In this work, the concept of multicontinuum approach has been extended to investigate permeation flux decline with time due to fouling in crossflow filtration systems. In this work, the decline of permeation flux has been attributed, mainly, to the decline of the available area for the flow due to either or both of two mechanisms; namely, oil droplets pinning and/or oil droplets coalescence. In this work, we consider the first mechanism in which fouling is attributed to the pinning of oil droplets at the membrane surface. In another work, we consider the more general mechanism contributing to the problem of fouling, which involves oil droplets coalescence and clustering. Under the pinning mechanism, the porous membrane and the oil droplets have been divided into a number of continua according to the pores and droplets size distributions. These continua interact according the conditions for permeation, rejection, breakup and pinning. The decline of the porosity of each porous continuum has been captured and likewise the decline of the critical velocity and the permeation flux. This model introduces two fitting parameters that are essentially dependent on the type of filtration technique. Comparisons with the experimental data available in literature show a very good match.