OPTIMUM SEQUENCE OF NONSHARP DISTILLATION COLUMNS
Transcription
OPTIMUM SEQUENCE OF NONSHARP DISTILLATION COLUMNS
OPTIMUM SEQUENCE OF NONSHARP DISTILLATION COLUMNS FOR TERNARY SEPARATION Javad Ivakpour, Norollah Kasiri* Computer Aided Process Engineering Lab, Chemical Engineering Department, Iran University of Science & Technology *Email: [email protected] Abstract: The optimization of distillation column sequences for nonsharp separation of ternary mixture is studied. The four possible basic sequences are compared based on the cost functions. Each sequence contains one or two distillation columns and an adequate number of splitters and mixers for considering possible bypass streams. The column specifications and bypass stream flow rates are optimized by genetic algorithm based on rigorous simulation results. In the proposed method each component can be distributed in each column and no constraint is applied for component recovery fraction. Implementation of the proposed method for three examples shows that nonsharp separators with distributed components and complex column arrangements can frequently reduce the separation costs up to 77% compared to the optimum sequence with sharp separators. Keywords: Distillation, Sequencing, Optimization, Nonsharp Separation, Bypass 1. INTRODUCTION For separation of multi-component mixtures, different sequences of distillation columns can be used with different separation costs. This fact provides a saving possibility in separation cost by selecting the optimum sequence (Doherty and Malone, 2001). The amount of possible saving is a function of many factors the most important ones being the required separation specifications, components physical properties and the structure types of sequences. Separation of a mixture using the simple sharp-split columns is the most frequently used situation in distillation column sequencing problems. Direct and indirect sequences are two well known examples of this type. In this kind of sequences, number of possible states is a function of the number of products (King, 1980). There are 3, 5 and 14 possible states for separation of 2, 3 and 4 products, respectively. The differences between the costs of these sequences are significant and can be up to 70% for a five product separation (Doherty and Malone, 2001). Implementation of complex columns with more than one feed and/or side-stream(s) products can result in new sequences and consequently further cost reduction possibility. Prefractionator structure is a commonly used sequence of this category. Sequences in which each column has its own condenser and reboiler are known as basic states (Agrawal, 2003). More complex configurations such as thermally coupled, heat integrated (Caballero and Grossmann, 2006) and dividing wall columns (Schultz et al., 2002) can be generated from the basic state sequences (Agrawal, 2003). When the products purity are not required to be very high, there is a possibility of bypassing some parts of streams and as a result the separation costs can be decreased significantly (Heckl et al., 2007; Kovacs et al.; 2000, Floudas, 1987; Wehe and Westerberg, 1987). Also, it is possible to turn to non-sharp separation with lower cost. Hence, there is a trade-off between the amount to be bypassed and the degree of non-sharp separation. Bampoulos et al (1988) show that employing non-sharp separation on an example problem of four components can result in annual cost savings of 42% compared to the best sequence with sharp separation. This result was obtained from sequences consisting of sharp distillation columns and bypass streams only. Also, Aggarwal and Floudas (1990) show that using non-sharp separations can result in savings of 10-70% as compared to sharp separation based on simple nonsharp distillation columns and mixing and bypassing possibilities. In nonsharp separation problems, it is also possible to perform the required separation using less than N-1 columns (Kim and Wankat, 2004). Although the less number of columns is used in these sequences, but the separation cost may be higher than the sequences with more columns because of the impurity in the side-streams locations. In the previous works, the approximated methods have been used for design and optimization purposes. The most commonly use approximated methods are Fenske-Underwood-Gilliland methods (Kister, 1992) for design of simple distillation columns. Malone extended the approximated method to complex columns (1987) and the proposed method has been used in a number of works. The approximated methods are