Analytical solution and mechanisms of fluid production from hydraulically fractured wells with finite fracture conductivity
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- 作者：Yan Jin ; Kang Ping Chen ; Mian Chen
- 关键词：Finite fracture conductivity ; Fluid production mechanism ; Porous media flow ; Pressure gradient singularity
- 刊名：Journal of Engineering Mathematics
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：92
- 期：1
- 页码：103-122
- 全文大小：6,685 KB
- 参考文献：1.Clarkson CR (2013) Production data analysis of unconventional gas wells: review of theory and best practices. Int J Coal Geol 109鈥?10:101鈥?46View Article
2.Ratts PAC (2007) Uptake of water from soils by plant roots. Transp Porous Med 68:5鈥?8View Article
3.Roose T, Schnepf A (2008) Mathematical models for plant鈥搒oil interaction. Phil Trans R Soc A 366:4597鈥?611View Article ADS MathSciNet
4.Prats M (1961) Effect of vertical fractures on reservoir behavior鈥攊ncompressible fluid case. SPE J 1(2):105鈥?18View Article
5.Prats M, Hazebroek P, Strickler WR (1962) Effect of vertical fractures on reservoir behavior鈥攃ompressible fluids case. SPE J 2(2):87鈥?4View Article
6.Raghavan R, Cady GV, Ramey HJ Jr (1972) Well-test analysis for vertically fractured wells. J Pet Technol 24(8):1014鈥?020View Article
7.Gringarten AC, Ramsey HJ Jr (1974) Unsteady pressure distribution created by a well with a single infinite-conductivity vertical fracture. SPE J 14:347鈥?60View Article
8.Gringarten AC, Ramey HJ Jr, Raghavan R (1975) Applied pressure analysis for fractured wells. J Pet Technol 27(7):887鈥?92View Article
9.Earlougher R (1977) Advances in well test analysis. Society of Petroleum Engineers of AIME, Dallas
10.Cinco-Ley H, Samaniego VF, Dominguez AN (1978) Transient pressure behavior for a well with a finite-conductivity vertical fracture. SPE J 18(4):253鈥?64View Article
11.Agarwal RG, Carter RD, Pollock CB (1979) Evaluation and performance prediction of low-permeability gas wells stimulated by massive hydraulic fracturing. J Pet Technol 31(3):362鈥?72View Article
12.Kuchuk FJ, Brigham WE (1979) Transient flow in elliptical systems. SPE J 19(6):401鈥?10View Article
13.Kuchuk FJ, Brigham WE (1981) Unsteady-state water influx in elliptic and anisotropic reservoir/aquifer systems. SPE J 21(3):309鈥?14
14.Cinco-Ley H, Samaniego VF (1981) Transient pressure analysis for fractured wells. J Pet Technol 33(9):1749鈥?766View Article
15.Lee ST, Brockenbrough JR (1986) A new approximate analytic solution for finite-conductivity vertical fractures. SPE Form Eval 1(1):75鈥?8View Article
16.Obuto ST, Ertekin T (1987) A composite system solution in elliptic flow geometry. SPE Form Eval 2(3):227鈥?38View Article
17.Wilkinson DJ (1989) New results for pressure transient behavior of hydraulically-fractured wells. SPE Paper 18950
18.Riley MF (1991) Finite conductivity fractures in elliptical coordinates. Ph.D. Dissertation, Stanford University, Stanford
19.Valko P, Economides MJ (1995) Hydraulic fracture mechanics. Wiley, Chichester
20.Bourdet D (2002) Well test analysis: the use of advanced interpretation models. Elsevier, Amsterdam
21.Meyer B, Jacot R (2005) Pseudosteady-state analysis of finite conductivity vertical fractures. SPE Paper 95941
22.Amini S, IIik D, Blasingame TA (2007) Evaluation of the elliptical flow period for hydraulically-fractured wells in tight gas sands-theoretical aspects and practical considerations. SPE Paper 106308
23.Kamal M, Abbaszadeh M, Cinco-Ley H, Hegeman P, Horne R, Houze O, Kabir S, Kikani J, Kuchuk F, Landa J, Murray M, Ozkan E, Raghavan R, Samaniego F, Soliman M (2009) Transient well testing. Society of Petroleum Engineers of AIME, Dallas
24.Ozkan E (2012) Releasing shale gas potential with fractured horizontal wells. SPE Distinguished Lecture
25.Biryukov D, Kuchuk FJ (2012) Transient pressure behavior of reservoirs with discrete conductive faults and fractures. Transp Porous Med 95:239鈥?68View Article MathSciNet
26.Economides MJ, Nolte KG (eds) (2000) Reservoir stimulation, 3rd edn. Wiley, New York
27.Chen KP, Jin Y, Chen M (2013) Pressure-gradient singularity and production enhancement for hydraulically-fractured wells. Geophys J Int 195:923鈥?31View Article ADS
28.Lafe OE, Montes JS, Cheng AH-D, Liggett JA, Liu PL-F (1980) Singularities in Darcy flow through porous media. J Hydraul Div Proc ASCE 106(HY6):977
29.Phillips OM (1991) Flow and reactions in permeable rocks. Cambridge University Press, New York
30.Kikani J (1995) Flux determination of finite conductivity fractures using higher order interpolation functions. SPE Adv Technol Ser 3(1):76鈥?4View Article
31.Chin WC (2002) Quantitative methods in reservoir engineering. Gulf Professional Publishing, Woburn
32.Matth盲i SK, Belayneh M (2004) Fluid flow partitioning between fractures and a permeable rock matrix. Geophys Res Lett 31(7):L07602View Article ADS
33.Mathias SA, van Reeuwijk M (2009) Hydraulic fracture propagation with 3-D leak-off. Transp Porous Med 80(3):1573鈥?634View Article
34.Mathias SA, Tsang C, van Reeuwijk M (2010) Investigation of hydromechanical processes during cyclic extraction recovery testing of a deformable rock fracture. Int J Rock Mech Min Sci 47(3):517鈥?22View Article
35.Exadaktylos G (2012) A study of the transient fluid flow around a semi-infinite crack. Int J Solids Struct 49(23鈥?4):3323鈥?334View Article
36.Pouya A (2012) Three-dimensional flow in fractured porous media: a potential solution based on singular integral equations. Adv Water Res 35:30鈥?0View Article
37.Pouya A, Ghabezloo S (2010) Flow around a crack in a porous matrix and related problems. Transp Porous Med 84:511鈥?32View Article MathSciNet
38.Pouya A, Vu MN (2012) Fluid flow and effective permeability of an infinite matrix containing disc-shaped cracks. Adv Water Res 42:37鈥?6View Article
39.Cheng Y, Lee WJ, McVay DA (2009) A new approach for reliable estimation of hydraulic fracture properties using elliptical flow data in tight gas wells. SPE Reserv Eval Eng 12(2):254鈥?62View Article
40.Craft BC, Hawkins M (1959) Applied petroleum reservoir engineering. Prentice-Hall, Englewood Cliffs - 作者单位：Yan Jin (1)
Kang Ping Chen (2)
Mian Chen (1)
1. College of Petroleum Engineering, China University of Petroleum, Beijing, 102200, China
2. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, 85287-6106, USA - 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Mechanics
Applications of Mathematics
Analysis
Mathematical Modeling and IndustrialMathematics
Numeric Computing - 出版者：Springer Netherlands
- ISSN：1573-2703
文摘
A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.