Process modelling on a canonical basis
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Based on an equation oriented solving strategy, this thesis investigates a new approach to process modelling. Homogeneous thermodynamic state functions represent consistent mathematical models of thermodynamic properties. Such state functions of solely extensive canonical state variables are the basis of this work, as they are natural objective functions in optimisation nodes to calculate thermodynamic equilibrium regarding phase-interaction and chemical reactions. Analytical state function derivatives are utilised within the solution process as well as interpreted as physical properties. By this approach, only a limited range of imaginable process constraints are considered, namely linear balance equations of state variables. A second-order update of source contributions to these balance equations is obtained by an additional constitutive equation system. These equations are general dependent on state variables and first-order sensitivities, and cover therefore practically all potential process constraints. Symbolic computation technology efficiently provides sparsity and derivative information of active equations to avoid performance problems regarding robustness and computational effort. A benefit of detaching the constitutive equation system is that the structure of the main equation system remains unaffected by these constraints, and a priori information allows to implement an efficient solving strategy and a concise error diagnosis. A tailor-made linear algebra library handles the sparse recursive block structures efficiently. The optimisation principle for single modules of thermodynamic equilibrium is extended to host entire process models. State variables of different modules interact through balance equations, representing material flows from one module to the other. To account for reusability and encapsulation of process module details, modular process modelling is supported by a recursive module structure. The second-order solving algorithm makes it possible to retrieve symbolically obtained derivatives of arbitrary process properties with respect to process parameters efficiently as a post calculation. The approach is therefore perfectly suitable to perform advanced process systems engineering tasks, such as sensitivity analysis, process optimisation, and data reconciliation. The concept of canonical modelling yields a natural definition of a general exergy state function for second law analysis. By partitioning of exergy into latent, mechanical, and chemical contributions, irreversible effects can be identified specifically, even for black-box models. The calculation core of a new process simulator called Yasim is developed and implemented. The software design follows the concepts described in the theoretical part of this thesis. Numerous exemplary process models are presented to address various subtopics of canonical modelling.