Investigation of the operability for four-product dividing wall column with two partition walls☆

Xiaolong Ge *,Botong Liu ,Botan Liu Hongxing Wang Xigang Yuan ,*

1 College of Chemical Engineering and Materials and Science,Tianjin Key Laboratory of Marine Resources and Chemistry,Tianjin University of Science and Technology,Tianjin 300457,China

2 State Key Laboratory of Chemical Engineering,Tianjin University,Tianjin 300354,China

Keywords:Distillation Four-product dividing wall column Vapor split Operability

ABSTRACT For separating some specific four component mixtures into four products,the four-product dividing wall column(FPDWC)with two partition walls can provide the same utility consumption with the extended Petlyuk configuration,although with structure simplicity.However,the reluctance to implement this kind of four product dividing wall column industrially also consists in the two uncontrollable vaporsplits associated with it.The vapor split ratios are set at the design stage and might not be the optimal value for changed feed composition,thus minimum energy consumption could not be ensured.In the present work,a sequential iterative optimization approach was initially employed to determine the parameters of cost-effective FPDWC.Then the effect of maintaining the vapor split ratios at their nominal value on the energy penalty was investigated for the FPDWC with two partition walls,in case of feed composition disturbance.The result shows that no more than+2%above the optimal energy requirements could be ensured for 20%feed composition disturbances,which is encouraging for industrial implementation.

1.Introduction

Thermally coupled distillation column has proved to be energy efficient compared to a conventional distillation system for multicomponent mixtures[1–5].It is usually constructed as the dividing wall column(DWC)for practical implementation[6,7].Although more than 250 DWCs for three product separation have been in operation up to now[8],there are very few applications for the four product dividing wall column(FPDWC),especially for the FPDWC with multipartition walls.The main reason is the design complexity and operation difficulty associated with it[9,10].

For four product separation,the arrangement with multi-partition walls could be more energy-efficient than the configuration with just one partition wall—called Kaibel column as shown in Fig.1[11–14],however,the increased vapor and liquid split numbers associated with partition walls aggravate the uncertainty ofthis distillation system.For FPDWCs,there are two main aspects resulting in the operation uncertainty.On the one hand,the key parameter–vapor split ratio for DWC is decided at the design stage by optimally placing the dividing wall and cannot be manipulated in operation[15].It can be influenced by the flow resistance in the two sides of the partition walls and could shift from its optimal value.On the other hand,the vapor split ratio designed for the original feed composition could not be optimal if the feed composition changes.The situation was similar with the case discussed for a three product dividing wall column[16–18].

Preliminary operability analysis has been conducted for some specific FPDWCs.For the simplest configuration—Kaibel column,Ghadrdan Maryam et al.[19,20]pointed that fixing the vapor split ratio could result in energy penalty in the face of some feed composition disturbance.Dwivedi Deeptanshu et al.[21]regarded the vapor splitratio as a degree of freedom in operation and concluded that together with the adjustable liquid split full energy savings could be realized.They also investigated the dynamic behavior of the most complex configuration–extended Petlyuk column[22].In that ideal case,four decentralized control structures were proposed and all of the steady state variables including vapor split ratio were available for manipulation.

To our knowledge,previous research just concentrated on investigating the vapor splitratio's effect of the Kaibel column[23–26].Configurations with two partition walls in Fig.2 have not been extensively studied,denoted as A–C and B–D for representing the component split conducted in the prefractionator,respectively.For example,A–C configuration represents component A/C non-sharp split is conducted in the prefractionator for the ABCD component mixture with descending order of volatility.These configurations can provide almost the same utility consumption with the extended Petlyuk configuration for some specific four component mixtures,which has been validated in the previous work in terms of minimum vapor flow.However,its internal structure is dramatically simplified,with only two liquid and vapor splits.The two vapor split ratios were set at the optimal value by equaling the pressure drop in the two sides of the dividing walls and could not be manipulated in operation[27–29].In this way,optimal energy consumption might not be ensured in the face of feed composition disturbance.An important point is to calculate how much energy penalty may occur if the two vapor split ratios were kept at the original design value.

Fig.1.Configuration of FPDWC with one partition wall-Kaibel column.

The content of present work was outlined as follows:before investigating the steady behavior of the FPDWC with two partition walls,a sequential procedure was proposed to optimal design of the column based on rigorous simulation.Then the effect of maintaining the vapor split ratio at its nominal value on the energy penalty was investigated for FPDWC with two partition walls,in case of feed composition disturbance.Finally,the sensitivity of reboiler duty to each vapor split ratio was also analyzed and minimumvapor flow across column section was employed to interpret the result.

