Convergence difficulties remain a long-standing problem for steady state process modeling software. Since process models are nonlinear, conventional numerical algorithms are prone to fail in manners that are well-known. Additionally, it is not difficult to specify process models that are ill-posed and have no definite solution. Infeasibility can arise from improper parameter specifications (e.g. while fixing intensive states, compositions, conversions, etc.). It may also result when using common submodel formulations that work for some situations, yet lack certain subsystem interactions that are part of the actual physics. The need for these interactions may depend on the nature of the interconnections of the submodels within the overall process network structure, and neglecting these may leave some states underdetermined. Simply counting variables and equations may not prevent this. Currently, software construction requires significant skill on the part of the modeler to avoid such problems.

In this paper we present a formulation approach for steady state process models that provides an unambiguous mechanism to diagnose and correct misformulation. It is not a numerical procedure as much as a canonical structure for model formulation. Composite process models assembled from subsystems of the described form can be guaranteed to be consistent, adequately specified, and have a solution within the physically-real domain.

In the new approach, each subsystem model may be expressed as a primal-dual variational problem. Solving the coupled subsystems then becomes a problem in noncooperative equilibria. In this form, rigorous existence theorems apply, and homotopy methods can be used for solution. The individual subsystem models are novel in that their linear and nonlinear portions are explicitly separated. The linear portions are used to test the feasibility of the network as a whole, and to determine the subsystem process specifications that are allowable while maintaining network feasibility. The nonlinear portion is required to be have a feasible solution any time the linear portion of the model is satisfied.

The interconnection network structure is unlike the traditional modular paradigm in that flows are not regarded as subsystem "outputs" in the direction of the flow, but rather as global variables that are properties of the network as a whole. Moreover, flows of the conserved quantities are bidirectional on the network connections. This aspect is important to ensure that subsystems will be mutually feasible (i.e. flow between subsystems is negotiated, not implied).

The subsystem interconnection network provides a set of linear relations among the conserved quantities, and also a set of linear relations among the variational adjoint variables (typically thermodynamic or mechanical potentials). These linear relations are combined with the linear portions of the subsystem models to form a global linear system. This global linear system is then analyzed using standard techniques to determine the feasibility of the network structure itself, the space onto which the process specifications must project in order to ensure feasibility of the overall process model, and whether or not the balances on conserved quantities are sufficient for the system to be fully specified.

The formulation is described and its properties explained. Simple illustrative examples are presented showing how faulty specifications are diagnosed or prevented.

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