Article
Computer Science, Interdisciplinary Applications
Roza Asadi, Behzad Ataie-Ashtiani
Summary: This study utilized advanced finite volume schemes to model the coupled fluid-solid system, considering various parameters and testing the performance of hydro-mechanical models through different cases. While both MPFA O-FEM and DDFV-FEM methods showed good agreement with analytical solutions in homogeneous porous media, the DDFV-FEM demonstrated higher accuracy in situations with high heterogeneity.
COMPUTERS AND GEOTECHNICS
(2021)
Article
Mechanics
Graham P. Benham, Mike J. Bickle, Jerome A. Neufeld
Summary: This study focuses on upscaling the effect of heterogeneities in porous media, specifically in relation to multiphase flow and the transition between viscous and capillary flow regimes. By modifying the classic Buckley-Leverett problem, the study demonstrates how and where the flow transitions between these regimes and its impact on flooding speeds. The implications of these results in the context of carbon dioxide sequestration are also discussed and compared with field data.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Water Resources
Hrvoje Gotovac, Luka Malenica, Blaz Gotovac
Summary: Many groundwater transport applications require solving Darcy flow in heterogeneous porous media, which can be computationally challenging. Isogeometric analysis (IGA) has been developed to bridge the gap between CAD and numerical analysis, offering continuous velocity fields with optimal convergence rates. Control Volume IsoGeometric Analysis (CV-IGA) methodology enables local and global mass conservation as well as multiresolution description of all heterogeneity scales, providing a more accurate and efficient approach for flow simulations.
ADVANCES IN WATER RESOURCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Zahra Mehrdoost
Summary: The multiscale finite volume method is developed for discrete fracture modeling in highly heterogeneous porous media, with efficient algorithms devised for generating adaptive unstructured coarse grids. Significant improvement of the method in highly heterogeneous fractured porous media is achieved, with good accuracy in flow simulation in challenging test cases.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mechanics
L. C. Auton, S. Pramanik, M. P. Dalwadi, C. W. MacMinn, I. M. Griffiths
Summary: The study explores the link between microstructure and macroscale flow and transport through the use of homogenisation theory with idealised microstructures. The research focuses on the impact of obstacle size and spacing on macroscopic properties and provides insights for designing filters or studying transport impacts in soft porous media.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics, Applied
Rui Li, Yongchao Zhang, Jianhua Wu, Zhangxin Chen
Summary: This paper presents a numerical simulation of the single phase Darcy flow model in two-dimensional fractured porous media. The model is described as a reduced problem by coupling the bulk problem in porous matrix and the fracture problem in fractures. Numerical experiments demonstrate the accuracy, flexibility, and robustness of the discrete formulation for complicated networks of fractures in porous media domain.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Khaled Bouadjila, Ali Samir Saad, Mazen Saad, Wissal Mesfar
Summary: This paper focuses on the convergence analysis of a combined finite volume-non-conforming finite element scheme for approximating the incompressible two-phase flow with dynamic capillary pressure in anisotropic porous media. The diffusion terms are discretized using piecewise linear non-conforming triangular finite elements, while the mobilities are discretized on dual diamond mesh. The mobilities are approximated in a non-standard way to ensure a priori estimates on the global pressure and water saturation. Under the assumption of non-degeneracy of mobilities, the convergence of the combined scheme for the complete two-phase flow, including the non-equilibrium capillary pressure, is proven.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Geosciences, Multidisciplinary
Tao Huang, Xin Liao, Zhaoqin Huang, Renyi Wang
Summary: Ferrofluid, a magnetic fluid, has attracted extensive attention in the oil industry due to its controllable flow by an external magnetic field. Studies have shown that the flow of ferrofluid in complex porous media is significantly affected by magnetic force, offering potential for enhancing oil recovery efficiency in oil fields.
FRONTIERS IN EARTH SCIENCE
(2021)
Article
Mathematics, Applied
Marcin Los, Maciej Paszynski
Summary: Using isogeometric analysis, a highly optimized FORTRAN code is presented for simulations of three-dimensional non-linear flow problem in heterogeneous media. The weak formulations are derived, discretization is done with the forward Euler scheme, and right-hand side computation is implemented. Validation of the numerical solution is performed using properties of exact solutions of heat transport and non-linear flow in heterogeneous media problems. Stability analysis of the explicit time-stepping scheme is carried out, and the behavior close to the stability limit is investigated.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Environmental
Yuqing Zhou, Danny J. Lohan, Feng Zhou, Tsuyoshi Nomura, Ercan M. Dede
Summary: In this paper, an inverse design and dehomogenization framework is proposed to discover innovative microreactor flow field designs. Through numerical simulations, trade-offs between reaction performance and fluid flow performance are found for multiple optimized microreactor flow fields. Applying the findings of this study to new reactor flow field designs can enhance performance in biomedical, pharmaceutical, and energy applications.
