Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits

Kim, J.; Tchelepi, Hamdi A.; Juanes, Rubén

doi:10.1016/j.cma.2011.02.011

Cited by 171 publications

(163 citation statements)

References 53 publications

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“…In a separate paper [36], we investigated the stability and convergence of the drained and undrained splits for coupled flow and mechanics rigorously. Both schemes solve mechanics first, followed by flow.…”

Section: Introductionmentioning

confidence: 99%

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

Kim

Tchelepi

Juanes

2011

Computer Methods in Applied Mechanics and Engineering

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336

296

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Section: Introductionmentioning

confidence: 99%

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

Kim

Tchelepi

Juanes

2011

Computer Methods in Applied Mechanics and Engineering

Self Cite

336

296

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“…The finite volume method has been used by [31,32] to discretize the flow. This results in a discontinuous approximation of the fluid pressure which is able to overcome localised pressure oscillations due to steep pressure gradients in the solution.…”

Section: Previous Results: Infinitesimal Strainmentioning

confidence: 99%

A stabilized finite element method for finite-strain three-field poroelasticity

Berger¹,

Bordas

Kay

et al. 2017

Comput Mech

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We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

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“…After the sequential solution of the subproblems, either a more accurate solution can be obtained by additional iterations, or the time can be advanced and the solution at the new time step can begin. Kim et al (2011c) and Kim et al (2011d) investigated the numerical stability and convergence of the four sequential methods discussed earlier under isothermal conditions. They showed that the undrained and fixed-stress splits are unconditionally stable, and that the fixed-stress split yields higher accuracy than the undrained split, particularly under high coupling strength conditions.…”

Section: Sequential Approach and Implementationmentioning

confidence: 99%

Numerical Studies on Two-Way Coupled Fluid Flow and Geomechanics in Hydrate Deposits

et al. 2012

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Coupled flow and geomechanics play an important role in the analysis of gas hydrate reservoirs under production. The stiffness of the rock skeleton and the deformation of the reservoir, as well as porosity and permeability, are directly influenced by (and interrelated with) changes in pressure, temperature and fluid (water and gas) and solid (hydrate and ice) phase saturations. Fluid and solid phases may coexist, which, coupled with steep temperature and pressure gradients, result in strong nonlinearities in the coupled flow and mechanics processes, making the description of system behavior in dissociating hydrate deposits exceptionally complicated.In previous studies, the geological stability of hydrate-bearing sediments was investigated using one-way coupled analysis, in which the changes in fluid properties affect mechanics within the gas hydrate reservoirs, but with no feedback from geomechanics to fluid flow. In this paper, we develop and test a rigorous two-way coupling between fluid flow and geomechanics, in which the solutions from mechanics are reflected in the solution of the flow problem through the adjustment of affected hydraulic properties. We employ the fixed-stress split method, which results in a convergent sequential implicit scheme.In this study of several hydrate reservoir cases, we find noticeable differences between the results based on one-and twoway couplings. The nature of the elliptic boundary value problem of quasi-static mechanics results in instantaneous compaction or dilation over the domain, through loading from reservoir fluid production. This induces a pressure rise or drop at early times (low pressure diffusion), and consequently changes the effective stress instantaneously, possibly causing geological instability. Additionally, the pressure and temperature regime affects the various phase saturations, the rock stiffness, porosity, and permeability, thus affecting the fluid flow regime. These changes are not captured accurately by the simpler one-way coupling. The tightly coupled sequential approach we propose provides a rigorous, two-way coupling model that captures the interrelationship between geomechanical and flow properties and processes, accurately describes the system behavior, and can be readily applied to large-scale problems of hydrate behavior in geologic media. IntroductionBackground. The interrelationship between fluid flow through porous media and the geomechanical status of the system is controlled by the properties of the specifics of flow, various phases present in the pores (e.g., gas, aqueous, oil/organic, ice, etc.) and of the solid system (i.e., the individual grains of the geologic medium and the reservoir skeleton). Under certain conditions, the interrelationship is strong, and coupling of the flow processes with geomechanics is necessary to accurately describe the system behavior. In such cases, changes in pressure brought about by flow (e.g., in the process of fluid production from reservoirs) alter the stress fields, resulting in changes in por...

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Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits

Cited by 171 publications

References 53 publications

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

A stabilized finite element method for finite-strain three-field poroelasticity

Numerical Studies on Two-Way Coupled Fluid Flow and Geomechanics in Hydrate Deposits

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