Summary: We derive and implement an interwell-numerical-simulation model (INSIM), which can be used as a calculation tool to approximate the performance of a reservoir under waterflooding. In INSIM, the reservoir is characterized as a coarse model consisting of a number of interwell control units, where each unit has two specific parameters: transmissibility and control pore volume (PV). By solving the mass-material-balance and front-tracking equations for the control units, the interwell fluid rates and saturations are obtained so that phase-producing rates can be predicted. The ability of INSIM to predict water cut and phase rates is the most important innovation included in INSIM. INSIM is applied to perform history matching and to infer the interwell connectivity and geological characteristics. INSIM has a number of advantages. First, the model parameters estimated from history matching provide a relative characterization of interwell-formation properties. The model can handle changes in the flow directions caused by changing well rates, including shutting in wells or converting producers to injectors, whereas with the common correlation-based interwell-connectivity method, the well interactions are assumed to be fixed. Second, the previous methods, which have similar computational complexity to INSIM, can only provide the total liquid-production rate, whereas with our procedure, we can calculate the oil- and water-flow rates and hence history match water-cut data. Third, because we can calculate the oil- and water-flow rates, our method can be used for waterflooding optimization but with far-less computational effort than with the traditional method by use of a reservoir simulator.

This paper applies generalized finite difference method (GFDM) to a compressible two-phase flow in anisotropic porous media with the aim of further extending the wider application of this class of meshless methods. We develop an implicit Euler scheme in time and a GFDM discretization in space based on two treatments of the anisotropic permeability tensor in continuous function expression and discrete distribution. The effectiveness and generality of GFDM for two-phase flow problems in anisotropic porous media are verified by three examples with rectangular, irregular, and complex boundaries. Also, the computational performance of the method is verified according to the error calculation with L2 absolute error functions in different node collocation schemes. In addition, the sensitivity analysis of the radius of the influence domain to the transient pressure equation (parabolic equation) and the saturation equation (hyperbolic equation) is considered. It generally holds that the larger the radius of the influence domain, the lower the calculation accuracy in the case of Cartesian collocation. This may be a preliminary rule for the radius choice of the influence domain for GFDM. In sum, this work provides an efficient and accurate meshless solver to handle two-phase flow problems in anisotropic porous media under the GFDM framework, which reveals the great application potential of GFDM in reservoir numerical simulation.

Displacement behavior of methane in organic nanochannels in aqueous environment

The distribution of matrix pressure and water saturation during the fracturing and shut-in period significantly impacts shale gas production. However, traditional numerical simulations primarily focus on the production period, often overlooking the impact of fracturing and shut-in on the seepage field and production rates. This study uses the dual-porosity/dual-permeability-embedded discrete fracture model (DPDK-EDFM) to characterize matrix mixed wettability and the natural/hydraulic fracture geometry. A multiscale numerical simulation model is constructed to encompass the whole life cycle of shale fracturing, shut-in, and production. The model provides a comprehensive understanding for considering the changes in rock properties and the diverse migration mechanisms. Subsequently, the life cycle model is used for sensitivity analysis on capillary pressure, shut-in time, and fracturing fluid volume. The findings demonstrate that (1) capillary pressure strongly impacts flowback rate. As surface tension increases from 0 to 72 mN/m, the flowback rate decreases from 113.00% to 68.25%. (2) The shut-in time strongly affects the uniformity of pressure distribution. (3) The fracturing fluid volume is directly proportional to the rise in formation pressure. This innovative model provides a robust framework for simulating and analyzing the seepage field behavior of shale gas reservoirs throughout the life cycle. Furthermore, through a comprehensive investigation of the main controlling factors, this study provides valuable insights into the efficient development of shale gas reservoirs, carrying both theoretical and practical significance.

This study combines convolutional neural networks, spatial pyramid pooling, and long short-term memory networks (LSTM) with self-attention (SA) mechanisms (abbreviated as CSAL) to address the problem of production dynamics prediction in tight reservoirs during the CO2 water-alternating-gas (CO2-WAG) injection process. By integrating DenseNet and SPP modules, this method effectively captures and processes complex spatial features in tight reservoirs. Concurrently, the LSTM enhanced with SA mechanisms improves the prediction capability of temporal data during the CO2-WAG process. Experimental results demonstrate that the CSAL model performs excellently in both the training and testing phases, achieving a coefficient of determination (R2) exceeding 0.98, significantly enhancing the model's prediction accuracy. Compared to models without attention mechanisms, the CSAL model increases the R2 value in time series prediction by 10%. Furthermore, employing the Ensemble Smoother with Multiple Data Assimilation algorithm, the CSAL model achieves high-precision history matching, significantly reducing the error between predicted values and actual observations. This study validates the application potential and superiority of the CSAL model in the CO2-WAG process in tight reservoirs.

Summary: This paper presents a novel approach to the numerical simulation of fractured reservoirs, called the connection element method (CEM), which differs from traditional grid-based methods. The reservoir computational domain is discretized into a series of nodes, and a system of connection elements is constructed based on the given connection lengths and angles. The pressure diffusion term is approximated using generalized finite difference theory. Meanwhile, the transmissibility and volume of the connection elements are determined, and pressure equations are solved discretely to obtain pressure at nodes to approximate the upstream flux along connection elements. Then, we solve the transport equation to obtain oil saturation profiles with low numerical diffusion, utilizing the discontinuous Galerkin (DG) method. Moreover, the flow path tracking algorithm is introduced to quantify the flow allocation factors between wells. In all, the pressure equation can be solved at a global coarse-scale point cloud and the saturation equation is calculated at a local fine-scale connection element. In other words, CEM is of multiscale characteristics relatively. Finally, several numerical examples are implemented to demonstrate that CEM can achieve a relatively better balance between computational accuracy and efficiency compared with embedded discrete fracture modeling (EDFM). Furthermore, CEM adopts flexible meshless nodes instead of grids with strong topology, making it more practical to handle complex reservoir geometry such as fractured reservoirs.