Particle Transport In Sandstones
Authors: Donaldson E.C. , Baker B.A. , Carroll H.B. 
Published: December 2007

Abstract
Particle transport within the Berea, Noxie and Cleveland sandstones having mean pore sizes of 10, 15 and 30 microns, respectively, was studied by injection of aqueous suspensions of sand particles having mean particle sizes of 4, 6 and 7 microns. A constant flow rate was used, and the pressure drop across the core was continuously monitored. The pressure drop across the core was continuously monitored. The effluents were collected in a fraction collector, and the number of particles per milliliter and distribution of sizes of the particles were determined using a particle counter interfaced particles were determined using a particle counter interfaced with a computer. These data were used to postulate a theory of discrete particle transport within porous media from a statistical point of view. A statistical random walk model was developed using Poiseuille's capillary flow equation and the actual pore size distribution of the core to calculate the pressure drop across the core. Particles are selected using a pressure drop across the core. Particles are selected using a random number generator and the actual particle size distribution, and are tested for passage through the most probable capillary with a pressure threshold function. If the particle posses, another particle is generated; however, if the particle posses, another particle is generated; however, if the particle lodges, a new pressure is calculated, and each capillary is tested for particle breakout with the new pressure. This process is continued until a plugging pressure is attained or a process is continued until a plugging pressure is attained or a maximum number of particles pass through the core. The calculated pressures and distributions of effluent particles closely approximate the experimentally observed data. The process of particle transport, where colloidal forces are process of particle transport, where colloidal forces are negligible, is a random statistical process which can be represented by a statistical mathematical model.

Introduction
This work was initiated to develop a practical mathematical approach to particle transport within porous systems and the formation of a filter-cake at the face of the porous medium. This subject has previously been treated as a mass balance problem leading to experimental determination of numerous time dependent coefficients for the filtration process. Under these circumstances, each change of suspension process. Under these circumstances, each change of suspension or filter must be tested experimentally before mathematical analysis con be applied. However, the process of filtration is a natural statistical phenomenon since it results from the behavior of a porous medium having a distribution of pore sizes being contacted by a suspension containing a distribution of particles of various shapes and sizes. Hence, a statistical random walk mathematical model was developed using Poiseuille's capillary flow equation, the pore size distribution of the core, and the particle size distribution of the suspension. The model approximates the pressure fluctuations of the system, the cake build-up, and the transport of fine particles through the rock. At this stage of development, the model may be used for analysis of various processes involving the transfer of discrete particles in porous media in the absence of colloidal attractive forces. Three applications that are of immediate interest are:filtration of fluids prior to injection,selective plugging of high permeability prior to injection,selective plugging of high permeability zones anddrilling mud penetration.
This work will be continued with specific application to well logging problems since the accurate measurement of oil saturation is a critical aspect of enhanced oil recovery.

LITERATURE REVIEW
The principal mechanisms that cause deposition during transport of particles within a porous medium are sedimentation, direct interception and surface attractive properties of the particles and medium. The path of fluid flow within a geologic porous system is a tortuous one which is subject to frequent sudden changes in direction and velocity. Suspended particles with densities greater than the density of the carrier fluid will not follow the stream lines as the fluid suddenly changes direction of flow and will impinge on the walls of the pores due to forces inherent in gravity and inertia. Particles thus deposited will tend to form domes as observed experimentally (1,2,3).