Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid‐Dimensional Computational Model

Jin, Lei; Zoback, Mark D.

doi:10.1002/2017jb014892

Cited by 42 publications

(39 citation statements)

References 95 publications

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“…

\overset{Φ}{true} ((),, \underset{true¯}{x}, t^{bold-italic*})

reads differently for the decoupled and couple approaches:

\overset{Φ}{true} ((),, \underset{true¯}{x}, t *) = true{\begin{matrix} true \\ Φ (\underset{x}{true}, t *), pore pressure effect \\ Φ (\underset{x}{true}, t *) - α \nabla \cdot {\underset{u}{true}}_{p} (\underset{x}{true}, t *), poroelastic effect \end{matrix}

and

normalΦ ((),, \underset{true¯}{x}, t^{bold-italic*})

is the so‐called partial porosity of the faulted porous medium; it is in a sense a coalesced porosity obtained from the matrix porosity and the fault porosity under a given configuration. When evaluated at t *, it is calculated from the following expression using the fluid pressure at t * (see Jin and Zoback () for details):

normalΦ ((),, \underset{true¯}{x}, t^{*}) = Λ_{0} ((), \underset{true¯}{x}) ϕ_{m 0} ((), \underset{true¯}{x}) ((), 1 + C_{m} p ((),, \underset{true¯}{x}, t^{*})) + ((), 1 - Λ_{0} ((), \underset{true¯}{x})) ϕ_{f 0} ((), \underset{true¯}{x}) ((), 1 + C_{f} p ((),, \underset{true¯}{x}, t^{*}))

…”

Section: Problem Statementmentioning

confidence: 99%

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Jin

Zoback

2018

JGR Solid Earth

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Fluid perturbations play a pivotal role in triggering earthquakes. However, the role of fluid in the coseismic rupture process remains largely unknown. To this end, we develop a 2‐D fully dynamic spontaneous rupture model for fluid‐induced earthquakes. The effect of fluid in the preseismic quasi‐static regime is modeled as either pore pressure diffusion or fully coupled poroelasticity, using our Jin and Zoback (2017, https://doi.org/10.1002/2017JB014892) computational model. The two approaches lead to radically different predictions on the time of earthquake nucleation. Correspondingly, the evolved fluid pressure or poroelastic stress on the fault, together with the spatially altered density of the fluid‐saturated hosting rock, is passed to the dynamic regime. Under the assumption of an undrained coseismic fluid‐solid system, we discretize the fully dynamic Cauchy equation of motion subjected to an exact fault contact constraint using a split‐node finite element method in space and an implicit Newmark family finite difference method in time. Within each time step, a fully implicit Newton‐Raphson scheme is implemented iteratively for linearizing the fully discrete equations. Within each Newton iteration, a physics‐based and nonstationary preconditioner is designed to accelerate the convergence of the selected generalized minimal residual method iterative linear solver. The effect of fluid is highlighted throughout the discretization and computational procedures. Finally, by conducting a numerical experiment, we illustrate that a fully coupled poroelastic model can lead to significantly different predictions on coseismic rupture behaviors and wavefields compared to a decoupled model. Our computational model can also serve as one of the earliest full‐physics modeling tool for fluid‐induced earthquakes.

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“…

\overset{Φ}{true} ((),, \underset{true¯}{x}, t^{bold-italic*})

reads differently for the decoupled and couple approaches:

\overset{Φ}{true} ((),, \underset{true¯}{x}, t *) = true{\begin{matrix} true \\ Φ (\underset{x}{true}, t *), pore pressure effect \\ Φ (\underset{x}{true}, t *) - α \nabla \cdot {\underset{u}{true}}_{p} (\underset{x}{true}, t *), poroelastic effect \end{matrix}

and

normalΦ ((),, \underset{true¯}{x}, t^{bold-italic*})

normalΦ ((),, \underset{true¯}{x}, t^{*}) = Λ_{0} ((), \underset{true¯}{x}) ϕ_{m 0} ((), \underset{true¯}{x}) ((), 1 + C_{m} p ((),, \underset{true¯}{x}, t^{*})) + ((), 1 - Λ_{0} ((), \underset{true¯}{x})) ϕ_{f 0} ((), \underset{true¯}{x}) ((), 1 + C_{f} p ((),, \underset{true¯}{x}, t^{*}))

…”

Section: Problem Statementmentioning

confidence: 99%

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Jin

Zoback

2018

JGR Solid Earth

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“…We will also refer to the step solving for the fully coupled σp'(x, t) and p(x, t) by considering the LSDF as the fracture-poro-mechanical modeling. Within the framework of Biot's theory of poroelasticity, Jin & Zoback (2017) formulated the problem of fluid-solid fully coupled quasistatic poromechancis of an arbitrarily fractured and deformable porous solid saturated with a single-phase compressible fluid. Several key governing equations together with a brief description can be found in appendix A.1.…”

Section: Fracture-poro-mechanical Modelingmentioning

confidence: 99%

“…This is perhaps a misconception. Jin & Zoback (2017) demonstrated the fundamental difference between the two, which lies in how the fluid overpressure modifies the effective stress tensor that will be used for calculating stress on a fracture. Using the Biot effective stress law (Biot, 1941) as an example, the pore pressure effect is stated as:…”

Section: Introductionmentioning

confidence: 99%

Hydromechanical–Stochastic Modeling of Fluid-Induced Seismicity in Fractured Poroelastic Media

Jin¹

2018

Preprint

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We present a new method for modeling fluid-perturbation induced seismicity in a fluid-saturated poroelastic medium embedded with a dual network of fractures. The inter-seismic triggering is deterministically modeled using a quasi-static, nonlinear and fluid-solid fully coupled fracture-poro-mechanical approach that resolves only the large-scale fractures. The co-seismic dynamic rupture is not explicitly modeled. Instead, the seismicity-induced shear stress drop is approximated as a static quantity and stochastically modeled on a range computed from the evolving poroelastic stress in conjunction with the initial stress and the static and dynamic frictional strengths. These two steps are sequentially connected and then iterated via a prediction-correction type of fracture stress updating scheme, naturally producing repeating seismic events on certain fractures. As an example, we perform three progressive numerical experiments. By comparing the corresponding synthetic event catalogs, we investigate the effects of fractures and poroelastic coupling on the evolution and source characteristics of the seismicity. Main findings include (1) the seismicity clusters near large-scale fractures favorably oriented and subjected to sufficient perturbations, (2) poroelastic coupling enhances the clustering and substantially inhibits the seismicity in the nearfield and (3) source characteristics and the b-value seem not affected by fractures or poroelastic coupling. Our method can serve as a general physics-based tool for more realistically predicting induced seismicity in complex geological media.

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“…The model is valid under the assumptions of small deformations of the rock matrix, small variations of the porosity, and small relative variations of the fluid density. The interest of the poroelastic models considered here is particularly manifest in geosciences applications [27,28,31], where fluid flows in geological subsurface, modeled as a porous media, induce a deformation of the rock matrix. The challenge is then to design a discretization method able to (i) treat a complex geometry with polyhedral meshes and nonconforming interfaces, (ii) handle possible heterogeneities of the poromechanical parameters and nonlinearities of the stress-strain relation, and (iii) deal with the numerical instabilities encountered in this type of coupled problem.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

Botti

Pietro

Sochala

2019

Computational Methods in Applied Mathematics

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In this work we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients.

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Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid‐Dimensional Computational Model

Cited by 42 publications

References 95 publications

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Hydromechanical–Stochastic Modeling of Fluid-Induced Seismicity in Fractured Poroelastic Media

A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

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