- Acuna J.A., Ershaghi I., Yortsos Y.C. (1995) Practical application of fractal pressure-transient analysis in naturally fractured reservoirs, SPE Form. Eval. 10, 3, 173–179. DOI: 10.2118/24705-PA. [CrossRef] [Google Scholar]
- Agarwal R.G., Al-Hussainy R., Ramey H.J. Jr. (1970) An investigation of wellbore storage and skin effect in unsteady liquid flow: I. Analytical treatment, Soc. Pet. Eng. Jour. 10, 3, 279–290. [CrossRef] [Google Scholar]
- Albinali A., Holy R., Sarak H., Ozkan E. (2016) Modeling of 1D anomalous diffusion in fractured nanoporous media, Oil Gas Sci. Technol. - Rev. IFP Energies nouvelles 71, 56. [Google Scholar]
- Arps J.J. (1945) Analysis of decline curves, Trans. AIME 160, 228–247. DOI: 10.2118/945228-G. [CrossRef] [Google Scholar]
- Atangana A., Bildik B. (2013) The use of fractional order derivative to predict the groundwater flow, Math. Probl. Eng. 543026, 9. DOI: 10.1155/2013/543026. [Google Scholar]
- Ball R.C., Havlin S., Weiss G.H. (1987) Non-Gaussian random walks, J. Phys. A: Math. Gen. 20, 12, 4055–4059. DOI: 10.1088/0305-4470/20/12/052. [CrossRef] [MathSciNet] [Google Scholar]
- Beier R.A. (1990) Pressure transient field data showing fractal reservoir structure, Paper 90-04 Presented at the Annual Technical Meeting, Calgary, Alberta, Petroleum Society of Canada. DOI: 10.2118/90-04. [Google Scholar]
- Beier R.A. (1994) Pressure-transient model for a vertically fractured well in a fractal reservoir, SPE Form. Eval. 9, 2, 122–128. DOI: 10.2118/20582-PA. [CrossRef] [Google Scholar]
- Benson D.A., Tadjeran C., Meerschaert M.M., Farnham I., Pohll G. (2004) Radial fractional-order dispersion through fractured rock, Water Resour. Res. 40, W12416. DOI: 10.1029/2004WR003314. [Google Scholar]
- Bodvarsson G.S., Boyle W., Patterson R., Williams D. (1999) Overview of scientific investigations at Yucca Mountain: The potential repository for high-level nuclear waste, J. Contam. Hydrol. 38, 1–3, 3–24. [Google Scholar]
- Camacho-Velázquez R., Fuentes-Cruz G., Vásquez-Cruz M. (2008) Decline-curve analysis of fractured reservoirs with fractal geometry, SPE Reserv. Eval. Eng. 11, 3, 606–619. [CrossRef] [Google Scholar]
- Caputo M. (1967) Linear Models of dissipation whose Q is almost frequency independent-II, Geophys. J. R. Astron. Soc. 13, 5, 529–539. [Google Scholar]
- Carslaw H.S., Jaeger J.C. (1959) Conduction of heat in solids, 2nd edn., Clarendon Press, Oxford, p. 510. [Google Scholar]
- Chang J., Yortsos Y.C. (1990) Pressure-transient analysis of fractal reservoirs, SPE Form. Eval. 5, 1, 31–39. [CrossRef] [Google Scholar]
- Chu W.C., Garcia-Rivera J., Raghavan R. (1980) Analysis of interference test data influenced by wellbore storage and skin at the flowing well, J. Pet. Tech. 32, 1, 171–178. DOI: 10.2118/8029-PA. [CrossRef] [Google Scholar]
- Chu W., Pandya N., Flumerfelt R.W., Chen C. (2017) Rate-Transient analysis based on power-law behavior for Permian wells, Paper SPE-187180-MS, Presented at the SPE Annual Technical Conference and Exhibition, 9–11 October, San Antonio, Texas, USA, Society of Petroleum Engineers. DOI: 10.2118/187180-MS. [Google Scholar]
- Chu W., Scott K., Flumerfelt R.W., Chen C. (2018) A new technique for quantifying pressure interference in fractured horizontal shale wells, Paper SPE-191407-MS, presented at the Annual Technical Conference and Exhibition, 24–28 September, Dallas, TX, USA. [Google Scholar]
