三重介质部分射开渗流模型研究与试井曲线分析

Percolation model of partial penetration in triple-porosity reservoirs and well test analysis

陈方方 贾永禄 张福祥 雷胜林 杨向同 覃芳

Chen Fangfang Jia Yonglu Zhang Fuxiang Lei Shenglin Yang Xiangtong Qin Fang

针对缝洞型碳酸盐岩储层部分射开这一情形,建立了考虑井筒储集效应和表皮效应在封闭顶边界、封闭底边界、定压顶边界和定压底边界的相互组合边界条件下的不稳定渗流物理数学模型。通过Laplace变换和分离变量法对模型进行了求解,再利用Stehfest数值反演得到实空间的解,进而绘制了压力和压力导数双对数样版曲线。从物理渗流机理上对曲线形态特征进行了分析,并划分了流动阶段。研究结果表明:与部分射开相关的参数只影响压力导数曲线的早期形态;若用完全射开模型对部分射开井进行试井解释,将会解释出一个较大的表皮,产生一种井底污染严重的假象而得出不准确的判断;对打开程度较小的部分射开井,若选用完全射开模型进行试井解释,误差较大。所获得的结果可用于研究三重介质缝洞型碳酸盐岩储层中部分射开井的渗流规律,进行压力动态和试井分析。

In view of partial penetration in fractured-vuggy carbonate reservoirs,this paper establishes an unsta-ble mathematical percolation model with wellbore storage and skin effects incorporated under various combina-tions of sealing top boundary,sealing bottom boundary,constant top boundary and constant bottom boundary.La-place transform and variable separation methods are used to obtain solutions of the model,which are turned to real space solutions through Stehfest numerical inversion.Pressure and pressure derivative log-log type curves are drawn up based upon these real space solutions.Flow regime is divided after the characteristic analysis of the type curves based on percolation mechanism.The results show that parameters related to partial penetration affect early-stage shapes of derivative type curves only.When a full-penetration percolation model is applied to well test analysis in a partial penetration well,a bigger skin factor and thus a false image of severe wellbore damage might be generated,leading to inaccurate conclusion or errors.For a relatively low partial penetration well,well test analysis with a complete penetration model may have large error.The results obtained from the model can be used in the study of the flow pattern and the analysis of pressure transient and well testing of partial-penetration wells in triple-porosity fractured-vuggy carbonate reservoirs.

10.11743/ogg20080615