Abstract
This paper presents an extension of the theory of retention of fine particles in formations. The mechanism of interest is straining, which depends only on the shape and distribution of constrictions in pore space. To quantify the geometry of constrictions, we used computer-generated dense random packs of spheres as model porous media. A characteristic feature of dense packings is a pair of neighboring grains that do not quite touch. We refer to the void space between pairs of such spheres as gaps. Gaps are smaller than pore throats, which are the void space between three spheres. Geometric analysis of throats and gaps was combined with a new methodology to compute flow rates in gaps. The results were input to an existent straining theory to study the dependence of straining rate on fines size. Only the flow of a single fluid phase is considered.
Numerous experiments show evidence of straining of particles smaller than the smallest pore throat in the column, under conditions that exclude the possibility of filtration. The simplest test of a theory is whether it can account for these anomalous observations. Existing theories that consider pore throats as the constrictions cannot explain these observations, whereas including gaps in the set of pore space constrictions correctly predicts the observations.
A more stringent test of straining theory is to predict the dependence of particle straining rate in a column flow experiment upon the size of the particles. Classical pore-throat-based theories make the physically reasonable assumption that once a particle enters a small constriction, it is guaranteed to be trapped there. Thus the probability of trapping is proportional to the flow rate through the constriction. These theories significantly overestimate the influence of particle size for small particles. We argue that the probability of particle retention in a gap need not be 100% even if the particle enters the gap. The particle may rebound from the grain(s) rather than become wedged in the gap. If this happens, the particle may eventually be swept around the gap.
We therefore extend the theory by postulating retention probability to be proportional to flow rate through the gap and inversely proportional to the momentum or to the kinetic energy of the carrier fluid. The extensions bracket the scaling behavior reported in experiments.
Our analysis of particle straining in gaps explained a longstanding set of observations for which previous theories could not account. These results suggest that a more detailed study of particle/grain collisions is needed to explain fully the straining rates observed in experiments.
