Simulation of coupled columns with three phases

Computers them. Printed in Great

Engng,

Britain

Vol.

I?, No. 516, pp. 527-533,

SIMULATION

0098- I354/93

1993

$6.00 + 0.00

Pergamon Press Ltd

OF COUPLED COLUMNS THREE PHASES

WITH

B. LANDWEHR,’ G. WOZNY’ and H. HARTMANN* ‘Henkel KGaA, Postfach 1100, 4000 Diisseidorf 1, Germany 2RWTH-Aachen, 5 100 Aachen, Germany (Final

revision received

IO July

1992; received for Fubhxlion

30 September

1992)

Abstract-A new solution algorithm has been developed for the simulation of distillation columns with strongly nonideal mixtures including the possibility of two immiscible liquid phases on each tray of the column. Although

several papers about simulations of three-phase distillation processes can be found in the literature, they consider only single columns or fixed configurations of two coupled columns with a

common decanter. The algorithm represented here, however, facilitates the description of multiple columns with linking streams between any stages of the columns. The model is based on material balancei and-energy balances, equilibrium equations and the definition efficiency. The global Newton-Raphson method was used to solve the problem of Murphree-tray describing equations. Additionally stability tests for the phase splitting are included. Before starting this algorithm, initial estimates can be automatically created. The refiability of the algorithm is demonstrated by two examples.

INTRODUCTION

which may cause divergence or simply reduce the reliability. The objective here has been the simulation of single and interlinked three-phase distillation columns. A general model capable of describing coupled columns with interlinking streams between any stages of the columns was developed. These streams can be withdrawn as a vapor or liquid phase. In the case of a heterogeneous liquid a decanter application is taken into consideration. Interlinked streams can then be either the total amount or a specified value of one decanter phase. The Newton-Raphson algorithm was used to solve the whole model equation system. The required initial values can be calculated automatically. The initialization scheme developed here facilitates good perform-

Distillation of strongly nonideal mixtures with immiscible regions is of special interest in industrial processes. Most of these partly miscible systems possess at least one azeotropic point. Therefore one single column is commonly not sufficient to separate those mixtures. Multiple column systems with several interlinking streams are needed to facilitate good separation performance. A variety of three-phase distillation algorithms have been published in the literature. Cairns and Furzer (1990) give a good overview of existing simulation methods. Most of them handle single columns. The ability to describe column systems is restricted to the “conventional sequence” of two coupled columns with a common decanter (e.g. Bril et al., 1976). Pham and Doherty (1990b) analyzed the problem of column sequencing for heterogeneous azeotropic distillations using residue curve maps. Interpreting different sequences, they found that the conventional sequence frequently requires much larger reflux ratios than other alternatives. Recently Xien et al. (1990) presented an algorithm for the calculation of three-phase thermally coupled distillation processes. Their model described interlinking column sectors, but not really different coupled columns. Solution algorithms describing simple columns are reliable for those column systems where no recycle streams of a rear column are sent back to a previous one. In that case several reiterations would be needed,

ance in most cases. This is shown at two example systems, each consisting of two interlinked columns. An interesting influence of the initialization scheme on the results is explained at the second example.

MODELING

EQUATIONS

Figure 1 shows an example of two coupled columns having S, and S, stages, respectively. Phase separation and the use of a decanter is allowed at every stage of the system. The first column receives the main feed stream. The trays are numbered consecutively from the top of the first to the bottom of the last column. 521

B.

528

LANDWEEJR et al.

1 -

Dl

column 1 Fl

s1-1.

decantor

S1+82

Fig.

1. Exemplary model of an interlinked two-column system.

Material balances, phase equilibrium correlations, stoichiometric equations and energy balances are formulated for each tray. Figure 2 represents a model stage with all its possible input and output streams. The linking flows have two indices, the first one characterizes the origin and the second one the destination. The model equations are based on the following assumptions: -vapor-liquid equilibrium at the liquid surface, - validity of Murphree-tray-efficiency model, -ideally mixed liquid phase, -liquid-liquid equilibrium.

