## THERMAL SCIENCE

International Scientific Journal

### A NEW APPROACH TO ENTROPY PRODUCTION MINIMIZATION IN DIABATIC DISTILLATION COLUMN WITH TRAYS

**ABSTRACT**

Previous approach to direct numerical minimization of entropy production in diabatic distillation column in order to determine heat quantity to be exchanged at trays was based on temperatures on trays as control variables and it was applied only to simple binary columns. Also, previously developed theoretical models for determining optimal exchanged heat profile were determined only at such columns and while they were approximated they produced worse results than numerical minimum of entropy production. In this paper, as control variables for minimization, exchanged heat on the trays is used. It enables application to complex multicomponent diabatic columns. Ishii-Otto global method, based on model linearization and iterative solution by Newton-Raphson technique, is applied for solving column mathematical model. Needed thermodynamical properties for ideal systems are calculated using Lewis-Randall ideal solution model, and for non-ideal slightly polar systems they are calculated using Soave equation of state. Five direct methods are used for numerical optimization. Applied approach is successfully demonstrated at frequently used example of distillation of benzene and toluol mixture by using for these purposes specially written program. Simplex method appeared to be the most convenient optimization method for the considered problem.

**KEYWORDS**

PAPER SUBMITTED: 2009-12-09

PAPER REVISED: 2009-12-19

PAPER ACCEPTED: 2010-01-12

**THERMAL SCIENCE** YEAR

**2010**, VOLUME

**14**, ISSUE

**2**, PAGES [317 - 328]

- King, C. J., Separation Processes, McGraw-Hill, New York, USA, 1971
- Fonyo, Z., Thermodynamic Analysis of Rectification: 1. Reversible Model of Rectification, International Chemical Engineering, 14 (1974), 1, pp. 18-27
- Kaiser, V., Gourlia, J. P., The Ideal Column Concept: Applying Exergy to Distillation, Chemical Engineering, 92 (1985), 17, pp. 45-53
- Terranova, B. E., Westerberg, A. W., Temperature - Heat Diagrams for Complex Columns. 1. Intercooled/Interheated Distillation Columns, Industrial & Engineering Chemistry Research, 28 (1989), 9, pp. 1374-1379
- Kjelstrup Ratkje, S., et al., Analysis of Entropy Production Rates for Design of Distillation Columns, Industrial & Engineering Chemistry Research, 34 (1995), 9, pp. 3001-3007
- Agrawal, R., Fidkowski, Z.T., On the Use of Intermediate Reboilers in the Rectifying Section and Condensers in the Striping Section of Distillation Column, Industrial & Engineering Chemistry Research, 35 (1996), 8, pp. 2801-2807
- Aguirre, P., et al., Optimal Thermodynamic Approximation to Reversible Distillation by Means of Interheaters and Intercoolers, Industrial & Engineering Chemistry Research, 36 (1997), 11, pp. 4882-4893
- Andersen, T. R., et al., Energy Efficient Distillation by Optimal Distribution of Heating and Cooling Requirements, Proceedings (Ed. S. Pierucci), ESCAPE-10, Pisa, Italy, 2000, pp. 709-715
- de Koeijer, G. M., et al., Positioning Heat Exchangers in Binary Tray Distillation Using Isoforce Operation, Energy Conversion and Management, 43 (2002), 9-12, pp. 1571-1581
- Tondeur, D., Kvaalen, E., Equipartition of Entropy Production. An Optimality Criterion for Transfer and Separation Processes, Industrial & Engineering Chemistry Research, 26 (1987), 1, pp. 50-56
- Sauar, E., Kjelstrup Ratkje, S., Lien, K. M., Equipartition of Forces: A New Principle for Process Design and Optimization, Industrial & Engineering Chemistry Research, 35 (1996), 11, pp. 4147-4153
- Salamon, P., Nulton, J. D., The Geometry of Separation Processes: A Horse-Carrot Theorem for Steady Flow Systems, Europhysics Letters, 42 (1998), 5, pp. 571-576
- Andersen, B., Salamon, P., Optimal Distillation Using Thermodynamic Geometry, in: Thermodynamics of Energy Conservation and Transport (Eds. A. DeVos, S. Sieniutycz), Springer Verlag, Berlin, 2000, pp. 319-331
