Upscaling in Vertically Fractured Oil Reservoirs Using Homogenization |
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Authors: | Hamidreza Salimi Hans Bruining |
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Institution: | (1) Mechanical Engineering Department, Thapar Institute of Engineering and Technology, Patiala, 147004, India;(2) Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, 208016, India |
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Abstract: | Flow modeling in fractured reservoirs is largely confined to the so-called sugar cube model. Here, however, we consider vertically
fractured reservoirs, i.e., the situation that the reservoir geometry can be approximated by fractures enclosed columns running
from the base rock to the cap rock (aggregated columns). This article deals with the application of the homogenization method
to derive an upscaled equation for fractured reservoirs with aggregated columns. It turns out that vertical flow in the columns
plays an important role, whereas it can be usually disregarded in the sugar cube model. The vertical flow is caused by coupling
of the matrix and fracture pressure along the vertical faces of the columns. We formulate a fully implicit three-dimensional
upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach. As found previously for
the sugar cube model, the Peclet number, i.e., the ratio between the capillary diffusion time in the matrix and the residence
time of the fluids in the fracture, plays an important role. The gravity number plays a secondary role. For low Peclet numbers,
the results are sensitive to gravity, but relatively insensitive to the water injection rate, lateral matrix column size,
and reservoir geometry, i.e., sugar cube versus aggregated column. At a low Peclet number and sufficiently low gravity number,
the effective permeability model gives good results, which agree with the solution of the aggregated column model. However,
ECLIPSE simulations (Barenblatt or Warren and Root (BWR) approach) show deviations at low Peclet numbers, but show good agreement
at intermediate Peclet numbers. At high Peclet numbers, the results are relatively insensitive to gravity, but sensitive to
the other conditions mentioned above. The ECLIPSE simulations and the effective permeability model show large deviations from
the aggregated column model at high Peclet numbers. We conclude that at low Peclet numbers, it is advantageous to increase
the water injection rate to improve the net present value. However, at high Peclet numbers, increasing the flow rate may lead
to uneconomical water cuts. |
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