Development of transient Back Flow Cell Model (BFCM) for bubble columns

A Transient Back Flow Cell Model (BFCM) is presented as an alternative appr oach to describe the hydrodynamics of ozone bubble columns. Transient BFCM, when compared to the traditionally used models such as transient ADM or tr ansient CFSTR's in-series model, represents a flexible, reliable, accurate, and more importantly simple method to describe the backmixing in the liqui d phase in bubble columns. Transient BFCM consists of N-BFCM ordinary first -order differential equations in which N-BFCM unknowns (Y-j's) are to be de termined. This set of N-BFCM differential equations can be solved numerical ly as N-BFCM linear algebraic equations with respect to time as the indepen dent variable. This is achieved by applying an explicit technique for the d iscrete time which allows obtaining the solutions (Y-j(n+1)'s) of the N-BFC M algebraic equations simultaneously at time step "n+1" as functions of the (Y-j(n)'s) valus at time step "n".