- Weinhold, F., Metric Geometry of Equilibrium Thermodynamics, The Journal of Chemical Physics, 63 (1975), 6, pp. 2479-2483
- Sauar, E., et al., Diabatic Column Optimization Compare to Isoforce Columns, Energy Conversion and Management, 38 (1997), 15-17, pp. 1777-1783
- Andresen, B., Salamon, P., Thermodynamic Geometry Determines Optimal Temperature Profile in Distillation Column, in: Methods and Applications of Inversion, Springer Verlag, Berlin, 2000, pp. 15-30
- Schaller, M., et al., Numerically Optimized Performance of Diabatic Distillation Columns, Computers and Chemical Engineering, 25 (2001), 11-12, pp. 1537-1548
- Sauar, E., Siragusa, G., Andresen, B., Equal Thermodynamic Distance and Equipartition of Forces Principles Applied to Binary Distillation, Journal of Physical Chemistry A, 105 (2001), 11, pp. 2312-2320
- de Koeijer G. M., et al., Comparison of Entropy Production Rate Minimization Methods for Binary Diabatic Distillation, Industrial & Engineering Chemistry Research, 41 (2002), 23, pp. 5826-5834
- Schaller, M., et al., The Influence of Heat Transfer Irreversibilities on the Optimal Performance of Diabatic Distillation Columns, Journal of Non-Equilibrium Thermodynamics, 27 (2002), 3, pp. 257-269
- de Koeijer, G., Røsjorde, A., Kjelstrup, S., Distribution of Heat Exchange in Optimum Diabatic Distillation Columns, Energy, 29 (2004), 12-15, pp. 2425-2440
- Jimenez, E. S., et al., Optimization of a Diabatic Distillation Column with Sequential Heat Exchangers, Industrial & Engineering Chemistry Research, 43 (2004), 23, pp. 7566-7571
- Røsjorde, A., Kjelstrup, S., The Second Law Optimal State of a Diabatic Binary Tray Distillation Column, Chemical Engineering Science, 60 (2005), 5, pp. 1199-1210
- Johannessen, E., Røsjorde, A., Equipartition of Entropy Production as an Approximation to the State of Minimum Entropy Production in Diabatic Distillation, Energy, 32 (2007), 4, pp. 467-473
- Shu, L., Chen, L., Sun, F., Performance Optimization of a Diabatic Distillation-Column by Allocating a Sequential Heat-Exchanger Inventory, Applied Energy, 84 (2007), 9, pp. 893-903
- Ishii, Y., Otto, F. D., A General Algorithm for Multistage Multicomponent Separation Calculations, Canadian Journal of Chemical Engineering, 51 (1973), 5, pp. 601-606
- Browne, D. W., Ishii, Y., Otto, F. D., Solving Multicolumn Equilibrium Stage Operations by Total Linearization, Canadian Journal of Chemical Engineering, 55 (1977), 3, pp. 307-312
- Paunović, R., Janković, M., Škrbić, B., An Extended Ishii-Otto Algorithm for Multistage Multicomponent Separation Calculation with Stage Efficiencies Included, Computers and Chemical Engineering, 8 (1984), 3-4, pp. 249-251
- Ishii, Y., Otto, F. D., An Efficient Simultaneous Correction Procedure for Multicomponent, Multistage Separation Calculations for Non-Ideal Systems, Computers and Chemical Engineering, 25 (2001), 9-10, pp. 1285-1298
- Ishii, Y., Otto, F. D., A Method to Extend the Domain of Convergence for Difficult Multicomponent, Multistage Separation Problems, Computers and Chemical Engineering, 27 (2003), 6, pp. 855-865
- Rosenbrock, H. H., An Automatic Method for Finding the Greatest or Least Value of a Function, Computer Journal, 3 (1960), 3, pp. 175-184
- Hooke, R., Jeeves, T. A., Direct Search Solution of Numerical and Statistical Problems, Journal of the Association for Computing Machines, 8 (1961), 2, pp. 212-221
- Powell, M. J. D., An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives, Computer Journal, 7 (1964), 2, pp. 155-162
- Nelder, J. A., Mead, R., A Simplex Method for Function Minimization, Computer Journal, 8 (1965), 4, pp. 308-313
- Box, J. M., A New Method of Constrained Optimization and a Comparison with other Methods, Computer Journal, 8 (1965), 1, pp. 42-52
- Soave, G., Equilibrium Constants from a Modified Redlich-Kwong Equation of State, Chemical Engineering Science, 27 (1972), 6, pp. 1197-1203
- Lewis, G. N., Randall, M., Thermodynamics, McGraw-Hill, New York, USA, 1961
- Schaller, M., Numerically Optimized Diabatic Distillation Columns, Ph. D. thesis, Technische Universität Chemnitz, Chemnitz, Germany, 2007