design and control a heat-integrated distillation …

DESIGN AND CONTROL A HEAT-INTEGRATED

DISTILLATION TRAIN

KENT E. BRYAN, B.5. in Ch

A THESIS

CHEMICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

CHEMICAL ENGINEERING

Approvea

C-Op':^ ACKNOWLEDGEMENTS

I would like to thank the members of my committee, Dr.

James B. Riggs, Dr. H. R. Heichelheim, and Dr. Ernesto

Fischer, for their help and encouragement for this research

I would also like to give special thanks to my wife,

Judy, for her unbending love and support.

Finally, I would like to thank Texaco, Inc., for their

financial support of graduate research at Texas Tech

University which made this research possible.

11

TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENTS i i

LIST OF TABLES v

LIST OF FIGURES vi

NOMENCLATURE ix

CHAPTER 1 INTRODUCTION L

CHAPTER 2 LITERATURE SEARCH 5

2.1 Design of Heat-Integrated

Distillation Systems 5

2.2 Control of Heat—Integrated Columns 15

CHAPTER 3 DYNAMIC MODELLING OF A

DISTILLATION COLUMN 23

3 . 1 Tray-to-Tray Model 23

3 . 2 Approximate Model 27

CHAPTER 4 CASE STUDY IN HEAT-INTEGRATED

DISTILLATION 32

4.1 Steady-State Design 32

4.2 Control System Design 3 5

4.3 Column Dynamic Modelling 40

CHAPTER 5 DYNAMIC MODEL OF COMPLETE

DISTILLATION TRAIN 45

CHAPTER 6 CONTROL LOOP STABILITY ANALYSIS 82

CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 90

LITERATURE CITED 92

APPENDIX A SHORT-CUT DISTILLATION DESIGN 95

1 1 1

PAGE

APPENDIX B COLUMN SPECIFICATIONS AND STEADY-STATE VALUES 97

APPENDIX C PURE COMPONENT DATA 98

APPENDIX D COMPUTER PROGRAMS 100

APPENDIX E OPEN-LOOP TRANSFER FUNCTION MATRICES 145

IV

LIST OF TABLES

PAGE

Table 1. Control Schemes for Double—Effeet Distillation 21

Table 2. Pairings of Manipulative Variables with Control Variables for Columns 1 and 2 41

Table 3. Pairings of Manipulative Variables with

Control Variables for Columns 3 and 4 42

Table 4. Relative Gain Array for Column 1 86



V

LIST OF FIGURES

PAGE

Figure 1. Double—Effeet Distillation System for a Binary Separation 2

Figure 2. Heat—Integrated System Using One Column to Supply Heat to Two Other Columns 3

Figure 3. All Possible Separation Sequences for a Four—Component Mixture 6

Figure 4. Design of a Heat—Integrated System using the Concept of Available Energy 9

Figure 5. Design of a Heat-Integrated System using Column "Stacking." 11

Figure 6. Example of Column Stacking to find Minimum Utility Usage 13

Figure 7. Double—Effeet Distillation System Studied by Tyreus 16

Figure 8. Thermally Coupled Column System

Studied by Ryskamp 18

Figure 9. Typical Sieve Tray 24

Figure 10. Process Reaction Curve 28

Figure 11 . Transfer Function Matrix 30

Figure 12. Proposed Steady-State Flowsheet 33

Figure 13. Degree-of-Freedom Analysis for a Binary Distillation Column 36

Figure 14. Control Loop Configuration for Columns 1 and 2 37

Figure 15. Control Loop Configuration for Columns

3 and 4 38

Figure 16. Response of Column 1 to Test 1 50



VI

PAGE


























vi i

PAGE

Figure 44. Response of Column 2 and Column 4 Pressure when Allowed to Float 79

Figure 45. Response of Column 2 Pressure and Column 3 Bottoms Composition to Limited Reboiler Duty 81

VI 1 1

NOMENCLATURE

B = bottoms flow rate (kgmol/hr)

D = distillate flow rate (kgmol/hr)

D = tower diameter (m) c

F = feed rate (kgmol/hr)

F = cooling—water flow rate to condenser cw

F = steam flow rate to reboiler s

h- = liquid feed enthalpy (kJ/kgmol)

h. = liquid enthalpy on tray j (kJ/kgmol)

H. = vapor enthalpy on tray j (kJ/kgmol)

h = height of liquid over weir (m) ow

K = first order steady—state gain

K, = proportional controller constant for bottoms level control

K, = proportional controller constant for reflux drum level control

K, = pressure drop coefficient dp

L, = liquid flow rate leaving tray j (kgmol/hr)

1 = length of weir w

M, = liquid level in column base (kgmol) b

M, = liquid level in reflux drum (kgmol) a

M. = liquid holdup on tray j

N = actual number of plates

N = minimum number of plates m

P . = pressure on tray j (atm)

* _ = vapor pressure (mmHg)

IX

Q = liquid flow rate (gal/min)

Q = condenser duty (kJ/hr)

Q = reboiler duty (kj/hr)

R = reflux rate (kgmol/hr)

R = minimum reflux ratio m

T = feed temperature (K)

T, = temperature of tray j (K)

T = coolant utility temperature (K) o

T = first order time constant (hr)

t , = first order time delay (hr) d

V = Vapor overhead flow rate (kgmol/hr) t

V, = vapor rate leaving tray j (kgmol/hr)

x^ = feed concentration

X. = liquid composition on tray j 1

y = vapor composition on tray j 2

Greek letters

O^ = relative volatility

A = relative gain 3

D . = vapor density on tray j (g/cm ) 3

3 j3 = liquid density (g/cm )

3 jp = vapor density (g/cm )

X

CHAPTER 1

INTRODUCTION

Distillation is widely used throughout the chemical

process industries to separate a mixture into pure com

ponents. Due to the high energy usage of most distillation

systems, methods to reduce energy consumption are being

explored. Initial investigations considered the selection

of the best possible sequence for the separation to reduce

utility costs. Later investigations included the selection

of the best sequence and the use of heat integration—the

process of using the overhead vapors of a high—pressure

column to drive the reboiler of a lower—pressure column.

There are numerous applications of heat integration for

distillation systems. An example for a binary separation is

shown in Figure 1. Instead of using one column to separate

the mixture, the feed is sent to two columns with the pres

sure of column 2 set such that the overhead vapor tempera

ture is greater than the bottoms of column 1. The example

shown is known as a double—effect distillation system. In

some instances, it is possible to use the overhead vapors of

one column to drive the reboilers of two or more columns.

This setup is shown in Figure 2. The overhead vapor rate of

column 3 must be large enough'to provide the required re

boiler duties of columns 1 and 2. Pressures of columns 1

and 2 are normally set such that they have the same bottoms

temperature. The use of heat integration reduces the over-

•• A

X A B

O - 3

- ^ B

Figure 1. Double-Effect Distillation System for a Binary Separation.

r ^ <N

a a. 3

CO

o

c E 3 r-( 0

u

C

o

c CO CO

£ S 3 (D r-l

j-> 0

•o r 0) ^

JJ o (tJ u o tio ? 0) 5—

C 0

I

(TJ u O 0)

CM

0) u 3 60

all energy consumption nearly 50 percent (Roffel and

Fontein, 1979) when compared to a conventional system using

steam reboilers and water—cooled condensers. Thus there is

an economic incentive to use heat-integrated distillation

columns.

Heat integration provides substantial utility savings

but presents many control problems. The common reboiler-

condenser affects operation in both columns, making it dif

ficult to maintain product qualities. Any change in the

vapor rate of the high—pressure column affects the perfor

mance of the low—pressure column. The control problems

encountered may reduce the economic incentive to use a heat-

integrated system. The purpose of this research is to

design a reliable control strategy for a heat-integrated

distillation system that can overcome the effects of the

common reboiler—condenser and still maintain product

quality, thus utilizing the economic incentives of heat

integration.

CHAPTER 2

LITERATURE SEARCH

2.1 Design of Heat—Integrated Distillation Systems

The first criterion for the design of a heat-integrated

distillation system is determining the optimum sequence for

a given separation problem. For example, Figure 3 shows all

the possible sequences for the separation of a four—com

ponent mixture. King (1980) reports four heuristics, or

"rules of thumb," to determine which sequence is best.

These are:

(1) Separations where the relative volatility of the

components is close to unity should be performed in

the absence of non—key components.

(2) Sequences which remove the most volatile com

ponents one by one should be favored.

(3) Separations in which the distillate flow nearly

equals bottoms flow should be favored.

(4) High-recovery separations should be performed last

in a sequence.

The above heuristics are applicable to sequences with or

without heat integration. Heat integration does not change

the sequence, it determines the heat-exchanger network for

the sequence.

Figure 3 All Possible Separation Sequences for a Four-Component Mixture.

The first investigation of heat-integrated distillation

system synthesis was performed by Rathore, Van Wormer and

Powers (1974a, b ) . This scheme was started by generating

all possible reboiler-eondenser energy matches making sure

that the most volatile component went overhead in any column

and the least volatile component went to the bottom. The

overall problem was decomposed into subproblems consisting

of two columns, with the objective of matching the reboiler

duty of one of the columns to the condenser duty of the

other. Operating pressures and capital costs were estimated

for each subproblem. The total cost of each sequence was

determined by summing up the set of subproblems. The se

quence with the least cost was the optimum one.

Morari and Faith (1980) developed a synthesis procedure

using Lagrangian multipliers to calculate a lower utility

bound for a sequence. A flowsheet was chosen and the opti

mal cost of the flowsheet formed the upper bound cost.

Lower bounds on all possible sequences were calculated. Any

sequence with a lower bound higher than the upper bound was

discarded. The upper bound was improved and any flowsheet

whose lower bound exceeded the new upper bound was discar

ded. The optimum sequence was the one with the lowest cost.

Naka, Terashita and Takamatsu (1982) studied the syn

thesis of heat-integrated systems by using the concept of

available energy. The available energy concept for a dis

tillation sequence is the process of using heat sink and

8

heat source streams to provide the heating and cooling

requirements for each column. Heat sink streams include

cold utilities and heat demands of reboilers. Heat source

streams include hot utilities and the heat removed by con

densers. The synthesis problem is the process of maximizing

heat sources and sinks to minimize utility heating and

cooling requirements. This can be represented by a 1—(T /T)

versus Q diagram, where T is the coolant utility tempera— o

ture, Q is the reboiler or condenser duty and T is the

corresponding reboiler or condenser temperature. The dia

gram matches heat sources with heat sinks (the condenser

duty of one column is matched to the reboiler duty of

another column). A match is only possible where the tem

perature of the overhead vapors of a high pressure column is

greater than the bottoms temperature of a lower pressure

column. An example of this diagram is shown in Figure 4.

The horizontal lines represent the duty match and the verti

cal lines are used for connecting purposes. The vertical

lines are not perpendicular to the abscissa because the

horizontal distance traversed by these lines represents the

sensible heat change. Figure 4 shows that the reboiler duty

of column 1 is matched with the condenser duty of column 4.

Thus, in this example, the overhead vapors of column 4 would

be used to drive the reboiler of column 1 and the overhead

vapors of column 3 would be used to drive the reboiler of

Steam

Cooling water

Figure 4. Design of a Heat Integrated System using the Concept of Available Energy

10

column 4.

Configuration of a possible sequence would begin with a

proposed process flow sheet. Flow rates or reflux ratios

can be adjusted so that the condenser duty of one column

matches the reboiler duty of another column. The design may

not be optimum to begin with. An optimum sequence can be

found by drawing a 1-(T /T) versus Q diagram for each se-o

quence and estimating the utility usage and capital cost.

The sequence with the lowest capital cost and utility usage

would be the optimum one.

Andrecovich and Westerberg (1985) developed an algo

rithm based on the assumption that Q A T , the product of the

reboiler or condenser duty and the temperature difference

across the column is constant over a wide range of pres

sures. A T—Q diagram shows this product as an area and an

example is shown in Figure 5A. This diagram is used to

"stack" the columns between the coldest coolant utility

temperature and the highest hot utility temperature. Reduc

tion of the overall utility usage of a given sequence is

done through the concept of multi—effect distillation. Mul

ti-effect distillation is the process of splitting the feed

of a column into two parts and sending it to two columns.

The pressure of one of the columns is selected such that its

overhead vapor temperature is higher than the low pressure

column's reboiler. This procedure will reduce the overall

utility usage of the column by one—half. In the example

11

(5A) (5B)

3

1

2b

2a

Figure 5 Design of a Heat Integrated System using Column "Stacking."

12

shown in Figure 5, the only way to reduce the overall

utility consumption of the sequence is to reduce the duty of

column 2. A multi-effect distillation design is used for

column 2 and the result is shown in Figure 5B. Other col

umns could be selected for a multi-effect application as

long as the column stacking remained between the boundaries

mentioned above. Notice that the column stacking selects

the temperature and pressure for each column.

The procedure for determining the best possible se

quence begins by calculating QAT for each possible column in

the sequence. The T—Q diagram is drawn and multi—effect

distillation is applied to the column with the largest

reboiler duty. An example for the separation of a 5 com

ponent mixture is shown in Figure 6. For the separation of

components A, B, C, D, and E, column 1 separates component

A, column 2 separates component B and so forth. In this

example, multi—effect distillation is selected for column 1,

reducing its reboiler duty by one—half. The capital costs

and utility costs of this sequence are compared to the cost

of the non-heat integrated sequence. If the economics are

favorable, the use of multi-effect distillation continues.

Column 1 and then column 3 undergo multi-effect distilla

tion. When the incremental capital costs exceed the incre

mental utility savings, the investigation of the sequence is

stopped and another sequence is investigated. The minimum

13

(6A) (6B)

3b

3a

Figure 6 Example of Column Stacking to find Minimum Utility Usage.

14

utility configuration is shown in Figure 6B. Heat integra

tion has to stop at this point because the temperature

limits would be exceeded at the next step.

Shankar (1985) developed a method to determine the

optimum heat-integrated distillation sequence by defining an

Overall Difficulty of Separation factor for a given separa

tion problem. The ODOS was defined as

ODOS = (Q /dt)/F c

where dt is the temperature difference across the column and

F was defined as

F = min(L/V, V/L)

where V and L are the total amounts of top and bottom pro

ducts, respectively. The purpose of this research was to

find the best separation sequence and use this sequence for

heat integration. The use of the ODOS selected the best

sequence as well as "good" sequences and eliminated in

efficient ones.

For a given separation problem, Q and dT were calcu

lated for each binary separation. Values of F were then

determined for each separation in a group. For example, F

values would be calculated for A/BCD, AB/CD, and ABC/D for a

four—component separation where the slash represents the

split. The ODOS was then determined for each separation and

normalized by dividing by the smallest value. A large ODOS

15

meant that the separation was inefficient and these separa

tions were eliminated from further investigation. Small

values of ODOS meant that the separation was "good" and

still should be investigated. In this method, all sequences

were evaluated using the ODOS and the sequences with an ODOS

less than 4.0 were retained.

2.2 Control of Heat-Integrated Columns

The first extensive study in the control of heat inte

grated columns was performed by Tyreus (1975). This study

used a digital simulation of a two column system under high

and low reflux conditions. A simplified flowsheet of the

columns is shown in Figure 7. Tyreus investigated a number

of control loops to control four compositions, bottoms and

distillate of each column. The base case used feed split to

control bottoms composition in column 2, the low pressure

column. Vapor boilup controlled bottoms composition in col

umn 1. Distillate flow in both columns controlled dis

tillate composition. This scheme led to strong interactions

between the columns and both bottoms compositions were im

possible to control. The most reliable control system used

both an auxiliary reboiler and condenser. For column 1,

distillate was used to control column pressure and vapor

boilup was used to control bottoms composition. For column

2, distillate flow controlled liquid level in the reflux

drum. The heat-transfer rate in the auxiliary condenser

16

^H>f« f

03 3 (D U >s

>s

V 0)

T3 3

en

E 0)

00 >

cn

m

4J

u 0)

u I 0)

l—t

3 O

Q

0)

3 to

17

removed excess heat from column 1 and the trim reboiler was

used to makeup heat deficienees in column 2. This allowed

for bottom composition control in column 2. Distillate com

position in both columns was controlled by a reflux—to—feed-

rat io .

Roffel and Fontein (1979) studied the distillation of a

binary mixture using a conventional column, a column with

vapor recompression and a two column heat-integrated system.

For the heat-integrated system, distillate flow and bottoms

flow controlled liquid levels in the reflux drum and column

base, respectively. Referring to Figure 7, the reflux ratio

of column 2 was set as a function of the feed composition to

control distillate composition. The heat—transfer rate of

the condenser of column 2 was on pressure control. For

column 1, the heat—transfer rate in the reboiler was on

pressure control and reflux was used to control distillate

composition. Control of bottoms composition in both columns

was ignored. The feed split between columns 1 and 2 was

kept constant.

Ryskamp (1980) described a control system for thermally

coupled columns. His flow scheme differs from that of Tyreus

and is shown in Figure 8. This control scheme keeps the

heat—transfer rate constant in the common reboiler-eonden

ser. The vapor overhead signal of column 1 was sent to a

multiplier and summer. The top composition controller used

18

• ]K}-p •'

J ,

«N >

UgJ

r\ - ISO

\y

^

D •i-t

T3 3

in

s

CO

en

c 3

r-4 0

U

ID r-t

a. 3 0 u •

IJ CO e > o

CD

0}

u 3 00

1

19

the multiplier to set the distillate flow. Reflux flow was

adjusted to keep reflux plus distillate flow (R+D) constant.

For the high pressure column, column 1, heat input was on

pressure control to generate vapors and keep the heat bal

ance. Feed rate controlled bottom composition. Heat input

for the trim reboiler on column 2 was on bottoms composition

control .

For column 2, distillate composition was controlled by

the D/(R+D) signal. Feed or bottoms flow can be used to

control bottoms composition or bottom.s level. Due to de

creased time delay, bottoms flow was on level control lea

ving feed rate to control bottoms composition. Feedforward

control was used on heat input for the trim reboiler. Heat

transfer in the common reboiler-eondenser was subtracted

from the total heat required and the difference set the heat-

transfer rate in the trim reboiler.

Lenhoff and Morari (1982) investigated the control of

heat integrated columns by defining a dynamic performance

index (DPI) and an economic performance index (EPI). The

DPI was a measure of the operational aspects of the struc

ture and the EPI was a measure of the steady—state aspects.

The objective of the research was to minimize both indices.

Changes in flowsheet configurations and column specifica

tions were made to evaluate EPI. Changes in the control

loops were made to evaluate DPI. It was discovered that the

minimization of one index usually led to an increase in the

20

other index. If upsets were considered likely to occur, a

configuration with a low DPI should be used. If few upsets

were aniticipated, a configuration with a low EPI should be

used.

Frey, et al., (1984) studied a system similar to the

one studied by Tyreus. This study looked at four different

control loops to control all four compositions. The four

control schemes are shown in Table 1. Control schemes 1,2,

and 3 showed strong interaction and were discarded. Control

scheme 4 greatly reduced the interaction and its control

action is described. Referring to Figure 7, bottoms composi

tion in column 2 was controlled by a vapor boilup to feed

ratio (V /F ). The bottoms composition was measured, set-

ting the V^/F^ ratio. The flow rate of V was measured and

the feed rate was set as the product of the V flow rate and

the inverse of the V /F ratio. The feed rate to column 1

was the difference between total feed rate and F . For top

composition control in both columns, a reflux—to—overhead-

vapor ratio (R/V ) control was used. Distillate composition

was measured setting the R/V^ ratio. Reflux was set as the

product of the inverse of the R/V^ ratio and the V flow

rate. Vapor boilup controlled bottom composition in column

1. This method allows for all four compositions to be con

trolled without introducing the added costs of a trim re

boiler or condenser. Pressure—control loops were assumed

Table 1. Control Schemes for Double—Effect Distillation.

21

Control Variable in

Control Scheme #2 #3 #4

• b l

d l

•b2

• d 2

^1

^1

F, /F ,

^1

F^/F,

D.

V.

V / F 2 ^ 2

V.

22

not to have any interaction with the composition loops and

were not investigated.

Buckley (1983) briefly described a control scheme for a

heat—integrated system in which the pressure of the column

supplying heat was allowed to float. This usually led to a

system in which no trim condensers or reboilers were needed

and a simpler control scheme since there was no need for

pressure control.

CHAPTER 3

DYNAMIC MODELLING OF A

DISTILLATION COLUMN

3.1 Tray-to-Tray Model

The first step in developing a dynamic model for a

distillation column begins by performing unsteady—state mass

and energy balances around each tray. For a typical sieve

tray, shown in Figure 9, the equations are:

Total Mass Balance:

Component Mass Balance:

Overall Energy Balance:

Equation (2) assumes either a binary or psuedobinary system

for the column. The above equations assume that the vapor

holdup on each tray is negligible compared to the liquid

holdup. For the feed tray, the equations are:

Overall Mass Balance:

dM./dt = L.^, + V, . - V - L. + F (la)

Component Mass Balance:

Overall Energy Balance:

d«.h./dt = Lj^^h,^^ + Vj-l"j-l - ^j«j "h^j * ^^i <^^^

where j is the feed plate, F is the feed rate, x^ is the

23

'j+i

24

j -1

7.

f '3-1

L.

Figure 9. Typical Sieve Tray.

25

feed concentration, and h- is the liquid feed enthalpy. The

balances at the bottom and top of the column are, respec

tively :

Overall Mass Balances:

dM /dt = L^ - V^ - L^ (lb)

dM ,/dt = V , ^ - L . - D (Ic) 2 J - 1 2

Component Mass Balances:

dM^x^/dt = L^x^ -v^y^^ "^l^^l ^^^^

dM.x./dt = V. y. - (L. + D)x. (2b) 2 2 3 - 1 3 - 1 2 2

Overall Energy Balances:

dM h. /d t = L h - V H - L h +Q (3b) 1 1 2 2 1 1 1 1 r

dM^h^/dt = Vj_^Hj_^ - (Lj+ D)hj - Q (3c)

where tray j is the condfenser, Q is the reboiler duty, Q r c

is the condenser duty and L is bottoms flow rate.

Algebraic equations for phase equilibria, thermal

properties and equations of motion are also needed to

complete the model (Luyben, 1973).

Phase equilibrium:

y . = f (X,, T ., P .) (4) 2 2 2 2

Equations of Motion: Liquid: L = f(M,, V., X., T., P.) (5)

j 2 2 2 2 2

Vapor: V = f(P ., P . ,, Y ., T .) (6) j 2 J - 1 2 2

Thermal properties:

h = f (X ,T .) (7) 2 2 2

H = f(y .,T .,P .) (8) 2 2 2 2

h ^ = f(x^,T^) (9)

26

Lamb, et al., (1961) studied column dynamics by assum

ing equal molar overflow and constant tray holdups. These

assumptions led to equal vapor and liquid flow rates through

the stripping and rectifying sections and the left hand side

of equation 1 was set equal to zero. The model was reduced

to a material balance problem with one differential equation

for each tray. Huekaba, May and Franke (1962) included the

energy balance in their model by correlating enthalpies as

functions of composition. Equations (I) and (3) were

rearranged to solve for the vapor rate on each tray and the

enthalpy functions were used to calculate the time deriva

tive dh./dt. Luyben (1973) assumed equal molar overflow and

constant relative volatility to model a binary distillation

column. For a multicomponent column, pressure was assumed

constant, liquid hydraulics were calculated by the Francis

weir formula, perfect level control was assumed in the

reflux drum and column base and the energy balance was

assumed to be constant. Tung (1979) developed a similar

model to the one developed by Huekaba, et al., and incor

porated tray hydraulics to account for the time delay in the

response of bottoms composition to reflux rate pulses.

Weischedel (1980) developed a model for a binary system

assuming a constant energy balance, ideal solution behavior,

perfect level control in the reflux drum and column base,

and a one minute time—delay to model the composition meas

urement system. Holland and Liapus (1983) described the

27

modelling of a distillation column including tray hydraulics

and the control system. Equations for proportional—integral

controllers were developed and included in the model.

Equations (l)-(3) can be solved simultaneously and then

equations (4)-(9) can be used to calculate column profiles

of L, V, T, y, X, and P to any step input. Equations (1)-

(3) form a "stiff" set of differential equations. This

means that the system is made up of a system of equations

that represent both slow and fast dynamics. The overall

mass balance will come to steady—state before the component

mass balance. A number of integration techniques have been

proposed to solve the system of equations. Lamb, et al.

(1961), used a Runge—Kutta method with an Adams predictor-

corrector. Euler's method has also been used (Luyben,

1973). Gear's method (Gear, 1971) specifically designed for

stiff systems, has been used by Weischedel (1980) and

Holland and Liapus (1983).

3.2 Approximate Model

Most chemical processes, including distillation col

umns, respond linearly to small input step changes. For

example, bottoms composition response to a small step change

in feed rate should behave as shown in Figure 10 (Coughanowr

and Koppel, 1965). This behavior can lead to an approximate

dynamic model for the column. The plot of Figure 10 is known

28

(0 >

3 U

c 0

u 03

csi

OS IB (0 0 0 u au

(0 u 3

29

as a process reaction curve and the tray—to—tray model

described previously can be used to plot reaction curves for

each output. A step change in X (input variable) is made

and the tray—to—tray model is used to record the output

variable (Y) response. The response is plotted versus time

as shown in Figure 10. From this reaction curve, the re

sponse can be modeled as:

G(s)=K(exp(-t s)/(Ts+l) d

where K is the gain, t is the time delay and T is the time

constant. Values for T and t, can be estimated by deter-a

mining the times at which the response Y reaches 28.3% and

63.2% of its final value. From these two time values, T and

t, can be calculated by solving the two following equations d simultaneously (Clements, 1980):

^0.23 = d * ^^3

^0.63 = d * ^

The proportional gain, K, is calculated as the ratio of the

change in Y to the change in X.

All output responses can be determined in this way to

form a transfer function matrix for the column, as shown in

Figure 11. The approximate model uses the matrix to show

the response of any output to any input step change. The

algorithm consists of summing up each response to calculate

the final response (Stephanopoulous, 1984). An example for

30

^—w 1 (0

e i H t j

1

a X <u

c f - ^

: i !<

+ CO

c »^

H

/ — N

(0

c «V| T3

1

CU X <u

c CN

^^

+ CO

f»

CM H

• cn

c m T3

1

O. X (U

c en

^

+ CO

f H

en

c en

c e

c CO

c 6

X

,<—\ CO

CM r-t -T3

1

O. X (U

«N r-H

i^

+ CO

CM ^

H

X - N

CO CM CM

T3

1

C X (U

CM CM

:^

+ CO

CM CM

H

/-^ CO

f?^ •«

1

o. X <u CM

m 'bti

+ CO

c f

H

CM

cn

CO CM e

- 3 •u

1 C. X OJ

CM

s :^

f - t

+ CO

CM

e t*

c o

•r4

0 c 3 u. u 0)

3)

c u H

X

^—s

CO T - (

f-H •^

1

c X (U

f H ' . — ( '

:2i^

+ CO ^ P H

f -

/-^ (0

f - (

CM T3

1

a X (U

f - <

CN

u.

