压裂改造复合页岩气藏不稳定压力与产量分析方法

为了给页岩气现场开发提供理论依据,考虑页岩气扩散、黏性流、解吸等多种传质机理,建立了复合页岩气藏的综合流动数学模型。基质中考虑浓度差引起的非稳态流动,内外区裂缝中考虑达西流动,水力压裂主裂缝考虑为无限导流;引入了新的无因次量,在椭圆坐标系下综合运用拉氏变换、Mathieu函数、Stehfest数值反演等方法对数学模型进行了解析求解;分析了定产量条件下不稳定压力和定井底压力条件下产量的变化特征,基于不稳定压力曲线将页岩气流动划分为7个流动阶段,即井筒储集阶段、过渡流阶段、早期线性流阶段、基质向裂缝窜流阶段、早期径向流动阶段、第一径向流与第二径向流的过渡阶段、第二径向流动阶段,为复合页岩气藏生产动态分析提供了理论基础。研究结果表明:增大改造区域半径和渗透率可以提高页岩气产量;扩散系数越大、兰格缪尔体积和兰格缪尔压力越大,页岩气产量越大,气藏初始压力高对页岩气的开发具有积极的影响。结论认为,所建立的综合流动数学模型丰富了页岩气多级压裂水平井开发分析方法。

Transient pressure and production analysis methods for composite shale gas reservoirs stimulated by fracturing

Based on the multiple mass transfer mechanisms (diffusion, viscosity flow, and desorption), a comprehensive flow mathematical model was built up for composite shale gas reservoirs so as to provide theoretical basis for the field development of shale gas, with such aspects taken into consideration as unsteady-state flow induced by density difference for matrix, Darcy flow for fractures inside and outside the zones and infinite conductivity for main fractures in hydraulic fracturing. New dimensionless value was introduced, and the mathematical model was analytically solved in elliptic coordinate system by using Laplace transform, Mathieu function and Stehfest numerical inversion. Analysis was conducted on the change characteristics of transient pressure with fixed production rate and on that of production rate with fixed downhole pressure. Based on the transient pressure curve, shale gas flow is divided into seven stages, including borehole reservoir stage, transitional flow, early linear flow, channeling flow from matrix to fractures, early radial flow, transitional stage from the first radial flow to the second radial flow and the second radial flow, which provide theoretical basis for the composite shale gas reservoir production behavior analysis. It is indicated that the shale gas production rate will rise by increasing the radius and permeability of stimulated zones. The shale gas production rate will rise with the rising of diffusion coefficient and Langmuir volume and pressure. The development of shale gas is positively influenced by the high initial gas reservoir pressure. It is concluded that the comprehensive flow mathematical model established in this paper can be used to perform development analysis on the shale gas horizontal wells stimulated by multi-stage fracturing.