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Investigation of the operability for four-product dividing wall column with two partition walls
Accepted Manuscript Investigation of the operability for four-product dividing wall column with two partition walls
Xiaolong Ge, Botong Liu, Botan Liu, Hongxing Wang, Xigang Yuan PII: DOI: Reference:
S1004-9541(17)31077-7 doi:10.1016/j.cjche.2017.10.029 CJCHE 983
To appear in: Received date: Accepted date:
26 August 2017 12 October 2017
Please cite this article as: Xiaolong Ge, Botong Liu, Botan Liu, Hongxing Wang, Xigang Yuan , Investigation of the operability for four-product dividing wall column with two partition walls. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Cjche(2017), doi:10.1016/j.cjche.2017.10.029
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ACCEPTED MANUSCRIPT Supported by Open Research Project of State Key Laboratory of Chemical Engineering (SKL-ChE-16B06) and Yangtze Scholars and Innovative Research Team in Chinese University (IRT-17R81).
Special Issue for 2017PSE Investigation of the operability for four-product dividing wall column with two partition walls
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Xiaolong Ge1,* [email protected], Botong Liu2, Botan Liu1, Hongxing Wang1, Xigang Yuan2,* [email protected] 1
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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
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State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300354, China
*
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Corresponding authors.
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Abstract
For separating some specific four components mixture into four products, the four-product dividing
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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 the
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implement this kind of four products dividing wall column industrially also consists in the two uncontrollable vapor splits associated with it. The vapor split ratios are set at the design stage and might be not the optimal value for changed feed composition, thus minimum energy consumption
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could not be ensured. In the present work, sequential iterative optimization approach was initially employed to determine the parameters of cost-effective FPDWC. Then the effect of maintaining the
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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.
Keywords distillation, four-product dividing wall column, vapor split, operability
1 INTRODUCTION
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ACCEPTED MANUSCRIPT Thermally coupled distillation column has proved to be energy efficient compared to 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 products separation have been in operation up to now,[8] there are very few applications for the four products dividing wall column (FPDWC), especially for the FPDWC with multi-partition walls. The main reason is
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the design complexity and operation difficulty associated with it.[9, 10]
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For four products separation, the arrangement with multi-partition walls could be more energy-efficient than the configuration with just one partition wall-called Kaibel
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column as shown in Figure 1,[11-14] however, the increased vapor and liquid splits
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number associated with partition walls aggravate the uncertainty of this distillation system. For FPDWCs, there are two main aspects resulting in the operation uncertainty.
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On 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
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partition walls and could shift from its optimal value. On the other hand, the vapor split
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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 three
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products dividing wall column.[16-18] Preliminary operability analysis has been conducted for some specific FPDWCs.
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For most simplest configuration-Kaibel column, Ghadrdan Maryam et al[19, 20] pointed that fixing the vapor split ratio could result in energy penalty in face of some feed composition disturbance. Dwivedi Deeptanshu et al[21] regarded the vapor split ratio 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 2
ACCEPTED MANUSCRIPT split ratio’s effect of Kaibel column.[23-26] Configurations with two partition walls in Figure 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 components mixture with descending order of volatility. These configurations can provide almost the same utility consumption with the
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extended Petlyuk configuration for some specific four components mixture, which has
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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
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two vapor split ratios were set at the optimal value by equaling the pressure drop in the
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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 face of feed composition
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disturbance. An important point is to calculate how much energy penalty may occur if
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Liquid spilt ratio rl
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the two vapor split ratios were kept at the original design value.
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Feed
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Liquid spilt ratio rl
S1 Feed
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S2
S2 Vapor ratio rv
Vapor spilt Ratio rv
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spilt B
B
Figure 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 3
ACCEPTED MANUSCRIPT 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 minimum vapor flow across column section was employed to interpret
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the result.
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Figure 2 Arrangement of FPDWC with two independent dividing partition walls: (a) B-D configuration (b) A-C configuration
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, 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); the vapor split positions (NV1, NV2). The operating variables include the two 4
ACCEPTED MANUSCRIPT vapor split ratios (rv1, rv2) and two liquid split ratios (rl1, rl2); the reflux ratio (R) and reboiler duty (QR) of the column; flowrate of two side streams(FS1, FS2). For given structure of the FPDWC, (R, QR, FS1, FS2) is used to satisfy four product specifications. The left operating variables (rv1, rv2, rl1, rl2) could be implemented to conduct optimization. A sequential iterative approach was used to optimize the structure of FPDWC.
