2

Reaction Path Models• Used to model open systems• Variable composition; relative time scale (reaction

progress variable ξ)• Types:

– Titration or mixing (most common) (B Fig. 2.3)– Polythermal (B Fig. 2.2)– Buffering or sliding fugacity (B Fig. 2.4)– Flow-through: tracks evolution of fluid

composition as it flows through rock. Reaction products left behind, isolated from further reaction (like fractional crystallization).

– Flush: tracks chemical evolution of system through which fluid migrates; unreacted fluid displaces reacted fluid (B Fig. 2.7, ZA Fig. 2.5).

– Kinetic reaction path model

Reaction Path Models

• Describe irreversible reactions or processes using a series of partial equilibrium states.

• Thought of as a very slow titration.

• Results do not always correspond exactly to reality because we are using thermodynamics to describe a series of disequilibrium states. But still provide insights into the processes involved.

Alkalinity titration (Z&A 8.2)# React script, saved Sun Feb 23 2003 by Dabieshantitle = "Titrate Bear Creek sample MW-36 with HCl"data = "E:\Program Files\Gwb\Gtdata\thermo.com.v8.r6+.dat" verifytemperature = 151 kg free H2Ototal mg/l Ca++ = 158total mg/l Fe++ = .01total mg/l Mg++ = 21total mg/l Mn++ = .11total mg/l K+ = 17balance on Na+total mg/l Na+ = 61total mg/l SO4-- = 425total mg/l Cl- = 25total mg/l Al+++ = .01total mg/l SiO2(aq) = 5.6pH = 7.4total molality HCO3- = .00305react .004 mol of HCl(aq)

Dabieshan Sun Feb 23 2003

0 .001 .002 .003 .004 .0050

1

2

3

4

5

6

7

8

HCl(aq) reacted (moles)

pH

Titrate sample MW–36 with HCl

Compare w/ Fig. 8.2 calculated using Phreeqc (script in Table 8.1)

Acidity of Acid Mine Water (Z&A 8.3)# React scripttitle = "Titrate Bear Creek sample TS-3 with Calcite"data = “C:\Program Files\Gwb\Gtdata\

thermo.com.v8.r6+.dat" verifytemperature = 161 kg free H2Ototal mg/l Ca++ = 310total mg/l Fe++ = 1950total mg/l Mg++ = 1000total mg/l Mn++ = 66.3total mg/l K+ = 60balance on Na+total mg/l Na+ = 89total mg/l SO4-- = 16500total mg/l Cl- = 550total mg/l Al+++ = 1020total mg/l SiO2(aq) = 40.5pH = 3.8total mg/l HCO3- = 5react .25 mol of Calcitesuppress ALLunsuppress Fe(OH)3 Gibbsite Gypsum

• For acidic water the carbonate acidity is a small part of total acidity.

• Titrate solution with calcite to measure the“operational acidity”, the amount of CaCO3 required to saturate the solution.

Dabieshan Sun Feb 23 2003

0 .05 .1 .15 .2 .252.5

3

3.5

4

4.5

5

5.5

6

Calcite reacted (moles)

pH

Titration of calcite into TS–3 water

Compare with Fig. 4 Zhu & Anderson.

Dabieshan Sun Feb 23 2003

0 .05 .1 .15 .2 .25

.02

.04

.06

.08

.1

.12

.14

Calcite reacted (moles)

Min

era

ls (

mo

lal)

Titrate Bear Creek sample TS–3 with Calcite

Gibbsite

Gypsum

All minerals suppressed except gypsum, gibbsite & Fe(OH)3. Compare with Fig. 8.4 Zhu & Anderson.

Dabieshan Sun Feb 23 2003

0 .05 .1 .15 .2 .25

.02

.04

.06

.08

.1

.12

.14

Calcite reacted (moles)

Min

era

ls (

mo

lal)

Titrate Bear Creek sample TS–3 with Calcite

Gypsum

DiasporeSiderite

Dolomite-ord

Calcite

Weathering of K-feldspar• If water/rock ratio high, all K-feldspar

converted to kaolinite, composition of weathered rock determined by its environment, i.e., the composition of water.

