Slick-water fracturing is the most routine form of well stimulation in shales; however N 2 , LPG and CO 2 have all been used as ''exotic'' stimulants in various hydrocarbon reservoirs. We explore the use of these gases as stimulants on Green River shale to compare the form and behavior of fractures in shale driven by different gas compositions and states and indexed by breakdown pressure and the resulting morphology of the fracture networks. Fracturing is completed on cylindrical samples containing a single blind axial borehole under simple triaxial conditions with confining pressure ranging from 10 to 25 MPa and axial stress ranging from 0 to 35 MPa (r 1 [ r 2 = r 3 ). Results show that: (1) under the same stress conditions, CO 2 returns the highest breakdown pressure, followed by N 2 , and with H 2 O exhibiting the lowest breakdown pressure; (2) CO 2 fracturing, compared to other fracturing fluids, creates nominally the most complex fracturing patterns as well as the roughest fracture surface and with the greatest apparent local damage followed by H 2 O and then N 2 ; (3) under conditions of constant injection rate, the CO 2 pressure build-up record exhibits condensation between *5 and 7 MPa and transits from gas to liquid through a mixed-phase region rather than directly to liquid as for H 2 O and N 2 which do not; (4) there is a positive correlation between minimum principal stress and breakdown pressure for failure both by transverse fracturing (r 3 axial) and by longitudinal fracturing (r 3 radial) for each fracturing fluid with CO 2 having the highest correlation coefficient/slope and lowest for H 2 O. We explain these results in terms of a mechanistic understanding of breakdown, and through correlations with the specific properties of the stimulating fluids.
On the vertex operators of the elliptic quantum algebra U q , p ( s l 2 ) k J. Math. Phys. 49, 043513 (2008); 10.1063/1.2905151Dynamical symmetry group and quantum splittings for a free particle on the group manifold AdS 3 A grading of a Lie algebra is called fine if it could not be further refined. For a fine grading of a simple Lie algebra, we define its Weyl group to describe the symmetry of this grading. It is already known that the Weyl group of the fine grading of sl͑n , C͒ induced by the action of the group ⌸ n of the generalized Pauli matrices of rank n is SL͑2,Z n ͒, where Z n is the cyclic group of order n. In this paper, we consider the fine grading of sl͑n k , C͒ induced by the action of the group of k-fold tensor product of the generalized Pauli matrices of rank n. We prove that its Weyl group is Sp͑2k , Z n ͒ and is generated by transvections; therefore, this generalizes the previous result.
The dynamics of macroalgal communities and the impact of sewage on their growth were studied in the tidal zone around Zhanqiao Pier of the Qingdao coastal area, in the northwest of the Yellow Sea, China, from September 2001 to September 2003. The tidal zone of the study area is divided into western and eastern sections by the Zhanqiao Pier. Inorganic nitrogen and phosphorus in seawater showed higher concentrations on the eastern side of Zhanqiao Pier than on the western side, because a sewer drains into the eastern side. The macroalgal communities on each side of the Pier showed an obvious difference due to the effect of this sewage discharge. A total of 47 macroalgal species including 10 greens, 11 browns and 26 reds was identified in this study. The species composition and biomass indicated higher values in the nutrient-rich area on the eastern side of Zhanqiao Pier compared with the nutrient-poor area on the western side of Zhanqiao Pier. Some ephemeral and filamentous species dominated seasonally on the eastern side of Zhanqiao Pier, in contrast to the western side where slow-growing species dominated throughout the year. Nutrient gradients and temperature were considered the main factors affecting the distribution of macroalgae communities in time and space. The results are consistent with the common observation that nutrient-poor areas are dominated by slow-growing rather than ephemeral algal species. Moreover, the species diversity in the whole study area had declined when compared to previous records.
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