There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

비만아 부모의 돌봄 경험: q 방법론

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

Porosity plays a clearly important role in geology. It controls fluid storage in aquifers, oil and gas fields and geothermal systems, and the extent and connectivity of the pore structure control fluid flow and transport through geological formations, as well as the relationship between the properties of individual minerals and the bulk properties of the rock. In order to quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. The overall importance of porosity, at least with respect to the use of rocks as building stone was recognized by TS Hunt in his “Chemical and Geological Essays” (1875, reviewed by JD Dana 1875) who noted:

> “Other things being equal, it may properly be said that the value of a stone for building purposes is inversely as its porosity or absorbing power.”

In a Geological Survey report prepared for the U.S. Atomic Energy Commission, Manger (1963) summarized porosity and bulk density measurements for sedimentary rocks. He tabulated more than 900 items of porosity and bulk density data for sedimentary rocks with up to 2,109 porosity determinations per item. Amongst these he summarized several early studies, including those of Schwarz (1870–1871), Cook (1878), Wheeler (1896), Buckley (1898), Gary (1898), Moore (1904), Fuller (1906), Sorby (1908), Hirschwald (1912), Grubenmann et al. (1915), and Kessler (1919), many of which were concerned with rocks and clays of commercial utility. There have, of course, been many more such determinations since that time.

There are a large number of methods for quantifying porosity, and an increasingly complex idea of what it means to do so. Manger (1963) listed the techniques by which the porosity determinations he summarized were made. He separated these into seven methods for …

/pdf/characterization-and-analysis-of-porosity-and-pore-sea0mqjsa8.pdf

Tayfun Babadagli

Papers

Wettability alteration: A comprehensive review of materials/methods and testing the selected ones on heavy-oil containing oil-wet systems.

Status of electromagnetic heating for enhanced heavy oil/bitumen recovery and future prospects: A review

SAGD laboratory experimental and numerical simulation studies: A review of current status and future issues

Development of mature oil fields — A review

Viscosity reduction of heavy oil/bitumen using micro- and nano-metal particles during aqueous and non-aqueous thermal applications