Pseudosteady-State Analysis of Finite Conductivity Vertical Fractures

Abstract

A new solution methodology for pseudosteady-state behaviorof a well with a finite-conductivity vertical fracture isformulated using a reservoir/fracture domain resistivityconcept. The formulation encompasses a transformed resistivitydomain based on an equivalent or effective wellbore radius. Theresulting pseudosteady solution is presented in the form of thedimensionless productivity index (JD). Some of the major advantages of this pseudosteady solutionfor finite-conductivity vertical fractures are 1) the methodologyis based on fundamental principles, 2) the solution is analyticaland easily implemented, 3) the equations are formulated forrectangular reservoirs, 4) the model includes wellbore flow(i.e., wellbore radius effect) which is important for low-conductivity fractures, and 5) the formulation accounts for apiece-wise continuous linearly varying fracture conductivityincluding: proppant tail-ins, over-flushing, pinch zones, chokedflow (internal), and external skin mechanisms. The stimulation ratios for finite-conductivity fractures withan undamaged well are compared with those of McGuire and Sikora[1] (1960), and Holditch[2] (1974). The accuracy andvalidity of the pseudosteady model is also illustrated bycomparison with the works of Prats[3,4] (1961,1962), Gringartenet al.[5,6] (1974), Cinco-Ley et al.[7–10] (1978,1981), Barker and Ramey[11] (1978), and Valko and Economides[12] (1998). A summary of the fundamental building blocks, effectivewellbore radius concept, pseudo-skin functions and fractureskin are discussed. An improvement to Gringarten'sdimensionless productivity solution for infinite-conductivityvertical fractures in rectangular closed reservoirs is alsopresented. Introduction Since hydraulic fracturing is one of the most widely used andaccepted methods for enhancing well performance, pressuretransient analysis of fractured reservoirs has become aninvaluable tool in determining the productivity increase andbenefits of fracturing. McGuire and Sikora[1] (1960) published a classic paper on"The Effect of Vertical Fractures on Well Productivity"whereby they used an electric analogue computer to study theeffect of finite-conductivity vertical fractures on theproductivity of wells in expanding fluid-drive reservoirs (i.e., pseudosteady-state behavior). These curves are still one of themost widely referenced and used diagnostic plots forproductivity forecasting. The McGuire and Sikora curvesdemonstrate the productivity increase benefits from hydraulicfracturing as a function of fracture length (penetration) andrelative fracture conductivity.

Analytical solution and mechanisms of fluid production from hydraulically fractured wells with finite fracture conductivity

“…In other words, ξ = constant are not isobars when C fD is finite. Another very useful interpretation of the production rate formula (21) is that a finite dimensionless fracture conductivity reduces production by pushing the outer boundary from the confocal ellipse ξ = ξ e to a larger confocal elliptic effective outer boundary ξ = ξ e,eff with the same pressure drawdown (for brevity, we have neglected ξ 1 in what follows):…”

“…The equivalent well radius was obtained from consideration of special situations or completely empirical in nature [15,40]. These formulas are ad hoc in nature, and they should never be confused with the exact analytical formula of (21). If anything, the exact analytical formula of (21) should be used to derive the equivalent well radius to be used in the radial flow-rate formula.…”

“…This observation is consistent with our conclusion in Sect. 3 that the overall production rate only depends on the confocal elliptical flow component of the reservoir flow [relation (21)]. For convenience, we define a dimensionless flux on the fracture surfaceq(η):…”

“…These types of analyses for hydraulically fractured wells have been carried out for more than 50 years. Representative of this voluminous literature are [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Some of these studies have included such factors as rectangular and elliptical fracture geometries, fully and partially penetrated fractures, near well formation damage, and anisotropy of the reservoir.…”

Gas Condensate Flow Around Hydraulically Fractured Wells

“…Most of the available methods described in the literature for estimation of fracture skin or effective wellbore radius of a HFW were developed for single phase Darcy flow systems (McGuire and Sikora 1960;Prats 1961;Cinco-Ley and Samaniego-V 1977;Cinco-Ley et al 1978;Romero et al 2003;Meyer and Jakot 2005).…”