A Wavelet-Galerkin Method applied to Separation Processes

Abstract

Many fluid mixtures encountered in chemical and hydrocarbon processing industries are ill-defined in the sense that they contain far too many components for a detailed compositional analysis and subsequent modeling in terms of pure component mass balances. Common examples of such mixtures are frequently related to processes of high economic relevance and include petroleum and reservoir fluids as well as polymer solutions and polyreaction systems [6]. The concept of continuous thermodynamics is a well-established approach for the modeling of these mixtures [2, 6]. The compositional complexity of the mixture is represented in terms of a time-dependent continuous distribution function t) of some characterizing fluid property £ (e.g. molecular weight, natural boiling point or Single Carbon Number). The relation between the discrete mole fraction of any component and the distribution function is given by

$${x_l}\left(t \right) = {\smallint _{\Delta \xi l}}F\left({\xi,t} \right)d\xi $$

((1.1))

.Using definition eq. (1.1), a complete framework of thermodynamic relations analogous to the discrete case can be derived [6, 13].