页岩气藏广泛采用常规气藏产量递减模型进行动态分析,而页岩气在储层中的赋存方式具有一定的特殊性,主要以吸附态和游离态为主,所以常规气藏递减分析方法已不再适应。本文在传统裂缝-基质双重介质模型基础上,引入无因次应力敏感系数,定义两个无因次吸附参数——无因次Langmuir体积和无因次Langmuir压力,建立了考虑应力敏感和吸附效应影响的裂缝性页岩气藏产量递减数学模型。利用隐式差分和牛顿迭代方法,进行数值离散,获得产量的数值解,并绘制了Blasingame型产量递减曲线。分析表明,裂缝性页岩气藏应力敏感越大,无因次产量、产量积分及产量积分导数越小;页岩气基质吸附量越大,无因次产量递减积分导数曲线出现下凹的时间越晚;同时结合页岩气井生产数据,页岩气藏的吸附常数和其他地层参数,以及应力敏感效应引起的产量下降都可以通过典型曲线得到。

The production decline model for conventional gas reservoirs is widely used for dynamic analysis of shale gas reservoirs at home and abroad, but due to some special features of the occurrence of the shale gas involving mainly adsorption state and free state, the regressive analysis methods of conventional gas reservoirs are no longer valid. Based on the traditional dual-porosity model, a mathematical model with consideration of the stress sensitivity and the sorption effects is established by introducing the non-dimensional stress sensitive coefficient and defining two non-dimensional adsorption parameters--dimensionless Langmuir volume and dimensionless Langmuir pressure. The numerical solution of the production is obtained together with the production decline Blasingame type curves through the numerical difference and Newton iterative methods. It is shown that the higher the stress sensitivity, the smaller the non-dimensional production, the production integral and the production decline integral derivative will be. The larger the adsorption of the shale gas matrix, the more delayed the point will be where the non-dimensional production decline integral derivative curve becomes concave down. At the same time, with the help of the shale gas well production data, the shale gas reservoir adsorption constants, other formation parameters, and the stress sensitive effect caused by the decline in the production can be obtained by typical curves.