Reservoir Engineering – General - A Numerical Method for Computing Recovery of Oil by Hot Water Injection in a Radial System

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus: