chang yeongsiang thesis flash carbonization

1 Optimization of the

Flash Carbonization Process

A Thesis Presented t o the Faculty

of the Engineering College of Ohio University

In Par t ia l Fulf illsnent

of the Requirement fo r the Degree

Master of Science

BY

Yeong-Siarg Chang, - - 1

August 1984

ACKNOWLEDGEMENTS

I would especially l ike t o thank Dr . Wen-Jia Chen, my

thesis advisor, who suggested this topic and gave generously

of his tirne and guidance during the course of t h i s study.

I am grateful t o D r . Robert L. Savage f o r h i s

constructive cri t icisms and useful suggestions t o t h i s

thesis . Ny thanks a re a l so due D r . J. R. Col l ier and Dr . N.

Dinos f o r t h e i r help during my stay i n Ohio University.

My wife, Huoy-Jen, has offered me her understanding and

support over the duration of this task. I am more than

grateful fo r that .

Finally, I wish t o express a deep grati tude t o my

parents f o r t h e i r encouragement and support which make t h i s

studjr possible. This work is dedicated t o them.

P e e

TABLE OF CONTENTS ....................................... v

LIST OF FIGURES ......................................... v i

LIST OF TABLES .......................................... v i i

1.0 INTRODUCTION ........................................ 01 1.1 Coal Gasif'ication and the Flash Carbonization

Process ......................................... 01

.... 1.2 Econorni cs of the Flash Carbonization Process 05

........................... 1.3 Purpose of the Thesis 09

2.0 L I r n T J R E &'VIEW ................................... 10

2.1 Gasification Reaction ........................... 10

2.2 Equilibrium Computation ......................... 12

2.3 Overview of Optirmun Seeking Methods ............. 15

................ 2.4 Overview of Experimental Designs 18

.................................. 3.0 OBJECTIVE FUNCTION 26

3.1 Assumptions ..................................... 26

3.2 Data and Parameters ............................. 28

................ 3.3 Flnal Form of Objective Function 29

4.0 OUTLINE OF OPTIMIZATION STKAmY .................... 32

.......... 4 .1 A Sample Calculation of Response Value 32

..... 4.2 The Considerations of Optimization Strategy 43

4.3 F i r s t Order Design and Direction of Steepest

v

.......................................... Ascent 44

4.4 Second Order Design ............................. 46 ............................. 5.0 REsULTS AND DISCUSSIONS 48

6.0 CONCLUSIONS .......................................... 64 APPENDIX I ........................................ 65 REFFWSNCES .............................................. 66

LIST OF FIGURES

Figure 3-1 The Block Diagram of a Single-stage

Gasi f ier ..................................... 30

v i i

LIST OF TABLES

Table 2-1 Heat of Reactions(HR : Kcal) and Equilibrium

Constants(KP) of Selected Reactions ........... 23

Table 2-2 Yatels Algorithm .............................. 25

Table 3-1-A Unit Cost of Feedstock and U t i l i t i e s ........ 31

Table 3-1-B Unit Varket Price of Products ............... 31

.......... Table 4-1 Composition of Coal(Ohio Clarion 4A) 37

Table 4-2 Calculation of Heat of Formation of Coal ...... 38

Table 4-3 The Equilibrium Composition and Moles of Fach

Component ..................................... 39

Table 4-4 Calculation of Heat of Reaction a t 1200K ...... 40

Table 4-5 Total Cost in the Sample Calculation .......... 41

........ Table 4-6 Total Credit i n the Sample Calculation 42

Table 5-1 Search on Stage-1 ............................. 53




............................. Table 5-5 Search on Stage-5 6 1

............................. Table 5-6 Search on Stage-6 63

1.1 Coal Gasification

Zxtensive programs have been undertaken t o develop

processes f o r the comnercial production of synthetic fuels

from coal, o i l shale, t a r sands, or biomass.(l) The

objective is t o replace exhausted or costly supplies of

natural gas and petroleum-based fuels. Coal gasification is

a f lexible method f o r the production of synthetic fuels.

Products can be varied t o include low-, medium-, high-Btu

gas, and raw materials f o r l iquid fuels , such as gasoline,

methanol, and petrochemlcal products. It is also less

costly f o r chemical m u f a c t u r e , and more operable on lower

quali ty coals than coal liquefaction.

Many gasif icat ion processes have been developed with

differences i n mdes of operation and characteris t i c s of

the products produced. Each gas i f i e r has been described f o r

a specif ic application and the type of coal avaiable as

feedstock. The three m i n character is t ics of gas i f ie rs

sur,mrized by Probstein and Hicks(2), are the method of

supplying the heat, the gasifying medium and amount, and the

reactor type. Once they a re specified, the other dependent

characterist ics such as the s t a t e of the so l id residue (dry

o r slagging), the properties of the product gas, and the

gasification temperature w i l l be fixed. There a r e three

t y p e s of r e a c t o r s : t h e moving bed , t h e f l u i d i z e d bed, and

t h e e n t r a i n e d f low r z a c t o r . The r e a c t o r t y p e h e a v i l y

domina tes t h e t e m p e r a t u r e d i s t r i b u t i o n , t h e r e f o r e , t h o s e

dependent c h a r a c t e r i s t i c s a r e a l l i n f l u e n c e d . There a r e

a l s o two ne thods of s u p p l y i n g t h e h e a t : d i r e c t and

i n d i r e c t . The d i r e c t method i s t o supp ly oxygen o r a i r ,

where h e a t i s g e n e r a t e d from t h e combust ion r e a c t i o n s of

c o a l . The i n d i r e c t method a p p l i e s an e x t e r n a l h e a t i n g

s o u r c e , s team o r e l e c t r i c i t y , t o supp ly h e a t f o r

g a s i f i c a t i o n r e a c t i o n s . The p o s s i b l e g a s i f y i n g media f o r

g a s i f i c a t i o n a r e oxygen, a i r , hydrogen, s team. Oxygen and

a i r a r e t h e s o u r c e s of oxygen i n t h e r e a c t i o n s f o r t h e

p r o d u c t i o n of ca rbon monoxide. Hydrogen g a s and s t eam a r e

t h e s o u r c e of hydrogen f o r t h e p r o d u c t i o n of methane and

hydrogen r e s p e c t i v e l y . I t i s . a l s o obv ious t h a t t h e anount

and t h e k i n d o f h e a t i n g medium o r g a s i f y i n g medium i n f l u e n c e

t h e t h r e e dependent c h a r a c t e r i s t i c s . I n t h i s s e c t i o n , a

b r i e f d e s c r i p t i o n of t h e c h a r a c t e r i s t i c s of t h e major

s i n g l e - r e a c t o r , d i r e c t - h e a t g a s i f i e r s i s g i v e n .

The d ry -a sh and s l a g g i n g - a s h L u r g i p r o c e s s e s ( 3 , 4 ) a r e

moving bed p r o c e s s e s and p r i m a r i l y t o be c o n s i d e r e d f o r t h e

p r o d u c t i o n of S y n t h e t i c N a t u r a l Gas(SNG). Moving bed

g a s i f i e r s o p e r a t e w i t h c o u n t e r c u r r e n t f l ow. The c o a l i s

i n t r o d u c e d downward t h r o u g h t h e upward f l o w i n g g a s e s . I t i s

d r i e d f i r s t , t h e n d e v o l a t i l i z e d , and t h e n g a s i f i e d a t t h e

lower s e c t i o n . The bot tom s e c t i o n i s t h e combust ion zone

where t h e r e n a i n i n g c o a l i s b u r n t t o s u p p l y h e a t f o r t h e

3

gasification zone. The s l a ~ i n g - a s h process is bet ter than

the dry-ash process both in the tt- roughp put and i n thennal

efficiency because of higher temperature operation. By

reducing the steam injection requirements, the capi tal

investment is reduced, and the process t h e m 1 efficiency is

increased. The pressurized gas FTier favors high methane

cantent yield and leads to a significant overall process

economy because, i n most cases, the gas w i l l be processed

further at elevated pressure. The disadvantages is that it

requires a sized noncaking coal which increases the cost of

coal. The reactor with a slowly downward moving bed is

basically a low-throughput device that requires a large

number of gasif iers occupying a large area. However, the

Lurgi dry ash process is the only gasification process fo r

which the technology has been commercialized. 'The Sasol

projects have applied this process to produce Synthetic

Nqtural Gas.

The Texaco and Shell-Koppers ( 5,6,7) processes

mnufacture e i ther low- or medium-Btu synthesis gas i n a

manner tha t is closely similiar t o the production of

synthesis gas from petroleum fue l residues. The 'Texaco

water s lurry injection system produces a high hydrogen t o

carbon monoxide ra t io product gas and solves the problem of

feeding coal into a pressurized gasif ier , but introducing a

t h e r m l inefficiency i n operation. The potential for the

application of th i s process is cons iderable . Tennessee

%stman Co. has applied it t o the production of acetic

4

anhydride from co-al(8) . The Shell-Kogpers process,

developed from Kopper-Totzek process, uses the ,Ininimum

mount of s t e m f o r high thermal efficiency and produces a

low hydrogen t o carbon monoxide ra t io . Both gas i f ie r s are

entrained bed processes i n high temperature operation,

therefore, both process uni ts require a high-temperature

heat exchanger which represents a costly technical problem.

