Abstract
A thermodynamically consistent model of a double porosity medium with scattered fracture of a matrix is developed. Fracture formation in the matrix is facilitated by the anomalously high reservoir pressure. It is assumed that that damage development in the matrix enhances mass transfer between the subsystems of a double porosity medium. By the example of the problem of productivity of a long cylindrical well, the influence of the abnormal high reservoir pressure on the fluid flow rate is qualitatively demonstrated.
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