Partially Penetrating Vertical Fractures: Pressure Transient Behavior of a Finite-Conductivity Fracture

Abstract

ABSTRACT A semianalytical solution was developed for the transient flow behavior of a reservoir with a well intersecting a partially-penetrating vertical fracture of finite conductivity. The transient pressure behavior of a well in this kind of system consists mainly of three flow periods: 1) the early time, 2) the infinite acting and 3) the pseudoradial flow periods. The results of this study show that the flow behavior of the partially-penetrating fracture during the early time period is equivalent to that of a totally-penetrating fracture. This period consists of a bilinear flow period for low conductivity fractures, and of a linear reservoir flow period for moderate to highly-conductive fractures. The onset of the infinite-acting flow period is directly proportional to the square of the dimensionless fracture height, which is defined as the ratio between the fracture height and the fracture half length. The results show that as the value of this ratio becomes small, the infinite-acting flow period starts at very early times,such that the bilinear and the linear reservoir flow periods might not appear in the well response for practical values of time. The approximate start of the pseudo-radial flow period does not depend significantly on the fracture conductivity, on the fracture penetration ratio, or on the dimensionless fracture height, for moderate to highly conductive fractures, and for fracture penetration ratios larger than about 0.2. The effect of the dimensionless fracture height on the pressure response of a partially-penetrating fractured well becomes negligible for penetration ratios larger than about 0.8. The vertical location of the fracture affects the behavior of the well only after the upper and/or lower boundaries of the reservoir become noticeable in the pressure response of the well. The same solutions are found for the early time and for the infinite-acting flow periods, until the boundary effects become evident.