A waste heat boi ler m y give about half of the available

energy i n the fonn of stean(Mangold, 1982, p.122), which can

be u t i l i zed i n a refinery o r chemical plant, but m y not be

used i n other applications.

A l l the gasi f icat ion processes discussed so f a r aim t o

gasify completely the coal fed in to the gasif'ier. Though it

is possible t o convert coal t o t a l l y t o gas frorn a

thermodynamic point of view, it is extremely d i f f i c u l t o r

expensive t o do it from a kinet ics consideration. In

practice, it is impossible t o convert the l a s t f i v e t o ten

percent of coal t o gas even under the rnost.favorable kinet ic

condition. Therefore, it i s preferable t o use a pa r t i a l

coal gasi f icat ion process, i f both the gas and the sol id

products can be ut i l ized.

Savage and Chen(9) a r e act ively developing the Flash

Carbonization process a t Ohio University f o r the concurrent

production of synthesis gas and a low sulf ur, low vo la t i l e

char which is sui table f o r indus t r ia l and povJer plant use

along the Ohio River.

Using an entrained bed reactor, oxygen and steam, along

5

with finely-&rounded coal(-40+100, -100+200, ?ksh No.), a re

introduced from the top of the reactor. A char with forty

t o eighty percent of the original carbon, together with a

systhesis gas is produced a t the botton of the reactor.

Coal, oxygen, and steam are fed a t rates of 2.27Kg per hour,

5000c.c per ninute, and 2c. c. per minute respectively.

Atmospheric pressure and temperatures ranging from 1 1 8 0 ~ t o

1450K were chosen fo r the operating conditions in a ser ies

of experiments. Also, the residence times were varied.

In general, being an entrained bed system, the process

has several advantages over the other gasification

processes ( l o ) , m i n l y ;

( a ) the a b i l i t y t o handle caking coal and low grade

coal, and

(b) the product gas is f r ee of t a r s and Phenols.

More importantly, the moderate temperature (1100K-1500K)

employed avoids the aisadvantages of a high temperature - ( >1500K) process such as ( l o ) :

( a ) the large mounts of energy(oxygen) required t o

maintain a high temperature condition,

(b) the high cost i n refractor ies and construction

material necessary i n the combustion zone,

( c ) the large m u n t of energy loss i n product gas o r

high cost i n heat recovery system.

1.2 Econmics of the Flash Carbonization Process

The rigorous economic analysis of a chemical process

includes detailed narket research, capt ial cost and to t a l

production cost estimation, and other economic f ac to r s . ( l l )

A t the present stage economic evaluation f o r the Flash

Carbonization process is d i f f icu l t because the new

technology involves rnany uncertainties i n process

performance, operability, a n r e l i ab i l i t y . A rigorous

es t i m t i o n is, theref ore, not necessary. Alternatively, a

quick calculation always meets the need i n priliminary

design stages. Savage(9) has shown the predesign capital

and operating cost of the Flash Carbonization process, based

on the assumgtion of equilibrium yields. He also compared

the production cost a t the experimental operat iw point with

other coal gasification processes, such as, Texaco process

and Koppers-Totzek process.

The next step, followed by h is work, i n economic

analysis is to f ind the best operating point i n the process

i t s e l f . In general, the best or o p t i m operating point

implies that it w i l l yield a maxlmum profi t . Net profi t , by

definition, equals t o t a l income minus a l l expenses. Total

income is the sum of each product amount multiplied by i ts

sel l ing price. A l l expenses are the to t a l production costs.

A typical t o t a l production cost analysis(l2) contains

several items, direct production cost, fixed charges, plant

overhead costs, administrative expenses, and distribution

7

and marketing expenses. The first three items a re sometimes

referred as manufacturing cost. The l a s t two items are so

called general expenses. The first item is the dominating

factor i n evaluating the op t i rm operating point. A typical

list of direct production cost contains(Peters, 1968 p.192)

r a w materials

u t i l i t i e s cost(steam, e lec t r ic i ty , fuel ,

ref rigeration, water, etc. )

operating labor and supervision

maintenance and repairs

operating supplies

laboratory charges

catalysts and solvents

For a given process o r a plant, raw materials and u t i l i t i e s

cost are the rmst inf luent ial factors i n direct production

cost. Therefore, the prof i t model can be simplified and

related t o the following factors:

(a) the amount and the price of each product.

(b) the m u n t and the cost of each raw material.

(c) u t i l i t i e s cost.

These three factors can be estimated i f the material and

energy balance are known. In general, a kinetic model

should be used t o predict the material and energy balance at

different operating conditions. However, fo r high

temperature processes, the thermodynamic equilibrium model

produces as good a prediction as the kinetic model. 4 t the

present stage, no kinet ic model f o r the Flash Carbonization

8

i s available. We w i l l use a thermodynamic equilibrium m d e l

f o r the p rof i t calculations. Any p ro f i t model f o r a

chemical process is naturs l ly constrained by chemical and

physical principles and economics rules. Chemical and

physical contraints consist of mss conservation and

therrmdynamics laws. Gcononic constraints a re the rules of

exis t ing m r k e t sys te~m. The search f o r the rmxirnum prof it

w i l l give us an explanation of how rnuch the constraints

influence t'ne prof it and operating point.

The character is t ics of p a r t i a l gas i f icat ion i n Flash

Carbonization has raised a se r ies of questions. Since the

process is not energy sel f -suff ic ient , which way is more

economical i n supplying reaction heat-by e l e c t r i c i t y

( indirect method) o r by oxygen (di rect method) - is unknown.

The low temperature operation favors char production and

decreases energy required i n the reactor as well as heat

waste i n the product s t r e a m ; it a l so decreases the

production of syngas because of themdynamic equ i l ib r ia i n

t he system. From t h e economical point of view, what is the

optimal operating point i n the Flash Carbonization f o r

naxFinum prof it is not c lear .

1.3 Purpose of the Thesis

This study is to f ind a auick estimation f o r the

optimum operating point of the Flash Carbonization process.

Constrained by both thermodynamic and economic

considemtions, an objective function has been defined f o r

the prof i t of each operating poigt. 4n experimental design

i s used as an optinim seeking method since it is an

implementation of optimization i n the real world. A

discussion on the search path is given with the cornbination

of chedca l stoichiometry, equilibrium constant, and

reaction heats involved i n the system. The resul t , a t the

o p t i r m operating point, is cmpared with those of the

experimental points using the same prof i t model.

2 .o LITERATURE m1w

2.1 G a s i f ica t ion React ion

The principal chemical and physical changes of coal i n

a gas i f i e r can be described by four categories: drying,

pyrolysis, combustion, and gasi f icat ion. Each physical o r

chemical transformation can be silnply represented by the

following equations : (bhngold, 1982, p. 132)

Drying

Coal (high moisture) ---- > Coal (dry)

Pyrolysis

Coal (dry) ----- > Char + Volati les (CO, H2 , C02

CH4 , Tar, H S, Ha 0, e tc . ) (2.2) 2

Combustion

Combustible vo l a t i l e s (CO, H2 , CH4 , Tar)

----- > co2 + 5 0

11

G a s if'ication

Char + 5 0 ---- > co + 5 + H s + N c ~ s h (2.5) 2 2

Char + C02 ----- > 2 C O + H 2 0 + % + H 2 S +

N2 + AS^ (2.6)

Char + 2H2 ----- > CB4 + H2 3 + H2 S + N2 +

Ash (2.7)

In order t o discuss and apply the present data, the

main reactions i n a gas i f ie r are simplified and summarized

i n Table 2-1. The overall reaction can be represented by the

following equation:

aCoal + b02 + cH 0 ===== 2 dCO + eH2 + f H 2 0 + gC02 +

hCH4 + i H 2 S + jN2 + kChar + etc. (2.9)

Reactions involved i n a reactor are generally defined

and constrained by stoichiometry, themdynamic equilibrium,

kinet ics , and transport ra tes (~nass, energy, and m e n t u n ) .

Since t h i s is a general analysis of the operating point i n

any gasif'ier with syngas production, the discussion

concentrates on stoichiometry and equilibrium. A

stoichiornetric analysis of coal gasification has been made

by Wei(l3). Through detailed vectorial and gemet r ic

12

explanations and comparisons of the resu l t t o comercia l and

p i l o t plant data, Wei found a narrow feasible operating

regian which is only limited by t h e m 1 balance and

stoichiometric constraints . However, the basis of his

studies is on the complete gasi f icat ion and thermal balance

which a re di f ferent f ron the assumption of t h i s study.

