Simulation Optimization and Experimental Study of Cross-Wall Adiabatic Dividing Wall Column Used to Separate Hexane-Heptane-Octane System

Hu Yuqi; Fang Jing; Li Chunli

(School of Chemical Engineering and Technology, Hebei University of Technology, Tianjin 300130)

Simulation Optimization and Experimental Study of Cross-Wall Adiabatic Dividing Wall Column Used to Separate Hexane-Heptane-Octane System

Hu Yuqi; Fang Jing; Li Chunli

(School of Chemical Engineering and Technology, Hebei University of Technology, Tianjin 300130)

Through separation of the hexane-heptane–octane system in a cross-wall adiabatic dividing wall column, the effects of feed position, side-draw position, liquid split ratio, vapor split ratio and their interactions on the energy consumption were analyzed by Aspen Plus under the constant product purity, and the response surface model for the energy consumption was regressed. Based on the restriction on the optimal operating zone, the comparison of different combinations of surrogate models and optimization methods showed that, the combination of the Kriging model and multi-island genetic algorithm (Kriging-MIGA) had better prediction ability than the combination of the response surface model and partial derivative method (RSM-PD), and RSM-PD had better optimization effect than Kriging-MIGA. With a self-made cross-wall adiabatic dividing wall column, the temperature at measuring points and the energy consumption were measured during experiments, the comparison between measured values and simulated ones demonstrated that the optimized values of variables searched by RSM-PD and Kriging-MIGA could be both used as the optimum technological conditions since the experimental reliability was ensured, with the optimum technological conditions shown below: The feed position is 6, the side-draw position is 7, the combinations of liquid split ratio and vapor split ratio are [0.14, 0.5] and [0.16, 0.52], respectively. RSM-PD and Kriging-MIGA can provide the appropriate optimization methods for the dividing wall column.

dividing wall column; simulation; optimization; experimental validation

1 Introduction

As one of the major representatives of the fully thermally coupled column, the dividing wall column[1](DWC, Figure 1) is a typical device used to reduce the energy consumption of the distillation system. Compared with the conventional sequences columns, DWC can perform the complete separation task in a single shell[2-3], avoid the remixing effect and the irreversibility that the effect may bring about[4], and save the energy as well as the equipment investment[5].

From the perspective of heat transfer process across the dividing wall (namely the location between the prefractionator and the side-draw section), DWC can be classified into three types, viz.: the cross-wall adiabatic column, the cross-wall partially adiabatic column and the crosswall diabatic column. Different types of DWC have different impacts on the energy consumption and the operating points[6]. It is generally accepted by the researchers that many factors can influence the energy consumption of the cross-wall adiabatic dividing wall column, including the liquid split ratio, the vapor split ratio, the feed position, the side-draw position, the reflux ratio, the flowrate of the side-draw product and the bottom product, and the product purity. Recently, the analyses of the single factors mentioned above have been studied more carefully by simulations or experiments[7-14]. However, there is little research regarding the effects of multi-factors interactions on the energy consumption and the effects of different combinations of surrogate models and optimization methods on the optimum technological conditions.

Figure 1 Dividing wall column1—Public rectifying section; 2—Prefractionator; 3—Side-draw section; 4—Public stripping section

In this paper during separation of an industrial paraffin mixture composed of n-hexane, n-heptane and n-octane, the influence of the single factors and multi-factors interactions upon the energy consumption of the cross-wall adiabatic dividing wall column was investigated, and the response surface model for the energy consumption was regressed. Based on the restrictions on the optimal operating zone, the combinations of the model and the optimization method, which were most suitable for searching the optimum technological conditions, were screened by simulation analysis and tested by experiments.

2 Model Simulation and Optimization

Since the constant product purity is the prerequisite condition of the comparison in the energy consumption, three adjusting variables are needed to ensure the purity of distillate, side-draw and bottom products. Abdul Mutalib, et al.[7]used the relative gain array to analyze the controllability, and they pointed out that controlling the reflux ratio, and the flow rate of the side-draw and the bottom stream for maintaining the product purity should be a better scheme. Based on their research, this section will design the simulation scheme of the rest of variables by applying the Central Composite Design, including the feed position (Nf), the side-draw position (Ns), the liquid split ratio (RL), and the vapor split ratio (RV) to simulate the effects of Nf, Ns, RL, RV and their interactions on the energy consumption (Q) which could function as the response factor in the four columns model (Figure 2, where the four columns model replaces the cross-wall adiabatic dividing wall column model in Aspen Plus simulation), and to regress the RSM model for the energy consumption according to the simulation results.

