Solution of bivariate population balance equations with high-order moment-conserving method of classes

• HMMC is extended to treat bivariate population balances.
• Two-component pure aggregation is studied as test case.
• A realistic liquid–liquid extraction problem is also considered.
• Results show that high accuracy can be achieved with reasonable number of categories.

In this work the high-order moment-conserving method of classes (HMMC) (Alopaeus et al., 2006) is extended to solve the bivariate Population Balance Equation (PBE). The method is capable of guaranteeing the internal consistency of the discretized equations for a generic moment set, including mixed-order moments of the distribution. The construction of the product tables in the case of aggregation, breakage and convection in internal coordinate space are discussed. Eventually, several test cases are considered to assess the accuracy of the method. The application to a realistic mass transfer problems in a liquid–liquid system is preliminarily discussed. The comparison with analytical solutions of pure aggregation problems shows that the proposed method is accurate with only a limited number of categories.