Summary
Fracability characterizes the ease of gas shale to form a complex-fracture network with hydraulic-fracturing treatments. Previous methods of fracability evaluation take into account some mechanical properties of gas shale, such as brittleness and fracture toughness. However, very little work has been performed to verify these methods by comparing the predicted fracability against the actual result of fracturing stimulation. Moreover, the prediction models of fracture toughness used in the previous methods are derived from conventional shale rather than from gas shale, which leads to the low resolution of these methods. In this paper, new prediction models for both the Mode-I and the Mode-II fracture toughness of gas shale are developed by use of straight-notched-Brazilian-disk (SNBD) tests and logging data. Furthermore, an improved fracability-evaluation model is proposed on the basis of the new toughness models. The new fracability model takes into account the brittleness, fracture toughness, and minimum horizontal in-situ stress of the gas-shale reservoirs. Compared with the previous models, the new model has better resolution in identifying fracability. The accuracy of the proposed model is verified with the efficiency of field hydraulic-fracturing jobs.
The possibility of estimating the minimum total flow in a cascade with concentrations of a target component given in the product and waste flows by means of a model match abundance ratio cascade (MARC) is studied. The parameters required to describe MARC characteristics are the total number of separation stages, the feed flow location, and the M Ã parameter, which is equal to a half-sum of mass numbers of the target and the supporting components. Specific research carried out independently in two scientific labs in China and Russia has demonstrated that the integral parameters of the MARC, optimized by the M Ã parameter, are very close to that of the optimum by the minimum total flow cascade found by means of numerical optimization. The calculation is performed for separation of krypton isotopes when the end component 78 Kr and the intermediate component 83 Kr are considered to be the targets. It paves the way to use the optimized MARC parameters for two purposes: first, for fast and easy evaluation of the real cascade parameters and second, as an initial guess in its further direct numerical optimization, thereby allowing significant savings in computation time.
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