Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture

L., Heber Cinco

doi:10.2118/6014-pa

Cited by 608 publications

(275 citation statements)

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“…The two equations are coupled by the fluid flow between matrix (subscript m) and fracture (subscript F), q F (t) (see, for example, Cinco-Ley et al, 1978 …”

Section: Governing Equations For the Hydraulics Of A Fractured Wellmentioning

confidence: 99%

“…F is the classical definition of dimensionless time for an infinite reservoir adapted for the flow in fractures by replacing radial distance r with half-fracture length x F (Cinco- Ley et al, 1978;Earlougher, 1977;Matthews and Russell, 1967). Furthermore, the dimensionless fracture conductivity is defined by…”

Section: Dimensionless Formulationmentioning

confidence: 99%

“…The theoretical background of bilinear flow was first presented by Cinco-Ley et al (1978) and Cinco-Ley and Samaniego-V. (1981), who studied the solution of (1) and (2) using a two-dimensional numerical model and Laplace transform, respectively. They demonstrated that the pressure in a vertically fractured well producing at constant flow rate is proportional to the fourth root of time in the bilinear flow regime.…”

Section: Previously Presented Solutions For Bilinear Flowmentioning

confidence: 99%

“…In contrast, fluid flow and pressure propagation in fractures is accompanied by fluid exchange with a permeable rock matrix, a rather complex problem for mathematical treatment. A first analytical solution was presented in the context of well testing (Cinco-Ley et al, 1978) that applies to the case of fluid production from boreholes subsequent to hydraulic fracturing (for the simplified geometry of a single fracture aligned with a borehole, see Fig. 1a).…”

mentioning

confidence: 99%

“…1a). Cinco-Ley et al (1978) simplified the flow field as a superposition of two fields of parallel flow: one in the fracture and one in the rock matrix, the latter perpendicular to the fracture plane (see Fig. 1b).…”

mentioning

confidence: 99%

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Two-dimensional numerical investigations on the termination of bilinear flow in fractures

Jung

Renner

2013

Solid Earth

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Abstract. Bilinear flow occurs when fluid is drained from a permeable matrix by producing it through an enclosed fracture of finite conductivity intersecting a well along its axis. The terminology reflects the combination of two approximately linear flow regimes: one in the matrix with flow essentially perpendicular to the fracture, and one along the fracture itself associated with the non-negligible pressure drop in it. We investigated the characteristics, in particular the termination, of bilinear flow by numerical modeling allowing for an examination of the entire flow field without prescribing the flow geometry in the matrix. Fracture storage capacity was neglected relying on previous findings that bilinear flow is associated with a quasi-steady flow in the fracture. Numerical results were generalized by dimensionless presentation. Definition of a dimensionless time that, other than in previous approaches, does not use geometrical parameters of the fracture permitted identifying the dimensionless well pressure for the infinitely long fracture as the master curve for type curves of all fractures with finite length from the beginning of bilinear flow up to fully developed radial flow. In log-log scale the master curve's logarithmic derivative initially follows a 1/4-slope straight line (characteristic for bilinear flow) and gradually bends into a horizontal line (characteristic for radial flow) for long times. During the bilinear flow period, isobars normalized to well pressure propagate with the fourth and second root of time in fracture and matrix, respectively. The width-to-length ratio of the pressure field increases proportional to the fourth root of time during the bilinear period, and starts to deviate from this relation close to the deviation of well pressure and its derivative from their fourth-root-oftime relations. At this time, isobars are already significantly inclined with respect to the fracture. The type curves of finite fractures all deviate counterclockwise from the master curve instead of clockwise or counterclockwise from the 1/4-slope straight line as previously proposed. The counterclockwise deviation from the master curve was identified as the arrival of a normalized isobar reflected at the fracture tip 16 times earlier. Nevertheless, two distinct regimes were found in regard to pressure at the fracture tip when bilinear flow ends. For dimensionless fracture conductivities T D < 1, a significant pressure increase is not observed at the fracture tip until bilinear flow is succeeded by radial flow at a fixed dimensionless time. For T D > 10, the pressure at the fracture tip has reached substantial fractions of the associated change in well pressure when the flow field transforms towards intermittent formation linear flow at times that scale inversely with the fourth power of dimensionless fracture conductivity. Our results suggest that semi-log plots of normalized well pressure provide a means for the determination of hydraulic parameters of fracture and matrix after shorter test duration ...

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“…The two equations are coupled by the fluid flow between matrix (subscript m) and fracture (subscript F), q F (t) (see, for example, Cinco-Ley et al, 1978 …”

Section: Governing Equations For the Hydraulics Of A Fractured Wellmentioning

confidence: 99%

Section: Dimensionless Formulationmentioning

confidence: 99%

Section: Previously Presented Solutions For Bilinear Flowmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Two-dimensional numerical investigations on the termination of bilinear flow in fractures

Jung

Renner

2013

Solid Earth

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Finite element analysis for a finite conductivity fracture in an infinite poroelastic medium

Li¹

1999

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYIn the technology of oil recovery, oil production rate can be increased by generation of a vertical conductive fracture adjacent to the well-bore. In this paper the seepage flow and isothermal deformation in both the oil formation and the fracture are studied by modelling the formation as a two-dimensional infinite poroelastic medium and the conductive fracture as a one-dimensional poroelastic material, saturated by a one-phase compressible fluid. The plane strain condition is employed. Solutions for a growing conductive fracture and a stationary conductive fracture in the infinite medium are obtained by means of the finite element method based on a variational principle for the formation which can impose the governing equations of the fracture. Infinite elements are used outside the finite element domain. Numerical results indicate that the injection rate, the applied pressure and the crack mouth opening displacement at the well-bore oscillate during the propagation of the conductive fracture. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture. Finally, a new definition of the conductivity coefficient for the conductive fracture is presented.

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Hydraulic Fracturing

Valkó

2014

Kirk-Othmer Encyclopedia of Chemical Technology

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Hydraulic fracturing is a well completion/stimulation technique that became the focus of attention because of its significance in the exploitation of unconventional oil and gas reserves. This article starts with a brief history of the operation, followed by a discussion of its unique role in productivity enhancement. Following the overview of materials, equipment, and procedures involved, a review of the diagnostics and other evaluation methods, as well as an outline of the current modeling efforts, will be discussed. One section provides a glimpse into the newest trends in completion hardware, highlighting multistage fracture treatment systems developed for long horizontal wells. In the last section, the commercial and environmental impacts of the technology are considered. The article concludes that hydraulic fracturing has substantially widened the spectrum of choices communities face in arbitrating among potential energy supply options, and hence, it will continue flourishing in the long term.

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Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture

Cited by 608 publications

References 3 publications

Two-dimensional numerical investigations on the termination of bilinear flow in fractures

Two-dimensional numerical investigations on the termination of bilinear flow in fractures

Finite element analysis for a finite conductivity fracture in an infinite poroelastic medium

Hydraulic Fracturing

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