Superstructure Optimization of the Olefin Separation Process

BCDEFGHB/CDEFGHBCD/EFGHBCD/CDEFGHBCDEF/CDEFGHBCDEF/EFGHCDEFGHCD/EFGHCDEF/EFGHCDEF/GHCDEFG/HEFGHEF/GHEFG/HEFGEF/GGHG/HC5HGA/BCDEFGHBCDEF/GHBCDEFG/HC4C3H8AB/CDEFGHCD/EFGFABCD/CDEFGHB/CDEFGCDEFGCDEF/EFGEFE/FABCDEF/CDEFGHABCDEFGHABCDEF/EFGHABCD/EFGHBCDEFGBCD/CDEFGBCDEF/CDEFGBCDEF/EFGBCD/EFGBCDEF/GBCDEFCDEF/GB/CDEFBCD/CDEFCDEFCD/EFEC3H6C2H6DABCDEF/GHBCD/EFCDC/DABCDEFG/HABCDEFGA/BCDEFGAB/CDEFGABCD/CDEFGABCDEF/CDEFGCC2H4CH4BSTATESTASKSABCDEF/EFGABCD/EFGABCDEF/GNON-SHARPABCDEFA/BCDEFAB/CDEFABCD/CDEFABCD/EFABCDBCDA/BCDAB/CDB/CDABA/BAH2Figure 1: Superstructure of separation systemTable 1: Separation technologiesT1 Distillation columnT2 Physical absorption towerT3 Membrane separatorT4 DephlegmatorT5 Pressure Swing Adsorption (PSA)T6 Cold BoxT7 Chemical Absorption tower2. GDP modelWe propose a generalized disjunctive programming model for optimizing thesuperstructure of the separation system shown in Figure 1 (see Yeomans andGrossmann, 1999a, 1999b). The first level in the embedded disjunction corresponds tothe selection of the separation task. Once the separation task is selected, the second leveldisjunction is for the selection of the separation technologies. For example, if adistillation column is chosen, then the mass and energy balances for distillation columnare enforced and the corresponding cost term is considered. An additional disjunction isthe heat integration for the distillation columns, and another disjunction is forcompression, pumping or pressure reduction of each state. For the separation units,simple mass/energy balances are used. Assumptions for modeling the separation systemare as follows:1) Vapor pressure of the stream is calculated with Raoult’s law and by the Antoineequation (Reid et al., 1977)2) Utility (cooling water/hot steam) cost is given by a function of temperature (seeFigure 2)3) Investment cost is given by concave cost functions (Douglas, 1988)

Based on these assumptions, the following nonconvex GDP model is constructed:Indicesi States k Distillation columns Separation task st Separation technologySetsI States i K Distillation column kS i Separation task s for state i ST s Separation technology st for task sParametersEMAT Minimum T differenceCR L Lower bound for comp. ratio CR U Upper bound for comp. RatioVariablesx i Flowrate of state i T i Temperature of state IP i Pressure of state i IC i Investment cost for separation of iCC i Compressor cost for state i UC i Utility cost for separation of IYS i,s Selection of separation task YZ i,k Selection of heat integration for state iYT s,st Selection of separation tech. YC i Selection of compression for state iRT i Top recovery ratio of state i RB i Bottom recovery ratio of state iQEX i,k Heat transferred from state i to distillation column kQ i Heat generated or consumed by state ICT i Condenser temperature in distillation column for IRT k Reboiler temperature in distillation column kModel Olefin1:a) Minimize the annualized cost of capital investment, compression and utilityb) Overall mass balancesmin Z= ∑ i i +i( IC + CC UC )s . t.Ax = 0c) Pressure and temperature calculation by Antoine equationiPi= fa(T ),i∀i∈ Id) Embedded disjunction for the separation task∨s∈Si⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣∨st∈STsYSi,s⎤⎥top feedxi= RTixi⎥btm feed⎥xi= RBixi⎥⎡YTsst⎤⎥,,⎢⎥⎥⎢ mass balance : fm(xi) = 0 ⎥⎥⎢⎥energy balance : fe(xi,Ti, Pi, Q ⎥i ) = 0⎢⎥⎥⎢ t fuction ICiUCifc xiTiPiQ ⎥⎣cos: ( , ) = ( , , , i ) ⎥⎦⎦∀i∈ I

