1992
DOI: 10.1007/bf01063964
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Self-similar solution for deep-penetrating hydraulic fracture propagation

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Cited by 14 publications
(11 citation statements)
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“…Surprisingly, only a handful of papers deal with the mathematical formulation and the construction of solutions for the PKN fracture model, despite its importance for the design of hydraulic fracturing treatments when the fracture remains confined to the reservoir (Perkins and Kern 1961;Nordgren 1972;Kemp 1990;Gordeyev and Zazovsky 1992). These contributions are now briefly reviewed.…”
mentioning
confidence: 98%
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“…Surprisingly, only a handful of papers deal with the mathematical formulation and the construction of solutions for the PKN fracture model, despite its importance for the design of hydraulic fracturing treatments when the fracture remains confined to the reservoir (Perkins and Kern 1961;Nordgren 1972;Kemp 1990;Gordeyev and Zazovsky 1992). These contributions are now briefly reviewed.…”
mentioning
confidence: 98%
“…However, the nature of the boundary conditions at the tip when there is leak-off remains ambiguous, due in part, as explained in this article, to the presence of a boundary layer at the tip. Construction of self-similar solutions for the PKN model when the leak-off is not restricted by Carter's law is presented by Gordeyev and Zazovsky (1992), who derived solutions for a constant pressure at the fracture inlet, by neglecting the pore pressure gradient along the crack. Approximated solutions for the case where the injection rate is prescribed at the inlet are proposed by Economides et al (2007).…”
mentioning
confidence: 99%
“…After pioneering work of [Hubbert and Willis, 1957;Hubbert and Rubey, 1959] 23 which explored pore fluid pressure as an important factor for small scale hydrofracturing in 1 tectonic processes, significant efforts have been made in the development of theoretical 2 fundamentals [Biot et al, 1986; J M Cleary and Illinois State Geological Survey., 1958; 3 Daneshy, 1973;Secor, 1965;Valkó and Economides, 1995]. Apart from theoretical aspects, a 4 significant amount of analytical and numerical solutions have also been put forward by many 5 investigators to address this coupled process in a qualitative and quantitative manner [M P 6 Cleary and Wong, 1985;Flekkøy et al, 2002;Gordeyev and Zazovsky, 1992;Meyer, 1986; 7 Tzschichholz et al, 1994;Yu.N, 1993]. …”
mentioning
confidence: 99%
“…A fracture growth rate versus time expression was derived by Gordeyev and Zazovsky (1992), who showed that for a fracture of constant height (i.e., the fracture does not grow in the vertical direction), a linear fracture propagation obeys the equation:…”
Section: Analytical Solution For Fracture Growth Areamentioning
confidence: 99%