Equilibrium

at liquid surface:

(21 Liquid-liquid

equilibrium: EL&=x’ k.1

Murphree-tray

k.J

.-~L~~“.=O k.J k./

(3)

.

efficiency correlation: (4)

~ck.j=~k,j-EjY~j+Yk,j+l(Ej-‘l)=O’

Stoichiometric

equations: slj=

F

yk.i-

1 =o,

(5)

xiJ-

1 = 0.

(6)

k=l NK

Component

material mass balance:

sq=

c k=l

CBk,i = Fi~.,j + V;.+ 1 Yk,j -

+ 1 +

WR,,jYk. p

Total mass balance in case of immiscibility

( 5 f W, + WR,mIv*.]

+L’_,x:j_,+L” J . _

J

1

MB,=q+

x”k.1 _ I

WR,,-(Vj+

-(L!‘+I

- (Li” + Uj’ + URj,;)x& = 0.

(1)

Definition

U!‘ I+

UR!)=O J.r

Enthalpy

-
-

vi+1

L’I

v L' j

Fig. 2. Model of stage j.

V;-+,hlv,l+ Wj+

WRp,hT

WRj.,)hY

UR;‘,

+L!_,hF!, /

u’i

+ UR;, ,h:’ + UR:tjht”

URi q

(=I

.

balance:

Hj=F,h,F+Qj+

-

(74

*

of no second liquid phase (2 phases): MB I =L!‘=O J

4

WRj,,)

- (Li’ + U, + UR;., )

- (Lf + CJf+ UR;;,)&

c

Wj+

+Lj’_,+L,“,+UR:,+UR:ti

URj,/x:,i + UR;,lix::,

+

v;+,+

(3 phases):

+ Lf’_,h;!

-

(L; + U; + URj.,)hjL

-

(Li” + Ul” + URj.;)h~”

I

= 0.

(8)

529

Simulation of coupled columns with three phases The indices used in the upper equations indicate the component number k (k = 1, . . . , NK) and the tray , NST). The methods used to number j (j=l,... estimate the physical properties are described in Appendix A. As indicated in equation (7a) and (7b), the equation set depends on the number of liquid phases. In the case of miscibility (7b) must be used to avoid dependency of the upper equation system. Therefore, the phase pattern of the whole column must be fixed during one iteration step. In the case of condenser or reboiler the enthalpy balance is replaced by specification equations. Those are equations characterizing given reflux ratios and distillate flows or defining component purities.

MATHEMATICAL

SOLUTION

The balance equations are solved by using a global Newton-Raphson method. Concentrations, flowrates and temperatures are used as iteration variables. Without the recycle stream, the involved Jacobian matrix would have a tridiagonal structure. An interlinking stream from tray q to tray j couples variable information from tray q and tray j and therefore causes the appearance of an off-element outside the tridiagonal structure. The derivatives of the Jacobian matrix were analytically determined, except of some temperature-dependent variables. Starting values (X0) are automatically created. This procedure, based on simplifications, generates consecutive initial values for every column. The temperature profile and a first mean liquid concentration profile are supposed to lie between the dew and boiling state of the mean feed concentration. The flow rates are determined by assuming constant molar overflow. Then liquid and vapor concentrations are calculated using component balances with definite K-values and vapor-liquid equilibrium. Normally, two phases are assumed. In problematic cases a modified K-value [similar to Schuil and Boo1 (1985)] can be used, which is able to include phase splitting even at the beginning. Apart from this, initial values can as well be provided by the user. An important routine of the algorithm is a phase stability test, which examines and corrects the phase pattern in the columns. This test is based on the solution of the isoactivity constraints and additional mass balances. This equation system is solved by the Newton-Raphson technique. The necessary initial values are determined with Shah’s method [Shah (1980)]. This check of the phase pattern is a time-consuming simulation step. Furthermore, it has been observed that a check after each iteration does not CACE17-5,6-H

