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In engineering, gelled acids play a crucial role in facilitating reactive flow phenomena across diverse mediums. This study undertakes a comprehensive numerical investigation into the reactive flow dynamics within fracture-vuggy carbonates, employing gelled acid as the agent. The mathematical model intricately couples thermal, hydrological, and chemical aspects to provide a holistic understanding of the process. Fractures are meticulously modeled using a pseudo-fracture approach, while vugs are delineated as highly porous matrix clusters. The simulation meticulously examines the influence of vugs and fractures, in conjunction with the rheological behavior of gelled acid, on the dissolution process. Our findings reveal that compared to hydrochloric acid, gelled acid is more effective in treating high-temperature carbonate rocks. A lower power law index induces a more pronounced response in shear stress, resulting in a more uniform dissolution pattern. Moreover, the presence of vugs and fractures exerts a significant impact on both the trajectory of wormhole growth and its penetration depth. As the length of fractures increases and their number multiplies, their dominant influence on the growth of wormholes becomes more pronounced. Furthermore, an abundance of fractures may attenuate the influence of vugs. This study highlights the importance of controlling the power-law index and understanding the complex interactions between fractures and vugs for reactive flow.

The rapid and accurate forecasting of two-phase flow in porous media is a critical challenge in oil field development, exerting a substantial impact on optimization and decision-making processes. Although the Convolutional Long Short-Term Memory (ConvLSTM) network effectively captures spatiotemporal dynamics, its generalization in predicting complex engineering problems remains limited. Similarly, although the Fourier Neural Operator (FNO) demonstrates adeptness at learning operators for solving partial differential equations (PDEs), it struggles with three-dimensional, long-term prediction. In response to these limitations, we introduce an innovative hybrid model, the Convolutional Long Short-Term Memory-Fourier Neural Operator (CL-FNO), specifically designed for the long-term prediction of three-dimensional two-phase flows. This model integrates a 3D convolutional encoder–decoder structure to extract and generate hierarchical spatial features of the flow fields. It incorporates physical constraints to enhance the model's forecasts with robustness through the infusion of prior knowledge. Additionally, a temporal function, constructed using gated memory-forgetting mechanisms, augments the model's capacity to analyze time series data. The efficacy and practicality of the CL-FNO model are validated using a synthetic three-dimensional case study and application to an actual reservoir model. [ABSTRACT FROM AUTHOR]

Machine learning techniques have garnered significant attention in various engineering disciplines due to their potential and benefits. Specifically, in reservoir numerical simulations, the core process revolves around solving the partial differential equations delineating oil, gas, and water flow dynamics in porous media. Discretizing these partial differential equations via numerical methods is one cornerstone of this simulation process. The synergy between traditional numerical methods and machine learning can enhance the precision of partial differential equation discretization. Moreover, machine learning algorithms can be employed to solve partial differential equations directly, yielding rapid convergence, heightened computational efficiency, and accuracies surpassing 95%. This manuscript offers an overview of the predominant numerical methods in reservoir simulations, focusing on integrating machine learning methodologies. The innovations in fusing deep learning techniques to solve reservoir partial differential equations are illuminated, coupled with a concise discussion of their inherent advantages and constraints. As machine learning continues to evolve, its conjunction with numerical methods is poised to be pivotal in addressing complex reservoir engineering challenges. [ABSTRACT FROM AUTHOR]

Acidizing is an economical and effective practice to remove the near wellbore damage, which is performed by injecting acid into the formation through the wellbore. The injected acid dissolves the rock, by which the permeability nearby the wellbore can be improved. For a carbonate reservoir, the injected acid dissolves some of the minerals and some narrow and long channels, named wormholes, are formed then. These wormholes can bypass the damaged zone and hence improve the productivity of the well. The process for acid dissolving rocks involves complex physicochemical change, including the chemical reactions at the pore scale and the fluid flow at Darcy scale. In this paper, a 3-D reactive flow model with non-Darcy framework is developed based on the two-scale continuum model, and is solved by using the finite volume method. Five types of dissolution patterns, named face dissolution, conical wormhole, wormhole, ramified wormhole, and uniform dissolution, are obtained as the injection velocity increases. The effect of non-Darcy flow on dissolution pattern and breakthrough volume is analyzed. It is found that there is no effect of non-Darcy on dissolution structure and breakthrough volume when the injection velocity is very low. However, when the injection velocity is very high, the generated wormhole has more branches when using the Forchheimer equation than using the Darcy equation. Moreover, the optimal injection velocity is found to be the same whether considering the non-Darcy flow or not.

