A coupled model for analyzing transient pressure behavior of horizontal drainholes

Conventional horizontal well transient response models are generally based on the line source approximation of the partially penetrating vertical fracture solution1. These models have three major limitations: (i) wellbore pressure is computed at a finite radius outside the source; it is impossible to compute wellbore pressure within the source, (ii) it is difficult to conduct a realistic comparison between horizontal well and vertical fracture productivities, because wellbore pressures are not computed at the same point, and (iii) the line source approximation may not be adequate for reservoirs with thin pay zones. This work attempts to overcome these limitations by developing a more flexible analytical solution using the solid bar approximation. A technique that permits the conversion of the pressure response of any horizontal well system into a physically equivalent vertical fracture response is also presented. A new type curve solution is developed for a horizontal well producing from a solid bar source in an infinite-Acting reservoir by means of Newman's product solution2. Analysis of computed wellbore pressures reveals that error ranging from 5 to 20% was introduced by the line source assumption depending on the value of dimensionless radius (rwD). Computations show that for rwD ≤ 10-4 the transient response of a horizontal well is identical to that of a partially penetrating vertical fracture system, and for rwD > 0.01 the transient response of a horizontal well is indistinguishable from that of a horizontal fracture system. Type-curve plots for the ranges 0.01 ≤ dimensionless length (LD) ≤ 10, and 10-4 ≤ rwD ≤ 1.0 are presented. A dimensionless rate function ( β-function) is introduced to convert the transient-response of a horizontal well into an equivalent vertical fracture response. A step-wise algorithm for the computation of β-function is developed using Duhamel's principle. This provides an easier way of representing horizontal wells in numerical reservoir simulation without the rigor of employing complex formulations for the computation of effective well block radius.