分形煤层气藏数值模拟研究——Douglas-Jones预估-校正法的应用

传统的煤层气动力学模型多建立在欧几里得基础上,难以描述煤层气孔隙结构的复杂性和形状的不规则性。为此,以分形理论为基础,通过引入煤层基质和裂缝的分形维数来刻画煤层气孔隙结构的复杂性和吸附特性,建立了双重分形介质渗流模型,采用Douglas-Jones预估-校正法对非线性方程组进行离散,获得了无限大地层和有限地层定产量生产时拟稳态吸附模型的差分方程,求得数值解。结果表明,Douglas-Jones预估-校正法可以有效解决这类非线性模型的求解问题,获得无限大地层定产量生产时变形双重分形介质模型的数值解;分析各种分形参数下的煤层压力动态,做出了典型压力曲线图。对无限大地层,初期分形维数对压力影响不大,后期分形维数越小,压力越高。对有限地层,初期分形维数的影响明显,且分形维数越大,压力越低。压力随分形指数的减小量呈现先增大后减小的趋势,在末期压力平稳趋向同一值。

Application of Douglas-Jones predictor-corrector method in fractal coalbed methane reservoir

Conventional mathematical models of coalbed methane were mostly based on Euclid Geometry and difficult to describe the complexity of pore structure and the irregularity of shape.In this paper,basing on fractal theory,new percolation models with the double porosity in fractal fracture network were established by introducing fractal parameters to describe the complexity of pore structure and the adsorption effect in coal bed.In the low permeability reservoir,the partial differential equation is nonlinear,so the numerical calculation is carried with the Douglas-Jones predictor-corrector method.The numerical solution of the pseudo-steady sorption formulation with constant rate production and the unsteady sorption formulation with constant rate production in a infinitely large system and finitely closed system were obtained.Analysis pressure transient with fractal parameters,draw typical pressure curves.Produced with constant rate in an infinitely large system,fractal dimension influences the pressure small in the early stage,but in the later stage,the smaller the fractal dimension,the higher the pressure.Produced with constant rate in a finitely closed system,fractal dimension has a great influence on the pressure in the early stage,pressure drops with the increase of fractal dimension,pressure first increases and then decreases with the reduction of fractal index,the pressure tends to the same value finally.