2.1 Model simulation analysis

When the response surface regression method is used to analyze the Aspen Plus simulation results, the statistical analysis results are summarized in Table 1. It can be seen from Table 1 that the Prob>F value of the model is less than 0.000 1, and the value of the determination coefficient is 0.999 2, which demonstrates that the model is extremely significant and it fully reflects the relationship between the variables, interactions and the response factor; the value of the signal-to-noise ratio is very high, which illustrates that this model can be used for prediction; the value of the variation coefficient is acceptable. It can be concluded from the above points that using this model to analyze the cross-wall adiabatic dividing wall column is feasible.

As shown in Table 1, the degree of significance on the energy consumption for single factor is as follows: C>A>D>B, and that for interaction of multi-factors is: AD>AB>BD>CD>BC>AC. After the non-significant factors AC and D2are rejected according to the definition of response surface, the final RSM model for the energy consumption of the cross-wall adiabatic dividing wall column is as follows:

Figure 2 Schematic diagram of four columns model1—Public rectifying section; 2—Prefractionator; 3—Side-draw section; 4—Public stripping section; 1+3+4—Main columns. L—Liquid flow rate; V—Vapor flow rate

Q=2 037.8-279.98Nf-160.91Ns+4 481.8RL-3 013.8RV-3.477 3Nf·Ns+523.95Nf·RV-69.194Ns·RL+254.24Ns·RV-9 770.2RL·RV+2.224 9Nf2+4.215 8Ns2+3 040.8RL2

Figure 3 shows the response surface diagrams of the multi-factors interactions. As shown in Figure 3(a) and Figure 3(b), when Nf and RL lie in a certain range, with the decrease of Ns, Q initially falls within a minimum value followed by a steep rise, which occurs because of the regulation showing that there is an initial rise to a maximum value followed by a fall in the content of n-heptane in the main column. When Nf is smaller, the paths of nhexane and n-heptane (path 2-1-6 in Figure 4(a)) in the prefractionator are compressed, which leads to the phenomenon making some n-octane species merge into these paths and the purity of side-draw product decreases, and in order to maintain a constant product purity, Q needs to be increased. When Nf is larger, some n-hexane species merge into the paths of n-heptane and n-octane (path 3-4-5 in Figure 4(b)), and Q also increases. Therefore, suitable Nf ensures higher separation degree between n-hexane and n-octane in the prefractionator along with a lower Q. When RL is smaller, the recovery of n-heptane at the top of the prefractionator (namely the ratio of net flow rate of n-heptane at the top of the prefractionator to that in the feed) is larger, which makes most of n-heptane species gather at the upper part of the main column, while the purity of distillate product decreases. When RL is larger, most of n-heptane species gather at the lower part of the main column and the purity of bottom product decreases. The decreasing product purity would result in the increase of Q. Consequently, suitable RL ensures higher separation efficiency at the upper part as well as at the lower part of the main column, leading to a lower Q. As shown in Figure 3(c) and Figure 3(d), Q achieves a lower value whenRL and RV, Nf and RV show the features of direct and inverse proportional changes respectively; the former is to guarantee the mutual matching of vapor and liquid load both in the prefractionator and in the side-draw section, and the latter is to ensure the clear paths of n-hexane and n-octane that are not occupied by each other, resulting in a higher separation degree between n-hexane and n-octane in the prefractionator. Figure 3(e) shows that Q decreases with the decrease in RV when Ns is larger, but the decrease of RV goes against the decrease of Q when Ns is smaller. Based on the analysis of response surface diagrams, some conclusions can be made as shown below: The coupling interactions of variables are strong, and the influence of these interactions on the energy consumption of the cross-wall adiabatic dividing wall column is rather complicated. Thus, it is necessary to screen the precise model for the energy consumption and find an appropriate optimization method for realizing the optimum technological conditions.

Table 1 Statistical analysis results

Figure 3 Response surface diagrams of the multi-factors interactions affecting the energy consumption

2.2 Optimization of technological conditions

2.2.1 RSM model optimization

When the partial derivative method (PD) is used to optimize the RSM model, the optimized values of variables are shown below: The feed position is 6, the side-draw position is 7, the combination of liquid and vapor split ratios is [0.14, 0.5], and the minimum response value, i. e.: the optimized value of the energy consumption of the cross-wall adiabatic dividing wall column, is 260.9 W. When the optimized values of variables mentioned above are used as the input conditions of Aspen Plus simulation, the simulated value of the energy consumption is 271.2 W.