• If water/rock ratio low, water dissolves soluble primary minerals (K-spar) & precipitates insoluble secondary minerals (kaolinite), concentrations of dissolved K+ and H4SiO4 ↑:

2 KAlSi3O8 + 9 H2O + 2 H+ Al⇌ 2Si2O5(OH)4 + 2 K+ + 4 H4SiO4

log Keq = 4 log [H4SiO4] + 2 log [K+] – 2 log [H+]

log Keq = 4 log [H4SiO4] + 2 log [K+]/[H+]

log [K+]/[H+] = ½ log Keq – 2 log [H4SiO4]

plot y = [K+]/[H+] and x = log [H4SiO4], get straight line

with m = -2 and b = ½ log Keq .

2

2444

][

][][

H

KSiOHKeq

-5 -4.5 -4 -3.5 -3 -2.5 -2

-4

-2

0

2

4

6

8

10

log a SiO2(aq)

log

a K

+/H

+

Gibbsite

Kaolinite

Maximum MicroclineMuscovite

Pyrophyllite

25°C

Dabieshan Thu Mar 14 2002

Dia

gram

Kao

linite

, T

=

25 C

, P

=

1.0

13 b

ars,

a [

mai

n]

= 1

, a

[H2O

] =

1;

Sup

pres

sed:

Clin

optil

-K,

Mor

deni

te-K

React Script: K-feldspar weathering

data = "e:\program files\gwb\gtdata\thermo.dat" verifywork_dir = E:\Users\Ayers\GEO320\GWB temperature = 251 kg free H2Ototal mg/kg Na+ = 5total mg/kg K+ = 1total mg/kg Ca++ = 15total mg/kg Mg++ = 3total ug/kg Al+++ = 1total mg/kg SiO2(aq) = 3total mg/kg Cl- = 30total mg/kg SO4-- = 8total mg/kg HCO3- = 50pH = 5react 2 mmol of K-feldsparsuppress Clinoptil-K Mordenite-K

-5 -4.5 -4 -3.5 -3 -2.5 -2

-4

-2

0

2

4

6

8

10

log a SiO2(aq)

log

a K

+/H

+

� � ���������������������������������������������������������������������������������������������������

Gibbsite

K-feldspar

Kaolinite

Muscovite

Pyrophyllite

25°C

Dabieshan Thu Mar 14 2002

Dia

gram

K-f

elds

par,

T

= 2

5 C

, P

=

1.0

13 b

ars,

a [

mai

n]

= 1

, a

[H2O

] =

1;

Sup

pres

sed:

Clin

optil

-K,

Mor

deni

te-K

, M

axim

um M

icro

clin

e

Dabieshan Thu Mar 14 2002

0 .5 1 1.5 20

.5

1

1.5

2

2.5

K-feldspar reacted (mmoles)

Min

eral

s (m

mol

es)

Kaolinite

Quartz

Muscovite

Phengite

K-feldspar

Extracting the Overall Reaction

• When mmoles of secondary minerals produced are plotted as a function of mmoles of primary mineral consumed, the slopes of the lines give the reaction coefficient for each species and mineral in the overall reaction (only if both axes use linear scales and consistent units).

• Three reaction segments: 1) precipitation of kaolinite, 2) transformation of kaolinite to muscovite, 3) further formation of muscovite once kaolinite exhausted.

