Open Access
Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles
Volume 76, 2021
Article Number 80
Number of page(s) 10
Published online 21 December 2021
  • Al-Hussainy R., Ramey H.J. Jr, Crawford P.B. (1966) The flow of real gases through porous media, J. Pet. Tech. 18, 624–636. [Google Scholar]
  • Barros-Galvis N., Samaniego V.F., Cinco-Ley H. (2018) Fluid dynamics in naturally fractured tectonic reservoirs, J. Petrol. Explor. Prod. Technol. 8, 1–6. [Google Scholar]
  • Bateman H. (1915) Some recent researches on the motion of fluids, Mon. Weather Rev. 43, 163–170. [Google Scholar]
  • Bertini L., Giacomin G. (1997) Stochastic Burgers and KPZ equations from particle systems, Comm. Math. Phys. 183, 571–607. [Google Scholar]
  • Braeuning S., Jelmert T.A., Vik S.A. (1998) The effect of the quadratic gradient term on variable-rate well-tests, J. Pet. Sci. Eng. 21, 203–222. [Google Scholar]
  • Burgers J.M. (1940) Application of a model system to illustrate some points of the statistical theory of free turbulence, Proc. Nederl. Akad. Wetensch 43, 2–12. [Google Scholar]
  • Burnell J.G., McNabb A., Weir G.J., Young R. (1989) Two-phase boundary layer formation in a semi-infinite porous slab, Trans. Porous Med. 4, 395–420. [Google Scholar]
  • Carslaw H.S., Jaeger J.C. (1959) Conduction of heat in solids, 2nd edn., Clarendon Press, Oxford, 510p. [Google Scholar]
  • Chakrabarty C., Farouq Ali S.M., Tortike W.S. (1993) Analytical solutions for radial pressure distribution including the effects of the quadratic-gradient term, Water Resour. Res. 29, 1171–1177. [Google Scholar]
  • Chen C., Raghavan R. (1995) Modeling a fractured well in a composite reservoir, SPE Form. Eval. 10, 241–246. [Google Scholar]
  • Chin L.Y., Raghavan R., Thomas L.K. (2000) Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability, SPE J. 5, 32–45. [Google Scholar]
  • Cole J.D. (1951) On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9, 225–236. [Google Scholar]
  • Duhamel J.M.C. (1833) Mémoire sur la méthode générale relative au mouvement de la chaleur dans les corps solides plongés dans les milieux dont la température varie avec le temps, J. de Éc. Polyt. Paris 14, 20–77. [Google Scholar]
  • Earlougher R.C. Jr (1977) Advances in well test analysis, SPE Monograph Series 5, 264. [Google Scholar]
  • Finjord J. (1986) Curling up the slope: Effects of the quadratic gradient term in the infinite-acting period for two dimensional reservoir flow, SPE-16451-MS, Society of Petroleum Engineers. [Google Scholar]
  • Finjord J., Aadnoy B.S. (1989) Effects of the quadratic gradient term in steady-state and semisteady-state solutions for reservoir pressure, SPE Form. Eval. 4, 413–417. [Google Scholar]
  • Forsyth A.R. (1906) Theory of differential equations, Vol. VI,Cambridge University Press, p. 102, Ex. 3. [Google Scholar]
  • Friedrichs K.O. (1948) Formation and decay of shock waves, Comm. Pure Appl. Math 1, 211–245. [Google Scholar]
  • Hopf E. (1950) The partial differential equation ut + uux =uxx, Comm. Pure Appl. Math. 3, 201–230. [Google Scholar]
  • Horner D.R. (1951) Pressure buildup in wells, in: Brill E.J. (ed.), Proceedings of the Third World Petroleum Congress, Vol. II, Leiden, pp. 503–521. [Google Scholar]
  • Jacob E.E. (1947) Drawdown test to determine effective radius of artesian well, Trans. Am. Soc. Civ. Eng. 112, 1047–1070. [Google Scholar]
  • Jaeger J.C., Carslaw H. (1943) Heat flow in the region bounded internally by a circular cylinder, Proc. R. Soc. Edinb. A: Math. Phys. Sci. 61, 223–228. [Google Scholar]
  • Jelmert T.A., Vik S.A. (1996) Analytic solution to the non-linear diffusion equation for fluids of constant compressibility, J. Pet. Sci. Eng. 14, 231–233. [Google Scholar]
  • Kikani J., Pedrosa O.A. Jr (1991) Perturbation analysis of stress-sensitive reservoirs, SPE Form. Eval. 6, 379–386. [Google Scholar]
