Abstract As ultra-tight porous media that include organic contents, shale gas resources are technically known as complex systems having various mechanisms that impact storage and flow. The slippage, Knudsen diffusion, the process of desorption, an adsorbed layer that affects apparent permeability, and solute gas in kerogen are recognized to be the most important ones. However, simultaneous effects of multi-mechanism flow and storage, and influences of scattered organic contents on shale gas flow behaviour are not well-understood yet. According to the mass conservation law, a basic mathematical model has been developed to investigate, step-by-step, the effects of different changes that are introduced, and examine whether patterns of how kerogen is distributed affect the production plateaus. The discretization of the second-order nonlinear Partial Differential Equation (PDE) that is evolved results in a certain number of nonlinear simultaneous algebraic equations, which are conventionally solved with the application of Newton’s method. To overcome the inherent difficulties of the initial guess, the derivations, and the inversion of the Jacobian matrix, a new application of Particle Swarm Optimization (PSO) as a nonlinear solver was applied to extract the anticipated pressure profile for each step in time outside the bounds of the reference equations. The results show that not only can the PSO effectively meet the required criteria, but also it performed faster than conventional techniques, especially in cases with a larger number of grids that encompass more phenomena. It was further revealed that the insertion of a multi-mechanism apparent permeability model in which the pore radius is also a pressure-dependent parameter causes the lower rate of production. A higher level of production has been recorded after including storage terms of adsorption and solute gas in kerogens. Although different patterns of kerogen distribution have finally overlapped, the different taken trend of each production profile underlines the impact of kerogen distribution as an important parameter within the procedure of history matching.

中文翻译：

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求解非线性流动方程的新方法：准确评估页岩气资源的下一步

摘要 页岩气资源是一种含有有机物的超致密多孔介质，技术上被称为具有影响储流和流动的各种机制的复杂系统。滑脱、Knudsen 扩散、解吸过程、影响表观渗透率的吸附层和干酪根中的溶质气体被认为是最重要的。然而，多机制流动和储存的同时影响以及分散的有机物含量对页岩气流动行为的影响尚不清楚。根据质量守恒定律，建立了基本的数学模型，逐步研究引入的不同变化的影响，并检验干酪根的分布模式是否影响生产高原。演化出的二阶非线性偏微分方程 (PDE) 的离散化导致了一定数量的非线性联立代数方程，这些方程通常应用牛顿法求解。为了克服初始猜测、推导和雅可比矩阵求逆的固有困难，应用了粒子群优化 (PSO) 作为非线性求解器的新应用，以在时间之外提取每个步骤的预期压力分布。参考方程的边界。结果表明，PSO 不仅可以有效地满足要求的标准，而且比传统技术执行得更快，尤其是在包含更多现象的大量网格的情况下。进一步揭示，插入孔隙半径也是压力相关参数的多机制表观渗透率模型导致较低的生产率。在包括干酪根中吸附和溶质气体的储存条件后，记录了更高水平的产量。尽管不同的干酪根分布模式最终出现了重叠，但每个生产剖面的不同趋势凸显了干酪根分布作为历史匹配过程中的一个重要参数的影响。