+ CO

r-t CM

H

--v CO

f H

m TJ

1

a. X (U

1—(

r i u:

+ to

p

f H

X

S •a

a X

t-H m

(0 u 3 00

CO

>* m

31

a 2 X 2 matri X IS :

Y^(s)

Y2(s)

G,^(s)

G^2^s)

G,,(s)

G^^Cs)

X^(s)

The response of Y and Y can be calculated by

Y.(s) = G,^(s)X,(s) + G,^(s)X,(s) 11 12

Y,(s) = G^,(s)X-(s) + G,,(s)X,(s) 21. 22

In the time domain, the response can be determined by inte

grating the following derivatives:

dY^/dt = (K^iX^(t-t^,,)-Y^)/T^, ^

^^2^2<^-^dl2>-^^/^12

dYl/dt = (K-.,.X-(t-t^^, )-Y )/T ,. + 21 "I d21 21

(K22X2(t-t^22^~^2^^'^22

where Y, refers to either the initial conditions or the J

value of the function at the previous time step. The re

sponse is zero when the integration is performed over a time interval less than or equal to the time delay.

CHAPTER 4

CASE STUDY IN HEAT-INTEGRATED

DISTILLATION

To study the design and control of a heat-integrated

system, the separation of a four-component mixture was cho

sen. The feed composition was:

Feed Component Feed Cone.

C^ 0.15

C^ 0.20 6

C^ 0.40

Cg 0.25

Feed Rate = 500 kgmol/hr

One feature of this example is the large concentration of C-,

in the feed. It may be possible to use the overhead vapors from a C —C splitter to drive the reboilers of two or more

7 8

columns.

4.1 Steady-State Design

The design procedure of Naka, et al., was used to

construct the process flowsheet. The design procedure began

by constructing a possible process flowsheet. This flow

sheet consisted of a double—effect column for the dspentani-

zers, followed by a dehexanizer, then a C -C splitter.

This flowsheet is shown in Figure 12. Feed rate and reflux

of column 1 was set such that the reboiler duty of column 1

matched the condenser duty of column 2. The pressure of

32

00

33

v0

K

r ^

en

<j.

CM

- T

0) (D

CO

0

in I

•o (0

j j

cn

•o 0) CO 0

a 0 u a.

CM

0}

3 00

l O v ^ r^ 00 CJ CJ U O

34

column 2 was set such that its overhead vapors temperature

was 10 degrees (K) greater than the bottoms of column 1.

The pressure of column 3 was set so that its bottom tempera

ture was about the same as the bottoms temperature of column

2. The reflux of column 4 was set such that the condenser

duty of column 4 matched the reboiler duties of columns 2

and 3. Column 4 pressure was set such that the temperature

of the overhead vapors of column 4 was 10 degrees greater

than the bottoms of columns 2 and 3. Heat requirements for

column 4 were supplied by a reboiler using 600 psia steam.

A computer program (Chang, 1980) using standard short-cut

techniques as described in Appendix A was written to design

each, column. A listing for the program is shown in Appendix

D. Steady—state values for flow rates and column design

specifications are shown in Appendix B.

The economic incentives for the proposed flowsheet were

determined by a comparison with a standard flowsheet using 3

columns to separate the mixture. Each column in the stand

ard flowsheet used a steam reboiler for heat input. Steam

pressure for the standard flowsheet was assumed to be 100

psia. Steam cost was estimated by using a base cost of

$2.73/MMBtu for natural gas and a boiler efficiency of 80

percent. The base case used 34260 #/hr of 100 psia steam and

the proposed flowsheet used 8960 #/hr of 600 psia steam,

resulting in an annual estimated savings of over $200,000

per year.

35

4.2 Control System Design

The first step taken in designing the control system

was performing a degrees—of—freedom analysis around each

column to determine possible pairings of manipulative varia

bles with control variables. A better understanding of this

analysis starts by looking at a conventional column. The

degrees—of-freedom analysis for a conventional column is

shown in Figure 13 (Stephanopoulos, 1984). Figure 13 shows

that each control variable can be paired with a manipulative

variable. A control scheme for this column might manipulate

bottoms and distillate flow to control liquid levels M^ and

M , respectively. Distillate and bottoms composition could d

be controlled by reflux and steam rate, respectively. Column

pressure could be controlled by the cooling—water rate. A

column in a heat—integrated system may lose degrees of

freedom and it may not be possible to pair a control var

iable with a manipulative variable. For example, in Figure

12, heat transfer in the common reboiler-eondenser for col

umns 1 and 2 cannot be manipulated. This implies that

bottoms composition of column 1 and the pressure of column 2

cannot be controlled unless other manipulative variables are

introduced.

Using the control ideas of Ryskamp, Frey, et al., and

a degrees—of—freedom analysis for each column, a suggested

control scheme for the flowsheet of Figure 12 is shown in

Figures 14 and 15. It was decided to use distillate and

3 6

^ o u ij

a o u

00 (U

fH

ua a) •H U <a >

J2 -o X X

' t t t f

(V4 X «,

CO

a a. a

Eb.

rrrrr 3

CO o

3} >

•H <U CO CQ 3J

a . CQ >H -H a u <Q eQ s >

(0

u 0 u 03

•»H CO >s

f H

fl

c <

E 0

T3 0) (S U u. 1

^ 0 1 m 0) 0) u 00 0

Q

• C E 3

i - <

C u

c 0

•f-»

^ (5

f H

f H f-l

4J 00

• H Q

> U (B c fl

33

<r)

0) U 3 60

37

(-•/** tV / ' / ' -»v-

M i l l

-i-r- - A :

Figure 14. Control Loop Configuration for Columns 1 and 2.

38

r-<Sri

(M: i r ^ rMSH

en

* l-O :>vy^

CM

c a

O 'J

'<>4

CM

3

o

o

•0

c

m CO C £ 3

rH 0 u u 0

c

0

(0

u 3 &0 c o 'J

a 0 0

0 u c 0 u

i n

0

3 tio

' f

39

bottoms flow rates for control of liquid levels in all

columns, leaving only three control variables—pressure and

both compositions.

For column 1, bottoms composition was controlled by a

vapor—boilup—to—feed ratio. The bottoms composition con

troller sets the ratio and the feed rate was set as:

F = V^ (X^/X^ )/(V /F^ ) 1 1 b bs 1 1

Pressure was controlled by the heat—transfer rate in the

condenser. Distillate composition was controlled by a re

flux—to—vapor-overhead (R/V ) ratio. The distillate compo— t

sition recorder sets the ratio and the reflux rate was set

as :

R = V^(X, /X,)(R/V^) t ds d t

Feed rate to column 2 was set as the difference between

the total flow rate and F . Due to a loss in the degrees of

freedom, either pressure or bottoms composition in column 2

can be controlled by a trim reboiler, but not both. It was

decided to put the trim reboiler on pressure control because

a drop in pressure reduces the heat transfer across the

common reboiler-eondenser affecting the performance of col

umn 1. Distillate composition was controlled in the same

manner as described for column 1. Bottoms composition of

column 2 was not controlled.

40

Bottoms composition in column 3 was controlled by the

heat—transfer rate in a trim reboiler. Pressure was con

trolled by the heat—transfer rate in the condenser. Dis

tillate composition was controlled by a reflux—to—vapor-

overhead ratio control.

Distillate composition in column 4 was controlled by

the same method as in the other columns. The heat—transfer

rate in the reboiler was on pressure control because of the

need to generate enough overhead vapors to drive the re

boilers for columns 2 and 3. This arrangement leaves the

feed rate as the only variable left to control bottoms

pressure. It was decided to send the bottoms of column 3 to

a storage tank and let the bottoms compostion recorder of

column 4 set the feed rate. A summary of the pairings of

manipulative variables with control variables is shown in

Tables 2 and 3.

4.3 Column Dynamic Modelling

To understand the flowsheet dynamics, a tray-to—tray

dynamic model was developed for each column. Equations (1)

and (2) from chapter 2 were used to describe the dynamic

behavior of the liquid holdup and liquid composition on each

tray. The energy balance and the overall mass balance were

combined to solve for the vapor rate on each tray.

41

Table 2. Pairings of Manipulative Variables with Control Variables for Columns 1 and 2.

Column 1

Manipulative Control ^^^^^^1® Variable

^ X

B

D

R

Q c

B

D

R

Q

Column 2

b M b

M d

X d

M b

M d

X d

42

Table 3. Pairings of Manipulative Variables with Control Variables for Columns 3 and 4.

Column 3

Manipulative Control ^^^i^^l^ Variable

B

D

R

Q

Q

"d

^d

F

B

D

R

Q,

Column 4

"b

"d

= 4

43

Ch 1-h ") 4- V CH -h "i-

j J+1 V.=(L._ (h._^l-h.) + V. ^ (H. -h. ) -

J+I J 3-1 J-1 J M,(dh./dt))/(H -h ) 3 3 J J

It was assumed that the term M.(dh./dt) was small in com-J J

parison with the other terms in the equation and was ig

nored. The Francis weir formula (Bolles, 1946) was used to

equate liquid holdups to liquid rates on each tray.

h = 0.48(Q/1 ) ' ^ ^ ^ ow w

where Q is liquid flow rate in gal/min and h and 1 have ow w

dimension of inches. The following equation was used to

determine pressure drop as a function of the vapor rate

(Luyben, 1973). «

P. , - P. = K, j>. V^

where jj , refers to the vapor density. Liquid level in the

reflux drum and liquid level in the column base were con

trolled by distillate flow and bottoms flow respectively.

Proportional control was used.

D = D + K. (M, -(M,)^) r d d a r

B = B + K, (M, - (M, ) ) r b b o r

Each column was assumed to be adequately described as a

psuedobinary system. Recovery of the light key in the

distillate of upstream columns was specified so that it

would not affect the operation of a downstream column.

44

Calculation of thermal properties and vapor-liquid equilib

rium were made assuming ideal solution behavior. Calcula

tion of pure component data is shown in Appendix C. The set

of differential equations was solved by the Gear method.

Appendix D shows a simplified flowsheet for the program and

the program listing.

The tray—to—tray model was used to determine the open-

loop transfer function matrix for each column. Step changes

were made in feed rate, feed composition, reflux rate,

reboiler duty and condenser duty to form the matrix for each

column. For example, the feed rate to column 1 was changed

by 2% and the response of the column pressure and bottoms

and distillate compositions were plotted against time. From

these plots, steady—state gains, time delays and time con

stants were determined as described in Chapter 2. The

matrices are shown in Appendix E. The column matrices were

combined with the proposed control scheme to develop an

overall dynamic model of the system. The overall dynamic

model is described in Chapter 5.

CHAPTER 5

DYNAMIC MODEL OF COMPLETE

DISTILLATION TRAIN

To describe the dynamics of the complete distillation

train the approximate dynamic column models were combined

with the proposed control strategy. The open—loop transfer

function matrices were used to predict the behavior of each

column to any step change. The control strategy was then

implemented to bring product specifications on line. The use

of the model can be explained by describing the procedure to

model the response of columns 1 and 2. First, a step change

was introduced into the total feed rate. Since the step

change reaches these two columns at the same time, their

responses were calculated simultaneously from the open-loop

transfer function matrices. The control equations then

checked column pressure and compositions to determine what

action to take. Any output that was off specification

forced the necessary control action. Finally, bottoms flow

rate of both columns were added together and sent to col

umn 3. Column responses were recorded every 3 minutes.

To describe the flowsheet dynamics more accurately,

time delays between the columns were included during the

initial introduction of the step change to the system. Nine

minutes after the step change was introduced, the heat-

transfer rate in the common reboiler-eondenser of columns 1

and 2 would change. Fifteen minutes after the step change,

45

46

the feed to column 3 would be affected. At time equal to 25

minutes, the feed to column 4 would change. The last effect

of the step change would be to change the heat-transfer rate

in the reboilers of- columns 2 and 3 forty—five minutes after

the step change. After 45 minutes, it was assumed that any

system changes would occur continuously.

The dynamic model used the following assumptions:

1) The dynamics of the bottoms, distillate and vapor

overhead rates were assumed to occur almost instan

taneously and were determined from steady—state

calculations.

2) The dynamics of the pressure, bottoms and distil

late composition and the vapor boilup were calcu

lated from the approximate dynamic model for each

column.

3) Heats of vaporization were constant for the over

head vapors and bottoms of each column.

4) No subcooling of the reflux in columns 2 and 4

was allowed.

5) Feedback control of pressure in each column was

under proportional control. Feedback control of

bottoms composition of columns 3 and 4 was under

proportional control.

47

6) The storage tank between columns 3 and 4 was large

enough to handle all upsets in flow rates and its

dynamics were neglected.

The listing for the program is shown in Appendix D.

The proportional controller settings were initially

calculated by the method of Cohen and Coon (1953) for

single—input, single—output systems. This led to good con

trol for columns 1,2 and 3 but led to serious interaction

between the control of column pressure and bottoms compo

sition in column 4. To overcome this interaction, the

controllers were tuned by using the Routh stability cri

terion as described by Stephanopoulos (1984). The column

was reduced to a 2 X 2 transfer function matrix with the

controlled variables being bottoms composition and column

pressure. The two manipulative variables were the feed rate

and the heat—transfer rate in the reboiler. The transfer

function matrix now becomes:

X = -.243E-2exp(-.05s) F + .41lE-7exp(-.lls)Q b .433s + 1 .420s + 1 ^

P = -.151E-1 F + .118E-5 Q .048s + 1 .032s + 1 ^

The stability of the above system was determined by deter

mining the roots of the characteristic equation

Q(s) = (1+H G )(1+H^^G ) - H ^H^ G G^ = 0 (10) 11 1 22 2 12 21 1 2 ^

48

where H,, are the four transfer functions above and G 13 J

refers to the transfer functions of the controllers. If the

roots of the above equation have negative real parts, the

system is stable. Setting G, to K, and Go to K2 and substi

tuting the transfer functions in the above equation, equa

tion (10) becomes.

Q(s) = (I -/.243E-2 .433s + 1

.118E-5 032s -H

( .411E-7 A { -.151E-1 > V .420s + 1 y \ 048s + 1 J

K-,_K2 = 0

The above equation was rearranged in powers of s and then

the Routh stability test was used to calculate the con

troller settings. K^ was set to 2.5E5 kj/hr/atm, leading to

a value of 425.0 kgmol/hr for K . These values produced

stable results.

The following tests were performed to determine the

reliability of the proposed control strategy.

Test 1: Increase total feed rate to 525 kgmol/hr.

Test 2: Decrease total feed rate to 480 kgmol/hr.

Test 3: Increase total feed rate to 525 kgmol/hr and

decrease C concentration by 3 percent. Oc

tane concentration would be increased.

Test 4: Decrease total feed rate to 480 kgmol/hr and

decrease C-, concentration by 3 percent.

49

Test 5: Increase feed rate to 525 kgmol/hr and reduce

the heat of vaporization of each column's

overhead vapor by 3 percent, simulating a

rainstorm.

Test 6: Decrease feed rate to 480 kgmol/hr and simu

late a rainstorm.

Test 7: Increase feed rate, decrease C_ concentration

and simulate a rainstorm as described above.

Figures 16 through 19 show the response of each column

to Test I. Notice that the control scheme of column 4

reduced the feed rate nearly to the steady—state value. The

increase in the bottoms concentration of column 2 had little

effect on the performance of column 3. The response was

quite good, with little oscillation in either controlled or

manipulated variables. Figures 20 through 23 show the sys

tem response to Test 2. The response was very similar to

Test 1 and the control system showed the ability to handle

this upset.

Figures 24 through 31 show the system response to Tests

3 and 4. The trim reboilers were able to compensate for the

loss in C concentration and kept columns 2 and 3 on speci

fication. If the trim reboilers were not included, there

would be a limit to the heat—transfer rate available to

columns 2 and 3 and these columns could have gone off spec

ification. Figures 32 through 39 show the response of the

columns to Tests 5 and 6. In this test, the trim reboilers

50

h

0.96 4

I 0.94

0.08

'o.04 -j

1.50 "

1.00

70.0 -'

65.0 -

200. -

180.

30.0 -

Q^xiO^ 20.0 i

1

1 2 3 Time ( h r )

1

4 5

Figure 16. Response of Column 1 to Test 1

51

-•-3 4

Time (hr)

Figure 17. Response of Column 2 to Test 1.

0.96 -

0.94

52

0.06 -

h 0.04 H

6.50 -

5.50

400. H

380.

140. Q^xlO^

130.

120-Q^xlO^

110. 1

Time (hr)


53

h

0.99 <

I 0.97 -

0.04 -

0.02 -

8.50 i

7.50

900. i

880.

350.

310. -

J\

285. A Q^xlO^

^275. -•

3 4 Time (h r )

F i g u r e 1 9 . R e s p o n s e of Column 4 t o T e s t 1

54

0,96 -

0.94 -

0.08 -I

h 0.04

1.50 1

1.00 "

70.0 -

60.0

220. i

200. •

ISO. -^

30.0 i

a xio^ ' 20.0 -i

Time (hr)


X

0.99 -

'0.97 -

55

110. H

90.0 -I

120.

Q^xlO^ 100.

3 4 Time (hr)


56

\

0.96 -

I 0.95 -

0.06 -

0.04 -

6.00 -

5.00

400. -

390,

uo. Q xio^ ^130.

120. 1

7 Q xlO c

100.

Time (hr)


57

h

0.99 1 I 0.97

Q.04

0.00

8.50

7.50 -

900. -

880. •

330.

320. -

300. -

7 Q xlO ^r

260.

Time (hr)

Figure 23. Response of Column 4 to Test 2.

0.95

0.94 •

58

h 0.06 -

0.04 '

1.50 H

I.OO

80.0 -

60.0 -

200. -

180. 4

30.0 Q XlO

20.0

3 4 Time (hr)


X 0.99

0.97 •

110. -.

59

80.0 -

120.. Q xlO^ r 110, -

3 4 Time (hr)


60

X.

h

0.97 -I

0.95 -

0.06 -

0.04 -

6.50 .

5.50 -

400.

380. .

140- -1 QpXlO^

130.

110.

Q^xlO^ ^100. •

3 4 Time (hr)


X

h

0.98 '^ I 0 . 9 7 .

0.04 .

0.02 .

8.50 -

7.50 •

910. 1

R

870. .

350. -J\ 310. i

290 7 Q^xlO

280. "

61

3 4 Time ( h r )


62

0.96 -I

0.04 -

1.50 •

1.00 -

80.0 -

60.0 -

200. -F 180. •

30.0 -Q XlO c 20.0 -

Time (hr)


63

X 0.99 i

0.97

120- -Q^xlO^ [^

110.

Time (hr)


64

X

\

0.97 .

I 0.95-

0.06 .

0.04 -

6.50 •

5.50 -

410. -I

R

370. -

140. • Q xlO r

130. -•

110. Q xlO^ c 100.

Time (hr)


65

0.98 4

I 0.97

0.04 1

0.00 H

8.50 -

7.50 -

900.

880.

350. -

310. -»

290.

1 rXlO^ ^

270.

Time (hr)


66

h

0.96 -

I 0.94 *!

0.06

0.04 1

1.50 -

1.00

80.0

60.0 -

200. -

F

180.

30.0 i Q^xlO^

20.0

L

Time (hr)


0.98

0.97 4

67

h 0.06 -j

I

0.04

8.00

7.00

100.

80.0 -

120. Q^xlO''

110.

Time (hr)


68

0.96 ,

Xd

\

0.95 -

0.06 •

0.04 •

6.50 -

5.50 -

400. 1

380. '

140. -

Q_xlO^ 130. -*

110. -

QpXlO^ '100. -

3 4 Time (h r )


69

X

\

0.99 .

^0.97 '

0.04 4

0.02

8.50 -»

7.50

390. -I

870.

350. -

Jl 310. '

290. -»

Qrxl07

270.

3 4 Time ( h r )


70

0.96 -I

'0.04 -

1.50 -

1.00

80.0

60.0 -

200. -

180.

30.0

Qc^O''

20.0

3 4 Time (hr)


0 .99 •

^d — 0.97 -

71

0.04 - •

h 0,02 -

8.00 1

90.0 1

120. -Q j j c lO^ .

110. -

Time (hr)

F i g u r e 3 7 . R e s p o n s e of Column 2 t o T e s t 6

72

0.96 -

I 0.94 -•

0.06

h 0.04 -

6.50 J

5.50

400.

380.

140.

Qr^lO^

130.

110.

100.

Time (hr)


73

Xd

^

0.99 J

0.97

0.04

0.02

8.50

7.50

900.

860. ->

340.

320.

290. '

Q xlO'

270. -

Time (hr)


74

make up the heat loss produced by the rainstorm.

The most severe test for the system was Test 7. The

response of the system to this series of step changes is

shown in Figures 40 through 43. Again, the overall response

was quite good.

The response of the system to the above step changes

was quite good and the proposed control system should be

able to handle a variety of upsets, which could become quite

numerous and it would be impossible to simulate all of them.

It would also be desirable to look at other control stra

tegies that might be just as effective as the proposed

control system.

One dilemma that was discovered in the control system

design was the control of column pressure and bottoms compo

sition. For example, it would be possible to control the

bottoms compostion in columns 2 and 4 with the heat—transfer

rate in the reboilers and let column pressure float. The

dynamic model was modified for this control scheme and

subjected to a step increase in total feed rate. Pressures

in columns 2 and 4 decreased to the extent that heat trans

fer in the reboilers of columns 1,2 and 3 did not occur, as

shown in Figure 44. The system crashed. Thus, pressure

control is very important for this system.

One of the critical factors of the control system

design is the size of the trim reboilers of columns 2 and 3.

75

0.96 J

0,04 .

20.0 '

3 4 Time (hr)


76

0.99 -I

8.00 -

7.00

110.

90.0 ,

120.

Qj-xlO^

110.

Time (hr)


77

h

0.96 -

I 0.94 -

0.06 -

0.04 -

6.50 -

5.50 -

400. -

380, -

140. , Q rxlO^

130. -t

110. -

100.

Time (hr)


78

X.

h

0.99 ,

I 0.97 -

0.04 .

0.02 .

8.50 J

7.50 1

900. -

880. -

350. -

310. .

290. -

270. -

a

3 4 Time (hr)


79

8.0 -

Column 4

7.7 -

7.3

Column 2

7 . 1

Time (hr)

F i g u r e 44 Response of Column 2 and Column 4 Pressure when Allowed to Float.

80

If the trim reboilers are undersized or become fouled, the

heat—transfer rate may not be large enough to maintain

column specifications. The dynamics of the flowsheet were

evaluated by limiting the heat-transfer rate in the trim

reboilers of columns 2 and 3. Three different limits were

imposed—1.001 times the steady—state reboiler duty, 1.002

times the steady—state reboiler duty and 1.004 times the

steady—state reboiler duty. Response of these columns are

shown in Figure 45. As can be seen, both column 2 pressure

and bottoms composition of column 3 decreased. The drop in

column 2 pressure prevented heat transfer across the common

reboiler-eondenser of columns 1 and 2, preventing fractiona

tion in column 1. The results show the need for the trim

reboilers and that the trim reboilers need to be sized to

handle all possible upsets.

81

A

B

l.OOlxQ

1.002xQ

1.004:q^

rs

7.3

6.8 .

0.06 . -J X*

0.04 «

B C

Time (hr)

Figure 45. Response of Column 2 Pressure and Column 3 Bottoms Composition to Limited Reboiler Duty

CHAPTER 6

CONTROL LOOP STABILITY ANALYSIS

An important consideration in control-loop system de

sign is stability. A tool that can be used to determine the

stability of a multi-input, multi-output (MIMO) control

system is the relative gain array (RGA) developed by Bristol

(1966). The use of the RGA aids in the pairing of manipula

tive variables with control variables. Development of the

RGA begins by calculating all open—loop gains between con

trolled variables and manipulated variables in the system.

For example, a system with 3 controlled variables and 3

manipulated variables would have 9 open—loop gains as shown

below.

m m m,

dy /dm

dy /dm

dy /dm

dy /<^^2

dy /dm^

dy^/dm^

dy /dm

dy /dm

dy^/dm^

The value dy /dm is evaluated by placing a small perturba-j i

tion in m and determing the change in y., while holding all i 2

other manipulative variables constant. If an open-loop

transfer function matrix is available for the system, the

steady-state gains make up the matrix shown above. The RGA

can n cw be calculated as

82

83

A (dy /dm ) = 1 j ni

-l (dy./dm.) 1 3 y

which is the ratio of the open-loop effect, (dy /dm ) , to a i j m

perfect closed-loop effect, (dy./dm ) . The calculation of 5. 2 y

the RGA for a 2 X 2 system will be used for an example. The

transfer function matrix is (Stephanopoulos, 1984):

y^ = (l/(s+l))m^ + (l/(0.1s+l))m

y^ = (-.2/(0.5s+l))m, + (.8/(s+l))m^ 2 1 2

A step change is made in m while holding m constant. The

value for y is calculated by using the final value theorem,

thus y is equal to 1, so (dy /dm ) is 1/1 or 1. Next, the

1 1 1 m^ control of y is assumed to be perfect, that is y =0. From

the bottom equation, m„ is evaluated in terms of m . 2 1

m = (0.2(s + l)/(0.8(0.5s-i-l)) )m 2 1

This value is placed in the top equation and y is calcu

lated by the final value theorem.

y = l i m ( s y ) = l i m ( (s(_l 1_ + 1 0.2 S-K1 i_ ) ) = 1 .25 1 "-'° 1 "' ^ s+1 s .ls + 1 0.8 .5s + l s

so (dy /dm ) = 1.25/1 = 1.25 1 1 y2

The relative gain of y to m is:

\

(dy /dm )

i 1 2 = . L = 0.8 ^^ (dy /dm ) ^'^^

1. 1 To

The rows and columns of the RGA must add up to 1.0. Thus,

84

the other terms in the matrix can be calculated from this

identity. The RGA is:

0.8

0.2

0.2

0.8

To determine the control—manipulative variable pairings, the

following rule is used:

Always pair on positive RGA elements that are

closest to 1.0.

Thus, in this example, m. should be paired with y, and m,, , 1 i - t

w i t h Y ry.

The RGA can also be determined for higher—order sys

tems. Suppose the following 3 X 3 open—loop gain matrix was

determined (McAvoy, 1983).

2.662

.3816

0

8.351

-.5586

11.896

8.351

-.5586

-.3511

m^

m 2

m o

The RGA can be calculated by standard matrix operations.

First, the inverse of the matrix is calculated, then its

transpose is determined.