- Cinco-Ley H., Meng H.-Z. (1988) Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs, Presented at the SPE Annual Technical Conference and Exhibition, 2–5 October, Houston, Texas. DOI: 10.2118/18172-MS. [Google Scholar]
- Cooper H.H., Jacob C.E. (1946) A generalized graphical method for evaluating formation constants and summarizing well-field history, Trans. AGU. 27, 526–534. [CrossRef] [Google Scholar]
- Dassas Y., Duby Y. (1995) Diffusion toward fractal interfaces, potentiostatic, galvanostatic, and linear sweep voltammetric techniques, J. Electrochem. Soc. 142, 12, 4175–4180. [Google Scholar]
- de Swaan-O A. (1976) Analytical solutions for determining naturally fractured reservoir properties by well testing, Soc. Pet. Eng. Jour. 16, 3, 117–122. DOI: 10.2118/5346-PA. [Google Scholar]
- Fetkovich M.J. (1980) Decline curve analysis using type curves, J. Pet. Tech. 32, 6, 1065–1077. [CrossRef] [Google Scholar]
- Flamenco-Lopez F., Camacho-Velázquez R. (2001) Fractal transient pressure behavior of naturally fractured reservoirs, Paper 71591 Presented at the Annual Technical Conference and Exhibition, New Orleans, LA, Society of Petroleum Engineers. DOI: 10.2118/71591-MS. [Google Scholar]
- Gao C., Jones J.R., Raghavan R., Lee W.J. (1994) Responses of commingled systems with mixed inner and outer boundary conditions using derivatives, SPE Form. Eval. 9, 4, 264–271. [Google Scholar]
- Gefen Y., Aharony A., Alexander S. (1983) Anomalous diffusion on percolating clusters, Phys. Rev. Lett. 50, 1, 77–80. DOI: 10.1103/PhysRevLett.50.77. [Google Scholar]
- Hawkins M.F. Jr. (1956) A note on the skin effect, Trans. AIME 207, 356–357. [Google Scholar]
- Henry B.I., Langlands T.A.M., Straka P. (2010) An introduction to fractional diffusion, in: Dewar R.L., Detering F. (eds), Complex physical, biophysical and econophysical systems, World Scientific, Hackensack, NJ, p. 400. [Google Scholar]
- IPCC special report on carbon dioxide capture and storage (2005) Prepared by working group III of the Intergovernmental Panel on Climate Change, in: Metz B., Davidson O., de Coninck H.C., Loos M., Meyer L.A. (eds), Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 442 p. [Google Scholar]
- Kim S., Kavvas M.L., Ercan A. (2015) Fractional ensemble average governing equations of transport by time-space nonstationary stochastic fractional advective velocity and fractional dispersion, II: numerical investigation, J. Hydrol. Eng. 20, 2, 04014040. [Google Scholar]
- Le Borgne T., Bour O., de Dreuzy J.R., Davy P., Touchard F. (2004) Equivalent mean flow models for fractured aquifers: Insights from a pumping tests scaling interpretation, Water Resour. Res. 40, W03512. DOI: 10.1029/2003WR002436. [Google Scholar]
- Le Borgne T., Bour O., de Dreuzy J.R., Davy P. (2007) Characterizing flow in natural fracture networks: Comparison of the discrete and continuous descriptions, 437–450, in: Krazny J., Sharp J.M., Groundwater in Fractured Rocks: Selected papers from the Groundwater in Fractured Rocks on Hydrogeology, Prague 2003, Taylor & Francis/Balkema, The Netherlands, 647 pp. [Google Scholar]
- Le Mẽhautẽ A. (1984) Transfer processes in fractal media, J. Stat. Phys. 36, 5–6, 665–676. DOI: 10.1007/BF01012930. [Google Scholar]
- Mainardi M., Pagnini G., Saxena R.K. (2005) Fox H functions in fractional diffusion, J. Comput. Appl. Math. 178, 1–2, 321–331. [Google Scholar]
