分形理论在煤层气非平衡吸附模型中的应用

传统的煤层气动力学模型均是建立在欧几里得几何基础上的,难以描述煤层孔隙结构的复杂性及形状的不规则性。本文以分形理论为基础,通过引入分形维数来刻画煤层孔隙结构的复杂性并考虑煤层的吸附特性、双重介质特征及介质的变形,建立基于Fick第二定律的分形介质煤层气非稳态渗流数学模型。由于流动方程的强非线性,结合各类边界条件用正则摄动法和Laplace变换得到模型在拉氏空间上的近似解析解,再利用Laplace数值反演求得实空间上的数值解。对参数进行敏感性分析并绘制了典型压力曲线,这些结果为煤层气开采提供了理论依据和试井方法。

Application of fractal theory in nonequilibrium adsorption model of coalbed methane

Most of gas stored in coalbed methane reservoirs exists in adsorbed state rather than in free state,therefore the study on gas flow in coalbed methane reservoirs is of great importance.However,conventional mathematical models of coalbed methane were based on Euclid Geometry and difficult to describe the complexity of pore structure and the irregularity of shape.In this paper,in consideration of the double porosity,the adsorption effect of coal beds and the deformation of media,new unsteady percolation models based on Fick's second law were established by introducing fractal parameters to describe the complexity of pore structure in coal beds.Owing to the strong nonlinearity of new flow equations,models combining various boundary conditions were solved by use of regular perturbation method and Laplace transform,and the zero-order perturbation solution were obtained through Laplace numerical inversion.The change rules of dimensionless pressure along with the changes in parameters were discussed,and typical pressure curves were drawn up through new models.All of these results have provided a theoretical basis and new well test models for coalbed methane reservoir development.