2.2 Equilibrium Computation

A t the present time, there is no unifying model f o r

coal gasi f icat ion kinet ics because the e f fec t s of ~nany

factors (such as the mechanism of pyrolysis, gasi f icat ion

reaction, hydrodynamics, and the difference in coals)

involved i n the reactions are not cmplete ly understood. As

an a l ternat ive , themdynamic analysis is always a guide i n

the preliminary design work. The information about chemical

equilibnun composition of a reaction allows us t o estimate

the theoret ical mass and energy balance f o r the system. The

calculation can be applied t o the design and analysis of the

process. l%ny examples were presented i n Shewood's

t ex t (14). In a complex reaction such as coal gasification,

equilibrium computation may provide information about the

upper boundary of yield f o r the f i r s t step i n assessing a

synfuel technology. Batchelder and Sternberg(l5) had a

discussion of equilibrium composition f o r suspension

gasi f icat ion of pulverized coal. Recently, Wiser and

13

Kithany ( 16) investigated a new ca ta ly t ic hydrogenation of

coal slurry- prepared i n s hydrogen-donor solvent, with

steam and hydrogen gas. The potential application and

operating point of the process was found by estimating the

equilibrium composition and heating value of product gas.

An entrainment gas i f ie r is always operated under high

tanperature conditions. Therefore, the overall performance

i n these gas i f ie rs can be determined approximately by

equilibrium considerations. Furtherimre, f o r an idealized

o r a large reactor, the residence tirne of coal par t ic les is

supposed t o be long enough t o reach equilibrium condition.

In a chemical system, equilibrium constraint includes

stoichiometric constraints and mass conservation constraints

f o r each principle reactions, the calculated equilibrium

cmpos i t ion f u l f i l l s both constraints . Two categories f o r the computation(l7) are the

equilibrium constant method and the f r ee energy minimization

method. The former aethod uses equilibrium constants t o

express cer ta in species i n terms of a s e t of a rb i t r a r i l y

chosen species . Kandiner and Brinkley ( 18) had a calculation

of the combustion of propane i n a i r by this method. The

equilibrium system contained ten gaseous constituents, with

o r without the formation of sol id carbon. This method was

designed f o r a specif ic problem and often took some

advantage of special character is t ics of the par t icular

problem. So, it is necessary t o find those compositions

which sa t i s fy the mass balance, the t o t a l presssure

s p c i f i c a t i o n s , and a l l the simultaneous equi l ibr ia

involved. It seems tedious f o r a rnoderateljr complex system.

An a l te rna t ive method, f r e e energy minimization method,

based on the f ac t tha t the t o t a l Gibbs f r ee energy of the

system reaches its minimum value a t guil ibriurn, subject t o

the constraints of the material balance. The necessary

data, chanical potent ia l of each species, can be calculated

from spectroscopic constants by evaluating the canonical

par t i t ion function of s t a t i s t i c a l thermodynamics. Oliver,

S t ephanou and Baier ( 19) computed the equilibrium

dis t r ibut ion of species resul t ing frorn reacti-ng 5 moles of

oxygen with 1 rnole of methane a t 873K by th i s method. They

a l so c i ted some addit ional application, such as, calculation

of the adiabatic flame temperature a t a sgecified pressure

and rocket motor performance calculations.

A NASA cmputer progrm(20) has been developed s h c e

the 1950's f o r multipurpose application. Rased on the l a t t e r

method, the program calculates the equilibrium canposition

f o r any thermodynamic s t a t e which is described by two

themdynamic parameters. The two thernodynanic paraneters

show the properties of the system, the (H,P) problem gives

adiabatic constant pressure combustion properties, the (U,V)

problem gives adiabatic constant volume combustion

properties, the rocket problen uses (T,P), o r (H,P), o r

(S,P), the detonation problem uses (H,P) or (T,P), where

T=Temperature, V=Volu-;le, P=Pressure, Y=Enthalpy, S=E;ntropy,

U=Internal Energy.

15

Savage and Chen have applied it to calculate

equilibrium yields f o r the comparison with the experimental

data. They found the experimental yields and the

canpositions of synthesis (H2 and CO) gas approached the

resu l t s calculated from the NASA program.

2.3 Overview of 3ptir;wn Seeking iflethods

Optimization is the way of finding the ~naxirnum o r

i-illnim values of an objective function. In chemical

engineering , optimization plays an important role f o r

process evaluation, e i t he r economically o r technically. For

example, such economic improvement as min im costs o r

m a x i m prof i t is required f o r a process design, and the

possible technical aims might contain the maximum amounts of

yield from a reactor o r a minimum s i ze of a cooling tower.

I n s p i t e of various kinds of mathematical rnodels of

objectives, the basic o p t i r m seeking methods are fixed.

Which method o r what par t icular group of methods can be

applied t o a specif ic objective function with high

efficiency and accuracy is s t i l l an act ive f i e l d f o r an

engineer.

Many texts(21,22,23) presented the information of

optimization techniques fo r most engineering problem. In

general, optimization techniques can be c lass i f ied in to two

broad categories: analyt ical methods and numerical methods.

16

These a re applied t o two dif ferent types of objective mde l s

respectively. (Beveridge 1977, p. 26) The f i r s t type is a

mathematical model which is a s e t of analyt ical expressions.

The second type is the so-called black-box model i n which

the response t o a par t i cu la r input is detemined by

numerical computation, m experiment, o r a computer program.

Sometimes a inathematical m d e l is too coinplex t o f ind an

optimum with analyt ic methods, then, it might be solved ~ i t h

nunerical methods.(Bveridge 1977, p.53)

We are not going t o review a l l the optimization

techniques . We are only concerned with the possible

optimum seekirg method i n the unconstrained multivariable

problem. The review here w i l l be a basis f o r the se lect ion

of an optimization technique i n t h i s study. There are three

methods summrized from most texts .

(a) univariate search

(b) s teepest ascent and

( c ) simplex method

(a) univar ia te search

The Univariate search is a kind of d i rec t method;

sometLzes, it is also called 'one fac tor a t a time methodf

o r sectioning method1 . (Beveridge 1977, p.355-363) By

s t a r t i n g an i n i t i a l point and keeping k-1 of the k variables

fixed a t some level , a mximm o r minirum value can be found

along this dimension. Therefore, an e f f i c i en t single-

variable search is necessary f o r t h i s type of search. The

17

o p t i m l point Is substi tuted into the function and the

objective function is again optimized with another variable.

The process continues : m t i l the successive change of

variables and object value is l e s s than a tolerance.(24) 'The

disadvantage of univariant search is that it is d i f f i c u l t t o

be used i n a system containning a ridge or steep contours.

The s tep s ize must not be kept too large because the process

my stop a t a n ~ n o p t i m l point.

(b) steepest ascent - It is a kind of gradient method. (kver idge, 1977 p.407)

The gradient vector is nor,ml t o the contour l i n e or surface

and indicates the direction of steepest ascent(or descent).

The steps f o r t h i s method(Stocker, 1980 p.180) a r e as

follows :

( a ) Select a t r i a l point.

(b) Evaluate the gradient a t the current point and the

relationship of the changes of the x variable.

( c ) Decide s tep s ize and then move tha t distance.

(d) Determine the maximum o r minimurn point along the

direction.

(e ) Check whether the o p t i m has been achieved. I f

not, return t o step(b) . There are many variations of s tep(c) and s tep(d) , which

depend on the chamcterization of the system.

18

( c ) simplex ;nethod - If we have an objective function with k variables,

(k+l) points are necessary t o form a simplex. For example,

a simplex i n two dimensions i s a t r i ang le and i n three

dimensions is a tetrahedron. The general direction of

search my be taken i n a direction away from the worst

p o h t . A new point is then selected along this direction

and passes through the center of gravity of the remaining

points. (Beveridge, 1977 p. 367) [The search w i l l stop on a

region, where no knprovenent can be achieved. The s tep s ize

sha l l be decreased t o s t a r t t'ne search from there u n t i l the

desired accuracy is reached f o r optirnurn.

2.4 berview of Experimental Designs

The purpose of any experimental work is to understand

mona bout the system being investigated. Experinental

designs have been introduced t o provide the l ea s t number of

experimental trials. In section (2.2) , only the response

values without experimental e r ror have been considered. kJe

have t o use a method derived from experimental designs that

is applicable when experimental e r ro r is s ignif icant . In

t h i s study, we are considering an effect ive experimental

method of f i t t i n g response surface and of locating an

optimum operating point. The basic experimental designs are

indicated i n many texts(25,26,27) and reviewed i n t h i s

1 Y

section as a basis of solut ion algorithm f o r t h i s study.

Factor ia l Designs at two leve l s -- A general f a c t o r i a l design is the se lect ion of a f ixed

number of l eve l s f o r each of a number of

var lables(factors) and the experiments with a l l possible

combinations. In general, two leve l f a c t o r i a l d e s i g s a re

more important by the following reasons: (Pox, 1978 p.306)

( a ) They require re la t ive ly few runs per' f a c to r

studied.

(b ) \*en needed, they a r e eas i ly augmnted t o form a

composite d e s i g .

( c ) Through two level f rac t ional f a c t o r i a l design, the

number of runs can be decreased fur ther .

(d) The use of building blocks reduces the degree of

complexity of the problem.

( e ) It is easy t o in te rpre t the observations.