Inverse modeling can provide a reliable geological model for subsurface flow numerical simulation, which is a challenging issue that requires calibration of the uncertain parameters of the geological model to establish an acceptable match between simulation data and observation data. The general inverse modeling method needs to iteratively adjust the uncertain parameters, which is a difficult and time‐consuming high‐dimensional sampling problem. To address this problem, we propose a deep‐learning‐based inverse modeling method called pix2pixGAN‐DSI. In this method, the deep‐learning‐based image‐to‐image generative adversarial network (pix2pixGAN) is constructed to directly predict the posterior parameter fields from the posterior dynamic responses obtained by the data‐space inversion (DSI) method. This inverse modeling method does not need to iteratively adjust the uncertain parameters, which improves computational efficiency. The effectiveness of the proposed method is verified through a Gaussian model case and two non‐Gaussian channelized model cases. Through the analysis of posterior realizations, matching and forecast of production data, and uncertainty quantification, the results show that the proposed method can obtain reasonable estimates without iteration and parameterization. Plain Language Summary: Numerical simulation is an effective means to characterize the flow of subsurface fluid and achieve efficient development of subsurface resources. Inverse modeling can calibrate the uncertain parameters of the numerical model and thus ensure simulation accuracy. However, most inverse modeling methods are based on iteratively adjusting the uncertain parameters, which requires performing a great deal of time‐consuming numerical simulations. In the last decades, significant progress has been made in the field of machine learning, especially in the field of deep learning. In this study, we use the generative adversarial network (a key achievement of deep learning) in combination with the data‐space inversion method to establish a novel inverse modeling workflow. The effectiveness of the proposed method is validated by three case analyses. Key Points: A deep conditional generative adversarial network is developed to generate posterior parameter fields from the posterior dynamic responsesThe data‐space inversion method is implemented to sample the posterior dynamic responses from prior model simulations and observed dataThe proposed method is end‐to‐end, avoids parameterization, and can deal with complex geological parameter inversion problems [ABSTRACT FROM AUTHOR]

Waterflooding reservoir interwell connectivity characterization is the fundamental work in oil development, aiming to inverse the vital connecting channels between injectors and producers. In this paper, we endow an artificial neural network (ANN) with strong interpretability through the ordinary differential equation (ODE) of the material balance equation, proposing a physical knowledge fusion neural network (PKFNN). In addition, the proposed model could inherit the knowledge learned from different injector–producer pairs, fully improving the training efficiency. In this way, PKFNN combines the merits of both physical and machine learning approaches. Firstly, based on the physical control law and the ODE of the material balance equation, we endow the model with highly transparent modular architectures in the framework of feedforward neural network. In this way, our work has both high interpretability and excellent approximation ability, combining the merits of the physical and machine learning approaches. The proposed model shows great performance on productivity forecast and interwell connectivity reflection in several reservoir experiments. PKFNN provides a novel way to enhance the interpretability and robustness of the data-driven-based interwell connectivity-analyzing models by integrating the physical knowledge of waterflooding reservoirs. [ABSTRACT FROM AUTHOR]

Acidizing is a widely adopted approach for stimulating carbonate reservoirs. The two-scale continuum (TSC) model is the most widely used model for simulating the reactive process in a carbonate reservoir during acidizing. In realistic cases, there are overburden pressure and pore pressure at present. When the injected acid reacts with the rock, the dissolution of the rock and the consumption of the acid in the pore will break the mechanical balance of the rock. Many experimental studies show that cores after acidizing have lower strength. However, it is still not clear how the deformation of rocks by the change of ground stress influences the acidizing dynamics. For fractured carbonate reservoirs, fractures play a leading role in the flow of injected acid, which preferentially flows into the fractures and dissolves the fracture walls. The effect of the combined action of rock mechanical balance broken and fracture wall dissolution on the formation of wormholes in fractured carbonate reservoirs remains to be studied. To address the above-mentioned issues, a thermal-hydrologic-mechanical-chemical coupled model is presented based on the TSC model for studying the wormhole propagation in fractured carbonate reservoirs under practical conditions. Linear and radial flow cases are simulated to investigate the influences of fracture distribution, reaction temperature, and effective stress on acidizing dynamics. The simulation results show that more wormhole branches are formed by acidizing if the fractures are perpendicular to the flow direction of acid. Temperature is a key parameter affecting the acidification dissolution patterns, so the influence of temperature cannot be ignored during the acidification design. As the effective stress of the formation increases, the diameter of the wormhole gradually decreases, and the branching decreases. More acid is needed for the same stimulation result under higher effective stress. [ABSTRACT FROM AUTHOR]

The formation of stratigraphy in shallow marine environments has long been an important topic within the geologic community. Although many advances have been made in the field of forward stratigraphic modeling (FSM), there are still some areas that can be improved in the existing models. In this work, the authors present our recent development and application of Sedapp, which is a new nonlinear open-source R code for FSM. This code uses an integrated depth–distance related function as the expression of the transport coefficient to underpin the FSM with more alongshore details. In addition to conventional parameters, a negative-feedback sediment supply rate and a differentiated deposition–erosion ratio were also introduced. All parameters were implemented in a nonlinear manner. Sedapp is a 2DH tool that is also capable of running 1DH scenarios. Two simplified case studies were conducted. The results showed that Sedapp not only assists in geologic interpretation but is also an efficient tool for internal architecture predictions. [ABSTRACT FROM AUTHOR]

