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 achieve carbon dioxide (CO₂) storage through enhanced oil recovery, accurate forecasting of CO₂ subsurface storage and cumulative oil production is essential. This study develops hybrid predictive models for the determination of CO₂ storage mass and cumulative oil production in unconventional reservoirs. It does so with two multi-layer perceptron neural networks (MLPNN) and a least-squares support vector machine (LSSVM), hybridized with grey wolf optimization (GWO) and/or particle swarm optimization (PSO). Large, simulated datasets were divided into training (70%) and testing (30%) groups, with normalization applied to both groups. Mahalanobis distance identifies/eliminates outliers in the training subset only. A non-dominated sorting genetic algorithm (NSGA-Ⅱ) combined with LSSVM selected seven influential features from the nine available input parameters: reservoir depth, porosity, permeability, thickness, bottom-hole pressure, area, CO₂ injection rate, residual oil saturation to gas flooding, and residual oil saturation to water flooding. Predictive models were developed and tested, with performance evaluated with an overfitting index (OFI), scoring analysis, and partial dependence plots (PDP), during training and independent testing to enhance model focus and effectiveness. The LSSVM-GWO model generated the lowest root mean square error (RMSE) values (0.4052 MMT for CO₂ storage and 9.7392 MMbbl for cumulative oil production) in the training group. That trained model also exhibited excellent generalization and minimal overfitting when applied to the testing group (RMSE of 0.6224 MMT for CO₂ storage and 12.5143 MMbbl for cumulative oil production). PDP analysis revealed that the input features “area” and “porosity” had the most influence on the LSSVM-GWO model's prediction performance. This paper presents a new hybrid modeling approach that achieves accurate forecasting of CO₂ subsurface storage and cumulative oil production. It also establishes a new standard for such forecasting, which can lead to the development of more effective and sustainable solutions for oil recovery.