Partially saturated porous solids under dynamic hydraulic fracturing

Abstract

Hydraulic fracturing is a technique where fracking fluids are pressed into the ground to initiate and open fractures, increasing the rock’s permeability. Although this technique is widely used in practice, the fracturing process is controversially discussed and scientifically still not well established. Based on methodical developments, this doctoral thesis enlarges the understanding of the coupled processes occurring during fluid-driven fracturing in partially saturated porous media, where the pore space of the solid skeleton contains both an incompressible liquid and a compressible pore gas. Two main issues are treated simultaneously: the multiphasic nature of solid-fluid interactions in porous media and the crack initiation and propagation in the solid skeleton. The Theory of Porous Media (TPM) allows a rigorous and consistent formulation of the coupled behaviour of the abovementioned three phases. The setup of the continuum-mechanical model is based on the first principles of continuum thermodynamics. In addition, considering the fracturing process in porous media, the phase-field approach to fracture is embedded in the elaborated TPM model. Thereby, the unbroken and broken states of the solid skeleton are differentiated with a scalar phase-field variable. This method avoids the occurrence of a discontinuous jump in the fracturing process and facilitates numerical implementation. The phase field is added to the process variables and integrated into the free energy formulation. This latter is based on a spectral decomposition of the solid strain, such that the phase-field variable reduces the elastic energy under tension, not compression. The model is further enhanced by introducing a crack-opening indicator into the fluid constitutive relations. This procedure enables a transfer from Darcy-type flow in the intact porous material to Stokes-type flow in the fully broken area in a consistent manner. Moreover, special attention is given to the fluid pressure. The liquid and gas phases interact in partially saturated porous material under equilibrium through capillary forces. However, considering injection is a highly dynamic process, the standard hydromechanical relations do not apply here. Therefore, a modified pressure-difference-saturation relation, mapping both equilibrium and dynamic fluid interactions, is proposed and discussed in this thesis. The numerical study builds on the Finite-Element Method. The coupled partial differential equations are solved monolithically with the numerical code PANDAS. Different numerical examples are computed. Specifically, proceeding from a single crack, the solid skeleton’s coupled deformation and fracturing behaviour is examined by considering the different energy proportions. Then, the mutual interaction of the fluids during fracturing is considered in detail. Among others, a gas pressure compression and subsequent gas reflux into the crack are observed. A comparison of fully saturated and partially saturated simulations reveals that the existence of pore gas mainly slows down the fracturing process. This deceleration results from a slower pore pressure build-up induced by gas compressibility. Finally, two kinds of heterogeneities are assessed, going one step further towards realistic scenarios. First, heterogeneities caused by external loads are evaluated. This case is relevant as soils and rocks are frequently under external stresses in nature. Numerical examples with two differently oriented cracks are computed under distinct loading conditions and compared. These examples show the model’s capability to describe open and closed cracks and to discuss the flow behaviour of the liquid and gas phases in both cases. Second, heterogeneities in the porous structure are considered by defining location-dependent material parameters. In this sense, a fluid-driven fracturing process with predefined imperfection areas of higher stiffness is juxtaposed with the homogenous case. As a result, crack branching is observed in the two-field case. Additionally, the model is improved by implementing statistical fields of geomechanical properties. In order to study the influence of this latter, numerical examples with different statistical correlation lengths are compared. Due to the statistical fields of the solid properties, the local stresses spatially vary, and the crack path deviates characteristically. Conclusively, this thesis applied the phase-field approach to fracture within the Theory of Porous Media for fully dynamical problems of partially saturated porous media. It was shown that the gas phase slows down the crack propagation and to what extent local and global heterogeneities influence the crack and flow behaviour. The presented methodical and basis-oriented model can be used for various applications.