An Analytical Solution for Variable Viscosity Flow in Fractured Media: Development and Comparative Analysis With Numerical Simulations

Author:

Younes Anis1ORCID,Rajabi Mohammad Mahdi23ORCID,Rezaiezadeh Roukerd Fatemeh2,Fahs Marwan1ORCID

Affiliation:

1. ITES University of Strasbourg CNRS ENGEES Strasbourg France

2. Faculty of Civil and Environmental Engineering Tarbiat Modares University Tehran Iran

3. Department of Engineering Institute of Computational Engineering University of Luxembourg Esch Sur Alzette Luxembourg

Abstract

AbstractExplicit fracture models often use analytical solutions for predicting flow in fractured media, usually assuming uniform fluid viscosity for simplicity. This assumption, however, can be inaccurate as fluid viscosity varies due to factors like composition, temperature, and dissolved substances. Our study, recognizing these discrepancies, abandons this uniform viscosity assumption for a more realistic model of variable viscosity flow, focusing on viscous displacement scenarios. This includes instances like injecting viscous surfactants for hydrocarbon recovery in fractured reservoirs or soil decontamination. This presents a significant challenge, enhancing our understanding of transport within fractures, mainly governed by advection. Our study centers on a low‐permeability rock matrix intersected by two fractures with variable apertures. We employ two methods: an analytical approach with a new solution and numerical simulations with two distinct in‐house codes, discretizing both the rock matrix and fractures with two‐dimensional triangular elements. The first code uses a Discontinuous Galerkin finite element method, while the second utilizes a finite‐volume method, allowing a comprehensive comparison of solutions. Additionally, we investigate parameter identifiability, like fracture apertures and viscosity ratios, using breakthrough curves from our analytical solution, applying the Markov Chain Monte Carlo technique.

Publisher

American Geophysical Union (AGU)

Reference84 articles.

1. Lie similarity analysis of MHD flow past a stretching surface embedded in porous medium along with imposed heat source/sink and variable viscosity

2. Effects of heat transfer on MHD oscillatory flow of Jeffrey fluid with variable viscosity through porous medium;Al‐Khafajy D. G.;Advances in Applied Science Research,2016

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