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The reboiler duty increase with decreasing the stage numbers in column sections.
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Initially, the stage numbers in each column section were set at approximately infinite values (N>4Nmin). Then the number of stages in the column section gradually
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decreased until the reboiler duty increase significantly in order to satisfy the products’
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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
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independent variables. The optimization procedure is as summarized as below. Fixed the operating pressure of the FPDWC: Step 1: Optimization of the main column:
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1) Set the stage numbers at approximately infinite values (NT1, NT2, NT3).
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2) Set the vapor and liquid split location of main column: (NV1, NV2, NL1) for B-D arrangement, (NV1, NL1, NL2) for A-C arrangement, and side streams
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location (NS1, NS2).
3) Optimize the reboiler duty with vapor and liquid split ratios (rv1, rv2, rl1, rl2)
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as variables, which is the inner iterative loop for optimization.
4) Change vapor and liquid split location, side stream location for main column, which constitutes the middle iterative loop.
5) Reduce the stage numbers in the main columns incrementally until the reboiler duty increase obviously. Changing NT3 makes up the outer iterative loop. Step 2: Optimization for the middle column: 1) Set the stage number for the middle column at effectively infinite value (NT2). 5
ACCEPTED MANUSCRIPT 2) Set the interlinking stage between the middle column and prefractionator: for B-D arrangement (NL2), for A-C arrangement (NV2). 3) For 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
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prefractionator (NL2 or NV2), which constitute the middle iterative loop.
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5) Reduce the stage numbers in the middle columns (NT2) gradually until the
loop.
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Step 3: Optimization for the prefrationator:
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reboiler duty increase obviously and this step make up the outer iterative
1) Set the stage number in the prefractionator near infinite value (NT1).
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2) Set the feed stage location to the prefrationator (NF). 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.
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iterative loop.
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4) Change the feed location of the prefrationator NF, which is the middle
5) Decrease the stage number in the prefratinator NT3 until the reboiler duty
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of the FPDWC increase obviously.
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The sequential iterative optimization procedure is illustrated in Figure 3.
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Give NT3
Give NT1
Set NL2 or NV2
Set NF
Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
Set (NV1, NV2, NL1) or (NV1, NL1, NL2), NS1, NS2
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Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
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Give NT2
Calculate QR
No
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Yes
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Is QR minimal with NT3 fixed?
No
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Calculate QR
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Is QR increase significant?
Yes
Get optimal NT3, (NV1, NV2, NL1) or (NV1, NL1, NL2), NS1, NS2
Calculate QR
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Is QR minimal with NT2 fixed?
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No
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Calculate QR
Is QR minimal with NT1 fixed?
Yes Yes
Calculate QR
Calculate QR
No Is QR increase significant?
Yes
Get optimal NT2, NL2 or NV2
No Is QR increase significant?
Yes
Get optimal NT1, NF
Figure 3 Sequential optimization procedure for the FPDWC
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ACCEPTED MANUSCRIPT The mixture used for separation is aromatic hydrocarbon, and the feed composition, product specification and thermodynamic properties was displayed in Table 1. The condenser pressure of the FPDWC is set as 2.2bar. Following the above-mentioned sequential optimization procedure, the optimal parameters for the A-C and B-D configuration was obtained, which was shown in Table 2.
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31730 kg/hr 3.01bar 37℃ 0.25 0.25 0.25 0.25
2-Methylpentane:96% Benzene:96% Toluene:96% P-xylene:96%
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Feed property Feed Mass flow rate Feed Pressure Feed Temperature Mass fraction 2-Methylpentane Benzene Toluene P-xylene Product specification(mass fraction) Distillate Side stream-1 Side stream-2 Bottom Physical properties Peng–Robinson equation of state
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Table 1 feed, product specification and physical properties for simulating the FPDWC
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Table 2 optimal design parameters of A-C and B-D configuration of the FPDWC
Configuration
Parameters
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NT1 NT2 NT3 NS1 NS2 NV1 NV2 NL1 NL2 NF rv1 rv2 rl1 rl2 R QR(kW) FS1(kg/hr) FS2(kg/hr)
A-C
B-D
22 20 85 32 55 70 14 17 43 10 0.76 0.73 0.15 0.23 4.36 5275 7896.8 7633.8
22 20 80 32 51 39 67 24 8 10 0.37 0.655 0.499 0.314 4.40 5284 7704.6 7805.1
3 Performance of FPDWC with constant vapor split ratio 8
ACCEPTED MANUSCRIPT 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 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
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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
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mean the composition of components A and B in the feed ranges from 0.2/0.3 to 0.3/0.2,
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which deviate from the nominal feed composition for 20%. For each combination of rv1 and rv2, the liquid split ratios-rl1 and rl2 are adjusted to reach minimum energy
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consumption. As shown in Figure 4 and Figure 5, it is possible to operate the two kinds of FPDWC within 2% energy penalty by fixing the vapor splits at constant value, for
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all of the three main feed composition disturbances including a/b, b/c and c/d direction.
