**ABSTRACT**

This work presents a procedure for direct numerical minimization of entropy production in a diabatic tray column with heat exchanged on the trays as control variables, as opposed to previously used procedures with temperature on the trays as control variables. The procedure, which had previously been demonstrated on a binary mixture, was in this work applied to a multicomponent mixture, with minor modifications. The procedure comprised the complex optimization method and the Ishii-Otto method for solving the equations of a column model based on the iterative Newton-Raphson technique with partial linearization of the equations. The desired separation of the components was realized by the addition of a penalty function to the goal function, i.e. entropy production in the column. The required thermodynamic characteristics were calculated by the Soave equation of state. As an illustration, an industrial debutanizer with five components was used whose data, obtained by simulation, were compared with the optimization results of a diabatic column with the same desired separation and number of trays. After the diabatic column optimization procedure, the value of 91.91 J/Ks was obtained as the best result for entropy production. According to the best solution, entropy production in the diabatic column was 23.2% lower than in the adiabatic column. The heat to be removed from the column increased by 24.7%, while the heat to be added to the column increased by 28.8%.

**KEYWORDS**

PAPER SUBMITTED: 2018-12-06

PAPER REVISED: 2019-06-08

PAPER ACCEPTED: 2019-06-17

PUBLISHED ONLINE: 2019-07-06

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 3**, PAGES [2256 - 2266]

- Kaiser, V., Gourlia, J.P., The ideal column concept: Applying exergy to distillation, Chemical Engineering, 92 (1985), 17, pp. 45-53
- 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
- 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
- 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
- Andresen, B., Salamon, P., Optimal distillation using thermodynamic geometry, in: Thermodynamics of Energy Conservation and Transport (Eds. A. DeVos, S. Sieniutycz), Springer Verlag, 2000, pp. 319-331
- Alcántara-Avila, J.R., Sotowa, K.-I., Horikawa, T., Entropy production and economic analysis in diabatic distillation columns with heat exchangers in series, Energy, 93 (2015), pp. 1719-1730
- Schaller, M. et al., Numerically optimized performance of diabatic distillation columns, Computers and Chemical Engineering, 25 (2001), 11-12, pp. 1537-1548
- 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
- Sauar, E., Siragusa, G., Andresen, B., Equal Thermodynamic Distance and Equipartition of Forces Principles Applied to Binary Distillation, The Journal of Physical Chemistry A, 105 (2001), 11, pp. 2312-2320
- de Koeijer, G., Røsjorde, A., Kjelstrup, S., Distribution of heat exchange in optimum diabatic distillation columns, Energy, 29 (2004), 12-15, pp. 2425-2440
- 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
- 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
- Spasojević, M., Đ., Janković, M.R., Đaković, D.D., A New Approach to Entropy Production Minimization in Diabatic Distillation Column with Trays, Thermal Science, 14 (2010), 2, pp. 317-328
- Sauar, E. et al., Diabatic Column Optimization Compared 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, 92, 2000, pp. 15-30
- Mendoza, D.F., Riascos, C.A., Design and optimization of diabatic single and double feed distillation columns with sequential heat exchangers, 2nd International Conference on Engineering Optimization, September 6-9 (2010), Lisbon, Portugal
- Kjelstrup, S., Bedeaux, D., Johannessen, E., Gross, J., Non-Euilibrium Thermodynamics for Engineers, World Scientific, Singapore, 2010
- Burgos-Madrigal, P., Mendoza, D.F., López de Haro, M., On Entropy Generation and the Effect of Heat and Mass Transfer Coupling in a Distillation Process, Journal of Non-equilibrium Thermodynamics, 43 (2018), 1, pp. 57-74
- Ishii, Y., Otto, F.D., A general algorithm for multistage multicomponent separation calculations, Canadian Journal of Chemical Engineering, 51 (1973), 5, pp. 601-606
- Soave, G., Equilibrium constants from a modified Redlich-Kwong equation of state, Chemical Engineering Science, 27 (1972), 6, pp. 1197-1203
- Reid, R.C., Prausnitz, J.M., Poling, B.E., The Properties of Gases and Liquids, 4th ed., McGraw Hill, New York, 1987
- Box, J.M., A New Method of Constrained Optimization and a Comparison with other Methods, Computer Journal, 8 (1965), 1, pp. 42-52
- Soares Pinto, F., Zemp, R., Jobson, M., Smith, R., Thermodynamic optimization of distillation columns, Chemical Engineering Science, 66 (2011), pp. 2920-2934
- Salehi, G.R., Salehi, A., Ghorbani, B., Amidpour, M., Maleki, M., Kimiaghalam, F., A Pareto Front Approach to Bi-objective of Distillation Column Operation Using Genetic Algorithm, Energy Science and Technology, 3 (2012), 2, pp. 63-73
- Özeçelik, Y., Mert, S.O., Exergoeconomic Distillation Sequencing by Multi-objective Optimization through a Hybrid Genetic Algorithm, Chemical and Biochemical Engineering Quarterly, 30 (2016), 3, pp. 305-315