select a specific utility stream. However, as shown in Figure 2, the utility cost can beapproximated by a smooth function of the temperature. In this way, we can avoidintroducing the binary variables and simplify the modeling of utility system. Weconstruct a third order regression of the utility cost, which yields a good approximation.This approximation generally provides an underestimation of the actual cost of the utilitystreams because we introduce a continuous relaxation of the temperature levels of theutilities.Utility Cost-200.00 -100.00 0.00 100.00 200.00 300.00 400.00 500.00Temp FFigure 2: Utility stream temperatureTotal cost: 110.82 M$/yrAH2heatercompressorDephlegmatorABCDEFGH100F480PsigvalvecoolerABCDCDEFGH84F190Psig480Psig480PsigcompressorDE74F170PsigDeethanizer214F170PsigFigure 3: GAMS optimal solutionEFGH169F160PsigvalveFG238F140Psig109F140PsigDepropanizerpumppumpAB-141F900Psig410 Mkwh/yrGH226F160PsigCold BoxCD-41F160Psig236F140PsigEF83F160PsigGHA/BCD-31F140Psig72F140PsigEF123F140Psig900Psig-51F140PsigChemicalAbsorberC3Splitter99F140PsigDebutanizerBCDEFGHCH4C2H4C2H6C3H6C3H8C4C54. Numerical resultsFigure 3 shows the optimal solution for the superstructure shown in Figure 1. First thecompressors are used to increase the pressure of the feed stream to the dephlegmator,which separates the hydrogen and methane from the heavier components. Then thehydrogen/methane mixture is sent to the cold box and hydrogen is separated from

methane. The cold box operates at the low temperature and high pressure which requiresadditional refrigeration and compression. The C 2 -C 5 mixture is sent to the deethanizer(distillation column) and the C 2 mixture is recovered as top product. The C 3 mixture isseparated by the depropanizer, and the C 4 -C 5 mixture is sent to the debutanizer. Achemical absorber is used for the C 2 split and distillation column is used for the C 3 split.All the separation units perform sharp separations. Note that there is a heat exchangebetween the depropanizer and the C 3 splitter to reduce the utility cost. The annualizedcapital cost of the process is 39.1M$/yr. The power cost for the compressors is29.8M$/yr and the utility cost for the separation units is 41.9M$/yr. The energy cost isabout 75% of the total cost. Since the olefin separation process is highly energyintensive,a significant amount of utility cost can be saved by the heat integration. Table2 shows the statistics of the problem, where it can be seen that the MINLP problem isvery large. This MINLP was solved in about 2 hours on a Pentium PIII PC usingGAMS/DICOPT++, an algorithm for MINLP problems that is based on the OuterApproximation (OA) with Equality Relaxation and Augmented Penalty (Viswanathanand Grossmann, 1990). CPLEX was used for the MILP solver and CONOPT2 was usedfor the NLP solver in GAMS (release 20.7). The heuristic termination was used that isbased on the lack of improvement in the objective.Table 2: GAMS computational resultsMINLP problem sizeDICOPT++ solutionNumber of constraints 52,703 Number of iterations 5Number of variables 24,475 CPU seconds 8,778Number of binary variables 5,851 First integer solution 142.9 M$/yrReferencesBrooke A., Kendrick D., Meeraus A. and Raman R., 1997, GAMS language guide,Release 2.25, Version 92. GAMS Development Corporation.Biegler L.T., Grossmann I.E. and Westerberg A.W., 1997, Systematic methods ofchemical process design. Prentice Hall, New Jersey.Douglas J.M., 1988, Conceptual design of chemical processes. McGraw-Hill, New York.Duran M.A. and Grossmann I.E., 1986, An Outer-Approximation Algorithm for a classof Mixed-Integer Nonlinear Programs. Mathematical Programming, 36, 307.Lee S. and Grossmann I.E., 2000, New Algorithms for Nonlinear GeneralizedDisjunctive Programming, Computers and Chem. Eng. 24, 2125.Reid R.C., Prausnitz J.M. and Sherwood T.K., 1977, The properties of Gases andLiquids, 3 rd edition. McGraw-Hill, New York.Viswanathan J. and Grossmann I.E., 1990, A Combined Penalty Function and Outer-Approximation Method for MINLP Optimization, Computers and Chem. Eng.14, 769.Yeomans H. and Grossmann I.E., 1999a, A Systematic Modeling Framework ofSuperstructure Optimization in Process Synthesis, Computers and Chem. Eng.23, 709.Yeomans H. and Grossmann I.E., 1999b, Nonlinear disjunctive programming models forthe synthesis of heat integrated distillation sequences, Computers and Chem.Eng. 23, 1127.AcknowledgmentsThe authors would like to thank BP for financial support of this project