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(b) 0.20.3 0.250.25 0.30.2
0.70 0.68 0.66 0.64 0.62
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rv1
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(c) Figure 4 contours for +2% above the minimum energy consumption in face of various feed composition disturbance 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, (c) c/d direction changes from 0.3/0.2 to 0.2/0.3
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0.84 0.78
0.20.3 0.250.25 0.30.2
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0.20.3 0.250.25 0.30.2
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(c)
Figure 5 contours for +2% above the minimum energy consumption in face of various feed composition disturbance for A-C configuration: (a) a/b direction changes from 0.3/0.2 to 0.2/0.3,
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(b) b/c direction changes from 0.3/0.2 to 0.2/0.3, (c) c/d direction changes from 0.3/0.2 to 0.2/0.3
For B-D configuration, the range of rv1 in the +2% contour plot is narrower than rv2 and they have almost independent effect on the energy consumption. If feed
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composition changes along a/b direction, the optimal rv1 remains at the original value
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while the rv2 varies dramatically. However, that is not the situation for feed composition disturbance in b/c and c/d directions. The range of rv1 and rv2 in the A-C configuration is similar and rv1, rv2 show
interactive effect on the energy consumption, as a bottom of a ship. Along the direction that both rv1 and rv2 increase, the reboiler duty increases dramatically. Thus it is difficult to operate the FPDWC at this situation. In contrary, the energy consumption would stay at the “bottom of the valley”. Changes in rv1 and rv2 in that direction could not lead to significant energy penalty.
3.2 Sensitivity of energy consumption to single vapor split 10
ACCEPTED MANUSCRIPT 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 rv1 could be obtained while fixing rv2 at nominal value 0.655 for 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)
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was summarized in Figure 6. How much energy we may lose while keeping one vapor
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split constant could also be acquired.
0.250.25 0.30.2O 0.30.2 0.20.3O 0.20.3
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0.60 0.62 0.64 0.66 0.68 0.70 0.72 rv2
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(a) Reboiler duty versus rv2 by fixing rv1 for feed composition changes in a/b direction
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(b) Reboiler duty versus rv1 by fixing rv2 for feed composition changes in a/b direction Figure 6 Effect of fixing one vapor split on the sensitivity of reboiler duty vs another vapor split for B-D arrangement
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 rv1 would vary from 0.37 to 0.39. However, the rv1 has been fixed at 0.37 previously, thus the relation between reboiler duty and rv2 was different from the case that rv1 was optimized at 0.39 (the red line 0.30.2O represents the case with rv1
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ACCEPTED MANUSCRIPT optimized while the black line 0.30.2 shows the case with rv1 as the original value). The effect of fixing rv1 was not significant for feed composition changes in a/b direction, as shown in Figure 6(a). In contrary, fixing rv2 at original value 0.655 in face of feed disturbance increases the energy consumption in average 0.9% and the geometrical property of two curves is similar. The corresponding result is shown in Figure 6(b).
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3.3 Analysis based on minimum vapor flow diagram Vmin The minimum vapor flow diagram (Vmin) constructed from Underwood
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equations[30] could provide initial vapor split ratio for rigorous simulation. The
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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 face of feed composition
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disturbance in a/b direction, the optimal vapor split ratios obtained from the shortcut method is shown in Table 3. The changes in optimal vapor split ratios are no more than
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1.2% for B-D arrangement and 5.4% for A-C arrangement, respectively. This validates that keeping vapor split ratios constant could not incur significant energy penalty.
