The productivity prediction of deep coalbed methane (CBM) wells is significantly influenced by gas-water two-phase flow characteristics and seepage parameters of the fracture network. While numerical simulations offer a comprehensive approach, analytical models are favored for their faster and broader applicability. However, conventional analytical models often oversimplify the complex problem of two-phase seepage equations, leading to substantial errors in dynamic analysis outcomes. Addressing this shortcoming, we establish a gas-water two-phase productivity prediction model for deep CBM reservoirs. This model takes into account the two-phase flow characteristics within the reservoir and fracture network, as well as the stress sensitivity of the reservoir and fractures. Additionally, a modified trilinear flow model characterizes the fractured modification body. By integrating the flowing material balance equation with the Newton Iteration method, we gradually update the seepage model’s nonlinear parameters using the average formation pressure. We also linearize the gas-water two-phase model through successive iterations to derive a semi-analytical solution. The accuracy of the model was verified through comparison with commercial numerical simulation software results and field application. The model also enabled us to scrutinize the influence of reservoir and fracture network parameters on productivity. Our research findings suggest that the semi-analytical solution approach can efficiently address the nonlinear seepage problem of gas-water two-phase flow, enabling quick and accurate prediction of deep CBM well productivity. Moreover, appropriate fracture network parameters are paramount for enhancing the productivity of deep CBM wells. Lastly, during the development of deep CBM reservoirs, it is crucial to control the production pressure difference appropriately to minimize the stress sensitivity impact on production capacity.

In the production process of tight gas wells, reservoir fluid distribution and gas-water relative permeability vary with time. However, traditional models fail to handle the time-dependent mechanism and stress sensitivity effect in the reservoir, leading to significant errors in the dynamic analysis results. To address this issue, this article presents a prediction model for fractured well production in tight gas reservoirs. It is based on a three-dimensional embedded discrete fracture model (EDFM), which considers the influences of the time-dependent mechanism and stress-dependent reservoir permeability. Transient flow equations are treated by using the finite volume method to obtain the solution of the model. The accuracy and reliability of the model are verified by comparison with the results of the commercial simulator Eclipse and the field application. Based on the model's solution, this study emphasizes the analysis of the impact of the time-dependent mechanism and reservoir stress sensitivity on gas well productivity. Simulation results show that the time-dependent relative permeability curve can decrease the level of irreducible water saturation and promote the migration of irreducible water, resulting in an increase in water permeability and a decrease in gas permeability. This effect will reduce the period of stable gas production and increase the level of water production. Besides, reservoir stress sensitivity will reduce daily water production and accelerate gas well decline. It is necessary to control the production pressure difference reasonably during the production process to effectively reduce the negative impact of stress sensitivity effects. The results indicate that when the relative permeability curve and the reservoir permeability are constant, the real gas production capacity of the reservoir will be strengthened. The application of field case studies shows that the theoretical model exhibits stronger adaptability, achieves better fitting results, and can guide the compilation and adjustment of development plans for water-bearing tight gas reservoirs. These findings provide insights into understanding the effects of the time-dependent mechanism on gas production rates in tight gas reservoirs. Furthermore, this study offers useful guidance for the prediction of field-scale gas production.

In the field of CO₂ capture utilization and storage (CCUS), recent advancements in active-source monitoring have significantly enhanced the capabilities of time-lapse acoustical imaging, facilitating continuous capture of detailed physical parameter images from acoustic signals. Central to these advancements is time-lapse full waveform inversion (TLFWI), which is increasingly recognized for its ability to extract high-resolution images from active-source datasets. However, conventional TLFWI methodologies, which are reliant on gradient optimization, face a significant challenge due to the need for complex, explicit formulation of the physical model gradient relative to the misfit function between observed and predicted data over time. Addressing this limitation, our study introduces automatic differentiation (AD) into the TLFWI process, utilizing deep learning frameworks such as PyTorch to automate gradient calculation using the chain rule. This novel approach, AD-TLFWI, not only streamlines the inversion of time-lapse images for CO₂ monitoring but also tackles the issue of local minima commonly encountered in deep learning optimizers. The effectiveness of AD-TLFWI was validated using a realistic model from the Frio-II CO₂ injection site, where it successfully produced high-resolution images that demonstrate significant changes in velocity due to CO₂ injection. This advancement in TLFWI methodology, underpinned by the integration of AD, represents a pivotal development in active-source monitoring systems, enhancing information extraction capabilities and providing potential solutions to complex multiphysics monitoring challenges.