2.2.2 Combinations of models and optimization methodsComparison of different combinations of models and optimization methods, in which the Kriging model[15]belongs to the surrogate model like the RSM model, and some optimization methods that are distinctively distinguished from PD in the optimization principle are being considered, including the sequential quadratic programming method (SQP), the downhill simplex method (DS) and the multi-island genetic algorithm (MIGA), as shown in Table 2, illustrate that the energy consumption deviation of optimized values and simulated ones in the combinations composed of the Kriging model and arbitrary optimization methods are smaller than that in RSM-PD. The combinations involving the Kriging model have excellent ability to predict the energy consumption. This occurs because of the precision differences between these two surrogate models. Compared with the RSM model fitted by quadratic polynomial, the Kriging model as the unbiased estimation model, which is provided for minimum estimation variance, has more precise local estimation capability with higher precision. Compared with other optimization methods in combination with the Kriging model, the energy consumption deviation in MIGA is smaller. This can be explained as follows: MIGA uses individual population to do the genetic operation, and searches for the optimization values from a large amount of new population by iterative method rather than by calculating the gradientand the derivative of the nonlinear equations; and these characteristics make a wide global searching range and can avoid the single direction searching.

Figure 4 Paths of n-hexane and n-octane in DWCNet flow rate of component: ωi=Vn·yi,n-Ln+1·xi,n+1(i=n-hexane, n-octne; x—mole fraction of liquid phase; y—mole fraction of vapor phase; n—stage)

Table 2 Comparison of different combinations of surrogate models and optimization methods

As shown in Table 2, in comparison with MIGA, the optimized value of energy consumption in PD is more ideal. The combination with PD has an excellent optimization effect. This is because PD can find the minimum point accurately, but owing to the genetic operation (crossover, migration, mutation, etc.) in MIGA, only the satisfactory solutions can be found in the region surrounding the minimum point.

2.2.3 Optimal operating zone

Although the advantages of RSM-PD and Kriging-MIGA are observed, the latter has better prediction ability than the former, while the former has better optimization effect than the latter, and there is little discrepancy in simulated values of energy consumption between these two combinations. This is because the values of optimized variables searched by these two combinations are all within the optimal operating zone of the cross-wall adiabatic dividing wall column as shown in Figure 5(a), which indicates that there is a point [RL, RV], known as the optimal combined point, where the minimum energy consumption appears, around which there is an area with gentle curves of the energy consumption (fluctuating within 1% as defined) that constrains the optimal operating zone (enclosed shadow in Figure 5(a)), whereas Figure 5(b) shows the twodimensional plane of this zone.

As shown in Figure 5(b), when Nf is 6 and Ns is 7, although RL and RV searched by RSM-PD are 12.50% and 3.85% less than that in Kriging-MIGA, respectively, these optimized variables are all within the optimal operating zone, resulting in little discrepancy of the energy consumption.

Adjusting the feed position (Nf=5) has little effect on the area of the optimal operating zone, which only makes this zone move to the left, resulting in an increase of the ratio of vapor to liquid split ratio for fulfilling the separation demand. The reason which causes the higher deviation between the optimized value and the simulated value of the energy consumption in Kriging-SQP is that the values of RL and RV optimized by SQP are beyond the optimal operating zone, so the optimized variables searched by Kriging-SQP do not satisfy the standard of the optimum technological conditions. Unlike the feed position, adjusting the side-draw position (Ns=8) makes the zone move to the upper right and brings on an increase of vapor and liquid split ratios. Since RL and RV optimized by DS are within that zone, the deviation between the optimized value and the simulated one in Kriging-DS is smaller than that in Kriging-SQP, but it is still slightly greater than that in Kriging-MIGA. As a result, by taking into account the restrictions on the optimal operating zone, the optimized values of variables searched by RSM-PD and Kriging-MIGA are selected as the optimum technological conditions (note①in Table 2), in which: the feed position is 6, the side-draw position is 7, and the combinations of liquid and vapor split ratios are [0.14, 0.5] and [0.16, 0.52], respectively.

Figure 5 Optimal operating zone●—Nf=6, Ns=7;▲—Nf=5, Ns=7; ■—Nf=6, Ns=8

3 Experimental Validation

By comparing the temperature at measuring points and the energy consumption obtained from the simulation with that measured during the experiments, the reliability of the optimum technological conditions searched byRSM-PD and Kriging-MIGA can be tested.

3.1 Experimental device

Figure 6 shows a self-made cross-wall adiabatic dividing wall column. The number of stages of every section in this self-made device has been calibrated by a carbon tetrachloride-benzene standard system operating under the total reflux ratio[16]. The conditions of every section in experiment are approximately similar to that used in the simulation. The parameters of the device and the experimental conditions are summarized in Table 3.

