Fracture Flow Analysis

Example 2-1. Single straight-line fracture in an isotropic circular reservoir containing incompressible fluid. 

We will consider the effects of nonzero thickness in Example 2-3, where high-order corrections for thickness (or more precisely, open fracture effects) are developed. The basic slit solution is considered here. For convenience, introduce the nondimensional variables x, y, and p, defined by 

Recourse to numerical methods is understandable, given the variabihty in pf(x) and the finite size of the reservoir. Fortunately, this is not necessary. 

Singular integral equation analysis. A closed form analytical solution can be obtained. We use results from thin airfoil theory (e.g., Ashley and Landahl, 1965) and singular integral equations (Muskhelishvili, 1953 Gakhov, 1966 Carrier, Krook and Pearson, 1966). Now the standard log r source 

can be viewed as a general point source position over which the effects of numerous sources can be summed. But rather than examining multiple discrete point sources, we examine continuous line source distributions placed along the fracture to represent it. This is clearly the situation physically many simulators model fractures using point sources, which allow fictitious flow between points. We consider the superposition -tl 

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Hybrid model of Discrete Fracture Network (DFN) and Discrete Element Method (DEM) for coupled stress-flow analysis of rock slope stability (Wang, 2000) ... 

Wu Y and Zhang Z. 1996. An application of generalized double porosity media model for coupled stress and groundwater flow analysis in fractured rock mass. J. of Engineering Geology, 1(3), pp. 40-46. 

Analysis of fracture-flow dynamics. The results of investigations by Su et al. (27) demonstrated phenomena of intermittent flow imder unsaturated... 

A pipe break need not be assumed if a successful qualification for leak before break, for break preclusion or for low probability of failure has been performed for the piping under consideration, resulting in a sufficiently low frequency of the occurrence of a spontaneous break In general, a fracture mechanics analysis should be performed to calculate the leak size. In lieu of such an analysis, a subcritical crack corresponding to a leak size of 10% of the flow cross-section should be postulated The leak detection system should be shown to have a sensitivity that is adequate to detect the minimum leakage from a crack that is just subcritical. 

Tbrian s secondary flow analysis ignores the fiee surface. But it appears that in any case the failure shown in Figure 5.4.7 may be due more to elastic effects. Hutton (1969) applied an elastic eneigy criterion to predict the failure, while Tanner and Keentok (1983) used a fracture mechanics approach. However, the experimental results of Hutton (1969) and Broyer and Macosko (1975)... 

Even, limited PSAs use and contain much information. This information may come as memos and process reports and flow sheets, equipment layout, system descriptions, toxic inventory, hazardous chemical reactions, test, maintenance and operating descriptions. From this, data and analyses are prepared regarding release quantities, doses, equipment reliability, probability of exposure, and the risk to workers, public, and environment. An executive summary analysis is detailed, and recommendations made for risk reduction. Thus the information will be text, calculations of envelope fracture stresses, temperatures, fire propagation, air dispersion, doses, and failure probabilities - primarily in tabular form. 

Zigrye, J.L., Osborne, M.W., and Westbrook, G.H. "Field Analysis and Flow Loop Tests Diagnose Problems with Delayed Action Crosslinked Fracturing Fluid Systems," SPE paper 15633, 1986 Annual Technical Conference and Exhibition of the SPE, New Orleans, October 5-8. 

Jenkins, J. D. and Prentice, J. K., 1982, Theory for Aquifer Test Analysis in Fractured Rock under Linear (Non-Radial) Flow Conditions Ground Water, Vol. 20, pp. 12-21. 

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