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

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

doi:10.1016/j.cma.2010.12.022

Cited by 336 publications

(311 citation statements)

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“…For early times or a low permeability system, the effects resulting from the different time scales of fluid flow and geomechanics can become large. We also confirm that full 3D simulations for hydrate reservoirs support the a-priori numerical stability and convergence estimates in Kim et al (2011d).…”

Section: Discussionsupporting

confidence: 65%

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

et al. 2011

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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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Section: Discussionsupporting

confidence: 65%

“…For elastoplasticity, the elastoplastic tangent bulk modulus is estimated from the relationship (Kim et al, 2011d)…”

Section: Sequential Approach and Implementationmentioning

confidence: 99%

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

et al. 2011

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“…According to Kim et al (2011), the fixed stress sequential method can provide unconditional stability and high accuracy, comparable to the fully coupled methods. The fixedstress method solves the flow problem, fixing the total stress field, where the strain and displacement fields can be changed, and considering the contribution of geomechanics to flow explicitly.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…For the modeling of coupled flow and geomechanics, we use a sequential implicit method, employing the fixedstress split, which can provide unconditional stability and high accuracy, considering two-way coupling between flow and geomechanics (Kim et al 2011). Specifically, flow is solved first, fixing the total stress fields and considering the contribution of geomechanics to flow explicitly, and then geomechanics is solved from the solutions obtained at the previous flow step.…”

Section: Introductionmentioning

confidence: 99%

Investigation of possible wellbore cement failures during hydraulic fracturing operations

Kim

Moridis

Martínez

2016

Journal of Petroleum Science and Engineering

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We model and assess the possibility of shear failure, using the Mohr-Coulomb model -along the vertical well by employing a rigorous coupled flow-geomechanic analysis. To this end, we vary the values of cohesion between the well casing and the surrounding cement to representing different quality levels of the cementing operation (low cohesion corresponds to low-quality cement and/or incomplete cementing). The simulation results show that there is very little fracturing when the cement is of high quality.. Conversely, incomplete cementing and/or weak cement can causes significant shear failure and the evolution of long fractures/cracks along the vertical well. Specifically, low cohesion between the well and cemented areas can cause significant shear failure along the well, but the same cohesion as the cemented zone does not cause shear failure. When the hydraulic fracturing pressure is high, low cohesion of the cement can causes fast propagation of shear failure and of the resulting fracture/crack, but a highquality cement with no weak zones exhibits limited shear failure that is concentrated near the bottom of the vertical part of the well. Thus, high-quality cement and complete cementing along the vertical well appears to be the strongest protection against shear failure of the wellbore cement and, consequently, against contamination hazards to drinking water aquifers during hydraulic fracturing operations.

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“…This sequential-implicit method basically consists in solving the flow problem first fixing the volumetric mean total stress, and then the mechanics part is solved from the values obtained 25 at the previous flow step. The unconditional stability of the fixed-stress split method is shown in [7] using a von Neumann analysis. In addition, stability and convergence of the fixed-stress split method have been rigorously established in [8].…”

Section: Introductionmentioning

confidence: 99%

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

Gaspar

Rodrigo

2017

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: F.J. Gaspar, C. Rodrigo, On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics, Comput. Methods Appl. Mech. Engrg. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics This solver combines the advantages of being a fully coupled method, with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm. Moreover, the fixed-stress split smoother is based on the physics of the problem, and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori. A local Fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained. The proposed geometric multigrid algorithm is used to solve several tests in semi-structured triangular grids, in order to show the good behaviour of the method and its practical utility.

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

Cited by 336 publications

References 50 publications

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

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

Investigation of possible wellbore cement failures during hydraulic fracturing operations

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

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