In general, the two leve l f a c t o r i a l design gives a

f i r s t order equation t o represent loca l surface. There a r e

many texts(Davis, 1967 p.271; k x , 1978 p.510; a x 1954)

comparing the two l eve l f a c t o r i a l design with the one f ac to r

a t a time nethod. In general, the differences between them

are:

( a ) When in te rac t ion e f f ec t s a r e s ignif icant , a

f a c t o r i a l design avoid leading wrong conclusions.

For exanple, one f ac to r at a time w i l l be valueless

when the response surf ace contains a ridge, but

20

f ac to r i a l de s im my identify it and give the

direction of the axis of the ridge so tha t

improvement is possible.

(b) The discovery of fac tor dependence of a par t icu la r

type provides the information i n connection with

the experimenter's theoret ical knowledge. It is

helpful f o r fu ther experimentation.

( c ) For multivariables experimental design, f ac to r i a l

design t e l l s exactly which factor and how . m y

factors should be varied.

Fractional f ac to r i a l design

When a model contains more than three variables, the

f u l l f ac to r i a l designs a re tedious and unmanageable.

Fractional f ac to r i a l design is needed f o r fewer design

points and enough in formt ion about the nature of the

response function we a r e exploring. There a r e many examples

presented i n the well hewn textbooks (Davis, 1976 p. 454;

Orthogonal design

If we arrange the levels of each fac tor i n such a way

that the diagonal terms in the normal equations (when

performing l e a s t square) would be vanished, the design is

said t o be orthogonal. The design matrix and the

calculation of e f fec t s a re shown i n Table 2-2.

Composite d e s i ~

Box and Wilson(24) or iginal ly introduced the concept i n

1951. Factorial design can be augmented t o form composite

design. Therefore, f i t t i n g a response surface is possible

with a second order equation. Many examples are presented

i n the paper. (28,29)

Response Surf ace Method

The response surface method(24) has been selected with

success on locating the o p t i m point through experinent

design.

Two survey a r t i c l e s , H i l l and Hunter(30), and Nead and

PFke(31), l i s t e d references t o those studies.

B e l t and Roder(32) studied the rapid entrainment

carbonization of powdered coal under pressure i n a pa r t i a l

hydrogen atmosphere f o r the production of low sulfur char.

They established the relat ionship betrreen process variables

md char yield a s well a s qual i ty by the application of

response surface analysis. It is c lear tha t i n the rea l

world the exact form of a response function would be

unknown. Also, the complete theoret ical mchanisms of nost

indus t r ia l processes are not available. In fac t , the exact

function is not necessary because the m e d i a t e concerns f o r

process design are questions such as(25)

(a) What values of a given s e t of inputs w i l l yield a

22

maximn o r reach a maximurn p ro f i t ?

( b ) What is the shape of the response surface close t o

this maximum, o r over some specified regions of

in te res t?

The response surface nethod has been applied t o answer these

questions.

One s t r i k i w application of the response surface method

is 'Evolutionary 0peration1(EVOP).(33,34) The basic idea is

la process should be run so as t o generate product plus

inf'ormation on how t o improve the product' . (34) The

experiments fo r t r ue optimum yields nust be carr ied out on

the ful l -scale plant.

TABLE 2-1

HEAT OF REACTIONS ( kB : KCAL ) AND EQUILIBRIUJ'JI CONSTANTS ( KP )

OF SELFXTED @ACTIONS

........................................................... 3eact ions 298K 7 00K lOOOK 1500K

............................................................ ............................................................

Combustion

...........................................................

I-tR -26.4 -26.4 -26.74 -27 75

Continued

24 Gasificat ion

Gas Eieact ions

---> H3+C02 - KP 0.07 0.15 0.20 0.28

......................................................... HR -49.26 -52.68 -53 87 -54 59

CO + 3H2 .............................................. --->CH +H 0 KP

4 2 14.83 1.15 -0 .g6 -1 -75

.......................................................... Source from Reference (1)

- - - - - - - - - - - - - -

Temperature Oxygen St earn

Unit ( K ) (wt% > ( w t % )

T 0 H

Center Condition 1180 0.20127 0.09526

Step Size 20 0.01 0.002

+ 1200 0.21127 0.09726

- 1160 0.19127 0.09326

T O H Y (1) (2) (3) divisor effect

- - - 96.00 90.36 186.09 372.46 8 46.56 ave

+ - - 44.36 95.73 186.37 -6.55 4 -1.64 T

- + - 48.68 90.50 -3.27 10.74 4 2.69 O

.......................................................... m i n effects: T , 0, H two factor interaction: TO, THY HO three factor interaction: T9H

3.0 OBJECTIVE FUNCTION

3.1 A s sump t ions

A rigorous p ro f i t m d e l has Seen discussed i n chapter

One. A simplified one contains the following factors :

( a ) the a i i un t and pr ice of each product.

(b) the amunt and cost of raw m t e r i a l s .

( c ) u t i l i t i e s cost .

Once the amunt and cost of raw materials and the pr ice of

each product are specified, rigorous mss and energy

balances f o r each un i t process and un i t operation give us

the mount of each product and t he u t i l i t i e s cost . Here, we

w i l l a l so apply the simplif ied p ro f i t model f o r the Flash

Carbonization process. The necessary mass and enerw

balances f o r the objective function of the Flash

Carbonization process have been based on the following

assumptions :

process

( a ) Only a single-stage ga s i f i e r is i n t he system.

(b ) The operating cost of transmission machines (screw

feeder, pump, compressor) i s negligible.

( c ) The difference on the c red i t of heat ' recovery is

negligible.

27

(d) No steam recovery system.

( e ) E lec t r ic i ty is the only indirect heating source f o r

coal gasification i n endothemic condition.

gas i f ie r

( f ) Operated i n isothermal condition at 1 atmospheric

pressure. The block diagram of it is show i n

Figure 3-1.

(g) The products are under thermodynamic equ i l i b r im

condition. 'The NASA program provided the

equilibrium calculation. In the data bank of the

NASA program, there is no molecular f o m f o r char.

Therefore, it i s necessary t o replace char with

Graphite carbon(C). The element form of coal, i .e.

Cv Hw 0, Ny S, , also replaces coal i n Reaction

2.11.

aC H 0 N S, + b02 + cH2 0 ====== v w x y dCO + eH2 +

fH2 0 + gC02 + hCH4 + i H 2 S + j N 2 + kc + etc.

(h) applying Hessls law f o r the calculation of heat of

reaction a t the reactiorl temperature.

(i) applying the ideal gas law f o r the calculation of

sensible heat content f o r each conponent of product

gas.

3.2 Data and Parameters

The necessary data and parameters are discussed i n t h i s

section. Since cost and price are dependent on time, we

a rb i t r a r i l y referred them from the following reference.

cost and price --- ( j ) The uni t cost of e l ec t r i c i t y and raw m t e r i a l s are

shown i n Table 3-1-A.

( k ) The unit price of char and medium-Btu gas are shown

i n Table 3-1-B.

(1) No separation cost f o r char and product gas.

(m) The price of product should be varied with the

composition of it. However, the credi t of product

gas here is only calculated based on the heat

content of it.

physical and chemical data - - (n) Heat capacity equations and heat capacity

coefficients are f ran the data bank of the NPSA

prpgrun.

(0) Heats of Formation a t 298K are shown i n Table 2-1.

(p) Composition of coal(0hio Clarion 4 A ) is shown i n

Reference (9) .

29

3.3 Final Form of Objective Furction

After making the above assumptions, the objective

function w i l l be

U l , U 2 = f ( x l 9 X 2 , X 3 )

y = z u + Z 2 U 2 1 1 - ( c l + c 2 x 2 + c 3 x 3 + E)

y: prof it, response value

f : NASA program

u 1 , u 2 : equilibrium mount f o r char and

product gas

c ,c ,c :unit cost of coal, oxygen, s t e m 1 2 3

' 2 j X 3 : amount of oxygen and steam

x : temperature 1

z19z2 : unit price of char and medium-Btu gas

E: cost of e l ec t r i c i t y

HEAT 4 I I

\t/

YIGURE: 3-1 THE BLOCK DIAGRAM OF A SINGLE-STAGE GASIFIEB

TABLE 3-1-A

UNIT COST OF FEEDSMCK AND UTILITIFS

............................................................ Item U n i t cos t ........................................................... ...........................................................

Feedstock

Coal(0hio Clarion 4 A ) (Dry and Ash Free)

Oxygen

S t e m

$15.00 per ton

$26.90 per ton

$3.50 per Lvl lb

Ut i l i t y

E lec t r i c Power $0.035 per IQih

........................................................... Source from Reference(9).

UNIT !'hWKST PRICE OF PRODUCTS

.......................................................... Item Unit pr ice ............................................................ ............................................................

Char $14.00 per ton %

Medim-BTU gas $5.30 per MM Btu * ........................................................... %Source from Reference(9). *Source from Reference(37).

4.0 OUTLINE OF THE OPTIMIZATION STHAmY

4.1 R SAMPLE CALCULATION OF RESPONSE VALUE

A calculat ion of response value based on the objective

function i n Chapter Three is shown in t h i s section. ble

a r b i t r a r i l y s e l ec t 1 ton of dry and ash f r e e coal a s a basis

t o ca lcu la te the necessary operating cost , the possible

c red i t , and the profit-response value.

