We present a new compact formulation and accurate solution strategy for modeling and simulation of natural gas liquefaction processes. The critical process units in liquefaction processes are cryogenic multistream heat exchangers, which are notoriously difficult to simulate and design rigorously due to their complex heat transfer behavior, made all the more difficult by the presence of phase changes and non-ideal thermodynamics. We extend a newly developed model for multistream heat exchangers to incorporate automatic detection and handling of phase changes in which the fluids are described by cubic equations of state. We formulate and solve our model as a small system of nonsmooth equations, rather than using the smoothing approximations or large optimization-based disjunctive programs which are found in the literature for handing these phenomena. Additionally, we employ an extension of automatic differentiation to automatically calculate computationally relevant generalized derivatives and a linear programming based Newton methodto guarantee that a precise, physically realizable result is found with a local quadratic convergence rate. A case study of the PRICO process is presented to demonstrate the model and solution algorithm.
 H. A. J. Watson, K. A. Khan, and P. I. Barton. “Multistream heat exchanger modeling and design.” Submitted.
 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.
 K. A. Khan and P. I. Barton, “A vector forward mode of automatic differentiation for generalized derivative evaluation.” In Press. Optimization Methods & Software.
 F. Facchinei, A. Fischer, and M. Herrich, “An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions,” Mathematical Programming, vol. 146, pp. 1–36, 2014.