Segment 1 Segment 2 Segment 3

CO2(aq) -1 0 -.67

HCO3- +1 0 +.67

K+ +1 0 +.67

H2O -1.5 +1 -.67

Quartz +2 +2 +2

Kaolinite +.5 -1

Muscovite +1 .33

1) KAlSi3O8 + 3/2 H2O + CO2(aq) 2 SiO⇌ 2 + ½ Al2Si2O5(OH)4 + HCO3- + K+

2) KAlSi3O8 + Al2Si2O5(OH)4 2 SiO⇌ 2 + KAl3Si3O10(OH)2 + H2O

3) KAlSi3O8 + 2/3 CO2(aq) + 2/3 H2O 2 SiO⇌ 2 + 1/3 KAl3Si3O10(OH)2 + 2/3 HCO3

- + 2/3 K+

K-feldspar weathering script in Phreeqci

SOLUTION_SPREAD -redox O(-2)/O(0) -units mg/kgw Na K Ca Mg Al Si Cl S(6) pH pe C(4) ug/kgw charge CO2(g) -2 O2(g) -0.7 5 0.0001 1 3 1 0.0001 30 8 5 10 50INCREMENTAL_REACTIONS TrueEQUILIBRIUM_PHASES 1 Gibbsite 0 0 Kaolinite 0 0 Muscovite 0 0 Pyrophyllite 0 0 SiO2(am) 0 0 K-Feldspar 0 0REACTION 1 K-feldspar 1 0.2 millimoles in 100 stepsSELECTED_OUTPUT -file Kfeldspar.out -reset false -step true -ph true -pe true -reaction true -totals Si -activities H+ K+ SiO2 -equilibrium_phases Kaolinite K-feldspar Muscovite Gibbsite Pyrophyllite SiO2(am) -saturation_indices Gibbsite Kaolinite K-Feldspar Muscovite Pyrophyllite SiO2(am)

Figure 6.--Phase diagram for the dissolution of K-feldspar (microcline) in pure water at 25oC showing stable phase-boundary intersections (example 6A) and reaction paths across stability fields (example 6B). Diagram was constructed using thermodynamic data for gibbsite, kaolinite, K-mica (muscovite), and microcline from Robie and others (1978).

Seawater Evaporation• # React script, saved Tue Feb 25 2003 by Dabieshan• data = "e:\program files\gwb\gtdata\thermo_hmw.dat" verify• temperature = 25• decouple ALL• swap CO2(g) for H+• 1 kg free H2O• fugacity CO2(g) = .000316227766• total mg/kg Na+ = 10760• total mg/kg Mg++ = 1290• total mg/kg Ca++ = 411• total mg/kg K+ = 399• balance on Cl-• total mg/kg Cl- = 19350• total mg/kg SO4-- = 2710• total mg/kg HCO3- = 142• TDS = 35000• react -996 gram of H2O• flow-through• delxi = .001 linear• dxplot = 0

Flow-through model described on pg. 118 of GWB Users Guide. Equivalent to fractional crystallization – solids separated from liquid, traces chemical evolution of liquid.

Dabieshan Tue Feb 25 2003

3 2.5 2 1.5 1 .5 0

–4

–3

–2

–1

0

1

Mass H2O (log grams)

Min

era

ls (

log

cm

3 )

Dolomite

Gypsum

Magnesite

Anhydrite

Halite

Glauberite

Polyhalite

Bloedite

Epsomite

Kainite

KieseriteCarnallite

Bischofite

Calcite precipitation in hot water heater

• # React script, saved Wed Mar 03 2004 by ayersj• data = "c:\program files\gwb\gtdata\thermo.dat" verify• temperature initial = 25, final = 50• swap Calcite for Ca++• swap CO2(g) for HCO3-• 1 kg free H2O• free gram Calcite = 1• balance on H+• fugacity CO2(g) = .000316227766• fix fugacity of CO2(g)

ayersj Wed Mar 03 2004

25 30 35 40 45 500

2

4

6

8

10

12

14

Temperature (C)

Ca

lcite

(d

elta

mg

/kg

)

ayersj Wed Mar 03 2004

25 30 35 40 45 50

8.221

8.222

8.223

8.224

8.225

8.226

8.227

8.228

8.229

8.23

8.231

Temperature (C)

pH

Ca++ + 2HCO3- = CaCO3 + H2CO3

Heat calcite-saturated water w/ 0.1 mmolal HCl

• First run previous script at T = 25C, then “pickup” fluid• # React script, saved Wed Mar 03 2004 by ayersj• data = "c:\program files\gwb\gtdata\thermo.dat" verify• temperature initial = 25, final = 50• swap CO2(g) for HCO3-• 1 kg free H2O• total mol Ca++ = .00044154404• fugacity CO2(g) = .000316227766• balance on H+• total mmolal H+ = .1• total mmolal Cl- = .1

Effect of 0.1 mmolal HCl inhibitor Saturation Indices

ayersj Wed Mar 03 2004

25 30 35 40 45 500

2

4

6

8

10

12

14

Temperature (C)

Ca

lcite

(d

elta

mg

/kg)

ayersj Wed Mar 03 2004

25 30 35 40 45 50

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

Temperature (C)

Sa

tura

tion

, Min

. w/ H

CO

3- (Q

/K)

Aragonite

Calcite

Monohydrocalcite