

can be found in Table 4.4 along with the corresponding logK values for the

mass laws; the tableau was calculated based on the following independent

reactions6

H2O = H+ +OH−, logK = −14.0

HAc = H+ +Ac−, logK = −4.76

CO2(g)+H2O = H2CO∗3, logK = −1.5

H2CO∗3 = H+ +HCO−

3 , logK = −6.3

HCO−3 = H+ + CO2−

3 , logK = −10.3

CaOH+ = Ca2+ +OH−, logK = −1.15

CaAc+ = Ca2+ +Ac−, logK = −1.2

CaHCO+3 = Ca2+ +HCO−

3 , logK = −1.26

CaCO3 = Ca2+ + CO2−3 , logK = −3.2

MgOH+ = Mg2+ +OH−, logK = −2.6

MgAc+ = Mg2+ +Ac−, logK = −1.3

MgHCO+3 = Mg2+ +HCO−

3 , logK = −1.01

MgCO3 = Mg2+ + CO2−3 , logK = −3.4.

(4.33)

Only logK at zero ionic strength was included in the tableau, since activity

coefficients will be used in the mass laws instead of corrected equilibrium

constants (see equation (3.11)). Each non-component row in the upper part

of the table corresponds to a mass law, hence thirteen mass law equations

can be written

γOH− [OH−] = 10−14.0γ−1H+ [H+]−1 (4.34)

6CaCO3 and MgCO3 stand for the ion pairs in solution, not the solids.

96

Table 4.4: Tableau-representation of the equilibrium model used for the liquidphase. Equilibrium constants at 25◦C and zero ionic strength.

Species H+ HAc Ca2+ Mg2+ CO2(g) logK

H+ 1OH− −1 −14.0HAc 1Ac− −1 1 −4.76CO2(g) 1H2CO

∗3 1 −1.5

HCO−3 −1 1 −7.8

CO2−3 −2 1 −18.1

Ca2+ 1CaOH+ −1 1 −12.85CaAc+ −1 1 1 −3.56CaHCO+

3 −1 1 1 −6.54CaCO3 −2 1 1 −14.9Mg2+ 1MgOH+ −1 1 −11.4MgAc+ −1 1 1 −3.46MgHCO+

3 −1 1 1 −6.79MgCO3 −2 1 1 −14.7

HAc 1 CTAc

CaCO3(s)/Ca(OH)2(s) −2 1 1/0 CTCa

MgCO3(s)/Mg(OH)2(s) −2 1 1/0 CTMg

CO2(g) 1 ?

97

γAc− [Ac−] = 10−4.76γ−1

H+ [H+]−1γHAc[HAc] (4.35)

γH2CO∗

3[H2CO

∗3] = 10−1.5PCO2

(4.36)

γHCO−

3[HCO−

3 ] = 10−7.8γ−1H+ [H+]−1PCO2

(4.37)

γCO2−

3[CO2−

3 ] = 10−18.1γ−2H+ [H+]−2PCO2

(4.38)

γCaOH+ [CaOH+] = 10−12.85γ−1H+ [H+]−1γCa2+ [Ca2+] (4.39)

γCaAc+ [CaAc+] = 10−3.56γ−1

H+ [H+]−1γHAc[HAc]γCa2+ [Ca2+] (4.40)

γCaHCO+

3[CaHCO+

3 ] = 10−6.54γ−1H+ [H+]−1γCa2+ [Ca2+]PCO2

(4.41)

γCaCO3[CaCO3] = 10−14.9γ−2

H+ [H+]−2γCa2+ [Ca2+]PCO2(4.42)

γMgOH+ [MgOH+] = 10−11.4γ−1H+ [H+]−1γMg2+ [Mg2+] (4.43)

γMgAc+ [MgAc+] = 10−3.46γ−1

H+ [H+]−1γHAc[HAc]γMg2+ [Mg2+] (4.44)

γMgHCO+

3[MgHCO+

3 ] = 10−6.79γ−1H+ [H+]−1γMg2+ [Mg2+]PCO2

(4.45)

γMgCO3[MgCO3] = 10−14.7γ−2

H+ [H+]−2γMg2+ [Mg2+]PCO2. (4.46)

The activity coefficients γi can be estimated from a semiempirical expression

like Davies’ formula

ln γi = −Az2i

(

I1/2

1 + I1/2− bI

)

, (4.47)

where the ionic strength I is defined by

I =1

2

∑

i

z2iCi, (4.48)

in the way it was discussed in Section 4.1 (see equations (3.4) and (3.6) for

further explanation). The pH is defined as the negative logarithm of H+-

activity, i.e., it can be calculated using

pH = − log γH+ [H+] (4.49)

98

from concentration and activity coefficient of H+.

The information given in the lower part of the tableau shows how the equi-

librium model is linked to the total concentrations of acetic acid (or acetate),

dissolved calcium (sum of all calcium species), and dissolved magnesium (sum

of all magnesium species) which are time-dependent functions denoted by

CTAc, C

TCa, and CT

Mg, respectively. In the case of acetic acid this is straightfor-

ward, for calcium and magnesium it is a little bit more complicated—here

one has to consider that all the calcium and magnesium present in the liquid

phase stems from the dissolution of either carbonates or hydroxides or both.

Therefore, solid species had to be included at this point, although they are

not considered part of the equilibrium system and consequently were omitted

from the top of the tableau. This is just a matter of accounting: one may

think of the system as being prepared by completely dissolving the solids

with an excess of acetic acid. Fortunately, carbonates as well as hydrox-

ides have the stoichiometric coefficient −2 in the H+-column of the tableau,

hence the TOTH balance can be written without knowledge about the ori-

gin of the dissolved material (carbonate, hydroxide, or both). Only in the

CO2(g)-column different coefficients occur, but since the TOTCO2 balance

is of no interest (PCO2in the gas phase is assumed to be fixed anyway), this

does not cause any difficulties. The same reasoning can be applied to the

double carbonate dolomite CaMg(CO3)2, because it may be simply consid-

ered as CaCO3 ·MgCO3 for this purpose. Hence from the first four columns

of the tableau, the mole balances for the components H+, HAc, Ca2+, and

Mg2+ are

TOTH = [H+]− [OH−]− [Ac−]− [HCO−3 ]− 2[CO

2−3 ]

− [CaOH+]− [CaAc+]− [CaHCO+3 ]− 2[CaCO3]

99

− [MgOH+]− [MgAc+]− [MgHCO+3 ]− 2[MgCO3]

= −2(CTCa + CT

Mg) (4.50)

TOTHAc = [HAc] + [Ac−] + [CaAc+] + [MgAc+]

= CTAc (4.51)

TOTCa = [Ca2+] + [CaOH+] + [CaAc+] + [CaHCO+3 ] + [CaCO3]

= CTCa (4.52)

TOTMg = [Mg2+] + [MgOH+] + [MgAc+] + [MgHCO+3 ] + [MgCO3]

= CTMg. (4.53)

Once CTAc, CT

Ca, and CTMg are known, the concentrations of all seventeen

individual species—excluding the “special” species H2O and CO2(g)—can

be calculated by solving the system of seventeen algebraic equations given

by (4.34)–(4.46) and (4.50)–(4.53) in conjunction with the expressions for

activity coefficients (4.47) and ionic strength (4.48).

Acetic Acid Production and Substrate Consumption

In order to derive equations for CTAc and CT

S the empirical expressions for

the rates of acetic acid production (2.10) and substrate uptake (2.13) by C.

thermoaceticum from Section 2.3.1 are used. Simple mole balances for acetic

acid and glucose in the liquid phase lead to the ordinary differential equations

dCTAc

dt=1

V

(

(αPµ+ βP)Nx − FCTAc

)

(4.54)

anddCT

S

dt=1

V

(

FCfS − (αSµ+ βS)Nx − FCT

S

)

, (4.55)

where the total amount of biomass Nx in the cell phase is described by

dNx

dt= µNx − (loss)x, (4.56)

100

and µ, αP, βP, αS, and βS are assumed to be known parameters. This as-

sumption might be justified under steady state conditions, but certainly not

during start up, since all these parameters are expected to be functions of

pH, CTS , C

TAc, and perhaps some other variables. A quantitative description

of these dependencies seems remote, it would require a lot more of experi-

mental and theoretical work than has been done so far. Similarly, the loss

of cells is difficult to quantify; in a more comprehensive modeling approach,

biological factors (e.g., cell lysis) as well as certain process characteristics

(e.g., effects of dilution rate, cell recycling, cell immobilization) would have

to be considered. Therefore, the use of the above equations is strictly limited

to cases where only minor changes occur in the dynamic variables, i.e., essen-

tially to steady state operation. Appropriate values for the parameters would

have to be determined experimentally under steady state process conditions.

The initial values of CTS , C

TAc, and Nx have no influence on the steady state

and would only have to be considered, if equations (4.54)–(4.56) could also

describe the dynamics of start up.

Dissolution of Solids

Differential equations for the remaining dynamic variables CTCa and CT

Mg can

be found using the results on dissolution kinetics from the beginning of this

chapter. First, dolomite shall be considered as neutralizing agent—the cor-

responding liquid phase mole balances for calcium and magnesium yield

dCTCa

dt=

1

V

(

AdolRdol − FCTCa

)

(4.57)

dCTMg

dt=

1

V

(

AdolRdol − FCTMg

)

, (4.58)

101

where Adol denotes the effective surface area of dolomite and Rdol is obtained

by combining equations (4.30) and (4.31) to

Rdol = k1γnH+ [H+]n + k2γ

nH2CO∗

3

[H2CO∗3]n + k3 − k4γHCO−

3[HCO−

3 ]. (4.59)

Since calcium and magnesium are released at the same rate Rdol after a very

short initial stage of dissolution, one should expect that

CTCa = CT

Mg (4.60)

is automatically satisfied in this case, i.e., there should be no difficulty in

maintaining the desired 1:1 molar ratio of Ca:Mg. The amount of dolomite

present in the solids phase can be described by

dNdol

dt= (feed)dol − AdolRdol − (discharge)dol. (4.61)

Much more difficult to quantify is the effective surface area Adol since it

depends on the particle size distribution which in the most general case

would have to be modeled using a population balance approach. The size of

each individual particle depends on its initial size, on the time it entered the

system, and on the conditions it met during its lifetime, i.e., on its entire

“history”. A simple shrinking sphere model like the one used by Barton

and Vatanatham [Bar76] is certainly not adequate because it is based on

the assumption that all particles start dissolving at the same time, and there

is no continuous feed of “fresh” particles. Population balance models have

been applied to processes like crystallization, but they involve rather complex

mathematics, hence using such a sophisticated approach is not justified in our

case considering the other serious limitations of our model. However, under

steady state conditions, the effective surface area as well as the amount of

102

dolomite are constant, and they are related by

Adol = cN 2/3dol , (4.62)

where c is a constant depending on the steady state particle size distribution.

