A mathematical study of the evolution of fouling and operating parameters throughout membrane sheets comprising spiral wound modules

Local experimental data on key process parameters, throughout membrane sheets of spiral-wound membrane (SWM) elements, are unavailable and very difficult to obtain; therefore, theoretical models are essential to better understand the evolution of fouling, which is helpful for improving design and operation of these modules. The mathematical model, formulated in a fundamental manner herein, takes into account the spatial flow field non-uniformities inside narrow channels with spacers (simulating SWM elements) and their interaction with the evolving deposits. A realistic meso-scale transient model, typical of the early stages of organic membrane fouling, is employed. Appropriate non-dimensionalization of model equations allows to treat separately the two (practically significant) cases of constant inlet pressure and constant average permeate flux. Several simplified cases are examined, for specific dimensionless parameter values, and asymptotic solutions are derived. The results of this analysis have guided the development of very efficient numerical techniques, most useful for future extensions towards the development of a comprehensive modeling tool, appropriate for module design calculations and for assessing detailed experimental data.

► Flow and fouling spatio-temporal evolution throughout membrane sheets is treated.
► The meso-scale model employed is typical of early stage colloidal fouling.
► Simplified cases are analyzed and useful asymptotic solutions are derived.
► The results guided development of efficient numerical techniques for model extension.