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Recent Submissions

  • Stability analysis of the water bridge in organic shale nanopores: A molecular dynamic study

    Liu, Jie; Zhang, Tao; Sun, Shuyu (Capillarity, Yandy Scientific Press, 2022-08-13) [Article]
    In the last decades, shale gas development has relieved the global energy crisis and slowed global warming problems. The water bridge plays an important role in the process of shale gas diffusion, but the stability of the water bridge in the shale nanochannel has not been revealed. In this work, the molecular dynamics method is applied to study the interaction between shale gas and water bridge, and the stability can be tested accordingly. CO2 can diffuse into the liquid H2O phase, but CH4 only diffuses at the boundary of the H2O phase. Due to the polarity of H2O molecules, the water bridge presents the wetting condition according to model snapshots and one-dimensional analyses, but the main body of the water bridge in the two-dimensional contour shows the non-wetting condition, which is reasonable. Due to the effect of the molecular polarity, CO2 prefers to diffuse into kerogen matrixes and the bulk phase of water bridge. In the bulk of the water bridge, where the interaction is weaker, CO2 has a lower energy state, implies that it has a good solubility in the liquid H2O phase. Higher temperature does not facilitate the diffusion of CO2 molecules, and higher pressure brings more CO2 molecules and enhances the solubility of CO2 in the H2O phase, in addition, a larger ratio of CO2 increases its content, which does the same effects with higher pressures. The stability of the water bridge is disturbed by diffused CO2 , and its waist is the weakest position by the potential energy distribution.
  • Study of the Seawater Desalination Performance by Electrodialysis

    Shi, Jihong; Gong, Liang; Zhang, Tao; Sun, Shuyu (Membranes, MDPI AG, 2022-08-05) [Article]
    The global scarcity of freshwater resources has greatly contributed to the development of desalination technologies, in which electrodialysis desalination is one of the most widely used and highly regarded methods. In this work, the first step was to design and assemble a experiment module for electrodialysis desalination. The ion removal efficiency and single membrane mass transfer flux of electrodialysis desalination were investigated. The results show that the desalination performance of the module is improved by increasing the voltage gradient, increasing the concentration of seawater and electrolyte and decreasing the membrane surface flux and that the optimum operating conditions for the module at 24 V operating voltage are feedstock concentration of 35 g/L, electrolyte concentration of 1.42 g/L which and system flow rate of 15 L/h. The results of the study will help to better investigate electrodialysis desalination technology.
  • Phase equilibrium in the hydrogen energy chain

    Zhang, Tao; Zhang, Yanhui; Katterbauer, Klemens; Al Shehri, Abdallah; Sun, Shuyu; Hoteit, Ibrahim (Fuel, Elsevier BV, 2022-07-22) [Article]
    In this paper, a thorough review of the current state of the hydrogen phase equilibrium approaches is presented. Potential applications of phase equilibrium calculations for the accurate simulation of the entire process are then identified. Based on the first and second laws of thermodynamics, an advanced constant (N), volume (V), and temperature (T) (NVT) flash calculation scheme is developed for fluid mixtures containing hydrogen, which can be used to calculate the phase equilibrium for various feed compositions. We produce reasonable predictions of the phase transition under various environmental conditions for a number of engineering scenarios during the hydrogen production and storage processes, thus demonstrating the effectiveness and robustness of the proposed phase equilibrium calculation scheme.
  • A quantitative study on the approximation error and speed-up of the multi-scale MCMC (Monte Carlo Markov chain) method for molecular dynamics

    Liu, Jie; Tang, Qinglin; Kou, Jisheng; Xu, Dingguo; Zhang, Tao; Sun, Shuyu (Journal of Computational Physics, Elsevier BV, 2022-07-21) [Article]
    The past two decades have borne remarkable progress in the application of the molecular dynamics method in a number of engineering problems. However, the computational efficiency is limited by the massive-atoms system, and the study of rare dynamically-relevant events is challenging at the timescale of molecular dynamics. In this work, a multi-scale molecular simulation algorithm is proposed with a novel toy model that can mimic the state transitions in extensive scenarios. The algorithm consists of two scales, including producing the realistic particle trajectory and probability transition matrix in the molecular dynamics scale and calculating the state distribution and residence time in the Monte Carlo scale. A new state definition is proposed to take the velocity direction into consideration, and different coarsening models are established in the spatial and time scales. The accuracy, efficiency, and robustness of our proposed multi-scale method have been validated, and the general applicability is also demonstrated by explaining two practical applications in the shale gas adsorption and protein folding problems respectively.
  • Scalable semismooth Newton methods with multilevel domain decomposition for subsurface flow and reactive transport in porous media