If selectively calcined dolomite or type S dolime are used for neutraliza-

tion, the governing equations are

dCTCa

dt=

1

V

(

ACaCO3RCaCO3

+ ACa(OH)2RCa(OH)2 − FCTCa

)

(4.63)

dCTMg

dt=

1

V

(

AMgCO3RMgCO3

+ AMg(OH)2RMg(OH)2 − FCTMg

)

, (4.64)

where again Ai denotes the effective surface area of solid species i. The

carbonate rates may be derived from equation (4.29)

RCaCO3= k1γH+ [H+] + k2γH2CO∗

3[H2CO

∗3] + k3

− k−3γCa2+[Ca2+]γCO2−

3[CO2−

3 ] (4.65)

RMgCO3= k1γH+ [H+] + k2γH2CO∗

3[H2CO

∗3] + k3

− k−3γMg2+[Mg2+]γCO2−

3[CO2−

3 ] (4.66)

using the proper sets of rate constants ki for CaCO3 and MgCO3, respec-

tively. The hydroxide rates can be estimated from the linear logR vs. pH

relationship discussed in Section 4.2.2 which leads to expressions of the form

logR = c1 − c2pH, (4.67)

where the constants c1 and c2 can be determined for Ca(OH)2 and Mg(OH)2

from the data presented in Table 4.3. Of course, the simple rate expres-

sions (4.67) are only very crude approximations, and more accurate relations

would definitely be desirable. The effective surface area Ai and the total

103

amount Ni of each solid species i behave in the same way as it was explained

above for dolomite, so no further discussion is necessary here. Ideally, ACaCO3

and AMgCO3are zero for type S dolime, and ACa(OH)2 and AMgCO3

are zero

for selectively calcined dolomite, but this is only true as long as there is

no precipitation of carbonates or direct transformation of solid hydroxides

into carbonates. Especially in case of selectively calcined dolomite, the CO2

generated by dissolution of CaCO3 might react with Mg(OH)2 to form some

MgCO3. Furthermore, it is unlikely that the solid rawmaterials are “pure”,

i.e., selectively calcined dolomite will almost certainly contain Ca(OH)2 and

MgCO3, while type S dolime might contain some CaCO3 and MgCO3, al-

though in this case the residual carbonates can be effectively eliminated by

grit removal after slaking. As can be seen from the rate expressions, now

generally

CTCa 6= CT

Mg, (4.68)

therefore, it might be more difficult to achieve a 1:1 molar ratio of Ca:Mg

with type S dolime or selectively calcined dolomite than it was in case of

dolomite.

Finally it should be pointed out again that also this part of the dynamic

model suffers from serious limitations:

1. The underlying empirical expressions for the dissolution rates are not

necessarily adequate for the chemical and hydromechanical conditions

encountered in the continuous bioreactor.

2. Possible effects of inhibitors or accelerators on dissolution rates have

been neglected since no appropriate models were available.

3. No attempt has been made to develop a comprehensive model for the

104

effective surface area Ai of the various solids, because this would have

been too much effort considering the limited reliability of other model

parts.

Out of these reasons, the results obtained from the model should not be

expected to carry too much information about the real process, even if con-

ditions of steady state are assumed.

Mathematical Model Structure

At this point a brief discussion of the mathematical model structure and

the methods available for numerical solution is in place, although no actual

simulation was made. All the equations derived in this section together form

a system of semi-explicit nonlinear differential-algebraic equations (DAEs)

which can be written as

dx

dt= f(x,y) (4.69)

0 = g(x,y), (4.70)

where the vector x contains all the dynamic variables of the model, while

y consists of the remaining algebraic variables. DAEs arise naturally in

many applications, and their study is an active field in applied mathematics.

Numerical methods to solve DAEs directly—i.e., without transformation into

a system of ordinary differential eqations (ODEs)—have been developed since

the early 1970s, and reliable algorithms exist. DAEs present numerical and

analytical difficulties which do not occur with ODEs, for instance the initial

values must be consistent with the algebraic constraints (4.70). An excellent

review of recent developments in theory and numerical methods for DAEs is

provided by Brenan et al. [Bre89].

105

4.3.2 Model Uncertainties and Conclusions

Originally, it was planned to use the dynamic model for process simulation

and as a basis to develop a control strategy. The idea was to maintain a

constant pH by controlling the total amount of lime solids present in the

system—so that the overall dissolution rate in the reactor just balances the

acetic acid production rate—and at the same time to ensure a 1:1 molar

ratio of Ca:Mg by adjusting the partial pressure of CO2 so that calcium and

magnesium compounds essentially dissolve at the same rate. Although some-

thing like this could be possibly done, the process model discussed above does

not provide the necessary basis for such a “sophisticated” approach, because

too many and too large uncertainties are involved which would almost cer-

tainly make the results useless for practical application. To summarize, the

apparent weak spots of the model are

• the limited reliability of the underlying expressions for dissolution rates,

• the difficulties to calculate the effective surface areas,

• the assumption that no reactions between substrate and other species

occur,

• the limited understanding of the factors influencing the rate of substrate

uptake and acetic acid production by the organism,

• the assumption that hydroxides are not directly transformed into car-

bonates by CO2.

Nevertheless, the model was helpful to gain some insight into the dynamic

structure of the process and to determine important variables and their in-

terdependencies. The two main implications for practical applications are:

106

1. The control of pH in the range between pH 6 and 6.8 is not expected to

cause major difficulties. For the fast reacting type S dolime, the amount

of undissolved solids in the system would be relatively small, and the pH

might overshoot if too much lime is added at a time, but this problem

could be easily eliminated by using a slow continuous feed of lime slurry

instead of separate additions. The very slow reacting dolomite could

pose the problem of excessively high solid concentrations that would be

necessary to maintain the required overall neutralization rate. In case

of selectively calcined dolomite none of these problems is expected.

2. It will be much more difficult to maintain the proposed 1:1 mole ra-

tio of Ca:Mg (or any other fixed mole ratio, if desired). A solution to

this problem will have to be found especially for type S dolime, since

Ca(OH)2 dissolves about ten times as fast as Mg(OH)2. For selectively

calcined dolomite, the dissolution rates derived in Section 4.2.2 seem

to indicate that CaCO3 and Mg(OH)2 dissolve at rates of at least the

same order of magnitude under process conditions (see Table 4.3). In

case of dolomite only the initial dissolution stage could cause difficul-

ties, because ultimately calcium and magnesium should be released

stoichiometrically. If very fine particles are used in order to achieve a

large surface area, this initial non-stoichiometric release could actually

have a significant effect on product composition.

In the next chapter, a more practical approach will be made to specifically

adress the mole ratio problem, and it will be shown how a 1:1 CMA can

be produced using a continuous process under steady state conditions. The

preliminary design of a small CMA plant will be presented, including a brief

economic analysis.

Chapter 5

Process Design Considerations

Various fermentation processes for CMA production have been proposed, but

none of them has been commercialized or even tested at a pilot plant level

yet. This is kind of surprising since the authors have all claimed signifi-

cant cost advantages for their processes compared to the conventional route

which is currently used for small scale production. A real breakthrough in

the commercialization of CMA just did not happen, probably for following

reasons:

• CMA is supposed to be a “cheap” bulk chemical rather than a valuable

speciality product; therefore, large plants are required to make its pro-

duction economically feasible, and high profits are not to be expected.

The plant capacities considered by the FHWA range from 100 tons per

day minimum to preferably 1,000 tons per day.

• Better organisms might be isolated or existing ones might be geneti-

cally improved in the near future—this would significantly reduce the

cost of fermentation since it would allow for instance higher produc-

107

108

tivity and higher final product concentrations. People tend to wait for

these possible improvements rather than to take the risk of an early

investment.

• There is still not much experimental data available in the literature;

the findings are often inconclusive, and some of them are not very

encouraging. Many design proposals are based on wishful thinking

rather than on experimental facts, thus making it sometimes difficult

to assess their real potential.

On the other hand, a case can be made also for rather small alternative CMA

plants, at least with respect to the next five to ten years, since it is not very

likely that large plants will be built during this time. There definitely is a

small market for CMA at prices of $ 500 per ton or even higher—for instance,

it can be sold to the State Highway Administrations for use on bridges, and

to environmentally concerned private consumers who would probably like to

use it on their sidewalks and driveways—and if a small scale fermentation

process can actually do better than the conventional route, it should really

be worth trying. One possibility to initiate such a small scale production of

CMA would be to establish CMA as a new byproduct of the pulp and paper

industry, made from unpurified waste sugars which otherwise would just be

burned. Quite much research has been done on new organosolv wood pulping

methods recently, and one of the most promising processes of this kind uses

concentrated acetic acid as cooking liquor. From the spent liquor of this

acetic acid pulping process an aqueous solution containing xylose, glucose,

and some acetic acid could be obtained after recovering other byproducts

and most of the acetic acid—a “waste” stream that would be ideally suited

for fermentation to CMA. The preliminary design for a CMA plant based on

109

this feedstock will be presented at the end of the chapter together with an

economic analysis.

None of the previously published CMA fermentation processes offered a

solution to the mole ratio problem which provided the starting point for this

study. In the next section, it will be shown that an amazingly simple solution

exists. First, the key features of a continuous process capable of producing

the desired mole ratio of Ca:Mg will be discussed, then the experimental

realization of such a process will be described, and results will be discussed

for three different types of raw materials (type S dolime, selectively calcined

dolomite, and dolomite). Finally, the potential of the new process as a whole

and of each of the raw materials will be assessed.