- Meehan D.N., Horne R.N., Ramey H.J. (1989) Interference testing of finite conductivity hydraulically fractured wells, Presented at the SPE Annual Technical Conference and Exhibition, 8–11 October, San Antonio, Texas, SPE-19784-MS. DOI: 10.2118/19784-MS [Google Scholar]
- Mendes G.A., Lenzi E.K., Mendes R.S., da Silva L.R. (2005) Anisotropic fractional diffusion equation, Physica A: Stat. Mech. Appli. 346, 3–4, 271–283. [CrossRef] [Google Scholar]
- Metzler R., Glockle W.G., Nonnenmacher T.F. (1994) Fractional model equation for anomalous diffusion, Physica A 211, 1, 13–24. [Google Scholar]
- Mousli N.A., Raghavan R., Cinco-Ley H., Samaniego-V F. (1982) The influence of vertical fractures intercepting active and observation wells on interference tests, Soc. Pet. Eng. Jour. 22, 6, 933–944. DOI: 10.2118/9346-PA. [CrossRef] [Google Scholar]
- Mueller T.D., Witherspoon P.A. (1965) Pressure interference effects within reservoirs and aquifers, J. Pet. Tech. 17, 4, 471–474. DOI: 10.2118/1020-PA. [CrossRef] [Google Scholar]
- Nigmatullin R.R. (1984) To the theoretical explanation of the universal response, Phys. Status Solidi B Basic Res. 123, 2, 739–745. [CrossRef] [Google Scholar]
- Nigmatullin R.R. (1986) The realization of the generalized transfer equation in a medium with fractal geometry, Phys. Status Solidi B Basic Res. 133, 1, 425–430. [CrossRef] [Google Scholar]
- Noetinger B., Estebenet T. (2000) Up-scaling of double porosity fractured media using continuous-time random walks methods, Transp. Porous Med. 39, 3, 315–337. [CrossRef] [Google Scholar]
- Noetinger B., Estebenet T., Landereau P. (2001) A direct determination of the transient exchange term of fractured media using a continuous time random walk method, Transp. Porous Med. 44, 3, 539–557. [CrossRef] [Google Scholar]
- Noetinger B., Roubinet D., Russian A., Le Borgne T., Delay F., Dentz M., Gouze P. (2016) Random walk methods for modeling hydrodynamic transport in porous and fractured media from pore to reservoir scale, Transp. Porous Med. 115, 2, 345–385. [CrossRef] [Google Scholar]
- Raghavan R. (2004) A review of applications to constrain pumping test responses to improve on geological description and uncertainty, Rev. Geophys. 42, RG4001. DOI: 10.1029/2003RG000142. [Google Scholar]
- Raghavan R. (2009a) A note on the drawdown, diffusive behavior of fractured rocks, Water Resour. Res. 45, 2, W02502. DOI: 10.1029/2008WR007158. [Google Scholar]
- Raghavan R. (2009b) Complex geology and pressure tests, J. Petrol. Sci. Eng. 69, 181–188. [CrossRef] [Google Scholar]
- Raghavan R. (2011) Fractional derivatives: Application to transient flow, J. Petrol. Sci. Eng. 80, 1, 7–13. DOI: 10.1016/j.petrol.2011.10.003. [CrossRef] [Google Scholar]
- Raghavan R. (2012) Fractional diffusion: Performance of fractured wells, J. Petrol. Sci. Eng. 92–93, 167–173. [CrossRef] [Google Scholar]
- Raghavan R., Chen C. (2013a) Fractured-well performance under anomalous diffusion, SPE Res. Eval. Eng. 16, 3, 237–245, DOI: 10.2118/165584-PA. [CrossRef] [Google Scholar]
- Raghavan R., Chen C. (2013b) Fractional diffusion in rocks produced by horizontal wells with multiple, transverse hydraulic fractures of finite conductivity, J. Petrol. Sci. Eng. 109, 133–143. [CrossRef] [Google Scholar]