.1195

1.787

0

2.341E-3

-.01633

.08165

.07931

-.5532

-.08165

Corresponding elements in the two above matrices are multi-

85

plied to form the Hadamard product. The RGA i

m^

.318

.682

0

m^

.0195

.00913

.971

m3

.663

.309

.0287

As can be seen, the rows and columns add up to 1.0. To

determine the pairings of controlled variables with manipu

lative variables, values closest to 1.0 should be used.

Thus y should be paired with m , y paired with m and y

paired with m . This leads to the control loop design with

least interaction.

If the RGA shows the pairings of m^-y., m^-y^,... m -

y , Niederlinski (1971) showed that the system is unstable n

when

•< 0

where |A| is the determinant of the open—loop gain matrix and

jja is the product of the diagonal elements in that matrix.

The RGA's for each column were calculated and Nieder—

linski's theorem was tested for closed loop stability.

Tables 4-6 show the RGA for columns 1, 3 and 4. The sta

bility test results in the following values.

Table 4. Relative Gain Array for Column 1.

Open-Loop Gain Matrix

86

-0.428E-3

0.118E-3

•0.718E-3

-0.336E-3

0.295E-2

-0.369E-2

1.21E-8

-1 .28E-8

•0. 158E-6

Relative Gain Array

0 .952

0 . 0 5 0

0 .098

- 0 . 0 4 0

0 .976

0 .065

0.088 1

0 . 0 7 4

0 . 8 3 7 J



87

X

2.42E-8

•0.72E-7

8.22E-7

-.149E-3

0.484E-2

-.641E-2

0.852E-9

•0.945E-8

-0. 228E-6

Relative Gain Array

1.02

0 .103

0 .081

- 0 . 1 3 1

1.09

0 .039

0 .109

0 .011

0.880


88


-0.243E-2

0,141E-2

-0.151E-1

-0.363E-3

0.200E-2

•0. 164E-2

0.441E-7

-0.144E-7

0.118E-5

X,

Relative Gain Array

1.42

0 . 2 9 0

0 . 1 2 7

- 0 . 2 8 6

1.28

0 . 0 0 5

- 0 . 1 3 1

0 . 0 0 9

1.12

89

Column 1 1.16

Column 3 1.03

Column 4 0.749

For column 2, there are only 2 manipulative variables and

two control variables and the stability test does not apply.

The results above show that the control system is stable.

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

The results of the dynamic model simulations for the

proposed heat-integrated system lead to the following con

clusions .

1) A degrees—of-freedom analysis, coupled with pres

sure control as an important constraint, led to a

stable control system for a case study in heat-

integrated distillation.

2) Sizing of trim reboilers for a heat-integrated

system must take into consideration all possible

upsets such that they are not undersized.

Recommendations for continued research in design and

control of heat-integrated distillation systems should

include:

1) Development of a dynamic model that would be ca

pable of simulating the startup of a column.

Startup presents some unique problems which have

not been investigated in the literature.

2) Comparison of control loop design for two competi

tive sequences. If two sequences are competitive

at the steady-state design, control loop design

could be the deciding factor as to which one is

chosen.

90

91

3) Development of control strategies for larger sys-

terns .

4) Use of more accurate, simplified col umn models.

LITERATURE CITED

Andrecovich, M. J., and Westerberg, A. U., "A Simple Synthesis Method Based on Utility Bounding for Heat-Integrated Distillation Sequences." AIChE J. 31, 363 (1985).

Bolles, W. J. "Rapid Graphical Method of Estimating Tower Diameter and Tray Spacing of Bubble-Plate Fractionators," Pet. Refiner.. 25(12). 103 (1946).

Bristol, E., "On a New Measure of Interaction for Multi-variable Process Design," IEEE Trans. Autom. Control AC-11. 133 (1966). ~

Buckley, P. S. ,"History of Distillation Control," AIChE Symp. Ser.. 235. 79, 46 (1983).

Chang, H. "Computer aids short-cut distillation design," Hydrocarbon Process.. 59(8). 79 (1980).

Clements Jr., W. C , "Black-box Dynamic Process Modeling Using Process Reaction Curves." AIChE Modular Instruction. Series A, Vol. 1, 51 (1980).

Coughanowr, D. R., and Koppel, L. B., Process Systems Analysis and Control. McGraw-Hill, New York, 1965.

DePriester, C. L., "Light-Hydrocarbon Vapor—Liquid Distribution Coefficients," AIChE Symp. Ser.. 2, 49, 1 (1953).

Fenske, M. R., "Fractionation of Straight—Run Pennsylvania Gasoline," Ind. Eng. Chem.. 24. 482 (1932).

Frey, R. M., Doherty, M. F., Douglas, J. M., and Malone, M. F., "Controlling Thermally Linked Distillation Columns," Ind. Eng. Chem. Process Pes. Dev.. 23. 483 (1984).

Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations. Prentice—Hall, Inc., Englewood Cliffs, N.J., 1971.

Geddes, R. L., "A General Index of Fractional Distillation Power for Hydrocarbon Mixtures." AIChE J. 4, 389 (1958).

Gilliand, E. R., "Multicomponent Rectification," Ind. Eng. Chem. , 3_2, 1101 (1940).

Hengstebeek, R. J., "A Simplified Method for Solving Multi-component Distillation Problems," Trans. AIChE. 42. 309 (1946).

92

93

Holland, C. D., Fundamentals of Multicomponent Distillation. McGraw-Hill, New York, 1981.

Holland, C. D., and Liapis, A. I., Computer Methods for Solving Dynamic Separation Problems." McGraw-Hill, New York, 1983.

Huekaba, C. E., May, F. P., Franke, F. R., "An Analysis of Transient Conditions in Continuous Distillation Operation," AIChE Symposium Series. 46. 59 (1963).

King, C. J., Separation Processes, 2nd ed., McGraw-Hill, New York, 1980.

Lamb, D. E., Pigford, R. L., and Rippin, D. W. T., "Dynamic Responses and Analogue Simulation of Distillation Columns," Chem. Eng. Prog. Sym. Ser., 57. 132 (1961).

Luyben, W. L., Process Modelling, Simulation, and Control for Chemical Engineers, McGraw-Hill, New York ,1973.

McAvoy, T. J., Interaction Analysis. ISA, Research Triangle Park, NC, 1983.

Molokanov, Y. K., Korabline, T. R., Mazuraina, N. I., and Nikiforov, G. A., "An Approximate Method for Calculating the Basic Parameters of Multicomponent Fractionation," International Chemical Engineering, 12(2), 209 (1972).

Morari, M., and Faith, D. C , "The Synthesis of Distillation Trains with Heat Integration." AIChE J. 29, 916 (1980).

Naka, Y., Terashita, M., and Takamatsu. T., "A Thermodynamic Approach to Multicomponent Distillation System Synthesis," AIChE J, 18, 812 (1982).

Niederlinski, A., "A Heuristic Approach to the Design of Linear Mul t ivar i able Control Systems." Automatica. 1_, 691 (1971).

Rathore, R. N. S., Van Wormer, K. A., and Powers, G. J., "Synthesis Strategies for Multicomponent Separation Systems with Energy Integration." AIChE J. 10, 491 (1974a).

Rathore, R. N. S., Van Wormer, K. A., and Powers, G. J., "Synthesis of Distillation Systems with Energy Integration," AIChE J, 10, 940 (1974b).

Roffel, B. and Fontein, H. J., "Constraint Control of Distillation Processes," Chem. En^. Science. 3_4, 1007, (1979).

94

Ryskamp, C. J., "New Strategy Improves Dual Composition Column Control," Hydrocarbon Process.. 60(6). 51 (1980).

Shankar, H., "Analysis and Optimization of Heat Integrated Sequences," Ph. D. Dissertation, Texas Tech University, Lubbock, TX, 1985.

Starling, K. E., Fluid Thermodynamic Properties for Light Hydrocarbon Systems. Gulf Publishing, Houston, 1973.

Stephanopoulos, G., Chemical Process Control. Prentice-Hall, Englewood Cliff, N.J., 1984.

Tung, L. S., "Analysis and Control of Large Scale Processes with Limited Measurements," Ph. D. Thesis, The University of Texas at Austin, Austin, TX, 1979.

Tyreus, B. .D., "Control of Multi—effect, Energy Conserving Distillation Systems," Ph. D. Thesis, Lehigh University, 1975.

Underwood, A. J. V., "Fractional Distillation of Multi-component Mixtures," Chem. Eng. Prog.. 44, 603 (1948).

Weischedel, K., "A Dynamic Study of Distillation Column Control Strategies," M. S. Thesis, University of Massachusetts, Amherst, 1980.

APPENDIX A

SHORT CUT DISTILLATION DESIGN

Minimum number of trays (Fesnke, 1932):

JJ + 1 = llc.D hk,D hk,B lk,B m , .

log c<, lk,avg

Minimum Reflux ratio (Underwood, 1948):

^ ^^I'^l.f = 1 - q

^ O C , - jZS

g<:i''i .D K = £

Number of Stages (Gilliand, 1940; Molkanov, et al., 1972):

Y=1-exp(1+54.4x)(x-l)/((11+117.2x*sqrt(x)))

where: x=(R-R^)/(R+l)

N=(Y+N,)/(1-Y)

Distribution of Components (Hengstebeek, 1946; Geddes, 1958):

C, = m (d^^/\^)

^2 = ^-^^^lk/^k>^\k/^k>/^""^lk

b. = f./(l+exp(C, + C^lncX. ) 1 1 1 2 1

d. = f. - b. I l l

95

96

Relative Volatility: Relative volatilities were calculated using the Harlacher vapor equation (Reid, et. al., 1977).

ln(P ) = A + B/T + Cln(T) + DP*/T^

where T is in units of degree K and P* is in units of millimeters of mercury.

Tower diameter (Holland, 1981)

D^ = (L^ - 500)/(5.22(V^ - 5) + 461)

(V^ - 5)/3.75 + 5.2

APPENDIX B

COLUMN SPECIFICATIONS AND STEADY-STATE VALUES

Column Feed B Qr

1 2 3 4

Column

kgmol hr

195. 305. 427. 330.

X

83 63

kgmol

166.85 260.98 330.63 123,38

X

kgmol hr

28,15 44.02 97.21 207.25

X

kJ Kr

0.29399E7 0.11484E8 0.13686E8 0.27943E8

P

kJ HF

0.22099E7 0,29435E7 0.10961E8 0.25172E8

R

I 2 3 4

Column

1 2 3 4

0,4286 0.4286 0.3396

• 0.6218

N

27 34 42 40

0.063 0,042 0.049 0.023

°c m

1.0 1.5 2.0 1.75

0.9491 0.9795 0.9538 0.9787

^w

m

0.75 1.25 1,50 1,25

atm

1,02 7.30 5.80 7.90

h ow

m

0.025 0.025 0.025 0.025

kgmol hr

67.7 98.8 392. 886.

97

APPENDIX C

PURE COMPONENT DATA

Equilibrium K values calculated as a polynomial in temperature at a reference pressure (DePriester, 1948).

K = a + bT + cT^ -4- dT'^

Reference pressure - 15 psia, T in degrees R

C5 3.6429 0.025822 -0.15026E-3 0.17096E-6 C, -1.4544 0.034514 -0.11924E-3 0.11308E-6 C^ -1.5521 0.023240 -0.72376E-4 0.64615E-7

8 C^ -1,2860. 0.015799 -0.45974E-4 0.39250E-7

Reference pressure = 100 psia

C.3 1.99070 -0.38170E-2 -0.89415E-5 0.17952E-7 C 0.95018 0.10178E-2 -0.13888E-4 0.16619E-7 C^ 0.45739 0.19254E-2 -0.11455E-4 0.11905E-7 C^ 0.2339E-3 0,32735E-2 -0.11507E-4 0.10200E-7

Enthalpies (kJ/kg) calculated as a function of temperature (K) (Starling, 1973).

2 Liquid enthalpy h = a + bT + cT

C C C C

0.20207E4 \ 0.19802E4 ^ 0.19693E4 ' 0.18454E4

/apor Enthalpy

1 1

1 1

00

00

H

.41052

.71188

.89387

.53511

= a + bT

-0.31141E-2 -0.25658E-2 -0,22605E-2 -0.26960E-2

-2 3 + cT -f dT

C O , c; 0, c ° 0, c ' 0.

,19170E4 ,22425E4 , 16867E4 , 17838E4

-0, -0. -0, -0.

.21165E1

.49341E1

.12350E1

.21368E1

0. 0.

-0. 0.

.68046E-3

.75165E-2

. 13905E-2

.11536E-2

-1.5503E-6 -7,0217E-6 l,8258E-7

-2.1886E-6 8

98

99

Liquid densities (s/cm^) calculated as a function in temperature (K) .

p = a -»• bT + cT^

C 0.85754 -0.62062E-3 -0.60661E-6 C^ 1.03750 -0.14362E-2 0.57917E-6 C° 0.99099 -0.11263E-2 0.29083E-6 C'' 0.83388 -0.40809E-3 -0.39766E-6 8

APPENDIX D

COMPUTER PROGRAMS

SHORT-CUT DISTILLATION DESIGN

C THIS PPOG-RAH BSSTGIfS 1 DISTILL»TI01» COLUfllf OSIHG C SHORT-CUT T2CHTIIQES. C DEFIHITIQHS: C A i y » « R n . A T I 7 Z 70LATILITT C AHW-ATCTAGS flOLZCTTLAH HEIGHT C IflT « ATTOAGI HOLZCnLA? lEIGHT OF 7APCS C B»BOTTOnS n o w BATE OF C0nP0J»E5T C BO, 81 » COJfSTAWTS OSED TO CALCOLATE Z FOR GAS C BFHK-IHITIAL GOESS OF FRACTION REC07EHT OF HEATT KEY IH BOTTOHS C CCOST» COLOHH COST C CIBL « COHPOHEHT HAHE C DC« DIAHETES OF COLOHH (FT) C DEJIA,DEirB,DEHC » COHSTAHTS USED TO CALCOLATE LIQ DEHSITT AS C FtlHCTIOH OF T2HP (K) . C DFLX« IHITIAL GUESS OF FRACTIOH H2C0TERT OF LIGHT KET IH C DISTILLATE C BTA» TRAT EFFICIIHCT C EK » EQUILIBRIOH K 7AL0E C EXC » COHSTAHTS OSED TO CALCOALTE EQUIL K 7AL0E AS A FOHCTIOH C OF TEHP (R) C F!)»FEED HATE KGHOL/HR C F « COHPOHEHT HOLAR FEED HATE C FI « IHFLATIOH IHDEX COST FACTOR C HC » HEIGHT OF COLOHH (FT) C HK a HEA7T HET CCHP HO. C H7C « COHSTAHTS OSED TO CALCULATE 7APCR BHTHALPT AS C FUHC OF TEHP (K) C HLC « COHSTAHTS OSZD TO CALCULATE LIQUID EHTHALPT AS C FUHC OF TEHP (H) C LK = LIGHT KZJ COHPOHEHT HUHBER C L » LIQUID LOAOIHG C HC s HUHBER OF COHPOHEHTS C HT « HUHBER OF THAIS C HHIH « HIHIHUH HUHBER OF TRATS C P 7 A , P 7 B , P 7 C , P 7 D » HARLACHER 7AP0R EQH COHSTAHTS FOB EACH COHP. C PCOL » COLOHH PRESSURE (ATH) C PHSF » REFER EHCE PRESSURE FOR EQUIL K 7ALU F CALCULATIOH (ATH) C P7P « 7AP0R PRESSURE (HHHG) C Q » F K D TH^RHAL COHDITIOH C QCOHD » COHOEHSEP DUTT (J/HR) C QBEB « REBOILZB DUTT (J/HR) C PHI « COHSTAHT OSED IH OHDERTJOOD'S EQUATIOHS C H » REFLOX RATIO C RHJOL»LIQUID DEHSITT (G/CH**3) C Re07«7AP0R DEHSITT (G/Cn**3) C RHIH « HIHIHUH REFLUX RATIO C RRH » SET 7ALUE FOR REFLUX RATIO—R = RHIH*HRH C SUHB » BOTTOnS FLOS RATE C SUHO « DISTILLATE FLOW RATE C TBOT » BOTTOHS TIHPERATURE (H) C TTOP » 07ERHEA0 7AP0RS TEHFERATURB C TOUTC « DISTILLATE TEHPERATURE C TFD » FEED TEHPERATURE C TRTCST « THAT COST

100

101

c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c

WH « HOLECULAR HEIGHT XF » FEED COHPOSmOH XDHK « HOLE FRACTIOH OF HEA7T XHLK « HOLE FRACTIOH OF LIGHT XP a Z - COHPRESSABILITT FACTOR

KEY IH DISTHIATE KET IH BOTTOHS

SHORT-CUT DISTILLATIOH DESIGH

THE STSTEH

COHPOHEHT H-PEHTAHB H-HEXAHE H-HEPTAHE H-OCTAHE

LIQUID EHTHALPIIS (HL) AHO 7AP0R EHTBALPIZS CALCULATED BI A POLTHOHIAL IH TEHP(X)

TC 969 .600 507 .a 00 510 .200 568 .800

PC 33 .300 29 .300 27 .000 29 .500

« 0 .251 0 .296 0 .351 0 .259

HW 72 . 151 86 . 170

100.20 0 118.232

(H7) HERE

H-PEHTAHE H-HEXAH-S H-HEPTAHE H-OCTAHE

H-PEHTAHE H-HEXAHE H-HEPTAHE H-OCTAH"S

BLA 0 . 2 0 2 0 7 E 0 . 1 9 8 0 2 E 0 . 19693E 0 . 1 8 9 5 9 E

H7A 0 . 1 9 1 7 0 E 0 . 2 2 a 2 5 B 0 . 1 6 a 6 7 E 0 . 1 7 3 8 3 E

00 - 0 . 9 1 0 5 2 E 00 Oa - 0 - 7 1 1 8 8 E 00 09 - 0 . 8 g 3 87E 00 09 - 0 . 5 3 5 1 1 E 00

H 7B 09 - 0 . 2 1 1 6 5 E 01 09 - 0 . 9 9 3 9 1 E 01 09 - 0 . 1 2 3 5 0 E 01 09 - 0 . 2 1 3 6 8 E 01

HLC - 0 . 3 1 191E-02 - 0 . 2 S 6 5 8 E - 0 2 - 0 . 2 2 6 0 S E - 0 2 - 0 . 2 6 9 6 0 E - 0 2

O.QQOOOE O.OOOOOE O.OOOOOE O.OOOOOE

00 00 00 00

H7C 0. 68 0 0 6 B - 0 3 - 0 . 1 5 S 0 3 E - 0 5 0 . 7 S 1 6 5 E - 0 2 - 0 . 7 0 2 1 7 E - 0 5

- 0 . 1 3 9 0 5 E - 0 2 0 . 1 8 2 3 8 E - 0 6 0 . 1 1 5 3 6 E - 0 2 - 0 . 2 1 8 8 6 Z - 0 5

HARLACHER 7AP

H-PEHTAHE H-BEXAHE H-HEPTAHE H-OCTAHE

EQH COHSTS P7A

5 2 - 6 8 2 5 7 . 2 7 9 6 1 . 2 7 6 6 6 . 6 3 9

P7B - 9 8 2 7 . 0 7 8 - 5 5 8 7 . 9 2 2 - 6 3 0 3 . 8 7 1 - 7 1 0 0 . 6 9 1

PTC • 5 . 3 1 3 •5 .885 • 6 . 373 •7 .053

PTD 3 . 6 8 0 9 . 7 7 8 6 . 0 0 0 7 . 3 1 0

EQUIL K TALOES HERE EH1

1 0 . 3 6 9 2 9 E 01 2 - 0 . 1 9 5 9 9 1 01 3 - 0 . 1 5 5 2 1 Z 01 9 - 0 . 1 2 8 6 0 1 01

CALCULATED EH 2

0 . 2 5 8 2 2 E - 0 1 0 . 3 9 5 1 9 E - 0 1 0 . 2 3 2 9 0 E - 0 1 0 . 1 5 7 9 9 Z - 0 1

HITH A POIIHOBIAL EH 3

- 0 . 1 5 0 2 6 E - 0 3 - 0 . 1 1 9 2 9 E - 0 3 - 0 . 7 2 3 7 6 E - 0 9 - C . 9 5 9 79E-09

IH TEHP EH 9

0 . 1 7 0 9 6 E - 0 6 0 . 1 1 3 0 8 E - 0 6 0 . 6 9 6 1 5 E - O 7 0 - 3 9 2 5 0 E - 0 7

LIQUID DEHSTTIIS CALCULATED AS QUADRATIC IH TEHPERATURE DEHA DEHB DEHC

0 , 8 5 7 5 9 Z 00 - 0 . 6 2 0 6 2 E - 0 3 - 0 . 6 0 6 6 1 Z - 0 6

102


2 3 9

0 . 1 0 3 7 5 E 0 . 9 9 0 9 9 E 0 . 8 3 3 8 8 E

01 - 0 . 1 9 3 6 2 S - 0 2 00 - 0 . 1 1 2 6 3 E - 0 2 00 - 0 . 9 0 8 0 9 E - 0 3

0 . 5 7 9 17E-06 0 . 2 9 O e 3 E - 0 6

- 0 . 3 9 7 6 6 E - 0 6

THE COLOHH PRESSURE IS 1 . 0 2 0 ATH THE FEED RATE IS 1 9 0 . 0 0 0 KG HOL/HP

THE FEED COHPOSITIOH I S I XI (I )

1 0 .1500 2 0 .2000 3 0 .9000 9 0 .2500

LIGHT HET I S COHPOHEHT HO. HEA7T SET IS CCHPOHEHT HO.

THE OPSRATIHG REFLOX RATIO I S THE SPECIFIED HOLE FRACTIOHS O:

IH THE DISTILLATE AHD XD (HK) * 0 . 0 2 0 0

1 . 0 6 0 TIHES RHIH THE H2TS

THE BOTTOHS ARE XB(LK) = 0 . 0 1 0 0

THE IHITIAL GUESSED 7ALUES OF THE DISTRIB OTIOHS ARE

DFLK a 0 . 9 8 0 0 BFLK » 0 . 9 8 0 0

AFTER

OUTPUT * • • * « •

1 ITEPATIOHS THE ACCEPTED 7ALUES OF THE DISTRIBOTIOHS ARE

I 1 2 3 9

TOTAL

DFLK » D(I )

0 . 2 6 8 7 9 2 Z 05 0 . 5 9 8 5 1 8 E 03 0 . 1 0 6 2 5 0 E 01 O.OOOOOOE 00

0.9930 BFHK 0 . 9 85 6 TD(I)

0 . 9 7 9 9 6 0 E 00 0 . 2 0 0 0 1 6 E - 0 1 0 . 3 8 7 9 38E-09 O.OOOOOOE 00

B { I ) 0 . 1 6 2 5 8 1 E 09 0 . 3 7 9 5 1 5 E 05 0 . 7 5 9 9 8 9 E 05 0 . 9 7 5 0 0 0 E 05

XB(I) 0 . 1 0 0 0 0 3 E - 0 1 0 . 2 3 0 3 6 3 E 00 Q.967966E 00 0 . 2 9 2 1 7 1 E 00

ALFA (I) 0 . 2 5 t t 1 9 9 E O.IOOOOOE 0 . 3 9 7 5 1 0 E 0 . 1 6 5 5 6 1 E

01 01 00 00

2 7 . 9 2 3 8 1 6 2 - 5 7 6 1 KG HOL/HR

HIHIHUH HUHBER OF PLATES = 7 . 5 3 9 PHI » 1 . 6 8 2 9 0 7 RHIH « 1 . 8 7 0 AT P • 1 . 9 8 3 HO- OF THBOR. PLATES FEED THEPHAL COHDITIOH Q I S 1 - 0 0

THE FEED TEHP I S 3 5 1 . 0 K

2 1 . 7 6 0

BOTTOHS TEHP 3 7 9 , 1 0 1 K TOP DZH TEHP

REB D0T7 = 0 . 2 8 3 5 3 E 10 J/HR COHO DUTT EHTHALPIES J/HR

3 1 2 - 1 3 9 K

0 . 1 8 6 1 2 E 10 J/HR

103

c C FEED -0.13356E 06 C BOTTOHS -0.13069Z 06 C TOPS -0.11505E 06 C c C COLUHH HEIGHT « 6 0 . 9 0 0 7 F T C COLOHH DIAH « 2 . 7 8 1 F T C

IHTECER LK,HK REAL HT,HHIH COHHOH/BLOCK1/XF(15) , XD (15) ,ALFA (15) C0nH0H/BL0CH2/FD,SUHB,SUHD, D(15) , B (15) , F (15) , XB (15) COHHOS HC,LK,HK COHHOH/FIT/ EK(5) , E K C ( 5 , 5 ) ,PREF COHHOH/EHT7/H7C(5,5) ,HLC ( 5 , 5 ) ,HH(5) COHHOH/BL0CH3/TB0T,TFD,TTOP,TOUTC COHHOH/RECT/XDHK,XBLK,DFLK,BFHK,Q,BRH,HaiH,PHI,RHIH,K COaaOH/BLOCK9/H,HT,ETA COHHOH/BHTH/SUBHF,SUHHB,SUHHC C0HH0H/BL0CK9/0C,HC,CC0ST,TRTCST COHHOH / 2 S T H / P7A (1 0) ,P7B {1 0) , PTC (10) , P7D (10)

COHHOH/BBB/X{10) , 1 ( 1 0 ) COHHOH/AAA/CLBL(6,6) ,PCOL#T, PBOT

COHHOH/DUTT/QPEB,QCOHD C0HH0H/DAT1/ PC (5) ,TC (5) ,H (5) COHHOH/DEH/ DEHA (5) ,DEHB (5) ,DEHC (5)

DIHEHSIOH TrL(IO) ,XFL(10) HAHELIST/CHK/R,SUHB,SOHO,ALFA,PHI,RHIH,XD

C CALL DATAIH

IQ«IFTX(Q) DO 3 0 I « 1 , H C

30 T F L ( I ) » X F ( I ) GO TO ( 2 1 , 1 1 ) , I Q

C I F F2ED I S SATURATED LIQUID Q IS 1 AHO FEED TEHP I S CALCULATED C ELSE TFD IS KHOHH AHD FE2D THERHAL CONDITIO If Q IS CALCULATED C 11 COHTIHUE

TBP-TFD CALL aUBDE?(PC0L,I7 ,TFL,TBP, 1 , 1 ) TDW»1.05*TBP CALL BUBDEH (PCOL,XF, IFL,TDH,2 ,1 ) CALL GETQ(Q,TBP,TDH,TFD) GO TO 31

21 COHTIHUE CALL BUBDEH (PCOL,XF,TFL,TFD, 1 , 1 )

TEHP WITH SUBROUTIHE TEHEST

31 C C

COHTIHUE

ESTIHATE TOP AHD BOTTOH COLUHH ETA-. 8

CALL PRHTA FD"FD*1000.

