Discrete Wellbore and Fracture Productivity Modeling for Unconventional Wells and Unconventional Reservoirs
- Randy D. Hazlett (University of Tulsa) | Desarazu K. Babu (Potential Research Solutions)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2014
- Document Type
- Journal Paper
- 19 - 33
- 2013. Society of Petroleum Engineers
- 3 Production and Well Operations, 5.8.1 Tight Gas, 5.1 Reservoir Characterisation, 5.8.2 Shale Gas, 5.6.9 Production Forecasting, 5.5 Reservoir Simulation
- 6 in the last 30 days
- 649 since 2007
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Newly developed, generalized analytic solutions to the heat equation forarbitrary 3D well trajectory in anisotropic media are demonstrated to solvebenchmark horizontal- and slanted-well productivity problems with unprecedentedspeed and accuracy. Arbitrary well trajectory is constructed as an assemblageof spatially integrated, linear well segments, as opposed to a distribution ofnumerically integrated point sources, to provide advantages in bothcomputational speed and accuracy in singularity handling. Production from eacharbitrarily oriented segment is reduced to a combination of purely analyticexpressions and rapidly convergent, exponentially damped infinite sumapproximations. With offered flexibility in cell boundary conditions, theexpressions can yield standalone well-productivity estimates for complex wellsor serve as the basis for advanced well equations, if integrated within anumerical reservoir simulator. Transients are also computed with analyticalintegrations in time, thus requiring no time marching. The breakthrough speedand accuracy in productivity assessment open possibilities for advancedwell-testing and reservoir-characterization methods.
We further demonstrate the usefulness of analytic methodology with severaltime-dependent, discrete fracture problems for shale gas production withtypical Barnett conditions, allowing direct use of complex fracture patterns,such as those interpreted from microseismic mapping. In addition touniform-flux and uniform-pressure modeling options, a new analytic model isintroduced that is capable of modeling both time-dependent material transportbetween matrix and a stimulated zone and the interplay between a well andfracture. We illustrate our solution method with Barnett fractured-wellexamples from the literature. With optional effects such as gas desorption andstress-dependent fracture conductivity as easy add-ons, we can producefull-operational-life production forecasts for shale or tight gas reservoirsfrom discrete, complex fracture patterns along with reservoir-pressure mappingsin a matter of minutes on common PC platforms.
|File Size||1 MB||Number of Pages||15|
Aavatsmark, I. and Klausen, R. A. 2003. Well Index in Reservoir Simulationfor Slanted and Slightly Curved Wells in 3D Grids. SPE J. 8(1): 41-48. http://dx.doi.org/10.2118/75275-PA.
Abou-Sayed, I. S., Sorrell, M. A., Foster, R. A., et al. 2011. HaynesvilleShale Development Program-From Vertical to Horizontal. Paper SPE 144425presented at the North American Unconventional Gas Conference and Exhibition,The Woodlands, Texas, 14-16 June. http://dx.doi.org/10.2118/144425-MS.
Al-Mohannadi, N., Ozkan, E. and Kazemi, H. 2007. Grid-System Requirements inNumerical Modeing of Pressure-Transient Tests in Horizontal Wells. SPE ResEval & Eng 10 (2): 122-131. http://dx.doi.org/10.2118/92041-PA.
Babu, D. K. and Odeh, A. S. 1989. Productivity of a Horizontal Well. SPERes Eng 4 (4): 417-421. http://dx.doi.org/10.2118/18298-PA.
Babu, D. K., Odeh, A. S., Al-Khalifa, A. J., et al. 1991. The RelationshipBetween Wellblock and Wellbore Pressures in Numerical Simulation of HorizontalWells. SPE Res Eng 6 (3): 324-328. http://dx.doi.org/10.2118/20161-PA.
Besson, J. 1990. Performance of Slanted and Horizontal Wells on anAnisotropic Medium. Paper SPE 20965 presented at European Petroleum Conference,The Hague, the Netherlands, 21-24 October. http://dx.doi.org/10.2118/20965-MS.
Brigham, W. E. 1990. Discussion of Productivity of a Horizontal Well. SPERes Eng 4 (4): 254-255. http://dx.doi.org/10.2118/18298-PA.
Carslaw, H. S. and Jaeger, J. C. 1959. Conduction of Heat in Solids.Oxford, UK: Oxford University Press.
Cinco, H., Miller, F. G., and Ramey, H. J. 1975. Unsteady-State PressureDistribution Created By a Directionally Drilled Well. J. Pet Tech 27 (11): 1392-1400. http://dx.doi.org/10.2118/5131-PA.
