致密砂岩垂直裂缝井CO2混相驱试井模型研究

向地层注入CO2可以有效地提高致密砂岩原油采收率，常规的试井解释数学模型不能满足致密砂岩无限导流垂直裂缝井CO2混相驱试井解释的需求．因此，基于渗流力学基本原理建立考虑应力敏感影响的无限导流垂直裂缝井CO2混相驱试井解释数学模型，利用Laplace变换、摄动变换和Stehfest数值反演的方法进行求解，编程绘制典型特征曲线并进行敏感性分析．研究表明：该模型典型特征曲线共划分为八个流动阶段．由于应力敏感效应的影响，径向流阶段内、外区压力导数曲线不再是0.5和0.5M13水平线，而是呈“上翘”的曲线，并且应力敏感系数越大，曲线“上翘”越明显；混相区压力导数曲线符合幂律型变化指数规律且高于(1-n)/(3-n)斜率直线；内区、混相区半径和M12的变化都会使得外区压力曲线升高；通过该模型可以有效地对致密砂岩压裂井CO2混相驱试井资料进行解释．

Study of Well Test Model on CO2 Miscible Flooding in the Tight Sand Reservoirs with Fractured Well

Oil recovery can be effectively enhanced by injecting CO2 in the tight sand reservoirs. However, coventional well test model can not meet the need of CO2 miscible flooding of the tight sand reservoirs with infinite-conductivity fractured well. Therefore, Based on basic principle of seepage theory, well-test mathematical model considering stress sensitivity of CO2 miscible flooding with infinite-conductivity fractured well is established. The methods of Laplace transform and perturbation transform were used to obtain analytical solution. By means of Stehfest numerical inversion, dimensionless pressure and pressure-derivative typical well-test curves with infinite outer boundery were plotted. The study shows that the curves can be divided into eight stages by characteristic of pressure-derivatives. When stress sensitivity is considered, the pressure and pressure-derivative curves of radial flow of inner and outer zones are no longer horizontal lines at 0.5 and 0.5M12, but instead tilt upwards, with larger slope for a stronger stress sensitivity. The pressure-derivative curve of miscible zones follows power law with the power index higher than (1-n)/(3-n). The changes of the inner zone radius, miscrible zone radius and M12 could increase the magnitude of the pressure curve of outer zone. The model can provide an effective interpretation for the well-test document of CO2 miscible flooding of the tight sand reservoirs with infinite-conductivity fractured well.