Model for the Straining of Fines in Unconsolidated Sands
Authors: Rodriguez Elena 
Published: June 2014

Abstract
The pressure gradient during oil production causes the migration of fine particles through the reservoir. We investigate the trapping of fines by straining, a simple geometric mechanism: fines remain in the formation when they arrive at constrictions in the pore space too small to admit them. However, several experiments reported the retention of fines too small to be strained. We hypothesize that particles are strained in gaps between pairs of grains besides throats between three grains. We characterize gaps in model formations (computer generated) and compute flow rates in gaps. We predict the dependence of particle straining rate upon the size of the particles by introducing the results into an existent straining theory.
The probability of trapping is typically assumed to be proportional to the flow rate through the constriction. Furthermore we consider the rebound and swept of the particle around the grains, proposing that the retention probability is proportional to the flow rate through the gap and inversely proportional to the momentum or to the kinetic energy of the carrier fluid.
Our analysis yields straining exponents that bracket the scaling behavior reported in experiments, explaining a long series of observations for which previous theories could not account.

Introduction
Fines migration is an important problem in oil reservoirs. Fines are small particles of clay, quartz or similar materials that are present in most naturally occurring porous media. Like colloids, fines generally have a size of the order 1 µm and a net surface charge. Kaolinite and illite are the most common migrating clays. Fines migration refers to the movement of fine particles within the reservoir formation due to drag forces during oil and gas production and often occurs in an unconsolidated formation, or when an incompatible completion fluid releases fine particles. The migration of fine particles includes their release from the porous media, their motion with the flow of permeate, and finally their capture at some pore sites or their passage out of the porous medium.
There are two controlling mechanisms of fine retention: filtration and straining. Filtration is a physicochemical mechanism controlled by electrostatic, chemical and van der Waals forces which lead to the attachment/detachment of particles to the filter media. Straining is a simple geometric mechanism. Particles are retained by straining when they arrive at constrictions in pore space too small to allow their passage. This simple phenomenon of straining is still not well understood. Many investigators have independently reported anomalous retention of fine particles after experiments with flowing suspensions of particles 1,2,3,4. Pore throats have been typically considered the place where fine particles are trapped, however this experiments showed that particles smaller than the smallest nominal pore throat were trapped within the medium. The particles in these experiments were too small to be trapped in throats and also too large to undergo deep-bed filtration. These results suggest that filtration theory underestimates the extent of retention and also that the assumption that straining occurs only at pore throats is too restrictive. On the other hand, classical theories of straining in pore throats cannot accurately account for these observations.