The study of gas transport in low-permeability rocks is both practical and of significant importance to produce tight rock reservoirs. The presence of nanopores in tight rocks results in distinctly different gas transport mechanisms from those found in conventional reservoirs. Traditional Darcy’s law is inadequate for describing gas flow in this context. Instead, various modes of gas transport, such as continuum flow, slip flow, transition flow, and Knudsen diffusion for bulk gas, as well as surface diffusion and adsorption/desorption for adsorbed gas, coexist within these nanopores. This paper mainly focuses on studies of gas transport in nanopores that consider apparent permeability. To begin with, the pore structure characteristics and gas seepage mechanisms in shale are introduced. An overview of the three main methods for measuring apparent permeability including laboratory experiments, numerical simulations, and analytical techniques, is provided. Mathematical models describing gas transport within nanopores are emphasized as a foundational component of apparent permeability measurements. Furthermore, the factors that influence these models are discussed. Upon analyzing the existing models, it is evident that they are diverse and numerous. While these models typically encompass multiple mechanisms and influencing factors related to gas transportation, each model has its specific limitations. Therefore, there is a continued need for the development of more comprehensive and general models. This study offers the most detailed overview of gas transport mechanisms and mathematical models in low-permeability rocks, aiming to support the evaluation and exploitation of tight rock reservoirs.

To reduce CO₂ emissions in response to global climate change, shale reservoirs could be ideal candidates for long-term carbon geo-sequestration involving multi-scale transport processes. However, most current CO₂ sequestration models do not adequately consider multiple transport mechanisms. Moreover, the evaluation of CO₂ storage processes usually involves laborious and time-consuming numerical simulations unsuitable for practical prediction and decision-making. In this paper, an integrated model involving gas diffusion, adsorption, dissolution, slip flow, and Darcy flow is proposed to accurately characterize CO₂ storage in depleted shale reservoirs, supporting the establishment of a training database. On this basis, a hybrid physics-informed data-driven neural network (HPDNN) is developed as a deep learning surrogate for prediction and inversion. By incorporating multiple sources of scientific knowledge, the HPDNN can be configured with limited simulation resources, significantly accelerating the forward and inversion processes. Furthermore, the HPDNN can more intelligently predict injection performance, precisely perform reservoir parameter inversion, and reasonably evaluate the CO₂ storage capacity under complicated scenarios. The validation and test results demonstrate that the HPDNN can ensure high accuracy and strong robustness across an extensive applicability range when dealing with field data with multiple noise sources. This study has tremendous potential to replace traditional modeling tools for predicting and making decisions about CO₂ storage projects in depleted shale reservoirs.