Pressure-driven filtration using membrane technology holds promise for the treatment of produced water but is restricted by the problem of fouling. Fouling is the accumulation of dispersed materials at the surface of the membrane, thereby decreasing the area available for filtration and decreasing the permeation flux. While this is intuitively understandable when the dispersals are solid particles, it is less clear when the dispersals are droplets of other fluid immiscible with the continuous one. Fluids can deform, squeeze, and take the shape of the pore. This questions the proposition and practice of many researchers to extend the blocking mechanisms, originally developed for the filtration of solid emulsions, to the filtration of fluid emulsions. To explore this topic, in this work, we perform experimental and numerical studies to investigate whether the blocking laws can still apply to the filtration of fluid emulsions. The experimental setup involves the use of three types of polymeric microfiltration membranes as well as three different oils. The results obtained show that the oil content in the permeate increases with time contrary to what would be the case if the dispersals were solid particles. Furthermore, the rejection capacity of the membrane decreases with time, implying that more oil permeates as fouling develops. Again, this is contrary to the observed practices in the filtration of solid emulsions where the solid content in the permeate also decreases as fouling develops. To confirm this behavior, three scenarios were investigated numerically using the tools of computational fluid dynamics. The numerical study highlights that, when a pore opening is filled with oil, larger droplets that would otherwise not permeate experience permeation. This enforces the understanding that, as fouling develops, the pores that are filled or blanketed with oil do not restrict oil from permeation; rather, they ease its movement and decrease the selectivity of the membrane. The filtration of fluid emulsions is fundamentally different from that of solid emulsions. Fluids can deform, squeeze, and take the shape of the pores. In this case, interfacial tension forces provide the criterion that defines the selectivity of the membranes.