5.1 How to Solve the Mole Ratio Problem

5.1.1 Stationary Solids Phase

When it became obvious that the “sophisticated” approach to solve the mole

ratio problem would fail because of the large uncertainties involved in the

model, an alternative solution was sought which does not require exact knowl-

edge about the real system. Just by considering the mass balances for calcium

and magnesium, a very promising new approach was actually found: if solids

are fed to a dissolver with a 1:1 molar ratio of Ca:Mg and a solids-free prod-

uct solution is withdrawn, i.e., essentially all solids are kept in the system,

then the system must eventually reach a steady state which is characterized

by the same 1:1 molar ratio of Ca:Mg for the solutes in the product stream—

what is put into the system in form of solids is what comes out as dissolved

material. In case of type S dolime for instance, assmuming that Ca(OH)2(s)

110

in fact dissolves ten times as fast as Mg(OH)2(s)at pH 6, the magnesium

mineral would build up in the solids phase until it has ten times the effective

surface area of the calcium mineral, and then the overall release of calcium

and magnesium from the solids phase would be the same. Theoretically this

should work regardless how different the individual dissolution rates might

be. In practice, however, there are certain limitations when at least one of the

components reacts very slowly, because this would lead to excessive amounts

of solids present in the system. As the dissolution of the double carbonate

dolomite shows, the buildup of the slower reacting component may occur

only on the particle surface and hence the stationary solids phase may have

essentially the same bulk composition as the feed solid. This could be true at

least to some extent for the selectively calcined material; it is rather unlikely

for the type S dolime because of its very small particle size and the porous,

microcrystalline structure of the particles.

Apart from possible limitations due to low reactivity, no exceptional prob-

lems are expected for the practical application of continuous steady-state

dissolution in the context of CMA production:

• The neutralization can take place right in the fermentor if a continuous

flow, stirred tank reactor (CSTR) is used; this fermentor type was

already assumed for the dynamic model in Section 4.3 and will also

be part of the proposed plant design. Cells and undissolved solids are

recycled together so that the stationary solids phase and a high cell

density can be maintained at the same time.

• If batch fermentation or a continuous packed bed reactor were used,

the in-fermentor neutralization approach would probably not be ap-

propriate, but it would still be possible to use a separate steady-state

111

dissolver in a recirculation loop and thus allow pH control while main-

taining the desired product composition. This design modification shall

not be discussed any further here.

• Either a centrifuge or a membrane filter can be used to separate the

cells and undissolved solids from the product solution; the separator

should be designed in a way that allows continuous recirculation of the

retentate. For instance, a disc-nozzle centrifuge or a cross flow filter

would meet this requirement. The decision between these two separator

types is quite difficult, especially since membrane filters have recently

found interesting new applications for product recovery in the context

of commercial fermentations (not only on a lab scale). In our case, the

decision was finally made in favour of the centrifuge because

– a centrifuge can be operated in a more flexible way, e.g., it is

possible to retain essentially all solids as well as to discharge a

certain fraction of them with the product stream, thus providing

an additional control variable,

– a membrane filter might get clogged during longer periods of op-

eration and then require cleaning or replacement, and

– there is still not very much experience with large scale applications

of membrane filters.

However, for the experiments that will be described in the next section,

a cross flow filter was used since it could be obtained more easily and

also provided simpler operation than a continuous centrifuge.

There might be two reasons for not recycling all solids—to prevent the

112

buildup of insolubles like silica which are always present in lime and lime-

stone, and to influence product composition, if the desired mole ratio does

not match the composition of the feed solids. This can be done by discharg-

ing solids directly with the product stream (a certain amount of solids in

the product could actually improve the deicing properties) or by splitting

the retentate stream and thus sending only part of it back to the fermentor

(again the solids could be added to the deicer product, and it would actually

be preferable to do that after the evaporation step in order to avoid scaling

problems in the evaporator system). In practice, it would be most desirable

to specifically separate out unwanted components from the recycle stream

rather than simply split the whole stream into two substreams of the same

composition. It is not unlikely that such a specific separation can be achieved

since there will probably be sufficient differences in size and density among

the solid components.

How will the three different kinds of solid base perform in the proposed

new process? Ultimately, this question can be answered only based on exper-

imental results, but a preliminary assessment of these raw materials can be

made by considering their general properties and the rate data from Chap-

ter 4:

1. In type S dolime, high dissolution rates for both minerals Ca(OH)2 and

Mg(OH)2 are combined with a very large effective surface area due to

small particles (most of them in the range 2–5 µm) of porous structure.

Therefore, a high overall reactivity and only a relatively small accumu-

lation of solids is expected. Although the dissolution rate of Ca(OH)2 is

about one order of magnitude higher than that of Mg(OH)2, a station-

ary state should be established quickly, because Mg(OH)2 still dissolves

113

at a fairly high rate. The stationary solids phase is expected to con-

tain mainly Mg(OH)2, hence the discharge of undissolved solids would

produce a high calcium CMA.

2. Selectively calcined dolomite will react more slowly, but the dissolution

rates for both CaCO3 and MgO should still be relatively high and of

the same order of magnitude. The material has to be ground to obtain

a powder because it does not decompose automatically when mixed

with water. Even in finely pulverized form it will probably have a

smaller effective surface area than type S dolime due to the less porous

structure. Although the MgO should be only light-burned and reactive,

it is difficult to predict whether the step

MgO + H2O −→ Mg(OH)2

is rate determining or not, i.e., whether the MgO will dissolve at es-

sentially the same rate as the Mg(OH)2 from type S dolime or rather

more slowly. From the rate data in Table 4.3 it would be expected that

the CaCO3 dissolves slightly faster than the MgO, but the difference

(factor two) is small compared to possible errors in the data, and the

opposite might be true. As a matter of fact, if MgO would turn out

to be the faster dissolving component, this would be a very interest-

ing property of the material, since it would allow the production of a

high magnesium CMA by discharging part of the undissolved solids.1

Compared to type S dolime, the necessary accumulation of solids in

the system will be higher, but it is not expected to be excessive. Since

1As discussed in Section 1.2, there exists a CMA double salt with a Ca:Mg mole ratio

between 2:3 and 3:7 which may have superior deicing properties compared to the 1:1 CMA.

114

the dissolution rates of CaCO3 and MgO should not differ too much,

the steady state is supposed to be established after a relatively short

period of time.

3. Dolomite dissolves at a very low rate compared to the other minerals

(at least ten times slower than CaCO3 and MgO), and like the selec-

tively calcined material it has to be pulverized mechanically. Calcium

and magnesium should be released stoichiometrically after the initial

dissolution stage; therefore, the discharge of solids is not expected to

significantly change the composition of the product (this might or might

not be an advantage). Although the high process temperature of 60◦C

might accelerate dissolution considerably, the accumulation of solids

will be very high, and problems are likely to occur. A steady state will

be established soon after the stationary solids concentration is reached,

because the initial non-stoichiometric dissolution stage of dolomite does

not last very long.

A comparative experimental study of these materials in the new process is

clearly necessary in order to decide which one would be most appropriate for

the production of CMA. From an economic point of view, all three raw mate-

rials should be available at a comparable cost, since the cheaper materials—

selectively calcined dolomite and dolomite—would have to be mechanically

crushed and ground, which is not required for the more expensive type S

dolime.

115

5.1.2 Experimental Realization

The Model System and Its Performance

Using a simplified model system, an experimental study of the new process

outlined in the last section was done; all three raw materials were tested. The

experiments were performed without the organism—instead, acetic acid was

fed into the system. An attempt was made to simulate the typical process

conditions that were chosen in Section 2.3.1 for a commercial CMA fermen-

tation, i.e.,

• acetic acid productivity 4 g l−1 h−1, corresponding to a CMA produc-

tion rate of 5 g l−1 h−1,

• CMA concentration of 50 g l−1 in the product solution,

• pH controlled at slightly above pH 6, and

• temperature of about 60◦C.

Unfortunately, the temperature controller failed during the first hour of op-

eration, so that all experiments had to be done at 26–31◦C (without tem-

perature control), since time constraints did not allow waiting for repair or

replacement of the broken unit. A schematic diagram of the experimental

system is given in Figure 5.1; some less important parts (temperature control,

volume control, stirrer, and fraction collector) are not shown.2 At the begin-

ning of each experiment, the dissolver (“fermentor”) was filled with V = 1.5 l

deionized water. The recirculation loop (pump P2) was operated at relatively

high flow rates of 0.27–0.43 l min−1 in an attempt to prevent the buildup

2For a complete list of equipment, see Appendix C.

116

dissolver(“fermentor”) pH control

unit

P4

6

¾

-

6

CO2

neutralizingagent(slurry)

P1

P2

P3

cross flowfilter

-

¾

?- -

6¾

?-

HAc feed(40 g l−1)

CMA product(≈ 50 g l−1)

Figure 5.1: Schematic diagram of the experimental system used for continu-ous production of CMA under steady state conditions.

117

of a filter cake in the cross flow filter, and the contents of the dissolver was

well mixed by stirring at 800–1000 rpm. The feed and the product stream

had exactly the same flow rate F = 0.15 l h−1; this was accomplished by

using one pump drive with two identical peristaltic pump heads P1 and P3.

Nevertheless, a volume control was required, because some additional water

was introduced with the neutralizer slurry. Whenever the liquid level in the

dissolver became too high, excess fluid was removed automatically by a pump

operating parallel to pump P3 (not shown in the diagram). Without these

additional streams the dilution rate would have been D = F/V = 0.1 h−1;

the actual value was slightly higher. The pH was controlled at a setpoint

of about pH 6 using a rather unsophisticated on/off-controller which actu-

ated the neutralizer feed pump P4. A high speed stirrer was used for the

slurry storage vessel to prevent settling of the particles. The system was

operated at atmospheric pressure; several openings in the headplate of the

dissolver provided a means for the discharge of CO2 generated by carbonate

dissolution.

