A modelling and simulation language for combined lumped and distributed parameter systems

Equation oriented approach to process flowsheeting

For many technical systems, the use of a refined network modeling approach leads to hyperbolic-type initial-boundary value problems of partial differential-algebraic equations (PDAEs). The boundary conditions of these systems are governed by time-dependent differential-algebraic equations (DAEs) that couple the PDAE system with the network elements that are modeled by DAEs in time only. In order to classify these systems, we extend some index notions that have already been introduced to treat parabolic-type problems. A perturbation index is considered that reflects the sensitivity of the mixed system to slight perturbations in the right-hand side of the PDAEs, as well as in the input signals of the DAE systems and initial values. In order to make an a posteriori analysis of semidiscretization in space and time, we introduce additionally a space and a method of lines (MOL) index. Here one is especially interested in whether the semidiscretized systems properly reflect the properties of the underlying systems. We will show that these indices may detect an artificial sensitivity with respect to perturbations, e.g., if the semidiscretization does not consider the information transport along the characteristics.

Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations

Chemical process engineering activities such as design, optimization, analysis, control, scheduling, diagnosis, and training all rely on mathematical models for solution of some engineering problem. Likewise, most of the undergraduate chemical engineering curricula are model-based. However, the lack of formalization and systematization associated with model development leads most students and engineers to view modeling as an art, not as a science. Consequently, model development in practice is usually left to specialized modeling experts. 
This work seeks to address this issue through development of a framework that raises the level of model development from procedural computations and mathematical equations to the fundamental concepts of chemical engineering science. This framework, suitable for implementation in a computer-aided environment, encompasses a phenomena-based modeling language and logical operators. The modeling language, which represents chemical processes in terms of interacting physicochemical phenomena, provides a high-level vocabulary for describing the topological and hierarchical structure of lumped or spatially distributed systems, mechanistic characterization of relevant phenomena (e.g., reactions, equilibria, heat and mass transport), and thermodynamic and physical characterization of process materials. The logical operators systematize the modeling process by explicitly capturing procedural and declarative aspects of the modeling activity. This enables a computer to provide assistance for analyzing and constructing phenomena-based models, detect model inconsistencies and incompleteness, and automatically derive and explain the resulting model equations from chemical engineering first principles. 
In order to provide an experimental apparatus suitable for evaluating this framework, the phenomena-based language and logical operators have been implemented in a computer-aided modeling environment, named MODEL.LA. MODEL.LA enables phenomena-based modeling of dynamic systems of arbitrary structure and spatial distribution, hierarchical levels of detail, and multicontext depictions. Additional components allow incorporation of thermodynamic and physical property data, integration of control structures, operational task scheduling, and external models, and assistance for specification and solution of the resulting mathematical model. Application of this environment to several modeling examples, as well as its classroom and industrial deployment, demonstrate the potential benefits of rapid, reliable, and documented chemical process modeling that may be realized from this high-level phenomena-based approach. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

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Liang Tseng Fan

Papers

Dynamic simulation of chemical processes described by distributed and lumped parameter models