461004 Global Optimization of Natural Gas Liquefaction Processes through Differentiable McCormick Relaxations

Wednesday, November 16, 2016: 4:50 PM
Monterey I (Hotel Nikko San Francisco)
Harry A. J. Watson1, Kamil A. Khan2 and Paul I. Barton1, (1)Process Systems Engineering Laboratory, Massachusetts Institute of Technology, Cambridge, MA, (2)Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL

We present a new methodology and framework for the global optimization of liquefied natural gas production processes. Liquefaction processes are inherently challenging to optimize (even locally), largely due to the difficulty in modeling the complex heat transfer behavior and phase transitions in multistream heat exchanger unit operations. Much of the state-of-the-art work found in the literature involves the use of either mixed-integer or complementarity-constrained programming formulations and associated solution methods.[1],[2] However, building on a recent nonsmooth modeling approach for multiphase multistream heat exchangers,[3],[4] we demonstrate that these complex flowsheet optimization problems can instead be formulated as much simpler nonsmooth nonlinear programs. These problems can then be solved effectively in a branch-and-bound global optimization framework with the use of newly developed continuously-differentiable McCormick relaxations.[5] This relaxation technique calculates differentiable convex underestimators, differentiable concave overestimators and their respective gradients for complex compositions of simple intrinsic functions, and can be performed automatically in a procedure analogous to the forward mode of automatic differentiation. Moreover, these relaxations are based on the multivariate McCormick relaxation framework,[6] and so they are particularly well suited for this application, owing to the frequent occurrence of bivariate product, min and max terms in the nonsmooth multistream heat exchanger constraints. Additionally, the local solvers used to calculate lower bounds on the global solution can readily provide dual multiplier information because the relaxations are differentiable, meaning effective range-reduction strategies can be implemented. In combination with the comparatively small problem size relative to other approaches, these range-reduction methods significantly enhance the convergence rate of the branch-and-bound algorithm. Comparisons with state-of-the-art global optimization software are provided on problems involving both simplified and industrially-relevant liquefaction processes to demonstrate the favorable performance of the new modeling and optimization framework.

[1] M. M. F. Hasan, I. A. Karimi, H. E. Alfadala and H. Grootjans, “Operational modeling of multistream heat exchangers with phase changes,” AIChE Journal, Vol. 55, No. 1, pp. 150–171, 2009.

[2] R. S. Kamath, L. T. Biegler and I. E. Grossmann, “Modeling multistream heat exchangers with and without phase changes for simultaneous optimization and heat integration,” AIChE Journal, Vol. 58, No. 1, pp. 190–204, 2012.

[3]H. A. J. Watson, K. A. Khan and P. I. Barton, “Multistream heat exchanger modeling and design,” AIChE Journal, Vol. 61, No. 10, pp. 3390-3403, 2015.

[4] H. A. J. Watson and P. I. Barton, “Modeling phase changes in multistream heat exchangers.” Submitted.

[5] K. A. Khan, H. A. J. Watson and P.I. Barton, “Differentiable McCormick relaxations.” Submitted.

[6] A. Tsoukalas and A. Mitsos, “Multivariate McCormick relaxations,” Journal of Global Optimization, Vol. 59, pp. 633–662, 2014.

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