Carbon Dioxide Effects on Wellbore-Pressure Response During Injection/Falloff Test
- Cíntia G. Machado (University of Tulsa) | Mohammadreza M. Firoozabad (University of Tulsa) | Albert C. Reynolds (University of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2018
- Document Type
- Journal Paper
- 919 - 936
- 2018.Society of Petroleum Engineers
- Carbonated Water Injection, Method of Characteristics (MOC), Multiphase Well Testing, Injection-Falloff Test
- 6 in the last 30 days
- 250 since 2007
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We provide analytical solutions for the wellbore pressure during an injection/falloff-test problem under radial-flow conditions in homogeneous porous media where the injected fluid is carbonated water. For both the injection and falloff periods, we assume an isothermal process with thermodynamic equilibrium, a linear adsorption isotherm, and viscosities that depend only on the carbon dioxide (CO2) concentration. We also neglect CO2 diffusion, gravity effects, and capillarity effects. For the injection period, we first determine the saturation and concentration distributions with time in the reservoir by applying the method of characteristics to solve the appropriate system of hyperbolic conservation equations, where we assume incompressible fluids. In solving for water saturation and CO2 concentration in water, we neglect the change in water volume caused by the variation of the CO2 concentration in water. After solving for the saturation and concentration profiles, the pressure solution can be obtained by integrating Darcy’s law, from the wellbore radius to infinity, while assuming an infinite-acting reservoir and invoking the Thompson-Reynolds steady-state theory (Thompson and Reynolds 1997b). Because Darcy’s law does not assume incompressible flow, the pressure solution generated does not assume incompressible flow. To obtain an analytical expression for the wellbore pressure, however, we do assume that for injection and falloff, the total flow-rate profile in the reservoir is constant in a region from the wellbore to a radius greater than the radius of the flood front. The region within this radius increases with time and it is referred to as the steady-state region or zone (Thompson and Reynolds 1997b). During the falloff stage, it is assumed that there is no change in saturation in the reservoir, which is reasonable because we neglect capillary pressure, the gravity force, and fluid compressibilities when determining the saturation profile. Using these assumptions, we generate analytical solutions for a carbonated-water-injection (CWI)/falloff test and compare these solutions with those obtained with a commercial reservoir simulator using very fine spatial grids and very small timesteps. This comparison suggests that the analytical solutions presented can be used reliably to analyze pressure data obtained during CWI/falloff tests.
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Abbaszadeh, M. and Kamal, M. 1989. Pressure-Transient Testing of Water-Injection Wells. SPE Res Eval & Eng 4 (1): 115–124. SPE-16744-PA. https://doi.org/10.2118/16744-PA.
Ballou, D. P. 1970. Solutions to Nonlinear Hyperbolic Cauchy Problems Without Convexity Conditions. Trans. Am. Math. Soc. 152 (2): 441–460. https://doi.org/10.2307/1995581.
Bedrikovetsky, P. 1993. Mathematical Theory of Oil and Gas Recovery: With Applications to ex-USSR Oil and Gas Fields, first edition. Dordrecht, The Netherlands: Springer.
Boughrara, A. 2006. Injection/Falloff Testing of Vertical and Horizontal Wells. PhD dissertation, University of Tulsa, Tulsa, Oklahoma.
Bratvold, R. 1989. An Analytical Study of 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. SPE-18111-PA. https://doi.org/10.2118/18111-PA.
Buckley, S. E. and Leverett, M. C. 1942. Mechanism of Fluid Displacement in Sands. Transactions of the AIME 146 (1): 107–116. SPE-942107-G. https://doi.org/10.2118/942107-G.
Christensen, R. J. 1961. Carbonated Waterflood Results—Texas and Oklahoma. Presented at the Annual Meeting of Rocky Mountain Petroleum Engineers of AIME, Farmington, New Mexico, 26–27 May. SPE-66-MS. https://doi.org/10.2118/66-MS.
Coleman, T. F. and Li, Y. 1994. On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds. Math. Program. 67 (13): 189–224. https://doi.org/10.1007/BF01582221.
Computer Modelling Group (CMG). 2013. GEM—Compositional and Unconventional Reservoir Simulator. Calgary: CMG.
Green, D. W. and Willhite, G. P. 1998. Enhanced Oil Recovery, Vol. 6. Richardson, Texas: Textbook Series, Society of Petroleum Engineers.
Grogan, A. T. and Pinczewski, W. V. 1987. The Role of Molecular Diffusion Processes in Tertiary CO2 Flooding. J Pet Technol 39 (5): 591–602. SPE-12706-PA. https://doi.org/10.2118/12706-PA.
Hawkins, M. F. Jr. 1956. A Note on the Skin Effect. J Pet Technol 8 (12): 65–66. SPE-732-G. https://doi.org/10.2118/732-G.
Hickok, C. W. and Ramsay, H. J. Jr. 1962. Case Histories of Carbonated Waterfloods in Dewey-Bartlesville Field. Presented at the SPE Secondary Recovery Symposium, Wichita Falls, Texas, 7–8 May. SPE-333-MS. https://doi.org/10.2118/333-MS.
Islam, A. W. and Carlson, E. S. 2012. Viscosity Models and Effects of Dissolved CO2. Energy Fuels 26 (8): 5330–5336. https://doi.org/10.1021/ef3006228.
Knobel, R. 1999. An Introduction to the Mathematical Theory of Waves, Vol. 3, first edition. Providence, Rhode Island: American Mathematical Society.
Lake, L. W. 2010. Enhanced Oil Recovery. Richardson, Texas: Society of Petroleum Engineers.
Logan, J. D. 1994. An Introduction to Nonlinear Partial Differential Equations, second edition. Hoboken, New Jersey: Wiley.
Orr, F. M. 2007. Theory of Gas Injection Processes. Holte, Denmark: Tie-Line Publications.
Peres, A. M. M. and Reynolds, A. C. 2003. Theory and Analysis of Injectivity Tests on Horizontal Wells. SPE J. 8 (2): 147–159. SPE-84957-PA. https://doi.org/10.2118/84957-PA.
Peres, A. M. M., Boughrara, A. A., and Reynolds, A. C. 2006. Rate Superposition for Generating Pressure Falloff Solutions. SPE J. 11 (3): 364–374. SPE-90907-PA. https://doi.org/10.2118/90907-PA.
Pope, G. A. 1980. The Application of Fractional Flow Theory to Enhanced Oil Recovery. SPE J. 20 (3): 191–205. SPE-7660-PA. https://doi.org/10.2118/7660-PA.
Thompson, L. G. and Reynolds, A. C. 1997a. Pressure Transient Analysis for Gas Condensate Reservoirs. In Situ 21 (2): 101–144.
Thompson, L. G. and Reynolds, A. C. 1997b. Well Testing for Radially Heterogeneous Reservoirs Under Single and Multiphase Flow Conditions. SPE Form Eval 12 (1): 57–64. SPE-30577-PA. https://doi.org/10.2118/30577-PA.