Electromagnetic excitation of particle suspensions in hydraulic fractures using a coupled lattice Boltzmann-discrete element model

Abstract

This paper describes the development of a computational framework that can be used to describe the electromagnetic excitation of rigid, spherical particles in suspension. In this model the mechanical interaction and kinematic behaviour of the particles is modelled using the discrete element method, while the surrounding fluid mechanics is modelled using the lattice Boltzmann method. Electromagnetic effects are applied to the particles as an additional set of discrete element forces, and the implementation of these effects was validated by comparison to the theoretical equations of point charges for Coulomb's law and the Lorentz force equation. Oscillating single and multiple particle tests are used to investigate the sensitivity of particle excitation to variations in particle charge, field strength, and frequency. The further capabilities of the model are then demonstrated by a numerical illustration, in which a hydraulic fracture fluid is excited and monitored within a hydraulic fracture. This modelling explores the feasibility of using particle vibrations within the fracture fluid to aid in the monitoring of fracture propagation in unconventional gas reservoirs.

Direct numerical simulation of coupled fluid-particle flow in hydraulic fractures

“…It is worth mentioning that when no solid obstacle is present in the lattice cell, the PSM for fluid-solid interaction can recover the standard LBE with γ = 0. In cases where multiple solid obstacles are mapped to the same LBM cell, a sub-grid-scale condition is applied [113]. This can occur when discrete elements approach or engage in contact, with the latter allowing slight overlap of boundaries.…”

“…The terms F and T denote the forces and torques acting on the particle, respectively, for both hydrodynamic fluid-particle interactions, [•] f , and mechanical particle-particle interactions, [•] c . Other forces, such as those arising from electrostatic [99] and electromagnetic interactions [100], can be included in a similar manner.…”

Numerical investigation of conjugate heat transfer and temperature-dependent viscosity in non-Brownian suspensions with application to hydraulic fracturing

“…Since then the LBM has seen a rapid uptake and development for a wide variety of flow regimes and scenarios. These include multiphase [39,43,42] and multicomponent [39,44,42,45,46] flows, thermal modelling [39,47], turbulent flow [39,42], reactive flow [39,48], porous media flows [44,43], particle suspensions with electromagnetic effects [45,46] and nano-scale regimes [44,42,49]. Situations that involve complex or evolving physical boundaries can be challenging to capture using conventional finite difference/volume/element methods.…”

“…Regardless of the specific numerical methodology being employed, the motion of particles reduces to an integration procedure being applied to Newton's second law. The forces acting on a particle may include those arising from contact with walls or other particles, hydrodynamic forces from the surrounding fluid, gravitational forces and external forces such as those from an externally applied electromagnetic field [86,46]. The approach for particles of finite size, with a detailed contact identification and resolution process, is typically a form of discrete element method (DEM).…”

“…The partially saturated method (PSM) developed by Noble and Torczynski [91] has been utilised in this work as the strategy for coupling DEM to LBM. Further details on the method can be found in [88,46]. Here, locations of the DEM particles are firstly mapped onto the LBM grid to identify fluid nodes covered by the solid.…”