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

Multiscale Pore Structure Characterization By Combining Image Analysis And Mercury Porosimetry

Mechanical skin develops around high-rate oil wells because of mineral salt precipitation in the near-wellbore region. because of fine-grained minerals accumulation that block the near-wellbore pore throats, because of capillary forces development that impair free flow, and because of asphaltene or other organic substance deposition that reduces effective porosity. The removal of mechanical skin is normally carricd out by workover techniques that require wellbore intervention. As early as 1994-95. it was found that for wells in poorly consolidated sandstones many of the problems of mechanical skin could be mitigated by producing the wells at a rate that allowed periodic sand bursts, yet without initiating massive sand influx Also, deliberate sand clean-up activities during well testing could be used to generate skin-removing bursts. The sand bursts are triggered by stress and by the increased hydrodynamic drag associated with steep exit gradients arising from skin, and they have a remarkable clean-up effect on the near-wellbore. bringing flow skin into the range of consistently negative values Wells that are amenable to this production methodology, called Sand Management, benefit from reduced completion costs, increased production rates. lowered intervention frequency, and the development and maintenance of a negative skin. Sand Management, in contrast to sand exclusion, requires coping with higher risks because episodic sand influx events carry with them some danger to integrity of the well and surface facilities. Risk management mplies three actions: high-quality evaluation and analysis before implementation, a commitment to monitoring during production, and a process of continuous re-evaluation of the well during its production life. These risk management activities and protocols form the basis of the Sand Management approach.

Skin Self-Cleaning in High-Rate Oil Wells Using Sand Management

Hydraulic fracturing of soil as an analogue to rock behaviour

THM response of a borehole in naturally fractured media

Large amounts of hydrocarbon reserves are trapped in naturally fractured reservoirs which arechallenging in terms of accurate recovery prediction because of their joint fabric complexity andlithological heterogeneity. Canada, for example, has over 400 billion barrels of crude oil in fracturedcarbonates in Alberta, most of this being bitumen of viscosity greater than 106 cP in the GrosmontFormation, which has an average porosity of about 13-15%. Thermal methods are the most commonexploitation approaches in such viscous oil reservoirs which, in the case of steam injection, are associatedwith up to 275-300°C temperature changes, leading to considerable thermoelastic expansion. Thistemperature change, combined with pore pressure changes from injection and production processes, leadsto massive effective stress variations in the reservoir and surrounding rocks. The thermally-induced(thermoelastic) stress changes can easily be an order of magnitude greater than the pore pressure effectsbecause of the high intrinsic stiffness of the low porosity limestone and bounding strata. Study of thesestress-pressure-temperature effects requires a thermo-hydro-mechanical (THM) coupling approach whichconsiders the simultaneous variation of effective stress, pore pressure, and temperature and theirinteractions. For example, thermal expansion can lead to significant joint dilation, increasing themacroscopic, joint-dominated transmissivity by an order of magnitude in front of and normal to thethermal front, while reducing it in the direction tangential to the heating front. This leads to stronginduced anisotropy of transport processes, which in turn affects the spatial distribution of the heatingarising from advective heat transfer.

/pdf/coupling-geomechanics-and-transport-in-naturally-fractured-e01gekpthe.pdf

Maurice B. Dusseault

Papers

Multiscale Pore Structure Characterization By Combining Image Analysis And Mercury Porosimetry

Skin Self-Cleaning in High-Rate Oil Wells Using Sand Management

Hydraulic fracturing of soil as an analogue to rock behaviour

THM response of a borehole in naturally fractured media

Coupling Geomechanics and Transport in Naturally Fractured Reservoirs