This paper presents an improved understanding of coupled hydro-thermo-mechanical (HTM) hydraulic fracturing of quasi-brittle rock using the bonded particle model (BPM) within the discrete element method (DEM). BPM has been recently extended by the authors to account for coupled convective–conductive heat flow and transport, and to enable full hydro-thermal fluid–solid coupled modeling. The application of the work is on enhanced geothermal systems (EGSs), and hydraulic fracturing of hot dry rock (HDR) is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convective–conductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

Two-phase flow in fractured porous media is investigated by means of a direct and complete numerical solution of the generalized Darcy equations in a three-dimensional discrete fracture description. The numerical model applies to arbitrary fracture network geometry, and to arbitrary distributions of permeabilities in the porous matrix and in the fractures. It is used here in order to obtain the steady-state macroscopic relative permeabilities of random fractured media. Results are presented as functions of the mean saturation and are discussed in comparison with simple models.

Two-phase flow through fractured porous media

. Modern land surface model simulations capture soil profile water movement through the use of soil hydraulics sub-models, but good hydraulic parameterisations are often lacking, especially in the tropics. We present much-improved gridded data sets of hydraulic parameters for surface soil for the critical area of tropical South America, describing soil profile water movement across the region to 30 cm depth. Optimal hydraulic parameter values are given for the Brooks and Corey, Campbell, van Genuchten–Mualem and van Genuchten–Burdine soil hydraulic models, which are widely used hydraulic sub-models in land surface models. This has been possible through interpolating soil measurements from several sources through the SOTERLAC soil and terrain data base and using the most recent pedotransfer functions (PTFs) derived for South American soils. All soil parameter data layers are provided at 15 arcsec resolution and available for download, this being 20x higher resolution than the best comparable parameter maps available to date. Specific examples are given of the use of PTFs and the importance highlighted of using PTFs that have been locally parameterised and that are not just based on soil texture. We discuss current developments in soil hydraulic modelling and how high-resolution parameter maps such as these can improve the simulation of vegetation development and productivity in land surface models.

/pdf/high-resolution-hydraulic-parameter-maps-for-surface-soils-1q0xlrroa0.pdf

High-resolution hydraulic parameter maps for surface soils in tropical South America

This paper presents the development, implementation and verification of a coupled convective–conductive heat flow and transport model in the discrete element method (DEM). Thermal conduction is already available in DEM codes such as the particle flow code (PFC). However, current DEM codes rarely account for convective heat transport. There are many important phenomena in different applications that involve convective heat transport due to flow of fluid through permeable solid material, where the fluid and the permeable solids have different initial temperatures. Heat transfer from convection is dependent on the fluid flow velocity through existing and new instantaneously forming flow paths in solid and is typically much faster than conduction. The complete formulation of the heat convection model, its implementation and coupling with fluid flow and heat conduction in PFC2D, and its validation are described in detail. While DEM has been widely used for studying fundamental mechanisms in geomaterials, little effort has been devoted toward extending DEM for studying coupling between conductive heat flow and convective heat transport problems. The developments presented in this paper will enable application of DEM to study coupled hydro-thermo-mechanical processes in geomaterials such as in geothermal systems, hydrocarbon production, environmental engineering and nuclear waste storage.

Formulation and implementation of coupled forced heat convection and heat conduction in DEM

This paper investigates the permeability of microcracked porous solids containing 2D random crack networks. The past works on permeability of crack networks are firstly reviewed. The geometry analysis is performed on numerical samples of crack networks with different crack length distributions, crack densities, domain size ratios and clustering degrees. The parameters from continuum percolation theory are used to characterize the geometry of random networks including the percolation threshold, the scaling exponents for percolation probability and correlation length of crack clusters, and the fractal dimension of spanning clusters. The crack density is used as the basic percolation variable, and a new connectivity factor is proposed for the cluster spanning in finite domain. Then the effective permeability of porous matrix containing 2D random crack networks is analyzed on numerical samples via finite element method. A scaling law for effective permeability is established near the percolation threshold taking into account the matrix permeability, crack opening aperture, crack connectivity and tortuosity. The results from geometry analysis and permeability analysis show that: (1) The new connectivity factor is proved pertinent to network percolation, related to both crack density and crack clustering degree; (2) the percolation parameters of uncorrelated crack networks are rather near to the universal values from the continuum percolation theory, but their values change with the clustering degree of crack networks; (3) the numerical results confirm the scaling law proposed for effective permeability, and the permeability is found to scale with the crack opening through a power law.

J.‐F. Thovert

Papers

Study of Single and Multiphase Flow in Fractured Porous Media, Using a Percolation Approach