J. Ignacio Laiglecia1, Rodrigo Lopez-Negrete2, M

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Presentation transcript:

A simultaneous Dynamic optimization approach for natural gas processing plants J. Ignacio Laiglecia1, Rodrigo Lopez-Negrete2, M. Soledad Diaz1, Lorenz T. Biegler2 sdiaz@plapiqui.edu.ar 1Planta Piloto de Ingeniería Química, Universidad Nacional del Sur, CONICET. Camino La Carrindanga km 7, 8000 Bahia Blanca, ARGENTINA 2Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 Motivation Optimization algorithm Minimize the offset between current ethane recovery and a set point value. Rigorous models for cryogenic sector: countercurrent heat exchangers with partial phase change (HE), separation tanks (HPS), distillation columns (DC) and a turboexpander (TE). Thermodynamic predictions are calculated with the SRK equation of state (Soave, 1972) to all equipments. Nonlinear DAE optimization problem Cryogenic Sector NLP Barrier subproblem TE DC HE1 HE2 HPS External refrigeration (not employed) Product (high C2 recovery) High C1 content Orthogonal collocation over finite elements Partial Phase Change Cryogenic Heat Exchangers details Large-scale NLP problem Newton´s Method Karush-Kuhn-Tucker conditions Newton Step IPOPT KKT Matrix Optimization problem KKT Matrix Inherits Sparsity and Structure of Dynamic Model Mathematical model in each unit DAE model Number of differential equations 183 Number of algebraic equations 855 HE2 Energy balances performed on microscopic elements on both shell and tube sides. i = cells index Method of lines NLP Optimization Problem Number of variables 82320 Number of constraints 81720 Number of lower bounds 31880 Number of upper bounds 1080 Number of nonzeros in Jacobian 565450 Number of nonzeros in Hessian 253600 AMPL environment HE1 The sub-model obtained for HE2 is applied to tube side and for shell side. Where are two phase flow, we have formulated the following equations: Monotonic temperature profiles Results Assuming state conditions at each grid point, Bell-Delaware method is considered. The parameters are function of HE geometry To avoid crossover temperature (HE1 and HE2) HPS DC Overall mass and energy balances in each tray. We have not neglected V holdup and it has kept a index one model. Model: overall dynamic mass balance and geometric equations. HE1 HE1 TE Model: fast dynamic => static model. HE1 HE2 + hydraulic correlations corresponding to sieve plates. The entire plant optimization has been performed in 51 CPUs on an Intel DuoCore 2.2 GHz personal computer. References Acknowledgements Biegler, L.T., V.M. Zavala (2008), Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization. Computers and Chemical Engineering 33 (2009) 575–582 Cervantes A. M., L. T. Biegler (1998). Large-scale DAE optimization using a simultaneous NLP formulation. AIChE Journal,44,1038-1050. Diaz, S., S. Tonelli, A. Bandoni, L.T. Biegler (2003), “Dynamic optimization for switching between steady states in cryogenic plants”, Found Comp Aided Process Oper 4, 601-604. Rodriguez, M., (2009) “Dynamic Modeling And Optimization of Cryogenic Separation Processes”, PhD Dissertation, Universidad Nacional del Sur, Bahia Blanca, Argentina. The authors gratefully acknowledge financial support from the National Research Council (CONICET), Universidad Nacional del Sur and ANPCYT, Argentina.