The paper presents a model of porosity and permeability change in a proppant pack initially containing spherical particles. Three assumptions were formulated for its development: proppant volume remains constant during compression; the number of channels through which liquid is filtered remains constant; maintaining the geometric similarity of the channels during compression. In accordance with the assumptions, the dependence of porosity on the deformation of the proppant pack was derived, the concept of a dimensionless porosity complex was introduced. Porosity complex contains the initial porosity and porosity after deformation, and proppant permeability depends on porosity complex linearly. The model was verified based on the results of tests to determine the permeability and conductivity of the proppant pack under various compressive stresses, carried out on equipment using methods that meet the standards of API RP 19C, API RP 60 and API PR 61. The test results of 115 proppants were used, which showed no signs of methodological errors in the measurements, and were submitted by various manufacturers from Russia and abroad. It is shown that the model satisfactorily describes the main features of the deformation of the proppant pack and changes in its permeability from small compressive stresses to 55 MPa (8000 psi), and is significantly better than the Kazeny-Karman formula.
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