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The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications.…

Numerical Analysis · Mathematics 2019-08-01 Alessio Fumagalli , Eirik Keilegavlen

Geological settings with reservoir characteristics include fractures with different material and geometrical properties. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow to…

Computational Physics · Physics 2020-08-17 Patrick Zulian , Philipp Schädle , Liudmila Karagyaur , Maria Nestola

Numerical modeling of hydraulic fracturing is complicated when a fracture reaches a stress barrier. For high barriers, it may require changing of a computational scheme. Despite there are examples of modeling propagation through barriers,…

Fluid Dynamics · Physics 2024-07-12 Aleksandr Linkov , Liliana Rybarska-Rusinek , Ewa Rejwer-Kosińska

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling…

Fluid Dynamics · Physics 2023-06-28 Mohammadhossein Firouznia , Spencer H. Bryngelson , David Saintillan

Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…

Computational Engineering, Finance, and Science · Computer Science 2017-12-21 Eirik Keilegavlen , Alessio Fumagalli , Runar Berge , Ivar Stefansson

Shear dilation based hydraulic stimulations enable exploitation of geothermal energy from reservoirs with inadequate initial permeability. While contributing to enhancing the reservoir's permeability, hydraulic stimulation processes may…

Geophysics · Physics 2018-08-01 Eren Ucar , Inga Berre , Eirik Keilegavlen

A mathematical model for computation of the fluid pressure in a reservoir drained by a horizontal multiple fractured well is proposed. The model is applicable for an arbitrary network of fractures with different finite conductivities of…

Fluid Dynamics · Physics 2016-02-15 S. V. Golovin , K. A. Gadylshina

Recent years have seen a significant interest in using phase field approaches to model hydraulic fracture, so as to optimise a process that is key to industries such as petroleum engineering, mining and geothermal energy extraction. Here,…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Y. Navidtehrani , C. Betegón , J. Vallejos , E. Martínez-Pañeda

We present an implicit, fully-coupled hydro-mechanical solver for the three dimensional simulation of fluid-driven rupture propagation along existing discontinuities. The solver handles simultaneously frictional slip (shear failure) and…

The fracturing-flooding technology is a new process for the development of low-permeability oil reservoirs, achieving a series of successful applications in oilfield production. However, existing numerical simulation methods for pressure…

Optimization and Control · Mathematics 2026-05-28 Xiang Wang , Wenjie Yu , Yixin Xie , Yanfeng He , Hui Xu , Xianxiang Chu , Changfu Li

The paper presents results of numerical experiments performed to evaluate the effective viscosity of a fluid-proppant mixture, used in hydraulic fracturing. The results, obtained by two complimenting methods (the particle dynamics and the…

Fluid Dynamics · Physics 2014-12-30 Vitaly A. Kuzkin , Anton M. Krivtsov , Aleksandr M. Linkov

The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…

Numerical Analysis · Mathematics 2018-06-07 Ondrej Maxian , Andrew T. Kassen , Wanda Strychalski

Geothermal energy, a promising renewable source, relies on efficiently utilizing geothermal reservoirs, especially in Enhanced Geothermal Systems (EGS), where fractures in hot rock formations enhance permeability. Understanding fracture…

Numerical Analysis · Mathematics 2025-01-13 Sanghyun Lee , Henry von Wahl , Thomas Wick

Hydraulic stimulation is a critical process for increasing the permeability of fractured geothermal reservoirs. This technique relies on coupled hydromechanical processes induced by reservoir stimulation through pressurized fluid injection…

Numerical Analysis · Mathematics 2023-05-02 Hau Trung Dang , Eirik Keilegavlen , Inga Berre

Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled…

In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations,…

Fluid Dynamics · Physics 2023-01-24 Hamza Riahi , Eric Goncalves , Marcello Meldi

In this work we present a model reduction procedure to derive a hybrid-dimensional framework for the mathematical modeling of reactive transport in fractured porous media. Fractures are essential pathways in the underground which allow fast…

Numerical Analysis · Mathematics 2020-01-16 Alessio Fumagalli , Anna Scotti

To design a method to solve the issues of handling 'dirty' and highly complex geometries, the topology-free method combined with the immersed boundary method is presented for viscous and incompressible flows at a high Reynolds number. The…

Computational Engineering, Finance, and Science · Computer Science 2022-06-06 Keiji Onishi , Makoto Tsubokura

A coupled mech-hydro-chemical model for rock geometry alteration of fractures under water-rock interaction (WRI) and geostress is developed. Processes including WRI, asperity deformation, mineral chemical dissolution and pressure…

Geophysics · Physics 2019-04-12 Cheng Yu

We introduce a coupled system of PDEs for the modeling of the fluid-fluid and fluid-solid interaction in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation,…

Numerical Analysis · Mathematics 2016-08-15 Katja K. Hanowski , Oliver Sander