An improved scaling procedure for analysis and simplification of process models

Systematic scaling analysis of model equations can be valuable as a tool for developing computationally tractable simulations of physical systems. The scaling analysis methods in literature pose difficulties in the calculation of scale and reference values, when nonlinear terms are involved in the model equations. Further, existing methods involve trial and error procedures in the scaling process. In this paper, a systematic approach for handling nonlinear terms is suggested, which results in appropriate scale and reference values that render the dimensionless variable variations to be of order one. Further, trial and error procedures are avoided through a new approach wherein a set of nonlinear algebraic equations are solved to identify the scale and reference values. The proposed scaling approach is common to any given model equations with fixed parameters. However, it is to be noted that the proposed procedure may not handle situations when model equations exhibit steady state multiplicity and have dynamic multi-mode regimes. The proposed scaling procedure is illustrated through various examples of different complexities. A 1D model of WGS reactor as a case study shows the effectiveness of the obtained scale and reference values in obtaining simplified model which represents the steady state and dynamic variations of the variables.