The feed stream contained 40 g l−1 acetic acid, thus simulating an acetic

acid productivity of 4 g l−1 h−1 in the “fermentor”. Under conditions of

steady state, this translates into approximately 50 g l−1 CMA in the prod-

uct stream, if the dilution by the slurry feed can be neglected. The total

concentration of acetate ion in the dissolver CAc can be described by

dCAc/dt = D(CfAc − CAc)

CAc(0) = 0,(5.1)

where CfAc is the feed concentration of acetate ion, and D = F/V the dilution

rate. Equation (5.1) has the solution

CAc(t) = CfAc(1− e−Dt), (5.2)

118

i.e., the steady state acetate concentration CfAc will be approached very closely

after 40–50 h of operation. Therefore, a duration of 50 h was chosen for the

experiments, and it was hoped that this amount of time would also allow the

solids phase to get close to steady state.

Hourly samples of the solids-free product solution were taken with an

automatic fraction collector; these samples were later analyzed for calcium,

magnesium, and several other dissolved ions by inductively coupled plasma

emission spectroscopy (ICP). From the analyses, the total concentration of

CMA in the product solution and the Ca:Mg mole ratio could be determined

as functions of time.

The cross flow filter with pore size 1.2 µm performed well in retaining even

the finest lime particles—a perfectly clear product solution was obtained.

However, there were problems with the accumulation of a filter cake in all

experiments, and it was not possible to prevent this by increasing the flow

rate in the recirculation loop (perhaps it just could not be increased enough).

Shaking of the filter capsule from time to time allowed recirculation of part

of the accumulated solids, but new cake formed quickly. The amount of

solids “trapped” in the cake (and hence essentially removed from the active,

dissolving part of the solids phase) was significant compared to the total

amount of solids present in the system. As will be seen from the discussion

of results, it was mainly this effect of “quasi solids removal” which made it

difficult to approach the steady state. Another problem that occurred only

in the experiment with selectively calcined dolomite was the clogging of the

neutralizer feed mechanism due to fast settling of the slurry. One time the

neutralizer feed was cut off for several hours, which produced quite interesting

effects, but of course seriously disturbed the course of the experiment from

119

the way it was planned. Time constraints made it impossible to repeat the

experiment with an improved system; therefore, the presumed undisturbed

behaviour had to be extrapolated from the available data.

Discussion of Results

The first experiment was done with type S dolime supplied by The Western

Lime & Cement Co. in West Bend, Wisconsin; it had a Ca:Mg mole ratio

of 1.04:1.3 A slurry was prepared from one part dry lime and two parts deion-

ized water. The total amount of dolime consumed during 50 h of operation

was about 170 g; therefore, approximately 340 g of water were introduced

with the slurry—this amounts to less than 5% of the total feed of water,

thus increasing the dilution rate only slightly. As already mentioned, the

temperature controller failed during the first hour after start up, and it was

decided to continue the experiment without temperature control. The tem-

perature fell to the range of 26–31◦C, about 5 K above ambient temperature

due to the heat generated by stirrer and pumps. During the first 10 min

of the experiment, the pH varied between pH 4.87 and 9.81, i.e., there was

some overshooting each time when dolime was added, but after 25 min it

had already stabilized in the range of pH 6.00–6.11. As more solids built

up in the system and the total acetate concentration increased, the range

narrowed further so that an essentially constant value of pH 6.02 could be

maintained. Starting after a few hours of operation, a brownish, gel-like filter

cake accumulated in the filter capsule which could not be removed during

the experiment. Backflushing at high flowrates had to be applied afterwards

in order to clean the filter for the next experiment.

3Analyses of this material and the mole ratio calculation can be found in Appendix B.1.

120

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45 50

Ca:Mgmoleratio

time (h)

CMA from type S dolime 3

3

3

33333

333 3 33

3 3 3 3

Figure 5.2: Mole ratio vs. time for CMA produced from type S dolime;determined from ICP analyses of the product samples.

The Ca:Mg mole ratio in the product was calculated for some of the

hourly samples; the results are shown in Figure 5.2.4 As expected, the

calcium hydroxide turned out to dissolve much faster than the magnesium

hydroxide—at the beginning the Ca:Mg mole ratio in the product was as high

as 2:1. Thereafter, magnesium hydroxide started to build up in the dissolving

solids phase, and the mole ratio decreased rapidly. After only seven hours

of operation, the theoretical value 1.04:1 was reached, although there had

already been some minor accumulation of filter cake which caused the curve

to turn up slightly between hour 3 and 5. Obviously, serious cake accumula-

tion started just before hour 8, because there suddenly was a jump towards

4Original results of the sample analyses are given in Appendix A.2.

121

higher calcium content, and for the rest of the experiment the mole ratio

remained in the range between 1.20:1 and 1.35:1. The filter cake contained

high amounts of magnesium, alumina, and iron (which was responsible for

the brown color). The amount of solids that made up the solids phase in the

dissolver was very small (probably less than 5 g l−1) due to the fast reaction

of both minerals. At the end of the experiment, the concentration of CMA

in the product stream was about 45 g l−1. Dry CMA was recovered from 2 l

product solution collected during the last 13 h of operation.

In the second experiment, selectively calcined dolomite was used as neu-

tralizer. The uncalcined stone was again supplied by The Western Lime

& Cement Co.; it had a Ca:Mg mole ratio of 1.03:1, i.e., it was essentially

pure dolomite.5 Samples of this stone were calcined for half an hour at

about 700◦C in an electrical furnace. Ideally, only the magnesium part of

the dolomite should be decomposed under these conditions according to the

reaction

CaMg(CO3)2 −→ CaCO3 +MgO + CO2 ↑, (5.3)

and the theoretical weight loss can be calculated from the amount of CO2 re-

leased. For the selective calcination of pure dolomite, the theoretical weight

loss is 23.9%, and if all carbonate is decomposed (full calcination), the weight

loss would be 47.7% instead. The actual weight losses of the calcined sam-

ples used in this experiment ranged from 17.7% to 23.6%, indicating that

there remained a small portion of unreacted dolomite. Before the slurry was

prepared, all samples were mixed and pulverized; the powder was screened

using a 35 mesh sieve. A total amount of 377.4 g dry powder was obtained.

The first batch of slurry was prepared from one part selectively calcined ma-

5A chemical analysis can be found in Appendix B.2.

122

terial and two parts deionized water. No observable reaction occurred when

the water was added—this confirmed that the material was practically free

of CaO which would have been hydrated in a fast and highly exothermal

reaction. Unfortunately, in this experiment the slurry feed mechanism did

not work as well as it had done with the type S dolime because the solids

tended to settle in the tubing. In an attempt to prevent clogging, an ele-

vated neutralizer storage vessel was used, and the slurry was diluted with

more water. Thus a relatively high amount of about 1.18 l water was added

to the system with the slurry, corresponding to almost 14% of the total feed

of water (this caused a significant increase of the overall dilution rate, and a

more dilute product solution was obtained). But still the clogging problem

was not solved completely, and one time the neutralizer feed was blocked for

several hours before the failure was discovered. Definitely, it would be a bet-

ter idea to feed the dry powder or a putty instead of the slurry using a screw

conveyor or similar piece of equipment when repeating the experiment. The

theoretical amount of selectively calcined dolomite which had to be dissolved

during 50 h of operation was 175.5 g, but the actual amount fed into the

system was higher, since much more undissolved solids accumulated than in

the first experiment due to the lower reactivity of the material. Right after

the experiment had been started, the pH fell from about pH 7 to 5.07, and

then started rising slowly, as slurry was added continuously. About 10 min

later the setpoint of pH 6.00 was reached. Enough solids had built up in

the dissolver to maintain the required overall neutralization rate at around

pH 6, and the neutralizer feed became discontinuous. There was no signif-

icant overshooting like with type S dolime, the pH just varied in the range

of pH 5.96–6.03. Within a few hours of operation this range narrowed fur-

123

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45 50

Ca:Mgmoleratio

time (h)

CMA from selectively calcined dolomite 2

222222222222 2

222

2

2

2

2

22 2

2

Figure 5.3: Mole ratio vs. time for CMA produced from selectively calcineddolomite; determined from ICP analyses of the product samples.

ther due to the buffering effect of the increasing acetate concentration. The

problem with the accumulation of filter cake started even earlier than in the

first experiment, although the cake was less “sticky” and could be removed

more easily during operation. Again, some nonideality in the behaviour of

the system had to be expected.

Figure 5.3 shows the Ca:Mg mole ratio for the product during the course

of the experiment.6 The two most important observations are:

1. The magnesium oxide clearly dissolved faster than the calcium carbon-

ate at pH 6, in contradiction to the rate estimates from Section 4.2.2

(Table 4.3). After eleven hours of operation the Ca:Mg mole ratio was

6See Appendix A.2 for the original results of the analyses.

124

as low as 1:3.5, and then started moving up slowly towards a higher

calcium content. The two sudden peaks at hour 24 and hour 50 were

both caused by failures of the slurry feed—in the first case the feed

pump got clogged sometimes after hour 17 (when it was repaired at

hour 26, the pH had already dropped to pH 5.07), in the second case

the system simply ran out of neutralizer slurry (the pH was down at

pH 5.66 when the experiment was finished). If the first failure had not

occurred, the system would probably have come much closer to a true

steady state. Now the planned course of the experiment was seriously

disturbed, but the system behaved exactly as one would have expected:

once the feed of fresh neutralizer was cut off, the mole ratio markedly

increased as the faster reacting magnesium oxide got more and more

depleted in the solids phase. Another effect which may have acceler-

ated the calcium surge is the decrease of pH. If the rate data presented

in Table 4.3 are at least qualitatively correct, then the rate of calcite

dissolution should increase significantly relative to the magnesium ox-

ide rate with decreasing pH. This could mean that already at pH 5 the

calcium carbonate actually dissolves faster than the magnesium oxide

which would reverse the outcome of the dissolution experiment if done

at lower pH.

