Numerical Algorithms for Simulation of a Fluid-Filed Fracture Evolution in a Poroelastic Medium

The paper deals with the computational framework for the numerical simulation of the three dimensional fluid-filled fracture evolution in a poroelastic medium. The model consists of several groups of equations including the Biot poroelastic model to describe a bulk medium behavior, Reynold’s lubrication equations to describe a flow inside fracture and corresponding bulk/fracture interface conditions. The geometric model of the fracture assumes that it is described as an arbitrary sufficiently smooth surface with a boundary. Main attention is paid to describing numerical algorithms for particular problems (poroelasticity, fracture fluid flow, fracture evolution) as well as an algorithm for the coupled problem solution. An implicit fracture mid-surface representation approach based on the closest point projection operator is a particular feature of the proposed algorithms. Such a representation is used to describe the fracture mid-surface in the poroelastic solver, Reynold’s lubrication equation solver and for simulation of fracture evolutions. The poroelastic solver is based on a special variant of X-FEM algorithms, which uses the closest point representation of the fracture. To solve Reynold’s lubrication equations, which model the fluid flow in fracture, a finite element version of the closet point projection method for PDEs surface is used. As a result, the algorithm for the coupled problem is purely Eulerian and uses the same finite element mesh to solve equations defined in the bulk and on the fracture mid-surface. Finally, we present results of the numerical simulations which demonstrate possibilities of the proposed numerical techniques, in particular, a problem in a media with a heterogeneous distribution of transport, elastic and toughness properties.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium

PurposeThe purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.Design/methodology/approachTorsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.FindingsPhase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.Originality/valueInitial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

Bounding the Multi-Scale Domain in Numerical Modelling and Meta-Heuristics Optimization: Application to Poroelastic Media with Damageable Cracks

It is very common for natural or synthetic materials to be characterized by a periodic or quasi-periodic micro-structure. This micro-structure, under the different loading conditions may play an important role on the apparent, macroscopic behaviour of the material. Although, fine, detailed information can be implemented at the micro-structure level, it still remains a challenging task to obtain experimental metrics at this scale. In this work, a constitutive law obtained by the asymptotic homogenization of a cracked, damageable, poroelastic medium is first evaluated for multi-scale use. For a given range of micro-scale parameters, due to the complex mechanical behaviour at micro-scale, such multi-scale approaches are needed to describe the (macro) material’s behaviour. To overcome possible limitations regarding input data, meta-heuristics are used to calibrate the micro-scale parameters targeted on a synthetic failure envelope. Results show the validity of the approach to model micro-fractured materials such as coal or crystalline rocks.