Numerical investigations on compressible non-linear fluid flow associated with a stress -sensitive fractured reservoir
18 Jun 2020-Energy Sources Part A-recovery Utilization and Environmental Effects (Taylor & Francis)-pp 1-20
TL;DR: In this article, the authors developed an improved mathematical model to understand the single-phase gas flow in a coupled matrix-fracture fluid mass exchange in a stress-sensitive reservoir.
Abstract: This paper emphasizes on the development of an improved mathematical model to understand the single-phase gas flow in a coupled matrix-fracture fluid mass exchange in a stress-sensitive reservoir a...
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TL;DR: In this paper, a comprehensive geofluid flow model for a well in a subsurface formation was established and solved, and a general solution method for this model and its general solutions were obtained for vertical and horizontal wells in ordinary, fractured and fractured-vuggy formations.
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TL;DR: In this article, an analytical solution for pore pressure coupling with the deformation in a porous medium is developed by taking the quadratic term into account, and a solution for a nonlinear diffusion equation is obtained by setting up a fluid continuity equation according to the mass conservation law rather than from energy principles in terms of volume.
Abstract: When compressible fluid continuity in a fluid-saturated compressible porous medium under transient conditions is considered, we cannot obtain a standard linear diffusion equation in terms of pressure unless we ignore the quadratic terms in the pressure gradient expression, for example [∂p/∂r]2 for cylindrical plane strain coordinates. They are assumed to be so small that their contribution can be ignored in pressure analysis. Thereby, a nonlinear equation can be avoided. During hydraulic fracturing, rapid drawdown, or slug testing, the pressure difference can reach a high value “instantly.” An extremely steep pressure gradient is generated, and it may not be appropriate to neglect quadratic terms. In this paper, an analytical solution for pore pressure coupling with the deformation in a porous medium is developed by taking the quadratic term into account. By Laplace transformation, we obtain a solution for a nonlinear diffusion equation by setting up a fluid continuity equation according to the mass conservation law rather than from energy principles in terms of volume. Deviations from existing solutions are identified in cases of high pressure gradients, and these deviations are related to the compressibility of the pore and injected fluids. It would seem that the new solution gives a more correct early time response in these cases. To calculate the effective stresses and pore pressure, we need to carefully define hydraulic diflfusivity. We have related the coefficients of Biot and Geertsma to those of mass conservation, which are commonly used in hydrology.
34 citations
"Numerical investigations on compres..." refers background in this paper
...The concept of the dual continuum was than extended to fractured petroleum reservoir for pressure transient analysis (Warren and Root 1963)....
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TL;DR: In this paper, an improved mathematical model is suggested that better describes fluid flow through a coupled fracture-matrix system using a dual-porosity approach, which differs from a conventional model as the fracture flow equation contains a hyperbolic term in addition to the conventional dispersive term.
Abstract: The present paper addresses critical issues that describe the transient transfer of stored rock-matrix flow into high-permeable fractures and rate-limited diffusive solute flux into low-permeable rock matrix using a typical dual-porosity approach. An improved mathematical model is suggested that better describes fluid flow through a coupled fracture-matrix system using a dual-porosity approach. The suggested model differs from a conventional model as the fracture flow equation contains a hyperbolic term in addition to the conventional dispersive term. The matrix flow equation contains the coupling term that controls the transient nature of fluid exchange from the stored rock matrix into the hydraulic conductors. The Langmuir sorption isotherm is suggested to describe the limited sorption sites available on fracture walls, while the Freundlich sorption isotherm is recommended to describe the unlimited sorption sites available within the rock matrix. The dispersion mechanism in a coupled fracture-ma...
34 citations
TL;DR: In this article, a nonlinear dual-porosity formulation incorporating a quadratic gradient term in the governing flow equation is presented to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the matrix from the fractures is furnished by assuming a quasi-steady-state flow with the pressure difference between matrix and fractures as a primary unknown.
31 citations
"Numerical investigations on compres..." refers background in this paper
...But the assumption of small pressure gradient results in error in pore pressure prediction in case of hydraulic fracturing, well testing and large pressure drawdown (Bai, Ma, and Roegiers 1994)....
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...Later Bai, Ma, and Roegiers (1994) presented the analytical solution for a naturally fractured reservoir using a decoupled dual-porosity model by incorporating the quadratic gradient term in fracture flow equation and demonstrated that drastic change in pressure occurs at later stages of production....
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TL;DR: In this article, a semi-analytical model of a multiple fractured horizontal (MFH) well with stimulated reservoir volume (SRV) including the quadratic gradient term (QGT) is presented.
22 citations
TL;DR: In this paper, the effects of the quadratic gradient term on the one-phase radial flow equation were analyzed for an oil reservoir with constant diffusivity and compressibility, and it was shown that the standard condition allowing the gradient term to be neglected (crho<<1) is incorrect; pressure should be replaced by a function of the production rate and other reservoir parameters except absolute pressure.
Abstract: Constant-rate analytical solutions of the one-phase radial-flow equation in two dimensions, including effects of the quadratic gradient terms, are derived for an oil reservoir with constant diffusivity and compressibility. In this paper the combinations of compressibility contributions to the various terms are analyzed. It is shown that the standard condition allowing the quadratic gradient term to be neglected (crho<<1) is incorrect; pressure, rho, should be replaced by a function of the production rate and other reservoir parameters except absolute pressure. The effect of the quadratic gradient term, for which quantitative expressions are given for steady-state and semisteady-state flow, may amount to several percent of the pressure drawdown at the wellbore.
21 citations
"Numerical investigations on compres..." refers background in this paper
...It is observed by Finjord and Aadnoy (1989) that in case of large pressure drawdowns near the wellbore, the addition of nonlinear term can influence the wellbore pressure by 100 psi and it should not be misinterpreted as a rate dependent skin effect....
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