Hollow-fiber membrane adsorber: Mathematical model

Two opposite design strategies for ultrafiltration/microfiltration filters: (1) reduction of concentration polarization and particle deposition to increase permeate velocity and (2) utilization of particle deposition on membrane surface to produce an additional (to permeate) volume of clarified water, are analyzed. It is shown that the first strategy is always associated with additional expenditures in power or other material resources, making it not enough cost-effective to be competitive with non-membrane filtration processes in some water treatment applications. At the same time, the second strategy does not require additional power expenditures and provides high water recovery and cost-effectiveness. The mathematical model describing the performance of hollow-fiber membrane adsorber, which represents a second-strategy filter, is studied. A general form of the particle-deposition equation is introduced, and its terms are analyzed. As a result, its linearized form, looking like a linear equation of reversible adsorption, is chosen. A numerical solution to the system of governing equations is obtained and used to assess the accuracy of approximate solutions. A new approximate solution allowing one to evaluate the adsorber particle retentions with an acceptable accuracy is suggested.