    Cheng, Tianpei; Yang, Haijian; Yang, Chao; Sun, Shuyu (Journal of Computational Physics, Elsevier BV, 2022-07-14) [Article]
    Large-scale modeling and predictive simulations of the subsurface flow and reactive transport system in porous media is significantly challenging, due to the high nonlinearity of the governing equations and the strong heterogeneity of material coefficients. The design of novel mathematical models and state-of-the-art methods for the flow simulation through porous media typically needs to satisfy the so-called bound-preserving property, i.e., the computed solution should stay inside a physically meaningful range. This paper presents a robust, scalable numerical framework based on the variational inequality formulation and the semismooth Newton method in a fully implicit manner, to model and simulate highly nonlinear flows without violating the boundedness requirement of the solution. Rigorous theoretical analysis for the variational inequality formulation of the problem is provided for facilitating the design of algorithms. Specifically, our approach further enhances the numerical formulation by utilizing a family of multilevel monolithic overlapping Schwarz methods for efficiently preconditioning, and the parallel implementation of the bound-preserving solver is based on the fast and robust domain decomposition technique. Numerical experiments are presented to demonstrate the efficiency and parallel scalability of the solution strategy for both standard benchmarks as well as realistic flow problems involving strong heterogeneity and high nonlinearity. We also show that the proposed framework is more robust and efficient than the commonly used inexact Newton algorithm in terms of the bound-preserving property.
  • Scalable semismooth Newton methods with multilevel domain decomposition for subsurface flow and reactive transport in porous media

    Cheng, Tianpei; Yang, Haijian; Yang, Chao; Sun, Shuyu (Journal of Computational Physics, Elsevier BV, 2022-07-14) [Article]
    Large-scale modeling and predictive simulations of the subsurface flow and reactive transport system in porous media is significantly challenging, due to the high nonlinearity of the governing equations and the strong heterogeneity of material coefficients. The design of novel mathematical models and state-of-the-art methods for the flow simulation through porous media typically needs to satisfy the so-called bound-preserving property, i.e., the computed solution should stay inside a physically meaningful range. This paper presents a robust, scalable numerical framework based on the variational inequality formulation and the semismooth Newton method in a fully implicit manner, to model and simulate highly nonlinear flows without violating the boundedness requirement of the solution. Rigorous theoretical analysis for the variational inequality formulation of the problem is provided for facilitating the design of algorithms. Specifically, our approach further enhances the numerical formulation by utilizing a family of multilevel monolithic overlapping Schwarz methods for efficiently preconditioning, and the parallel implementation of the bound-preserving solver is based on the fast and robust domain decomposition technique. Numerical experiments are presented to demonstrate the efficiency and parallel scalability of the solution strategy for both standard benchmarks as well as realistic flow problems involving strong heterogeneity and high nonlinearity. We also show that the proposed framework is more robust and efficient than the commonly used inexact Newton algorithm in terms of the bound-preserving property.
  • Thermodynamically-consistent flash calculation in energy industry: From iterative schemes to a unified thermodynamics-informed neural network

    Zhang, Tao; Sun, Shuyu; Bai, Hua (International Journal of Energy Research, John Wiley and Sons Ltd, 2022-06-29) [Article]
    Multicomponent multiphase fluid flows are commonly seen in the engineering practice of hydrocarbon production and transportation; thus, the phase-wise heat and mass transfer mechanisms underneath the macroscopic flow and transport behaviors are essentially needed for better understanding of the physical phenomena and optimization of the industrial processes. Flash calculation, as the main approach computing phase equilibrium conditions, has arisen increasing interests to establish the thermodynamic foundations of multiphase flow simulation, as well as to determine whether two-phase model is needed. In this paper, the general thermodynamically-consistent flash calculation scheme will be developed, and the general adaptability to various special mechanisms will be analyzed. A unified framework of thermodynamics-informed neural network will also be designed to accelerate conventional iterative flash calculation schemes that will be applied in various engineering scenarios to provide certain suggestions to the energy industry based on the predictions and analysis. Novelty Statement: A thermodynamically-consistent flash calculation scheme incorporating various special mechanisms that are often met in energy industry. A unified thermodynamics-informed neural network structure for various engineering demands in the energy industry. Suggestions to the energy industry to optimize the productions based on the phase transition predictions and analysis.
  • Study on the multiphase heat and mass transfer mechanism in the dissociation of methane hydrate in reconstructed real-shape porous sediments

