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Consistent initialization of mixed-dimensional multiphysics models for fractured reservoirs under geomechanical constraints and field measurements

Jakub Wiktor Both, Inga Berre

Abstract

Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical states and state dependent material laws. While in-situ field measurements consistently describe the deformed equilibrium configuration, computational models typically start from an idealized reference configuration and require explicit initialization of the in-situ stress state. This mismatch complicates initialization and linearization of constitutive laws. As a consequence, due to the two scale nature of fractured media, this can induce large deviations in fracture aperture directly impacting flow predictions. To address this, a discrete fracture model is introduced whose constitutive laws are expressed with respect to the unknown equilibrium state. This is paired with a fixed point initialization strategy that consistently reconstructs the reference configuration, consistent with both geomechanical constraints and field measurements up to load-path dependence. This data-consistent strategy provides a foundation for extending models to more complex scenarios, including multiphase and multicomponent flow in fractured reservoirs.

Consistent initialization of mixed-dimensional multiphysics models for fractured reservoirs under geomechanical constraints and field measurements

Abstract

Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical states and state dependent material laws. While in-situ field measurements consistently describe the deformed equilibrium configuration, computational models typically start from an idealized reference configuration and require explicit initialization of the in-situ stress state. This mismatch complicates initialization and linearization of constitutive laws. As a consequence, due to the two scale nature of fractured media, this can induce large deviations in fracture aperture directly impacting flow predictions. To address this, a discrete fracture model is introduced whose constitutive laws are expressed with respect to the unknown equilibrium state. This is paired with a fixed point initialization strategy that consistently reconstructs the reference configuration, consistent with both geomechanical constraints and field measurements up to load-path dependence. This data-consistent strategy provides a foundation for extending models to more complex scenarios, including multiphase and multicomponent flow in fractured reservoirs.
Paper Structure (14 sections, 10 equations, 4 figures, 1 algorithm)

This paper contains 14 sections, 10 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Poromechanics modeling around reference states
  3. Modeling assumptions
  4. Mixed-dimensional geometry and computational domain
  5. Primary variables and the special role of mechanical displacements
  6. Constitutive modeling of poroelastic materials
  7. Coupled model characterizing reference and current states
  8. Effective initialization strategies for obtaining reference states
  9. Numerical consistency check in light of path-dependence
  10. Consistent modeling of the reference state.
  11. Path-dependence.
  12. Concluding remarks
  13. Acknowledgment.
  14. Data availability statement

Figures (4)

  • Figure 1: Illustration of spatial stress-free, equilibrium and dynamic configurations with associated notion of mechanical displacement in between these.
  • Figure 2: Fracture aperture modeling: Open, closed, and shear-dilated fracture modes. In closed state, positive residual aperture $a_\mathrm{res}$ remains available. In open and dilated states, a non-negative mechanical aperture contributes, while in the latter, it is governed through the fracture gap model, cf. \ref{['eq:contact-normal-1']}--\ref{['eq:contact-normal-3']}.
  • Figure 3: Left: Salt Cove, modified excerpt from finnila2021revisions, the box marks the considered ca. 150 $\times$ 150 m sized fracture network embedded in a vertical 2d domains and subject to geomechanical constraints (hydrostatic, lithostatic and horizontal stress for 3000 - 4000 m) Right: Equilibrated state with highlighted boxes; consistent and inconsistent apertures (green top left), background deformation (blue, bottom left, and outside the boxes), fracture pressure (pink, top right), slip tendency (yellow, bottom right).
  • Figure 4: Path dependence of fractured systems under quasi-static friction. Final states after initialization with different initial friction values: 0.0 (left), 0.5 (center), 0.6 (right). Consistency in terms of far-field deformation, near-field deformation and contact traction shows (significant) differences.

Theorems & Definitions (6)

  • Remark 1: Quasi-static evolution
  • Remark 2: Non-unique characterization of the reference state
  • Remark 3: Consistency of the modeling approach
  • Remark 4: Numerical discretization
  • Remark 5: Improved initial guesses
  • Remark 6: Alternative models