Cipolla, C. L., Lolon, E. P., Erdle, J. C., et al. 2010. Reservoir Modelingin Shale-Gas Reservoirs. SPE Res Eval & Eng 13 (4):638-653. http://dx.doi.org/10.2118/125530-PA.
Clarkson, C. R., Jensen, J. L. and Blasingame, T. A. 2011. ReservoirEngineering for Unconventional Gas Reservoirs: What Do We Have to Consider?Paper SPE 145080 presented at the North American Unconventional Gas Conferenceand Exhibition, The Woodlands, Texas, 14-16 June. http://dx.doi.org/10.2118/145080-MS.
Davlau, F., Mouronval, G., Bourdarot, G., et al. 1988. PressureAnalysis for Horizontal Wells. SPE Form Eval 3 (4):716-724. http://dx.doi.org/10.2118/14251-PA.
Dikken, B. J. 1990. Pressure Drop in Horizontal Wells and Its Effect onProduction Performance. J. Pet Tech 42 (11): 1426-1433. http://dx.doi.org/10.2118/19824-PA.
Durlofsky, L. J. and Aziz, K. 2000. Advanced Techniques for ReservoirSimulation and Modeling of Non-Conventional Wells. DOE Annual Report No.DE-AC26-99BC15213, Stanford University, Stanford, California (1 June 2000-31August 2000).
Earlougher, R. C. Jr. 1977. Advances in Well Test Analysis, Vol. 5.Dallas, Texas: Monograph Series, SPE.
Economides, M. J., Brand, C. W. and Frick, T. P. 1996. Well Configurationsin Anisotropic Reservoirs. SPE Form Eval 11 (4): 257-262.http://dx.doi.org/10.2118/27980-PA.
Economides, M. J., Deimbacher, F. X., Brand, C. W., et al. 1991.Comprehensive Simulation of Horizontal-Well Performance. SPE Form Eval 6 (4): 418-426. http://dx.doi.org/10.2118/20717-PA.
Fisher, M. K., Heinze, J. R., Davidson, B. M., et al. 2004. OptimizingHorizontal Completion Techniques in the Barnett Shale Using MicroseismicFracture Mapping. Paper SPE 90051 presented at the SPE Annual TechnicalConference and Exhibition, Houston, Texas, 26-29 September. http://dx.doi.org/10.2118/90051-MS.
Gökta, B. and Ertekin, T. 1999. Implementation of a Local Grid RefinementTechnique in Modeling Slanted, Undulating Horizontal and Multi-Lateral Wells.Paper SPE 56624 presented at the SPE Annual Technical Conference andExhibition, Houson, Texas, 3-6 October. http://dx.doi.org/10.2118/56624-MS.
Goode, P. A. and Thambynayagam, R. K. M. 1987. Pressure Drawdown and BuildupAnalysis of Horizontal Wells in Anisotropic Media. SPE Form Eval 2 (4): 683-697. http://dx.doi.org/10.2118/14250-PA.
Goode, P. A. and Wilkinson, D. J. 1991. Inflow Performance of Partially OpenHorizontal Wells. J. Pet Tech 43 (8): 983-987. http://dx.doi.org/10.2118/19341-PA.
Gradshteyn, I. S. and Rhyzik, I. M. 1980. Table of Integrals, Series, andProducts. New York: Academic Press.
Gringarten, A.C., Ramey, H. J. and Raghavan, R. 1974. Unsteady-StatePressure Distributions Created by a Well With a Single Infinite-ConductivityVertical Fracture. SPE J. 14 (4): 347-360. http://dx.doi.org/10.2118/4051-PA.
Hazlett, R. D. and Babu, D. K. 2005. Optimal Well Placement in HeterogeneousReservoirs Through Semi-analytic Modeling. SPE J 10(3): 286-296. http://dx.doi.org/10.2118/84281-PA.
Hazlett, R. D. and Babu, D. K. 2009a. Method and System for RepresentingWells in Modeling a Physical Fluid Reservoir. US Patent Application No.12/436,779.
Hazlett, R. D. and Babu, D. K. 2009b. Readily Computable Green's and NeumannFunctions for Symmetry-Preserving Triangles. Q. Appl. Math. 67:579-592. http://dx.doi.org/10.1090/S0033-569X-09-01157-X.
Jasti, J., Penmatcha, V. R. and Babu, D. K. 1999. Use of AnalyticalSolutions to Improve Simulator Accuracy. SPE J. 4 (1):47-56. http://dx.doi.org/10.2118/55225-PA.
Joshi, S. D. 1988a. Production Forecasting Methods for Horizontal Wells.Paper SPE 17580 presented at the International Meeting on PetroleumEngineering, Tianjin, China, 1-4 November. http://dx.doi.org/10.2118/17580-MS.