    Song, Rui; Liu, Jianjun; Yang, Chunhe; Sun, Shuyu (Energy, Elsevier BV, 2022-06-09) [Article]
    As the first effort in literature, this paper conducts pore scale modeling on the methane hydrate dissociation and transportation in the reconstructed three-dimensional models of the MH-bearing sediment. The porous MH sample is synthesized using excess-gas method and imaged by micro-CT, which is used as input for the reconstructed mesh models. The real-time distribution of MH & water & methane, velocity and temperature is investigated. The effects of the temperature, pressure and flow rate of the injected water on MH dissociation and transportation are simulated and discussed. The results indicate that: 1) The hydrate generated by the excess - gas method is mainly cementing and mineral-coating on the sands surface, and occupies the small pores firstly. 2) The heterogeneity of the porous MH sediments is one of the key factors which influences the dissociation and the transportation process of the MH. 3) A lack of heat supply will restrict the dissociating rate of the MH reaching the maximum under the given PT conditions. 4) The gathering of the gas will decrease the flowing capacity of both water and methane. This study provides a new method to predict the multiple physicochemical and thermodynamical properties of the porous MH bearing sediments.
  • An Energy Stable SPH Method for Incompressible Fluid Flow

    Zhu, Xingyu; Sun, Shuyu; Kou, Jisheng (ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, Global Science Press, 2022-06) [Article]
    In this paper, a novel unconditionally energy stable Smoothed Particle Hydrodynamics (SPH) method is proposed and implemented for incompressible fluid flows. In this method, we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term separately. The idea behind the splitting is to simplify the calculation while still maintaining energy stability, and the resulted algorithm, a type of improved pressure correction scheme, is both efficient and energy stable. We show in detail that energy stability is preserved at each full-time step, ensuring unconditionally numerical stability. Numerical examples are presented and compared to the analytical solutions, suggesting that the proposed method has better accuracy and stability. Moreover, we observe that if we are interested in steady-state solutions only, our method has good performance as it can achieve the steady-state solutions rapidly and accurately.
  • Molecular anatomy and macroscopic behavior of oil extraction from nanopores by CO2 and CH4

    Moh, Do Yoon; Zhang, Hongwei; Sun, Shuyu; Qiao, Rui (Fuel, Elsevier BV, 2022-05-28) [Article]
    Injecting gas to enhance oil production from unconventional reservoirs dominated by nanoscale pores has been practiced in past decades with varying success, in part due to the lack of a fundamental understanding of the underlying physical processes. Here, we report molecular dynamics simulations of gas-enhanced recovery of decane from single 4 nm-wide calcite pores under reservoir conditions (383 K and 345 bar). Two gases, CO2 and CH4, are considered due to their different adsorption strength on calcite pore walls and practical considerations such as their availability and benefits for carbon sequestration. We show that, upon entering a pore, both gases form two molecular populations (free and adsorbed molecules), and their accumulation leads to the extraction of corresponding decane populations. The CO2-decane exchange is initially significantly driven by the evolution of the adsorbed populations, but a transition to the dominance by free populations occurs later; For the CH4-decane exchange, the opposite occurs. Despite this difference, the overall gas accumulation and decane extraction behavior follow the same diffusive law for CO2 and CH4 gases. The CH4-decane exchange has higher effective diffusivities than the CO2-decane exchange, i.e., CH4 enables faster decane extraction under the conditions studied here. These effective diffusivities do not always align well with the self-diffusion coefficients of CO2, CH4, and decane in nanopores.
  • A rock fabric classification method based on the grey level co-occurrence matrix and the Gaussian mixture model

    Wang, Yuzhu; Sun, Shuyu (Journal of Natural Gas Science and Engineering, Elsevier BV, 2022-05-27) [Article]
    Accurate classification of the rock fabric plays a crucial role in revealing the heterogeneity of the reservoir at different scales. This paper proposes an image-based rock fabric classification method using grey level co-occurrence matrix (GLCM) properties and Gaussian Mixture Model (GMM) as texture descriptors and classifier, respectively. The proposed method is successfully used to classify the images with heterogeneous pore structures and the pictures of outcrops with different sedimentary beddings without preparing the training dataset. According to our results, the classification performance decreases along with the increase of the number of fabric types and the decrease of the structure contrast among different rock types.
  • Thermal cooling performance of convective non-Newtonian nanofluid flowing with variant power-index across moving extending surface