CHEMICAL ENGINEERING JOURNAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Hongtao Yang, Boyang Yu, Yonghai Li, Guangwei Yuan
Summary: The paper applies monotonicity correction to second-order element finite volume methods, obtaining a second-order monotone finite volume scheme. By correcting the numerical fluxes with nonlinear monotone correction, a corrected second order element finite volume scheme with a monotone matrix stiffness is obtained, leading to high order unconditional positivity-preserving finite volume schemes. Experimental results show that the corrected schemes maintain the convergence order of the original schemes while ensuring monotonicity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Sergey Solovyev, Mikhail Novikov, Vadim Lisitsa
Summary: This paper presents an original algorithm for simulating quasi-static loading of complex fluid-saturated fractured-porous media. The resulting model is anisotropic viscoelastic and is defined by a complex-valued frequency-dependent stiffness tensor. The algorithm allows for efficient solving of large-scale problems and has been applied to study the effects of fracture connectivity and anisotropy on seismic waves in complex fluid-saturated fractured media.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
K. Brenner, R. Masson, E. H. Quenjel, J. Droniou
Summary: This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The scheme utilizes a global pressure concept to analyze stability and convergence, and combines gradient normal fluxes and a hybrid approximation method to accurately capture nonlinear transmission conditions. Numerical experiments demonstrate the increased robustness of the proposed scheme compared to traditional approaches.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Nicholas J. Moore, Jake Cherry, Shang-Huan Chiu, Bryan D. Quaife
Summary: Using a Cauchy integral formulation, we simulated the erosion of a porous medium consisting of solid bodies in a two-dimensional Stokes flow. Microscopic changes in grain morphology resulted in larger-scale features and anisotropy in the medium. Our results suggest that erosion from groundwater flows may contribute to anisotropy in natural porous media.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mechanics
Graham P. P. Benham, Jerome A. A. Neufeld, Andrew W. W. Woods
Summary: This study explores the motion of an axisymmetric gravity current in an anisotropic porous medium with horizontal permeability larger than vertical permeability. The presence of an unphysical singularity near the origin in classical axisymmetric gravity currents is addressed by considering a pressure-dominated region near the origin. The findings provide quantitative insights into the dominant dynamics controlling CO2 migration through permeable aquifers, which has significance in the context of carbon capture and storage.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Engineering, Multidisciplinary
G. Galindez-Ramirez, F. R. L. Contreras, D. K. E. Carvalho, P. R. M. Lyra
Summary: In this paper, a new high-order numerical methodology based on unstructured quadrilateral meshes is proposed for modeling oil-water displacements in highly heterogeneous and anisotropic petroleum reservoirs. The method achieves comparable accuracy to lower-order counterparts while reducing computational cost, and its accuracy, efficiency, and robustness are demonstrated through representative examples.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Engineering, Multidisciplinary
Artur Castiel Reis de Souza, Darlan Karlo Elisiario de Carvalho, Jose Cicero Araujo dos Santos, Ramiro Brito Willmersdorf, Paulo Roberto Maciel Lyra, Michael G. Edwards
Summary: This paper introduces a new multiscale finite volume framework for simulating multi-phase flow in heterogeneous and anisotropic porous media. The framework allows the use of geophysical grid defined properties on high-definition grids, addressing the issues of basis function leakage and mass conservation. The accuracy of the framework is validated through comparisons with direct simulations on fine-scale, and the results demonstrate its ability to produce well-resolved solutions for complex geological formations found in petroleum reservoir problems.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Engineering, Civil
Rodolfo M. S. Cabral, Adriano D. M. Ferreira, Julio T. Pimentel, Marco A. F. da Silva Cabral, Paulo R. M. Lyra, Silvana M. B. Afonso, Ramiro B. Willmersdorf
Summary: This paper presents a new methodology for predicting pipelines failure pressure using axisymmetric modeling and the River Bottom Profile (RBP) of corrosion defects. This practical tool allows pipeline engineers in the oil and gas industry to quickly and accurately assess pipeline integrity.