B-D configuration 0.25/0.25 0.3/0.2 0.169 0.171 0.488 0.491
0.2/0.3 0.168 0.486
0.25/0.25 0.645 0.765
A-C configuration 0.3/0.2 0.636 0.806
0.2/0.3 0.653 0.725
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rv1 rv2
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disturbance in a/b direction
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Table 3 optimal vapor split ratios obtained from shortcut method in face of feed composition
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4 Conclusions
Two kinds of FPDWC, A-C and B-D configuration with two independent partition
walls, were designed and optimized with sequential interactive approach. In 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 minor effect on the sensitivity of energy consumption versus rv2 (rv1). For A-C configuration, rv1 and rv2 have interactive effect on the energy requirement. If rv2 decreases with the increase of rv1, the energy
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ACCEPTED MANUSCRIPT consumption could stay at near minimum energy consumption. Therefore, it provides the basis that designing and operating rv1 and rv2 should be along above-mentioned direction. The steady behavior above mentioned indicates the way for optimal operation of FPDWCs in face of feed disturbance. To make the FPDWCs more flexible to handle feed fluctuation, an optimization control loop with liquid split ratios as manipulated
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variables should be added in the control structure, with vapor split ratio fixed at design
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value. In this way, the energy consumption could be maintained near the optimal value without employing the vapor split ratio control instrument.
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Another important issue about FPDWCs with two partition walls is investigate the
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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
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liquid spit ratios as variables. This is our future work.
NOMENCLATURE
mass flow rate of side stream, kg-·hr-1
N
stage number in each column section
QR
reboiler duty, kW
R
reflux ratio
rv
vapor split ratio
rl
liquid split ratio
Vmin
minimum vapor flow diagram
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coupling links to liquid-only transfer streams: An enumeration method for new FTC dividing wall columns, AIChE J. 62 (4) (2016) 1200-1211. [30] Halvorsen, Ivar J.,Skogestad, Sigurd, Minimum Energy Consumption in Multicomponent Distillation. 3. More Than Three Products and Generalized Petlyuk Arrangements, Ind. Eng. Chem. Res. 42 (3) (2003) 616-629.
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Graphical abstract
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Xiaolong Ge, Botong Liu, Botan Liu, Hongxing Wang, Xigang Yuan PII: DOI: Reference:
S1004-9541(17)31077-7 doi:10.1016/j.cjche.2017.10.029 CJCHE 983
To appear in: Received date: Accepted date:
26 August 2017 12 October 2017
Please cite this article as: Xiaolong Ge, Botong Liu, Botan Liu, Hongxing Wang, Xigang Yuan , Investigation of the operability for four-product dividing wall column with two partition walls. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Cjche(2017), doi:10.1016/j.cjche.2017.10.029
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Supported by Open Research Project of State Key Laboratory of Chemical Engineering (SKL-ChE-16B06) and Yangtze Scholars and Innovative Research Team in Chinese University (IRT-17R81).
Special Issue for 2017PSE Investigation of the operability for four-product dividing wall column with two partition walls
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Xiaolong Ge1,* [email protected], Botong Liu2, Botan Liu1, Hongxing Wang1, Xigang Yuan2,* [email protected] 1
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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
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State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300354, China
*
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Corresponding authors.
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Abstract
For separating some specific four components mixture into four products, the four-product dividing
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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 the
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implement this kind of four products dividing wall column industrially also consists in the two uncontrollable vapor splits associated with it. The vapor split ratios are set at the design stage and might be not the optimal value for changed feed composition, thus minimum energy consumption
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could not be ensured. In the present work, sequential iterative optimization approach was initially employed to determine the parameters of cost-effective FPDWC. Then the effect of maintaining the
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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.
Keywords distillation, four-product dividing wall column, vapor split, operability
1 INTRODUCTION
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ACCEPTED MANUSCRIPT Thermally coupled distillation column has proved to be energy efficient compared to 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 products separation have been in operation up to now,[8] there are very few applications for the four products dividing wall column (FPDWC), especially for the FPDWC with multi-partition walls. The main reason is
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the design complexity and operation difficulty associated with it.[9, 10]
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For four products separation, the arrangement with multi-partition walls could be more energy-efficient than the configuration with just one partition wall-called Kaibel
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column as shown in Figure 1,[11-14] however, the increased vapor and liquid splits
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number associated with partition walls aggravate the uncertainty of this distillation system. For FPDWCs, there are two main aspects resulting in the operation uncertainty.
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On 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
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partition walls and could shift from its optimal value. On the other hand, the vapor split
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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 three
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products dividing wall column.[16-18] Preliminary operability analysis has been conducted for some specific FPDWCs.