2. It is not possible to explain the significant decrease in the mole ratio

between start up and hour 11, if the difference between the dissolu-

tion rates of the two minerals is assumed to remain constant through-

out the experiment—although a decrease in the mole ratio could be

caused by filter cake accumulation (removal of calcium carbonate from

the actively dissolving solids phase), this alone would never lead to a

125

mole ratio below the start up level. Therefore, “quasi solids removal”

might be responsible for delaying the upturn towards steady state after

hour 11, but definitely not for the observed minimum itself. A likely

explanation for this strange behaviour is that the dissolution rate of

the magnesium oxide significantly increased during the first hours of

operation. As briefly mentioned in Section 4.2.2, acetate acts as an

accelerator in the dissolution of magnesium hydroxide, and the same

might be true for bicarbonate. The concentrations of both acetate and

and bicarbonate increased after start up,7 hence an accelerating effect

might very well occur. Since for selectively calcined dolomite the disso-

lution rates are of the same order of magnitude, even a relatively small

acceleration of magnesium oxide dissolution is observable which is not

necessarily true for type S dolime due to the much higher reactivity of

calcium hydroxide.

The chemical analysis of the solids phase showed that it contained calcium

and magnesium in a molar ratio of 3.07:1, and also significant amounts of

sulfur, alumina, and iron. The solids concentration in the dissolver was

approximately 45 g l−1—higher than in the first experiment, but not unrea-

sonably high. A final CMA concentration of about 38 g l−1 was reached, and

again dry CMA was recovered from 2 l product solution.

In the third experiment, the same dolomitic limestone was used as in the

second experiment, but without the calcining. The stone was just pulverized

(less than 35 mesh), and a slurry was prepared from one part dolomite and

about three parts water. Some difficulties with a high accumulation of solids

7The bicarbonate formed by dissolution of calcium carbonate is likely to accumulate

to a certain level due to slow carbon dioxide exsolution.

126

had been expected, but it was still surprising how soon the system had to

be shut down because of complete failure. Immediately after the experiment

had been started, the pH dropped to pH 4.70, then stabilized and started

rising slowly as limestone was continuously fed into the system. However,

about 20 min later there was already an excessive buildup of dolomite in

the filter capsule, and the pH had just reached pH 5.40—still far below the

setpoint. The solids concentration was so high that even shaking of the filter

capsule could not prevent further accumulation of cake. Only 35 min after

start up the cross flow filter got clogged, and the recirculation pump had to

be turned off. The acetic acid feed was stopped as well, only the pH con-

trol was left operating. It took another 10 min of continuous limestone feed,

before the setpoint pH was reached. Clearly, the uncalcined material was

too slow to maintain pH 6 at a reasonable concentration of solids under the

chosen process conditions. Perhaps the performance would have been better

at higher temperature (60◦C) and for a smaller particle size. High solids con-

centrations could probably be handled using a more sophisticated equipment

(e.g., a centrifuge instead of the filter), but the other two materials which

can do the job at much lower accumulations would definitely be preferable

in the context of a fermentation process. An analysis of the product solution

collected during the first 35 min of operation showed that it had a Ca:Mg

mole ratio of 1.12:1; another sample taken at pH 8.14 after solids and liquid

in the dissolver had equilibrated for several hours had an even higher ratio of

1.50:1. These results confirm again the significance of the initial dissolution

stage which already had been found in the equilibrium experiment described

in Section 3.3.

Based on the results of these experiments, a better evaluation of the pro-

127

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45 50

Ca:Mgmoleratio

time (h)

CMA from type S dolime 3

3

33

3333333333333333333333

CMA from selectively calcined dolomite 2

2

22

22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Figure 5.4: Ideal mole ratio curves.

posed process and the tested raw materials could be made. It should be

possible to avoid the adverse effects of filter cake accumulation by using a

continuous centrifuge instead of the filter—such a system will be able to op-

erate under conditions of steady state for long periods of time. Although the

experimental system described above was far from ideal, it performed well

enough to confirm the feasibility of the new process. A more ideal system

would probably have shown a behaviour similar to that given in Figure 5.4;

the curves for both type S dolime and selectively calcined dolomite were

obtained from the available data by correcting for the effects of cake accu-

mulation and control system failure. The type S curve approaches the 1:1

steady state mole ratio from above, and the curve for the selectively calcined

material comes from below (it initially turns down due to acceleration of

128

magnesium oxide dissolution, and then turns up again because of the accu-

mulation of calcium carbonate in the solids phase). A curve for uncalcined

dolomite would probably look quite similar to the type S curve, if this ma-

terial could be successfully applied in spite of its low reactivity.

The potential of the three raw materials tested can now be assessed in

the following way:

1. Type S dolime performes well at very low solids accumulation. A steady

state is established within a few hours of operation, and it should not

be too difficult to produce a 1:1 CMA by completely recycling the

undissolved solids. High calcium CMA could be made by discharging

some of the solids, but if such a product is desired (e.g. for flue gas

desulfurization), it would be better to use a high calcium lime instead

of the dolime, unless the magnesium-rich solids discharge can be sold

as a byproduct.

2. Selectively calcined dolomite requires a higher accumulation of solids

(about ten times that of type S dolime), but this is not expected to

cause any difficulties. It may take also about ten times longer to reach

the steady state (perhaps 50–70 h), but again this is not judged to

be a problem, and it should be possible to produce a 1:1 CMA using

the proper equipment. Even more interesting is the option to make a

high magnesium CMA by discharging part of the solids. Any Ca:Mg

mole ratio between 1:3.5 and 1:1 can be achieved in the product through

controlling the solids discharge, thus it would be no problem to produce

the mole ratio of 4:6 to 3:7 which is required for the calcium magnesium

double salt described by [Tod90].

129

3. Uncalcined dolomite did not perform well enough to be considered as

a real alternative to the other two materials. The main problem is

its very low reactivity which would possibly require a solids concen-

tration of 400–500 g l−1 for 35 mesh particles. Of course, a smaller

particle size could be used, and perhaps the material would dissolve

significantly better at higher temperature, but it is not expected that

a performance comparable with the other materials can be achieved.

Therefore, chances are slim that dolomite will ever be used as a neutral-

izer in CMA fermentations—in fact the same conclusion was already

made by Marynowski et al. [Mar85].

In the next section, the proposed process will be incorporated in the prelim-

inary design of a fermentation plant for the production of CMA from wood

hydrolyzate, and the economics of such a plant will be briefly discussed.

Then a summary of the advantages of this new process compared to other

proposed processes will be given.

5.2 Preliminary Plant Design

As already mentioned in the introduction to this chapter, CMA shall be

examined as a valuable new byproduct of the pulp and paper industry, hence

not a large stand-alone CMA plant will be discussed here, but rather a small

scale operation that could easily be added to an acetic acid wood pulping

plant. It was decided to use selectively calcined dolomite as neutralizer,

because this material offers interesting design options, and it has never been

used in a commercial process before. The design for a process using type S

dolime would be quite similar.

130

5.2.1 Process Description and Flowsheet

Conventional wood pulping processes like the kraft process utilize only the

cellulosic fraction of the wood (about 50 wt%) which is transformed into

pulp—the organics dissolved during the pulping operation, especially sugars

from hemicelluloses and lignin, are usually burned, providing just enough

energy for the evaporators that are needed to concentrate them before they

can be sent to the furnace. Furthermore, the kraft process has serious envi-

ronmental drawbacks, e.g. the emission of malodorous sulfur compounds like

hydrogen sulfide and methyl mercaptan. Hence there is a growing interest in

alternative pulping methods that allow the recovery of valuable byproducts

and are environmentally safe. Various organosolv processes which use organic

solvents instead of aqueous solutions of sodium sulfide and sodium hydroxide

have been proposed since the 1930s. One of these processes uses concentrated

acetic acid as solvent, and this makes it particularly “compatible” with the

production of CMA. A simple block flow diagram of such an operation is

given in Figure 5.5; more details can be found in [DeH71, Nim86]. Dry

hardwood consists of 40–45 wt% cellulose, 20–30 wt% hemicelluloses, and

20–30 wt% lignin, so that for each ton of pulp produced, roughly half a ton

of sugars (mainly xylose) and half a ton of lignin can be recovered as byprod-

ucts. The sugars are obtained in form of an aqueous solution which may also

contain some traces of acetic acid, furfural, levulinic acid, and minerals re-

leased from the wood. It is not expected that these impurities would cause

any difficulties in the context of CMA fermentation or have an adverse effect

on product properties (in fact, the acetic acid will react to CMA); there-

fore, it should be possible to feed this aqueous sugar solution directly to the

fermentor.

131

digestion

evaporationand drying

ligninprecipitation

?

?

?

?

-

- -

-

-

acetic acid(from recovery)

water

pulp

acetic acid,byproducts(to recovery)

sugar solution(to fermentation)

wood chips

lignin

Figure 5.5: Simple block flow diagram of the acetic acid pulping process; thesolvent recovery system which is essential to make this process economicallyviable is not shown in the diagram.

132

Another advantage of oganosolv pulping is that the plants can be smaller

than conventional kraft mills which usually have a capacity of more than

1000 tons per day pulp. Hence a rather small pulping plant was chosen as

basis for the design. The following major assumptions and design specifica-

tions were made:8

• The pulping process has a capacity of 100 t per day pulp. About 330 t

per day hardwood chips (40 wt% moisture) are required as feed, and

it is assumed that among other byproducts 50 t per day sugars can be

recovered for fermentation to CMA.

• The fermentor is operated at 60◦C and at slightly below atmospheric

pressure (in order to facilitate the exsolution of carbon dioxide). It

is assumed that no sterilization of fermentor and feeds is necessary to

prevent contamination.

• Of the sugars fed to the fermentor, 95% are utilized by the organism,

and only 5% are lost with the product stream (and form part of the

deicer product). For 1 g of sugar consumed by the organism, 0.85 g

of acetic acid are produced, i.e., the yield on a weight basis is 85%.

Therefore, 0.95× 0.85× 50 t = 40 t per day acetic acid are produced;

that corresponds to 50 t per day pure CMA product.

• As before, a concentration of 50 g l−1 CMA in the product stream

is assumed. This requires the same concentration of 50 g l−1 for the

sugars in the feed stream. Feed and product stream have a volumetric

flowrate of 1000 m3 per day (or 41.7 m3 h−1 or 11.6 l s−1), hence about

8Metric units were used consistently in the design calculations, e.g. metric tons (t)

instead of U.S. tons; the main results will be given in both unit systems.

133

1000 t water have to be evaporated per day in order to recover the

product.

