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Thermophoresis of spheroidal colloids in aqueous media under the thermal conductivity effect is analyzed. The thermophoretic velocity and the thermodiffusion coefficient of spheroidal colloids have been formulated for extremely thin electric double layer (EDL) cases. Furthermore, a numerical thermophoretic model is built for arbitrary EDL thickness cases. The parametric studies show that the thermal conductivity mismatch of particle and liquid gives rise to a nonlinear temperature region around the spheroid, with the thickness close to the minor semiaxis. When the EDL region is thin relative to such nonlinear temperature region, the thermal conductivity effect on the thermophoresis of spheroidal colloids is significant, which strongly depends on the ratio of the minor semiaxis to the EDL thickness, the thermal conductivity ratio of particle to liquid, and the particle aspect ratio. Finally, to estimate the thermodiffusion coefficient of spheroidal colloids with arbitrary thermal conductivity, electrolyte concentration, and particle shape, the average dimensionless axial temperature gradient on the spheroidal equator plane in the EDL region is proposed.

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The reservoir permeability coefficient is one of the essential parameters for reservoir modeling, oilfield development, and groundwater pollution control. The seepage function of underground fluid shows different properties due to the other particle gradation. This paper used standard quartz sand to conduct a series of tests, such as particle size, porosity, compactness, and permeability coefficient tests, and establish an empirical correlation formula for estimating the permeability coefficient. In order to optimize the coefficients of the proposed relationship, particle size analysis tests were carried out on several samples. Their permeability coefficients were calculated and predicted, and several parallel experiments verified the accuracy of their formulas. The results indicated that (1) The permeability coefficient is affected by the comprehensive effects of gravel particle size and pore particle size in the gravel with the same mineral composition, compactness, and uniformity coefficient. Therefore, careful consideration should be taken in evaluating the permeability coefficient. (2) Within a specific particle size range, the permeability coefficient also decreases with the decrease of gravel particle size and pore size, especially in the range of coarse sand. The permeability coefficient decreases nonlinearly with the increase in compactness. With the increase of the uniformity coefficient, the permeability coefficient decreases first and then increases. (3) The above test and analysis established three mathematical models considering particle size, porosity, compactness, and uniformity coefficient. Model C was the optimal permeability coefficient model, and its determination coefficient R2 was more than 0.98. The above analysis results could provide a reliable basis for sand-filling design, hydrate exploitation, and non-cohesive soil permeability coefficient prediction.