based on two main assumptions: constant relative volatility and constant molar overflow. Therefore, their accuracy is a function of the assumptions validity. Furthermore, as a rule of thumb the optimum reflux is considered to be 1.1 to 1.2 times of the minimum required value from the Underwood equation. All the assumptions used in the approximated method can result in low accuracy and possible wrong selection of optimum sequences. In the current work, the separation of a ternary feed mixture through four possible basic state sequences of Figure 1 is studied. The possibility of bypass streams, nonsharp separation, complex columns and separation with one column are considered in the sequences. Design of each column is performed based on the entire sequence purpose. Therefore, it is not required to specify the columns separation duty because it is optimized in the optimization step. The optimization is done by Genetic Algorithm (Goldberg, 1989) based on the rigorous simulation results to optimize the separation cost while the required separation is obtained. 2. SEQUENCE DESIGN & OPTIMIZATION 1.1. Sequence Structures There are two methods for selection of optimum distillation column sequence; optimization of superstructure and optimize each possible structure individually. In the first method the superstructure is proposed so that all possible sequence structures can be derived from it by setting one or more stream(s) flow rate to zero. In the second method an algorithm is proposed to generate all possible structures systematically and the optimum one can be determined by optimization of the sequence structure. Therefore, the optimum cost of each structure must be evaluated initially before the best structure is determined comparing the optimum values. However, in the former method the number of local optima are higher while in the second approach the two step optimization required results in a larger execution time. In this work, because there are only four possible sequence structures all of them are optimized separately. The four possible states are shown in Figure 1. As can be seen in this figure, the structure of Figure (1.a) can be considered as a superstructure for all sequences because all other sequences are a special case of it. Figure 1.a represents a prefractionator structure. Direct and indirect sequences have been shown in Figure 1.b and 1.c respectively. Figure 1.d illustrates a sequence with single column only that can be used in nonsharp separations. 1.2. Design & Optimization The investigated problem can be stated as follow: Given the feed specifications and the desired products flow rates and compositions, find the optimum structure to perform the required separation with the minimum Total Annual Cost (TAC) using the following assumptions: a. Consider nonsharp separation in each column. b. Implement one or two column(s) in each structure to separate feed stream into three final products. c. Consider desired products as the mixtures of other products. d. Consider the bypass streams. Therefore, the objective function to be minimized is TAC. Genetic Algorithm is used for optimization of column specifications and stream flow rates. Deviation from the desired products specifications is considered as the penalty function relative to the deviation value added to objective function. The penalty function of equation 1 is used in the current work as follow: P A in which F is the main feed flow rate, ( x ji ) 2 (F j Pj ) i 1 Pj is deviation from the required flow rate of desired product j, x ji is deviation from the required composition of component i in the desired product j and A is a constant value that determine the importance of constraints. Very high value of A causes any deviation to be considered as an impossible condition. Conversely, very low value of A cause disregarding of constraints. In this work it is found that the mean value of TACs in the first iteration of Genetic Algorithm is a good estimate for A . Figure 1: four possible basic state structures for ternary separation The TAC and deviation values must be determined from the simulation results. Distillation column simulation is performed based on the inside-out algorithm (Seader and Henley, 1998). Damping factor procedure proposed by Ivakpour and Kasiri is implemented to increase the speed and convergence properties (2008). Each column is simulated having determined column pressure, number of trays, feeds tray location, side-stream(s) tray locations, reflux ratio and the products flow rate ratios from GA optimization