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Three basic problem formulations for the simultaneous-modular approach are discussed, as are three alternative methods for computing the flowsheet-level Jacobian. A new algorithm for partitioning and tearing when using the Simultaneous-modular approach is also presented. SIMMOD, our implementation of the simultaneous-modular approach is then outlined. In subsequent papers in this series we use SIMMOD to study the performance of the simultaneous-modular approach on process simulation and optimization problems, as well as to perform experiments on different numerical strategies for implementing the simultaneous-modular approach.

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The performance of the simultaneous-modular approach on four process optimization problems is studied, and numerical experiments using different computational strategies are also performed. The simultaneous-modular approach is found to be very effective on process optimization problems, and the strategies used in our implementation SIMMOD are found to be more efficient than those used in previous implementations of the simultaneous-modular approach for process optimization.