Performance of Finite-Conductivity, Vertically Fractured Wells in Single-Layer Reservoirs

Abstract

Summary Although even a perfunctory survey of the literature suggests that considerable information is available on the response of finite-conductivity fractures in single-layer systems, the influence of the settling of propping agents and the effect of fracture height on the well response need to be examined. These topics are examined in this paper. We suggest methods to analyze well performance when the fracture paper. We suggest methods to analyze well performance when the fracture conductivity is a function of fracture height and fracture length. The performance of wells with fracture height greater than the formation performance of wells with fracture height greater than the formation thickness is documented. The consequences of being unable to contain the fracture within the pay zone are also examined. Although incidental to this study, we found that solutions presented by various authors are not in agreement for all time ranges. In this paper, we discuss a systematic procedure to obtain a grid (mesh) so that paper, we discuss a systematic procedure to obtain a grid (mesh) so that accurate results are obtained by a finite-difference model. This procedure can be used for both two-dimensional (2D) and three-dimensional (3D) problems. problems. Introduction This paper examines the performance of wells intercepting finite-conductivity vertical fractures. Although much work has been presented in this area of pressure analysis, several aspects of well behavior have yet to be examined. We examine some of these topics. In this work we examine the influence of vertical variations in fracture conductivity on well performance. Concerns regarding the effect of the settling of propping agents on well productivity addressed in this paper complement our work on the influence of lateral variations in fracture conductivity. We also examine situations where the fracture extends below and/or above the productive interval. We consider two possibilities:the fracture length is assumed to be fixed and the fracture height is variable (volume of fracture treatment is variable); andthe fracture volume is assumed to be fixed (the product of the fracture half-length and fracture height is assumed to be constant). The latter case is of interest if one is not able to contain the fracture within the pay zone of interest. In the former case, we show that this approach provides a means to increase the effective fracture conductivity. These topics have not previously been examined in the literature. Verification of the finite-difference model used in this study consumed a significant portion of the time spent in this study. Although some works have reported problems in obtaining accurate solutions, no guidelines for choosing a grid (mesh) for this problem are available. We give empirical guidelines for systematically choosing a grid to obtain accurate solutions. We believe that these guidelines will significantly reduce the time spent by researchers in developing their own models and consider it an important contribution. We also present methods to modify grids developed for a given set of conditions if the fracture and/or reservoir dimensions are changed.