Mathematical and numerical analysis of classes of property models

A general analysis is presented to focus on the mathematical and numerical elements of property models for stand-alone results as well as within other calculations. This includes listing all of the equations that constitute a property model and articulating the sets of known and unknown variables for given problems. Ordering of equations is done to determine if a direct solution is feasible where the incidence matrix of unknown variables and equations can be written in tridiagonal form or if simultaneous or iterative solution of multiple equations is required. Example pure compound and mixture property models are: cubic equations of state; more advanced non-cubic equations of state; activity coefficient models; and models for polymer and electrolyte systems. Uses of this analysis are discussed for property calculations as a part of other calculations, such as for process models and parameter regression.