algorithm. Furthermore, the splitters products flow rate ratios are determined by GA. The products flow rate ratios are determined independently and normalized later. Therefore, the summation of them over each column or splitter remains unity and the ratios can change unboundedly. The variables values are determined randomly at the first iteration of GA for each individual. Then the equipments are simulated and columns are designed based on the simulation results and the costs are evaluated. Evaluations are performed based on the TAC values from Guthrie’s cost correlations (Douglas, 1988). Penalty values will be added to the objective function if there is any deviation. Having all individuals evaluated, the optimum ones can be selected for generating new and better individuals by the combination and changing of the selected individuals’ variables. The procedure is iterated until the optimum objective value in the latest iteration loop improves relative to the specified number of previous iteration loops (in this work relative to the 100 iteration loops before the current one). 3. RESULTS A previously published nonsharp example has been examined with the proposed method with three different conditions. The main feed and desired products specifications have been shown in Table 1. This example previously was studied in sequences with sharp separators and bypass streams possibility for separation of hypothetical ternary component set (Wehe and Westerberg, 1987). In this work, the effects of component properties and nonsharp separators on the optimum structure have been studied for the separation given at Table 1. Therefore, this separation is run with two different sets of components; set 1 consists of n-Pentane, n-Hexane and n-Heptane and set 2 consists of i-Butane, n-Butane and n-Pentane. The component relative volatilities are obviously higher in set 1. Table 1: Main feed stream and desired products component flow rates (kmol/hr) (These specifications are same for all studied examples) Component Feed Desired Product 1 Desired Product 2 A 100 70 30 B 100 50 50 C 100 70 30 Total 300 190 110 Example 1 is considered as the separation with nonsharp separators for component set 1. The optimization results have been shown in Table 2. As can be seen in this table the prefractionator structure is the optimum structure for this separation. Also, single column sequence separates the feed mixture with lower cost than direct and indirect sequences. Therefore, in this nonsharp example the structures with complex columns have lower cost than structures with only simple column. In this example, prefractionator sequence can cause in 36% saving comparing to the direct sequence. Table 2: Optimized TACs for studied examples TAC (105 $/yr) Component Set Nonsharp Separators Sequence Structure: Prefractionator Direct Indirect Single Column Time* (hr) *All of the optimizations were Example 1 1 Yes Example 2 1 No Example 3 2 Yes 0.983 1.555 1.835 1.458 3.1 5.712 4.287 5.410 --2.8 2.520 2.173 3.401 2.679 3.4 performed in Microsoft Visual C++.Net platform with parallel processing possibility on an 8*2.33 GHz CPU (Intel Xeon) with 3 GB of RAM. Furthermore, the streams flow rates and compositions are shown in Figure 2 for the optimum sequence (prefractionator structure). Closer look at this table reveals that in the optimum condition nonsharp separation is performed in both columns. Also, it can be seen that a part of main feed stream is injected to the second column directly. A part of each middle product is bypassed to the desired product too. Hence, combination of nonsharp separation and bypass streams can be seen in the optimum condition. Table 3: Stream flow rates at optimum condition of sequence structure 1.a From To Feed S1 S1 S1P1 Feed S1P2 S2 S2 S2 Feed S1P1 S1P2 S2F1 S2F3 S1P2 S2F2 S2F3 S1 S1P1 S1P2 S2 S2 S2 S2F1 S2F2 S2F3 D1 D1 D1 D1 D1 D2 D2 D2 Flow 246.1 12.8 233.4 11.1 51.8 149.1 38.7 76.4 96.9 2.1 1.6 57.2 38.7 90.4 27.0 76.4 6.5 190.0 110.0 X1 X2 X3 0.33 0.33 0.33 0.82 0.17 0.01 0.31 0.34 0.35 0.82 0.17 0.01 0.33 0.33 0.33 0.95 0.05 0.00 0.29 0.49 0.22 0.14 0.32 0.54 0.33 0.33 0.33 0.82 0.17 0.01 0.31 0.34 0.35 0.95 0.05 0.00 0.14 0.32 0.54 0.31 0.34 0.35 0.29 0.49 0.22 0.14 0.32 0.54 0.36 0.27 0.37 0.31 0.34 0.35 D1 - D2 - 0.28 0.44 0.27 Repetition of the optimization procedure for the same structure frequently results in optimum values which are slightly different (less than 5%). Despite the slight difference between the final optimum values of different repetition, the optimum stream flow rates and columns operating