2.Optimal Design of FPDWC With Two Partition Walls

A number of variables for the B–D and A–C arrangement should be determined.The structural variables include stage number in the prefractionator,middle column,and main column(NT1,NT2,NT3);feed stage location in the prefractionator(NF)and two side stream positions in the main column(NS1,NS2);the liquid split positions(NL1,NL2);and the vapor split positions(NV1,NV2).The operating variables include the two vapor split ratios(rv1,rv2)and two liquid split ratios(rl1,rl2);the reflux ratio(R)and reboiler duty(QR)of the column;and flowrate of two side streams(FS1,FS2).For a given structure of the FPDWC,(R,QR,FS1,FS2)is used to satisfy four product specifications.The leftoperating variables(rv1,rv2,rl1,rl2)could be implemented to conduct optimization.

As equentialiterative approach was used to optimize the structure of FPDWC.The reboiler duty increases with decreasing stage numbers in column sections.Initially,the stage numbers in each column section were set at approximately in finite values(N＞4Nmin).Then the number of stages in the column section gradually decreased until the reboiler duty increases significantly in order to satisfy the products' specification.For every given structure,the optimization tool embedded in the simulator was used to minimize the reboiler duty,employing(rv1,rv2,rl1,rl2)as independent variables.The optimization procedure is summarized as below.

Fixed the operating pressure of the FPDWC:

Step 1:Optimization of the main column:

1)Set the stage numbers at approximately in finite values(NT1,NT2,NT3).

2)Set the vapor and liquid split location of the main column:(NV1,NV2,NL1)for B–D arrangement,(NV1,NL1,NL2)for A–C arrangement,and side stream location(NS1,NS2).

3)Optimize the reboiler duty with vapor and liquid split ratios(rv1,rv2,rl1,rl2)as variables,which is the inner iterative loop for optimization.

4)Change vapor and liquid split location,side stream location for the main column,which constitutes the middle iterative loop.

5)Reduce the stage numbers in the main columns incrementally until the reboiler duty increases obviously.Changing NT3makes up the outer iterative loop.

Step 2:Optimization for the middle column:

1)Setthe stage number for the middle column at effectively infinite value(NT2).

2)Set the interlinking stage between the middle column and prefractionator:for B–D arrangement(NL2),for A–C arrangement(NV2).

3)For a given structure,change the vapor and liquid split ratios to minimize the reboiler duty(rv1,rv2,rl1,rl2),which was regarded as the inner iterative loop for optimizing the middle column.

4)Change the interlinking stage between the middle column and prefractionator(NL2or NV2),which constitute the middle iterative loop.

5)Reduce the stage numbers in the middle columns(NT2)gradually until the reboiler duty increases obviously and this step makes up the outer iterative loop.

Step 3:Optimization for the prefractionator:

1)Set the stage number in the prefractionator near infinite value(NT1).

2)Set the feed stage location to the prefractionator(NF).

Fig.2.Arrangement of FPDWC with two independent dividing partition walls:(a)B–D configuration and(b)A–C configuration.

3)Optimize the vapor and liquid split ratios(rv1,rv2,rl1,rl2)to minimize the reboiler duty,which is the inner iterative loop for optimization.

4)Change the feed location of the prefractionator NF,which is the middle iterative loop.

5)Decrease the stage number in the prefractionator NT3until the reboiler duty of the FPDWC increase obviously.

The sequential iterative optimization procedure is illustrated in Fig.3.

The mixture used for separation is aromatic hydrocarbon,and the feed composition,product specification and thermodynamic properties were displayed in Table 1.The condenser pressure of the FPDWC is set as 2.2×105Pa.Following the above-mentioned sequential optimization procedure,the optimal parameters for the A–C and B–D configurations were obtained,which were shown in Table 2.

3.Performance of FPDWC With Constant Vapor Split Ratio

3.1.Effect of vapor split ratio on energy consumption

The vapor split ratios in A–C and B–D arrangement could not be manipulated in operation.However,the vapor split designed for specific feed composition might not be optimal in the face of feed composition disturbance.Therefore,a vital point is to investigate how much energy penalty it may result in if we keep two vapor splits constant.+2%above the minimum energy is assumed still acceptable and could not lead to flooding in the column.For feed composition disturbance in a/b direction,we mean the composition of components A and B in the feed ranges from 0.2/0.3 to 0.3/0.2,which deviate from the nominal feed composition for 20%.For each combination of rv1and rv2,the liquid split ratios—rl1and rl2are adjusted to reach minimum energy consumption.As shown in Figs.4 and 5,it is possible to operate the two kinds of FPDWC within 2%energy penalty by fixing the vapor splits at constant value,for all of the three main feed composition disturbances including a/b,b/c and c/d directions.

Fig.3.Sequential optimization procedure for the FPDWC.

Table 1 Feed,product specification and physical properties for simulating the FPDWC

For the B–D configuration,the range of rv1in the+2%contour plot is narrower than rv2and they have an almost independent effect on the energy consumption.If feed composition changes along a/b direction,the optimal rv1remains at the original value while the rv2varies dramatically.However,that is not the situation for feed composition disturbance in b/c and c/d directions.