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For most simplest configuration-Kaibel column, Ghadrdan Maryam et al[19, 20] pointed that fixing the vapor split ratio could result in energy penalty in face of some feed composition disturbance. Dwivedi Deeptanshu et al[21] regarded the vapor split ratio 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 2
ACCEPTED MANUSCRIPT split ratio’s effect of Kaibel column.[23-26] Configurations with two partition walls in Figure 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 components mixture with descending order of volatility. These configurations can provide almost the same utility consumption with the
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extended Petlyuk configuration for some specific four components mixture, which has
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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
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two vapor split ratios were set at the optimal value by equaling the pressure drop in the
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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 face of feed composition
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disturbance. An important point is to calculate how much energy penalty may occur if
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Liquid spilt ratio rl
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the two vapor split ratios were kept at the original design value.
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Feed
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Liquid spilt ratio rl
S1 Feed
S1
S2
S2 Vapor ratio rv
Vapor spilt Ratio rv
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spilt B
B
Figure 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 3
ACCEPTED MANUSCRIPT 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 minimum vapor flow across column section was employed to interpret
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the result.
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Figure 2 Arrangement of FPDWC with two independent dividing partition walls: (a) B-D configuration (b) A-C configuration
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, 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); the vapor split positions (NV1, NV2). The operating variables include the two 4
ACCEPTED MANUSCRIPT vapor split ratios (rv1, rv2) and two liquid split ratios (rl1, rl2); the reflux ratio (R) and reboiler duty (QR) of the column; flowrate of two side streams(FS1, FS2). For given structure of the FPDWC, (R, QR, FS1, FS2) is used to satisfy four product specifications. The left operating variables (rv1, rv2, rl1, rl2) could be implemented to conduct optimization. A sequential iterative approach was used to optimize the structure of FPDWC.
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The reboiler duty increase with decreasing the stage numbers in column sections.
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Initially, the stage numbers in each column section were set at approximately infinite values (N>4Nmin). Then the number of stages in the column section gradually
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decreased until the reboiler duty increase significantly in order to satisfy the products’
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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
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independent variables. The optimization procedure is as summarized as below. Fixed the operating pressure of the FPDWC: Step 1: Optimization of the main column:
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1) Set the stage numbers at approximately infinite values (NT1, NT2, NT3).
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2) Set the vapor and liquid split location of main column: (NV1, NV2, NL1) for B-D arrangement, (NV1, NL1, NL2) for A-C arrangement, and side streams
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location (NS1, NS2).
3) Optimize the reboiler duty with vapor and liquid split ratios (rv1, rv2, rl1, rl2)
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as variables, which is the inner iterative loop for optimization.
4) Change vapor and liquid split location, side stream location for main column, which constitutes the middle iterative loop.
5) Reduce the stage numbers in the main columns incrementally until the reboiler duty increase obviously. Changing NT3 makes up the outer iterative loop. Step 2: Optimization for the middle column: 1) Set the stage number for the middle column at effectively infinite value (NT2). 5
ACCEPTED MANUSCRIPT 2) Set the interlinking stage between the middle column and prefractionator: for B-D arrangement (NL2), for A-C arrangement (NV2). 3) For 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
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prefractionator (NL2 or NV2), which constitute the middle iterative loop.
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5) Reduce the stage numbers in the middle columns (NT2) gradually until the
loop.
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Step 3: Optimization for the prefrationator:
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reboiler duty increase obviously and this step make up the outer iterative
1) Set the stage number in the prefractionator near infinite value (NT1).
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2) Set the feed stage location to the prefrationator (NF). 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.
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iterative loop.
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4) Change the feed location of the prefrationator NF, which is the middle
5) Decrease the stage number in the prefratinator NT3 until the reboiler duty
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of the FPDWC increase obviously.
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The sequential iterative optimization procedure is illustrated in Figure 3.
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Give NT3
Give NT1
Set NL2 or NV2
Set NF
Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
Set (NV1, NV2, NL1) or (NV1, NL1, NL2), NS1, NS2
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Vary R, QR, FS1, FS2 to meet the product specification, use rv1, rv2, rl1, rl2 to minimize QR
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Give NT2
Calculate QR
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Yes
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Is QR minimal with NT3 fixed?
No
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Calculate QR
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Is QR increase significant?