• Again, a value of 5 g l−1 h−1 is used for the CMA production rate per

unit volume of the fermentor, and hence a fermentor volume of 416 m3

is required.

• Although the sugar feed stream might already contain some nutrients in

addition to the substrate itself (e.g. minerals from the wood), and others

might be supplied by the lime, it is most likely that at least additional

sources of nitrogen, sulfur, and phosphorus have to be provided in the

medium for growth of the organism. These nutrients are assumed to

be already added to the sugar feed stream.

• The fermentor effluent at pH 6 still contains 2.18 g l−1 undissoci-

ated acetic acid as calculated by the Henderson-Hasselbalch equa-

tion (2.15). This remaining acid is neutralized by adjusting the pH of

the product stream to pH 8–9 before evaporation.

• Selectively calcined dolomite is used as neutralizer in the fermentor,

and the pH of the product solution is adjusted using a small amount

of calcium hydroxide (high-calcium hydrated lime). Two cases are con-

sidered for the product composition:

1. Production of a 1:1 CMA which would most likely consist of a

physical mixture of the two individual acetate salts. Figure 5.6

shows a mass balance for this case on a basis of metric tons per day.

The unfinished product stream leaving the fermentor at pH 6 has

to contain slightly more magnesium than calcium, since only cal-

134

H2O 1, 000.00HAc 40.00

CaCO3 17.12MgO 6.90

? ?

Ca:Mg1:1

fermentor (pH 6)

Ca:Mg1:1.12

?

Ca:Mg5:1

-

H2O 1, 005.67HAc 2.18CaAc2 23.46MgAc2 23.71

CO2 6.51CaCO3 2.30MgO 0.18

Ca(OH)2 1.35

? ?

neutralizer tank (pH 8–9)

Ca:Mg1:1

?

H2O 1, 006.32CaAc2 26.34MgAc2 23.71

Figure 5.6: Mass balance for the production of a 1:1 CMA from selectivelycalcined dolomite; all figures are given in units of metric tons per day.

135

cium hydroxide is used in the neutralization tank for final pH ad-

justment. Therefore, a small amount of solids must be discharged;

that may also help to get rid of inerts contained in the lime. In

order to determine the necessary amounts of lime feed and solids

discharge, the composition of the stationary solids phase has to

be known—from the experimental results discussed above, it was

estimated that for a 1:1.12 product, the mole ratio in the solids

phase has to be at least 5:1, perhaps even higher. Based on this

assumption, the feed of selectively calcined dolomite is 24.02 t per

day, and 2.48 t per day solids have to be discharged. For the

pH adjustment, 1.35 t per day calcium hydroxide are required. Of

course, the solids can be added to the deicer product as a traction

aid and would probably enhance its properties.

2. Production of a 2:3 CMA suitable for crystallization as a double

salt. Now a much higher fraction of the solids has to be discharged

in order to maintain the high magnesium concentration in the

product. The corresponding mass balance is given in Figure 5.7;

a 4:1 mole ratio was assumed for the stationary solids phase. The

feed of selectively calcined dolomite is 32.07 t per day, and 12.50 t

per day solids have to be discharged that can be added to the

product. Again, 1.35 t per day calcium hydroxide are required for

the pH adjustment.

In both cases, 2.50 t per day sugars would also be contained in the

deicer. Therefore, the total amount of deicer material produced would

be 55.03 t per day in case 1 and 64.51 t per day in case 2 if all discharged

solids were added to the product.

136

H2O 1, 000.00HAc 40.00

CaCO3 22.87MgO 9.20

? ?

Ca:Mg1:1

fermentor (pH 6)

Ca:Mg1:1.74

?

Ca:Mg4:1

-

H2O 1, 005.67HAc 2.18CaAc2 18.18MgAc2 28.45

CO2 5.08CaCO3 11.36MgO 1.14

Ca(OH)2 1.35

? ?

neutralizer tank (pH 8–9)

Ca:Mg2:3

?

H2O 1, 006.32CaAc2 21.06MgAc2 28.45

Figure 5.7: Mass balance for the production of a 2:3 CMA from selectivelycalcined dolomite; all figures are given in units of metric tons per day.

137

wat

ersu

gar

feed

carb

ondi

oxid

e

dry

CM

Apr

oduc

t

LP

stea

m

LP

stea

m

cond

.

cond

.

14

5

sele

ctiv

ely

calc

ined

dolo

mite

calc

ium

hydr

oxid

e

Figure5.8:Processflow

diagram

forsmall-scaleCMAproductionfrom

wastesugarsandselectively

calcineddolomite.

138

A process flow diagram is given in Figure 5.8; the process flow through all

of the important pieces of equipment shall be briefly described at this point.

The fresh medium containing the sugars and additional nutrients is first

heated to 60◦C and then enters the 416 m3 fermentor which is a continuous-

flow stirred-tank reactor (CSTR). A heating coil—or, alternatively, a steam

jacket—provide a means to maintain the process temperature inside the fer-

mentor. Selectively calcined dolomite is purchased in crushed form; it is first

pulverized using a grinder and then mixed with a very small amount of wa-

ter. The resulting putty is directly fed to the fermentor by a screw conveyor

which is actuated by the pH controller. Fermentation broth containing prod-

uct, undissolved lime solids, and cells is sent to a disc nozzle type centrifuge

capable of producing an overflow essentially free of solids and cells while dis-

charging these continuously along with a variable portion of the liquid phase

in the underflow. The solids concentration in the underflow does not have to

be exceptionally high, as a matter of fact, it would probably be preferable

to maintain a high flowrate at relatively low solids concentration to avoid

settling problems. A second, smaller centrifuge is used to separate out the

fraction of lime solids which has to be discharged; essentially all cells and

the remaining lime solids are recycled back to the fermentor with the over-

flow. The overflow of the first centrifuge is sent to a 40 m3 neutralizer tank,

where a small amount of calcium hydroxide is added in order to raise the

product pH to about pH 8–9. Complete reaction of the calcium base in the

neutralizer can be assumed, and the essentially solids-free product stream is

then sent to a multi-effect evaporator for concentration of the CMA to about

40 wt%. The available total temperature difference is constrained by the de-

composition temperature of CMA which is about 160◦C. For instance, if the

139

evaporator was operated in the range between 60◦C and 140◦C, the number

of effects would be limited to five assuming a minimum approach temperature

of 16 K. The design could be further improved by using an adiabatic flash in

order to bring the temperature of the evaporator feed down to about 45◦C

(this would widen the available temperature difference for the evaporator

and at the same time already remove some of the water), and the maxi-

mum number of effects could be increased by thermal or mechanical vapor

recompression. These possibilities shall not be considered in this preliminary

design, although they could significantly reduce the cost of evaporation. A

five-effect evaporator with a steam efficiency of 4.4 is assumed, i.e., each ton

of low pressure steam at 3.614 bar, 140◦C evaporates 4.4 tons of water. The

concentrated CMA solution is then mixed with the solids discharged from

the second centrifuge and sent to a steam heated drum dryer/flaker, where

the dry deicer product is recovered in the form of coarse flakes.

At this point, the major design specifications shall be summarized, and

the results shall be given in both metric and U.S. units:

• The required amounts of raw materials are

– 50.0 t (55.1 ton) per day waste sugars as feedstock (additional

nutrients are not exactly known),

– 24.0 t (26.5 ton) per day and 32.1 t (35.4 ton) per day selectively

calcined dolomite as neutralizer for the production of 1:1 CMA

and 2:3 CMA, respectively,

– 1.35 t (1.49 ton) per day calcium hydroxide for the pH adjustment.

• The plant output of deicer product (including discharged solids and

sugars) is

140

– 55.0 t (60.6 ton) per day for 1:1 CMA,

– 64.5 t (71.1 ton) per day for 2:3 CMA.

These specifications will be used in the next section as a basis for the eco-

nomic evaluation of the process.

5.2.2 Economic Analysis and Discussion

An economic analysis shall be presented only for the CMA process, not for

the entire acetic acid pulping plant. Furthermore, only the case of producing

a 2:3 CMA shall be considered here, the other case could be examined in a

similar manner. In addition to the design specifications already discussed,

the following assumptions were made:

• The equipment is installed in an existing plant, where auxiliary facilities

are existing and adequate.

• Carbon steel is used for the evaporator and drum dryer/flaker, but all

other major equipment items have to be made from stainless steel.

• Neither the waste acetic acid contained in the sugar feed stream nor

the additional amount of CMA product formed from this acid are con-

sidered in the calculations.

• The sugars are available at their fuel value, i.e. for about $ 25.00/t

($ 22.70/ton).

• Other nutrients required by the organism are assumed to cost $ 15.00

per metric ton of deicer produced ($ 13.60 per U.S. ton of product).

141

Table 5.1: Capital requirement for a small CMA plant with 64.5 t (71.1 ton)per day output of 2:3 CMA deicer (including lime solids and sugars).

Item Cost (U.S. $)

lime storage 40,000grinder 60,000screw conveyor 20,000fermentor (416 m3) 500,000agitator (750 kW) 860,000disc-nozzle centrifuge (760 mm Ø) 150,000disc-nozzle centrifuge (400 mm Ø) 80,000neutralizer tank (40 m3) 50,000evaporator (5 effects) 2,940,000drum dryer/flaker 1,790,000product storage 80,000

total bare module capital 6,570,000

total fixed capital 7,750,000

• Low pressure steam at 3.614 bar, 140◦C is available at a cost of $ 5.00/t

($ 4.54/ton).

• Electric energy costs $ 0.06 per kWh; total power requirements for

stirrer, centrifuges, and pumps are estimated at 1,250 kW.

An estimate of the capital requirement for such a plant addition was made

based on the cost data provided by [Ulr84]; all prices were escalated to

1991 using the CE Plant Cost Index. Table 5.1 lists the prices found for the

major individual equipment items. These prices are bare module prices , i.e.,

installation is already included. Their sum has just to be multiplied by the

142

Table 5.2: Annual operating cost for the same CMA plant, assuming a90% plant service factor, i.e., an output of 21,190 t (23,360 ton) per yearof 2:3 CMA deicer.