Heat of formation of coal 7- --

(a) Molecular formula of coal

de derive the molecular formula from the element

composition t ab l e of coal.(Table 4-1) The

molecular form is:

(b ) Heating value of coal

Frotn Dulongls formula(35), the heating value of

coal can be expressed by:

Q (Btu/lb) = 14544 * C + 62028 * (H - 0/8)

+ 4050 * S

where C, H, 0, and S a r e weight f rac t ion of each

element . Combining the formula and the elenent composition

3 3

tab le (Table 4-1) , the heating value of coal (Ohio

Clarion 4A) is 12880 Btu per l b , which i s eqlal t o

124.8 Kcal per g m l e dry and ash f r ee coal.

( c ) Heat of formation of coal a t 298K

I n order t o ca lcula te the heat of formation of

coal, we have t o apply the combustion reaction of

coal.

Standard heat of Higher heating Combustion per = value of 1 p l e p l e of coal of coal

The sum of heats The sum of heats = of formation of - of formation of

products at 298K reactants a t 298K

The only unkno\m value i n the last equation is the

Standard heat of formation of coal. Heating value

has been e s t i m t e d i n Page 32. Standard heats of

f o r m t i o n of other component can be found i n many

texts . Table 4-2 gives a d e t a i l calculat ion.

Therefore, the standard heat of formation of coal

is -2.08 (-126.88-(-124.8) ) Kcal/gmle at 298K.

The NASA program -- (a ) Input data

We a rb i t r a r i l y assume the flow rates of coal,

oxygen, steam so tha t the weight r a t i o of oxygen t o

coal is 0.21127 and the weight r a t i o of s t e m t o

coal i s 0.09726. Therefore, the input data f o r the

NASA program i n t h i s sample calculation are:

Molecular formula of coal, oxygen, and s t e m

Pressure = 1 atm

Temperature = 1200K

The amount of coal = 1

The amount of oxygen = 0.21127

The amount of steam = 0.09726

(b) Output resu l t

The output resu l t f o r calculated equilibrium

component dis t r ibut ion i s l i s t e d i n Table 4-3. In

order t o convert mle f rac t ion in to mole basis of

each component, we have t o calculate the t o t a l

moles of the equilibrium mixture. Here, we use the

element balance of carbon t o ge t the t o t a l moles of

carbon atorn i n the system and the t o t a l mole

fractions of carbon compounds i n the mixture.

Therefore,

The t o t a l moles of carbon atom

= 1000000 (kg coal) / 15.15 ( g / g m l e of coal)

= 65972 p l e

The t o t a l mole f ract ions of carbon compounds

(Table 4-3).

= 0.429 ( f o r C) + 0.003 ( fo r CH4 )

+ 0.219 ( fo r CO) + 0.00036 ( f o r COS )

+ 0.002 ( f o r C02 ) + 0.000014 ( fo r CS2 )

= 0.653

The t o t a1 moles of equilibrium mixtures

The t o t a l moles of carbon atom - - ..................................... The t o t a l mole f rac t ions of carbon compounds

Once the t o t a l moles of equilibrium mixtures is

calculated, the moles of each component can be

estirrated and the resu l t is indicated i n Table 4-3.

Heat of reaction at 1200K -- -- Heat of Heat of Sensible Sens i b l e reaction = reaction - heat of + heat of a t 1200K at 298" react ants products

Each i t e m i n the r igh t hand s ide of t h i s equation

is calculated i n the Table 4-4. Therefore,

The heat of reaction at 1200K

= 350000 Ycal/ton coal

It is an endot-hermic reaction i n t h i s sample

calculat ion.

Note t ha t the formula t o ca lcu la te

sensible heat is : f m

+A5 * ( ~ 5 - 2985 )/5

where Cp = heat capacity

R = gas constant

!I1, A;, A3, A4, A5 = parameters of each

canponent a re from data bank of the NASA

program.

Cost, Credit, and Prof i t - - Total cos t is indicated i n Table 4-5. Total c red i t

is indicated i n Table 4-6. The prof i t , response

value is equal t o t o t a l c red i t .minus t o t a l cos t

which is $88.03 - $40.19 (= $47.12) f o r one ton dry

and ash f r e e coal i n t h i s sample calculat ion.

TABLE 4-1

COMPOSITION OF C O L (OHIO CLARION 4A)

........................................................... Component Weight % Molecular Mole % Mole %

Weight se t C = l

C 70.3 12 5 -86 1

H 5.3 1 5 03 0 *go5

0 7.2 16 0.45 0.078

N 1.2 14 0.086 0.015

S 4.8 3 2 0.15 0.026

Inert 11 .O

TABLE 4-2

CALCULATION OF HEAT OF FORMATION OF COAL

....................................................... Component Amount Standard Heat Heat of

of F o m t i o n Formation a t 298K at 298K

Reactants

Coal 1 x x

...........................................................

Total x

Products

Total -125.88

39 TABLE 4-3

THE ECJUILIBRIUM COME"G'SITION AND MOLES OF EACH COMPONFQJT

Component Mole Fraction mles (By NASA program) (By calc.) ........................................................... ...........................................................

COS 3 . 5 8 3 - 0 4 3 7

............................................................ ............................................................ Total 9 999 101127

...........................................................

40 TABLE 4-11

........................................................... Somponent Moles Standard Heat of Sensible Sensible

Heat of Formation Heat Heat of Formation at 298K each a t 298K component

gmol~? K c a l / @ ~ l e Kcal Kcal/gmole Kcal ............................................................ ............................................................

input streams

coal 65972 -2.08 -137749 0 0 oqgen 6602 0 0 0 0 s t e a m 5403 -57.598 -31120 1 0.539 2913.3 ............................................................ ............................................................ Total -448950 2913 3

............................................................ output s t r e w 1200K

COS 37 -32.080 -1195 11.378 424

............................................................ Total -6569 66 557313

TABLE 4-5

TOTAL COST I N THE SAMPLE CALCULATION

........................................................... I tm Amount Unit Conversion Cost

cost Fact o r

$ ........................................................... Feedstock

Coal 1 ton 15 $/ton 15.00 Oxygen 0.21127ton 26 $/ton 5 -49 Steam 0.99726 ton 3.5 $/klb 2.2 klb/ton 0 .75

U t i l i t y

3 lec t 350 000 0.035 0.0016222 19.67 Kcal $/kw-hr kw-hr/Kcal

......................................................... Total 40.91 ..........................................................

TABLE 4-6

TGTAL CREDIT I N A SAMPLE CALCULATION

........................................................... I t a n Amount Unit Price Conversion Credit

Factor

grm l e $ .......................................................... Char 42496 1 4 .000012 7 .I4

$/ton ton/gmole

Medium-Bt u Gas

Methane 288

Carbon 22976 Monoxide

Hydrogen 32688

Total

4.2 The Considerations of Optimization Strategy

Three independent variables are assigned i n the

objective function. i.e.

Y = f ( x l , X * , x 3 )

where

y : prof it

x :weight ra t io of Oxygen to Coal 2

3 :weight ra t io of Steam t o Coal

The 05jective function, defined i n Chapter Three, showed

i ts complex calculation involved the NASA prograrn. A

combination of optimization technique and experimental

design method is used t o determine the optimal value of the

objective function. The following considerations influence

the selection of step s ize and direction f o r optimization.

(a) Experimental design provides a structure fo r the

investigator I s learning process (36) . Hunter and Nay l o r

said ' A successful learning requires the f u l l use of

prior knowledge in proposing useful models and

s t rategies for gathering evidence useful for synthesis

and conjecture.'

(b) It provides a basis f o r Evolutionary Operation l a t e r ,

whm we want t o search an optimum operating point on a

4 4

comnercial plant.

( c ) The s t a r t i ng point of the search is close t o one of the

experimental points. We assume it is not f a r from the

optimum point. I f it is, we are interested also i n the

local surface f o r those experimental points.

The s t a r t i ng point is a rb i t r a r i l y taken t o be close t o

the operating p o h t reported by Savage. (APPENDIX I) Two

level fac tor ia l design gives us a direction of steepest

ascent and a local surf ace picture. However, i f the step

s i ze is too big, the direction w i l l be meaningless.

Therefore, a smll s tep s ize is always used i n fac tor ia l

desim. Once the direction is determined, a variable s tep

s ize f o r open-ended search is employed t o f ind the optimwn

point along the given direction. I f the s ize is too big, we

might mlss the best point along the direction. If the s ize

is too small, w e might have an unefficient search.

4.2 F i r s t Order Design and Direction of Steepest Ascent

A t the beginning point of the investigation, there was

probably some distance from the maximum. From calculus

point of view, the local character is t ics of the surface can

be represented by its gradient, i .e.

where

xO : a local point

x : a neighborhood point around point xo

yo : response of xo

y : response of x

Vy : gradient vector a t x

Rewrite Equation fo r three independent variables as :

Y = b o + b l * x l + b 2 * % + b 3 * 5 gradient a t y = (b b 2 b )

Table 5-1 shows how the two level fac tor ia l design

determines the local slope of the surface. The least squares

es t imt ion of b o is the average of a l l eight responses.