Low-permeability reservoirs have tiny pores with winding and complicated pore throats. The oil recovery efficiency of low-permeability reservoirs can be enhanced through the displacement of reservoir oil through imbibition. In the present study, experiments were conducted to investigate variations in the imbibition height of hydrophilic and weakly-hydrophilic rock samples under different interfacial tensions. An imbibition model considering imbibition resistance and bending of pore throats was established based on fractal theory. According to the experimental results, variations in the imbibition height of low-permeability rock samples with time can be divided into three stages. In the first stage, the capillary force plays a dominant role, while the viscous force and gravity have very slight effects. The imbibition height first increases rapidly and then levels off to a constant rate. With the increase in interfacial tension, the imbibition rate in the first stage increases, the ultimate imbibition height increases initially and then decreases, and the contribution of the imbibition height in the first stage to the ultimate imbibition height becomes greater. There is an optimal interfacial tension that causes the ultimate imbibition height to reach its maximum. The calculated results obtained from the proposed imbibition model are consistent with the experimental results, indicating that the model can accurately reflect the change in the imbibition height in low-permeability reservoirs in the first stage. [ABSTRACT FROM AUTHOR]

• An enriched physics-informed neural network named E-PINN is developed for predicting two-phase flow in 2D/3D heterogeneous and fractured porous media without labeled data. • A novel physics-informed neural network architecture adopting the adjacency-location anchoring, adaptive activation function, skip connection and gated updating is developed to enrich the pressure information and enhance the learning ability of neural network. • The superiority and applicability of E-PINN to complex practical problems is demonstrated through the simulations of immiscible displacement in 2D/3D heterogeneous and fractured reservoirs. Physics-informed neural networks (PINNs) have received great attention as a promising paradigm for forward, inverse, and surrogate modeling of various physical processes with limited or no labeled data. However, PINNs are rarely used to predict two-phase flow in heterogeneous and fractured porous media, which is critical to lots of subsurface applications, due to the significant challenges in their training. In this work, we present an Enriched Physics-Informed Neural Network (E-PINN) to overcome these barriers and realize the simulation of such flow. Specifically, the Embedded Discrete Fracture Model (EDFM) is adopted to explicitly represent fractures, and then the finite volume method (FVM) instead of the Automatic Differentiation (AD) is used to evaluate spatial derivatives and construct the physics-informed loss function, so that the flux continuity between neighboring elements with different properties (e.g. matrix and fracture) can be defined rigorously. Besides, we develop a novel physics-informed neural network (NN) architecture adopting the adjacency-location anchoring, adaptive activation function, skip connection and gated updating to enrich the pressure information and enhance the learning ability of NN. Additionally, the initial and boundary conditions are constrained through a hard approach, which encodes them into network design, to improve the accuracy and efficiency of network training. In order to further reduce the difficulty of training, the Implicit-Pressure Explicit-Saturation (IMPES) scheme is used to calculate pressure and saturation, in which only the pressure needs to be solved by training NN. Finally, the superiority and applicability of E-PINN to complex practical problems is demonstrated through the simulations of immiscible displacement in 2D/3D heterogeneous and fractured reservoirs. [ABSTRACT FROM AUTHOR]

Highlights • An efficient numerical model is proposed to simulate the hydro-mechanical coupling in the fractured vuggy porous media containing multi-scale fractures and vugs. • An improved equivalent continuum model, which is obtained through the asymptotic homogenization method, is applied to model micro fractures and vugs. • New mixed space discretization (i.e., mimetic finite difference method for flow and stabilized eXtended finite element method for geomechanics) and fully coupled methods are applied to solve the proposed model. Abstract In this study, an efficient numerical model is proposed to simulate the hydro-mechanical coupling in the fractured vuggy porous media containing multi-scale fractures and vugs. Specifically, an improved Equivalent Continuum Model (ECM), which is obtained through the asymptotic homogenization method, is applied to model micro fractures and vugs, while macro fractures are modeled explicitly by using the Embedded Discrete Fracture Model (EDFM) and non-matching grids. As an important feature of the explicit representment, the effects of fillings and fluid pressure on preventing macro fractures from closing can be considered. After that, the new mixed space discretization (i.e., Mimetic Finite Difference (MFD) method for flow and stabilized eXtended Finite Element Method (XFEM) for geomechanics) and fully coupled methods are applied to solve the proposed model. The mixed space discretization can deal with complex heterogeneous properties (e.g., full tensor permeability), and yields the benefits of local mass conservation and numerical stability in space. Finally, we demonstrate the accuracy and application of the proposed model to capture the coupled hydro-mechanical impacts of multiscale fractures and vugs on fluid flow in fractured porous media. [ABSTRACT FROM AUTHOR]

We use a two-scale continuum model to simulate reactive flow and wormhole formation in carbonate rocks under 3-D radial flow conditions. More specifically, we present a new structure-property relationship based on the fractal geometry theory, to describe the evolution of local permeability, pore radius, and specific area with porosity variation. In the numerical calculation, to improve the convergence rate, the heterogeneous medium in question is extended by adding a thin layer of homogeneous porous medium to its inlet. We compare the simulation results with the available experimental observations and find that they are qualitatively consistent with each other. Additionally, sensitivity analysis of the dissolution process with respect to acid injection rate and rock heterogeneity, including heterogeneity magnitude and correlation length, is presented.