A numerical method is presented for the solution of a moving boundary problem of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient (TPG) for the case of a constant flow rate at the inner boundary. In order to overcome the difficulty in the space discretization of the transient flow region with a moving boundary in the process of numerical solution, the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method. Then a stable, fully implicit finite difference method is adopted to obtain its numerical solution. Finally, numerical results of transient distance of the moving boundary, transient production pressure of wellbore, and formation pressure distribution are compared graphically with those from a published exact analytical solution under different values of dimensionless TPG as calculated from actual experimental data. Comparison analysis shows that numerical solutions are in good agreement with the exact analytical solutions, and there is a big difference of model solutions between Darcy's flow and the fluid flow in porous media with TPG, especially for the case of a large dimensionless TPG.

Threshold pressure gradient (TPG) is a key parameter determining the pore-scale fluid dynamics. In tight gas reservoirs, both gas and water exist in the porous rock, and the existing water can be divided into irreducible and movable water. However, how movable water saturation will influence TPG has not yet been investigated. Therefore herein, nuclear magnetic resonance (NMR) and high-pressure mercury intrusion (HPMI) experiments were performed to determine pore-scale water distribution, movable water saturation, and pore throat distribution in the core plugs. Subsequently, the air bubble method was used to measure TPG as a function of movable water saturation and permeability inside tight gas core plugs, finding that TPG increased from 0.01 MPa/m to 0.25 MPa/m with the movable saturation increased from 2% to 35%. Finally, a semi-empirical model was derived to describe the correlation between TPG, movable water saturation, and permeability, which performed better than previous models in the literature. These insights will advance the fundamental understanding of TPG in tight gas reservoirs and provide useful guidance on tight gas reservoirs development.

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.

Non-Darcy flow with a threshold in fractal porous media has been widely used in the development of unconventional petroleum resources such as heavy oil and tight oil. Mathematical modeling of such challenging “threshold flow” problems with strong nonlinearity has great significance in improving petroleum science and technology. Based on a fractal theory, a new non-Darcy kinematic equation with a fractal threshold pressure gradient (TPG) is mathematically deduced in order to describe the non-Darcy flow of a non-Newtonian Bingham fluid with a threshold in fractal porous media. Then mathematical modeling of planar radial non-Darcy flow in a fractal heavy oil reservoir is performed as a nonlinear moving boundary problem. In addition, a steady analytical solution method and a transient numerical solution method are developed. The analytical solution of an ordinary differential equation system for a simple steady model is derived directly, and the transient numerical solution of a partial differential equation system for an unsteady flow model is obtained based on the finite element method with good convergence. These two model solutions are validated by cross-comparisons. It is found from the calculation results that for the steady state, the extremely disturbed moving boundary and its corresponding pressure distribution are affected only by a TPG, production pressure, and a transport exponent; by contrast, for the unsteady state, the moving boundary and its corresponding pressure distribution are affected by many more factors including the fractal dimension. Furthermore, neglect of the fractal TPG and the induced moving boundary can lead to high overestimation of well productivity.

With the continuous development of conventional oil and gas resources, the strategic transformation of energy structure is imminent. Shale condensate gas reservoir has high development value because of its abundant reserves. However, due to the multi-scale flow of shale gas, adsorption and desorption, the strong stress sensitivity of matrix and fractures, the abnormal condensation phase transition mechanism, high-speed non-Darcy seepage in artificial fractures, and heterogeneity of reservoir and multiphase flows, the multi-scale nonlinear seepage mechanisms are extremely complicated in shale condensate gas reservoirs. A certain theoretical basis for the engineering development can be provided by mastering the percolation law of shale condensate gas reservoirs, such as improvement of productivity prediction and recovery efficiency. The productivity evaluation method of shale condensate gas wells based on empirical method is simple in calculation but poor in reliability. The characteristic curve analysis method has strong reliability but a great dependence on the selection of the seepage model. The artificial intelligence method can deal with complex data and has a high prediction accuracy. Establishing an efficient shale condensate gas reservoir development simulation technology and accurately predicting the production performance of production wells will help to rationally formulate a stable and high-yield mining scheme, so as to obtain better economic benefits.

Heavy oil resources are abundant globally, holding immense development potential. However, conventional thermal recovery methods such as steam injection are plagued by high heat loss, substantial carbon emissions, and significant water consumption, making them incompatible with carbon reduction goals and the sustainable socioeconomic development demands. A new method of high-frequency electromagnetic in situ heating, which targets polar molecules, can convert electromagnetic energy into heat so as to achieve rapid volumetric heating of the reservoir. This method has the potential to overcome the drawbacks of traditional techniques. Nevertheless, it faces significant drawbacks such as limited heating range and inadequate energy supply during later production stages, which necessitates auxiliary enhancement measures. Various enhancement measures have been reported, including nitrogen injection, hydrocarbon solvent injection, or the use of nano-metal oxide injections. These methods are hindered by issues such as pure nitrogen being easy to breakthrough, high costs, and metal pollution. Through extensive literature review, this article charts the evolution of high-frequency electromagnetic in situ heating technology for heavy oil and the current understanding of the coupled heat and mass transfer mechanisms underlying this technology. Moreover, based on a profound analysis of the technology’s progression trends, this work introduces a new direction: CO₂-N₂ co-injection as an enhancement strategy for high-frequency electromagnetic in situ heavy oil recovery. There is promising potential for the development of new technologies in the future that combine high efficiency, low carbon emissions, environmental friendliness, economic viability, and energy conservation. Furthermore, some research prospects in low-carbon situations and challenges for the new technology in future are presented in detail. All in all, the contribution of the paper lies in the summarizing of some main drawbacks of current enhanced electromagnetic in situ thermal recovery methods, and presents a novel research direction of using CO₂-N₂ co-injection as an enhancement strategy based on its current research status in low-carbon situations.