ICASE-1

104

CALL TEHEST (PCOL,T,ICASE) TTOP»T ICASE«2 CALL T2HBST (PCOL,T,ICASE) TBOT=T

C DO 181 1 3 - 1 , 2

C C CALCULATE RBLATITZ TOLATILITIES HITH SOBROOTIHE GALFA

CALL GALFA (PCOL, PBOT) C C CALC. OIST. OF COHP., REFLUX, MfllH, AHD HO. OF TRAIS OSIHG HGFOF

CALL HGFUG DO 3 5 I » 1 , H C

35 X F L ( I ) « X D ( I ) C C CALC. TOP AHD BOT TEHP AHD TAPOR COHP.

CALL BUBDEH(PCOL,XD,IFL,TTOP, 2 , 1) C

CALL BUBDEH (PBOT,XB,TFL,TBOT, 1 , 1) C CALC. DISTILLAT2 T2HP.

TOUTC»TTOP CALL BUBDZH (PCOL,XD,T7L,TOUTC, 1 ,1)

181 COHTIHUE C CALC. COHDEHSZR DUTT

CALL CHDUTT (PCOL) C CALC. REBOILER DUTT

CALL HBDUTI (PCOL) C FIHD COLUHH DESIGH SPECIFICATIONS

CALL COLS PC (PCOL) C

CALL PHHTB GO TO 99

99 COHTIHUE STOP

EHD C c c

SUBROUTIHE GZTQ(Q,TBP,TDH,TFO) COHHOH HC,LK,HK COHHOH/BLOCX1/XF(15),ID(15) ,ALFA(15)

C C CALCULATE F"E2r THERHAL COHDITIOH Q

SUHHF'O. SUHHT»0. SUHHL»0. DO 7 1 I « 1 , H C SOHHF»SUHHF*XF(I)*HL(TFD,I) SUHHL»SUnHL*XF(I)*HL(TBP,I)

71 SUHHTaSUHHT*XF {I )*H7 (TDH,I) Q« (SUHHT-SUHHF) /(SUHHT-SUHHL) RETURH EHD

105

c SUBROUTIHE TEHEST(PCOL,T.ICASE) IHTEGER BK COHHOH / E S T R / PTA (10) ,P7B (1 0) , PTC (10) ,PTD (10)

COHHOH HC,LK,HK C C TO ESTIHATE TOP AHD BOTTOH TEHPERATURES FOR THE CALCULATIOH C OF RELATITE TOLATILITIES. HEHTOH» S flETHOD IS USED TO ESTI-C HATE THE TEHPERATURES BASED OH THE HARLACHER TAPOR EQH, C

TOL=0.1 PTP»PCOL•760.

6 0 TO ( 1 0 , 2 0 ) , I C A S E 10 L1«LK

GO TO 30 20 L1»HK 30 DO 5 I « 1 , 2 0

FT«PTA(L1) • ( P T B ( L I ) / T ) •PTC (LI) •ALOG (T) • PTD (LI) *PTP/ (T««2) 2-ALOG (PTP)

DFDT»-1.*PTB ( L 1 ) / ( T * * 2 ) •PTC (LI) / T - ( 2 * P T D (LI) *PTP) / ( T * « 3 ) T2»T- (FT/DFDT)

IF (ABS(FT ) .LT.TOL) GO TO 200 T ' T 2

5 COHTIHUZ HRITB ( 6 , 9 0 0 ) T,FT

900 FORnAT(« * , • TEHPEST DID HOT COHTRGE * , / , » T=» , E 1 5 . 5 , El 5 . 5 ) STOP

200 RETURH EHD

C SUBROUTIHE BUBDEH ( P , X F , X T , T , I B D , I T P ) EXTERHAL BDOBJ

C COnBOH/HBB/X(10 ) ,1 (10 )

COHHOH HC,LX,BK DIHEHSIOH XT (9) , X F ( 9 )

C

90

50

60

70 80

220 230

290 250 260

GO TO ( 9 0 , 6 0 ) , I B D DO 50 1=1,HC X ( I ) ' X F ( I ) T ( I ) « X T { I ) GO TO 80 DO 70 I « 1 , H C T ( I ) - X F ( I )

X ( I ) « X T ( I ) COHTIHUE

CALL EQS0L7 ( P , T ,BDOBJ,TOL,IBD) GO TO ( 2 2 0 , 2 9 0 ) , IBD DO 230 J a 1 , H C XI (J) »T (J) GO TO 260

DO 250 1=1 ,HC X T ( I ) « X ( I ) RETURH

106

EHD C

SUBROUTIHE GEQH(T,P) COHHOH/FIT/. ZK (5) ,ZKC ( 5 , 5 ) , PREF COHHOH RC,LK,HK

C C EQUIL K TALUES CALCULATED BT POLTHCHIAL IH TEHP (K) AT C REFEREHCE PRESSURE PREF

T R « 1 . 8«T DO 2 3 0 1=1,HC

S 1 = 0 . DO n J 2 » 1 , 9

17 S1 = S U ( 2 K C { I , J 2 ) *TR** ( J 2 - 1 ) ) EK(I)»(PRZF/P) 'SI

230 COHTIHUE HBTURH EHD

C SOPHOUTIHE GALFA (PCOL, PBOT) IHT2GER HK COHHOH/FIT/ ZK(5) , 2 K C ( 5 , 5 ) ,PREF COHHOS HC,LK,HK COnHOH/BL0CK3/TBOT,TFD, TTOP,TOUTC C0HH0H/BL0CK1/IF(15) ,XD(15) ,ALFA (15)

DIHEHSIOH EXTOP(10) ,EKHID(10) ,^KET(10) C C CALCULATE RELATT72 TOLATILITIES BASED UPOH T2HPEHATURES C -OBTAIHED FRCH ROUTIHE TSflZST.

THID » ( T T 0 P * T 3 0 T ) / 2 . DO 90 1=1 ,HC CALL GBQH(TTOP,PCOL)

90 EKTOP (I)»EX(I) DO 91 1=1,HC CALL GZQK (THID, PCOL)

91 EKHID(I)=EK(I) DO 92 1=1,HC CALL GEQK (TBOT,PBOT)

92 EKBT(I )»EK(I ) C

DO 10 1 I * 1 , H C 101 ALFA(D =( (EKTOP(I)/EKTOP(HK))* (EKHID (I ) /EKHID (HK) )

2 * (EKBT(D /EKBT (HK) ) } • * . 33333 RETURH EHD

C SUBROUTIHE CHEUTT (PCOL) COHHOH/BLOCX2/FD,SUHB,S0HD,D(15) , B (15) , 7 ( 1 5 ) , 1 3 ( 1 5 ) COHHOH/BL0CK3/TBOT,TFD,TTOP,TOOTC COHHOH HC,LK,HK COBHOH/EHTH/S0HHF,S0HHB,S0HHC C0nH0H/BL0CK1/TF(15) , XD (15) ,ALFA (15) COHflO H/BL0CK9/B,HT,ET A COHHOH/DUTT/QHEB,QCOHD

107

C CALCULATE COHDEHSER DUTT SUHHT«0. SUHHC«0. DO 22 I » 1 , H C SUHHT»SUHHT*XD(I) •BT(TTOP,I )

22 SOHHC«SUHHC*XD(I) •HL(TO0TC, I) QCOHO»SUHD« ( (R^ 1)•SUnHT-R*SUHHC-SUHHC) RETURH EHD

C SUBROUTIHE RBEUTT (PCOL) HEAL HT,HniH COHHOH/DOTT/QREB,QCOH D COnHOH/BLOCKVXF(15),XD(15) ,ALFA (15) COHHOH HC,LK,flK COHHOH/BLOCH2/FD,SUHB,SUHD,D(15) , B (15) , F (15) , X B ( 1 5 ) COHHOH/BL0CK3/TBOT,TFD,TTOP,TOUTC COHHOH/EHTa/SUHHF,SUHHB,SUHHC C0HHO»/BL0CK9/R,HT,ETA

C C CALCULATE BEBOILZR DUTT. C

SUHHF«0 SUHHB=0. DO 22 I » 1 , H C SUHHF=SUHHF*Xr(I)•HL(TFD,I) SUHHB»SUHHB+XE(D•HL(TBOT,I)

22 COHTIHUE QR2B«SUnD*SUHHC+SUHB«SUHHB*QC0HD-FD*SUHBF RETURH EHD

C SUBROUTIHE COtSPC(PCOL) REAL HT,HHIH,L(5) COHHOH HC,LK,.HK COHHOH/BLOCK 9/DC,HC,CCOST,TRTC ST COHHOH/BL0CH3/TBOT,TFD,TTOP,TOUTC COHHOH/BLOCH2/FD,SUHD,SUHD,D(15) , B (15) , F ( 1 5 ) , X B ( 1 5 )

C0HH0H/DAT1/ PC (5) ,TC (5) ,H (5) COHHOH/DEH/ DEHA (5) ,DEHB (5) ,DEHC (5)

C0HH0H/BL0CX9/R,HT,ZTA COHflOH/BL0CK1/XF (15) ,XD(15) ,ALFA(15) COHHOH/FIT/ EK(5) , 2 K C ( 5 , 5 ) ,PPEF COHHOH/EHTT/aTC(5,5) ,HLC(5 , 5) , Hn(5)

DIH2HSI0H T(5) ,HH0L(5) , 2 ( 5 ) , T ( 5 ) C C FIHD COLUHH SPECS — DIAH2T2R, HEIGHT AHD COST ESTIHAT2S C FOR TBAT AHD TOHER C

RG«8 2 . 0 5 CALL GZQK (PCOL,TOUTC) DO 2 1 I » 1 , H C L ( I ) «P*SOHD*XD (I) RHOL(I)«DEHA (I) •DEHB (I ) •TTOP^ DEHC |I) • (TT0P**2)

108

P 0 « 0 . 0 8 3 - 0 . 9 2 2 / ( ( T T O P / T C ( I ) ) * * 1 . 6) B 1 « 0 . 1 3 9 - 0 . 1 7 2 / ( (TTOP/TC (I) ) * * 9 . 2 ) 2 ( I ) » 1 . * ( H 0 + 1 ( I ) • B l ) • ( P C O L / P C ( I ) ) / ( T T O P / T C ( I ) ) I ( I ) « E K ( I ) , ^ T D ( I )

21 T ( I ) »(E*SUHD + SOHD) • T ( I ) C

SDRL»0, SHRL'O. SUHZ«0. AHH-0. AflT=0. DO 3 1 I « 1 , H C SHRL»SHRL*L (I ) •HH (I ) SDRL»SDRL*L (I) •HH (I) /RHOL(I) SUHZ=SUH2^T (I) •Z (I) AHH=AHH*XD(I)^HH (I) AflT«AflT»I(I) •WHd)

31 C0HTIHU2 C

RHJOL-SHHL/SDRL BH0Ta<PC0L/SUH2/RG/TTOP) •AHH LL» (SHRL/60-/RHJOL) • 2 6 9 . 17E-6 T L » ( A H T / 3 6 0 0 / R H O T ) • ( 3 5 . 3 1 9 5 / 1 0 ^ ^ 6 ) F l - 1 . 7 9 5 X P » 1 .

C D C - ( ( L L - 5 0 0 . ) / ( 5 . 2 2 ^ ( T L - 5 . ) +46 1-) ) • ( ( T L - 5 . ) / 3 . 75) + 5 . 2

C HC=«(29 . /12 )^(HT/2TA) • 6 -

F P « 1 . 0 I F (PCOL.GT. ; - ) F P - 1 . 1

C C O S T « ( 6 2 0 . ^ 3 9 8 . ^ ( D C - 2 . ) ) ^ ( ( H C / 9 . ) • • 0 . 8 ) ^ F P ^ F I I F ( D C . G T . 3 . ) X P » 1 . 1 6

I F (DC. GT. 5 . ) XP=1 .36 IF ( D C . G T . 7 . ) X P a 1 , 9 7

TRTCST= (HT/2TA) • ( 1 6 ^ ( (DC/2 . )^^XP) ) • F I C

R2TURH EHD

C FUHCTIOH HL(T,I) C0HH0H/EHTT/HTC(S,5) , HLC ( 5 , 5 ) ,HH(5)

C C LIQUID EHTHALPI2S CALCULATED BT POLTHOEIAL IH TEHP OBTAIHED C BT L2AST SQUARE F I T . SAHE IS TRUE FOR TAPOR EHTHALPIES.

SUflL'O. DO 19 J 2 = 1 , 9

19 SUHL«SUHL^(HLC(I ,J2 )^T^*(J2-1 ) ) HL«-1 .^«f l ( I ) •SUHL RETURH EHD

C FUHCTIOH H T ( T , I ) COHHOH/EHTT/HTC(5,5) , HLC ( 5 , 5) , HH (5)

109

SUHT-0. DO 16 J 2 « 1 , 9

16 S U H T « S U n T * ( H T C ( I , J 2 ) ^ T ^ ^ ( J 2 - 1 ) ) H 7 « ( - 1 . )^HH^I)^SUnT

c c

BETURH EHD

FUHCTIOH BDOBJ ( P , T , IBD) C

COHHOH HC,LK,HK COHHOH/BBB/X(10) ,T(10)

COHHOH/FIT/ ZK(5) ,EKC ( 5 , 5 ) ,PREF C

TOL'-OI S 0 « 1 . DO 130 I C T * 1 , 9 0 CALL GEQK (T,P) S 1 - 0 . GO TO ( 9 0 , 6 0 ) , I B D

90 DO 50 1=1,HC I ( D = E K ( I ) ^ X ( I )

50 S 1 « S 1 * I ( I ) GO TO 30

60 DO 70 I « 1 , H C I ( I ) « T ( I ) / E K { I )

70 S 1 » S 1 * X ( I ) C 80 I F (ABS(SI -SO) .LT-TOL) GO TO 190

S0-S1 GO TO ( 9 0 , 110) , IBD

90 DO 100 I « 1 , H C 100 T ( I ) » T ( I ) / S 1

GO TO 130 110 DO 120 1=1,HC 120 X ( I ) « X ( I ) / S 1 130 COHTIHUE

HHITE ( 6 , 1 9 1 ) HRIT2 ( 6 , 1 9 5 ) SI

195 FORHAT (• • , » SI = • , F 9 , 9 ) STOP

190 B D 0 B J - S 1 - 1 . GO TO (150,170) ,IBD

1S0 DO 160 1=1,HC 160 T(I)»T(D/S1

GO TO 190 170 DO 180 I»1,HC 180 X(I)«X(I)/S1 190 COHTIHUE 191 FORHAT (• ' , • BDOBJ DID HOT COHTERCI«)

RETURH EHD

C SUBROUTIHE EQSOLT ( P , T , BDOBJ ,TOL, IBB)

no

TOL*.01 T1«T F1»BD0BJ(P ,Jr i , IBD) T 2 « 1 . 2 5 * T 1

r 2 » B D O B J ( ? , T 2 , I B D ) C

DO 10 I H L « 1 , 2 0 I F ( F 1 * F 2 . G T . O . ) GO TO 5 T « ( T 1 ^ F 2 - T 2 ^ T 1 ) / ( F 2 - F 1 ) GO TO 8

5 T » T 1 - ( 1 . - . 6 ^ ^ I H L ) • F l ^ (T2-T1) / ( F 2 - F 1) 8 F 3 « B D 0 B J ( P , T , I B D )

I F (ABS(F3)-LT-TOL) GO TO 20 T1«T2 T2»T F 1 - F 2

10 F2»F3 WHITE ( 6 , 9 2 ) STOP

2 0 RETURH 9 2 FORHATC » , ' 2QS0L7 DID HOT COHTERGE')

EHD C C PROGRAH HGFUG C THIS PROGRAH CACLULATES DISTILLATE AHD BOTTOHS C COHPOSITIOHS FOR A DISTILLATION COLOHH. C HEHGST2BECK-GZDDES-F2HSKE-0HDERHO0D-GILLIAHD SflORT-C CUT DISTILLATIOH HBTHOD. CC C THE OUTPUT CONSISTS OF TH2 FOLLOWING: C 1 . HO. OF IT2RATI0HS IN TH2 HEHTCH RAPHSOH HETHOD C 2- C0H7ERGED TALUES OF DFLK AHD ZFHK C 3.DISTILLATE AHD BOTTOHS COHP-C 9.HHIH BT FEHSKE'S EQH. C 5 . PHI AHD RHIH BI TH2 OHDERHOOO* S ZQNS, C 6 . NO. OF TH20R, PLATES AT SPECIFIED H BT C GILLIAHD'S CORRELATIOHS. C C HEF2HEHC2:HTDR0CARB0H PROCESSING, AOGOST, 1 9 8 0 , PG. 8 0 .

SUBBOUTIHE HGIUG REAL HT,HHIH IHT2GER LK,BK D1H2HSI0H FUHC(2) , S ( 2 ) ,G(2 ) ,DG ( 2 , 2 ) COnHOH/BLOCK1/XF(15),XD(15) ,ALFA (15) COHHOH/BL0CX2/FD,SUHB,SUHD,D(15) ,8(15) ,F(15),IB(15) COHHOH HC,LK,BK C0flHOH/BL0CK9/R,NT,ETA BQUI7ALEHCE (C2,HHIH) , (S (1 ) ,DFLK) , (S(2) ,BFHK) COHHOH/RBCT/XCHK,XBLK,DFLK,BFHK,Q,BPH,N HIH,PHI,BHIH,K

C C CASBT OUT NEWTON RAPHSOH C

KHAX»20

I l l

DELTA*.00001 DO 100 K«1,KHAX CALL H G ( S ( 1 ) , S ( 2 ) ,C2 ) FUHC(1)=XD(HK)-XDHK FUHC ( 2) «XB (LK) -XBLK I F (ABS (FUHC ( 1 ) ) - L T - . 0 0 0 1 . AND. ABS (IDHC ( 2) ) . L T . 0 0 0 1 )

2 GO TO 2 0 0 C C ESTIHATE THE FOUR PARTIAL DERI7ATITES C

DO 5 1 = 1 , 2 5 G(I )=FUHC(I )

0 0 20 1 = 1 , 2 S ( I ) « S ( I ) •DELTA CALL HG(S(1) , S ( 2 ) ,C2) FUHC (1) »XD (HK) -XDHK FUHC ( 2) =XB (LK) -XBLK 0 0 10 J » 1 , 2

10 DC ( J , I) » (FUHC ( J ) - G (J) ) /DELTA 20 S ( 1 ) » S ( I ) - D E L T A C C UPDATE DFLK AND BFHK C

DH=DG ( 1 , 1 ) •OG ( 2 , 2 ) - D G ( 1 , 2 ) ^ 0 G ( 2 , 1) D E L S 1 » ( G ( 2 ) ^ D G ( 1 , 2 ) - G (1) •DG ( 2 , 2) ) / D f l D E L S 2 « ( G ( 1 ) ^ D G ( 2 , 1) - G ( 2 ) ^ D G ( 1 , 1 ) ) / D n S (1) = S (1 ) • D E L S I S ( 2 ) = S ( 2 ) •DELS2 I F ( S ( I ) . G T . 1.) S ( 1 ) = . 9 9 9 9 I F ( S ( 2 ) . G T . 1.) S (2) = . 9 9 9 9

100 COHTIHUE GO TO 500

C c 200 COHTIHUE C CALCULATE HHIH BT UHDERHOOD'S EQNS. C

CALL UWD(Q,PHI,RHIH) C C FIHD HO. OF THEOR. PL. AT SPECIFIED R BT C GILLIAHD'S CORRELATION, C

B«RRH*RHIH CALL GLLD(B, RHIH, HT, HHIH)

500 BETURH EHD

C SUBROUTIHE HG (DFLK, BFHK ,C2) INTEGER LK,HK C0HHOH/BLOan/XF(15) ,XD (15) ,ALFA (15) C0HHON/BL0CX2/FD,SUHB,SUHD, D(15) , 3 ( 1 5 ) , F ( 1 5 ) , IB (15) COHHOH HC,LK,BK

C C ESTIHAT2 OISTRIBUTIOH OF COHPOHEHTS IN THE DISTILLATE

112

C AHD THE BOTTOHS BT THE HENGSTEBECK-GEDDZS HETHOD. C

DO 10 1=1 ,HC 10 F ( I ) « P D ^ X F f l )

D(LX) «DFLX^F(LK) B(LK)«F(LK)-D(LK) 0 (HK) » (1 . -BFHK) *F (HK) B(HK) «F(HK)-D(HK) C1«AL0G(D (HK)/B(HK) ) C2«AL0G(D(LK)/D(HK) -B (HK)/B (LK) )/ALOG (AIFA (LK) ) DO 20 1=1 ,HC I F ( I . 2 Q . L K ) GO TO 20 IF ( I . E Q . HK) GO TO 20 B ( I ) « F ( I ) / ( 1 ^ E X P (C1^C2ÂL0G (ALFA ( I ) ) ) ) D ( I ) « F ( D - B ( I )

20 CONTINUE C C CALCULATE THZ HOLE FRACTIOHS C

SUHD«0 SUHB»0 DO 30 1=1 ,HC SUHD«SUHD^D(I)

30 SUHB«SUHB^B(I) 0 0 90 1=1 ,HC ID ( I ) «D (I ) /SUHO

90 X B ( I ) = B ( I ) / S U H B RETURH END

C SUBR0UTIN2 UWD (Q,PHI,HHIH)

C THIS SUBRO0TIH2 CALCULATES RHIH BT TH2 OHDERWOOD'S C EQUATIOHS. THE 7ALUE OF PHI LTING BETHZEH THE ALFAS OF C THE KETS I S OBTAINED BT THE BISECTION HITHOD C

REAL HT,HHIH IHTEGER LK,HK C0HH0H/BL0CK1/X7(15) ,XD(15) , ALFA (15) COHHOH HC,LK,HK PHILL=ALF A (HK) PHIULÂLFA (HK-1) DO 10 1 = 1 , 2 0 PHI«0.5^(PHILL^PHIUL) F P H I - 0 - 1 . DO 20 J=1 ,HC

20 FPHI«FPHIÂLFA(J) •XF (J ) / (ALFA ( J ) - P H I ) I F (FPHI) 3 0 , 5 0 , 9 0

30 PH11L=PHI • GO TO 10

9 0 PHIUL»PHI 10 COHTIHUE 50 R H I N - - 1 .

DO 60 I « 1 , N C 60 BHIN»RHINÂLFA (I) •XD (I) /(ALFA ( I ) -PHI)

113

RETURH 2HD

C SUBROUTIHZ -GLID (S ,RHIN, NT,HHIH) BEAL NT,HHIH X - ( H - B H I H ) / ( H ^ 1 . ) 1 = 1.-EXP ( ( 1 * 5 9 , 9 ^ X ) ^ ( X - 1 - ) / ( ( 1 1 . + 117.2^X)^SQRT(X)) ) N T » ( 7 + N H I H ) / ( 1 . - T ) BETURH EHD

C SUBROUTIHE DATAIN IHTEGER LK,HK REAL HT,HHIN C0HH0H/BL0CH1/XF(15) , XD (15) , ALFA (15) C0HHOI/BL0CK2/FD,SUHB,SUHD, D(15) , B (15) , F (15) , XB(15) COHHOH HC,LK,aK COHHOH/FIT/ ZK(5) , E K C ( 5 , 5 ) ,PHEF COHHOH/BL0CK3/TBOT,TFD,TTOP,TOUTC COHHON/BECT/XEHK,XBLK,DFLK,BFHK,Q,RRH,NNIN,PHI,PHIH, K

C0HH0H/DAT1/ PC (5) ,TC(5) ,W(5) COHHOH/DEH/ DEHA (5) , DENB (5) , DEHC (5)

COHHON/BLOCK 9/R , HT, ETA C0HH0H/2HT7/HTC(S,5) , HLC ( 5 , 5) ,HH(5)

COHHON/AAA/CL8L(8,6),PCOL,T,PBOT COHHOH / E S T R / PTA (10) ,PTB (10) , PTC (10) ,?TD (10)

READ ( 5 , 9 1 ) PCOL,T,TFD, PBOT,PR2F HEAD ( 5 , 9 2 ) NC,LK,HK DO 10 1=1,HC

10 READ ( 5 , 9 3 ) (CLBL(I,K) , K = 1 , 5 ) , T C ( I ) , P C ( D , H ( I ) ,HH(I) DO 15 1=1 ,NC R2A0 ( 5 , 9 6 ) ( H L C ( I , J 2 ) , J 2 = 1 , 9 ) R2AD ( 5 , 9 6 ) ( B 7 C ( I , J 2 ) , J 2 = 1 , 9 ) READ ( 5 , 9 1 ) PTA(I ) , P T B ( I ) , P T C ( I ) , P T D ( I ) READ ( 5 , 9 6 ) (ZHC ( I , J2) , J 2 = 1 , 9)

IS READ ( 5 , 9 6 ) DEHA ( I ) , DENB ( I ) , DEHC (I ) READ ( 5 , 9 1) Q,RRH,XDHK,XBLK DO 30 1=1 ,NC

30 READ ( 5 , 9 1 ) XT (I ) HEAD ( 5 , 9 1 ) DFLK,BFHK READ ( 5 , 9 1 ) FE

c 91 92 93 96 C

FORHAT (10F10.3) FORHAT (912) FORHAT (5A9,9ri0.3) FORHAT(5(211.5,9X))

RETURH END

SUBROUTIHE PRNTA IHTEGER LK,HK REAL NT,HHIH

114

10

15

16

20

HRIT2 DO 10 HRITE WRIT2 WRITE DO 15 HRIT2 WRITE DO 16 WRITE WRIT2 DO 20 WHITE

97

39

25

301

302 C 303 309 305 307

309

311 312

C0flHOH/BL0CX1/XF(15) , XD (15) , ALFA (15) C0nH0H/BL0CH2/FD,SUHB,SUnD, 0 ( 1 5 ) , B(15) , F ( 1 5 ) , I B ( 1 5 ) COHHOH NC,LK,HK COHHOH/FIT/-EK (5) , E K C ( 5 , 5 ) ,PREF COHflOH/BLOCH 3/TBOT,TFD,TTOP,TOOTC COHnOH/RECV/IEflK,XBLK,DFLK,BFHK,Q,RRH,HHIH,PHI,RHIH,K

C0HH0H/DAT1/ PC(5) ,TC(5) ,H(5) COHHON/DEN/ DEHA (5) , DENB (5) , DEHC (5)

C0HH0H/BL0CK9/R,HT,ETA COnflON/EHT7/HTC{5,5) , HLC(5, 5) , WH{5) COHHOH/BLOCK9/DC,HC,CCOST,TRTCST

COflHOH/AAA/CLBL(6,6) ,PCOL, T,PBOT COHHOH / E S T R / PTA(IO) ,PTB(10) , PTC (10) ,PTD(10) WRITE ( 6 , 3 0 1 )

( 6 , 3 0 2 ) 1=1 ,NC ( 6 , 3 0 3 ) ( 6 , 3 3 1 ) ( 6 , 3 0 9 ) 1=1 ,NC ( 6 . 3 0 5 ) ( 6 , 3 3 7 )

