Laplace-Transform Finite-Difference and Quasistationary Solution Method for Water-Injection/Falloff Tests
- Authors
- Azeb D. Habte (Universiti Teknologi PETRONAS) | Mustafa Onur (Istanbul Technical University)
- DOI
- https://doi.org/10.2118/168221-PA
- Document ID
- SPE-168221-PA
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Journal
- Volume
- 19
- Issue
- 03
- Publication Date
- June 2014
- Document Type
- Journal Paper
- Pages
- 398 - 409
- Language
- English
- ISSN
- 1086-055X
- Copyright
- 2013.Society of Petroleum Engineers
- Disciplines
- 5.6.4 Drillstem/Well Testing, 6.5.2 Water use, produced water discharge and disposal
- Keywords
- Skin, Wellbore storage, Laplace transform finite difference method, Variable-rate test, Injection/Falloff tests
- Downloads
- 1 in the last 30 days
- 974 since 2007
- Show more detail
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Summary
In this work, we present a method for efficiently and accurately simulating the pressure-transient behavior of oil/water flow associated with water-injection/falloff tests. The method uses the Laplace-transform finite-difference (LTFD) method coupled with the well-known Buckley-Leverett frontal-advance formula to solve the radial diffusivity equation describing slightly compressible oil/water two-phase flow. The method is semianalytical in time, and as a result, the issue of time discretization in the finite-difference approximation method is eliminated. Thus, stability and convergence problems caused by time discretization are avoided. Two approaches are presented and compared in terms of accuracy for simulating the tests with multiple-rate injection and falloff periods: One is based on solving the initial-boundary-value (IVB) problem with the initial condition attained from the end of the previous flow period, and the other is based on the conventional superposition on the basis of the single-phase flow of a slightly compressible fluid. The former is shown to always provide a more accurate and efficient solution. The method is quite general in that it allows one to incorporate the effect of wellbore storage and thick-skin and finite outer-boundary conditions. The accuracy of the method was evaluated by considering various synthetic test cases with favorable and unfavorable mobility ratios and by comparing the pressure and pressure-derivative signatures with a commercial black-oil simulator, and an excellent agreement was seen.
| File Size | 1 MB | Number of Pages | 12 |
References
Abbaszadeh, M. and Kamal, M. 1988. Automatic Type-Curve Matching for Well Test Analysis. SPE J. 3 (3): 567-577. http://dx.doi.org/10.2118/16443-PA.
Abbaszadeh, M. and Kamal, M. 1989. Pressure Transient Testing of Water-Injection Wells. SPE Res Eng 4 (1): 115-124. http://dx.doi.org/10.2118/16744-PA.
Barkve, T. 1989. An Analytical Study of Reservoir Pressure During Water-Injection Tests. http://dx.doi.org/10.2118/15791-MS.
Boughrara, A., Peres, A.M.M., Chen, S. et al. 2007. Approximate Analytical Solutions for the Pressure Response at a Water-Injection Well. SPE J. 12 (1): 19-34. http://dx.doi.org/10.2118/90079-PA.
Bourdet, D., Ayoub, J.A., and Pirard, Y.M. 1989. Use of Pressure Derivativein Well-Test Interpretation. SPE Form Eval 4 (2): 293-302.http://dx.doi.org/10.2118/12777-PA.
Bratvold, R.B. 1989. An Analytical Study of Reservoir Pressure Response Following Cold Water Injection. PhD dissertation, Stanford University,Stanford, California.
Bratvold, R.B. and Horne, R.N. 1990. Analysis of Pressure-Falloff Tests Following Cold-Water Injection. SPE Form Eval 5 (3):293-302. http://dx.doi.org/10.2118/18111-PA.
Buckley, S.E. and Leverett, M.C. 1942. Mechanism of Fluid Displacement inSands. Trans., AIME 146: 107.
Dubner, H. and Abate, J. 1968. Numerical Inversion of Laplace Transforms by Relating Them to Finite Fourier Cosine Transform. J. Assn. Comp. Mach. 15: 115.
Eclipse 100 (Version 2011.2). Reference Manual, Houston: SchlumbergerGeoquest.
El-Khatib, N.A.F. 1999. Transient Pressure Behavior of Composite Reservoirs With Moving Boundaries. Paper SPE 53153 presented at the 1999 SPE Middle EastOil Show in Bahrain, Bahrain, 20-23 February. http://dx.doi.org/10.2118/53153-MS.
Hawkins, M.F. Jr. 1956. A Note on the Skin Effect. J. Pet Tech 8 (12): 65-66. http://dx.doi.org/10.2118/732-G-PA.
Kuchuk, F.J., Onur, M., and Hollaender, F. 2010. Pressure TransientFormation and Well Testing: Convolution, Deconvolution, and NonlinearEstimation. Amsterdam, The Netherlands: Elsevier.
Levitan, M.M. 2003. Application of Water Injection/Falloff Tests for Reservoir Appraisal: New Analytical Solution Method for Two-Phase Variable RateProblems. SPE J. 8 (4): 341-349. http://dx.doi.org/10.2118/77532-PA.
MacDonald R.C. and Coats, K.H. 1970. Methods for Numerical Simulation of Water and Gas Coning. SPE J. 10 (4): 425-436. http://dx.doi.org/10.2118/2796-PA.
Moridis, G.J., McVay, D.A., Holditch, S.A. et al. 1994. The LaplaceTransform Finite Difference (LTFD) Numerical Method for the Simulation of Compressible Liquid Flow in Reservoirs. SATS 2 (2):122-131. http://dx.doi.org/10.2118/22888-PA.
Peres, A.M.M., Boughrara, A., and Reynolds, A.C. 2006. Rate Superpositionfor Generating Pressure Falloff Solutions. SPE J. 11 (3):364-374. http://dx.doi.org/10.2118/90907-PA.
Peres, A.M.M. and Reynolds, A.C. 2003. Theory and Analysis of Injectivity Tests on Horizontal Wells. SPE J. 8 (2): 147-159. http://dx.doi.org/10.2118/84957-PA.
Ramakrishnan T.S. and Kuchuk, F.J. 1994. Testing Injection Wells With Rateand Pressure Data. SPE Form Eval 9 (3): 228-236.http://dx.doi.org/10.2118/20536-PA.
Rosa, A.J. and Horne, R.N. 1983. Automated Type-Curve Matching in Well Test Analysis Using Laplace Space Determination Parameter Gradients. Paper SPE 12131presented at the SPE Annual Technical Conference and Exhibition, San Francisco,California, 5-8 October. http://dx.doi.org/10.2118/12131-MS.
Sever, A. 2012. Numerical Simulation of Two-Phase Oil and Water Flow. MSc dissertation, Istanbul Technical University, Turkey.
Stehfest, H. 1970. Numerical Inversion of Laplace Transforms. ACM,Vol. 13, Algorithm 368.
Van Everdingen, A.F. and Hurst, W. 1949. The Application of the LaplaceTransformation to Flow Problems in Reservoirs. SPE J. 1(12): 305-324. http://dx.doi.org/10.2118/949305-G-PA.
