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

Abstract

In this thesis, proppant transport and the conductivity of proppant-packed hydraulic fractures are studied via the implementation of a numerical approach which couples the lattice Boltzmann method (LBM) to the discrete element method (DEM).Recent growth in the production of oil and gas from shales, and to lesser extent gas from coal seams, can be attributed to the successful application of hydraulic fracturing. However, contemporary numerical models of fluid injection and proppant transport are based on empirical approximations of the suspension as a continuous medium and, in some cases, experimental data. Assumptions related to Stokes drag on particles and a lumped suspension viscosity are not valid under practical conditions, while experiments provide limited information that can be used in predictions. To provide reliable predictions and further improve operation efficiency, an accurate modelling approach has become increasingly important.In this research, a particle-scale computational model is implemented to provide fundamental new insights on proppant injection by exploring the relationship between fluid and proppant properties, fracture network geometries, and evolving deformable fracture boundaries. This represents a direct numerical simulation (DNS) approach for problems at the small to intermediate scale. In the developed model, a two-relaxation-time (TRT) collision operator is applied to improve the accuracy and stability of the LBM modelling. The particulate proppant phase is modelled by the DEM. For the two-phase fluid-particle system, the LBM and DEM are coupled via an improved partially saturated method (PSM) to provide two-way hydrodynamic coupling.This project starts with the testing and improvement of the coupled LBM-DEM framework. Validations are presented through a range of flow configurations, including sphere packs, duct flows, and settling spheres, with good accuracy and convergence observed. Results also show that the improved model exhibits reasonable viscosity-independence, which has been reported to be one of the main concerns of many LBM applications. In the case of fluid flow past a single sphere, the fluctuation of error in drag coefficient can be restricted within 1% when changing the LBM relaxation parameter, tau, from 0.53 to 1.0. This feature of the improved LBM-DEM framework allows for more flexibility in choosing the simulation parameters, which simultaneously improves the applicability of the numerical approach.The developed model is then applied to aspects of hydraulic fracturing modelling, focusing on the numerical rheometry of dense particle suspensions, which is often characterised by semi-empirical models. In this project, the developed model aims at capturing the shear-dependent behaviour of the suspensions by computing the effective suspension viscosity and the hydrodynamic and mechanical reactions from the suspensions. The results are validated and compared to the semi-empirical expressions for the effective viscosity observed in particle suspensions. This study also demonstrates the impact of solid volume fraction on shear-dependent behaviour of the suspensions.To provide practical predictions to the industry, the influence of proppant embedment on fracture conductivity is then investigated. The investigation starts with the replication of a numerical model in which the Hertz elastic contact theory is applied to characterise the interaction between the fracture surface and proppant. A fracture permeability diameter is generated to find the optimal proppant concentration under various confining stresses, at which the maximum fracture permeability can be reached. In order to ensure the accuracy and veracity of the research, an elastoplastic model is developed, in which the finite element modelling is utilised to generated the fracture geometry after proppant embedment. The resultant fracture permeability diagram is then used to predict the well production using a set of theoretical solutions, highlighting the significant impact of proppant injection during hydraulic fracturing.This project demonstrates the potential of the improved LBM-DEM model in providing fundamental new insights on the shear-dependent behaviour of suspensions and enhancement of well productivity by proppant injection. As potential extensions to the current model, future developments including non-Newtonian fluids, upscaling modelling, and random proppant distribution across the fracture surface are expected.