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Research Papers: Petroleum Wells-Drilling/Production/Construction

Modified Extended Finite Element Methods for Gas Flow in Fractured Reservoirs: A Pseudo-Pressure Approach

[+] Author and Article Information
Youshi Jiang

State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation,
Southwest Petroleum University,
Chengdu 610500, China

Arash Dahi-Taleghani

Department of Energy and Mineral Engineering,
Pennsylvania State University,
State College, PA 16801
e-mail: arash.dahi@psu.edu

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received December 19, 2017; final manuscript received January 22, 2018; published online March 29, 2018. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 140(7), 073101 (Mar 29, 2018) (11 pages) Paper No: JERT-17-1723; doi: 10.1115/1.4039327 History: Received December 19, 2017; Revised January 22, 2018

Fluid flow in fractured porous media has always been important in different engineering applications especially in hydrology and reservoir engineering. However, by the onset of the hydraulic fracturing revolution, massive fracturing jobs have been implemented in unconventional hydrocarbon resources such as tight gas and shale gas reservoirs that make understanding fluid flow in fractured media more significant. Considering ultralow permeability of these reservoirs, induced complex fracture networks play a significant role in economic production of these resources. Hence, having a robust and fast numerical technique to evaluate flow through complex fracture networks can play a crucial role in the progress of inversion methods to determine fracture geometries in the subsurface. Current methods for tight gas flow in fractured reservoirs, despite their advantages, still have several shortcomings that make their application for real field problems limited. For instance, the dual permeability theory assumes an ideal uniform orthogonal distribution of fractures, which is quite different from field observation; on the other hand, numerical methods like discrete fracture network (DFN) models can portray the irregular distribution of fractures, but requires massive mesh refinements to have the fractures aligned with the grid/element edges, which can greatly increase the computational cost and simulation time. This paper combines the extended finite element methods (XFEM) and the gas pseudo-pressure to simulate gas flow in fractured tight gas reservoirs by incorporating the strong-discontinuity enrichment scheme to capture the weak-discontinuity feature induced by highly permeable fractures. Utilizing pseudo-pressure formulations simplifies the governing equations and reduces the nonlinearity of the problem significantly. This technique can consider multiple fracture sets and their intersection to mimic real fracture networks on a plain structured mesh. Here, we utilize the unified Hagen–Poiseuille-type equation to compute the permeability of tight gas, and finally adopt Newton–Raphson iteration method to solve the highly nonlinear equations. Numerical results illustrate that XFEM is considerably effective in fast calculation of gas flow in fractured porous media.

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Figures

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Fig. 1

Fluid flow in a fractured porous media

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Fig. 2

Different possible patterns that fractures may have inside an element

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Fig. 3

Relationship curve between pressure and pseudo-pressure

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Fig. 4

Meshes for the cases of different fracture patterns: (a) the straight biwing fracture case and (b) the complex fracture network case

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Fig. 5

Convergence curve. As the mesh becomes finer, the relative L2 norm error decreases.

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Fig. 6

Pressure distribution (0.1 day). In the both cases, pressure wave covers the whole fracture in a relatively short time: (a) biwing fractures and (b) fracture network.

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Fig. 7

Pressure distribution (1 day). While gas is continuously produced, pressure wave is gradually expanding inside the matrix: (a) biwing fractures and (b) fracture network.

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Fig. 8

Pressure distribution (104.2 days). The bottomhole pressure in the biwing fracture case descends more quickly: (a) biwing fractures and (b) fracture network.

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Fig. 9

Impact of matrix permeability on bottomhole pressure performance. (a) Bi-wing fracture case; as the matrix permeability decreases, the pressure decline curve goes down as a whole. (b) Fracture network case; as the matrix permeability decreases, the pressure decline curve goes down as a whole, but the descent rate is smaller, compared to the bi-wing fracture case.

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Fig. 10

Impact of production rate on bottomhole pressure performance. (a) Bi-wing fracture; as the production rate increases, the bottomhole pressure declines more quickly. (b) Fracture network; as the production rate increases, the pressure decline curve also goes down as a whole, but the descent rate decreases.

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Fig. 11

Impact of fracture pattern on bottomhole pressure performance (semi-log graph). For the fracture network case, the bottomhole pressure declines more slowly, compared to the bi-wing fracture case.

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