The paper derives mathematical model and optimal operation of batch diafiltration processes with partial recirculation of retentate, i.e. batch closed-loop membrane processes. A generalized mathematical model of the process is developed in the form of a set of non-linear ordinary differential and algebraic equations. Two process variables are used as manipulated and optimized degrees of freedom: recirculation rate and diluant addition rate. Optimal operation aims to minimize a weighted combination of processing time, power consumption, and diluent consumption. A theoretical analysis of the process is combined with numerical optimization techniques. Based on selected case studies, conclusions are drawn on economics of the process operation to identify when the process design with recirculation adds substantial benefits compared to the classical (open-loop) design without recirculation. Simulation studies suggest that minimum time operation does not require recirculation loop. On the other hand, minimum power operation consumes about 70-95% less power in closed-loop design when compared to open-loop setup. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.