    Ferdows, M; Shamshuddin, M D; Salawu, S O; Sun, Shuyu (Scientific reports, Springer Science and Business Media LLC, 2022-05-24) [Article]
    This communication focuses on assessing the effectiveness of nanoparticles, and a power-law variation fluid on a moving stretching surface is analyzed. Newtonian fluids for different nanomaterials are considered due to its industrial demand. The partial differential equations describing the flow are transformed to ordinary differential equations by employing local similarity transformations and then solved numerically by an effective numerical approach, namely, the local nonsimilarity method (LNS). The numerical solution is computed for different parameters by using the computational software MATLAB. Different types of nanoparticles are considered, and the impact of those nanoparticles as well as the impact of different pertaining parameters on velocity, temperature, missing velocity slope, and missing temperature slope are presented graphically. Comparisons are made with the available results in the open literature. Our investigation conveys a better impact on [Formula: see text] nanoparticles due to their higher thermal conductivity. Furthermore, an increase in the free stream velocity, missing temperature slope and velocity slope is enhanced, but after a point of separation, the missing temperature slope decays.
  • A fully explicit and unconditionally energy-stable scheme for Peng-Robinson VT flash calculation based on dynamic modeling

    Feng, Xiaoyu; Chen, Meng-Huo; Wu, Yuanqing; Sun, Shuyu (Journal of Computational Physics, Elsevier BV, 2022-05-10) [Article]
    Since the Peng-Robinson (PR) equation of state (EoS) has proven itself to be one of the most reliable EoS, especially in the chemical and petroleum industries, the flash calculation based on the PR EoS is considered to be a foundation for describing complex compositional flows and for evaluating hydrocarbon reservoirs. Compared to the traditional Pressure-Temperature (PT) flash calculation, the novel Volume-Temperature (VT) flash calculation has become more appealing due to its advantages, such as less sensitivity to primary variables like pressure or volume. However, previous numerical schemes of the VT flash calculation involved many complicated nonlinear systems, which makes convergence hard to achieve. To treat this challenge, a fully explicit and unconditionally energy-stable scheme is proposed in this work. It is known that the dynamic model for VT flash calculation can preserve both the Onsager's reciprocal principle and the energy dissipation law. By combining the dynamic model and the linear semi-implicit scheme, the moles and volume can be updated, with the advantage that the energy-dissipation feature can be preserved at a discrete level unconditionally. Then, with the convex-concave splitting approach and the component-wise iteration framework, the scheme becomes fully explicit. The scheme shows promising potential not only because it inherits the original energy stability to ensure convergence, but it also reduces the implementation burden significantly in some engineering scenarios. A lot of numerical experiments are carried out. The numerical results show good agreement with benchmark data and the energy decaying trend at a very large time step demonstrates the stability and efficiency of the proposed scheme.
  • Numerical investigations of the PUGA geothermal reservoir with multistage hydraulic fractures and well patterns using fully coupled thermo-hydro-geomechanical modeling

    Gudala, Manojkumar; Govindarajan, Suresh Kumar; Yan, Bicheng; Sun, Shuyu (Energy, Elsevier BV, 2022-05-06) [Article]
    The Puga geothermal reservoir is located in the south-eastern part of Ladakh (Himalayan region, India), and it is providing encouraging results towards heat production. We proposed an improved mathematical model for the fully coupled thermo-hydro-geomechanical model to examine the variations in the Puga geothermal reservoir at between 4500 m from the surface with three, four, and seven hydraulic fractures in the reservoir along with four-spot, five-spot, seven-spot, and nine-spot well patterns. The distribution of low-temperature region is found in each fracture, and it is low in the reservoir with seven hydraulic fractures. The changes in the rock and fluid properties are examined effectively. Thermal strain is dominated in the fractures, and mechanical strain is impressive in the rock matrix; it is dependent on the number of hydraulic fractures and well patterns. The thermal performance of the Puga reservoir is examined with the geothermal life, reservoir impedance, and heat power and found that the number of hydraulic fractures and well patterns are influenced significantly in the multistage modeling of the Puga geothermal reservoir. Thus, the proposed mathematical model can effectively evaluate and predict the variations that occur in the Puga geothermal reservoir with dynamic rock, fracture, and fluid properties.
  • Generalized multiscale finite element methods for the reduced model of darcy flow in fractured porous media