Because of the orthogonality of each independent variable,

the coefficient b is the change tha t occurs i n the

response when x is changed by one unit . Yatests algorithm

gives a rapid calculation of effects, The significance of

main effects m y be checked by higher order interactions.

They are supposed t o be negligible because of experimental

errors. Curvature effects w i l l be checked also. I f it is

significant, then the f i t t i n g second degree equation w i l l be

considered. I f some of main effects and interaction effects

a re signiricant, we m y discard the interaction t e r n and

follow the direction of main effects.

The next s tep is to search along the direction of

steepest ascent. For one dimensiorlal open ended o r

unbracketed search, the method of Swam (Beveridge 1977,

46

p.154 and Beightler 1979, p.190) has been used. This method

reyuires that the design points would be chosen t o have a

s tep s i ze double t he i r previous points u n t i l reaching a

point where no fur ther progress seem l ikely. Sometimes, a

point is necessary i n the region between the l a s t two

points. O f the four equally spaced values, we select e i ther

the f i r s t three or the last three. It depends on which s e t

has a bigger center objective value.

Having carried out an open ended search and defined the

optimum within a bracketed region, we may f i t a second order

p o l y n d a l curve w n g t h i s region and locate the best point

f o r t h i s curve by intewolat ion. Other one dimensional

searchs in a limited region, such as, Fibonacci search, e tc ,

are not considered.

4.4 Second Order Design

Sooner o r l a t e r it would becotne c lear t ha t t o f i t a

f i r s t degree equation representing a local surface is not

possible. Besides, no fur ther progress can be obtained by

t h i s method. It seem tha t a near stationary region is

reached and f i t t i n g a second degree equation is necessary.

SomtFmes, w e a re a f ra id of the stationary point caused by

the small s tep s ize . Therefore, t o double or t r i p l e the

s tep s i ze is necessary around t-his region.

A two leve l f ac to r i a l design was augmented with fur ther

47

-points which allowed the quadratic e f fec t s t o be detemined

also. A central composite design w a s formed i n t h i s study.

F i t t ing a second order equation was possible. The necessary

condition f o r finding the maximum on t h i s equation w a s the

vanishing of the f i r s t derivative. The suff ic ient condition

fo r it is t o calculate the Hessian matrix o r t o transform

the equation t o canonical form.

5.0 RESULTS AND DISCUSSIONS

The optimum operating point -

The resu l t s of searching are displayed from Table 5-1

t o 5-6. We divided them in to s ix stages. The f i r s t f i ve

stages included a direction change and an one-dimensional

search. Each one-dimensional search consisted an open-ended

search and a close-ended search. In Table 5-1, a two-level

fac tor ia l design was f i r s t used t o f ind the direction of

steepest ascent based on a s t a r t i ng point (T=1180, 0=0.20127,

H=0.09526) with objective value 46.56. Along t h i s direction

an arbi t rary increment is taken t o be (-16, 0.0134,

0.00007). SignFficant irnprovernents were observed along t h i s

direction u n t i l the point (2=7) where the objective value

was 63.37. Then, another two-level f ac to r i a l design was

used t o f ind a new direction and the whole procedure

repeated i n Table 5-2 t o 5-5. The l a s t stage was a

composite design.

Star t ing from an i n i t i a l point, the f i r s t stage showed

e l ec t r i c charge was the doininating factor because the feed

m u n t of oxygen was sm11. The system was endothermic. It

was c lear that the direction of steepest ascent was toward

decreasing temperature and increasing the amount of oxygen.

Besides, t o supply heat from e l ec t r i c i t y was not so

4 9

economical as by oxygen. The heat, supplied by 0.02 kg

oxygen, costs $0.50. It costs $1.80 by e lec t r ic i ty . The

following one-dimensional search was ended a t a point i n

which the system was close t o them1 neutral . The point

(y=63.37) seemed very close t o the maxium point along t h i s

direction because the difference between it and its

succeeding point was two times the difference I~ tween it and

i ts preceding point.

The second stage showed how oxygen and steatn affected

the production of carbon monoxide and hydrogen after the

systern was around the rml ly neutral . Large amounts of

oxygen increased the production of CO from $36.78 t o $78.04,

a l t h o u e the cost of oxygen increased from $8.51 t o $26.81.

The one-dimensional search was ended where the excess oxygen

reacted with CO and 3 , I n table 2-1, these two combustion

reactions only produced H2 0 and C02 . The th i rd stage showed how temperature affected the

production of CO and H2 a t the temperature range

(1066-1166K). The temperature e f fec t s seemed constant a t

the temperature range ( 1166-1566K) because the response

value had not been changed much ($108.63-107.37) . This

could be explained because the equilibrium constants of the

main gas if icat ion react ions were nearly constant a t the

temperature range. (Table 2-1 )

The fourth stage showed how steam positively affected

the production of H2 and oxygen inversely affected the

production of CO. It was obvious tha t a stationary point

50

was a p p r o a c h i n g , p a r t l y because t h e i n t e r a c t i o n e f f e c t s were

i m p o r t a n t now and p a r t l y b e c a u s e no b i g d i f f e r e n c e was

o b s e r v e d i n r e s p o n s e v a l u e s .

The f i f t h s t a g e c o n f i r m e d a s t a t i o n a r y p o i n t was a round

t h e p o i n t (T=1193, 0=0 .72107 , H=0.30049) b e c a u s e two of t h e

main e f f e c t s ( 0 . 1 2 , 0 .07 , 0 . 95 ) were l e s s t h a n t h e

i n t e r a c t i o n e f f e c t s ( 0 . 1 7 , -0 .54 , -0 .76 , 0 . 3 3 ) .

One p o s s i b l e m i s t a k e we c o u l d have i n o p t i m i z a t i o n was

i f t h e s t e p s i z e was t o o small and , t h e r e f o r e , t h e

s t a t i o n a r y p o i n t was m e a n i n g l e s s . So, t o i n c r e a s e t h e s t e p

s i z e was n e c e s s a r y f o r t h e s i x t h s t a g e . From t h e c o m p o s i t e

d e s i d n , a s e c o n d a r y e q u a t i o n was f i t t e d by l e a s t s q u a r e

method.

By v a n i s h i n g t h e 1st d e r i v a t i v e , t h e optimum p o i n t was

xl* = -0 .0741

x2* = 0.24476

x3* = 0.445

By t r a n s f o r m i n g t h e coded v a l u e i n t o a b s o l u t e v a l u e , we g o t

T* = 1 1 9 1

0* = 0 .7 2841

H* = 0.31384

The qual i ty of char -

The optimum point thus obtained did not consider the quali ty

of char. Suppose the minirrnun requirement of carbon content

i n char c as 50 weight percent, our search f o r optimization

would be stopped a t the other point. We assumed the weight

percent of ash content i n coal was 0.11. The amount of ash

would be 0.12 ton if 1 ton of ash f r ee coal was reacted. In

order t o meet the requirement, the r n i n i m carbon amount

unreacted i n char should be 0.12 ton also. This number

corresponded t o a point i n the second stage (T=1066,

O=O. 5199, H=O .13775).

The com~arisons

With the same prof i t model, we compared the resul ts

with the e x p e r i i ~ n t a l points reported by Savage. It simply

means that we applied the sane objective function f o r the

calculation of p rof i t on those experimental points. The

most in f luen t ia l parameters i n the p ro f i t mode1,is the un i t

price of products and the uni t cost of feedstock. We would

l i ke t o calculate the objective values based on dif ferent

uni t prices and un i t costs. Ve expressed them as two cases,

case A and case B. Case A was the one we already agplied

f o r the search of the optimm point. Case 9 jus t included

the modification of the Table 3-1-A and Table 3-1-B in the

following way:

unit cost of coal = 25 $/ton

unit price of &ar = 25 $/ton

unit price of inedium-Btu gas = 4.0 $/MMBtu

Now, we can see the objective values of the op t i rm point

were always bigger than those of experimental points.

The Experimental points The optinnun point

prof it ($ )

case A 50.54 43.26 39.62 119.62

case B 31.88 24.27 20.57 71.36

Note that the objective values were based on 1 ton dry and

ash free coal. A l l were a t 1 atmosphere pressure in

isotherm1 condition.

TABLE 5-1

SEARCH ON STAGE-1

Factor ia l Design

---- - -

Temperature Oxygen Steam

U n i t (K) ( w t % ) (wt%>

T 0 H


Step Size 20 0.01 0.002

+ 1200 0.21127 0.09726

- 1160 0.19127 0.09326

- -

COST OF CFEDIT OF

T C ) H y e f fec t ELECT (CO + XYD) CHAR

$ $ $ $ $

............................................................. .............................................................

