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Research Papers: Petroleum Engineering

A General Boundary Integral Solution for Fluid Flow Analysis in Reservoirs With Complex Fracture Geometries

[+] Author and Article Information
Miao Zhang, Luis F. Ayala

Department of Energy and Mineral Engineering,
The Pennsylvania State University,
University Park, PA 16802

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 19, 2017; final manuscript received December 4, 2017; published online January 22, 2018. Assoc. Editor: Reza Sheikhi.

J. Energy Resour. Technol 140(5), 052907 (Jan 22, 2018) (15 pages) Paper No: JERT-17-1373; doi: 10.1115/1.4038845 History: Received July 19, 2017; Revised December 04, 2017

Modeling fractured reservoirs, especially those with complex, nonorthogonal fracture network, can prove to be a challenging task. This work proposes a general integral solution applicable to two-dimensional (2D) fluid flow analysis in fractured reservoirs that reduces the original 2D problem to equivalent integral equation problem written along boundary and fracture domains. The integral formulation is analytically derived from the governing partial differential equations written for the fluid flow problem in reservoirs with complex fracture geometries, and the solution is obtained via solving system of equations that combines contributions from both boundary and fracture domains. Compared to more generally used numerical simulation methods for discrete fracture modeling such as finite volume and finite element methods, this work only requires discretization along the boundary and fractures, resulting in much fewer discretized elements. The validity of proposed solution is verified using several case studies through comparison with available analytical solutions (for simplified, single-fracture cases) and finite difference/finite volume finely gridded numerical simulators (for multiple, complex, and nonorthogonal fracture network cases).

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Figures

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Fig. 1

(a) Actual reservoir configuration and (b) BEM discretized system

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Fig. 2

The combined BEM-FVM matrix

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Fig. 3

Well pressure responses in infinite-large reservoirs under different fracture conductivity scenarios

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Fig. 4

Well rate responses in various size reservoirs under finite fracture conductivity (CFD = 5)

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Fig. 5

Well pressure responses in various size reservoirs under infinite fracture conductivity

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Fig. 6

Reservoir and well configuration

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Fig. 7

Production rate and cutline pressure profile comparisons

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Fig. 8

Pressure distribution comparison for t = 1 day

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Fig. 9

(a) Finite element discretization in comsol (2243 elements), and (b): Discretized BEM-FVM model in this work (117 elements)

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Fig. 10

Cutline location (a) and pressure comparison (b) along the cutline

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Fig. 11

Production rate comparison between comsol and this work

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Fig. 12

Pressure distribution comparison under various production times

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Fig. 13

Boundary element discretization with constant elements

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Fig. 14

Local coordinate system for integration

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Fig. 15

Special cells in finite volume fracture model

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