Calculation Of Well Productivity In A Reservoir Simulator (I)

Abstract

Abstract One of the objectives of reservoir performance prediction is to determine the number of wells needed for future development of a field. It is known that most of the wells are deviated, especially in offshore environment. It is also known that conventional simulators cannot simulate the performance of slanted wells with acceptable accuracy in many eases. Many simulators cannot calculate the flowing bottom hole pressure of the wells accurately, even for vertical and horizontal wells in which well block aspect ratios are far from unity or where the well completion interval is short or the well is close to the reservoir boundaries. This paper presents formulations with which the flowing bottom hole pressure of wells (hence their productivity) can be accurately calculated for all wells. These will include vertical, horizontal and slanted wells and generally any well whose trajectory is not parallel with the simulation grid. A methodology is presented by which a conventional finite difference simulator can be used together with an analytical model that we have developed to calculate accurate well pressure and productivity for many types of wells. At this stage the solutions we offer cover a single well in an infinite slab reservoir or in a fixed boundary rectangular box shaped reservoir with a single phase fluid and only for homogeneous or anisotropic uniform permeability reservoirs. Research is in progress for other situations. Sensitivity studies on variables such as reservoir rock and fluid properties, simulation gridding, reservoir geometry and well geometry have been conducted. The validity of the new methodology is demonstrated by comparing the results of our analytical method with numerical solutions for cases in which there is no doubt on validity of the numerical results. Comparison is made between our analytical method and those available in the literature. The results demonstrate the superiority of the method. Furthermore, we have developed a new computer program which has coupled our analytical program with a numerical simulator in one package by which the necessary skin factor can be calculated in one run. It is demonstrated that the use of this program eliminates the need for a refined grid and it is less time consuming and much more economical than local grid refinement, where local grid refinement is used only to improve the numerical accuracy and not for inclusion of more detailed geological and petrophysical data. Introduction The flow equation for a bounded radial reservoir which contains compressible liquid may be written as: P. 273