A mathematic model of yield is developed as real-time function and state function based on the mass balance. It describes the filtration processes of intermittent feed diafiltration (IFD) and continuous feed diafiltration (CFD). We have hypothesized the permeation coefficient of the microsolute (0 <= P <= 1) and continuous stirred tank reactor. The concentration of microsolute in the retentate and the yield of microsolute in the filtrate are calculated and the parameters as the dilution ratio, the pre-concentration ratio and the post-concentration ratio are defined according to the diatiltration process. In the diafiltration process of Cephalosporin C ferment broth, the yield can be estimated properly. The results show that the model can help for optimizing the diafiltration process by estimating and controlling the concentration and the yield in the process of diafiltration. (C) 2007 Elsevier B.V. All rights reserved.