Straining of small particles in porous media
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Modeling the retention of colloidal particles in soils is important to understanding water contamination from viruses, bacteria or contaminants adsorbed on colloids. Particles transported by fluid remain in the soil when they arrive at constrictions in the pore space too small to admit them. This phenomenon, called “straining”, depends on the size and shape of constrictions in pore space. An analogy can be made between the retention of colloidal particles in soils and the trapping of fine particles within reservoir formations. Fine particles of clay or quartz are naturally present in the porous media. They may also enter the reservoir from external sources, like completion fluids. Once in the reservoir, fine particles can be mobilized by a chemical composition of the water in contact with the formation or simply by the shear forces during production. In their movement through the reservoir, fines can get trapped at small pore constrictions, reducing flow through the porous medium and causing a decline in reservoir productivity. The terms colloid and fine particle are interchangeable in this thesis. While theories of straining predict that dilute concentrations of particles smaller than the smallest nominal pore throats should migrate without being strained, experiments show that such particles are nevertheless retained in the porous medium. This thesis tests the hypothesis that particles are strained not just in throats between three grains, but also in gaps between pairs of grains. To test that hypothesis the number, width and distribution of such gaps has been quantified in model soils. The Finney packing (a widely used model for ideal soils) and ten new computer generated packings have been used for this purpose. All of them are dense random packings of mono-disperse spheres. The characterization of gaps in these ideal soils has confirmed that their occurrence in the packings is large enough to trap a considerable number of particles. The statistics of gap widths and point contacts in the Finney packing are comparable to the statistics from the computer generated packings, making the latter packings acceptable models of ideal soils. A range of gap widths of interest has been defined according to the size of the particles that show non-classical straining behavior in experiments. This range includes gap widths between 0.03 and 0.1 times the radius of the soil grains. The flow velocity through the gap, necessary to evaluate theories of particle straining, has been estimated assuming that the gap is a slit of width equal to the gap width. The range of capture specific to each gap width and particle size has been calculated in order to compute the volumetric flow appropriate to the particle being strained. This range of capture indicates the distance from the minimum constriction at which a particle approaching the gap can be strained. The calculated volumetric flows in gaps were between two and three orders of magnitude smaller than the flows in adjacent pore throats, obtained from a steady-state single–phase flow calculation. The distribution of gap widths and the volumetric flow through gaps in the Finney pack have been combined into a flow-rate-weighted distribution of gap widths. This distribution has been used in the theory of particle straining developed by Sharma and Yortsos (1987, a, c) in order to predict the probability of particle trapping in gaps. The theoretical rate constant for straining has been determined for several particle sizes and its scaling with particle size has been evaluated. This result has been compared to an empirical correlation reported by Bradford (2002). There was no concordance between the scaling correlation calculated in this work using a flow-weighted distribution of gap widths and the one reported in the literature. The data suggest a much weaker dependence of the straining rate on the volumetric flow through gaps than postulated in the theory. Another evaluation of the theory was made, this time assuming that straining rate is independent of flow rate through the gap. In this case, the predicted scaling exponent was smaller than the experimental value. The two evaluations of the straining theory yielded two relationships for straining rate constant that bound the observations. These evaluations represent two limiting cases when studying the dependence of straining with particle size. This suggests that the gap geometry obtained here, combined with a more refined evaluation of flow in the vicinity of gaps, could account for the experimental observations. evaluations represent two limiting cases when studying the dependence of straining with particle size. This suggests that the gap geometry obtained here, combined with a more refined evaluation of flow in the vicinity of gaps, could account for the experimental observations.