Most of the mathematical models that are employed to model the performance of bubble columns are based on the assumption that either plug flow or complete mixing conditions prevail in the liquid phase. Although due to the liquid-phase axial dispersion, the actual flow pattern in bubble columns is usually closer to being mixed flow rather than plug flow, but still not completely mixed flow. Therefore, the back flow cell model (BFCM), that hypothesises both back flow and exchange flow to characterise the liquid-phase axial dispersion, is presented as an alternative approach to describe the hydrodynamics and mass transfer of ozone bubble columns. BFCM is easy to formulate and solve. It is an accurate and reliable design model. Transient BFCM consists of NBFCM ordinary-first-order differential equations in which NBFCM unknowns (Yj) are to be determined. That set of equations was solved numerically as NBFCM linear algebraic equations. Steady-state BFCM consists of 3 × NBFCM non-linear algebraic equations in which 3 × NBFCM unknowns (qG,j, Xj, and Yj) are to be determined. Those non-linear algebraic equations were solved numerically using Newton–Raphson technique. Steady-state BFCM was initially tested using the pilot-scale experimental data of Zhou. BFCM provided excellent predictions of the dissolved ozone profiles under different operating conditions for both counter and co-current flow modes.

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