通过梯度开挖损伤区的双孔隙流动的广义解
Generalized Solution for Double-Porosity Flow through a Graded Excavation Damaged Zone
AI总结：
本文将单孔隙梯度导率解与任意维度流动解相结合，扩展到双孔隙模型的两种实现方式，提出了具有井筒储集的指定流量新解和适用于任意井筒边界条件的更具物理真实性的解，并推导了改进的基质扩散闭式表达式。
摘要：
预测裂隙低渗透岩石中流向钻孔或开挖面的流体对于资源开采、处置或封存活动具有重要意义。流体压力和流量的解析解在可用时是强大、直观且高效的工具，可用于参数估计和不确定性量化。本文推导了一个适用于任意物理维度的灵活多孔介质流动解，并将其扩展到双孔隙模型，用于描述当渗透率和孔隙度随远离钻孔或开口呈幂律径向递减时的汇聚径向流。这种分布可能源于与钻探或采矿相关的应力释放所导致的损伤累积。单孔隙梯度导率解最初是在热传导研究中得到的，任意维度流动解来自水文学，而同时具有任意维度和梯度渗透率分布的解析解则出现在油藏工程中。本文将上述现有解进行组合，并扩展到双孔隙概念模型的两种实现方式，既包括较简单的薄膜质量传递，也包括更具物理真实性的裂隙与基质之间的扩散。本文针对较简单的双孔隙模型提出了一个新的具有井筒储集效应的指定流量解，并针对任意井筒边界条件提出了一个新的更具物理真实性的解。针对基质扩散解，本文推导了一个新的闭式表达式（适用于均质和梯度问题），改进了此前的无穷级数表达式。
英文摘要：
Prediction of flow to boreholes or excavations in fractured low-permeability rocks is important for resource extraction and disposal or sequestration activities. Analytical solutions for fluid pressure and flowrate, when available, are powerful, insightful, and efficient tools enabling parameter estimation and uncertainty quantification. A flexible porous media flow solution for arbitrary physical dimension is derived and extended to double porosity for converging radial flow when permeability and porosity decrease radially as a power law away from a borehole or opening. This distribution can arise from damage accumulation due to stress relief associated with drilling or mining. The single-porosity graded conductivity solution was initially found for heat conduction, the arbitrary dimension flow solution comes from hydrology, and the solution with both arbitrary dimension and graded permeability distribution appeared in reservoir engineering. These existing solutions are here combined and extended to two implementations of the double-porosity conceptual model, for both a simpler thin-film mass transfer and more physically realistic diffusion between fracture and matrix. This work presents a new specified-flowrate solution with wellbore storage for the simpler double-porosity model, and a new more physically realistic solution for any wellbore boundary condition. A new closed-form expression is derived for the matrix diffusion solution (applicable to both homogeneous and graded problems), improving on previous infinite series expressions.
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