New Solutions for Wells With Finite-Conductivity Fractures Including Wellbore Storage and Fracture-Face Skin

Abstract

SPE Members Abstract This paper presents new solutions for wells with finite-conductivity fractures including wellbore storage and fracture-face skin damage. An infinite-conductivity fracture is included as a limiting case. The new solutions are obtained numerically by modeling a well with an elliptical finite-conductivity fracture in an elliptically composite reservoir. The new solutions are as accurate as published analytical solutions, which are available only for limiting cases. In addition, this study finds and confirms that an "apparent" skin results in a well with a finite-conductivity fracture and fracture-face skin; this "apparent" skin is larger than the true fracture-face skin. The new solutions presented in this paper can be used to analyze production and well-test data for wells with finite-conductivity fractures including wellbore storage and fracture-face skin. Examples are provided. Introduction A hydraulic fracture can be characterized as finite conductivity, infinite conductivity, or uniform flux. For transient pressure analysis of hydraulically fractured wells, several solutions have been published in the literature. Gringarten et al. and Cinco et al. presented transient pressure solutions for wells with infinite and finite conductivity fractures respectively. These solutions can be considered as classic semianalytical solutions of hydraulic fracture problems. In Cinco et al.'s model, a rectangular fracture is assumed. In both studies, the effects of wellbore/fracture storage and fracture/formation damage were excluded. In a later study, Cinco et al. considered the effects of wellbore storage and damage on the transient pressure behavior of hydraulic fractures. They considered an infinitesimal skin around the fracture. The skin was handled as a dimensionless "steady-state skin factor". As the authors noted briefly and without specific detail, their results and solution method were not internally consistent. Thus, it seems that the problem of hydraulic fractures with fracture-face skin effect was not resolved. In another study, Cinco et al. compared finite conductivity fracture cases with damaged infinite conductivity fracture cases. They considered both choked fracture damage and near-fracture fluid loss damage. Pressure behavior for both damage cases looks similar in pressure-time graphs, but is significantly different from that for finite conductivity fractures. The authors did not consider fracture-face skin damage for finite conductivity fractures. Kuchuk et al., Obut et al., and Stanislav et al. studied transient pressure behavior of wells with elliptical infinite conductivity fractures in homogeneous or elliptically-composite infinite-acting reservoirs. The results are summations of infinite series of Mathieu functions in terms of the Laplace variable. Numerical inversion is then applied to obtain pressure solutions. These studies did not deal with finite conductivity fractures and did not include wellbore storage and skin effects. Recently, Riley et al. obtained transient solutions for elliptical finite conductivity fractures. Their solutions are expressed in terms of the Laplace variable. Their solutions are quite complex due to the nature of this finite conductivity fracture problem. This study did not include wellbore storage and skin effects. P. 221^