improve the reliability of the algorithm. In some cases it even increases the number of iterations. The following procedure was found to be very reliable: Two stability tests are at least applied. The first one after a few iterations, when the value of the Newton correction vector is lower than a given limit, and the second one when convergence constraints are achieved. The last one represents a check to confirm the resulting phase pattern. Additional phase checks are applied when a maximum number of iterations without phase pattern tests is exceeded. The flowchart in Fig. 3 illustrates the whole simulation procedure. After the input of the problem specification parameters, initial values are created. Then the Newton-Raphson iterations including phase pattern tests are performed. In the case of an interlinking stream being a decanter phase, its concentration changes sharply when immiscibility is detected or removed. This provokes the feedstream of the coupled column into changing as well. If this change is significant, new values for this column are calculated using the initialization scheme mentioned above. The method described above was recently extended by Landwehr et al. (1992) to dynamic problems in order to simulate open- and closed-loop systems. CASE

STUDY

Different examples described in literature have been simulated for a first test of our algorithm. Good agreement mostly has been found in those cases, where interaction parameters (NRTL or UNIQUACparameters) were available. The iteration number commonly lies between 5 and 20. Example

1

Our first example analyzes a water-butanot butylacetate distillation plant. The triangular diagram in Fig. 4 describes the miscibility and separation behavior of the ternary system. Three distillation boundaries, connecting the three binary azeotropes with the ternary one, divide the system into three different distillation regions. The problem specifications are summarized in Appendix B. The flowsheet in Fig. 5 shows the simulated twocolumn sequence. In the proposed sequence, column 1 is fed with the main feed F,, whose concentration lies in the right region. The distillate is separated in a decanter and the top-layer phase is sent to the second column. There, a new distillation once again produces an immiscible distillate stream, whose top layer phase now is sent back to column 1. The balance lines of this process are shown in Fig. 4.

530

B. LAND~EHR et al.

llOWbdtl8lYOhlOO

for

cohm

NC

Fig. 3. Flowchart of the simulation.

While the main feed FI, the distillated D, and the bottom flow B, of column 1 lie in the right region, the two phases of D, are situated in the left and upper ones, respectively. Although distillation boundaries theoretically present an impassable border for standard distillation, in our case a decanter facilitates crossing them. Concentrations and distillate flows are given in Figs 4 and 5. Apart from the two decanters immiscibility was only found on the second stage of column 1. Initial values are calculated automatically and final convergence is obtained after 12 iterations. The computing time was 84 CPU s. The computer used was a Microvax. Example 2 The second example handles a two-column plant separating a mixutre of acetonitrile, acrylonitrile and

water. Similar to the first example the process is illustrated with a ternary diagram (Fig. 6). As shown in Fig. 6 a homogeneous binary azeotrope is situated between water and acrylonitrile and a heterogeneous one between water and acetonitrile. A distillation boundary connecting the two minimum azeotropes generates two distillation regions. Figure 7 shows the structure of the two-column system. Further specification information can be found in Appendix B. The main feed F, and the recycle stream entering the first column are separated in a water-rich distillate flow, leaving the decanter at the condenser, and a bottom product. The latter is fed in the second column, where concentrated acrylonitrile is withdrawn at the bottom. The distillate product is recycled to the first column. Like in the first example, the immiscibility region facilitates crossing the distillation boundary.

