Effects of Fracture Boundary Conditions on Matrix-fracture Transfer Shape Factor |
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Authors: | Hassan Hassanzadeh Mehran Pooladi-Darvish |
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Institution: | (1) Department of Chemical & Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada, T2N 1N4 |
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Abstract: | The matrix-fracture transfer shape factor is one of the important parameters in modeling naturally fractured reservoirs. Four
decades after Warren and Root (1963, SPEJ, 245–255.) introduced the double porosity concept and suggested a relation for it, this parameter is still not completely
understood. Even for a single-phase flow problem, investigators report different shape factors. This study shows that for
a single-phase flow in a particular matrix block, the shape factor that Warren and Root defined is not unique and depends
on the pressure in the fracture and how it changes with time. We use the Laplace domain analytical solutions of the diffusivity
equation for different geometries and different boundary conditions to show that the shape factor depends on the fracture
pressure change with time. In particular, by imposing a constant fracture pressure as it is typically done, one obtains the
shape factor that Lim and Aziz (1995, J. Petrolean Sci. Eng. 13, 169.) calculated. However, other shape factors, similar to those reported in other studies are obtained, when other boundary
conditions are chosen. Although, the time variability of the boundary conditions can be accounted for by the Duhamel’s theorem,
in practice using large time-steps in numerical simulations can potentially introduce large errors in simulation results.
However, numerical simulation models make use of a stepwise approximation of this theorem. It is shown in this paper that
this approximation could lead to large errors in matrix-fracture transfer rate if large time-steps are chosen. |
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Keywords: | shape factor fractured reservoirs matrix block matrix-fracture boundary condition |
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