考虑基质收缩效应的页岩气双孔双渗模型

为了研究吸附性页岩储层基质收缩效应对气体渗流特征的影响，引入吉布斯表面自由能函数，建立考虑基质收缩效应、应力敏感效应、滑脱效应和自由分子流动效应的双孔双渗介质数学模型;采用隐式裂缝压力-显式基质压力离散方法对模型求解。并针对鄂尔多斯盆地古生界山西组页岩讨论基质收缩效应、应力敏感效应、滑脱效应和自由分子流动效应对气体流动机制及产量的影响。结果表明:①基质绝对渗透率的反弹点和兰缪尔体积、页岩密度、温度、杨氏模量、压缩系数有关，与兰缪尔压力无关;②基质收缩效应减少黏性流量占总流通量比例，增加滑脱流量和自由分子流量占总流通量比例;③基质收缩效应和应力敏感效应在基质孔径较大时对产量影响比较显著，当孔径小于2nm时，可以忽略基质收缩效应和应力敏感效应的影响;④滑脱效应和自由分子流动效应在低压小孔时对产量的贡献量变大，当孔径大于50nm时，滑脱效应和自由分子流动效应对产量基本没有贡献。

Shale Gas Dual Porosity-dual Permeability Model with Matrix Shrinking

In order to investigate the effect of matrix shrinkage on the behavior of gas seepage,Gibbs surface free energy function was introduced to establish a dual porosity-dual permeability model considering matrix shrinkage,effective stress,slippage and free molecular flow effect.Implicit fracture pressure and explicit matrix pressure method was applied to discretize governing equations.We discuss the effect of matrix shrinkage,effective stress,slippage and free molecular flow on gas flow mechanism and production rate in the Upper Paleozoic Shanxi Formation in the Ordos Basin.The results showed that,the rebound of absolute permeability has relationship with Langmuir volume,shale density,temperature,Young modulus,rock compressibility,instead of Langmuir pressure.Matrix shrinkage reduces the ration of viscous flow to total flow rate and decreases the ration of slip flow and free molecular flow to total flow rate.Matrix shrinkage and stress sensitivity have a considerable influence on production rate in large diameter and the influence can be ignored when pore diameter is smaller than 2nm.Slippage and free molecular flow contribute largely to production rate in low pressure and small pore.There is no contribution to production rate when pore diameter is bigger than 50nm.