- - - 46.00 46.56 18.61 30.05 46.07 7.41

+ - - 44.36 -1.638 20.89 30.64 46.62 7.38

- + - 48.68 2.685 16.85 31.73 46.07 7.21

+ + - 47.05 0.008 19.18 32.36 46.63 7.18

- - + 46.07 0.07 19.09 30.35 46.37 7.38

+ - + 44.43 -0.003 21.39 30.94 46.93 7.34

- + + 48.75 0. 17.33 32.03 46.37 7.18

+ + + 47.12 0.003 19.67 32.66 46.94 7.14

.................................................... Continued

Open-ended he-dimensional Search

............................................................

direction: (-0.82 1.34 0.04)

s t ep s ize : -16 0.013426 0.00007

Z: the number of s t eps from or ig ina l point

~ ~ ----

COST OF CREDIT OF

y X E C T ( CO + HYD) C;&W

$ $ $ $ $

............................................................ .............................................................

0 1180 0.20127 0.09526 46.56 19.17 31.39 46.53 7.27

11164 0.21470 0.09533 49.01 17.05 32.26 46.29 7.15

3 1131 0.24155 0.09547 53.92 12.40 33.65 45.66 6.94

7 1066 0.29525 0.09575 63.37 0.80 34.10 43.46 6.66

15 936 0.40265 0.09631 41.50 0. 19.03 32.81 7.21

Close-ended One-dimensional Search

%cause (63.37-41.50) / (63.37-53.92) = (15-7) / (7-3)

z* = 7

The bes t point: T: 1066, 0:0.29525, H:O .09575

TABLE 5-2

SEARCH ON STAGE-2

Pactor ia l Design


Unit (0 ( w t X > ( w t % )

'T 0 H

Center Condition 1066 0 29525 0 09575

Step Size 10 0.01 0.006

+ 1076 0.30525 0 .lo175

- 1056 0.28525 0.08975

........................................................... COST OF cmn OF

T O H y e f f e c t ELECT (CO + SYD) CHAR

$ S $ $ $

............................................................. .............................................................

- - - 52.06 62.69 0. 32.09 42.55 6.86

+ - - 51.62 0.22 2.40 33.80 43.47 6-75

- + - 52.66 1.89 0. 33.48 42.53 5.68

+ + - 54.25 0.76 0.45 35.27 43.46 6.56

- - + 52.48 0.59 1.07 32.85 43.40 6.76

+ - + 51.85 -0.36 3.70 34.60 44.34 6.65

- + + 64.14 0.26 0. 34.24 43.38 6.55

+ + + 64.49 -0.26 1.75 36.07 44.33 6.46

............................................................. Continued

Open-ended One-dimensional Search

.......................................................... direction: (0 . 0.95 0.30)

s t ep s ize : 0 0.03195 0.006

Z: t he number of s t eps f r ~ m or ig ina l point

............................................................

COST OF cmrr OF

y OXY (CO + rn) C U R

$ $ $ $ $

............................................................. .............................................................

0 1066 0.29525 0.09575 63.37 7.68 34.10 43.46 6.66

1 1066 0.32720 0.10175 65.97 8.51 36.78 43.57 6.32

3 1066 0.39110 0.11375 69.56 10.17 42.11 44.69 5.62

7 1066 0.51990 0.13775 76.81 13.52 52.82 46.35 4.23

15 1066 0.77550 0.18575 91.30 20.16 73.97 49.70 1.46

31 1066 1.28670 0.28175 55.66 33.45 62.52 43.52 0.

23 1066 1.03110 0.23375 85.26 26.81 78.04 49.80 0.

Slose-ended One-dimensional Search

F i t t i n g points : Z=7, y=76.81; Z=15, y=91.30; Z=23, y=85.26 2 2nd-order model: y=47.29 + 5.342 - 0.16Z , Z*=16.60

The best point: T:1066 0:0.8271 H: 0.19563

TABLE 5-3

SMCH ON STAGE-3

Factorial Design

........................................................

Tmperature Oxygen S t earn

Unit (K) (wt%> (wt%)

T 0 H


Step Size 2 0 0.01 0.006

+ lo86 0.83710 0.20163

- 1046 0.81710 0.18963

COST OF CREDIT OF

T O H y effect ELECT (CO + HYD) C M

$ $ $ $ $

Continued

Open-ended One-dimens ional Search

di rect ion: (5.02 0.33 0.75)

s t ep s ize : 100 0.00325 0.0045

Z : t he number of s t eps f r ~ m the o r i ; ~ i n a l points

SOST OF CREDI'I' OF

y ELECT (CO + HYD) CHaR

$ $ $ $


............................................................

The best point: T: 1166 0: 0.83035 H:0.20013 at Z = 1

Tmm 5-4

SFACkl ON STAGE-4

Factorial Design

.......................................................... Temperature Oxygen Steam

Unit (K) (&%I ( w t % )

T 0 H


Step Size 10 0.01 0.01

+ 1176 0.84035 0.21013

- 1156 0.82035 0.19013

...........................................................

SIiEDIT OF

'T O H Y effect (CO + HYD)

$ $ $

............................................................. ______-______-__-_-------------------------------------------

- - - 106.91 108.08 89 74 53.47

+ - - 108.29 0.42 90.98 53.87

- + - 107.51 -1.11 91.14 53 44

+ + - 107.62 -0.328 91.39 53 .70

- - + 109.63 1.013 91.22 54 099

+ - + 109 75 -0.323 91 49 55.28

- + + 107.46 -1.077 90 43 54.60

+ + + 107.54 0.308 90.65 54 .77

Continued

60


direction: (0.211 -0.556 0.506)

s t ep s ize : 4 -0.01113 0.01013

Z: t h e number of s t eps from the o r ig ina l points

COST OF CREDIT 9F

Z T 0 H Y OXY (CO + HYD)

$ $ $ $


F i t t i n g points: Z=3, y=112.26; Z=7 y=117.08; Z = l l , y=116.98 C

2nd-order rmdel: y= 105.42 + 2.72 - 0.152 , Z*=8.9

The best point: T: 1203 0: 0.73107 H: 0.29049

TABLE 5-5

SEARCH ON STAGE-5

F a c t o r i a l Design

...........................................................


Unit ( K ) ( w t % (wt%)

'T 0 H


Step S i z e 10 0.01 0.01

+ 1213 0.74107 0.30049

- 1193 0.72107 0.28049

.......................................................... COST OF C;IEDIT OF

T O H y e f f e c t ELECT (CO + kIYD)

$ $ $ B

............................................................ ------------_----__-_---------------------------.--__-_-_--__

- - - 116.89 118.18 0. 90.21 61.13

+ - - 117.70 0.12 0. 90 92 61.44

- + - 117.87 0.07 0. 91.92 61.14

+ + - 118.38 0.17 0. 92.42 61.43

- - + 4 6 0.95 0.21 91.73 62.68

+ - + 118.54 -0.54 1.95 92.46 63 .OO

- + + 118.28 -0.76 0. 91.66 62.41

+ + + 118.35 0.33 0. 91.83 62.56

........................................................... Continued


...........................................................

direction: (0. 0. 0.52)

s tep size: 0 0 0 .O1

Z: the number of s teps from original point

SOST OF CREDIT OF

Z T 0 H y ELECT STEhVI (CO + HYD)

$ $ $ $ $

........................................................... ............................................................

0 1203 0.73107 0.29049 119.21 0. 2.24 92.21 62.07

1 1203 0.73107 0.30049 119.41 0. 2.32 92.10 62.74

3 1203 0.73107 0.32049 119.35 0. 2.47 91.46 53.80

7 1203 0.73107 0.36049 118.52 0.61 2.78 90.04 65.56


............................................................

The best point is a t : T: 1193 0: 0.072107 H: 0.30049

63 TABLE 5-6

SEARCH ON STAGE-6

......................................................... Temperature Oxygen S t e m

Unit (K) (wt%) ( w t % ) T 0 H

Center Condition 1193 0.72107 0.30049 Step Size 3 0 0.03 0.03

+ 1223 0.75107 0.33049 - 1163 0.69107 0.27049

SOST OF CEiEDIT OF T O H y e f f ec t ELECT OXY (CO + FED) CXAR

$ rt; $ $ $ $ ............................................................ ............................................................ - - - 112.40 115.53 0. 17.97 85-42 59.77 0.73 + - - 113.56 0.17 1.57 17.97 87.84 60.79 0.57 - + - 115.22 2.22 0. 19-53 90.45 59.77 0.12 + + - 117.35 0.97 0. 19.53 92.47 60.74 0. - - + 117.23 1.79 3.41 17.97 89.93 64.37 0.18 + - + 114.48 -1.98 9.04 17.97 92.47 6 . 4 6 0.01 - + + 116.92 -1.09 0. 19.53 89.89 63.36 0. + + + 117.06 0.48 0. 19.53 90.41 63.51 0.

............................................................ ............................................................ augmented points t o make composite design ............................................................ ............................................................

a 0 0 117.62 2.95 18.75 92.61 63.18 0. -a 0 0 117.49 0. 18.75 89.79 61.92 0.18 0 9 0 116.45 0. 19.70 91.01 61.91 0. 0 -a O 114.54 3.36 17.80 88.62 62.68 0.42 0 0 a 118.68 1.69 18.75 91.21 64.86 0. 0 0 -a 114.61 0. 15.75 88.95 59.86 0.38 0 0 0 119.46 0.21 18.75 91.73 62.68 0.05

a:1.215 from 3eference(21)

CONCLUSIONS

1. Based on thermodynamic and a s p e c i f i e d economical

c o n s t r a i n t s , a l o c a l optiinum o p e r a t i n g p o i n t was found.

i . e .