conditions may differ significantly. This fact reveals that there are many local optima with close objective function values in the search space. However, the difference between two successive optimum values of the same sequence structure is much smaller than the difference between optimum values of two different structures and therefore the sorted ordering of sequences remain constant. It must be noted that this small difference is negligible compared to the accuracy of simulation results and cost function correlations. It can be interesting to perform the separation with sharp separators and bypass streams. Sharp separator is considered as a separator with the key component recovery larger than 99%. Example 2 of Table 2 shows the optimization results at this condition. As can be seen in this table the TACs increase significantly for all sequences comparing to the same sequences with nonsharp separators. Comparison of Example 1 with Example 2 from Table 2 shows that nonsharp separation can decrease the separation cost up to 77% compared to the best sequence with sharp separators for this ternary separation case study. Furthermore, the sorted ordering of sequences can change. Hence, using sharp separators for nonsharp separation can result in wrong selection of optimum sequence and significant higher separation cost. Optimization results of Table 1 with the component set 2 are shown in Example 3 of Table 2. Results show that the optimum structure is the direct sequence in this example. But differences between direct structure with prefractionator and single column structure are negligible. This new order is proved by the well known heuristic rule that the more difficult separation must be left to the end. Therefore, the optimum sequence structure can be changed with the component properties. 4. CONCLUSION Optimization of nonsharp distillation column sequencing has been examined in this article. Four possible basic state structures with bypass streams and nonsharp separator possibility have been optimized with three examples. The optimization has been performed based on the rigorous simulation results. The effects of using nonsharp separators and component physical properties on the optimum structure and TACs have been studied separately. Results show that using nonsharp separators can result in significant saving in costs. Also it was shown that the different component set can change the optimum structure. 5. REFRENCES Aggarwal, A., C.A. Floudas (1990). Synthesis of general distillation sequences, Nonsharp separations. Comput. Chem. Eng., 14(6), 631 Agrawal, R. (2003). Synthesis of Multicomponent Distillation Column Configurations. AIChE J., 49, 379. Bamopoulos, G., R. Nath, R. Motard (1988). Heuristic synthesis of nonsharp separation sequences, AIChE J., 34(5), 1988, 763. Caballero, J. A., I. E. Grossmann (2006), Structural considerations and modeling in the synthesis of heat-integratedthermally coupled distillation sequences. Ind. Eng. Chem. Res., 45(25), 8454 Doherty, M. F. and M. F. Malone (2001). Conceptual Design of Distillation Systems. McGraw Hill, New York. Douglas, J. M. (1998). Conceptual Design of Chemical Processes. McGraw-Hill, New York. Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Professional. Heckl, I., Z. Kovacs, F. Friedler, L.T. Fan, J. Liu (2007). Algorithmic synthesis of an optimal separation network comprising separators of different classes. Chem. Eng. Process., 46(7), 656. Ivakpour, J. and N. Kasiri (2008). Improve speed and convergence of distillation column simulation. Hydrocarbon Process., October, 75. Kim, J., P. Wankat (2004). Quaternary distillation systems with less than N - 1 columns, Ind. Eng. Chem. Res., 43(14), 3838. King, C. J. (1980). Separation Processes. McGraw-Hill, New York. Kister, H. Z. (1992). Distillation Design. McGraw-Hill, New York. Kovacs, Z., Z. Ercsey, F. Friedler, L.T. Fan (2000). Separation-network synthesis: global optimum through rigorous super-structure. Comput. Chem. Eng., 24(8), 1881. Nikolaides, I.P., M.F. Malone(1987). Approximate design of multiple-feed/side-stream distillation systems. Ind. Eng. Chem. Res., 26(9), 1987, 1839. Seader, J. D. And E.J. Henley (1998). Separation Process Principles. John Wiley & Sons, New York. Schultz, M. A., D. G. Stewart, J. M. Harris, S. P. Rosenblum, M. S. Shakur, D. E. O'Brien (2002). Reduce costs with dividing-wall columns. Chem. Eng. Prog., 98(5), 64 Wehe, R. R., A.W. Westerberg (1987). An algorithmic procedure for synthesis of distillation sequences with bypass. Comput. Chem. Eng., 11(6), 1987, 619