Calculation of Well Productivity in a Reservoir Simulator (II)

Abstract

Abstract Conventional simulators calculate the well productivity using Peaceman's equation[l] for equivalent block radius and the well block pressure. This is generally acceptable for most vertical and horizontal wells. However, no formulation is available for slanted wells. Even for vertical and horizontal wells in which block aspect ratios are far from unity or where the well completion interval is short or the well is located close to a reservoir boundary or other wells, the existing formulations can give erroneous answers. In our previous paper, a novel method was introduced for calculating very accurately the productivity of wells of any deviation (0–90) for a homogeneous reservoir. In this paper, we present a more general solution for general well position and applicable to multiple wells and heterogeneous reservoirs. A novel method is presented to convert the heterogeneous model to an anisotropic but uniform permeability model before applying the new analytical technique, in conjunction with a numerical simulator. The analytical model developed for this purpose is coupled with a numerical simulator to produce the necessary parameters needs for simulation of well performance in a conventional simulator. The results will have a wide field application for horizontal, vertical and deviated wells. Introduction In the petroleum industry, it is becoming common practice to increase oil and gas productivity by drilling highly deviated and increasingly horizontal wells. In the past few decades, numerous studies have been reported on the modelling of vertical wells. There have also been some studies of slanted wells. In view of the recent popularity of drilling deviated and horizontal wells, more effort has been spent on the modelling of their production and pressure performance. Several authors have recently developed analytical solutions for calculating productivity of a horizontal well, and some have published formulas based on various assumptions and approximations for a slanted well. Peaceman introduced a new formulation in his recent paper to calculate the equivalent block radii (ro,m) for a number of wells producing simultaneously in a finite size reservoir. He demonstrated that the value of ro, m for any well m in a reservoir with Nw wells is a function of (qk/qm), where qm is the flowrate of well m and qk is the flowrate for other wells. In other words, ro, m is affected by the flowrate of any other well in the reservoir. Therefore, the use of his 1983 formula produces erroneous results in multiple well cases. The effect of the distances of other wells were not considered. Slanted wells were not addressed. P. 441