1=1,HC ( 6 , 3 0 5 ) ( 6 , 3 0 7 )

1 = 1 , N C ( 6 , 3 0 3 ) (CLBL ( I , K ) , K = 1 , 5 ) , P T A ( I ) , P7B (I) , P T C ( I ) ,PTD (I)

WRITE ( 6 , 3 2 3 ) DO 97 1=1 ,NC WRITE ( 6 , 3 2 5 ) I , (EKC ( I » J 2 ) , J 2 = 1 , 9 )

WRrTE(6,391) 'DO 39 1=1,HC

I ,DEHA(I) ,DEHB(I) ,DZHC(I) ?C0L,7D

( C L B L ( I , K ) , K = 1 , 5 ) , T C ( D , P C ( I ) .W(D ,H?!(I)

(CLBL ( I , K ) , K = 1 , 5 ) , (HLC ( I , J2) , J 2 « 1 , 9 )

( C L 3 L ( I , K ) , K = 1 , 5 ) , ( H T C d , J2) , J 2 = 1 , a )

WHIT2(6,325) WHITE (6,309) WRITE (6,311) DO 25 1=1,NC WRIT2 (6,312) WRIT2 (6,902) WRIT2 (6,920) WRITE (6, 906) WRITE (6,907)

: : , i P ( i ) lK,flK RRH XDHK,XBLK DFLK,BFHK

FORHAT ( / / / • 1 » , 10X,'SHORT-CUT DISTILLATIOH D E S I C N » , / / , 1 5 1 , 2'THE STSTEH* , / / )

FORHAT ( / ' 0 « , 3 X , • C O H P O H E H T ' , 1 9 X , ' T C « , 8 X , ' P C ' , 8 1 , ' H » , 8 X , « n W » )

FORHAT (• « , 5 A 9 , 2 X , 5 F 1 0 . 3 ) FORHAT ( / / • • , 2 7 X , « H L A ' , 1 0 X , « H L B » , 1 1 X , ' H L C M FORHAT (• » , 5 A a , 5 E 1 3 . 5 ) FORHAT ( / / • «,5X,»HARLACHER TAP EQH C O H S T S • , / , 2 8 X , • P T A * ,

2 8 I , « P T B « , 9 X , * F 7 C ' , 9 T , ' P T D » ) FORHAT (' • , / # 5 X , ' T H 2 COLOHH PRESSORE I S • , F 1 0 . 3 , « A T H * , / ,

25X,»THE FEED RATE I S • , F 1 0 . 3 , ' KG POL/H S«) FORHAT ( / / , 1 0 X , ' T H E FEED COHPOSITIOH IS » , / , 5X , « I * , 1 2 1 , ' XF ( I ) ' ) FORHAT (• • , 2 2 , I 2 , 5 X , F 9 . 9 )

115

902 FORHATC • , / / , 5 X , ' L I G H T KET I S COHPOHEHT NO- ' , 1 5 , / , 25X,«HEATT KET I S COHPOHEHT HO. ' , 1 5 )

920 FORHATC • , 5 X , « T H B OPERATIHG RZFLOX RATIO I S » , F 8 . 3 , 2* TIHES Rfl£H «)

906 FORHATC • , S X , ' T H 2 SPECIFIED HOLE FRACTIOHS OF THE KETS ' , 2 ' I N THE DISTILLATE • ,5X,«AHD IN THE BOTTOHS ABE ' , / / , 3 1 0 X , ' I D ( H K ) « « , F 1 0 . 9 , 1 5 X , « I B ( L K ) » ' , F 1 0 . 9 )

907 FORHATC • , / / , 5 X , « T H E IHITIAL GOSSSED TALOES OF THE • 2 , 'DISTRIBUTIONS ARE ' , / / , 2 X , ' DFLK »« ,F1 0 . 9 , 5 X , • BFLK = ' , F 1 0 . U )

323 FORHAT (' ' , / , 5 X , • EQUIL K TALOZS WERE CALCOLATED WITH A • , • •POLTHOHIAL IN TEHP ' , / , 1 2 X , ' EKI • , 1 2 1 , • ZK2' , 1 2 1 . • E K 3 ' , 12X, • ZK9 »)

C 325 FORHATC • , 1 3 , 3 ( 5 X , 9 E 1 9 . 5 ) ) 331 FORHATC ' # / / , 5 X , » L I Q U I D EHTHALPIIS (HL) AND TAPOR ENTHALPIES',

1» (H7) IRE CALCULATED BT A POLTHOHIAL IN TEHP.') 337 FORHAT (• • , / , 2 7 X , • H7A' , 1 0 1 , ' H TB' , 10X, ' HTC ) 301 FORHATC ' , / , 5 X , ' L I Q U I D DEHSITIES CALCULATED AS QUADRATIC IN ' ,

1 ' T 2 H P E R A T U H E ' , / , 5 X , ' D E H A ' , 8 X , ' D E N B ' , 8 X , ' D E H C ' ) BETURH EHD SUBROOTIHE PRNTB

C INTEGER LK,HK REAL NT,HHIH C0HHOH/BL0CK1/XF(15) ,XD(15) ,ALFA( 15) COHHOH/BLOCK2/FD,SUHB,SnHD,D(15) , 3 (15) , F ( 1 5 ) ,XB(15) COHHOH NC,LK,aK COHHOH/FIT/ EK(5) , E K C ( 5 , 5 ) ,PREF COHHOH/DOTT/QHZB,QCOHD COHHOH/BLOCK 3/TBOT,TFD,TTOP,TOUTC C0flfl0H/R2C7/XEHK,XBLK,DFLK,BFHK,Q,RRH,HHIH,PHI,RHIH,K C0HHOH/BLOCH9/H,HT,ZTA COHHOH/EHTH/SUHHF,SUHHB,SUHHC COHHOH/CPDATA/CPA (5) , C P 8 ( 5 ) ,CPC(5) ,CPD(5) C0HH0N/BL0CK9/DC,HC,CCOST,TRTCST SUHB-SUH8/1000-SUflO-SUHD/1000. WRIT2 ( 6 , 9 0 8 ) WRITE ( 6 , 9 0 9 ) K,DFLK,BFHH WHITE ( 6 , 9 1 0 ) ( I , D ( I ) , XD (I) , 3 ( 1 ) ,XB (I) ,AIFA (I) , 1 = 1 , NC) WHIT2 ( 6 , 9 5 5 ) SUHO,SUHB WRIT2 ( 6 , 9 1 1 ) NHIH W8IT2 ( 6 , 9 1 2 ) P H I , RHIH WRIT2 ( 6 , 9 1 3 ) R,NT WRITE ( 6 , 9 0 3 ) Q WRIT2 ( 6 , 9 9 7 ) TFD WRIT2 ( 6 , 9 3 3 ) TBOT,TTOP,TOUTC,QRE3,QCOHD HRITE ( 6 , 9 9 1 ) SUHHF,SUnHB,SUnHC WRITS ( 6 , 9 3 5 ) HC,DC,CCOST,TRTCST

C 903 FORHATC ' , 5 X , ' F E E D THERHAL COHDITIOH Q I S • , F 7 . 2 ) 908 FORHATC ' , / / , 5 X , • • • • « • • OUTPUT • • • • * = t ) 909 FORHATC ' , / , 5 X , ' A F T E R ' , 1 5 , ' ITERATIONS THE ACCEPTED',

2 ' TALUES OF THE DISTRIBUTIOHS A R E ' , / / , 1 O X , ' D F L K « ' ,

116

3 F 1 0 . 9 , 5 X , » B F H K » ' , F 1 0 . 9 ) 910 FORHATC ' , 9X,» I ' , 8 X , ' D (I) • , 1 1 X, » XD (I) ' , 1 0 X , ' B (I) ' , 1 1 1 ,

2 ' I B ( I ) ' , 1 I X , ' A L F A (I ) ' , / , ( 1 5 , 5 2 1 5 . 6 ) ) 911 FORHATC » ; / / , 5 X , ' H I H I H U H HUHBER Of PLATES « « , F a - 3 ) 9 1 2 FORHATC « , 5 X , ' P H I «» , F 1 0 . 6 , 5 X , ' R H I H » ' , F 8 . 3 ) 913 FORHATC « , 5 X , ' A T R = • , F 7 . 3 , 5 X , • HO. OF THEOR. PLATES « '

2 , F 7 . 3 ) 955 FORHATC ' , 2 X , ' T O T A L ' , F 1 3 . 9 , 1 5 I , F 1 3 . 9 , ' KG NOL/HR') 933 FORHAT (' » , / / , 5 X , ' BOTTOHS TErP = • , F 8 , 3 , ' K«,6X,

2'TOP DEH TEHP « ' , F 8 . 3 , ' K ' , 5 X , ' T 0 P BUB TEHP = ' , F 8 , 3 , ' K 3 / / , 5 X , ' R E B O I L I R DUTT » ' , 2 1 3 . 5 , ' J / H R ' , 1 0 X , 9»C0HDENSER DOT! = ' , E 1 3 . 5 , ' J /HH')

991 FORHAT (' ' , ' EHTHALPIES - J/HR ' , / / , 2 5 X , ' F E E D ' , T 3 2 , E 1 3 . 5 , / , 5 X , ' B O T T O H S ' , T 3 2 , E13 . 5 , / , 5 X , ' T O P S ' , 3 T 3 2 , E 1 3 . S )

935 FORHATC • , / / , 5 X , ' C O L U H H HEIGHT « • , r 9 . 9 , » F T ' , / , 5 X , 2'COLnHN DIAH » « , F 1 0 . 3 , ' F T ' , / , 5 X , ' C C L O H H COST = ' , E 1 3 . 5 , / , 2SX,'TRAT COST = ' , E 1 3 . 5 , ' 1977 DOLLARS')

997 FORHAT ( ' » , / , 5 X , ' T H 2 F22D TEHP IS ' , F 6 . 1 , ' K') RETURH END

C S2HTRT

TRAY-TO-TRAY DYNAMIC MODEL 117

C THIS IS THE UNSTEADT-STAT2 SIHULATION OF A C DISTILLATIOH COLUHH,

REAL L , L S , L C , H T , D 2 ( 1 0 0 ) ,WK(1100) , L 1 S IHTEGER IWr(IOO)

COHHON/PHTS/ TC (5) , P C ( 5 ) , W ( 5 ) , PDK (50) , SHOT (50) , AHT (50) COHHOH/BLOCK2/FD,BF,DF,TFD,PCOL,CLflL(6,6) ,WH(15) , I F ( 1 5 ) ,PFD,PBZF COHHON NC,NT,HFT,NTH1,IBC,ITC COHflON/FIT/ ZK(5) . E K C ( 5 , 5 ) COHHOH/TRAT/7(50) , L ( 5 0 ) , T ( 5 0 ) ,DEHS(SO) , JHW(50) ,PT(50) ,LC C0BH0N/F22D/XID(5) ,TFD(5) ,FDT, FDL,FFL,HF7 C0flH0H/EHT7/H7C ( 5 , 5 ) , HLC ( 5 , 5) COHHON/XICHP/X(50,5) , T ( S 0 , 5 ) , H L ( 5 0 ) ,HT(50)

COBflOH/PSD/LS (50) , XS (50) , I S (50 ) , TS (50) ,FDD,XFSD, DPS COHflOH/DUTT/QHB,QCHD COflHON/COLSP/WL , HOW , DC, PB, PD, PKCB, PKCD, S COHHOH/BB B/XH ( 1 0) , TH (10) C0HH0N/IHIT/H1 (50) , HT (50) C0HH0H/DHW/D2NA (5) ,D2NB (5) ,DEHC (5) DIHEHSIOH XT (5) , I F L ( 5 ) , 2 ( 1 0 0 ) EXT2RHAL D2P,FCNJ N A H E L I S T / A H H / X , T , T , T , L , I S , T S , 2 , L S

C THIS PROGRAH USES TH2 IHSL DGEAR PACKAGE TO S0LT2 THE SET C OF DIFFEREHTIAL ZQHS DESCRIBING THE DTHAHICS OF i DISTILLATION C COLUHH, DIFF2RENTIAL 2QNS FOR OTEHALL HISS AND COHPOHEHT HASS C BALANCES ARE SOLTED. THE 2NERGT EQUATION I S ASSUHED TO BE AT C ST2A0I-STAT2. D2 I S TH2 ASRAT CONTAINING TH2 DIFF2aENTIAL C 2QHS. D2(1 ) TO 02 (NT) COHTAINS OTERALL HASS BALANCE EQNS. C D2(HT^J) CONTAINS COHPONBNT flASS 3ALANC2 FOB COHP 1 ON C J'TH TRAT. ARRAT 2 CONTAINS INITIAL CONDITIONS FOR TH2 SET C OF DIFFEREHTIAL EQNS- 2 ( 1 ) TO 2 (NT) I S FOR OTERALL HASS C BALANCE AND 2(HT+J) I S US2D FOR CCHPOHZNT BALANCES. C C rH2 HULTICOHPOHEHT STSTEH I S ASSUHED TO BZ ADEQUATELT C H002L2D BT A PSU2D0BINART WHERE COHP 1 IS THE LIGHT KET C AND COHP 2 I S THE HZA7T KET. C C C D2FINITI0NS: C C AHW=AT2RAG2 H0L2CULAR WEIGHT ON TRAT J (KG/KGHOL) C AflHTS=ST2ADT STATE NOLAR HOLDUP IN REFLUX EROn C Afl1S»STEADT STATI HOLAB HOLDUP IN BOTTOHS OF COLOHH C BF«BOTTOHS FLOW HATE (KGHOL/HH) C BO-CONSTAHT FOR CALCULATION FOR Z FOR GAS C B1-C0HSTAHT FOR CALCULATIOH FOR 2 FOR GAS C DC»COLUHN DIAHETIH (H) C D2HS-LIQUID DEHSTTT OH TRAT J (G/CH««3) C DF«DISTILLATE FLOW RATE (KGHOL/HR) C DELT=IHCHEHENTAL TIHE STEP (HR) C DF0-ST2ADT STATE TALU2 OF DISTILLAT2 ILOW C D2(J)=T0TAL HOLR BOLDUP 021tlTATI7E W/H TO IIHE OH TRAT J C D2(HT^J)-LIGHT KET COHPOHEHT (PSUEDOBINART) DERITATITE W/H TO TIHZ C FOR TRAT J C DEHA, DEHB, DEHC COHSTAHTS USED TO CALCULATE LIQ DEHS AS F(T2flP K)

118

C EK»EQUIL K TAL02 FOR SPECIES I C EXC COHSTAHTS OSID TO CALCOLATE EK ( I ) AS F { TEHP R) C FO«FEED RATE (XGHOL/HR) C F0D=PSU2D0BINA2T FEED RAT2 (KGHOL/HR) C H-DG2AR PARAHATER C HL-LIQ BNTHALPT CH TRAT J (KJ/KGHOL) C HT-TAPOR BNTHALPT OH TRAT J (KJ/KGHOL) C 3TC-C0HSTANTS OSID TO CALCOLATE HT (J) AS F (TEHP K) C HLC-COHSTAHTS " •» n HL(J) " * C aFL»FEED LIQUID ENTHALPT (KJ/KGNOL) C HOW=eEIGHT OF WETR (H) C IBC = INDEX FOR BOTTOHS COHPOSITIOH CCNTROl C ITC « INDEX FOR EISTILLATE COHPOSITIOH CONTROL C IWK«DGEAR ABB AT C L-LIQUID FLOW RATE ON TRAT J (KGHOL/BR) C L1S-STEADT STATE BOTTOHS FLOW (KGHOL/HR) C LS»PSU2D0BINAHT FLOW OF THAT J C HTaLIQUID HOLDUP OH TRAT J (KGHOL) C HETH »DG2AR PABAH2T2R C HIT2R»DG2AR PAHAn2T2R C NC=NUHBHB OF COHPOHEHTS C NT=NUHBEB OF TRATS C NFT«F22D TRAT HUHBER C NTH1«T0P TRAT C ?KC3»PH0PORTIONAL C0NTR0LL2H CONSTANT FOR BOTTOHS FLOW ON LIQUID C L2T2L CONTROL C PKCD«PROPORTIOHAL CONTROLLER CONSTANT FOR DISTILLATE FLOW ON LIQOID C •L27EL CONTBCL C PC=CBITICAL PRESSURE (ATH) C P0K-PHESSUR2 DHOP CONSTANT C PT=PHESURE ON TRAT J (ATH) C PREF»REFERENCE PRESSURE FOR EQUIL K TALUE CALCULATION (ATH) C PD»TOP PRESSUR2 C PB«BOTTOnS PRESSORE C QRB=REBOILZR DUTT (KJ/HR) C QCND'CONDENSER DUTT (KJ/RR) C QCHDS=STZADT STATE COND DOT! C RG»GAS COHSTAHT C TI=TIHE (HR) C T00T=INT2GRAT2 FROB TI TO TOUT C T« T2HP OH TRAT J (K) C TC=CRITICAL TEHP (X) C T«TAPOR FLOW RAT2 OF TRAT J (XGHOL/HR) C TS-PSUEDOBINART TAPOR FLOW OF TRAT J (XGHOL/HR) C WL'HEH? L2HGTH (H) C HH«flOL2CULAR HEIGHT C W-ACC2HTRIC FACTOR C X-LIQUID HOLE FRACTIOH OF SPECIES I CN TRAT J C XS-PSOEOOBINART LIQUID HOLZ FRACTION OF LIGHT KET ON THAT J C XF«FEED COHPOSITIOH C XFSD«PSUEDOBINART FEED COHPOSITIOH C T»TAPOR COHPOSITIOH OF SPECIES I ON TRAT J C TS=PSUEDOBINABT TAPOR COHPOSITION OF LIGHT XET ON TRAT J C

119


EXAnPL2 0HST2ADT STAT2 SIHULATIOH

THE STST2H •

C0nP0H2HT N-H2PTAH2 H-0CTAH2

N-H2PTANE N-0CTAN2

H-H2PTAH2 N-OCTAH2

TC 5 9 0 . 2 0 0 5 6 8 . 8 0 0

PC 27.000 29.500

w 0 .351 0.259

HOL WT 1 0 0 - 2 0 0 1 1 9 - 2 3 2

HL1 0 . 19693E 0 . 1 8 9 5 9 B

HL2 09 - 0 . 8 9 3 8 7 2 09 - 0 . 5 3 5 1 1 2

HTA 0 . 1 6 8 6 7 E 0 . 1 7 3 8 3 2

HTB 09 - 0 . 1 2 3 5 0 2 01 09 - 0 . 2 1 3 6 8 2 01

HL3 OC - 0 . 2 2 6 0 5 2 - 0 2 00 - 0 . 2 6 9 6 0 2 - 0 2

HTC - 0 . 1 3 9 0 5 2 - 0 2

0 . 1 1 5 3 6 E - 0 2 0.182382

- 0 . 2 1 8 8 6 2 - 0 6 - 0 5

EQUIL K TALU2S EX1

1 0 . 9 5 7 9 2 00 2 0 . 2 3 3 9 E - 0 3

W2R2 CALCULATED WITH A POLTHCHIAL IN T2HP 2X2 EX3 2X9

0 . 1 9 2 5 2 - 0 2 - 0 . 1 1 9 5 2 - 0 9 0 . 1 1 9 0 2 - 0 7 0 . 3 2 7 3 2 - 0 2 - 0 . 1 1 5 1 2 - 0 9 0 . 1 0 2 0 B - 0 7

LIQUID DEHSITT CALCULATED BT DEN A (I) DEHB (I )

1 0 .9910E 00 - 0 , 1 1 2 6 2 - 0 2 2 0 .83392 00 - 0 , 9 0 8 1 2 - 0 3

QUADRATIC IN T !«'P DEHC (I)

0 , 2 9 0 8 E - 0 6 - 0 , 3 9 7 7 E - 0 6

TH2 COLUHH PB2SSUR2 I S 7 , 9 0 0 ATH TH2 F22D RAT2 I S 3 3 0 . 6 2 8 KGHOL/HR

NUHB2R OF TRATS= 32 F22D TRAT I S HOHBZR 18

FEED COHPOSITIOH I XF 1 0 . 6 2 1 8 2 0 . 3 7 8 2

F22D TEHP » 9 6 9 . 9

THE IHITIAL COHDITIOHS AR2

F22D Pfl2SS 7 . 9 0 0

TPAT T2HP 1 5 0 9 , 9 9 1 2 5 0 8 . 9 6 2 3 5 0 8 . 3 6 9 9 5 0 7 . 6 3 5 5 5 0 6 . 7 2 8 6 5 0 5 . 6 2 5 7 5 0 9 . 3 0 5 8 5 0 2 - 7 6 9 9 5 0 1 . 0 2 0

10 9 9 9 . 1 1 2 11 9 9 7 - 1 0 7

0 . 12338E 03 0 . 1 2 6 6 5 E 09 0 . 1 2 6 9 2 E 09 0 . 1 2 6 1 5 2 09 0 . 1 2 5 8 9 E 09 0 . 1 2 5 5 0 E 09 0 . 1 2 5 1 5 E 09 0 . 12981E 09 0 . 1 2 9 5 2 E 09 0 - 12932E 09 0 . 1 2 9 2 5 Z 09

T 0 .119302 0.119072 0. 11380E 0.113992 0 .113162 0 . 11280E 0 . 1129 7E 0 . 11218E 0 . 11197E 0. 11190E 0 . 1119 6E

09 09 09 09 09 09 09 09 09 09 09

HT 0.100 0.191 0.191 0,191 0.191 0.191 0.191 0.191 0,192 0,192 0.192

OOE 03 70E 01 672 01 652 01 652 01 672 01 132 01 862 01 06E 01 36E 01 78E 01

I I 0 . 0 2 2 3 2 0 , 0 3 1 8 0 0 . 0 9 9 2 0 0 . 0 6 0 2 5 0 . 0 8 0 7 7 0 . 1 0 6 5 7 0 . 1 3 8 3 1 0 , 1 7 6 3 9 0 . 2 2 0 6 8 0 , 2 7 0 3 7 0 . 3 2 3 9 3

0. 0. 0 . 0. 0, 0. 0. 0 . 0 . 0 . 0.

1 2 9 7 7 6 3 9 6 8 2 0 95580 93975 91923 89393 8 6 1 6 9 8 2 3 6 1 7 7 9 3 2 7 2 9 6 3 676 07

120

C12 C13 C19 C15 C16 C17 C18 C19 C20 C21 C22 C23 C29 C25 C26 C27 C28 C29 C30 C31 C32 C C WE

9 9 5 . 0 8 7 9 9 3 . 1 3 9 9 9 1 . 3 3 5 9 8 9 . 7 2 7 9 8 8 . 3 9 1 9 8 7 . 1 7 7 9 8 6 . 2 2 2 9 8 5 . 2 8 2 9 8 9 . 2 8 8 9 8 3 . 2 5 8 9 8 2 . 2 1 5 9 8 1 . 1 8 6 9 8 0 . 1 9 9 9 7 9 . 2 6 0 9 7 8 . 3 9 9 9 7 7 , 6 2 1 9 7 6 . 9 3 0 9 7 6 , 3 2 3 9 7 5 - 7 9 7 9 7 5 , 3 9 9 9 7 9 . 9 5 3

:IR LENGTH C HEIR HGHT= C COLOHN DIAH C C BOTTOH PRES

0 . 1 2 9 3 1 2 0 . 1 2 9 5 0 E 0 . 1 2 9 8 1 2 0 . 1 - 2 5 1 8 2 0 . 1 2 5 5 8 2 0 . 1 2 5 9 6 E 0 . 1 2 6 3 0 E 0 . 8 3 7 6 6 E 0 . 8 9 0 8 9 E 0 . 8 9 9 5 8 E 0 . 8 9 868E 0 . 8 5 3 0 9 2 0 .8S7 '71E 0 . 8 6 2 3 7 2 0 . 8 6 6 9 3 2 0 , 8 7 1 2 S E 0 . 8 7 5 2 9 2 0 . 8 7 8 8 3 E 0 . 8 8 1 9 8 E 0 , 8 8 9 7 0 E 0 . 8 8 6 9 9 2

:= 1 , 2 5 0 0 , 0 2 5 n

1,"750

09 09 09 09 09 09 09 03 03 03 03 03 03 03 03 03 03 03 03 03 03

H

H

;SURE= 8 - 2 0 0 C TOP PRESSUR2= 7 . 9 0 0 C C D U T I 2 S - R E B 0 I L Z R C c C PR c

0 , 2 7 9 9 3 E

lOPORTINAI

c C STEP CHANG2 C T C c

• IHE= 0 .

ATH

0- 11215E 0 . 1 1 2 9 6 E 0 . 11283E 0- 113232 0 . 1136 IE 0 . 113952 0 - 1 0 9 9 8 2 0 . 10980E 0 . 10517E 0 . 10558E 0 . 1 0 6 0 2 E 0 . 10698E 0 . 1 0 6 9 5 E 0 . 1 0 7 9 0 E 0 . 1 0 7 8 9 E 0 . 1082 92 0 . 1 0 8 5 9 E 0 . 108912 0 . 10918B 0 . 10991B 0 . 0

ATH

C0ND2H 08 0 . 2 5 2 8 2 E

, GAINS - 9 5 7 .