Item Cost per Year(U.S. $)

raw materialssugar feedstock ($ 25/t) 410,600other nutrients 317,800selectively calcined dolomite, crushed ($ 50/t) 527,200high-calcium hydrated lime ($ 60/t) 26,600

utilitieselectricity ($ 0.06/kWh) 591,300low pressure steam at 3.614 bar, 140◦C ($ 5/t) 373,300

labor 500,000

fixed charges on capital 542,500

total annual operating cost 3,289,300

factor 1.18 to account for contingency and fee, yielding a total fixed capital

of $ 7,750,000.

Table 5.2 shows the annual operating costs for the production of 2:3 CMA

deicer, determined on the basis of a 90% plant service factor (21,290 t per

year output). If a 30% simple rate of return (ROR) before taxes is required

on the total fixed capital, the deicer product can be sold for $ 264/t or

$ 239/ton (at plant gate). This compares well to the cost estimates for other

fermentation processes, which range from about $ 260 to $500/ton, depending

on the feedstock and process scale. It also should be pointed out that this

low production cost could be achieved on a very small plant scale—all other

143

proposed CMA plants were much bigger; most of them were designed for a

capacity of 500–1,000 tons per day.

The new process for the production of a 2:3 CMA deicer from selectively

calcined dolomite has several advantages compared to previously proposed

processes (and even to the production of 1:1 CMA using the “same” process):

• Only inexpensive raw materials are used to make the 2:3 CMA which

is supposed to have superior deicing properties. In the conventional

Chevron process, expensive magnesia ($ 265–366/ton) has to be added

in order to achieve the 2:3 mole ratio, and together with the acetic acid

this contributes significantly to the high cost of the product (selling

price $ 657/ton).

• No waste streams are generated throughout the whole process, since

all solids that have to be discharged are included in the final product.

The resulting deicer might perform even better than “pure” CMA, and

the amount of product that can be sold is considerably higher.

• Inhibition of the organism is expected to be less severe than it would

be for the production of 1:1 CMA, because calcium is much more toxic

than magnesium (see Section 2.3.1).

• The solids discharge is roughly one third of the solids feed—this effec-

tively limits the undesired buildup of inerts in the solids phase.

Therefore, it may be concluded that the production of 2:3 CMA from se-

lectively calcined dolomite has the greatest potential and would definitely

justify further investigation.

Chapter 6

Analysis of Results

At this point, a brief summary of the most important results of this study

shall be given, and the major conclusions shall be discussed from the stand-

point of the original objectives of the research. This discussion will quite

naturally lead to the formulation of concrete recommendations for the prac-

tical application of some of the reported findings, and it will also lead to

specific suggestions for future work.

6.1 Results and Conclusions

In Chapter 1, CMA was introduced as a promising alternative deicer chemi-

cal: it is very effective as an deicer, non-corrosive, less damaging to concrete,

and environmentally safe. Furthermore, this chemical can be used as an ad-

ditive to coal combustion, acting as a catalyst and “sulfur grabber” at the

same time. However, it has not yet become a bulk chemical due to its pro-

hibitively high cost when produced from synthetic glacial acetic acid. The

deicing properties of the material depend on its chemical composition (Ca:Mg

144

145

mole ratio), on whether or not it has been crystallized as a double salt, and

also on its physical form (coarseness and form of the flakes). From the avail-

able literature it was concluded that suitable compositions for a CMA deicer

would be either a mole ratio of 1:1 which most likely results in a physical

mixture of the two acetate salts, or some ratio between 3:7 and 4:6 which

may lead to crystallization as a double salt. For the other possible applica-

tion as combustion aid, a calcium acetate (CA) might actually be preferred

to CMA, since the magnesium does not react.

The raw materials for the production of CMA—acetic acid, and various

kinds of dolomitic lime or limestone—were discussed in Chapter 2, and it

was found that acetic acid cost is the key factor determining the cost of the

final product, since CMA contains almost 80 wt% acetate. Synthetic glacial

acetic derived from petroleum or natural gas costs more than $ 500 per ton,

hence CMA has to be expensive unless a cheaper source of acetate can be

found. Compared to the acid, the cost of the possible neutralizer materials is

almost insignificant, and a choice should be made based on their properties

and suitability for the process rather than on their cost.

Three basically different processes for the manufacture of CMA were re-

viewed,

• conventional processes starting from purchased glacial or concentrated

acetic acid,

• fermentation processes employing bioconversion of glucose, corn, or

even organic waste materials into acetic acid, and

• alkaline fusion processes converting cellulose to acetate in an excess of

alkali under conditions of high temperature and pressure.

146

Fermentation was found to be an advantageous route compared to conven-

tional processes, especially if organic wastes can be used as a feedstock. As

one of several possible modifications of this route, in-fermentor production

of CMA was picked for further investigation.

Some important features of the anaerobic homoacetate fermentation with

Clostridium thermoaceticum were summarized, and optimal fermentation

conditions as well as performance limits of the organism were discussed.

The fermentation should be carried out at 60◦C and slightly above pH 6;

it is expected that—using a continuous process with cell recycling—a CMA

productivity of 5 g l−1 h−1 and a final CMA concentration of 50 g l−1 can be

achieved with currently available strains of C. thermoaceticum.

The starting point for the main part of this study was the problem of con-

trolling the composition of the CMA product which arises in this context. As

pointed out above, the chemical composition of the CMA strongly influences

its properties, and, of course, a product of uniform quality is desired. There-

fore, the specified mole ratio should be closely maintained, and this turned

out to be quite difficult due to the different reactivities and solubilities of

the various corresponding calcium and magnesium compounds, particularly

in dilute acetic acid solutions such as those present in the context of fer-

mentation. The available literature was very inconclusive regarding to this

problem; obviously, no serious effort had been made before to investigate it

further and to find a solution.

As a first step towards this goal, equilibrium models were examined both

theoretically and experimentally in order to obtain some information about

thermodynamic limitations which have to be expected for the relevant chem-

ical systems (Chapter 3). For the hydroxide system composed of HAc,

147

Ca(OH)2, and Mg(OH)2 no such limitations were found at pH < 9; only

at higher pH was Mg(OH)2 practically inert, while Ca(OH)2 could dissolve

readily up to pH > 12. Therefore, no difficulties should arise for the dissolu-

tion reaction at pH 6 in the fermentor. The observation reported by [Mar85]

that “MgO becomes essentially inert at pH > 6” was probably due to hard-

burned (sintered) MgO with low reactivity which did not hydrate readily at

pH > 6 to form Mg(OH)2, thus greatly inhibiting further dissolution. Three

possible solutions to this problem were found, namely

• dissolving MgO at pH < 6,

• using fully hydrated type S dolime Ca(OH)2 ·Mg(OH)2, or

• using selectively calcined dolomite CaCO3 ·MgO which contains light-

burned MgO with high reactivity.

In the carbonate system made from HAc, CaCO3, and MgCO3 there was no

profound difference between the behaviour of the calcium and the magnesium

compounds; both carbonates dissolved up to about pH 8. Experiments were

also made with dolomite (which showed a significantly different behaviour,

e.g. much lower reactivity, so that no true equilibrium was established within

24 h) and with a CO2-bubbled hydroxide system (which was essentially trans-

formed into a carbonate system within a few hours). From the latter result

it was concluded that CO2 bubbling is likely to have a strong influence on

product composition in a CMA fermentation.

The kinetics of the various dissolution reactions relevant for CMA pro-

duction were reviewed in Chapter 4. Rate data and models were collected

from the available literature for carbonates (calcite, magnesite, dolomite)

and oxide minerals (CaO, MgO). Included was also the discussion of several

148

engineering publications about the application of limestone for acid neutral-

ization (acidic waste water treatment). Estimates for the dissolution rates of

all minerals in the interesting pH range (pH 5–7) could be made as a result

of this literature search; the rate estimates were summarized in Table 4.3.

However, large uncertainties were expected in these results, since all of the

data and model equations had been derived for other acids than acetic acid

(mostly for strong mineral acids), and some of the sources were judged to be

not very reliable. Nevertheless, a dynamic model for a hypothetic continuous

CMA fermentation was developed, but the original plan to use this model

for simulations in order to examine process dynamics and control was aban-

doned in favour of a more practical approach. The continuous reactor was

modeled as an open system with lumped parameters; four phases were dis-

tinguished (liquid phase, solids phase, cells, and gas phase). All homogenous

chemical reactions in the liquid phase were assumed to be at equilibrium and

hence could be described by a system of algebraic equations. Acetic acid

production, substrate consumption, and solids dissolution were described by

ordinary differential equations. Together these equations formed a system of

semi-explicit nonlinear differential-algebraic equations (DAEs).

In Chapter 5, a simple solution to the mole ratio problem was presented—

it was shown that a stationary solids phase allows producing a stoichiometric

solution of CMA, and, more generally, that it is possible to achieve a wide

range of other product compositions if desired. Feasibility was confirmed by

an experimental continuous dissolution process, and the performance of three

different neutralizer materials was compared: type S dolime and selectively

calcined dolomite were both found to be suitable choices for future applica-

tions; however, the use of uncalcined dolomite is not recommended due to

149

its very low reactivity. Selectively calcined dolomite provides the option of

producing high-magnesium CMA without the addition of expensive magne-

sia; most interestingly, a 2:3 CMA can be made which might be suitable for

crystallization as a double salt. It has been claimed that this double salt has

superior deicing properties [Tod90]. The preliminary design of a small-scale

process for the production of CMA from wood hydrolyzate (waste sugars)

and selectively calcined dolomite was presented, and an economic analysis

showed that this new process compares well to previously proposed ones. It

was concluded that particularly the production of 2:3 CMA from selectively

calcined dolomite has much potential, and that further investigation of this

specific route would definitely be justified.

6.2 Future Work and Recommendations

Although the concept of continuous steady-state dissolution developed in

Chapter 5 seems to be promising and the experimental results were quite

encouraging, much more work has to be done before a pilot plant can be built.

