Program > Keynote Speakers > Maurice B. Dusseault

Upscaling HF Models to Simulate the Development of a Stimulated Zone
Maurice B. Dusseault, PhD, PEng
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, ON, Canada

Maurice is a Professional Engineer and teaches Geological Engineering at the University of Waterloo. He carries out research in deep underground engineering issues including oil production, hydraulic fracturing, energy storage, geothermal energy, carbon sequestration, and deep injection disposal of granular solids and liquid wastes (including biosolids, oilfield wastes, and civil wastes). He holds over 90 international patents and has about 570 full-text papers published in journals and conferences and has taught Petroleum Geomechanics short courses in 28 countries. Maurice is a well-known educator and consultant, and advised several Canadian provinces on matters relating to energy development and fracturing. He is involved in energy technologies that can be downscaled to community level to provide robust and reliable heat and power; these include geothermal, natural gas approaches, compressed air energy storage, and heat geo-storage. Many of the general energy processes he works on involve hydraulic fracture implementation to generate communication, or analysis to prevent hydraulic fracturing onset.


The development of a stimulated volume (SV) during hydraulic fracturing (HF) in a naturally fractured rock mass (NFR) is singularly challenging to simulate mathematically.  Similar to the upscaling of molecular dynamics (MD) models, we seek to represent the behavior of a discrete array of interacting bodies by a continuum approximation in order to achieve a tractable simulation time, without introducing weak assumptions.  The task is far more challenging than typical MD simulations because at the discrete level there are strong fabric issues (oriented joint sets, perhaps faults, and weak bedding planes), different joint properties, Biot coupling, advective-conductive heat transfer, and flow in joint arrays with changing apertures.  Complex discrete interaction laws for joints involve sliding Mohr-Coulomb friction with joint dilation (aperture increase), cohesion loss related to sliding and to extensional displacements across joints, strongly non-linear block contact stiffness behavior that deviates from Hertzian behavior, and loss of contacts during HF when some natural fractures become non-contacting.  Furthermore, the rock blocks delineated by the joints in the SV possess anisotropic properties, and large-scale heterogeneity also exists.

Some smart young persons have shown me a promising direction for upscaling.  Their new upscaled HF model for SV simulation if a NFR is a typical Galerkin FEM approach, including full Biot coupling, but using a continuum damage mechanics (CDM) formulation to track the evolution of bulk stiffness and fluid transmission properties.  A key factor is to develop an upscaled constitutive law from a discrete element model (DEM), and we use the DEM method of UDEC™ and 3DEC™ to quantify relationships such as the upscale permeability and stiffness changes as functions of average bulk displacement.  A representative elementary volume at a scale less than the upscaled model gives the CDM constitutive mechanical law, and we use porosity change – the sum of the new aperture from extension and shear dilation – to govern the coupled changes in stiffness and flow properties.

The preliminary results seem promising, and we have demonstrated a lack of mesh dependency (something that plagues conventional HF models in FEM formulations), rapid execution times, and results that look quite reasonable.  One 2-D and one 3D example images of the SV development are shown in the figures.  For example, as one would expect, a high deviatoric stress will lead to a narrower SV, but with greater length.  Because the CDM constitutive law is partially plastic (irreversible strains), the system retains memory of the damage.  So, in simulations of the pressure decline response after a HF “treatment”, or in cyclic pressurization (see second figure) the injection and the “shut-in” responses show both expected and unexpected characteristics because of the altered SV stiffness and liquid storativity, as well as changing fracture apertures as the effective stresses change.

I hope that this approach can be incorporated into simulation programs for actual field use to aid in the design of HF processes involving NFRs where significant SVs are generated.  At the very least, it should help in parametric analyses and insights for these complicated processes.

(Acknowledgements: Professor Rob Gracie, Dr Erfan Sarvaramini; Mr Mike Yetisir)