Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

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A User’s Guide

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.

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

The flow of homogeneous fluids through porous media: analogies with other physical problems

The present invention relates to engineered multivalent and multispecific binding proteins, methods of making, and specifically to their uses in the prevention, diagnosis, and/or treatment of disease.

Dual variable domain immunoglobulins and uses thereof

A process for geo-sequestration of a water-soluble fluid includes selection of a target water-laden geological formation bounded by an upper formation of low permeability, providing an injection well into the formation and injecting the fluid into the injection well under conditions of temperature, pressure and density contrast selected to cause the fluid to enter the formation and rise within the formation. This generates a density-driven convection current of formation water which promotes enhanced mixing of the water-soluble fluid with formation water.

Process for sequestration of fluids in geological formations

Renewable and sustainable energy sources can play an important role in meeting the world’s energy needs and also in addressing environmental challenges such as global warming and climate change. Geothermal well-doublet systems can produce both electrical and thermal energy through extracting heat from hot-water aquifers. In this paper, we examine some potential challenges associated with the operation of well-doublet systems, including heat conductivity, chemical, and mechanical issues. In these systems, geomechanics issues such as thermal short-circuiting and induced seismicity arise from temperature and pressure change impacts on the stress state in stiff rocks and fluid flow in fractured rock masses. Coupled chemical processes also can cause fluid channeling or formation and tubular goods plugging (scaling) with precipitates. Mechanical and chemical disequilibrium conditions lead to increased production uncertainties; hence risk, and therefore coupled geo-risk assessments and optimization analyses are needed for comparative commercialization evaluations among different sites. The challenges related to heat transfer processes are also examined. These studies can help better understand the issues that may arise during the operation of geothermal well-doublet systems and improve their effectiveness, subsequently reducing associated costs and risks.

https://www.mdpi.com/2076-3417/11/2/697/pdf

Maurice B. Dusseault

Papers

Process for sequestration of fluids in geological formations

Well-Doublets: A First-Order Assessment of Geothermal SedHeat Systems

Monitoring Mining-induced Rock Mass Deformation Using Distributed Strain Monitoring Based On Fiber Optics

Ensuring health and environmental protection in hydraulic fracturing: A focus on British Columbia and Alberta, Canada

Pressure Pulsing At the Reservoir Scale: A New IOR Approach