Temperature = ll9lK

Weight r a t i o of oxygen t o c o a l = 0.72841

Weight r a t i o of s t e a n t o c o a l = 0.31384

2 . Comparing t h e p r o f i t of t h e optimum p o i n t w i t h t h o s e of

t h e expe r imen ta l p o i n t s r e p o r t e d by Savage, we found t h e

complete g a s i f i c a t i o n of c o a l l e d more p r o f i t t han

p a r t i a l g a s i f i c a t i o n thermodynamica l ly . The change of

t h e c o n t r a i n t s on t h e q u a l i t y of s o l i d product and t h e

economical pararneters would a l t e r t h e optimum o p e r a t i n g

p o i n t .

3. A f u r t h e r s t u d y on t h e o p t i m i z a t i o n of t h e f l a s h

c a r b o n i z a t i o n p r o c e s s shou ld i n c l u d e a nore r i g o r o u s mass

and energy b a l a n c e and c a p i t a l c h a r g e s . Also, t h e n a t u r e

of s h o r t r e s i d e n c e t ime of t h e p r o c e s s s h o u l d be t a k e n

i n t o a c c o u n t .

APPENDIX I

Coal, oxygen, and steam were fed a t ra tes of

2.27kg/h, 5000 c.c./m, and 2 c.c. water/m reapectiveljr.

Consider the feed coal contained 2.9 percent moisture and

11.5 percent ash. Then, t he feed r a t e of the moisture

and ash f r ee coal w a s 2.27 0.971 * 0.885 which was

equal t o 1.95069 kg/h. We a l s o applied the idea l gas law

t o calcula te the feed r a t e of oxygen on weight basis:

where

P : pressure , 1 atm

T : temperature, 298K

R : gas constant, 0.08205

V : volme, 5 l i t e r s (= 5000 c.c. )

the feed r a t e of steam was 2 c.c. water/m which was equal

t o 0.12 kg/h.

So,

the r a t i o of oxygen t o coal = 0.39262/1.95069

= 0.20127

the r a t i o of steam t o coal = 0.12/1.95069

= 3.0615

(1) Baughman, G. L., 'Synthetic Fuels Data Handbook1,

Cameron mgineers Inc. 1978.

(2) Probsteh R. F. and Hicks, R. E. 'Synthetic Fuels l ,

McGraw-Hill Book Co. p. 145, 1982.

(3) Mongold, 'Coal Liquefaction and Gasification

Technologies l , Ann Arbor Science p. 229, 1982.

( 4 ) Anderson, L. L. and D. A. Tillman, 'Synthetic Fuels from

Coal l , Wiley-interscience, p. 45, 1979.

(5) Spinks, A., J. M. Thorns a n d J . Gibson 'New Coal

Chemistry1, Philosophical Transactions of the Royal

Society of London p.112, 1981.

(6) Nowacki, P., 'Coal Gasification Processes, Enera

Technology Review; 70' Noyes Data Co. p.254, 1981.

(7 ) Energy Research and Development Administration,

'Handbook of Gasifiers and Gas Treatment System1, Dravo

Co. p.20, 1976.

(8) Coover, H. W. and R. C. Hart, ' A Turn i n the Road:

Chemical from Coalf, Chem. Eng. Frog., v.78, no. 4 , p.72,

1982.

(9) Savage, R. L. and W. J. Chen 'Process for the Concurrent

Production of Hydrogen, Carbon Monoxide and Low-

Volatile, Low-Sulfur Char by Flash Carbonization of

Coal1, Int . J . Hydrogen Energy V.7, No.9, p.717, 1982.

67

Volati le, Low-Sulfur Char by Flash Carbonization of

CoalT, I n t . J. Hydrogen Energy V.7, No. 9, p. 717, 1982.

(10) Wen, C. Y. and T. Z. Chaung Ehtrainment Coal

Gasification Modeling', Ind. Eng. Chem. Process Des.

Dev. V.18, No.4, p.684, 1979.

(11) Alain Chauvel, e t . a l , 'Manual of Economic Analjrsis of

Chemical Process', I n s t i t u t e Francais du Petrole p.3,

1978.

(12) Peters, M. S. and K. D. Timnerlnaus, 'Plant @sign and

Economics f o r Chemical Engineers , McGraw-Hill, p .147,

1968.

(13) Wei, J. 'A Stoichiometric Analysis of Coal

3asFfication1, Ind. Eng. Chem. Process Des. Dev., v.18,

No* 3, ~05549 1979.

( 1 4 ) Sherwood, T. K. 'A Course i n Process DesignT, *The M-I-T

Press, 1963.

(15) Batchelder H. K. and J. C. Sternberg, lIhemdynamic

Study of Coal Gasification1, Industr ia l and Engineering

Chemistry, v.42, no.5, p.878, 1950.

(16) Wiser, W. H. and S. S. Kithany, 'Equilibrium

T h e m d y n d c Correlations i n Coal Hydrogenation t o Gas

Pipeline Gas l , Fuel V.57, p.485, 1978.

(17) Zeleznik, F. J. and S. Gordon lcalculation of Corilplex

Chemical Equilibrium', Ind. m d Eng. Chemistry, V.60,

No.6, p.27, Jun. 1968.

(18) Kmdiner H. J. and S. R. Rrinkley, lcalculat ion of

Complex Q u i l i b r i m Relations l , Ind. and %go

68

Chemistry, v.42, no.5, p.850, 1950.

(19) Oliver, R. C., Stephanou, S. E. and R. W. Baier,

'Calculating Free Energy Minimizationt, Chemical

Engineering, Feb. , p. 19, 1962.

(20) Gordon, S. and B. J. McBri.de, 'Computer Program f o r

Calculation of Complex Chemical Equi l ibr iui

Composition, Rocket Perfornance, Incident and Reflected

Shocks, and Chapman-Jouguet Detonations , NASA Lewis

Research Center 1971.

(21) Beveridge G. E. G. and R. S. Schechter, 'Optimization:

Theory a?d Prac t ice t , McGraw-Hill Book Co. p.26, 1977.

(22) Beightler, C. S., D. T. Ph i l l ips and D. J. Wilde,

tFoundations of Optimization' , Prentice 'Hall, 1979.

(23) Wilde, 'Optimun Seek- Methods' Prentice Hall 1964.

(24) Stoecker, W. F., tDesign of T h e m 1 Sys t emt , McGmw-

S i l l Rook Company, p.179, 1380.

(25) Box, G. E. P., Hunter, and Hunter, ' S t a t i s t i c s f o r

Experimenterst, Wiley-Interscience, p.510, 1978

(26) Davis, 0. I., 'Design and Analysis of Industr ia l

Experiment , Hafner Publishing Co . , p .27 1, 1967.

(27) H ~ m l b l a u , D. M., 'Process Analysis by S t a t i s t i c a l

Methodt s John IIJiley Sons Inc. 1967.

(28) Box, G. E. P. and K. B. Wilson, 'On t he Experimental

Attainment of O p t i m Conditions1, J. Roy. S ta t . Soc.,

Ser. B, v.13, No.1, 1951

(29) Box, G. E. P., ' 'fie Exploration and Exploitation of

Response Surfaces: Some General Considerations and

69

Examples1, Biometries V.10, p.16, 1954.

(30) H i l l , W. J. and W. G. Hunter, ' A Review of Response

Surf ace Methodology : A Li tera ture Survey l ,

Techno~netrics V.8, No.4, p.571, Nov. 1966.

(31) Mead, R . and D. J. Pike, ' A Review of Response Surface

Methodology from a B ime t r i c Viewpoint1, Biometries,

V.11, No.31, p.803, Dec. 1975.

(32) Belt , R. J. and M. 4 . Roder, 'Pollution Control and

Energy NeedsT, Advances i n Chemistry Series 127 Editor:

R . M. Jimeson and R. S. Spindt, p.121, 1973.

(33)Box, G. E. P. and N. R. Draper, lEvolutionary

Operation1, John Wiley & Sons, Inc., 1969.

(34) Box, G. E. P., 'Evolutionary merat ion: A .mthod f o r

Increasing Industr ia l Productivity1, Applied

S t a t i s t i c s , v.6, p.81, 1954.

(35) Harder, E. L., 'Fundamentals of Flergy Production1,

John Wiley cSr Sons, p. 29, 1982.

(36) Hunter, J. S. and T. H. Naylor, lExperhenta1 Designs

f o r Computer Simulation Experiments l , Management

Science, V.16, No.7, p.442, 1970.

(37)Orainger, L. a n d J . Gibson, 'Coal Ut i l i sa t ion,

Technology, Economics and Policy1 , Halsted Press 9.377,

1981.

chang yeongsiang thesis flash carbonization

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