Simulation of coupled columns with three phases Water -----Residue

the stability test and the decanter equations are included. In this case, however, a significant influence of the starting value vector on the calculated concentration profiles in both columns was observed. The condensate of vapor leaving the top of the first column consisted of two liquid phases, if initial estimates predicted two-liquid-phase behavior, also [Fig. 6, case (l)]. In the opposite case the condensate consisted only of one liquid phase [Fig. 6: case (211. In both cases the system configuration and product specifications were identical. The balance lines shown in Fig. 6b illustrate the different separation behavior of casts (1) and (2) caused by different starting values. The automatic generation of starting values permits only the prediction of the second case. Therefore, the generation procedure should be carefully used andsometimes-the initial estimates must be delivered by the user. In these cases the iteration numbers were 6 and 7, and the computing times 88 and 123 CPU s, respectively. In this example acrylonitrile could be regarded as an entrainer to separate water and acetonltrile. In the case of a decanter the entrainer is enriched in the upper column region, but not withdrawn at the top, because of phase splitting. This strong entrainer enrichment could not be predicted using the initialization scheme and therefore the homogeneous solution is found. Similar observations were made for other entrainer systems.

cuwcs

Liquid boiling EUVel0p.Z Balance lines

_

1.0

0.5

I-Butanol

Butylacetrt

531

Fig. 4. Butanol-water-butylacetate ternary diagram.

As Fig. 6a illustrates, the distillation boundary is situated near the acetonitrile edge of the immiscible region. Therefore, the reflux ratio of the first column is required to be high in order to gain enough water-rich phase for the distiliate flow. In our case the whole water-rich phase should be withdrawn as a fixed distillate stream. It results in a reflux ratio of 42.2 for the first column. In this example, the only stage where immiscibility occurs is the decanter. Once a decanter is chosen, for example at the top of column 1, the program is only able to use the decanter equations during iterations, if the current values show phase splitting. As long as no immiscibility is detected on tray one, the condenser is simulated as normal-without a decanter. Even with two-phase initial values, immiscibility is commonly detected by

CONCLUSIONS

Column systems with recycle streams play an important role in industrial processes, especially in the case of azeotropic mixtures. However, available

[ kmol/h ]

Dd = 27.3 x” = 0,420

[n#rxJ

d

D - 801 : 5 0,705 o,l51 O,#l

1

t

D,’ = 46.5

i *

Fig.

:z

I

I

5. Two

0,on 0.040 0,042

D,”

x 33,s

x” = 0 417 0;257 0,225

column flowsheet of: (1) water; (2) butanol; and (3) butylaeetate.

z 27 x’ n 0,557 0,055 0.544

02’

B. LANDWEHR et al.

532

Acetonitrile

(b) -----Residue -

curves

1.0

Heterogeneous Liquid boiling Envelope Balance lines (1) Balance lines (2)

_ k

0.9

0.8 BT 0.7

0.6 _--------0

0.5

0.5

1.0

0

0.1

Fig. 6. Acetonitrile-acrylonitriie-water

1 kmoVh [ mol % 1

ternary diagram.

1

r I

-I-

F, = 100 x

J

D2: Dl

0,054 0.010 0,936

0.04 0,70 0.26

I

xn

= 27

+

= 93

BI x

1

0.061

5

Fig. 7. Flowsheet

simulation tional

The

starting This

procecure

can lead

that

values

both

provided

facilitates

with

multiple

in the program

values

show

state

B = Bottom

a common

here

that

the

sometimes physical initial

is

solution

the reliability

to different automatic

for

of the different results.

values

for Example 2.

NOMENCLATURE

stages.

implemented initial

also

with

columns

any

examples

but

values

shows

starting

good

Two

model,

represented

several

distillation

or the conven-

and

by the user must be carefully

used. Acknowledgement-The authors would like to thank the BMFT’ (Bundesministerium fiir Forschung und Technologie), Germany, for providing financial support for this work.

0.155 0,552 0.293

B,.

73 0,955 0,010

of the column arrangements

three-phase columns

of two columns

between

to create

algorithm. new

of

streams

A special

the single

algorithm

description

linking able

for only

flxed structure

decanter. the

tools handle

20

x = 0,035

0.860 0.071

columns

0.2 Acrylonitrile

Acrylonitrile

Water

D = F= h= K = 15.= NK = NST = Q = T= U = UR = V = W = WR = x = y = .z = A = B=

flowrate Distillate flowrate Feed rate Enthalpy Equilibrium constant Liquid flowrate Number of components Total number of stages Heat flowrate Temperature Liquid side stream Liquid recycle stream Vapor Aowrate Vapor side stream Vapor recycle stream Liquid mole fraction Vapor mole fraction Feed mole fraction Difference Convergence accelerator

1.

