Extensive experiments have demonstrated that fluid flow in low‐permeability media deviates from Darcy's law at low pressure gradients, which is called pre‐Darcy flow. Although numerous pre‐Darcy flow models have been proposed, these models generally contain one or more empirical parameters with no clear physical meaning. In this paper, we present a simple unified model to describe pre‐Darcy flow in porous media by introducing the concept of loss permeability. The physical meaning of the loss permeability parameter and its relationship to permeability are analyzed. Based on the statistics of the loss permeability parameter results of 24 core samples, we found that there is a good positive correlation between the loss permeability parameter and the absolute permeability. A smaller loss permeability indicates a stronger fluid‐solid interaction and a stronger nonlinearity between the flow velocity and the pressure gradient. Taking a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium as an example, we solve the pressure diffusion equation based on the proposed model using a finite difference method. Our results demonstrate that the rate of pressure propagation for pre‐Darcy flow is slower than that for Darcy flow for the entire observation period, which corrects previous conclusions. This study is highly important for improving the understanding of fluid flow in low‐permeability media.

Dezhou City is located in northwestern Shandong Province, China, and is rich in geothermal resources. Approximately 30% of the geothermal wells and geothermal heating areas of Shandong Province are located in Dezhou. A doublet-well layout geothermal system was completed by the Lubei Geo-engineering Exploration Institute for local winter heating, which has been in operation for 4 years. The wellbores penetrated the Guantao Formation with a well spacing of 180 m. This study aims to assess the heat extraction performance of the current well layout and predict the temperature evolution and lifespan. Furthermore, larger well spacing schemes were used in a simulation to test the heat supply potential and sustainability. In this study, the thermal conductivity and permeability were calibrated using in situ measured data from a field production test. A relatively high permeability layer was found between the depths of 1468 and 1536 m. The temperature remained stable in the first 6 years and then started to decrease. The recharging (injection) water tended to concentrate along the bottom highly permeable layer and accounted for over 64% of the outflow in the 100th year of the simulation test. The outflow temperature decreased from 53.9°C to 50°C in the 32nd year, making it less viable for subsequent sustainable exploitation. Hence, a larger well spacing is required for long-term operation based on the same geothermal reservoir. It was found that a spacing of 400 m could guarantee an outflow temperature above 50°C over a 100-year lifespan with an 80 m³/h pumping (production) rate. Moreover, the sustainability of the 600-m spacing was almost 2.5 times that of the 400 m case. The modeling and analysis method can be useful for the development and optimization of a doublet-well geothermal system under similar conditions.

In CO₂ geological storage, multiphase flow plays a vital role in the movement and distribution of CO₂. However, due to the limitations of fluid buoyancy and capillary forces, CO₂ encounters challenges in penetrating the caprock, and the potential for leakage remains a concern due to variations in injection conditions. The migration and distribution of CO₂ in the process of CO₂ geological storage in saline formations are determined by relative permeability and capillary pressure, which are key factors. Consequently, this study focuses on two essential models: relative permeability and capillary pressure models. A two-dimensional isothermal reservoir–caprock model was constructed, utilizing data from the Shenhua CCS demonstration project. The analysis indicates that the core parameters in the model are residual gas saturation and residual water saturation. Specifically, residual gas saturation governs the diffusion distance of CO₂ within the reservoir–caprock system, while its combined effect with residual water saturation affects the permeation rate of CO₂. Through the application of the Analytic Hierarchy Process (AHP) to analyze the impact of different models on caprock integrity, it was determined that when selecting caprock models and optimizing parameters, precedence should be given to models with lower residual saturation and caprocks that offer sufficient capillary pressure for optimal sealing effects. These research findings can serve as references for practical CO₂ storage projects, providing guidance on activities such as adjusting water injection strategies and controlling gas injection pressures to optimize geological storage efficiency.