ENGINEERING STRUCTURES
(2022)
Letter
Computer Science, Interdisciplinary Applications
Jose Cicero Araujo dos Santos, Paulo Roberto Maciel Lyra, Joao Paulo Rodrigues de Andrade, Artur Castiel Reis de Souza, Ricardo Jorge Morais de Lira Filho, Darlan Karlo Elisiario de Carvalho
Summary: This paper proposes an adaptive flow-based dual volume agglomeration strategy for correcting non-physical terms in the coarse transmissibility matrix of classical multiscale finite volume (MsFV) methods. It also presents a framework to handle non-uniform levels at each coarse control volume, in order to reduce the size of coarse scale matrices. The proposed methodologies are applied to approximate pressure solutions in an Implicit Pressure Explicit Saturation (IMPES) strategy, and their accuracy and efficiency are demonstrated through testing with challenging benchmark problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
J. C. Teixeira, D. K. E. Carvalho, T. M. Cavalcante, K. C. L. Angelim, P. R. M. Lyra
Summary: This paper presents a numerical formulation for simulating two-phase flow in naturally fractured oil reservoirs using unstructured quadrilateral meshes and Hybrid-Grid MPFA-Streamline method. It can handle irregular polygonal grids and decouples transport equations using streamline-based method to solve advective saturation problems.
COMPUTERS AND GEOTECHNICS
(2022)
Article
Mathematics, Applied
T. M. Cavalcante, R. J. M. Lira Filho, A. C. R. Souza, D. K. E. Carvalho, P. R. M. Lyra
Summary: In this paper, we solve the steady state diffusion equation in 3D domains using the MPFA-DNL method, which guarantees the Discrete Maximum Principle by introducing a non-linear defect correction strategy. The method is locally conservative and capable of handling arbitrary anisotropic diffusion tensors and unstructured meshes while maintaining second order convergence rates.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Review
Water Resources
Fernando R. L. Contreras, Uewerton A. O. Vaz, Gustavo L. S. S. Pacheco, Alessandro R. E. Antunes, Paulo R. M. Lyra, Darlan K. E. Carvalho
Summary: This paper proposes a novel full finite volume method to solve the advection-dispersion transport equation, combining various numerical methods to ensure accuracy and robustness of the numerical solution. Numerical experiments show that the method can provide accurate solutions when simulating groundwater processes with complex physical and geological properties.
ADVANCES IN WATER RESOURCES
(2023)
Article
Energy & Fuels
M. E. S. Galindo, I. V. Lacerda, G. Galindez-Ramirez, P. R. M. Lyra, D. K. E. Carvalho
Summary: Compositional reservoir simulation is a crucial tool for modeling fluid flow in complex petroleum reservoirs, especially for volatile reservoir fluids or those involving enhanced oil recovery. Simple black-oil models are inadequate in these cases. The compositional model involves solving a large system of partial differential equations that describe mass conservation, Darcy's law, and fugacity constraints. However, the complexity and computational demands of the compositional problems are high due to the large number of equations and constraints. To improve accuracy and reduce computational costs, higher-order methods can be used to approximate the advective flux terms in the reservoir's multicomponent transport.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
Article
Energy & Fuels
Hygor V. C. Silva, Silvana M. B. Afonso, Ramiro B. Willmersdorf
Summary: This paper presents a variable fidelity surrogate framework for well control optimization, which combines multilevel wavelet-based local grid refinement with upscaling procedures to reduce computational costs and improve accuracy. Results show that this strategy can achieve similar or better results compared to traditional surrogate optimization, while saving about 90% of the computation cost.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Ashish Bhole, Herve Guillard, Boniface Nkonga, Francesca Rapetti
Summary: Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Federico Vismara, Tommaso Benacchio
Summary: This paper introduces a method for solving hyperbolic-parabolic problems on multidimensional semi-infinite domains. By dividing the computational domain into bounded and unbounded subdomains and coupling them using numerical fluxes at the interface, accurate numerical solutions are obtained. In addition, computational cost can be reduced by tuning the parameters of the basis functions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Keigo Enomoto, Takato Ishida, Yuya Doi, Takashi Uneyama, Yuichi Masubuchi
Summary: We have developed a novel Moving Particle Simulation (MPS) method to accurately reproduce the motion of fibers in sheared liquids. By introducing the micropolar fluid model, we address the issue of fibers being aligned with the flow direction in conventional MPS simulations. Our method is capable of accurately reproducing the fiber motion predicted by Jeffery's theory.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)