Case Study 2: air separation process schematic.

Case Study 2: air separation process schematic.

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A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval ov...

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... large-scale DAE air separation model is used, which considers the separation of nitrogen from air. The model used here was adapted from Cao [46], and a simplified process schematic is shown in Figure 4. As a first step, air enters from the atmosphere and is compressed using a multi-staged compressor (COM); impurities are then removed using several adsorption units; high pressure purified air is then cooled in a multi-path heat exchanger (PHX) using the returning gas product (GN2) and waste streams from a high pressure distillation column (HPC); the cooled air stream is then split where a portion goes through a turbine (EXP) to promote further cooling before entering the bottom of the distillation column, while the other stream goes directly to the distillation column. ...

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This article develops a sequential quadratic programming (SQP) algorithm that utilizes a parallel interior-point method (IPM) for the QP subproblems. Our approach is able to efficiently decompose and solve large-scale multiperiod nonlinear programming (NLP) formulations with embedded dynamic model representations, through the use of an explicit Schur-complement decomposition within the IPM. The algorithm implementation makes use of a computing environment that uses the parallel distributed computing message passing interface (MPI) and specialized vector-matrix class representations, as implemented in the third-party software package, OOPS. The proposed approach is assessed, with a focus on computational speedup, using several benchmark examples involving applications of parameter estimation and design under uncertainty which utilize static and dynamic models. Results indicate significant improvements in the NLP solution speedup when moving from a serial full-space direct factorization approach, to a serial Schur-complement decomposition, to a parallelized Schur-complement decomposition for the primal-dual linear system solution within the IPM.