Two-phase (⁠ $gas+water$⁠) flow is quite common in tight sandstone gas reservoirs during flowback and early-time production periods. However, many analytical models are restricted to single-phase flow problems and three-dimensional fracture characteristics are seldom considered. Numerical simulations are good choices for this problem, but it is time consuming in gridding and simulating. This paper presents a comprehensive hybrid model to characterize two-phase flow behaviour and predict the production performance of a fractured tight gas well with a three-dimensional discrete fracture. In this approach, the hydraulic fracture is discretized into several panels and the transient flow equation is solved by the finite difference method numerically. A three-dimensional volumetric source function and superposition principle are deployed to capture the flow behaviour in the reservoir analytically. The transient responses are obtained by coupling the flow in the reservoir and three-dimensional discrete fracture dynamically. The accuracy and practicability of the proposed model are validated by the numerical simulation result. The results indicate that the proposed model is highly efficient and precise in simulating the gas/water two-phase flow and evaluating the early-time production performance of fractured tight sandstone gas wells considering a three-dimensional discrete fracture. The results also show that the gas production rate will be overestimated without considering the two-phase flow in the hydraulic fracture. In addition, the influences of fracture permeability, fracture half-length, and matrix permeability on production performance are significant. The gas production rate will be higher with larger fracture permeability at the early production period, but the production curves will merge after fracturing fluid flows back. A larger fracture half-length and matrix permeability can enhance the gas production rate.

Water breaks through along fractures is a major concern in tight sandstone reservoirs with a bottom aquifer. Analytical models fail to handle the three-dimensional two-phase flow problem for partially penetrating inclined fractures, so time-consuming numerical simulation are often used for this problem. This paper presents an efficient semianalytical model for this problem considering three-dimensional fractures and two-phase flow. In the model, the hydraulic fracture is handled discretely with a numerical discrete method. The three-dimensional volumetric source function in real space and superposition principle are employed to solve the model analytically for fluid flow in the reservoir. The transient flow equations for flow in three-dimensional inclined fractures are solved by the finite difference method numerically, in which two-phase flow and stress-dependent properties are considered. The eventual solution of the model and transient responses are obtained by coupling the model for flow in the reservoir and discrete fracture dynamically. The validation of the semianalytical model is demonstrated in comparison to the solution of the commercial reservoir simulator Eclipse. Based on the proposed model, the effects of some critical parameters on the characteristics of water and oil flow performances are analyzed. The results show that the fracture conductivity, fracture permeability modulus, inclination angle of fractures, aquifer size, perforation location, and wellbore pressure drop significantly affect production rate and water breakthrough time. Lower fracture conductivity and larger inclination angle can delay the water breakthrough time and enhance the production rate, but the increment tends to decline gradually. Furthermore, water breakthrough will occur earlier if the wellbore pressure drop and aquifer size are larger. Besides, the stress sensitivity and perforation location can delay the water breakthrough time.

A novel colloidal dispersion gel (CDG) was synthesized by cross-linking polysaccharide-based hyperbranched polymer (SMHBP) with aluminum citrate. Four factors affecting gelation properties were investigated including SMHBP concentration, the weight ratio of polymer to cross-linker, NaCl concentration, and additive concentration. Environmental scanning electron microscope (ESEM) was used to observe the morphologies of the CDG to understand the cross-linked mechanism. The CDG is cross-linked by both intramolecular and intermolecular, and the formation of the CDG is dominated by the intramolecular cross-linking reaction. Core displacement experiments demonstrated that the novel CDG obtained excellent profile modification performances at a high temperature and high salinity.