  • Kirchhoff G. (1894) Vorlesungen über mathematische Physik, Theorie der Wärme, Vol. 4, Barth, Leipzig. [Google Scholar]
  • Leibenzon L.S. (1953) Underground hydraulics of water, oil, and gas, Vol. 2, Izd. AN SSSR (Publ. Acad. Sci.), Moscow, pp. 163–209. [Google Scholar]
  • Matthews C.S., Russell D.G. (1967) Pressure buildup and flow tests in wells, SPE Monograph Series 1, 163. [Google Scholar]
  • Marshall S.L. (2009) Nonlinear pressure diffusion in flow of compressible liquids through porous media, Transp. Porous Med. 77, 431–446. [Google Scholar]
  • Miura R.M. (1968) Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation, J. Math. Phys. 9, 1202–1204. [Google Scholar]
  • Mueller T.D., Witherspoon P.A. (1965) Pressure interference effects within reservoirs and aquifers, J. Pet. Tech. 17, 471–474. [Google Scholar]
  • Muskat M. (1934) The flow of compressible fluids through porous media and some problems in heat conduction, Physics 5, 71–94. [Google Scholar]
  • Odeh A.S., Babu D.K. (1988) Comparison of solutions of the nonlinear and linearized diffusion equations, SPE Reserv. Eng. 3, 1202–1206. [Google Scholar]
  • Ozkan E., Raghavan R. (1991) Some new solutions to solve problems in well test analysis: I – Analytical considerations, SPE Form. Eval. 63, 359–368. [Google Scholar]
  • Phillips W.R.C., Mahon P.J. (2011) On approximations to a class of Jaeger integrals, Proc. R. Soc. A. 467, 3570–3589. [Google Scholar]
  • Raghavan R. (1993) Well test analysis, Prentice Hall, Englewoods Cliffs, NJ.p. 40, Ex. 5. [Google Scholar]
  • Raghavan R. (1976) Well test analysis: Wells producing by solution gas drive, Soc. Pet. Eng. J. 16, 196–208. [Google Scholar]
  • Raghavan R., Scorer J.D.T., Miller F.G. (1972) An investigation by numerical methods of the effect of pressure-dependent rock and fluid properties on well flow tests, SPE J. 12, 267–275. [Google Scholar]
  • Raghavan R., Ozkan E. (1994) A method for computing unsteady flows in porous media, Pitman Research Notes in Mathematics Series, Vol. 318, Longman Scientific & Technical, Harlow, UK. [Google Scholar]
  • Ren J., Guo P. (2017) Nonlinear flow model of multiple fractured horizontal wells with stimulated reservoir volume including the quadratic gradient term, J. Hydrol. 554, 155–172. [Google Scholar]
  • Ritchie R.H., Sakakura A.Y. (1956) Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry, J. Appl. Phys. 27, 1453–1459. [Google Scholar]
  • Singh S.R., Sagar B. (1980) On Jacob’s approximation in flow through porous media, Water Resour. Res. 16, 377–380. [Google Scholar]
  • Stehfest H. (1970a) Algorithm 368: Numerical inversion of Laplace transforms [D5], Commun. ACM 13, 47–49. [Google Scholar]
  • Stehfest H. (1970b) Remark on algorithm 368: Numerical inversion of Laplace transforms, Commun. ACM 13, 624. [Google Scholar]
  • Theis C.V. (1935) The relationship between the lowering of the piezometric surface and the rate and duration of discharge using ground-water storage, EoS Trans. AGU 16, 519–524. [Google Scholar]
  • van Everdingen A.F., Hurst W. (1949) The application of the LaPlace transformation to flow problems in reservoirs, Trans. AIME 186, 305–324. [Google Scholar]
  • Vadasz P. (2010) Analytical solution to nonlinear thermal diffusion: Kirchhoff versus Cole-Hopf transformations, J. Heat Transfer 132, 121302. [Google Scholar]
  • Van Dusen M.S. (1930) Note on the theory of heat conduction, Bur. Stand. J. Res. 4, 753–756. [Google Scholar]
  • Wang Y., Dusseault M.B. (1991) The effect of quadratic gradient terms on the borehole solution in poroelastic media, Water Resour. Res. 27, 3215–3223. [Google Scholar]
  • Yeh H.-D., Wang C.-T. (2007) Large-time solutions for groundwater flow problems using the relationship of small p versus large t, Water Resour. Res. 43, W06502. [Google Scholar]

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