Yes
Get optimal NT3, (NV1, NV2, NL1) or (NV1, NL1, NL2), NS1, NS2
Calculate QR
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Is QR minimal with NT2 fixed?
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No
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Calculate QR
Is QR minimal with NT1 fixed?
Yes Yes
Calculate QR
Calculate QR
No Is QR increase significant?
Yes
Get optimal NT2, NL2 or NV2
No Is QR increase significant?
Yes
Get optimal NT1, NF
Figure 3 Sequential optimization procedure for the FPDWC
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ACCEPTED MANUSCRIPT The mixture used for separation is aromatic hydrocarbon, and the feed composition, product specification and thermodynamic properties was displayed in Table 1. The condenser pressure of the FPDWC is set as 2.2bar. Following the above-mentioned sequential optimization procedure, the optimal parameters for the A-C and B-D configuration was obtained, which was shown in Table 2.
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31730 kg/hr 3.01bar 37℃ 0.25 0.25 0.25 0.25
2-Methylpentane:96% Benzene:96% Toluene:96% P-xylene:96%
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Feed property Feed Mass flow rate Feed Pressure Feed Temperature Mass fraction 2-Methylpentane Benzene Toluene P-xylene Product specification(mass fraction) Distillate Side stream-1 Side stream-2 Bottom Physical properties Peng–Robinson equation of state
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Table 1 feed, product specification and physical properties for simulating the FPDWC
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Table 2 optimal design parameters of A-C and B-D configuration of the FPDWC
Configuration
Parameters
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NT1 NT2 NT3 NS1 NS2 NV1 NV2 NL1 NL2 NF rv1 rv2 rl1 rl2 R QR(kW) FS1(kg/hr) FS2(kg/hr)
A-C
B-D
22 20 85 32 55 70 14 17 43 10 0.76 0.73 0.15 0.23 4.36 5275 7896.8 7633.8
22 20 80 32 51 39 67 24 8 10 0.37 0.655 0.499 0.314 4.40 5284 7704.6 7805.1
3 Performance of FPDWC with constant vapor split ratio 8
ACCEPTED MANUSCRIPT 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 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
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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
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mean the composition of components A and B in the feed ranges from 0.2/0.3 to 0.3/0.2,
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which deviate from the nominal feed composition for 20%. For each combination of rv1 and rv2, the liquid split ratios-rl1 and rl2 are adjusted to reach minimum energy
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consumption. As shown in Figure 4 and Figure 5, it is possible to operate the two kinds of FPDWC within 2% energy penalty by fixing the vapor splits at constant value, for
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all of the three main feed composition disturbances including a/b, b/c and c/d direction.
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0.20.3 0.250.25 0.30.2
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0.64 0.62 0.60 0.2
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0.20.3 0.250.25 0.30.2
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0.4 rv1
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0.66 0.64 0.2
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0.3
rv2
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0.4 rv1
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(b) 0.20.3 0.250.25 0.30.2
0.70 0.68 0.66 0.64 0.62
0.2
0.3
rv1
0.4
0.5
(c) Figure 4 contours for +2% above the minimum energy consumption in face of various feed composition disturbance 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, (c) c/d direction changes from 0.3/0.2 to 0.2/0.3
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0.84 0.78
0.20.3 0.250.25 0.30.2
0.84
0.20.3 0.250.25 0.30.2
0.78
0.72
rv2
rv2
0.72
0.66
0.66
0.60
0.60 0.72
0.78 rv1
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rv1
(a)
(b)
0.20.3 0.250.25 0.30.2
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(c)
Figure 5 contours for +2% above the minimum energy consumption in face of various feed composition disturbance for A-C configuration: (a) a/b direction changes from 0.3/0.2 to 0.2/0.3,
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(b) b/c direction changes from 0.3/0.2 to 0.2/0.3, (c) c/d direction changes from 0.3/0.2 to 0.2/0.3
For B-D configuration, the range of rv1 in the +2% contour plot is narrower than rv2 and they have almost independent effect on the energy consumption. If feed
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composition changes along a/b direction, the optimal rv1 remains at the original value
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while the rv2 varies dramatically. However, that is not the situation for feed composition disturbance in b/c and c/d directions. The range of rv1 and rv2 in the A-C configuration is similar and rv1, rv2 show
interactive effect on the energy consumption, as a bottom of a ship. Along the direction that both rv1 and rv2 increase, the reboiler duty increases dramatically. Thus it is difficult to operate the FPDWC at this situation. In contrary, the energy consumption would stay at the “bottom of the valley”. Changes in rv1 and rv2 in that direction could not lead to significant energy penalty.