The range of rv1and rv2in the A–C configuration is similar and rv1and rv2show an interactive effect on the energy consumption,as a bottom of a ship.Along the direction that both rv1and rv2increase,the reboiler duty increases dramatically.Thus it is difficult to operate the FPDWC at this situation.On the contrary,the energy consumption would stay at the “bottom of the valley”.Changes in rv1and rv2in that direction could not lead to significant energy penalty.

Table 2 Optimal design parameters of A–C and B–D configurations of the FPDWC

3.2.Sensitivity of energy consumption to single vapor split

Another important point with respect to operability of FPDWC is to investigate the effect of fixing one vapor split on the sensitivity of energy consumption to another vapor split.For example,the relation between reboiler duty and rv1could be obtained while fixing rv2at nominal value 0.655 for the B–D arrangement,in case of three kinds of feed composition disturbance.The results for feed composition disturbance in a/b direction(i.e.feed composition changes from 0.2/0.3/0.25/0.25 to 0.3/0.2/0.25/0.25)were summarized in Fig.6.How much energy we may lose while keeping one vapor split constant could also be acquired.

If the feed composition changes from 0.25/0.25/0.25/0.25 to 0.3/0.2/0.25/0.25,the optimal value for rv1would vary from 0.37 to 0.39.However,the rv1has been fixed at0.37 previously,thus the relation between reboiler duty and rv2was different from the case that rv1was optimized at 0.39(the red line 0.30.2O represents the case with rv1optimized while the black line 0.30.2 shows the case with rv1as the original value).The effect of fixing rv1was not significant for feed composition changes in a/b direction,as shown in Fig.6(a).On the contrary, fixing rv2at original value 0.655 in the face of feed disturbance increases the energy consumption on average 0.9%and the geometrical property of two curves is similar.The corresponding result is shown in Fig.6(b).

3.3.Analysis based on minimum vapor flow diagram Vmin

The minimum vapor flow diagram(Vmin)constructed from Underwood equations[30]could provide an initial vapor split ratio for rigorous simulation.The relative volatility of the separation mixtures is[7.21,4.63,2.11,1],which is employed to calculate the optimal vapor split ratios.For example,in the face of feed composition disturbance in a/b direction,the optimal vapor split ratios obtained from the shortcut method are shown in Table 3.The changes in optimal vapor split ratios are no more than 1.2%for the B–D arrangement and 5.4%for the A–C arrangement,respectively.This validates that keeping vapor split ratios constant could not incur significant energy penalty.

4.Conclusions

Fig.4.Contours for+2%above the minimumenergy consumption in the face of various feed composition disturbances for B–D configuration:(a)a/b direction changes from 0.3/0.2 to 0.2/0.3,(b)b/c direction changes from 0.3/0.2 to 0.2/0.3,and(c)c/d direction changes from 0.3/0.2 to 0.2/0.3.

Fig.5.Contours for+2%above the minimum energy consumption in the face of various feed composition disturbances for A–C configuration:(a)a/b direction changes from 0.3/0.2 to 0.2/0.3,(b)b/c direction changes from 0.3/0.2 to 0.2/0.3,and(c)c/d direction changes from 0.3/0.2 to 0.2/0.3.

Fig.6.Effect of fixing one vapor spliton the sensitivity of reboiler duty vs another vapor split for B–D arrangement.(a)Reboiler duty versus r v2 by fixing r v1 for feed composition changes in a/b direction.(b)Reboiler duty versus r v1 by fixing r v2 for feed composition changes in a/b direction.

Table 3 Optimal vapor split ratios obtained from shortcut method in the face of feed composition disturbance in a/b direction

Two kinds of FPDWC,A–C and B–D configurations with two independent partition walls,were designed and optimized with a sequential interactive approach.In the face of expected feed composition changes,by adjusting the two liquid split ratios, fixing the vapor split ratios at originally optimized value could not result in significant energy penalty(within+2%).Moreover,constant rv1(rv2)has a minor effect on the sensitivity of energy consumption versus rv2(rv1).For the A–C configuration,rv1and rv2have an interactive effect on the energy requirement.If rv2decreases with the increase of rv1,the energy consumption could stay at near minimum energy consumption.Therefore,it provides the basis that designing and operating rv1and rv2should be along the above-mentioned direction.

The steady behavior above mentioned indicates the way for optimal operation of FPDWCs in the face of feed disturbance.To make the FPDWCs more flexible to handle feed fluctuation,an optimization control loop with liquid split ratios as manipulated variables should be added in the control structure,with the vapor split ratio fixed at the design value.In this way,the energy consumption could be maintained near the optimal value without employing the vapor split ratio control instrument.

Another important issue about FPDWCs with two partition walls is investigating the effect of fixing the vapor split ratios on the products' purity,which could be conducted by a series of rigorous simulations,with the sum of products' purity as objective and liquid spit ratios as variables.This is our future work.

Nomenclature