A new well test model for two-region heavy oil thermal recovery considering gravity override and heat loss

Abstract

In order to investigate the effect of gravity override and heat loss on well test interpretation for heavy oil thermal recovery, a two-region efficient wellbore radius mathematical model is established, considering gravity override and heat loss effect under the condition of oblique steam front and based on the idea of multiple-layer reservoir models. The analytical solutions of the model in Laplace space and the solution in real space are derived through Laplace transform and Stehfest numerical inversion arithmetic, respectively. The typical curves for well test interpretation are plotted. The effects of some parameters on the typical curves are analyzed such as steam condense coefficient, dimensionless thickness, steam front angle, etc. The results show that the degree of gravity override and heat loss can be responded by the characteristics of typical curves, mainly by the derivative curves, such as delay time of the first horizontal section, the start time of second peak and the second horizontal section, as well as the value of the second horizontal section of the derivative curves. The model can be used further to treat the problems of non-linear gravity override front and vertically heterogeneous reservoirs. 摘要: ： 为了研究重力超覆及热损失对稠油油藏试井分析的影响，基于多层油藏模型建立了斜直线蒸汽前缘条件下考虑重力超覆及热损失的两区有效井径数学模型。应用Laplace变换求得井底压力在Laplace空间的解析解，利用Stehfest数值反演方法得到实空间解，并绘制了试井典型曲线。分析了冷凝系数、无量纲油层厚度、前缘倾角对典型曲线的影响。研究表明，不同的重力超覆程度和热损失程度在试井典型曲线中均有明显反映，主要表现为导数曲线第1个水平段持续时间不同、第2个波峰及第2个水平段出现时间不同以及第2个水平段数值不同。该方法可进一步用于研究非直线重力超覆前缘及油藏纵向非均质问题。图6参15 Key words: heavy oil reservoir, gravity override, heat loss, thermal recovery, well testing