    Alotaibi, Manal; Chen, Huangxin; Sun, Shuyu (Journal of Computational and Applied Mathematics, Elsevier BV, 2022-04-19) [Article]
    In this work, we combine the generalized multiscale finite element method (GMsFEM) with a reduced model based on the discrete fracture model (DFM) to resolve the difficulties of simulating flow in fractured porous media while efficiently and accurately reducing the computational complexity resulting from resolving the fine scale effects of the fractures. The geometrical structure of the fractures is discretely resolved within the model using the DFM. The advantage of using GMsFEM is to represent the fracture effects on a coarse grid via multiscale basis functions constructed using local spectral problems. Solving local problems leads to consideration and usage of small scale information in each coarse grid. Besides, the multiscale basis functions, generated following GMsFEM framework, are parameter independent and constructed once in what we call offline stage. These basis functions can be re-used for solving the problem for any input parameter when it is needed. Combining GMsFEM and DFM has been introduced in other works assuming continuous pressure across the fractures interface. This continuity is obtained when the fractures are much more permeable than that in the matrix domain. In this work, we consider a general case for the permeability in both fracture and matrix domain using the reduced model presented in Martin et al. (2005). The proposed reduction technique has significant impact on enabling engineers and scientist to efficiently, accurately and inexpensively solve the large and complex system resulted from modeling flow in fractured porous media
  • Molecular dynamics simulation of swelling properties of Ca-montmorillonite at high temperatures

    Yang, Ya Fan; Wang, Jian Zhou; Shang, Xiang Yu; Wang, Tao; Sun, Shuyu (Wuli Xuebao/Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, 2022-02-20) [Article]
    The swelling of Ca-montmorillonite at elevated temperatures is important for many applications including geological disposal of radioactive waste, subsurface carbon sequestration, and shale gas exploration. However, the experimentally observed swelling behaviors of Ca-montmorillonite contacting liquid water and the temperature effects on the swelling pressure are not well understood. In this work, molecular dynamics simulations are carried out to study the swelling of Wyoming Ca-montmorillonite with a d-spacing (d) range of 1.40-4.00 nm at 5 MPa and various temperatures (298-500 K). The ClayFF and SPC are adopted for modeling Ca-montmorillonite and water, respectively. The simulation box is measured to be 11.15, 3.66, and 28.00 nm in the x-, y-, and z-direction. Atomistic pistons are used to control the bulk pressure of the water environment, and the implicit walls are implemented for preventing the ions from leaking from the pore into the water environment. The clay atoms are fixed during the simulation and the swelling pressure is calculated through dividing the force by the area. The equilibrium time is at least 20 ns and the production time falls in a range of 50-88 ns. The swelling pressure results show that for small d, high temperature reduces the magnitude of the oscillating curve of swelling pressure and also reduces the range of d where hydration force dominates the swelling pressure. This temperature effect is due to the weakened hydration force as evidenced from the weakened water density distributions inside the pore. For large d, high temperature reduces the swelling pressure, which is consistent with the experimental result, and increases the range of d where double layer force dominates the swelling pressure. The reduction of the swelling pressure can be explained by the enhanced ion correlation that reduces the double layer force according to the strong coupling theory, given that the calculated coupling parameters at higher temperatures are smaller. The swelling pressures are negative at elevated temperatures and large d, which prevents the clay from further swelling. However, the classical Poisson-Boltzmann (PB) equation predicts the positive double layer force since the ion correlation effect is not considered in the PB equation. Furthermore, the calculated swelling free energy curve shows that at 298 K and 5 MPa, it is difficult for Ca-montmorillonite to swell beyond a d-spacing of around 1.9 nm, which is in good agreement with the experimental result. The energy barrier for Ca-montmorillonite to swell to large d is larger than that for Na-montmorillonite, which means that it is more difficult for Ca-montmorillonite to swell to large d. This behavior is consistent with experimental observation and can be explained by the larger ion correlation effect in the Ca-montmorillonite system. These findings enhance the understanding of swelling of Ca-montmorillonite at elevated temperatures and could help to engineer better barrier materials for nuclear waste storage.
  • Effect of Temperature on Oil–Water Separations Using Membranes in Horizontal Separators