Joshi, S. D. 1988b. Augmentation of Well Productivity with Slant andHorizontal Wells. J. Pet Tech 40 (6): 729-739. http://dx.doi.org/10.2118/15375-PA.
Kuchuk, F. J., Goode, P. A., Brice, B. W., et al. 1990. Pressure-TransientAnalysis for Horizontal Wells. J. Pet Tech 42 (8): 974-979,1028-1031. http://dx.doi.org/10.2118/18300-PA.
Maizeret, P-D. 1996. Well Indices for Non-Conventional Wells. MS thesis,Stanford University, Stanford, California (June 1996).
Matthews, C. S. and Russell, D. G. 1967. Pressure Buildup and Flow Testsin Wells, Vol. 1. Dallas, Texas: Monograph Series, SPE.
Mayerhofer, M. J., Lolon, E. P., Warpinski, N. R., et al. 2010. What isStimulated Reservoir Volume? SPE Prod & Oper 25 (1):41-48. http://dx.doi.org/10.2118/119890-PA.
Mayerhofer, M. J., Lolon, E. P., Youngblood, J. E., et al. 2006. Integrationof Microseismic Fracture Mapping Results with Numerical Fracture NetworkProduction Modeling in the Barnett Shale. Paper SPE 102103 presented at the SPEAnnual Technical Conference and Exhibition, San Antonio, Texas, 24-27September. http://dx.doi.org/10.2118/102103-MS.
Muskat, M. 1949. Physical Principles of Oil Production. New YorkCity, New York: McGraw-Hill Book Company, Inc.
Novy, R. A. 1995. Pressure Drops in Horizontal Wells: When Can They BeIgnored? SPE Res Eng 10 (1): 29-35. http://dx.doi.org/10.2118/24941-PA.
Odeh, A. S. and Babu, D. K. 1990. Transient Flow Behavior of HorizontalWells: Pressure Drawdown and Buildup Analysis. SPE Form Eval 5 (1): 7-15. http://dx.doi.org/10.2118/18802-PA.
Ouyang, L-B. and Aziz, K. 2001. A General Single-Phase Wellbore/ReservoirCoupling Model for Multilateral Wells. SPE Res Eval & Eng 4 (4): 327-335. http://dx.doi.org/10.2118/72467-PA.
Ouyang, L-B., Thomas, L. K., Evans, C. E., et al. 1997. Simple But AccurateEquations for Wellbore Pressure Drawdown Calculation. Paper SPE 38314 presentedat the SPE Western Regional Meeting, Long Beach, California, 25-27 June. http://dx.doi.org/10.2118/38314-MS.
Ozkan, E., Raghavan, R. and Joshi, S. D. 1987. Horizontal Well PressureAnalysis. SPE Form Eval 4 (4): 567-575. http://dx.doi.org/10.2118/16378-PA.
Pan, Y., Kamal, M. M. and Kikani, J. 2010. Field Applications of aSemianalytical Model of Multilateral Wells in Multilayer Reservoirs. SPE ResEval & Eng 13 (6): 861-872. http://dx.doi.org/10.2118/121335-PA.
Peaceman, D.W. 1978. Interpretation of Well-Block Pressures in NumericalReservoir Simulation. SPE J. 18 (3): 183-194. http://dx.doi.org/10.2118/6893-PA.
Peaceman, D.W. 1983. Interpretation of Well-Block Pressures in NumericalReservoir Simulation with Nonsquare Grid Blocks and Anisotropic Permeability.SPE J. 23 (3): 531-543. http://dx.doi.org/10.2118/10528-PA.
Rosa, A.J., and Carvalho, R.D.S. 1989. A Mathematical Model for PressureEvaluation in an Infinite-Conductivity Horizontal Well. SPE Form Eval 4 (4): 559-566. http://dx.doi/org/10.2118/15967-PA.
Vanegas, J. S. 2007. Development of an Improved Methodology to AssessPotential Unconventional Gas Resources in North America. MS thesis, TexasA&M University, College Station, Texas (May 2007).
Wolfsteiner, C., Durlofsky, L. J. and Aziz, K. 1999. An Approximate Modelfor the Productivity of Non-Conventional Wells in Heterogeneous Reservoirs.Paper SPE 56754 presented at the SPE Annual Technical Conference andExhibition, Houston, Texas, 3-6 October. http://dx.doi.org/10.2118/56754-MS.
Wolfsteiner, C., Durlofsky, L. J. and Aziz, K. 2003. Calculation of WellIndex for Nonconventional Wells on Arbitrary Grids. Computat. Geosci. 7 (1): 61-82. http://dx.doi.org/10.1023/A:1022431729275.