1. A simultaneous Dynamic optimization approach for natural gas processing plants
J. Ignacio Laiglecia1, Rodrigo Lopez-Negrete2, M. Soledad Diaz1, Lorenz T. Biegler2
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,
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,
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.