Figure 6 Schematic diagram of self-made cross-wall adiabatic dividing wall column1—Voltage stabilizer; 2—Voltage regulator; 3—Power analyzer; 4—Resistance wire; 5—3-necked flask; 6—Public stripping section; 7—Differential manometer; 8—Chip thermometric instruments; 9—Prefractionator; 10—Rotameter; 11—Liquid split ratio controller, reflux ratio controller; 12—Public rectifying section; 13—Upper tank; 14—Thermometric instrument of overhead; 15—Product collector; 16—Side-draw section; 17—Valve; 18—Thermometric instrument at bottom.

Table 3 Parameters of device and experiment

3.2 Experimental method

After Nf, Ns, RL and RV are adjusted by some methods presented in the comments (during the experiments, the method for adjusting Nf and Ns is used to replace the prefractionator and the side-draw section which have different Nf and Ns, while the method for fine adjusting RV is used to regulate the area of gasket interface in the flange used to connect the public stripping section with the prefractionator, and the method for monitoring RV is applied to observe the pressure difference between the prefractionator and the side-draw section.), the samples of distillate, side-draw and bottom products are sent to the gas chromatograph for analysis when the equilibrium state of the experiment lasts more than 20 min. (Figure 7(a)—7(b) shows the temperature profiles and its gradient in simulation. It can be seen that the larger gradients appear at the top and at the bottom of the prefractionator, and next to the feed and side-draw positions, which illustrates that there are large changes in composition at these stages. Thus the temperature measuring points are set at the positions mentioned above, and at the top and bottom of the side-draw section and their intermediate positions in the device. Fluctuation of temperature at all these points within 0.2 ℃ is denoted by the equilibrium state.) If the purity of distillate, side-draw and bottom products does not satisfy the demand presented in Table 3, the refluxratio, flow rate of side-draw and the flow at bottom should be regulated to establish a new equilibrium state. Otherwise, the data of the energy consumption are recorded by the power analyzer and the temperature data at the measuring points are obtained by the chip thermometric instruments.

3.3 Analysis and discussion of experimental results

Figure 8 shows the comparison of the simulated values and the measured ones in terms of the temperature and the energy consumption at all measuring points, when the technological conditions searched by RSM-PD and Kriging-MIGA are taken into account during the experiments. In these two combinations, the trends of changes in the measured temperature values are basically the same as those obtained from the simulation. The measured temperature values are lower than the simulated temperatures in the prefractionator, while there is a contrary circumstance in the side-draw section, which generally leads to the situation that during the experiment the driving force of temperature within the range of compartment, in which the stages above the feed position in the prefractionator should correspond to the stages in the side-draw section, is lower than that obtained during simulation. However, the relationship between the driving force of temperature in the corresponding lower part of the side-draw section and that obtained from simulation is contrary to the previous one. In general, compared with the simulation circumstances, the driving force of temperature in the experiment tends to increase, which tallies with the fact that the measured energy consumption is higher than the simulated value.

Figure 7 Temperature profiles and its gradient of the four columns model

Figure 8 Comparisons of simulated values and measured ones in temperature at measuring points and energy consumption■—Simulated values in prefractionator;●—Simulated values in side-draw section;—Measured values in prefractionator;▲—Measured values in side-draw section

Figure 9 Comparison of simulated values and measured ones in energy consumption based on changing RL, RV, Nf, Ns in RSM-PD

Figure 10 Comparisons of simulated values and measured ones in energy consumption based on changing RL, RV, Nf, and Ns in Kriging-MIGA

Using the technological conditions searched by RSMPD and Kriging-MIGA as the benchmarks respectively (expressed as 0%), the comparison of the simulated values and the measured ones, upon specifying RL±20%, RV±4%, Nf±3 and Ns±3 (as shown in Figure 9 and Figure 10), gives the hints that changing the values of the variables leads to the increase of the measured energyconsumption, which tallies with the variation regularity in simulation; the minimum value of measured energy consumption approximately appears at the benchmark, which accords with the outcome of simulation. As a result, RSM-PD and Kriging-MIGA both are used to search for the optimum technological conditions of the cross-wall adiabatic dividing wall column to achieve the experimental reliability.

