The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Designing multi-well layout for enhanced geothermal system to better exploit hot dry rock geothermal energy

Numerical simulation of heat production potential from hot dry rock by water circulating through two horizontal wells at Desert Peak geothermal field

[1] The constitutive thermo-hydro-mechanical equations of fractured media are embodied in the theory of mixtures applied to three-phase poroelastic media. The solid skeleton contains two distinct cavities filled with the same fluid. Each of the three phases is endowed with its own temperature. The constitutive relations governing the thermomechanical behavior, generalized diffusion and transfer are structured by, and satisfy, the dissipation inequality. The cavities exchange both mass and energy. Mass exchanges are driven by the jump in scaled chemical potential, and energy exchanges by the jump in coldness. The finite element approximation uses the displacement vector, the two fluid pressures and the three temperatures as primary variables. It is used to analyze a generic hot dry rock geothermal reservoir. Three parameters of the model are calibrated from the thermal outputs of Fenton Hill and Rosemanowes HDR reservoirs. The calibrated model is next applied to simulate circulation tests at the Fenton Hill HDR reservoir. The finer thermo-hydro-mechanical response provided by the dual porosity model with respect to a single porosity model is highlighted in a parameter analysis. Emphasis is put on the influence of the fracture spacing, on the effective stress response and on the permeation of the fluid into the porous blocks. The dual porosity model yields a thermally induced effective stress that is less tensile compared with the single porosity response. This effect becomes significant for large fracture spacings. In agreement with field data, fluid loss is observed to be high initially and to decrease with time.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2012JB009161

A thermo-hydro-mechanical coupled model in local thermal non-equilibrium for fractured HDR reservoir with double porosity

A three-dimensional transient model for EGS subsurface thermo-hydraulic process

Fluid circulation and heat extraction from engineered geothermal reservoirs

This work analyzes the behavior of a numerical geothermal reservoir simulation with flow only in discrete fractures. GEOCRACK is a 2-D finite element model developed at Kansas State University for the Hot Dry Rock (HDR) research at Los Alamos National Laboratory. Its numerical simulations couple the mechanics of discrete fracture behavior with the state of earth stress, fluid flow, and heat transfer. This coupled model could also be of value for modeling reinjection and other reservoir operating strategies for liquid dominated fractured reservoirs. Because fracture surfaces cool quickly by fluid convection, and heat does not conduct quickly from the interior of reservoir rock, modeling the injection of cold fluid into a fractured reservoir is better simulated by a model with discrete fractures. This work contains knowledge gained from HDR reservoir simulation and continues to develop the general concept of heat mining, reservoir optimization. and the sensitivity of simulation to the uncertainties of fracture spacing and dynamic flow dispersion.

/pdf/insight-from-modelling-discrete-fractures-using-geocrack-1y90wly1d5.pdf

Robert DuTeaux

Papers

Fluid circulation and heat extraction from engineered geothermal reservoirs

Insight from modelling discrete fractures using GEOCRACK