Evaluation of the influence of a dimensionless threshold pressure gradient on deviation of filtration from classical filtration law

Depletion of hydrocarbon reserves in reservoirs with high and medium permeability increases the proportion of low permeability reservoirs in which nonlinear filtration effects are observed: at low pressure gradients, filtration does not obey the classical filtration law (Darcy’s law). One of the methods to describe the nonlinear filtration effects is to apply the filtration law with a threshold pressure gradient (TPG). The influence of this parameter on the deviation of filtration from Darcy's law has not been previously analyzed. The aim of this work is to evaluate this effect of the TPG. Piezoconductivity equations are nondimensionalized and solved according to the classical filtration law and the filtration law with TPG for plane radial flow and constant well pressure. In the framework of the classical filtration law, the piezoconductivity equation is solved by applying a self-simulated variable. Using the filtration law with TPG, the conductivity equation solution is solved by the method of integral relations. Relations between dimensionless production rate and dimensionless time for both filtration laws are found from the solved piezoconductivity equations. To prove the identity of the obtained solutions, a comparative analysis is performed for a threshold pressure gradient equal to zero. Comparison of production decline curves for classical filtration law and filtration law with TPG at various values TPG is carried out. The relation between the shapes of the production decline curves shape and various dimensionless TPG values is analyzed. With increasing dimensionless TPG, the influence of nonlinear effects on filtration increases: the nonlinear filtration effects become apparent earlier, and the production decline curves for the filtration law with TPG deviate greater from the production decline curve for the classical filtration law.