3.2 Sensitivity of energy consumption to single vapor split 10
ACCEPTED MANUSCRIPT 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 rv1 could be obtained while fixing rv2 at nominal value 0.655 for 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)
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was summarized in Figure 6. How much energy we may lose while keeping one vapor
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split constant could also be acquired.
0.250.25 0.30.2O 0.30.2 0.20.3O 0.20.3
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0.60 0.62 0.64 0.66 0.68 0.70 0.72 rv2
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(a) Reboiler duty versus rv2 by fixing rv1 for feed composition changes in a/b direction
0.20.3 0.20.3O 0.250.25 0.30.2O 0.30.2
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QB, KW
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5300 0.3
0.4 rv1
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0.6
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(b) Reboiler duty versus rv1 by fixing rv2 for feed composition changes in a/b direction Figure 6 Effect of fixing one vapor split on the sensitivity of reboiler duty vs another vapor split for B-D arrangement
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 rv1 would vary from 0.37 to 0.39. However, the rv1 has been fixed at 0.37 previously, thus the relation between reboiler duty and rv2 was different from the case that rv1 was optimized at 0.39 (the red line 0.30.2O represents the case with rv1
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ACCEPTED MANUSCRIPT optimized while the black line 0.30.2 shows the case with rv1 as the original value). The effect of fixing rv1 was not significant for feed composition changes in a/b direction, as shown in Figure 6(a). In contrary, fixing rv2 at original value 0.655 in face of feed disturbance increases the energy consumption in average 0.9% and the geometrical property of two curves is similar. The corresponding result is shown in Figure 6(b).
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3.3 Analysis based on minimum vapor flow diagram Vmin The minimum vapor flow diagram (Vmin) constructed from Underwood
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equations[30] could provide initial vapor split ratio for rigorous simulation. The
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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 face of feed composition
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disturbance in a/b direction, the optimal vapor split ratios obtained from the shortcut method is shown in Table 3. The changes in optimal vapor split ratios are no more than
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1.2% for B-D arrangement and 5.4% for A-C arrangement, respectively. This validates that keeping vapor split ratios constant could not incur significant energy penalty.
B-D configuration 0.25/0.25 0.3/0.2 0.169 0.171 0.488 0.491
0.2/0.3 0.168 0.486
0.25/0.25 0.645 0.765
A-C configuration 0.3/0.2 0.636 0.806
0.2/0.3 0.653 0.725
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rv1 rv2
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disturbance in a/b direction
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Table 3 optimal vapor split ratios obtained from shortcut method in face of feed composition
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4 Conclusions
Two kinds of FPDWC, A-C and B-D configuration with two independent partition
walls, were designed and optimized with sequential interactive approach. In 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 minor effect on the sensitivity of energy consumption versus rv2 (rv1). For A-C configuration, rv1 and rv2 have interactive effect on the energy requirement. If rv2 decreases with the increase of rv1, the energy
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ACCEPTED MANUSCRIPT consumption could stay at near minimum energy consumption. Therefore, it provides the basis that designing and operating rv1 and rv2 should be along above-mentioned direction. The steady behavior above mentioned indicates the way for optimal operation of FPDWCs in face of feed disturbance. To make the FPDWCs more flexible to handle feed fluctuation, an optimization control loop with liquid split ratios as manipulated
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variables should be added in the control structure, with vapor split ratio fixed at design
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value. In this way, the energy consumption could be maintained near the optimal value without employing the vapor split ratio control instrument.
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Another important issue about FPDWCs with two partition walls is investigate the
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liquid spit ratios as variables. This is our future work.
NOMENCLATURE
mass flow rate of side stream, kg-·hr-1
N
stage number in each column section
QR
reboiler duty, kW
R
reflux ratio
rv
vapor split ratio
rl
liquid split ratio
Vmin
minimum vapor flow diagram
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coupling links to liquid-only transfer streams: An enumeration method for new FTC dividing wall columns, AIChE J. 62 (4) (2016) 1200-1211. [30] Halvorsen, Ivar J.,Skogestad, Sigurd, Minimum Energy Consumption in Multicomponent Distillation. 3. More Than Three Products and Generalized Petlyuk Arrangements, Ind. Eng. Chem. Res. 42 (3) (2003) 616-629.
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Graphical abstract
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