A hybrid-dimensional approach for an efficient numerical modeling of the hydro-mechanics of fractures

Abstract

Characterization of subsurface fluid flow requires accounting for hydro-mechanical coupling between fluid-pressure variations and rock deformation. Particularly, flow of a compressible fluid along compliant hydraulic conduits, such as joints, fractures, or faults, is strongly affected by the associated deformation of the surrounding rock. We investigated and compared two alternative numerical modeling approaches that describe the transient fluid-pressure distribution along a single deformable fracture embedded in a rock matrix. First, we analyzed the coupled hydro-mechanical problem within the framework of Biot's poroelastic equations. Second, in a hybrid-dimensional approach, deformation characteristics of the surrounding rock were combined with a one-dimensional approximation of the fluid-flow problem to account for the high aspect ratios of fractures and the associated numerical problems. A dimensional analysis of the governing equations reveals that the occurring physical phenomena strongly depend on the geometry of the hydraulic conduit and on the boundary conditions. For the analyzed geometries, hydromechanical coupling effects dominate and convection effects can be neglected. Numerical solutions for coupled hydro-mechanical phenomena were obtained and compared to field data to characterize the fractured rock in the vicinity of an injection borehole. Either approach captures convection, diffusion, and hydro-mechanical effects, yet the hybrid-dimensional approach is advantageous due to its applicability to problems involving high-aspect-ratio features. For such cases, the modeling of pumping tests by means of the hybrid-dimensional approach showed that the observed inverse-pressure responses are the result of the coupling between the fluid flow in the fracture and the rock deformation caused by fluid-pressure variations along the fracture. Storage capacity as a single parameter of a fracture is insufficient to address all aspects of the coupling.

Identification of viscoelastic properties from numerical model reduction of pressure diffusion in fluid-saturated porous rock with fractures

“…In other words, we neglect any gradients perpendicular to ∂ F k . This hybrid-dimensional interface model is discussed in detail in [29].…”

The intrinsic permeability of microcracks in porous solids: Analytical models and Lattice Boltzmann simulations

“…Assuming, that the flow characteristics of such an idealized porous material is known, distributed microcracks ( Figure 1) of width w and length 2a, irrespective of their origin, influence the overall fluid flow characteristics in the material by creating new transport channels with enhanced flow characteristics specified by the geometry of the microcrack and the permeability of the surrounding porous region. In this paper, we assume that the microcrack geometry is fixed and does not consider changes of the microcrack configuration resulting from hydromechanical interactions [6][7][8] Let the velocity field across a microcrack of width w be u.y/8 y 2˝c (Figure 1). The averaged fluid velocity in the microcrack < u.y/ >D 1 w R w 2 w 2 u.y/dy is inversely proportional to the fluid viscosity and proportional to the averaged micro-scale pressure gradient g c D rp in the microcrack: < u.y/ >/ 1 g c .…”

Study of the filling mechanism and parameter optimization method for vacuum casting

“…The VC mold filling process obeys the laws of fluid dynamics and the laws of conservation of momentum, mass, and energy [7]. Given that most VC products are thin-walled parts, the thickness dimension is much smaller than the other two dimensions, so we can consider the material to flow in a flat cavity and make the following assumptions:…”