Complex flow mechanisms, such as Knudsen diffusion, are encountered in the shale matrix because of the presence of nanopores. Numerous apparent-permeability models have been proposed to capture the ensuing non-Darcy flow behavior. However, these models are not readily available in most commercial reservoir simulators, and ignoring these mechanisms can potentially underestimate the overall matrix conductivity. This work implements an explicit coupling strategy for integrating a pressure-dependent apparent-permeability model in reservoir simulation. The numerical models are subsequently used to study the effects of apparent-permeability modeling and natural-fracture distribution on gas production and water loss during flowback. The effects of multiphase-flow functions on fluid retention are also assessed.

A set of 3D reservoir models are constructed using field data obtained from the Horn River shale-gas reservoir. First, stochastic 3D discrete-fracture-network (DFN) models are scaled up into equivalent continuum dual-porosity/dual-permeability models. An apparent-permeability (K_app) model accounting for contributions of slip flow, Knudsen diffusion, and surface pore roughness is applied at each gridblock. A novel coupling scheme is formulated to facilitate the updating of K_app after a certain specified time interval, capturing the pressure dependency of the K_app. The sensitivity of the updating frequency is analyzed.

The results reveal that incorporating these additional flow mechanisms by means of the apparent-permeability formulation could potentially increase the overall gas-production prediction by up to 11%, depending on the average pore radius, reservoir pressure, and several other matrix or fluid properties. The implications of K_app modeling in water-loss mechanisms are further examined through a set of sensitivity analyses, where the effects of multiphase-flow functions and DFN distributions are systematically investigated. The following interesting findings are observed:

• Ignoring K_app modeling could overestimate water recovery.
• Fracturing-fluid propagation and long-term water recovery are strongly affected by the secondary-fracture intensity; increase in secondary-fracture intensity would enhance water loss during flowback.
• Gas production is highly affected by the amount of water in the near-well region.
• In a gas/water system, compressibility of the in-situ fluids renders the effects of countercurrent imbibition and water retention to be more complex from those observed in similar water/oil systems.

This work offers a novel, yet practical, scheme for representing the pressure-dependent matrix apparent permeability in the flow simulation of shale reservoirs. The proposed method captures the non-Darcy flow behavior caused by the complex transport mechanisms occurring in nanosized pores. Most importantly, this coupling procedure can be implemented in existing commercial reservoir-simulation packages. The results have revealed a few interesting insights regarding the potential implications in fracturing design and estimation of stimulated reservoir volume.

由于存在纳米孔，在页岩基质中遇到了复杂的流动机制，例如克努森扩散。已经提出了许多表观渗透率模型来捕获随后的非达西流动行为。但是，这些模型在大多数商业油藏模拟器中并不容易获得，并且忽略这些机制可能会低估总体基质电导率。这项工作实现了一个显式的耦合策略，用于将压力相关的表观渗透率模型集成到储层模拟中。数值模型随后被用于研究表观渗透率模型和自然裂缝分布对返排过程中天然气产量和水分损失的影响。还评估了多相流功能对流体滞留的影响。

使用从霍恩河页岩气储层获得的现场数据构建了一套3D储层模型。首先，将随机3D离散断裂网络（DFN）模型按比例放大为等效的连续双孔隙率/双渗透率模型。在每个网格块上_应用表观渗透率（K _app）模型，该模型考虑了滑流，Knudsen扩散和表面孔隙粗糙度的影响。制定了一种新颖的耦合方案，以促进在 一定的指定时间间隔后更新 K _app，从而捕获K _app的压力依赖性 。分析了更新频率的敏感性。

结果表明，通过视在渗透率公式合并这些附加的流动机理可能会使总的产气量预测提高多达11％，具体取决于平均孔隙半径，储层压力以及其他几种基质或流体性质。 通过一组敏感性分析，进一步检查了K _app建模在失水机理中的意义 ，在此系统地研究了多相流函数和DFN分布的影响。观察到以下有趣的发现：

• 忽略 K_应用程序 建模可能会高估水回收率。
• 次生裂缝强度强烈影响压裂液的传播和长期的水采收率。二次断裂强度的增加会增加回流过程中的水分流失。
• 天然气生产受到井附近地区水量的极大影响。
• 在天然气/水系统中，原位流体的可压缩性使逆流吸收和保水的作用比在类似的水/油系统中观察到的更为复杂。

这项工作提供了一种新颖而实用的方案，用于在页岩油藏流动模拟中表示与压力有关的基质视在渗透率。所提出的方法捕​​获了由纳米孔中复杂的传输机制引起的非达西流动行为。最重要的是，可以在现有的商业油藏模拟程序包中实施这种耦合程序。结果揭示了一些有趣的见解，涉及压裂设计和增产油藏估算中的潜在影响。