Performance of a horizontal well in a bounded anisotropic reservoir: Part II: Performance analysis of well length and reservoir geometry

Abstract

Evaluation of the performance of horizontal wells is an important aspect in the enhancement of their productivity. This study provides mathematical computations, and analysis for theoretical well and reservoir considerations. The study investigates how well design and reservoirs geometry affect the overall performance of a horizontal well in a completely bounded reservoir throughout its productive life. A horizontal well in a rectangular reservoir with completely sealed boundaries is considered and the effect of dimensionless well length L D \hspace{.25em}{L}_{\text{D}} , dimensionless reservoir length x eD \hspace{.25em}{x}_{\text{eD}} , and dimensionless reservoir width y eD {y}_{\text{eD}} on the pressure response over a given period of production using dimensionless time t D {t}_{\text{D}} is studied. The mathematical model used was derived using source and Green’s functions presented in part I of this study. Appropriate well and reservoir parameters are considered and the respective dimensionless parameters are computed which are then used in computing dimensionless pressure P D {P}_{\text{D}} and its dimensionless pressure derivative P D ′ \hspace{.25em}{P}_{\text{D}}^{^{\prime} } . From the computations, the results obtained are analysed in diagnostic log–log plots with a discussion of the flow periods. The results obtained indicate that an increase in dimensionless well length decreases pressure response during the infinite-acting flow at early times and during transition flows at middle time but increases the pressure response during the pseudosteady state flow at late times. The dimensionless reservoir width and length are observed not to influence dimensionless pressure response during the infinite-acting flow at early times and during the transition flows at middle time, only affecting the prevalence time of the flow periods. However it is observed that during the pseudosteady state flow at late times, dimensionless pressure response reduces with increased dimensionless reservoir length and width.