Christoph Schrank

Thermal‐elastic stresses and the criticality of the continental crust

Heating or cooling can lead to high stresses in rocks due to the different thermal-elastic properties of minerals. In the upper 4 km of the crust, such internal stresses might cause fracturing. Yet it is unclear if thermal elasticity contributes significantly to critical stresses and failure deeper in Earths continental crust, where ductile creep causes stress relaxation. We combined a heating experiment conducted in a Synchrotron microtomograph (Advanced Photon Source, USA) with numerical simulations to calculate the grain-scale stress field in granite generated by slow burial. We find that deviatoric stresses >100 MPa can be stored during burial, with relaxation times from 100s to 1000s ka, even in the ductile crust. Hence, grain-scale thermal-elastic stresses may serve as nuclei for instabilities, thus rendering the continental crust close to criticality.

A parallel computing tool for large-scale simulation of massive fluid injection in thermo-poro-mechanical systems

Massive fluid injections into the earth’s upper crust are commonly used to stimulate permeability in geothermal reservoirs, enhance recovery in oil reservoirs, store carbon dioxide and so forth. Currently used models for reservoir simulation are limited to small perturbations and/or hydraulic aspects that are insufficient to describe the complex thermal-hydraulic-mechanical behaviour of natural geomaterials. Comprehensive approaches, which take into account the non-linear mechanical deformations of rock masses, fluid flow in percolating pore spaces, and changes of temperature due to heat transfer, are necessary to predict the behaviour of deep geo-materials subjected to high pressure and temperature changes. In this paper, we introduce a thermodynamically consistent poromechanics formulation which includes coupled thermal, hydraulic and mechanical processes. Moreover, we propose a numerical integration strategy based on massively parallel computing. The proposed formulations and numerical integration are validated using analytical solutions of simple multi-physics problems. As a representative application, we investigate the massive injection of fluids within deep formation to mimic the conditions of reservoir stimulation. The model showed, for instance, the effects of initial pre-existing stress fields on the orientations of stimulation-induced failures.

Deep geothermal: The ‘Moon Landing’ mission in the unconventional energy and minerals space

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Entropic Bounds for Multi-Scale and Multi-Physics Coupling in Earth Sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

Earth's oldest stable crust in the Pilbara Craton formed by cyclic gravitational overturns

During the early Archaean, the Earth was too hot to sustain rigid lithospheric plates subject to Wilson Cycle-style plate tectonics. Yet by that time, up to 50% of the present-day continental crust was generated. Preserved continental fragments from the early Archaean have distinct granite-dome/greenstone-keel crust that is interpreted to be the result of a gravitationally unstable stratification of felsic proto-crust overlain by denser mafic volcanic rocks, subject to reorganization by Rayleigh–Taylor flow. Here we provide age constraints on the duration of gravitational overturn in the East Pilbara Terrane. Our U–Pb ages indicate the emplacement of ~3,600–3,460-million-year-old granitoid rocks, and their uplift during an overturn event ceasing about 3,413 million years ago. Exhumation and erosion of this felsic proto-crust accompanied crustal reorganization. Petrology and thermodynamic modelling suggest that the early felsic magmas were derived from the base of thick (~43 km) basaltic proto-crust. Combining our data with regional geochronological studies unveils characteristic growth cycles on the order of 100 million years. We propose that maturation of the early crust over three of these cycles was required before a stable, differentiated continent emerged with sufficient rigidity for plate-like behaviour.The oldest stable crust on Earth may have formed during pulsed growth cycles, according to geochemical analyses of rocks preserved in the Pilbara Craton, Western Australia.

Thermo-poro-mechanics Modelling of Gypsum Dehydration

Understanding the behaviour of natural calcium sulphates is important to ensure the sustainable integrity of civil structures. The phase transitions of these minerals are associated with considerable volume variations, creation of porosity with local defects, and water exchanges. Such changes can jeopardise the integrity of structures when the conditions that trigger the phase transitions are encountered. This paper uses advanced poromechanics to investigate the dehydration of gypsum when subjected to heating. The proposed approach includes the fundamental principles of non-equilibrium thermodynamics as well as the coupled multi-physics of thermal, hydraulic, mechanical and chemical (THMC) processes. A novel mathematical formulation is introduced to describe the coupled constitutive relationships in the reversible and dissipative regimes as well as the consequent partial differential equations that describe the THMC processes. The governing equations are integrated numerically using the finite element method. The obtained results show a significant correlation between gypsum dehydration and creation of fluid pathways. The proposed model can be generalised to describe the effects of dehydration in other minerals carrying water in their crystal structures.