To further the ability to design membranes for separation/fractionation of deformable particles (such as, cells, liposomes, vesicles, and droplets in emulsions and oil-water suspensions), we have developed a 2-d multiscale computational approach to study how the pressure drops and bulk flow within the depth of a porous "membrane" influences the mobility of an immiscible droplet through that structure. We use a combination of the extended finite element method to describe the creeping fluid flow (Re similar to 0) inside a portion of a filtration membrane with an embedded fluid droplet, coupled with a particle method that interpolates the droplet's interfacial position, as well as, the corresponding velocity and pressure fields using least square fitting. We calculated how the combination of several model 2-d porous network domain geometries (pore size and distribution), and a soft particle's deformation-related property (surface tension), influences the particles' velocity relative to the bulk fluid flux (aka sieving) in model porous domains made up of circular obstacles. The focus in this paper is on the scaling relationship between the particle's properties, the geometry of the system, and the overall droplet's sieving through a periodic domain. We present first the case of a droplet permeating through an individual pore to determine its critical pressure. Then, the base case of a single pore and droplet is extended to include arrays of obstacles (creating a porous network domain) with different droplet volume fraction. In this case, the applied trans-domain pressure gradient is not the same pressure drop each droplet experiences when it needs to deform in order to pass between obstacles (a pore throat), which results in a non-intuitive motion. These cases can provide a set of scaling rules to guide membrane design for droplet separation purposes.