    Zhang, Tao; LI, CHENGUANG; Sun, Shuyu (Membranes, MDPI AG, 2022-02-17) [Article]
    The effect of temperature on oil–water separations is studied in this paper, focusing on the changed penetration velocities of water droplets on the separation membrane in a horizontal separator. A compact numerical scheme is developed based on the phase-field model, and the temperature effect is first theoretically analyzed regarding the key thermodynamic properties that may affect the separation performance. The computational scenario is designed based on practical horizontal separators in the oil field, and the droplet motions in the oil–water two-phase flow are simulated using our scheme under various operation conditions. It was found that a higher temperature may result in a faster penetration of the water droplets, and a larger density difference in the oil–water system is also preferred to accelerate the separation using membranes. Furthermore, increasing the operation temperature is proved to benefit the separation of water and heavy oil.
  • Effects of grain shape and packing pattern on spontaneous imbibition under different boundary conditions: Pore-scale simulation

    Liu, Yang; Chen, Mingjie; Sun, Shuyu; Lei, Zhengdong; Zeng, Jianhui; Cai, Jianchao (Journal of Hydrology, Elsevier BV, 2022-02-09) [Article]
    Core-scale spontaneous imbibition experiments and numerical simulations have demonstrated that the macroscopic imbibition performance is significantly different under different boundary conditions. However, the detailed pore-scale flow mechanisms behind these phenomena and the influence of porous media's geometric features on the imbibition behavior under different boundaries have not been addressed in depth. In this work, an optimized color-gradient lattice Boltzmann model is applied to simulate spontaneous imbibition in granular media under four boundary conditions. The influence of grain shape and packing pattern on the two-phase interface evolution and the recovery factor during spontaneous imbibition is investigated while fixing different models' porosity, grain number, and size distribution. It is found that the grain shape has little influence on the drainage interface evolution at the initial stage but it has a more significant influence on the imbibition interface during counter-current spontaneous imbibition. The grain packing pattern influences the evolution of drainage and imbibition interfaces and the recovery factor. Spontaneous imbibition with different boundary conditions has different imbibition rates and ultimate recovery factors. The fastest imbibition rate and highest ultimate recovery are obtained under all faces open and two faces open (free) boundary conditions, respectively. This research provides pore-scale insights into the complex dynamic fluid displacement mechanism between the fracture and matrix of fractured oil and gas reservoirs.
  • A strongly mass conservative method for the coupled Brinkman-Darcy flow and transport

    Zhao, Lina; Sun, Shuyu (arXiv, 2021-12-14) [Preprint]
    In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed formulation with a suitable incorporation of the interface conditions. In particular, the interface conditions can be incorporated into the discrete formulation naturally without introducing additional variables. Moreover, the proposed scheme behaves uniformly robust for various values of viscosity. A novel upwinding staggered DG scheme in mixed form is exploited to solve the transport equation, where the boundary correction terms are added to improve the stability. A rigorous convergence analysis is carried out for the approximation of the flow equations. The velocity error is shown to be independent of the pressure and thus confirms the pressure-robustness. Stability and a priori error estimates are also obtained for the approximation of the transport equation; moreover, we are able to achieve a sharp stability and convergence error estimates thanks to the strong mass conservation preserved by our scheme. In particular, the stability estimate depends only on the true velocity on the inflow boundary rather than on the approximated velocity. Several numerical experiments are presented to verify the theoretical findings and demonstrate the performances of the method.
  • A decoupled scheme to solve the mass and momentum conservation equations of the improved Darcy–Brinkman–Forchheimer framework in matrix acidization

    Wu, Yuanqing; Kou, Jisheng; Wu, Yu-Shu; Sun, Shuyu; Xia, Yilin (AIP Advances, AIP Publishing, 2021-12-01) [Article]
    Matrix acidization simulation is a challenging task in the study of flows in porous media due to the changing porosity in the procedure. The improved Darcy–Brinkman–Forchheimer framework is one model to do this simulation. In this framework, the mass and momentum conservation equations are discretized to form a pressure–velocity linear system. However, the coefficient matrix of the linear system has a large condition number, and solving the linear system belongs to the saddle point problem. As a result of that, convergence is hard to achieve when solving it with iterative solvers. It is well known that the scale of the linear systems in matrix acidization simulation is large, and therefore, the usage of iterative solvers is required. Thus, a decoupled scheme is proposed in this work to decouple the pressure–velocity linear system into two independent linear systems: one is to solve for pressure, and the other one is to solve for velocity. It is emphasized that both of the linear systems are discretized from the elliptical partial differential equations, which guarantees fast convergence can be achieved by iterative solvers. A numerical experiment is carried out to demonstrate the correctness of the decoupled scheme and its higher computing efficiency. After that, the decoupled scheme is applied in investigating the factors that cannot change the optimal injected velocity and the dissolution pattern in matrix acidization.

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