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Abstract

Summary

The modeling of oil and gas production processes such as hydraulic fracturing or oil displacement requires coupled description of free flow and flow in a porous medium.

In this work we used Stokes’ equation for free viscous flow coupled with Brinkman’s equation for liquid flow in a porous medium. The latter is differential equation of the same order as Stokes’ equation. Both equations together with continuity equation and proper boundary conditions present mathematically correct formulation of the coupled flow boundary value problem. For two-dimensional and axial symmetric geometry we showed analytically that the solution of Brinkman equation totally coincides with Darcy’s velocity in the whole region of a porous medium, except for a thin layer adjacent to impermeable wall. The thickness of the mentioned layer depends on specific permeability of porous material.

Stokes-Brinkman model was used for simulation of flows in finite dead-end channel with porous walls. This model is aimed at the simulation of flow through a hydraulic fracture or flow in a natural crack inside a porous medium. The results were compared with experiments fulfilled at the Institute of Geospheres Dynamics RAS and have demonstrated excellent agreement.

The work is partially supported by RFBR (grant #14-08-00893a) and CRDF-Global (grant #FSAX-14-60158-0).

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.20141819
2014-09-08
2024-04-25

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Modeling Of Flow in a Fracture Inside Porous Medium
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