Model of nonlinear single-phase filtration in a proppant pack at high Reynolds numbers

UDK: 532.546.3, 539.383

DOI: 10.24887/0028-2448-2025-7-94-98

Key words: proppant, Reynolds number, filtration, turbulent flow, effective permeability

Authors: I.R. Safiullin (RN-BashNIPIneft LLC, RF, Ufa), N.A. Onegov (RN-BashNIPIneft LLC, RF, Ufa, Ufa State Petroleum Technologica)University, RF, Ufa ), S.S. Tsybin (RN-BashNIPIneft LLC, RF, Ufa, Ufa State Petroleum Technological), M.S. Antonov (RN-TECHNOLOGIES, RF, Moscow, Ufa State Petroleum Technological University, RF, Ufa)

The paper presents a model of dependence of effective permeability of proppant pack on Reynolds number during fluid flow in pore space. In the process of model development, the results of measurements of β-factor and permeability coefficient for different proppants were analyzed, as well as the results of measuring the dependence of effective permeability of proppants at high values of Reynolds number of flow (almost before the occurrence of turbulent regime) with the use of the unique Stim-Lab equipment (USA). These data were published in the period from 2004 to 2012. An expression for the dependence of the effective permeability on the Reynolds number and the value of the β-factor was proposed, which satisfactorily describes the experimental results for a wide range of ceramic proppants. Recommendations are given for the use of the obtained results in various cases encountered in practice. For the calculation, it is possible to use parameters measured by standard means, which can be considered an advantage over the Barree and Conway model, which requires using proppant parameters determined exclusively on unique equipment (for example, effective permeability at an infinitely high filtration rate). The obtained universal dependence can be useful for specialists calculating the inflow of formation fluids into a well through a hydraulic fracturing crack in the initial periods of operation, as well as the inflow of gas and degassed oil over the entire period of operation.

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