Influence of Fracture Heterogeneity and Wing Length on the Response of Vertically Fractured Wells

Abstract

Abstract A finite-conductivity vertical fracture intersecting a well produced at a constant rate or at a constant pressure is considered. The pressure (or rate) response is obtained from a numerical model. Two aspects of this problem are considered:variable fracture conductivity andunequal fracture wing lengths. The first part of this paper examines the influence of fracture conductivity on the well response. In practice, the fracture conductivity is a decreasing function of distance from the wellbore. If the fracture conductivity decreases monotonically with distance from the wellbore, then at late times the variable fracture conductivity solutions behave like a constant-conductivity fracture, with conductivity equal to the arithmetic average of the conductivity. At early times the response is identical to that of a constant-conductivity fracture, corresponding to the highest conductivity of the fracture. For the variable fracture conductivity case, the bilinear flow period characterized by a one-quarter slope line may be obscured. Thus, analysis of short-time data can be difficult. We also consider situations where the fracture conductivity does not decrease monotonically with distance. The response for these cases is discussed in detail. The second part of the paper examines the effect of unequal wing lengths on the pressure response. We delineate conditions under which the effect of wing length on the response will become dominant. We discuss the influence of wing length on both early- and long-time data. Introduction To our knowledge no quantitative information is available in the literature regarding the effect of nonuniform fracture conductivity on the transient behavior of a fractured well. (In this work, nonuniform or variable fracture conductivity refers to the situation where the fracture conductivity is a function of distance from the wellbore.) The fracture is usually considered to be of constant width and constant permeability. However, in virtually all situations, fractures are designed such that the fracture conductivity is not uniform. The principal thrust of the first part of this paper concerns the influence of nonuniform (variable) fracture conductivity on the transient behavior of the well. We evaluate the consequences of neglecting variations in fracture conductivity when constant (uniform) conductivity solutions are used to determine the fracture half-length. We found that the effect of variable conductivity on well performance could be quantified in general terms if the conductivity decreases uniformly from the wellbore to the tip of the fracture. The behavior of a fractured well that is plugged is examined. The effect of a damaged zone (within the fracture) adjacent to the wellbore is also examined. Virtually all studies on transient pressure response assume that the well is located at the center of the fracture-i.e., the fracture wing lengths are equal. SPEJ P. 219^