: I S F D « 0 , 050HR

C TRAT T2HP L C 1 C 2 C 3 C 9 C 7 C IO C13 C16 C19 C22 C25 C28 C31

5 0 9 . 9 9 1 5 0 8 . 9 6 3 5 0 8 . 3 6 9 5 0 7 . 6 3 9 5 0 9 . 3 0 5 9 9 9 . 1 1 1 9 9 3 . 1 3 9 9 8 8 . 3 9 1 9 8 5 . 2 8 2 9 8 2 - 2 1 5 9 7 9 . 2 5 9 9 7 6 . 9 2 8 9 7 5 . 3 9 2

0 , 12333E 0 . 126692 0 , 1 2 6 9 1 2 0 . 1 2 6 1 9 2 0 . 125192 0 . 129322 0 . 1 2 9 5 0 2 0 . 1 2 5 5 7 2 0 . 8 3 7 6 9 E 0 . 8 9 8 6 6 2 0 . 8 6 2 3 9 2 0 . 8 7 5 2 3 2 0 . 8 8 9 6 7 2

98^

03 09 09 09 09 09 09 09 03 03 03 03 03

08 KJ/HR

0 0 0 - 2 0 6 0 ,

FD

T

09 09 09 09 09 09 09 09 09 09 09 09 09 09 09 09 09 09 09 09

, 0 0 0

0 . 11929E 09 0 . 0 , 1 1 9 0 6 E 09 0 . 0 . 113792 09 0 . 0 , 113992 09 0 , 0 . 1 1 2 9 6E 09 0 . 0 . 111892 09 0 , 0 , 11295E 09 0 , 0 . 1136 IE 09 0 , 0 , 10500E 09 0 . 0 . 10622E 09 0 . 0 . 10761E 09 0 . 0 , 108802 09 0 , 0 . 1 0 9 6 2 2 oa 0-

0 , 1 9 3 2 9 2 0 , 1 9 3 8 8 2 0 , 1 9 9 5 2 E 0 , 1 9 5 15B 0 . 1 9 5 752 0 . 1 9 6 2 9 B 0 , 1 9 6 75B 0 . 1 1 8 972 C-11993B 0 . 1 1 9 9 9 2 0 .120 982 0 . 1 2 1 092 0 . 1 2 1 6 2 E 0 . 1 2 2 192 0 . 1 2 2 732 0 , 1 2 3 2 9 E 0 . 1 2 3 702 0 , 1 2 9 112 0 . 1 2 9 972 0 , 1 2 9 78E 0 .1 00 OOE

HT 10000E 03 19169E 01 191662 01 1916 92 01 191732 01 19236E 01 19388E 01

'19579B 01 11896E 01 12097E 01 12218E 01 12370E 01 12977E 01

01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 03

0 , 3 7 9 1 9 0 . 9 3 3 6 9 0 , 9 8 5 0 9 0 . 5 3 1 5 5 0 . 5 7 1 9 5 0 . 6 0 5 8 9 0 . 6 3 3 6 0 0 . 6 6 1 0 9 0 . 6 9 0 7 3 0 . 7 2 1 9 3 0 . 7 5 3 9 3 0 . 7 8 5 9 1 0 . 8 1 7 0 0 0 , 8 9 6 9 5 0 . 8 7 3 6 3 0 . 8 9 8 1 9 0 . 9 1 9 7 5 0 , 9 3 8 9 9 0 . 9 5 9 3 9 0 . 9 6 7 6 6 0 . 9 7 8 6 9

X I 0 . 0 2 2 3 2 0 - 0 3 1 8 0 0 , 0 9 9 2 0 0 . 0 6 0 2 5 0 . 1 3 8 3 1 0 . 2 7 0 3 8 0 , 9 3 3 6 9 0 , 5 7 1 9 5 0 , 6 6 1 0 8 0 , 7 5 3 9 1 0 , 8 9 6 9 3 0 . 9 1 9 7 9 0 . 9 6 7 6 5

0 . 6 2 0 8 1 0 . 5 6 6 3 1 0 , 5 1 9 9 1 0 . 9 6 8 9 5 0 . 9 2 8 0 5 0 . 3 9 9 11 0 . 3 6 6 9 0 0 . 3 3 8 9 1 0 . 3 0 9 2 7 0 , 2 7 8 0 7 0 , 2 0 6 0 7 0 . 2 1 9 0 9 0 . 18300 0 , 1 5 3 5 5 0 . 12637

• 0 . 1 0 1 8 6 0 . 0 8 0 2 S 0 . 0 6 1 5 6 0 . 0 9 5 6 6 0 . 0 3 2 3 9 0 . 0 2 1 3 1

X2 0 , 9 7 7 6 8 0 , 9 6 8 2 0 0 , 9 5 5 8 0 0 . 9 3 9 7 5 0 , 8 6 1 6 9 0 . 7 2 9 6 2 0 . 5 6 6 3 1 0 . 9 2 8 0 5 0 . 3 3 8 9 2 0 , 2 9 6 0 9 0 - 1 5 3 5 7 0 , 0 8 0 2 6 0 , 0 3 2 3 5

121

C32 9 7 9 . 9 5 2 0 - 8 8 6 9 9 2 03 0 . 0 0 . 1 0 0 0 0 2 03 0 . 9 7 8 6 9 0 . 0 2 1 3 1 C C DISTILLAT2 FLOW » 0 . 2 0 5 8 0 2 03 C C A SIHPLIFI2D FL0WSH22T FOB THIS PROGRAH IS AS FOLLOWS: C C 1 . INPUT ST2ADT-STATE TAL02S OF X ( J ) , L ( J ) , QRB, QCHO C FROH SUBROUTINE DATAIN. INCLUD2D ARE COLUHH SPECS C (H, DC, NFT, ETC.) AND PURE C0HPCN2NT DATA (HLC, EKC, E T C . ) . C C 2. CALCULATE LIQUID FEED 2NTHALPT. C C 3, D2T2RHIN2 I (J) AND T(J) USING SUBROUTIN2 BUBDBW, C SUBROUTINB G2QK CALCULAT2S EQUILIBRIOH K TALUES C SOBROOTIHE EQSOLT CALCULATES THE HEW THPERATUBE C FUNCTION BDOBJ DBTEHHINKS IF THE SUH OF THE X'S ABB C 2QUAL TO 1 AT T2HPEHATURE PRCTIDED BT EQSOLT C C 9 , CALCnLAT2 T (J) OSIHG SDBB0UTIH2 TPFLC C C 5. D2T2RHIH2 INITIAL COHDITIOHS FROH SUBROUTINB INTCDS C US2 SUBB00TIH2 D2NnW TO CALCULATZ ATG BOL HGHT AND C LIQUID D2HSITT C C 6 . IHPUT ST2P CHANGE C C 7 , D2TERHINE PSUEDOBINART COHPOSITICHS FROH SUB, PSUBDO, C IHT2GPAT2 HASS BALANC2 2QUATI0HS USING IHSL DG2AH PACKAGE C C 8 , CALCULATE X (J) AHD N0HHALI2E C C 9 . CALCULATE L (J) FPOH FBANCIS HZIR FORH OLA OSIHG SOBBOOTINE C HTDRA C C 1 0 . CALCULATE L ( 1 ) , L(NT) AND DF FROH COHTHOL EQUATIONS C C 1 1 . PRINT RESULTS C C 1 2 . GO TO STEP 3 . CHANGE STEP 9 TO CALCOLATING PRESSURE C DROP, USE SOBROOTIHE 7APDSN TO CALCOLATE TAPOR DEHSITT C ELIHIHATE STEP 6 , C

HAH2LIST/GEA/I2R,T0UT,TI ,H,T0L,IHK ICOUHT-0 TOUT=0,

C C INPUT DATA C

CALL DATAIN C C CALCULATE FEED ZHTHALPT AND PHESSUBE PROFILE C

HFL=0. DO 8 9 1 = 1 , N C

122

89 HFL=HFL+XF(I)^HLIQ(TFD,I) DO 51 J=1 ,NT

51 P T ( J ) = P B - ( J ^ (PB-PD)/HT) T I « 0 . 0

C C CONTERT WL FROH H TO INCHES FOR SUBSFQUENT CALC, C

HL - WL ^ 3 9 , 3 7 NTH1=NT-1

TOL«.01 HETH»2 niT2R»3 NEQH«2^HT D 2 L T » . 0 0 0 5 0

C C S2T COHSTAHTS FOR R2F2RENCZ CONDITIONS C

PB0T«PT(1) PTOP«PT(HT) PKP«5. E+5 P2S»PT(2) 7B»T (1) TT«T (NTH 1) L1S=L(1) AHHTS»flT(HT) AH1S=HT(1) XDS=X(HT,1) DFO-DF

C DO 81 1 7 = 1 , 2 5 X B 0 « X ( 1 , 2 ) XD0«X(HT,1)

DO 82 1 9 = 1 , 1 0 0 IC0UHT«IC0aNT+1

c C CALCULATE T2nP AHD T PROFILES

DO 31 J = 1 , N T DO 91 1=1 ,NC

I T ( D « X ( J , I ) IF (IC0UNT.GT.1) GO TO 821

C TFL(I)=X (J,I)

GO TO 91 821 TFL (I) » T (J, I) 91 CONTINUE

TT«T (J) P-PT (J)

CALL BUBDEW(P,XT,TFL,TT,PREF, 1, 1) DO 57 1=1,NC

57 T(J,I)«TFL(I) 31 T(J)=TT C C CALC. LIQUID DENSITIES AND ATG HOL HT C

123

CALL D2NHW IF (ICOUNT.LT. 2) GO TO 109

C C CALC. HEW LIQUID PROFILE C

CALL HTDRA C CALL S L I T 2 T ( 1 , I X )

109 C0HTIHU2 C C CALC. TAPOR RATE PROFILZ C

CALL TPFLC (ICOUNT, D2LT) IF (ICOUNT. GT. 1) GO TO 932

C C CALC. IHITIAL COHDITIOHS C

CALL INTCDS (2) CALL PHHTA

C ST2P CHAHG2 GOES H2R2 X F ( 1 ) » 0 . 17

X F ( 2 ) « 0 . 1 8 FOD«FD*XF (1) •FD^XF (2) XFSD=sFD«XF(1)/FDD

CALL TAPDEN RH0T8=RH0T(1)

C C CALC. PRESSURE DROP COEFFICIEHTS C

P D K ( 1 ) = ( P T ( 1 ) - P T ( 2 ) ) DO 839 J»2,NTH1

839 PDX(J) » ( P T ( J - 1 ) - P T ( J ) ) / 1 (PHOT ( J ) ^ ( T ( J ) ^ T ( J ) ) )

W R I T 2 ( 6 , 8 2 3 ) 323 FORHATC ' , / / , 3 X , ' STEP CHANGE IS X F 1 » 0 . 1 7 XF2=0. 18 ' , / ) 932 COHTIHUE

CALL 7APD2H IF ( I 7 . G T , 1 ) GO TO 7 9 7

C C CALC. PS2SSUH2 PROFILE C

0P1«S^PDK ( 1 ) * ( ( (T (1)^HT (1) ) / (7B^AH1S) ) ^ ^ 1 , 8 9 ) ^ (HHOTB/RHOT ( 1 ) ) I F (7 ( 1 ) , G T , 1.002^TB) PT (1) =P30T^ DP 1 IF(T (1) -L2. 0,998^TB) PT(1) -PB0T-DP1

C 797 C0HTINU2

DO 871 J«2,HTH1 871 PT(J)«PT(J-1)-PDX(J) •(RHOT(J)

2 •(T(J)^*2)) HTH2=NT— 2 PT(HT)«PT(NTH1)-ABS(PT(NTH2)-PT(NTH1)) CALL PSU2D0(2)

I F ( I 9 . L 2 . 9 9 ) GO TO 182 WRITE ( 6 , 2 0 2 ) TOUT

202 F O R f l A T C 1 ' , / / , 1 0 X , ' T I H 2 « • , F 1 0 . 3 ,'HR •)

124

WRIT2 ( 6 , 9 2 2 ) 922 FOHHATC ' , / / , 5 X , ' • • • • • • RESULTS • • • • • « t , / ,

1 2 X , ' T R A T ' , 5 X , ' T 2 H P ' , 1 1 X , ' L ' , 1 1 X , ' T » , 1 2 X , ' H T ' 2 , 1 0 X , ' X 1 ' , ^ 0 2 , ' X 2 ' , 1 0 X , ' X 3 ' , 1 0 X , ' X 9 ' , 1 0 X , ' P T ' )

CALL PRNTB (2) WRIT2(6, 399) QRB

399 FORHATC ' , / , 5 X , ' E EB0IL2R DUTT=', F13 , 5 , ' KJ/HR') 182 C0HTINU2

IND»1 H = 1 . 0 E - 5

TOUT»TOUT+DEIT CALL DGEAR (NEQH,D2P,FCHJ,TI,H,2,TOUT,TOI,HETH,NITER,IHO,

2IWK,HK,IER) IF ( l E R . G T . 128) GO TO 999

C C CALC. N2H X 7ALUBS C

DO 3 2 J = 1 , N T I F (ABS ( 2 ( J ) ) . L T , 1 , B - 5 ) GO TO 9 9 1

XS (J) =2 (NT^ J) / (2 (J) • (X ( J , 1 ) • ! ( J , 2 ) ) ) IF (XS(J) . L T . 0 . 0 ) X S ( J ) = 0 .

32 COHTIHUE IF (NC.EQ,2) GO TO 611

C DO 9 15 J = 1 , N T SUHL=0, DO 9 19 1 = 3 , NC

919 SUHL»SUHL^X ( J , I ) X ( J , 1 ) = I S ( J ) • ( 1 . - S U H L )

915 X ( J , 2 ) = ( 1 . - X S ( J ) ) ^ ( 1 , - S U n L ) GO TO 6 1 2

611 DO 621 J = 1 , N T I ( J , 1 )=XS(J)

621 X { J , 2 ) = 1 . - X S ( J ) 612 CONTINUE

DO 37 J » 1 , N T SUHI=0-

DO 3 8 1 = 1 , NC 38 SUHI=SUHX^X(J,I)

DO 591 1 = 1 , N C X ( J , I ) » X ( J , I ) / S U H X

FLOHS

39 H T ( J ) = 2 ( J ) L(1) «L1S + PKCB^ (AHlS-n7 (1) ) DF=DFO^PKCD^ (AflNTS-HT (NT))

C C COHTROLLIR BESPOHSE FOR BOTTOHS COflP CCHTRCL C FOR IBC « 1 OSE F/T RATIO CONTROL C FOR IBC » 2 OSE REB0IL2R DUTT ON PFOPORTIONAL CONTROL

591 3 7 C C CALC. C

C0NTINU2 C0HTIHU2

, BOTTOHS J

DO 3 9 J = 1 ,

AND

,NT

DISTILLATE

125

C FOR IBC = 3 USES SUPPLIZS OHN CONTROL STRATZGT C

I F ( IBC.ZQ.1) FD = T ( 1 ) ^ ( F D / T ( 1 ) ) « ( X F S / X ( 1 , 1 ) ) IF (IBC-EQ.2) QRB = QRBS^PKQR^ ( JBS-X ( 1 , 1))

C C C0NTB0LL2R R2SP0HS2 FOR DIST COHP CONTROL C FOB ITC = 1 OSZ R/T RATIO CONTROL C FOR ITC " 2 US2R S0PPLI2S OWN COHTJOL SIRATEGI C

I F ( I T C , 2 Q . 1 ) L(NT) « T (NTHl) • ( 1 ( 1 ) / 7 (HTH1) • (XDS/X (NT , 1) ) 82 TI«TOOT

I F ( I 7 - L T - 1 1 ) GO TO 81 I F (ABS (XBO-X ( 1 , 2 ) ) . L T . 0 . 0 0 0 2 5 , AND. A3 S (XDO-I (NT, 1)) . L T ,

1 0 . 0 0 0 2 5 ) GO TO 907 81 C0HTINU2

GO TO 907 9 9 1 C0NTIHU2

WRIT2 ( 6 , 8 3 3 ) 833 FORHATC ' , 5 X , ' 2 TALU2 I S 2EH0 •)

WBIT2(6,AHN) GO TO 9 0 7

9 9 9 COHTIHUE WRIT2(6,G2A)

907 C0HTINU2 WRIT2 ( 6 , 5 1 1 ) TOOT

511 FORHAT ( ' 1 ' , / / , 10X, •TIH2= ' , F10 . 3 , ' HR') WRIT2 ( 6 , 5 1 2 )

512 FORHATC » , / / , 5 X , ' • • • • « • R2SULTS • * • • • • ' , / , 1 2 X , ' T R A T ' , 5 X , ' T 2 H P ' , 1 1 X , ' L ' , 1 I X , • T ' , 1 2 X , • H T ' 2 , 1 0 I , ' X 1 » , 1 0 X , » X 2 ' , 1 0 X , ' X 3 ' , 1 0 X , ' X 9 ' , 1 0 X , ' P T ' )

CALL PR HTB (2) STOP 2HD

C FUNCTION HLIQ(T ,D

C0HH0N/2NTT/H7C ( 5 , 5 ) , HLC ( 5 , 5) COHHOH/BLOCX2/FD,BF,DF,TFD,PCOL,CLBL(6,6) , WH( 1 5) ,XF (1 5) ,PFD,PBZF

C C CALCULATE TAPOR AND LIQUID ENTHALPIES WITH A POLTHOHIAL C IN TEHP. OBTAIHED BT LZAST SQUARE FIT.

SUHL=0, DO 19 J 2 « 1 , 3

19 S U H L » S U H L ^ ( H L C ( I , J 2 ) ^ T ^ * ( J 2 - 1 ) ) HLIQ=-1 , •WH ( I ) •SUHL R2TURH END

C FUNCTION HTAP(T,I) C0HBON/2HTT/HTC(5,5) , HLC ( 5 , 5) C0HH0H/BL0CX2/FD,PF,Dr,TFD, PCOL,CLBL(6, 6) , HH (1 5) , XF (1 5) ,PFD,PREF

SUHT«0, DO 16 J 2 » 1 , 9

16 SUHT»SUHT^ {HTC(I ,J2) •T^^ ( J 2 - 1 ) ) BTAP»-1 .^HH(I)•SUHT

126

RETURN 2ND

C SUBROUTINB DATAIH REAL L,LS ,LC,BT,LB2 ,LBA2,LBB2

COflflON/PHTS/ TC(5) , P C ( 5 ) ,W (5) ,PDX (50) , RHOT(50) ,AHT (50) C0HHON/BL0CX2/FD,BF,DF,TFD,PC0L,CLBL(6,6) ,WH(15) , I F ( 1 5 ) ,PFD,PREF COHHOH HC,HT,NFT,NTH1,IBC,ITC COHHOH/FIT/ ZX(5) ,2XC ( 5 , 5 ) COHHOH/COLSP/HL,HOW,0C,PB,PD, PKC3,PXCD,S C0HHON/D0TT/QRB,QCND C0HHON/2NT7/HTC ( 5 , 5 ) , HLC ( 5 , 5) C0HHOH/INIT/H1(50) , f l 7 ( 5 0 ) COHHOH/TRAT/T (50) , L ( 5 0) , T ( 5 0 ) , D2HS (50) , AHW (50) , P T ( 5 0 ) ,LC COflflON/TTCHP/X(50,5) , T ( 5 0 , 5 ) , f l L ( 5 0 ) ,HT(SO) COHHOH/DHW/02NA(5) , D2HB (5) , DEHC (5) 0I32HSIOH T F L ( 5 ) , X T ( 5 ) , X B ( 5 ) , X B 3 ( 5 ) , T H ( 5 ) ,TB2(5 )

HAH2LIST/DAIH/ QRB,QCHD,TT2,HLT,HTT,Lfl2,HLa,flTB C C SUBR0UTIH2 SUPPLI2S INPUT DATA C

R2AD ( 5 , 9 1 ) PCOL,TFD, PB,PD,PFD, PREF READ ( 5 , 9 2 ) NC, NT,NFT,IBC,ITC DO 10 1 = 1 , NC

10 READ ( 5 , 9 3 ) (CLBL ( 1 , 1 2 ) , 1 2 = 1, 5) ,TC (I) ,PC (I) ,H ( I ) , HH (I ) DO 15 1=1 ,NC R2A0 ( 5 , 9 9 ) (HLC(I ,J2 ) , J 2 = 1 , 9 ) R2AD ( 5 , 9 9 ) ( R 7 C ( I , J 2 ) , J 2 » 1 , a ) R2AD ( 5 , 9 9 ) ( I X C ( I , J 2 ) , J 2 = 1 , 9 )

15 B2AD ( 5 , 9 9 ) DZHA(I) ,D2NB(I) ,D2NC(I ) B2A0 ( 5 , 9 1 ) (XF(I ) , I = 1 , H C ) READ ( 5 , 9 1 ) FD,DF,BF DO 311 J « 1 , H T

311 R2AD ( 5 , 9 8 ) T (J) ,L (J) ,T (J) , (X ( J , I ) , 1 = 1 , FC) R2AD ( 5 , 9 1 ) WL,H0W,DC,flT(1) ,HT (NT) R2AD ( 5 , 9 9 ) QRB,QCND READ ( 5 , 9 1 ) PKCB,PKCD,S

C 91 FORHAT (10F10.9) 92 FORHAT (912) 93 FORHAT (5A9,9F10.3) 99 FORHAT (5(211.5,91)) 98 rORflAT(F7.3,9X,2(B11.5,9X) ,3 {F7,5,3X) ,r7.5) C

RETURN END

C SUBROUTINE PRNTA REAL L,LS,LC,HT COHHON/PHTS/ TC (5) ,PC (5) , W (5) , PDK (50) ,RHOT (50) ,AHT (50) C0HH0H/BL0CX2/FD,BF,DF,TFD,PCOL,CLBL(6, 6) ,HH(15) , X F ( 1 5 ) ,PFD,PBZF COHHON NC,HT,HFT,NTHl,IBC,ITC COHHOH/XTCHP/X ( 5 0 , 5 ) , T ( 5 0 , 5 ) , HL (50) ,H7( 50) COnHOH/TRAT/7(50) , L ( 5 0 ) , T ( 5 0 ) , DEHS (50) , AHW (50) , P T ( 5 0 ) ,LC

127

C0HHOH/COLSP/WL,H0W , DC, PB,PD, PKCB , FKCD, S COHHON/FIT/ ZX (5) ,EXC ( 5 , 5 ) COHHOH/EHTT/HTC(5,5) ,HLC ( 5 , 5) C0HH0N/FEED/XFD(5) ,TFD(5) ,FDT, FDL, £FL, HFT COHHOH/DUTT/QRB,QCND C0HHON/INIT/H1 (50) , n 7 (5 0) C0HH0H/DHW/DENA(5) ,D2HB (5) ,DEHC (5)

C C SUBROUTINE PRINTS OUT INPUT DATA AND STEADT-STATE TALOES C

WL1«WL/39,37 WRIT2 ( 6 , 3 0 1 ) WRIT2 ( 6 , 3 0 2 ) DO 10 1=1 ,NC

10 HRIT2 ( 6 . 3 0 3 ) ( C L B L ( I , X ) , K = 1 , 5 ) , T C ( I ) , P C ( I ) ,W(I ) ,WH(I ) 8RIT2 ( 6 , 3 0 9 ) DO 15 1=1 ,NC

15 WRIT2 ( 6 , 305) ( C L 3 L ( I , K ) , X = 1 , 5 ) , ( H L C ( I , J 2 ) , J 2 » 1 , 9 ) WBIT2 ( 6 , 3 3 1 )

DO 16 I « 1 , N C 16 WBITS ( 6 , 3 0 5 ) (CLBL ( I , K ) , K= 1, 5) , (HTC ( I , J2) , J 2 « 1 , 9)

WRITE ( 6 , 3 2 3 ) DO 97 1 = 1 , N C

«7 WRIT2 ( 6 , 3 2 5 ) I , (2XC ( I , J2) , J 2 = 1, 9) WRIT2(6 ,371)

DO 5 2 1=1 ,NC 52 WRITE ( 6 , 325) I ,D2NA (I) ,DENB ( I ) ,D2NC(I)

WRIT2 ( 6 , 3 0 9 ) PCOL,FD,PFD WRIT2 ( 6 , 3 5 0 ) HT,NFT WRIT2 ( 6 , 3 1 1 ) DO 25 1 = 1 , N C

25 HRIT2 ( 6 , 3 1 2 ) I , X F ( I ) WRIT2 ( 6 , 3 1 5 ) TFD

HRIT2 ( 6 , 3 6 1 ) DO 27 J=1 ,NT

27 HRITE(6, 362) J , T (J) , L (J) ,T (J) ,fl7 (J) , (X ( J , I ) , 1= 1, NC) , PT (J) H R I T 2 ( 6 , 3 6 3 ) HL1,H0H,DC,PB,PD H R I T B ( 6 , 3 6 9 ) QRB,QCND H R I T Z ( 6 , 3 6 7 ) PXCB,PXCD

301 FORHAT ( / / / ' 1 ' , 1 0 X , ' U N S T E A D T STATE SIHULATION • , / / , 1 5 X , 2'THE S T S T E H ' , / / )

302 FORHAT ( / ' 0 ' , 3X,'COHPOHEHT', 19 X,» HOL HT') 303 FORHAT (• ' ,5A9 , 2 X , 5 F 1 0 . 3 ) 309 FOPHAT ( / / ' ' , 2 7 X , ' H L 1 ' , 1 3 X , ' H L 2 ' , 1 3 X , ' H L 3 ' ) 305 FORHAT (' • , 5A9 , 5B1 9 . 5) 309 FORHAT (' • , / , 5 X , ' T H E COLOHN PR2SS0R2 I S » , F 1 0 . 3 , ' A T H ' , / ,

25X, 'THE F22D RAT2 I S ' , 2 1 2 . 3 , ' XGHOL/HB ' , 5 X , ' F 2 2 D P R E S S ' , F 9 , 3) 311 FORHAT ( / , 1 0 X , ' FEED COHPOSITIOH • , 5 X , ' I» , 1 2 1 , ' XF') 312 FORHAT (' ' , T 3 3 , I 2 , 7X , F 9 . 9 ) 323 FORHAT ( ' • , / , 5 X , ' E Q U I L K 7ALUZS HERE CALCULATED WITH i ' ,

• 'POLTHOHIAL IN TEHP • , / , 10X, • EX 1 • , 12X, ' EK2' , 12X, 3 ' E X 3 ' , 1 2 X , ' E X 9 ' )

325 FORHATC ' , 1 3 , 5 (5X, Z1 9 . 9 ) ) 315 FORHATC ' , 1 5 X , » F E E D TEflP = ' , F 6 , 1 )

128

331 FORHAT (' •,/,27X,'HTA' ,10X,'HT3' ,101,'nTC') 350 FORHAT (' ',/,5X,•NUHB2R OF TRATS= ',13,/,

1 5X,'F2BD TRAT IS HUHBER ',13) 361 FOBHATC v,/,?,x,»THE IHITIAL CONDITIONS ABE',//

1 . 2 1 , • T P A T ' , 5 X , ' T E H P ' , T 2 2 , ' L ' , T 3 9 , f T » , T 9 8 , • H T » , T 6 0 , ' I 1 ' , T 7 2 , 2 • X 2 ' , 9 X , ' X 3 ' , 9 X , ' X 9 ' , 9 X , ' P R E S S ' ) * . , *

362 FORHATC M 2 , 1 X , F 8 . 3 , 3 (2X. E 1 3 . 5) , 5 (2X , F 7 , 5) ) 363 FORHATC • , / / , 3X, ' HEIR L2NGTa = ' , F 8 . 3 , ' B ' , / , 3X, • HEIR HGHT=',

1 F 8 . 3 , ' H ' , / , 3 X , ' C O L U H H DIAH=' , F 8 . 3 , • H ' , / , 5 X 2 , / , ' BOTTOH PR2SSURE" ' , 2 8 . 3 , ' A T H ' , / , 3 5 X , ' T 0 P PR2SSURE= ' , F 8 . 3 , ' ATH')

C 369 FORHATC ' , / , 3 X , ' D U T I 2 S ~ ' ,T1 1 , • REBOILZR',T26 , ' CONDEN', / , 8 1 ,

1 2 2 1 3 . 5 , ' KJ/HS') 3 6 7 FORHATC • , / , 5 X , ' PROPORTINAL G A I N S ' , F 9 . 3 , 2X, F9, 3) 371 FORHATC ' , / , 5 1 , ' L I Q U I D DEHSITT CALCULATED BT QUADRATIC,