All experiments were done without the organism so far, and not even the

physical and chemical process conditions expected in a “real” fermentation

were maintained. Further research is required in the following areas:

1. The experimental results without organism should be confirmed using

a more sophisticated model system (e.g. the cross flow filter should

be replaced by a continuous centrifuge). Definitely, data should be

obtained at process conditions, i.e., at 60◦C, pH 6, and in the presence

of substrate. It would also be interesting to study the effects of different

pH values and temperatures on the process behaviour. Other problems

150

which could be addressed include the exsolution of carbon dioxide, the

accumulation of inerts in the solids phase, possible interactions between

ions and substrate, and the causes for the observed acceleration of

magnesium oxide dissolution.

2. The organism should be included in the experiments, and the validity of

the “performance assumptions” (attainable productivity and product

concentration) should be tested. Medium composition, cell density,

and several other fermentation conditions have to be optimized—for

instance, it has to be ensured that not too much oxygen is present in

the fermentor, since this would have a toxic effect on the organism.

3. CMA produced under realistic conditions should be recovered and its

deicing properties should be tested—since the material contains dis-

charged solids as well as substrate, it is not likely to have the same

properties as pure CMA.

If the lab scale results with the organism are still promising, the process

could be scaled up to pilot plant level. Chances are slim that an acetic acid

pulping plant will be built at this time because of high overcapacities in the

pulp and paper industry. However, should the need for a new plant arise,

this would be a very interesting alternative to a conventional kraft plant, and

CMA production could be tested at the pilot scale. Here in Wisconsin, an

almost ideal location for such a plant would be the Green Bay area, since

it has a long tradition in the manufacture of pulp and paper, large natural

supplies of dolomite, and lots of ice and snow to melt during the winter.

Appendix A

Original ICP Data

A.1 Equilibrium Experiments (Chapter 3)

The solution samples obtained from the equilibrium experiments described in

sections 3.2 and 3.3 were submitted to the University of Wisconsin-Madison

Soil & Plant Analysis Laboratory for the analysis of total soluble calcium

and magnesium concentrations by inductively coupled plasma emission spec-

troscopy (ICP). The original results as given in Table A.1 are on the ppm

scale (mass fractions for Ca and Mg). The mass fractions of H2O and Ac−

could be determined from the known initial composition of the system, as-

suming that the filtered solution consists only of the four components H2O,

Ac−, Ca2+, and Mg2+. From these mass fractions ξi the corresponding mole

fractions xi had to be calculated in order to determine the molar concentra-

tions Ci. This was done using the formula

xi =M

Mi

ξi (A.1)

151

152

Table A.1: Original results of the ICP analyses on six filtered solution samplesfrom equilibrium experiments; source: Soil & Plant Analysis Laboratory,University of Wisconsin-Madison.

Sample Mass Fraction (ppm)Ca Mg

blank deionized water < 0.043 < 0.104

Ca(OH)2 – Mg(OH)2 – HAc (Recipe 1) 11075 1.790

type S dolime – HAc 9928 0.940

CaCO3 – MgCO3 – HAc (Recipe 3) 139.5 5144

Ca(OH)2 – Mg(OH)2 – CO2 – HAc 179.7 6504

dolomitic limestone – HAc 4683 2000

where Mi is the molecular weight of component i and

M =1

∑

j M−1j ξj

(A.2)

is the molecular weight of the mixture. With the assumption that 1 l solution

contains 55.6 mol H2O, the molar concentrations in Tables 3.2 and 3.4 were

obtained.

153

A.2 CMA Production (Section 5.1.2)

The CMA solution samples obtained from the continuous dissolution exper-

iments described in section 5.1.2 were again submitted to the University of

Wisconsin-Madison Soil & Plant Analysis Laboratory for the analysis of to-

tal soluble calcium and magnesium concentrations by inductively coupled

plasma emission spectroscopy (ICP). The original results (mass fractions of

calcium and magnesium on the ppm scale) are given in Tables A.2 and A.3

for the CMA made from type S dolime and selectively calcined dolomite, re-

spectively. From these mass fractions, the Ca:Mg mole ratio could be easily

determined using the formula

xCa

xMg

=MMg

MCa

ξCa

ξMg

, (A.3)

where xi are the mole fractions, ξi the mass fractions, and Mi the molecular

weights. Table A.4 shows the detected ranges of concentration (minimum

and maximum) for several other elements that were present as impurities in

the product solution.

154

Table A.2: Original results of the ICP analyses on CMA solution samplesmade from type S dolime; source: Soil & Plant Analysis Laboratory, Univer-sity of Wisconsin-Madison.

Time Mass Fractions Ca:Mg Mole Ratio(h) (ppm)

1 758.1 225.6 2.042 1278 505.9 1.533 1600 754.0 1.294 2280 1033 1.345 2526 1246 1.236 2668 1502 1.087 2796 1628 1.048 3929 1841 1.299 4154 1900 1.3211 4566 2160 1.2814 4843 2313 1.2719 5707 2753 1.2624 6377 2891 1.3429 6057 3034 1.2134 6336 3102 1.2439 6153 3091 1.2144 6524 3129 1.2652 6247 3127 1.21

155

Table A.3: Original results of the ICP analyses on CMA solution samplesmade from selectively calcined dolomite; source: Soil & Plant Analysis Lab-oratory, University of Wisconsin-Madison.

Time Mass Fractions Ca:Mg Mole Ratio(h) (ppm)

1 474.9 388.7 0.742 785.2 748.2 0.643 1004 1164 0.524 1177 1512 0.475 1426 1748 0.496 1443 2035 0.437 1505 2461 0.378 1484 2686 0.339 1535 3066 0.3010 1525 3189 0.2911 1623 3473 0.2812 1577 3328 0.2914 2141 4207 0.3117 3136 3848 0.4918 3525 3641 0.5919 4083 3632 0.6820 4575 3229 0.8622 5083 2909 1.0524 6112 2746 1.3530 5091 3579 0.8636 2946 4727 0.3842 2553 5116 0.3046 2326 4950 0.2850 4231 3542 0.72

156

Table A.4: Ranges of concentration detected for other elements that werepresent as impurities in the CMA solution; source: Soil & Plant AnalysisLaboratory, University of Wisconsin-Madison.

Element Concentration Range (ppm)

type S dolime selectivelycalc. dolomite

P < 0.217 < 0.217–0.316

K < 0.621 < 0.621–3.852

S 7.591–48.80 4.665–31.42

Zn < 0.010–0.089 < 0.010–0.086

B 0.073–0.269 0.098–0.373

Mn 0.076–0.265 0.051–0.895

Fe < 0.011–0.543 < 0.011–0.920

Cu < 0.025–0.120 < 0.025–0.327

Al < 0.352–4.937 1.096–8.680

Na < 0.611–1.601 1.977–5.832

Appendix B

Lime and Limestone Analyses

B.1 Type S Dolomitic Hydrated Lime

The type S dolime used in some of the experiments in sections 3.2 and 5.1.2

was supplied by The Western Lime & Cement Co., West Bend, Wisconsin.

The company also provided a data sheet with the results of some analyses.

In addition to particle size distribution and chemical composition (as given

in Tables B.1 and B.2), the neutralizing value of the lime was reported to be

165% of the calcium carbonate equivalent. Using the formula

xCa(OH)2

xMg(OH)2

=MMg(OH)2

MCa(OH)2

ξCa(OH)2

ξMg(OH)2

, (B.1)

where xi are the mole fractions, ξi the mass fractions, and Mi the molec-

ular weights, the mole ratio of Ca:Mg can easily be calculated—the value

found from the given data is 1.04:1, i.e., the material has almost the desired

composition.

157

158

Table B.1: Sieve analysis of type S dolime; source: The Western Lime &Cement Co.

Sieve Size Passing Specification

30 mesh 100.0% 100.0%

100 mesh 99.0% 95.0% min

200 mesh 96.0% 90.0% min

Table B.2: Chemical analysis of type S dolime; source: The Western Lime &Cement Co.

Compound Mass Fraction (wt%)

calcium as CaO 42.40

magnesium as MgO 28.68

combined water 25.18

silica and insolubles 1.01

loss on ignition (CO2, SO3) 0.77

free water 0.50

alumina as Al2O3 0.42

iron as Fe2O3 0.25

calcium hydroxide Ca(OH)2 54.7

magnesium hydroxide Mg(OH)2 41.6

159

B.2 Dolomitic Limestone

The dolomitic limestone used in experiments in sections 3.3 and 5.1.2 was

also supplied by The Western Lime & Cement Co., West Bend, Wisconsin.

The stone had a slight yellow tint and seemed to be of sedimentary origin; it

was already finely crushed. A limestone analysis performed by the University

of Wisconsin-Madison Soil & Plant Analysis Laboratory confirmed that this

material was essentially pure dolomite. The mass fractions were found to be

22.3% for calcium and 13.1% for magnesium; the theoretical values for pure

dolomite are 21.7% and 13.2%, respectively. The neutralizing value of the

stone was reported to be 103.5% of the calcium carbonate equivalent. Again,

the mole ratio of Ca:Mg can be determined from the given mass fractions

using the formulaxCa

xMg

=MMg

MCa

ξCa

ξMg

, (B.2)

and the result obtained was 1.03:1 (essentially the same as for the type S

dolime).

Appendix C

Equipment List (Section 5.1.2)

The following equipment was used for the continuous dissolution experiment

described in section 5.1.2; brand names are given for identification purposes

only:

• glass/steel fermentor 3.7 dm3 (Bioengineering KLF 2000)

• fermentation control system (Valley Instrument Co.), consisting of

– support unit (Mod. 520MC)

– pH controller (Mod. 506M)

– temperature controller (Mod. 503M)

– speed controller (Mod. 508M)

– foam/pump controller (Mod. 517M)

• pH glass electrode (Ingold)

• heating element 800 W (Bioengineering 30355)

160

161

• temperature sensor (Bioengineering 30266)

• cross flow filter capsule with 1.2 µm pores, 900 cm2 area (Gelman

Acroflux)

• variable speed peristaltic pumps (Cole-Parmer)

– slow pump (Mod. 7520-35) with two identical heads (Mod. 7013-

21)

– fast pump (Mod. 7520-25) with head (Mod. 7016-21)

• flexible tubing (Masterflex 6411-13 and 6402-16)

• automatic fraction collector (Gilson FC 203)

• slurry stirrer (Glas-Col S25)

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