- Raghavan R., Chen C. (2017) Addressing the influence of a heterogeneous matrix on well performance in fractured rocks, Transp. Porous Med. 117, 1, 69–102. DOI: 10.1007/s11242-017-0820-5. [CrossRef] [Google Scholar]
- Raghavan R., Chen C. (2018) A conceptual structure to evaluate wells producing fractured rocks of the Permian Basin, Paper SPE-191484-MS, Presented at the Annual Technical Conference and Exhibition, 24–28 September, Dallas, TX, USA. [Google Scholar]
- Raghavan R., Ozkan E. (1994) A method for computing unsteady flows in porous media, Pitman Research Notes in Mathematics Series (318), Longman Scientific & Technical, Harlow, UK, 188 p. [Google Scholar]
- Romeu R.K., Noetinger B. (1995) Calculation of internodal transmissibilities in finite-difference models of flow in heterogeneous media, Water Resour. Res. 26, 2, 291–306. [Google Scholar]
- Sanchez-Vila X., Guadagnini A., Carrera J. (2006) Representative hydraulic conductivities in saturated groundwater flow, Rev. Geophys. 44, RG3002. DOI: 10.1029/2005RG000169. [Google Scholar]
- Saxena R.K., Mathai A.M., Haubold H.J. (2006) Fractional reaction-diffusion equations, Astrophys. Space Sci. 305, 3, 289–296. [Google Scholar]
- Schad H., Teutsch G. (1994) Effects of the investigation scale on pumping test results in heterogeneous porous aquifers, J. Hydrology 159, 61–77. [CrossRef] [Google Scholar]
- Stehfest H. (1970a) Algorithm 368: Numerical inversion of Laplace transforms [D5], Commun. ACM 13, 1, 47–49. [Google Scholar]
- Stehfest H. (1970b) Remark on algorithm 368: Numerical inversion of Laplace transforms, Commun. ACM 13, 10, 624. [Google Scholar]
- Su N., Nelson P.N., Connor S. (2015) The distributed-order fractional diffusion-wave equation of groundwater flow: Theory and application to pumping and slug tests, J. Hydrology 529, 1262–1273. [Google Scholar]
- Theis C.V. (1935) The relationship between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage, EOS Trans. AGU 2, 519–524. [Google Scholar]
- Thomas O.O., Raghavan R., Dixon T.N. (2005) Effect of scaleup and aggregation on the use of well tests to identify geological properties, SPE Res. Eval. Eng. 8, 3, 248–254. DOI: 10.2118/77452-PA. [CrossRef] [Google Scholar]
- Uraiet A., Raghavan R., Thomas G.W. (1977) Determination of the orientation of a vertical fracture by interference tests, J. Pet. Tech. 29, 1, 73–80. DOI: 10.2118/5845-PA. [CrossRef] [Google Scholar]
- Warren J.E., Price H.S. (1961) Flow in heterogeneous media, Soc. Pet. Eng. Jour. 1, 3, 153–169. [CrossRef] [Google Scholar]
- Warren J.E., Root P.J. (1963) The behavior of naturally fractured reservoirs, Soc. Pet. Eng. Jour. 3, 3, 245–255. DOI: 10.2118/426-PA. [Google Scholar]
- Weisstein, E.W. (2018) Fox H-Function. From MathWorld – A Wolfram web resource. http://mathworld.wolfram.com/FoxH-Function.html; see also, http://www.wolframalpha.com/input/?i=fox+h-function. [Google Scholar]
- Whiting R.L., Ramey H.J. (1969) Application of material and energy Balances to geothermal steam production, J. Pet. Tech. 21, 7, 893–900. DOI: 10.2118/1949-PA. [CrossRef] [Google Scholar]
Open Access
Issue |
Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles
Volume 74, 2019
|
|
---|---|---|
Article Number | 6 | |
Number of page(s) | 10 | |
DOI | https://doi.org/10.2516/ogst/2018081 | |
Published online | 14 January 2019 |
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