2 • IH T 2 H P ' , / , 9 X , ' 0 E H A ( D ' , 9 1 , 'D2NB(I) • , 9X, 'DENC(I) •) HBTURH 2HD

C SUBB0UTIN2 PRNTB (2) P2AL L , L S , L C , H 7 COH'HON/BLOCX2/FD,3F,DF,TFD,PCOL,CLBL(6, 6) ,HH(15) , X F ( 1 5 ) ,PFD,PHEF COHHON NC,NT,HFT,NTHl,IBC,ITC COHHOH/TRAT/7(50) , L ( 5 0 ) , T ( 5 0 ) , DBHS (50) , AHW ( S 0 ) , P T ( 5 0 ) , LC COHHOH/XTCHP/X ( 5 0 , 5 ) , T (SO,5) , S L ( S O ) ,HT(50)

DIH2NSI0N 2 ( 1 0 0 ) C C SUBS0UTIN2 PRINTS OUT TRAT-TO-TRAT R2SULTS AFT2H EACH TIHE STEP C

DO 70 1 J = 1 , 3 701 W B I T 2 ( 6 , a 9 3 ) J , T (J) , L (J) , 7 (J) , 2 (J) , (X (J , 1 ) , 1 = 1,NC) ,PT (J)

DO 7 0 2 J = 9 , N T H 1 , 3 7 0 2 WRIT2(6 ,89 3) J , T (J) ,L (J) , 7 (J) , 2 (J) , (X (J , 1 ) , 1= 1 ,HC) ,PT (J)

DO 70 3 J*NTH1,NT 703 H H I T 2 ( 6 , 8 9 3 ) J , T (J) ,L (J) , 7 (J) , 2 (J) , (X (J , 1 ) , 1 = 1 ,HC) ,PT (J) 893 FORHATC ' , 1 2 , 1 X , F 8 . 3 , 3 ( 2 X , 2 1 3 , 5 ) , 5 ( 2 1 , F 8 . 5) ) C

WRIT2 ( 6 , 8 9 5 ) DF 895 FORHATC « , / , 5 X , • DISTILLAT2 FLOW = ' , 2 1 3 . 5 )

H2TURH EHD

C SUBRO0TIN2 INTCDS (2) H2AL L,LS,LC,HT COHHOH/IHIT/HI (50) ,flT (50) COHHON/BLOCX2/FD,BF,DF,TFD,PCOL,CL3L(6,6) ,Hn(15 ) , X F ( 1 5 ) ,PFD,PRZF COHHOH HC,HT, HFT, NTHl, IBC, ITC COHflOH/TR A r / 7 (50) , L ( 5 0 ) , T ( 5 0 ) , DENS (50) , AHW (SO) ,PT(SO) ,LC COHHON/XTCHP/X(50,5) , T ( 5 0 , 5) , HL ( 5 0 ) , H 7 ( S 0 )

DIHEHSIOH 2 (100) COHHOH/COLSP/WL,HOW,DC,PB,PD,PKCB,PKCD,S

C C THIS SUBROUTINE CALCULATES THE INITIAL COHDITIOHS FOR TH2

129

C S2T OF DIFF2R2NTIAL 2QNS. C H1(J)=H2IGHT OF LIQUID 072R HEIR C C LIQUID FLOW RATES ARE C0N72RTED FRCH KGHOL/HR TO GAL/BIN TO C CALCULATE HI ( J ) . THE C0N7ERSI0N FACTOR I S 9 . 9 0 2 E - 3 C HI (J) I S IH INCHES AHD HOST BE CONVERTED TO NETEHS. THE C CONVERSION FACTOR IS 3 9 . 3 7 . H7(J) I S CALCOLATED AS LIQOID C HEIGHT^AREA C

P I » 3 . 19159 DO 21 J=2,HTH1

Q»L(J) •AHW(J)^9 .90 2E-3 /DEHS(J) C

HI (J) = 0 . 9 8 * ((Q/WL) • • . 6 6 6 6 6 6 7 ) HI (J) " H l ( J ) / 3 9 . 3 7 HT(J)« (H1 (J)^HOW)^PI^ ( ( D C / 2 ) ^ ^ 2 ) •DENS ( J ) • ( I . E ^ 3)/AHH (J)

21 C

25 C

COHTIHUE

00 25 J»1,NT 2(a) = HT(J) 2 (NT^J) =fl7(J)^X(J,1) C0HTIHU2

B2TUBH END

SUBROUTINB 7PFLC (ICOUNT,DELT) R2AL L , L S , L C , i T COflHON/BLOCX2/FD,BF,DF,TFD,PCOL,CLBL(6,6) , H H ( 1 S ) . X F ( 1 5 ) ,PFD,PBZF COHHON NC, NT, NFT, NTHl,IBC,ITC C O H H O H / 7 T C H P / I ( 5 0 , S ) , T ( 5 0 , S ) , H L ( 5 0 ) , H T ( 5 0 ) COHHOH/IHIT/HI (50) , HT (5 0) COHHON/TRAT/T(50) , L ( 5 0 ) , T ( 5 0 ) ,D2NS (50) , AHW (50) ,PT(SO) ,LC C 0 H H 0 N / F 2 2 D / i r D ( 5 ) ,TFD(5) ,FDT, FDL, FFL,HJT COHHOH/DUTT/QRB,QCND COHHOH/FIT/ ZX(5) , 2 X C ( 5 , 5 ) C0nHOH/2HTT/HTC(5,5) , HLC ( 5 , 5)

HAH2LIST/TPF/T ,L ,T , I ,HL,H7 ,HFL,HTT,FDL,FDT,Dr DIH2HSI0H DHDT(50)

C THIS S0BROUTIH2 CALC. TH2 TAPOR RATS EH0FIL2 FROH C TH2 ENERGT BALAHC2 FOR EACH THAT C C EHERGT SALAHCE EQH IS REARRAIGNED IN FORH OF C C 7 (J) « ( L ( J ^ l ) • (HL ( J ^ I ) - H L (J) ) • T ( J - 1) • (H T ( J - 1 ) -HL( J) ) C ) / ( H T ( J ) - H L ( J ) ) C CALCULATE LIQUID AHD TAPOR TRAT ENTHALPIES C

DO 31 J » 1 , H T HL(J) = 0 . H T ( J ) « 0 , TT=T(J) DO 33 1=1 ,HC HL(J) « H L ( J ) ^ X ( J , I ) * n L I Q ( T T , I )

130

33 H7(J) « H 7 ( J ) ^ T ( J , I ) ^ H T A P ( T T , I ) 31 C0NTIHU2 C C CALCULAT2 t (J) C

NFTH1«HFT-1 T ( 1 ) - ( L ( 2 ) ^ ( H L ( 2 ) - H L ( 1 ) ) ^ Q R B ) / ( H T ( 1 ) - H L ( 1 ) )

DO 191 J » 2 , N r T H l 191 7 ( J ) - ( L ( J ^ 1 ) ^ ( H L ( J + 1 ) - H L ( J ) ) ^ T ( J - 1 ) « ( H T ( J - 1 ) - H L ( J ) )

2 ) / ( H T ( J ) - H L ( J ) ) 7(HFT) = (L(NFT^1)^ (HL (HFT^I)-HL (NFT)) •T (NFT-1) • ( H T ( N F T - I ) -

2 HL (HFT) ) •FD^(HFL-HL (HFT) ) ) / ( H 7 (HFT) - H I (NFT) ) HFTP1-NFT+1 DO 193 J»NFTP1,NTH1

193 7 ( J ) - ( L ( J * 1 ) ^ ( H L ( J ^ 1 ) - H L ( J ) ) •T ( J - 1 ) • (HT (J-1) - HL (J) ) 2 ) / ( H 7 ( J ) - e L ( J ) )

C T (HT) « (QCHD- (7 (HTH1) • (H7 (HTH1) -HL (NT) ) ) ) / (HL (NT) -HT (HT) )

I F ( • ( H T ) . L T . 8 , E ^ 9 ) T (HT) = 0 , 7 (HTH1)«T(HTfl1)-T (NT)

DO 3 9 J « 1 , H T H 1 IF ( 7 ( J ) . L T . 0 , 0) T ( J ) » 0 . 0

39 S 7 7 « S 7 7 + T(J) I F ( S 7 7 . L T . 1) GO TO 939

GO TO 9 9 9 939 HRITE ( 6 , 8 9 9 ) 899 FORHATC ' , 5 X , » A L L 7 (J) ARE 2ER0')

W H I T 2 ( 6 , 7 P F ) STOP

999 H2TURH END

C SUBP0UTIN2 D 2 P ( N 2 Q N , T I , 2 , D 2 ) R2AL L , L S , H 7 , T I , 2 (N2QH) ,D2(N2QN) COHHOH HC,HT,NFT,NTHl,IBC,ITC C0HH0N/T8AI/7 (50) , L ( 5 0 ) ,T (50) , D2NS (50) , IflW (50) , P T ( 5 0 ) ,LC COHHOH/BL0CX2/FD,BF,DF,TFD,PCOL,CLBL(6, 6) ,HH(15) , I F ( 1 5 ) ,PFD,PRZ)

COHHCH/PSD/LS(50) ,XS(50) , T S ( 5 0 ) , T S ( 5 0) ,FDD,XFSD,DFS C0HHOH/INIT/H1 (SO) , HT (50)

C THIS SUB80UTIN2 COHTAINS TH2 S2T OF DIFF2R2HTIAL EQHS C DESCRIBING THZ DTHAHICS OF THZ LIQUID HOLDUP AND LIQUID C COHPOSITIOH OH ZACH TRAT-C THE FOLLOWING EQUATIONS ABB FOR THE LIQUID HOLDUP

D 2 ( 1 ) » L ( 2 ) - T ( 1 ) - L ( 1 ) D2(HT)«T(NTHl) -DF-L(NT) DO 91 J=2,NTH1

I F ( J . 2 Q - N F T ) GO TO 9 1 D2(J) »L ( J ^ l ) • T ( J - 1 ) - L ( J ) - T ( J )

91 C0NTINU2 D2(NFT)«FD^L(HFT^1) • • (NFT-1) -T (HFT)-L (HFT) '

C C TH2 FOLLOWING 2QNS AR2 FOR TH2 LIQUID COHPCSITIOH C

DO 92 J=2,HTH1

http://S77.lt

131

I F ( J . 2Q. HFT) GO TO 92 DZ (HT^J) «LS ( J ^ l ) •XS (J+ 1) • TS (J - 1) •TS ( J - 1 ) -TS (J) •TS (J)

2 - L S ( J ) ^ X S (J) 92 C0HTIHU2 • C

D2(NT»1)« ( L S ( 2 ) ^ X S ( 2 ) - T S ( 1 ) • T S ( I ) - I S ( 1 ) •XS{1) ) 02(HT+NFT) «FDD^XFSD^LS(NFT^1) •XS (HFT^I) •TS (NFT-1) • T S ( N F T - I )

2 -TS (NFT)^7S (NFT) -LS (NFT) •XS (NFT) D2(NT^NT) = (TS(NTHI) • T S ( N T H l ) - (LS(NT)^DFS) •XS(NT) ) R2TURN END

C SUBROUTINB D2NHW C O H H O N / r r C H P / X ( 5 0 , 5 ) , 1 ( 5 0 , 5 ) , e L ( 5 0 ) , H 7 ( 5 0 ) COHHOH HC,HT,NFT,NTHl,IBC,ITC COHHOH/Daw/D2HA (5) , D2HB (5) , D2NC (5) COHflON/TRAT/7(50) , L ( 5 0 ) , T ( 5 0 ) , D2HS (50) , AHW (50) , P T ( 5 0 ) ,LC COHHOH/BLOCX2/FD,3F,DF,TFD,PCOL,CLBL(6,6),HH(15) , X F ( 1 5 ) ,PFD,PREF

c c c c c

2 2

21

c

CALCULAT2 ATZRAG2 HOL WGHT AHD LIQUID D 2 N S m D2NSITT - « » G/CH^^3 CALCULAT2D BT POITNOHIAL IN TEHP 0BTAIH2D FROH L2AST SQUAH2 F I T .

DO 21 J « 1 , N T SHWaO.

SD2H»0, DO 22 1 = 1 , N C SD2H»S02N> (D2NA (I ) •D2NB (I) •T (J) •DEHC (I) • (T (J) • T ( J ) ) ) SHW=SHW*WH ( I ) • ! ( J , I ) CONTINUE D2HS(J)=SD2N AHW(J)=SflW

R2TURH END

• X ( J , I )

SUBB0UTIN2 FCNJ (N2QN,TI ,2 ,?D) R2AL T I , 2 (H2QN) ,PD(N2QH,N2QN)

DUHHT SUBROUTINB FOR DGZAR a2TUBH 2N0

SUBHOUTINB BUBDEW (P ,XF,XT,T,PR EF, IBD, IT P) EXTERNAL BDOBJ

COHflOH/BBB/IH(10) ,TH(10) COHHOH HC,NT,NFT,NTHl ,IBC,ITC

DIHEHSIOH XT (9) , X F ( 9 ) HAH2LIST/BUB/XH,TH

CALCULAT2S BUBBLE OR DZW POINTS c c c 90

THIS

GO TO DO 50 X H ( I ) '

SUBR0UTIH2

( 9 0 , 6 0 ) , I B D 1=1 ,NC

•XF(I )

132

50

60

70 80

220 230

290 250 260

TH(I)=XT(I) GO TO 80 DO 70 1=1,NC TH(I)-XF(I)' XH(I)«XT(I) C0HTINU2

CALL 2QS0L7 (P, T GO TO (220,290) ,IBD DO 230 J»1,NC IT (J) »TH(J) GO TO 260 DO 250 1 = 1,HC IT(I)«XH(I) H2TURH 2HD

,PHZF,BDOBJ,TOL,IBD)

SUBR0UTIH2 GZQX (T,P,PR2F) COHHON/FIT/ 2X(5) , Z X C ( 5 , 5 ) COHHOH HC,HT, HFT, NTHl,IBC,ITC

C C EQUIL K TALUES CALCULAT2D BT POLTHOHIAL IH TZHP C 0BTAIN2D BT L2AST SQUARES FIT

T R » 1 . 8 « T DO 230 1=1 ,NC

S 1 » 0 . DO 17 J 2 = 1 , 9

17 S1 = S 1 ^ ( E K C ( I , J 2 ) •TR^^ ( J 2 - 1 ) ) 2X ( I ) = (PR2F/P)^S1

230 C0NTIN02 R2TURN END

C FUNCTION 3 D 0 B J ( ? , T , P R 2 F , I B D ) COHHON NC,NT,NFT,HTH1,IBC,ITC

COHBOH/BBB/XH(10) ,Tf l (10) COHHON/FIT/ ZX(5) , 2 X C ( 5 , 5 )

HAfl2LIST/FOBJ/S1,S0 ,XH,IH C C THIS FUNCTION USZD TO CALCULATZ BUBBLE AND D2W PTS C BT USING TH2 SUH OF X'S = 1, C

TOL=.001

DO 130 I C T = 1 , 9 0 CALL G2QX (T,P ,PR2F) S1»0, GO TO ( 9 0 , 6 0 ) , I B 0

90 DO 50 1 - 1 , N C TH(D - E X ( I ) •XH(I )

50 S1 = S1^TH(I) GO TO 80

60 DO 70 I « 1 , H C X H ( I ) « T H ( I ) / Z K ( I )

70 S1=S1^XH(I)

133

c 80 I F (ABS(SI-SO) .LT.TOL) GO TO 190

S0«S1 GO TO ( 9 0 , 110) , I 3 D

90 DO 100 1=1,HC 100 TH(D « T H ( I ) / S 1

GO TO 130 110 DO 120 1 - 1 , H C 120 X H ( I ) = X H ( I ) / S 1 130 C0HTINU2

WRIT2 ( 6 , 1 9 1 ) WRIT2 ( 6 , 1 9 5 ) SI

195 FORHAT C ' , • SI « » , F 9 , 9 ) WRIT2 ( 6 , F 0 B J )

STOP 190 B D 0 8 J - S 1 - 1 .

GO TO ( 1 5 0 , 1 7 0 ) , I B D 150 DO 160 1 - 1 , N C 160 T H ( I ) » T H ( I ) / S 1

GO TO 190 170 DO 180 1=1 ,NC 180 XH(I) » X H ( I ) / S 1 190 C0HTINU2 191 FORHATC ',' BDOBJ DID NOT C0H72RGZ')

H2TURN EHD

C SUBR0UTIH2 2QS0L7 (P ,T,PR2F, BDOBJ, TCL,IB D)

NAH2LIST/2QS/T1,T2,FI,F2 C C THIS SUBROUTINB ZNABLZS N2W T2HPERATUH2S TO B2 CALCULAT20 FOR THZ C N2XT "GUESS" TO FIHD BUBBL2 OR DEH POIHT C

TOL-.001 T1=T Fl*BD0BJ(P,ri,PR2F,IBD) T 2 » 1 . lO^TI

F2-BD0BJ (P ,T2 ,PREF, IBD) C

DO 10 I H L » 1 , 2 0 I F ( F 1 * F 2 . G T . O . ) GO TO 5 T » ( T 1 ^ F 2 - T 2 « F 1 ) / ( F 2 - F 1 ) GO TO 8

5 T » T 1 - ( 1 . - . 6 * * I H L ) ^ F 1 ^ ( T 2 - T 1 ) / ( F 2 - F 1 ) 8 F3»BD0HJ(P,T,PREF,IBD)

I F (ABS ( F 3 ) . I T - T 0 L ) GO TO 20 T1«T2 T2«T F 1 - F 2

10 F2=F3 HRITE ( 6 , 9 2 )

92 FOBHATC ' , ' ZQS DID NOT C0N7ZHG2') HRIT2(6,EQS)

STOP

134

20 C0HTIHU2 BETURH 2HD

C SUBRO0TIH2 HTDRA H2AL L , L S , L C , 8 7

COHHOH NC,NT,NFT,NTHl , IBC,ITC COHHON/TBAT/7(S0) , L ( 5 0 ) , T ( 5 0 ) , DZHS (50) , AHW (50) , P T ( 5 0 ) ,LC C0HHOH/C0LSP/WL,HOW,DC,PB,PD,?XCB,PKCD,S COHnOH/BLOCX2/FD,PF,DF,TFD,PCOL,CLBL(6, 6) , HH ( 15) , XF (1 5) ,PFD,PRZF COHHOH/IHIT/HI (50) ,H7 (50)

C C USING THAI HTDRAULICS, HOW CALCULATZ NZW LIQUID FLOW C 1AT2S FROH NZW HOLAR HOLDUPS, C Q I S FLOW RAT2 IN GAL/HIN WHICH NZ2DS TO BZ C0N72HTED C TO XGHOL/HB. HOL IS HGHT OF LIQUID 07ZR B2IR C

P I « 3 . 1 9 1 5 9 DO 9 1 J»2 ,HTH1 H0L=H7 (J) •AHW (J) /D2HS (J) / ( {DC/2 . ) • (DC/2 . ) ) / P I / ( 1 . 2 » 3 ) -HOW HOL=HOL^39.37 I F (HOL. LT. 0 . 0 ) GO TO 39 Q«WL^( ( H 0 L / , 9 f l ) * * 1 , 5 ) L (J) -OENS (J) •Q/AHW (J) / 9 . 9 0 2 E - 3

39 COHTIHUE I F (HOL.LT. 0 . 0 ) L ( J ) » 0 .

91 COHTIHUE RETURH END

C SUBROUTIHE 7APD2N COHHON/PHTS/ TC(5) ,PC(5 ) ,W(5) ,PDX (50) , RHOT (50) , AH7 (50)

COHHOH NC,NT,HFT,NTH1,IBC,ITC COflHOH/BLOCX2/FD,BF,DF,TFD,PCOL,CLBL(6,6) ,WH(15) , X F ( 1 5 ) ,PFD,PHEF COHHOH/TRAT/7 (50) , L ( 5 0) , T ( 5 0 ) , DENS ( 5 0 ) , AHW (50) , P T ( 5 0 ) ,LC COHHOH/XTCHP/X ( 5 0 , 5 ) , T ( 5 0 , 5 ) ,HL (50 ) , f l7( 50)

DIHEHSIOH 2 2 ( 5 0 , 5 ) C C CALCULATE 2 TALn2S FOR GAS AND TAPOR D2HSITI2S C

HG«82-05 DO 52 J= 1 , HTH 1

DO 2 1 I - 1 , H C B 0 - O . 0 8 3 - 0 , 9 2 2 / ( ( T ( J ) / T C ( D ) • • I , 6) B 1 - 0 . 1 3 9 - 0 . 1 7 2 / ( (T ( J ) / T C (I) ) • • 9 . 2 )

21 22 ( J , I ) « 1. • (BO^W ( I ) • 3 1 ) ^ (PT(J) / P C (I) ) / (T ( J ) / T C (I) ) 52 C0HTIHU2

DO 97 J«1 ,NTH1 S U H 2 - 0 . DO 3 1 I « 1 , N C SUH2»SUH2^I ( J , I ) ^22 ( J , I)

31 C0HTINU2 C

RH07 ( J ) « ( P T ( J ) / S U H 2 / R G / T ( J ) ) •AHW (J)

135

97 C0HTINU2 R2TURH EHD

C SUBROUTIHE PSUZD0(2)

REAL L , L S , L C , 2 ( 1 0 0 ) COHHON NC,NT,NFT,HTH1,IBC,ITC COHHOH/BL0CX2/FD,BF,DF,TFD,PC0L,CLaL(6, 6) ,WH(15) , I F ( 1 5 ) , PFD,PRZF COHHON/TRAT/T(50) , L ( 5 0 ) , T (50) , DENS ( 5 0 ) , AHW (50) ,PT(50) ,LC COHHOH/XTCHP/I ( 5 0 , 5 ) , I (SO, 5) , HL (50 ) , H 7 ( 5 0 )

COHHOH/PSD/LS(50) , XS (50) ,TS(SO) , 7S (5 0) ,FDD,XFSD, DFS C C THIS SUBROUTIHE CALCULAT2S THE PSOEDOBIHART COHPOSITIOHS C ON EACH STAGI BAS2D ON COHP 1 AS TH2 LIGBT KET AND COHP 2 C AS THE H2A7T K2T C

DO 3 1 J « 1 , H T LS(J)«L(J)^X(J,1)^L(J) •X(J,2) 7S(J) = T(J)^T (J,1)^T(J) •T(J,2) IF(ABS(7S(J)) .LT. 1.2-5) GO TO 36 IF (ABS (LS (J) ).LT.1.2-5) GO TO 31 TS(J)«T(J)^T(J,1)/7S(J)

36 XS(J)=L(J)^X(J,1)/LS(J) 31 C0HTIHU2

Drs«DF^(X(NT,1) •X(NT,2)) TS(NT)»0. R2TURH 2ND

C SUBROUTINB RZFT (TRF)

R2AL L COHHON/BLOCX2/FD,EF,DF,TFD,PCOL,CLBL(6,6) ,HH(15) ,XF(15) ,PFD,PBEF COHHOH NC,NT,NFT,NTHl , IBC,ITC COHHOH/TRAT/7 (50) , L (50) ,T (SO) , DBHS (50) , AHW (50) ,PT (50) ,LC C0HH0H/2HT7/HTC(5,S) ,HLC ( 5 , 5 ) COHHOH/XTCHP/X ( 5 0 , 5 ) , T ( 5 0 , 5 ) , HL (50) ,HT (SO) COHHOH/DUTT/QHB,QCND HAH2LIST/RFT/HL,H7,QCH0,7,L,DF

C C FOR SUBC00L2D REFLUX, THIS SUBPOUTINE CALC. SUBCOOLED C TEHP FROH 2N2RGT BALANC2 ABOUND CONDZNSER

HL (NT) = (H7 (NTH 1) •T (NTHl) -QCHD) / (L (NT) • DF) C

T1«0-8^T(NTH1) T2«1.20^T(NTH1) S1«0 . S2»0 . DO 3 1 1=1 ,NC S 1 « S U X ( N T , I ) ^ H L I Q ( T 1 , I )

31 S 2 « S 2 ^ X ( N T , I ) ^ H L I Q ( T 2 , 1 ) F1«f lL(HT) -S l F2«HL(HT)-S2 DO 37 1 3 - 1 , 3 5

I F ( F 1 ^ F 2 - G T . 0 . ) GO TO 5

136

T3= ( T U F 2 - T 2 ^ F 1 ) / (F2-F1) GO TO 8

5 T 3 « T 1 - { 1 , - . 6 ^ ^ I 3 ) • F l ^ ( T 2 - T 1 ) / ( F 2 - F 1 ) 8 S 3 - 0 .

DO 39 I » 1 , H C 39 S 3 - S 3 * X ( H T , I ) ^ H L I Q ( T 3 , I )

F 3 - H L ( N T ) - S 3 IF (ABS(T3-T2) . L T . 0 - 3 ) GO TO 89 T1-T2 T2=T3 F 1 - F 2

37 F2«F3 WRIT2(6 ,92) 1 3 , F 3

92 FORHATC ' , ' R2FT DID NOT C0N72RG2 T» ' , F 1 3 . 9 , 2 1 , E 1 3 . 5 ) WRITE (6,RFT)

89 TRF-T3 R2TUHH EHD

C / / G O . S T S I H DD •

DYNAMIC MODEL OF COMPLETE DISTILLATION TRAIN ^^^

C THIS PROGRAH CALCULATES RESPOHSE OF OUTPUT TO TARIOUS INPOTS C DISTURBANCES AR2 R2PR2S2NT2D BT K^BXP (-TH ZTA^S) / (TAU^S^ 1) C THZ DISTDRBAHCZS AH2 R2PRZS2HTED BT 1 TRANSFER FUNCTION C BATRIX WITH EACH 2L2H2HT OF THE HATRIX CONPOSING OF A GAIN, C TIH2 D2LAT AND TIH2 COHSTAHT. TH2 OUTPUT R2SP0NS2 I S CALCULAT2D C BT SUHHIHG UP TH2 R2SP0HS2 OF EACH ElEHENT CORRESPONDIHG TO THE C RESPONSE TAPIABLZ. C DEFINITIOHS C C 3-BOTTOHS FLOW RATE C BFS=BOTT0HS FLOW RATE AT STEADT STATE C D-DISTILLATE FLOW RATE C DFS»STEADT STATE DISTILLATE FLOW RATZ C DHTB-HZAT OF TAP0RI2ATI0H OF BOTTONS TAPOR KJ/KG C DH7T-=aEAT OF TAP0RI2ATI0N OF TOP TAPOB " C FD-FBED RATZ C FDS-ST2ADT STATE F2ED RATE C PXP-PHOPORTIOHAL GAIN FOR PRESSURE PROP CONTROLLER C PXC-GAINS FOR TRANSF2R FUHCTIOH 1ATRIX C QCND-COHDENSER DUTT KJ/HR C QCNDS«STEADT STATE COND DUTT C QR3«REB0ILER DUTTXJ/HR C QRBS=ST2ADT STATI REBOILER DUTT C R=REFLnX RATE C RFS=fl2FLUX BAT2 AT STEADT STAT2 C RT « REFLUX TO 0T2RHEAD TAPOR RATIO A3 STEADT-STATE C TAU=TIH2 COHSTAHT HR C THETA-TIHE DELAT HR C TR-STBADT STAT2 TOP TAPOR TO R2FLUX RATIO C 7»BOTT0flS TAPOR RAT2 C TT'TOP TAPOR RATZ C TF-80TT0HS TAPOR TO FEED "SATE RATIO AT STEADT STATE C TS»BOTTOHS TAPOR RATE AT STEADT STATE C TTS=TOP TAPOR RATE AT STEADT STATE C XBS=BOTTOHS COHP AT STEADT STATE C XDS-TOP COHP AT STEADT STATE C XD= DISTILL ATE COHP C XB=BOTTOHS COHP C IF1=FEED COHP OF COHP 1 C XF2«FE2D COHP OF COHP 2 C XF1S=F22D COHP OF COHP 1 AT STEADT STATE C XF2S-FEED COHP OF COHP 2 AT STEADT STATE C XFH « FEED CONPOSITIOH OF HEATI2R THAN HEA7T K2T COBPONENT C XHH « BOTTOHS COHP. OF COHP. HO. (HEA7T XET • 1) C C EXAHPLE C FD R TB P D C 0 - 1 9 5 0 0 E 03 0 . 6 7 7 1 2 E 02 0 . 9 5 9 9 6 E 02 0 , 1 6 6 8 S Z 03 0 . 2 8 1 9 5 E 02 C XF(1) XF(2) XB XD P C 0 , 1 5 0 0 0 0 ,20000 0,22516 0 .99912 1.02700 C QH QC C 0.29399E 07 0,22099E 07 C K TAO THBTA C - . 9 2 8 0 0 2 - 0 3 0 . 2 6 0 0 , 0 3 0

138

c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c

- . 3 5 3 0 0 2 00 0 . 3 1 2 0 0 2 - 0 7 - . 3 3 6 0 0 2 - 0 3 0 . 0 0 .118002 -03 0 . 1 1 3 8 0 2 01 - . 3 2 8 0 0 2 - 0 7 0 , 2 9 5 0 0 2 - 0 2 0 . 0 - , 5 9 9 0 0 2 - 0 1 0 . 0 0 . 3 5 9 0 0 2 - 0 9 - . 5 6 3 0 0 2 - 0 1 - , 9 7 9 0 0 2 - 0 9 - . 7 1 8 0 0 2 - 0 3 0 . 0 0 . 1 1 9 0 0 2 - 0 6 - . 3 6 9 0 0 2 - 0 2 - . 1 5 8 0 0 2 - 0 6

DH7T 0 - 3 0 6 7 0 2 05

H7 0 . 7 0 6 9 0

XFH 0 , 9 0 0 0 0

TIH2 1 2 3 9

0.05 0

0 , 3 7 5 0 - 2 9 5 0 , 2 9 0 0 , 0 3 0 0 , 165 0 . 5 7 0 0 . 2 6 5 0 . 3 9 5 0 . 0 1 0 0 . 2 3 0 0 . 0 6 3 0 . 1 9 5 0 . 1 7 5 0 . 2 2 0 0 , 0 9 3 0 . 0 3 0 0 . 0 3 2 0 . 0 3 2 0 . 0 3 2

DH7B 0 . 3 2 5 9 6 2 0 5

F7 0 . 9 8 9 7 0

XHKB 0 . 9 6 7 9 9

0. 0 , 0, 0 . 0 . 0 , 0 , 0 , 0 . 0. 0 , 0 . 0 . 0 . 0 . 0 . 0 . 0 , 0,

025 053 120 090 095 120 035 110 0 0 012 0 0 0 0 090 0 0 0

XB 0 , 2 2 5 1 6 0 . 2 3 0 2 8 0 . 0 0 . 0

XD 0 . 9 9 9 1 2 0, 0 . 9 7 9 9 9 0, 0 . 0 0. 0 . 0 0.