Simulation

of coupled

columns with three phases

Superscripts = * I II LL L T V VL

= = = = = = = = = =

vector matrix At the liquid surface First liquid phase Second liquid phase Liquid-liquid Liquid Transformed Vapor Vapor-liquid

Subscripts number k = Component j = Stage number

REFERENCES Bril Zh. A., A. S. Mozzhukhin, F. B. Petlyuk and L. A. Seraflmov, Mathematical Simulation and Investigation of the Heteroazeotropic Fractionation Process, pp. 761-770. Plenum, New York (1976). Buzzi Ferraris G. and M. Morbidelli, Distillation model for two partially immiscible liquids. AZChE JI 27, 881-888 (1981). Buzzi Ferraris G. and M. Morbidelli, An approximate mathematical model for three-phase multistaged separators. AIChE JI 28, 49-55 (1982). Cairns B. P. and I. A. Futzer, Multicomponent three-phase azeotropic distillation. 2. Phase stability and phase-splitting algorithms. Ind. Engng Chem. Res. 29, 1364-1382 (1990). Gmehling J., U. Onken and W. Arlt, Vapor-Liquid Equilibrium Data Collection, p. 656. DECHEMA, Frankfurt (1981). Landwehr B., G. Wozny and H. Hartmann, Steady state and dynamic simulation of three phase distillation for industrial application. IChemE Symp. Ser. No. 128. Bl l-B26 (1992). Pham H. N. and M. F. Doherty, Design and synthesis of heterogeneous azeotropic distillations-II. Residue curve maps. Chem. Engng Sci. 45, 1837-1843 (1990a).

533

Pham H. N. and M. F. Doherty, Design and synthesis of heterogeneous azeotropic distillations-III. Columns sequences. Chem. Engng Sci. 45, 1845-1854 (199Ob). Schuil J. A. and K. K. Bool, The phase flash and distillation. Compurers them. Engng 9, 295-300 (1985). Shah V. B., Multicomponent distillation with two liquid phases. Thesis, University of Toledo (1980). Xien X., L. Shouchun, W. Baogo and M. Haihong, Simulation of thermally-coupled distillation processes with two liquid phases. J. C/rem. Ind. Engng (China) 5, 133-142 (1990).

APPENDIX

A

The vapor phase was supposed to be ideal. The activity coefficients were calculatecl-using the UNIQUAC or the NRTL model. The enthalpies of the liauid and vauor vhases were assumed to be molar averages oi the pure component liquid and vapor enthalpies.

APPENDIX

I3

Example I Specifications Both columns consist of 5 theoretical stages, including condenser and decanter. For both columns reflux ratios (2.5,2) and distillate flows (80 kmol h-r, 30 kmol h-‘) were specified. Column pressure was 1.013 bar. The main feed enters column 1 on the third stage. The water pourer phase of the decanter separating the distillate flow of column 1 is fed to the second stage of column 2. The recycle stream is fed to column 1 on stage 4. NRTL-parameters were taken from Gmehling et al. (1981). The residue curves were calculated using the model equations corresponding to Pham and Doherty (1990a). Example 2 Spec$carions In this case, the first column has 18 theoretical stages and the second one 15. The reflux ratios were 42.2 and 20, respectively. The specified distillate flows are quoted in Fig. 7. The column pressure was supposed to be 1.013 bar throughout the columns. The main feed enters the first column on stage 12. The recycle streams enter the first column on stage 10, and the second one on stage 2. The NRTL-parameters used were taken from Buzzi Ferraris and Morbidelli (1981, 1982).