4 Conclusions

Based on RSM model for the energy consumption of the cross-wall adiabatic dividing wall column, the degree of significance on the energy consumption for single factor, in an order from high to low, covers: the liquid split ratio, the feed position, the vapor split ratio, and the sidedraw position; and that related with interactions of multifactors, in an order from high to low, includes the feed position-vapor split ratio, the feed position-side draw position, the side draw position-vapor split ratio, the liquid split ratio-vapor split ratio, the side draw position-liquid split ratio, and the feed position-liquid split ratio.

After being screened by the restriction on the optimal operating zone and tested by the experiments in which the self-made cross-wall adiabatic dividing wall column is used, the optimized values of the variables searched by the combination of RSM model and partial derivative method (RSM-PD) and the combination of Kriging model and multi-island genetic algorithm (Kriging-MIGA) can be used as the optimum technological conditions, denoting that: the feed position is 6, the side-draw position is 7, and the combinations of liquid split ratio and vapor split ratio are [0.14,0.5] and [0.16,0.52], respectively. RSM-PD and Kriging-MIGA can provide the optimization methods for the cross-wall adiabatic dividing wall column.

Acknowledgements:The authors are pleased to acknowledge the financial support by the National Natural Science Foundation of China (21306036).

[1] Wright R O, Elizabeth N J. Fractionation apparatus: US, 2471134[P]. 1949-05-24

[2] Yang Youqi. Simulation study of operational performance of thermally coupled distillation[J]. Journal of Chemical Industry and Engineering (China), 1990, 41( 4): 491-497 (in Chinese)

[3] Fang Jing, Wang Baodong, Li Chunli, et al. Separation of dichloromethane-acetonitrile-water-hexamethyl disiloxane with dividing wall column by azeotropic distillation[J]. Journal of Chemical Industry and Engineering (China), 2013, 64(3): 963-969 (in Chinese)

[4] S chultz M A, Stewart D G, Harris J M. Reduce costs with dividing-wall columns[J]. Chem Eng Prog, 2002, 98(5): 64-71

[5] R ong B G, Kraslawski A. Optimal design of distillation flow sheets with a lower number of thermal couplings for multicomponent separations[J]. Ind Eng Chem Res, 2002, 41(21): 5716-5725

[6] F ang Jing, Hu Yuqi, Li Chunli. Energy-saving mechanism in heat transfer optimization of dividing wall column[J]. Ind Eng Chem Res, 2013, 52(51): 18345-18355

[7] Abdul Mutalib M I, Smith R. Operation and control of dividing wall distillation column: Part 1: Degrees of freedom and dynamic simulation[J]. Chem Eng Res Des, 1998, 76(3): 308-318

[8] Long N V D, Lee S, Lee M. Design and optimization of a dividing wall column for debottlenecking of the acetic acid purification process[J].Chemical Engineering and Processing, 2010, 49(8): 825-835

[9] Dejanovic I, Matijasevic L, Halvorsen I J, et al. Designing four-product dividing wall columns for separation[J]. Chem Eng Res Des, 2011, 89(8): 1155-1167

[10] Dunnebier G, Pantelides C C. Optimal design of thermally coupled distillation columns[J]. Ind Eng Chem Res, 1999, 38(1): 162-176

[11] Ye Qing, Li Langtao, Qiu Zhaorong. Separation of pyrolysis gasoline by divided wall distillation column[J]. Acta Petrolei Sinica (Petroleum Processing Section), 2010, 26(4): 617-621 (in Chinese)

[12] Qian Chunjian, Ye Qing, Zhu Guobiao, et al. Study of using DWC to separate three components mixture[J]. Chemical Industry and Engineering Progress, 2007, 26(8): 1174-1177 (in Chinese)

[13] Li Jun, Sun Lanyi, Hu Youyuan, Li Qingsong. Study on production of dehydrated ethanol with azeotropic distillation dividing wall column[J]. Modern Chemical Industry, 2008, 28: 93-97 (in Chinese)

[14] QING Jiwei, ZHANG Hao, XIONG Xiaojuan, et al. The separation of benzene-cyclohexane system by extractive dividing wall column[J]. Acta Petrolei Sinica (Petroleum Processing Section), 2014, 30(4): 687-693 (in Chinese)

[15] Lophaven S N, Nielsen H B, Sondergaard J. Dace-A Matlab Kriging toolbox[DB/OL]. http://www2.imm.dtu. dk/~hbn/dace/dace.pdf, 2010-07-27.

[16] Zuiderweg F J, et al. Recommended Test Mixtures for Distillation Columns[M]. London: The Institution of Chemical Engineers, 1969

date: 2015-01-21; Accepted date: 2015-02-02.

Hu Yuqi, Telephone: +86-13820266338; E-mail: ctsthuyuqi@163.com.