Conductivity of proppant mixtures
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Hydraulic fracturing is a physically complex phenomenon, and there are many variables, both environmental and operational, that affect the overall success of a fracture treatment. Amongst the operational variables, the process of proppant selection is key to ensuring that the induced fractures remain open and permeable. A variety of physical mechanisms act to degrade the permeability of a given proppant packing after deposition in a fracture, the most important of which is the magnitude of the confining stress. The goal of this work is to understand how mixtures of unlike proppants behave under various stress conditions. Specifically, the permeability and conductivity of various mixtures of unlike proppants are measured as a function of confining stress. A secondary investigation is also made into the dependence of permeability on the areal concentration of proppant. Choices of proppants are restricted to those which are currently most common in industry, in terms of both material and size. To that end, mixtures consisted of primarily ceramics and sands with appropriate grain size distributions. Additionally, a light-weight plastic proppant was included in the study. Simple laboratory methods are employed to measure the permeability of the various proppant packings. Values obtained from direct experimentation are compared with values obtained from an independent analytical model. Given the assumptions which are inherent in the analytical model, the experimental and analytical results are in satisfactory agreement. Also, a correlation is developed for single proppants and binary mixtures which predicts permeability as a function of stress, grain size, material, and weight fraction. One key conclusion is that for a binary mixture of proppants, the mixture permeability will not generally be a weighted linear combination of the pure proppant permeabilities. In other words, the permeability of a mixture comprised of 50% (by weight) of one component and 50% of the second component will generally not be halfway between the permeabilities of the single components. A hypothesis is presented which posits that there are threshold weight fractions for each proppant pair that control the permeability of the mixture.