Water usage in variable volume diafiltration: comparison with ultrafiltration and constant volume diafiltration

Variable volume diafiltration (VVD), also known as volume-decreasing diafiltration, is a process in which fresh water is added continuously to the retentate in a batch ultrafiltration process at a rate that is less than the permeate flowrate, thus providing for simultaneous ultrafiltration (UF) and diafiltration. This process has been analysed recently and it is claimed that VVD uses less water than constant volume diafiltration (CVD) [1]. In this paper, we examine both VVD and UF–CVD and compare the water usage in each process. For a solution containing two solutes, A and B, with rejection coefficients σA = 1 and σB = 0, we show that VVD uses more water than CVD when CVD is performed at the final volume of a UF–CVD process. VVD uses less water than CVD only if the latter is performed at the initial volume of a UF–CVD process. When CVD is performed at the intermediate macrosolute concentration that minimises the process time, namely Cg/e where Cg is the gel concentration and e is the base of the natural logarithm, it will generally use less water than VVD.