Recent advancements in artificial intelligence (AI) technology have offered new ways to obtain the relative permeability curve that is crucial for subsurface engineering problems. The existing data-driven AI approaches for the relative permeability prediction are only suitable for a specific geometry rock size and lack the cross-size prediction ability. In this paper, we propose a new physics-informed prediction model called the three-dimensional (3D) spatial pyramid pooling convolutional network (3DSPPConvNet) model embedding three important parameters: computed tomography (CT) scanning resolution, interfacial tension, and contact angle distribution. Our model can deal with 3D digital rocks with variable sizes as it is based on a multi-size digital rock dataset containing 1512 couples of relative permeability curves. Their relative permeability curves for training and testing are obtained from pore network modeling (PNM) results with a linear postprocessing process. The results show that the physics-informed 3DSPPConvNet has a high prediction accuracy of 95.3%, with scale information being the most important physics feature accounting for 51%. In addition, compared with PNM, the computational time and memory of the intelligent model are saved by 63% and 80%, respectively.

Water injection with an oscillatory pressure boundary is a promising technology, which can achieve a more economical and environment-friendly EOR (enhanced oil recovery). However, due to the unclear critical injection frequency, its oil production performance has been unstable and is far from reaching the optimal level. Here, a numerical model is established for oil recovery by the water injection with the oscillatory boundary condition to find out the critical frequency for the optimal EOR. The correlations between the water injection frequency and the EOR level at diverse oil–water surface tensions and oil viscosities are integrated into the model. Our numerical model reveals that an optimal EOR of roughly 10% is achieved at the critical water injection frequency compared with water injection without an oscillatory boundary. The EOR mechanism is revealed showing that upon water injection with the optimum frequency, the formation of the preferential pathways is inhibited and the pressure transmits to the wall sides to displace the oil. Moreover, it is indicated that the required critical frequency increases with higher surface tension and larger oil viscosity. In addition, the difference between the residual oil saturation at the optimal frequency increases with the increase in surface tension compared with water injection without an oscillatory boundary. Last but not least, it is elucidated that at a constant injection frequency, a higher EOR is achieved when the water–oil surface tension is lower but the oil viscosity is larger. Our work promises economic, eco-friendly and controllable enhanced oil recovery.

Unconventional gas is a momentous energy source due to its considerable reserves and eco-friendly properties, where relative permeability is a key evaluative parameter of unconventional gas extraction. However, the geo-complexity, multiscale and multieffect of the unconventional gas reservoir challenge the relative permeability evaluation and production enhancement. Here, we establish a gas–water flow model by integrating multifractal theory, covering from nanoscale to macroscale and regarding the effects of slip, gas desorption–diffusion and water film separation, to reliably evaluate the relative permeability evolution during unconventional gas development. Based on our model, we describe the permeability of the unconventional reservoir with an 88% less evaluation error compared to the single fractal Darcy with the literature benchmark. Moreover, we characterize the gas–water relative permeability with a no more than 10% evaluation error based on the experimental data. The slip effect plays the most crucial role in the evaluation precision of relative permeability. We reveal that the permeability of the unconventional gas reservoir is decreased by the increase of generalized fractal dimension which enhances the heterogeneity and tortuosity of pores. We uncover that the slip effect facilitates the relative permeability of gas and water. Besides, the gas desorption–diffusion boosts gas relative permeability while limiting water relative permeability, whereas water film separation enhances water relative permeability but hinders gas relative permeability. This work brings insights into the precise description of multiscale and multieffect gas–water porous flow in unconventional gas development.

The contact line pinning mechanisms of a non-wetting droplet penetrating a permeable substrate are theoretically explained by considering the force balance of volumetric force, capillary force, and pinning and depinning forces. We propose two dimensionless numbers, Bo∗—the ratio of the volumetric force to the capillary force, and Ct—the ratio of the depinning force to the pinning force, to establish a phase diagram that quickly determines the droplet penetration patterns. For Bo∗ ⩽ 1, the droplet will not penetrate the substrate; for Bo∗ > 1 and Ct ⩽ 1, the droplet will penetrate with a pinned contact line; for Bo∗ > 1 and Ct > 1, the droplet will penetrate with contact line shrinking. Contact angle dynamics during contact line pinning and shrinking are further clarified. The time evolutions of the contact area diameter Dc, the droplet height h, the penetrated droplet volume percentage Sp, and the apparent contact angle θ are derived. We further perform a series of lattice Boltzmann simulations, and the results match well with our theoretical analysis. These theoretical and numerical results pave the way to achieve better performances of many important applications that involve droplet penetration.