FD 1 9 5 0 0 2 0 305C0B 0 9 2 7 8 2 2 0 0

QRB 3 0 . 2 9 9 0 1 2 07 3 0 . 119892 08 3 0 . 0

0 . 0

PB2SS 1 . 0 2 7 0 0 7 . 3 0 8 0 0 0 , 0 0 . 0

RF 0 . 6 7 7 1 2 2 0 . 9 8 1 2 9 2 0 . 0 0 . 0

02 02

7B 0 . 9 5 9 9 6 2 0 . 9 3 9 0 3 2 0 . 0 0 , 0

02 03

B 0 , 1 6 6 8 5 E 0 . 2 6 0 9 7 2 0 . 0 0 . 0

03 03

D 0 . 2 8 1 C.990 0 . 0 0 . 0

52E 02 322 02

QCHD 0 . 2 2 0 9 9 E 07 0 . 3 1 0 8 0 E 07 0 , 0 0 , 0

COflHOH/BLX1/PKC(5,10 ,10) ,TAU(5 C0HHON/SS7/FDS(5) , X F 1 S ( S ) ,XF2S

2 DFS(S) , B F S ( 5 ) , 7 S (5) ,XBS(5) C0HH0H/DH7/DH7B (5) ,DH7T (5) COflHON/BLK2/AK(10,10) , A T A ( 1 0 , 1 0 ) , ATH ( 1 0 , 10) ,TT ( 5 , 5 0 ) , 0 (10) COHHON/HHK/XFH (5) ,IHH (5) DIHEHSIOH XB(5) , X D ( 5 ) , D ( 5 ) , 3 ( 5 DIHEHSIOH 7 ( 5 ) ,QCHD(S) ,QRB(5)

1 -9 ON

, 1 0 , 1 0 ) ,T (5) , BFS (5 xos(5),a7

0 . F 0 ( 5 ) ,X RF(5) ,QR3

H2TA(5 ,10 , 10) ) ,QCN0S(5) ,QHBS(S) , ( 5 ) , 7 F ( 5 ) , P S ( 5 )

F 1 ( 5 ) , X F 2 ( 5 ) , P ( 5 ) SP ( 5 ) , 7T(S)

c c c

PUT T2ST LIT2S

CALL SLIT2(1) CALL SLIT2(2) CALL SLITE(3) CALL SLITE(9)

139

c C SET CONSTANTS FOR PORPORTIORAL CONTROLLIRS C

P K P - 0 . 5 Z 6 • PXXB-1.5E7

P I - 3 . 19593 DELT-0 .05

C C S2T TIH2 2QUAL TO 22RO FOR ALL COLOHNS C

T I - 0 . T 1 - 0 . T 2 - 0 . T 3 - 0 . T 9 - 0 . DO 111 1 7 - 1 , 1 0 0 TO»TI^02LT

C C D2T2BHIN2 a2SP0NS2 OF COLOHHS 1 AND 2 C

T10-T1^02LT T20-T2+D2LT CALL C 0 L H N ( 1 , T 1 , T 1 0 , I B , I D , P , F D , X F 1 , X F 2 , T,QCND,QRB,aF) B ( 1 ) - F D ( 1 ) ^ X F B ( 1 ) / X H H ( 1 ) D ( 1 ) = F D ( 1 ) - B ( 1 ) T T ( 1 ) » ( R F ( 1 ) ^ E ( 1 ) ) B T ( 1 ) - R F ( 1 ) / T T ( 1 ) • y ( 1 ) - 7 ( 1 ) / F D ( 1 )

I F ( ABS ( ID (1) - IDS ( 1 ) ) . G T , 0 . 0 0 1 ) 2 H F ( 1 ) - B 7 ( 1 ) ^ T T ( 1 ) ^ ( ( X 0 S ( 1 ) / X D ( D ) • ^2)

I F ( A B S ( I B ( 1 ) - X B S ( 1 ) ) . G T . 0 . 0 0 1 ) 2 Z D ( 1 ) « ( T ( 1 ) / 7 F ( 1 ) ) ^ ( ( X B ( 1 ) / X B S C ) ) • • 2 )

I F (ABS ( F ( 1 ) - P S ( 1 ) ) . G T . 0 .0021 ) 2 QCHD (1)-QCHDS(1) •PXP^ ( P ( 1 ) - P S (1) )

QCND(2)=T (1) •DHTB(1) C C ST2P CHANG2 IH F22D RAT2 GOBS H2R2 C

F D ( 2 ) » 5 2 S . - F D ( 1 ) C

CALL C O L H H ( 2 , T 2 , T 2 0 , X B , X D , P , F D , X F 1 , X F 2 , T,QCHD, QRB, HF) 3 ( 2 ) - F D ( 2 ) ^ I F H ( 2 ) / X H a (2) D ( 2 ) - F 0 ( 2 ) - B ( 2 ) TT (2) - (RF (2) • £ ( 2 ) ) H T ( 2 ) - R F ( 2 ) / 7 T ( 2 )

IF (ABS (XD(2)-XDS(2)).GT. 0.0 01) 2 HF(2)-BT(2)^TT(2)*((XDS(2)/XD (2))^^2) QCNDA9«T(2) •DH7B(2)

C C CALCULAT2 H2AT SUPPLIED TO COLUHH 1

C QRB(1)»TT (2) •0HTT(2)

IF (ABS(P(2)-PS(2)) .GT.0,001) 2 QRB (2) -QRBS (2) -5. 00Z5^ (P (2 ) -PS (2) )

140

I F ( T I . G T . 0 . 9 5 . A H D . Q H B ( 2 ) . L T . QRBSP(2)) QR B (2) "QBBSP (2) I F (Q8B{2) . G T . 1 .001^QRBS(2) ) QRB (2) = 1 . 0 0 1 •QRBS (2)

F D ( 3 ) - B ( 1 ) + B ( 2 ) I F ( T I . L T . O . 18) GO TO 119 T30«T3^DELT

C C D2T2RHIN2 COLOHH 3 RZSP0NS2 C

CALL C O L H H ( 3 , T 3 , T 3 0 , X B , X D , P , F D , X F 1 , X F 2 , T,QCHD, QRB, RF) 3 (3) «FD (3) •XFH (3) /XHH (3) 0 ( 3 ) - F D ( 3 ) - B ( 3 ) T T ( 3 ) - ( R F ( 3 ) ^ D ( 3 ) ) R 7 ( 3 ) - R F ( 3 ) / T T ( 3 ) QCHDB9-7(3)^DHTB(3) QCHD (9) »QCN0E9^QCND A9

IF (ABS (XD(3) -XDS(3 ) ) .GT. 0 . 0 0 1 ) 2 R F ( 3 ) » B T ( 3 ) ^ T T ( 3 ) ^ ( ( X D S ( 3 ) /XD(3) ) ^ ^ 2 )

IF (ABS ( X B ( 3 ) - X B S ( 3 ) ) . G T . 0 . 0 0 1 ) 2 Q R B ( 3 ) - 0 5 3 5 ( 3 ) - 5 . 2 7 ^ ( X B ( 3 ) - X B S (3) )

I F (ABS (P ( 3 ) - P S (3) ) . G T . 0 . 0 0 1 ) 2 QCNO (3) »QCHDS(3) • P X P ^ ( P ( 3 ) - P S (3))

IF ( T I . G T , 0 . 9 5 . A N D . Q R B ( 3 ) .LT.QR8SP (3 ) ) QB B (3) «QBBS? (3) I F (QRB (3) . G T . 1 . 0 0 1 - Q R B S ( 3 ) ) QRB (3) =1 ,001*3RBS (3)

C I F ( T I . L T . 0 . 9 5 ) F D ( 9 ) = B ( 3 ) I F ( T I . L T . O . 2 7 ) GO TO 119 T90«T9^02LT

C C D2T2HHIN2 COLUHH 9 R2SP0NS2 C

CALL C 0 L H H ( 9 , T 9 , T 9 0 , I B , X D , P , F D , X F 1 , X F 2 , 7,QCND,QBB,aF) D (9) -FD (9) • (XF1 (9) - (1 . -XB (9 ) ) ) / (XD (9) - ( 1 . - 1 3 ( 9 ) ) ) B ( 9 ) - F D ( 9 ) - D ( 9 ) 7 T ( 9 ) - ( B F ( 9 ) ^ E ( 9 ) ) B 7 ( 9 ) « R F ( 9 ) / T T ( 9 ) 7 F ( 9 ) » T ( 9 ) / F D ( 9 )

C ir (ABS (XD ( 9 ) - I D S ( 9 ) ) . G T . 0 . 0 0 1 )

2 R F ( 9 ) » R T ( 9 ) ^ 7 T ( 9 ) * ( ( X D S ( 9 ) / X D (9) ) • • 2 ) IF (ABS ( X B ( 9 ) - X B S ( 9 ) ) . G T . 0 . 0 0 1 )

2 F D ( 9 ) » F D S ( 9 ) + ^ l i K ^ ( X B ( 9 ) - X B S ( 9 ) ) IF ( A B S ( P ( 9 ) - P S ( 9 ) ) . G T . 0 . 0 0 1 )

2 Q R B ( 9 ) - Q R B S ( 9 ) - 2 . S 2 S ^ ( P ( 9 ) - P S ( 9 ) ) I F ( T I . L T . O . 3 8 ) GO TO 119

C C D2T2aHIN2 H2AT SUPPLI2D TO COLOHHS 2 AND 3 C

QBBSP (2) - . 95626«TT ( 9) •0H7T (9) Q H B S P ( 3 ) - . 5 9 3 7 9 ^ 7 T ( 9 ) • 0 a 7 T ( 9 )

119 C0ITIN02

305 F 0 R H A T t ' ^ ° f / / ! 2 X , ' T I H 2 ' , F 8 . 3 , 10X, ' IB' , 8 X , ' XD' , 1 0 1 , ' FD' ,1 OX, 2 'QRB' , 1 0 X , ' P R 2 S S ' )

DO 80 1 1 - 1 , 9

141

801 WHIT2(6 ,311 ) I , X B ( I ) , I D ( I ) , F D ( I ) , Q R B ( I ) , P ( I ) 311 FORHATC • , I 2 , 1 6 X . 2 ( F 7 . 5 , 3 X ) , 2 ( 2 1 3 . S , 2 X ) , F 7 . 5 )

w a i T 2 ( 6 , 3 2 1 ) 321 FORHATC ' , * / / , 1 3 X , ' R F ' , 1 0 X , ' T B ' , 1 3 X , » B ' , 1 3 X , ' D ' , 1 3 I , ' 7 T ' ,

2 13X,'QCHD') DO 8 0 2 1 = 1 , 9

8 0 2 WBIT2 ( 6 , 3 5 1 ) I , R F (I ) , T ( I ) ,B (I) ,D ( I ) ,TT ( I ) , QCHD (I) 3 5 1 FOBHATC • , 2 X , 1 2 , 2X , 6 ( 2 1 3 . 5 , 2 1 ) )

GO TO 111 DO 127 1-1,20

127 WRIT2(6,315) TT (1,1) , TT (2,1) , TT (3,1) , IT (9,1) 315 FORHATC «,2X,213,5,21,213.5,21,213.5,21,213.5) 111 TI-TO

STOP 2ND

C SUBR0UTIH2 DATAIN (NCN) C0HHON/BLK1/PXC ( 5 , 1 0 , 10) , T A U ( S , 10 , 10) ,TB2TA ( 5 , 10 , 10) COHflOI/SST/FDS (5) , X F 1 S ( 5 ) ,XF2S (5) ,RFS (5) , QCNDS (5) , QRBS ( 5 ) ,

2 DFS(5) , B F S ( 5 ) , TS (5) ,XBS(5) , X D S ( 5 ) , R 7 (5) ,TF(5 ) , P S ( 5 ) COflBOH/DHT/DHTB (5) , DH7T (5) C0eHOH/HHX/XFH(S) ,IHH(5)

C C SUPPLT ST2A0T-STAT2 7ALU2S, GAINS, TIHE CONSTANTS, TIHE DELATS, C HEATS OF 7AP0BI2ATI0N C

R 2 A D ( 5 , 9 2 2 ) FES (NCN) ,RFS (NCN) , TS (NCN) ,BFS (NCN) , DFS (NCN) H2AD(5, 925) XFIS(NCN) ,XF2S(NCN) , I B S (NCN) ,XDS(HCN1 , PS (NCN) R 2 A D ( 5 , 9 2 2 ) QRBS (NCN) ,QCNDS (NCN) DO 31 J - 1 , 9

31 R2AD(5, 928) (PXC (NCN, J , I ) ,TAU (NCN, J , I ) , TH2TA(NCN, J , I ) , 1 = 1, 5) B 2 A D ( 5 , 9 2 2 ) DB7T (NCN) , DH7B (NCN) R2AD(S, 92 5) RT (NCR) , 7 F (NCN)

I F (NCH.GT-3) GO TO 97 B 2 A D ( 5 , 9 2 5 ) XFH (HCN) , XHH(NCN)

C 922 FORHAT (5 ( 2 1 1 , 5 , 9 X ) ) 9 2 5 FOBHAT(5(F10 .5 ) ) 928 F0BHAT(21 1 . 5 , 9 X , T 2 0 , P10 , 3 , F 1 0 . 3) 97 R2TURN

2HD C

SUBS0UTIN2 C0LflN(NCN,TI ,T0,X3, XD, P,FD,X F 1 , I F 2 , T,QCND,QRB,RF) C

I1T2G2R IWX(25) C O H H O N / B L X 1 / P X C ( 5 , 1 0 , 1 0 ) , T A O ( 5 , 1 0 , 1 0 ) ,TH2TA (5 , 1 0 , 10) COHnOH/SST/FDS(5) ,XF1S (5) ,XF2S (5) , RFS (5 ) ,QCHDS (5) , QRBS (5) ,

2 DFS (5) , B F S ( 5 ) , T S (5) ,XBS (5) , IDS (5) , RT (5) ,TF (5) , P S ( 5 ) COHHON/DflT/DHTB(S) ,DH7T(5) COHflOH/BLX2/AX(10,10) , A T A ( 1 0 , 1 0 ) , ATH( 10 , 10 ) ,TT ( 5 , 50) ,U (1 0) DIH2HSI0H X B ( 5 ) , I D ( 5 ) , D ( S ) , B ( 5 ) ,FD (5) ,XF1 (5) , XF2 (5) , P ( 5 ) DIH2HSI0N 7 ( 5 ) ,QCND(5) ,QRB(5) , R F ( 5 )

DIH2NSI0N T ( 5 0 ) , W X ( 7 S 0 ) , D T ( 5 0 ) EXTERHAL DTP, FCNJ

142

NAH2LIST/C2A/ IND,B,H2TH,niTER,T0L,N2QH,T,DT,AX, ATA, ATH C C THIS SUBB0UTIN2 INT2GRAT2S TH2 EQUATIONS FOR EACH COLUHH C OH FIRST CALL,'DATA I S READ IH AHD PRINTED OUT. ALL INPUT 7ARIABL2S C AR2 S2T TO STEADT STAT2 2XC2PT THE STEP CHANGZ 7ARIABLE. ON FIRST C CALL IHITIAL TAL02 OF TH2 D2RITATITES IRE SET TO 2ER0, AND THEN SET C TO PBETIOOS TALOZ ON THE HEXT CALL. C C CHECX TO SEE IF TEST LITE IS OH, IF ON, I K= 1 AND DATAIN IS READ. C I F OFF, IK=2 AND DATAIN I S 3TPASSED C

CALL SLITET(NCN,IX) I F ( I X . EQ.2) GO TO 21 CALL DATAIN (HCH) CALL PRNTIN(NCH) DO 27 J - 1 , 2 0

27 IT (NCN, J ) - 0 . GO TO ( 1 1 , 1 2 , 1 3 , 1 9 ) ,NCN

C C STEP CHANGE IN C0NC2NTRATI0N CAN GO H2R2 C 11 FD(HCN) =FDS(NCN)

XF1 (NCN)-XFIS (NCN) QRB (HCH) -QRBS (HCN) QCHD (NCN) -QCNES (NCN) GO TO 17

12 FD(NCN)»FDS (NCN) IF1 (HCH)»XF1S(NCN) QBB (HCH) = QRBS (HCN) GO TO 17

13 QRB(NC1)«QHBS (HCN) IF1(HCH)«XF1S(HCN) QCHD ( HCH) -QCNDS (NCN) GO TO 17

19 QaB(NCH)«QRBS (HCN) I F 1 (NCN)»XF1S(HCH)

17 C0NTIHU2 aF(NCN)=RFS(NCH)

21 C0HTIN02 DO 101 J - 1 , 2 0

101 T ( J ) = TI(NCN,J) C C U(J) COHTAIHS THZ INPUT 72CT0R

U(1) -FD(NCN) -FDS(HCH) 0 (2) -XF1 (NCN) -XF1S (NCN) U (3) «QRB(NCN) -ORBS (NCN) 0 (5) =QCN0 (NCN) -QCNDS (NCN) 0 (9) «RF (NCN) -RFS (NCN)

C PLAC2 TH2 P X C ' S , TAU'S , TH2TA'S IN DOHHT ARRATS TO BE OSED IH C IN SUBBOUTIHE DTP

DO 37 J = 1 , 9 DO 92 1=1 , 5 A X ( J , D «PXC(NCN,J , I )

143

ATA ( J , I ) - T A U (NCN, J , I) ATH (J , 1 ) -THETA (NCN, J , I )

92 C0NTIN02 37 C0HTINU2 •

IND-1 T O L - 0 . 0 1 H - 0 . 0 0 0 1 H2TH-1 flIT2R»0 N2QH-20 CALL DGZAR (N2CN, DTP,FCNJ,TI ,H, T,T0,TOL, fl2TH,niTEB, IND ,

2 IWX,WX,IER) I F ( I2R. GT, 128) GO TO 907

C C SI - BOTTOHS COHP H2SP0NS2 C S2 - DISTILLAT2 COHP R2SP0HS2 C S3 « 7AP0R BOILUP RESPONSE C S4 « PRESSURE BZSPONSE C

S1-0-S2-0. S3-0. S 9 - 0 -SS-0. DO 39 J = 1 , 5 SI-SI^T(J) S2=S2*T(J^5) S3-S3^T(J^10) S 9 « S 9 + T ( J ^ 1 5 )

39 CONTINUE C

XB (HCH) *S I^XBS (NCN) ID (HCN) - S 2 ^ I D S (HCH) T(HCN)-S3^TS(NCN) P(NCN) = S9^PS (NCN)

C DO 51 J - 1 , 2 0

51 TT(NCN,J) =T(J) GO TO 85

9 0 7 WBIT2(6,G2A) WBIT2 ( 6 , 7 7 8 ) TI ,TO

7 7 8 FORHATC ' , ' TI= ' , F 7 . 3 , ' T0= ' , 7 7 , 3 ) DO 79 0 J - 1 , 2 0

7 9 0 WRIT2 ( 6 , 3 8 5 ) T (J) 385 FOBHATC ' , E 1 3 , 5 )

STOP 35 RETURN

EHD C

SUBROOTIHE DTP (N2QN,TI , T,DT) B2AL TI,T(H2QN),DT(N2QN) COHHOH/BLX2/AX(10,10) , ATA ( 1 0 , 1 0 ) , A T H ( 1 0 , 1 0 ) , 1 1 ( 5 , 5 0 ) , 0 (1 0)

C C THIS SUBROUTINB CONTAINS THE SET OF DIFFEREHTIAL EQUATIONS

144

DO 22 1 = 1 , 5 D T ( D - ( - T ( I ) • A X ( 1 , I ) ^ U ( I ) ^ ( T I - A T H ( 1 , 1 ) ) ) / A T A ( 1 , I ) IF ( ( T I - A T H ( 1 , I ) ) , L T , 0 . 0 ) D T ( I ) = 0 , D T ( I ^ 5 ) - ( - T < I ^ 5 ) ^ A X ( 2 , I ) ^ 0 ( I ) « ( T I - A T H ( 2 , I ) ) ) / A T A ( 2 , I ) I F ( ( T I - A T H ( 2 , I ) ) . L T . 0 . 0 ) DT(I + 5 ) = 0 . D T ( I » 1 0 ) » ( - T ( I ^ 1 0 ) ^ A X ( 3 , I ) ^ U ( I ) ^ ( T I - A T H ( 3 , 1 ) ) ) / A T A ( 3 , 1 ) I F ( ( T I - A T H ( 3 , I ) ) . L T . 0 . 0 ) D T ( I ^ 1 0 ) » 0 . D T ( I ^ 1 S ) = ( - T ( I + 1 5 ) + A X ( 9 , I ) ^ U ( I ) ^ ( T I - A T H ( 9 , 1 ) ) ) / A r A ( 9 , I ) I F ( ( T I - A T H ( 9 , I ) ) . L T . 0 , 0 ) D T ( I ^ 1 5 ) » 0 ,

22 COHTIHUE RETURH END

C SUBR0UTIN2 FCNJ (N2QN, TI ,T,PD) B2AL T(N2QN) ,PD(NEQN^, NEQH) , T I BETURH END

C SUBROUTINE PRNTIN(NCN) C0HH0N/BLK1/PKC ( 5 , 1 0 , 1 0 ) ,TAU ( 5 , 1 0 , 1 0 ) ,THETA (5 , 10 , 10) C0HHON/SS7/FDS(S) , X F 1 S ( 5 ) ,XF2S (5) , RFS (5 ),QCNDS (5) , QRBS (5) ,

2 DFS (5) ,BFS ( 5 ) , T S ( 5 ) , X B S ( S ) , XDS (5 ) ,RT (5) , T F ( 5 ) , P S ( 5 ) C0HH0H/DH7/DHTB (5) ,DHTT (5) C0HH0N/HHX/XFH(5),XHH(5)

C WRITE ( 6 , 9 2 2 ) FDS (NCN) ,RFS (NCN) , 7S (NCN) , BFS (NCN) ,DFS (NCN) WRIT2 ( 6 , 9 2 5 ) XFIS(NCN) ,XF2S(NCN) ,XHS(NCH) , XDS (NCN) , PS (HCN) WRIT2 (6,922) QRBS (NCN) , QCNDS (NCN) DO 31 J=1,9

31 WRIT2(6,928) (PXC (HCH, J,I) ,TAO (NCN, J,I) ,THBTA ( NCN, J ,I) ,1=1. 5) WFIT2 (6,9 22) DH7T (NCN) , DH7B (NCN) WRIT2 (6,9 25) R7 (NCN) , 7F (HCH) IF (NCH.GT. 3) GO TO 97

WRITE (6,925) XFH (HCN) , XHH (NCN) C 922 FORHATC • , 1X ,5 ( 2 1 1 . 5 , 9 X ) ) 925 FORHATC • , 1 X,5 ( F 1 0 , 5 ) ) 928 FORHATC ' , 1 X , E 1 1 . 5 , 9 I , T 2 0 , F 1 0 , 3 , F 1 0 . 3 ) 97 RETURN

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