Edit on GitHub

Methodology

The methodology differs in the multiphysics coupling

i). Fully coupled model

  • assuming lithostatic total pressure gradient => decoupling of the fluid flow from shear deformation
  • prediction of stresses and pressure distribution in the porous matrix (geomechanics)

  • Benifit 1: Total pressure does not follow a lithostatic gradient?

  • Benifit 2: The shear deformation of the porous matrix is resolved?

a). Direct coupling (Industry-related simulator)

  • fluid pressure is transferred to the geomechanical module, but the geomechanics do not impact the fluid pressure

b). Iterative coupling

  • iterative coupling of the fluid-flow solver to a geomechanical solver

c). Single solver

  • fully coupling of the fluid flow and the Stokes matrix flow within a single solver

ii). Decompaction weakening model decompaction weakening while coupling Darcian and Stokes flows in 3-D

Decompaction weakening Räss et al. (2019)

Motivation

  • study of various phenomena of porous fluids (fingering, veining, channeling and focussing)

  • structure: subseabed pipes (eg. on the Nigerian continental shelf and in the Norwegian North Sea)

  • may act as preferential fluid pathways. Understanding how these pipes are formed and evolved can help us to accurately constrain subsurface fluid flow

[] What is the delocalization of the patterns of the flow?

  • Experiences: flow patterns are localized, induced by fractures

  • Theory: using classical Darcian model, diffusive behavior is expected => leads to never-ending spreading and delocalization

What is the decompaction weakening?

corresponds to high $\eta_d$ value

The degree of the decompaction weakening can be quantitatively determined by the quotient of the compaction bulk viscosity $\eta_c$ and its decompaction counterpart $\eta_d$.

\[R = \frac{\eta_c}{\eta_d}\]

  • Decompaction is significant $R >> 1$ => flow channeling

  • when $R=1$ we have blob-like porosity waves

The effective pressure $P_e$ can be used to monitor the compaction within a certain region.

  • Region in compaction $P_e > 0$

  • Region in decompaction $P_e < 0$

Mathematical model

Bulk viscosity

\[\eta_{\phi} = \eta_c \frac{\phi_0}{\phi} [1 + \frac{1}{2} (\frac{1}{R} - 1)(1 + \tanh [-\frac{p_e}{\lambda_p}])]\]

tanh_smoothing

Numerical experiment

  • Media: fluid-saturated

  • Objective: observation of the flow patterns

    • localized, delocalized?

    • formation?

    • propagation?

Numerical methods

The PT-method used in Räss et al. added the non-linear residual terms $f_v, f_{p^{[t]}}, f_{p^{[f]}}$ to 3 of the governing equations and aims to obtain the solution by minimizing the residuals iteratively within a pseudo-time loop

Results

Decompaction weaknening

3x-higher fluid-flow rate than the pure Darcy model