Stochastic modeling of fracture initiation and propagation during fluid flow in carbonate reservoir

DOI10.1016/J.RINAM.2022.100244zbMath1493.65164OpenAlexW4220722876MaRDI QIDQ2668195

Dulian Zeqiraj

Publication date: 3 March 2022

Published in: Results in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.rinam.2022.100244

zbMATH Keywords

fracture energy minimizationfracture initiation and propagationfractured carbonate reservoirsgeomechanical processesstochastic Brinkman optimal control

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Brittle fracture (74R10) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Finite element methods applied to problems in solid mechanics (74S05) Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Soil and rock mechanics (74L10) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in solid mechanics (74S20) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs with randomness, stochastic partial differential equations (35R60) PDEs in connection with mechanics of deformable solids (35Q74) PDE constrained optimization (numerical aspects) (49M41) Energy minimization in dynamical problems in solid mechanics (74H80)

Uses Software

• FEniCS

Cites Work

• Unnamed Item
• Crack kinking in brittle materials
• Automated solution of differential equations by the finite element method. The FEniCS book
• Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data
• On the convergence of generalized polynomial chaos expansions
• A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem
• A Low-Rank in Time Approach to PDE-Constrained Optimization
• A method for multiple crack growth in brittle materials without remeshing

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