Analysis and Interpretation of Pressure-Decay Tests for Gas/Bitumen and Oil/Bitumen Systems: Methodology Development and Application of New Linearized and Robust Parameter-Estimation Technique Using Laboratory Data
- Ram R. Ratnakar (Shell International Exploration and Production) | Birol Dindoruk (Shell International Exploration and Production)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2019
- Document Type
- Journal Paper
- 951 - 972
- 2019.Society of Petroleum Engineers
- Modeling and Experiments, Early and Late Transient Solution, Solubility, Integral Technique, Diffusivity
- 9 in the last 30 days
- 391 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Diffusion mixing is a dominant process in the absence of convective mixing in various reservoir processes, such as carbon dioxide (CO2) flooding of fractured reservoirs, heavy-oil and bitumen recovery, solution-gas-drive processes, and the gas-redissolution process in a depleted reservoir. In these processes, the diffusivity governs the rate and extent of mixing of light hydrocarbons/nonhydrocarbons with the oil that enhances the oil recovery through in-situ viscosity reduction. It is one of the key parameters for the design and understanding of displacement processes.
Because of its significance in various aspects of oil-recovery processes, several experimental and theoretical studies were recently performed on the measurement of gas diffusivity in oils. Experimental work most commonly uses the pressure-decay (PD) concept because of its simplicity and the potential extraction of other necessary parameters, such as Henry’s constant. However, the parameter estimation from these tests is dependent on nonlinear regression, which might have several issues such as nonconvergence, nonuniqueness or multiplicity in solution, and high sensitivity toward noise and the time span of the data. Therefore, in this paper, Ratnakar and Dindoruk (2015) is extended and
- New experimental data are provided from a PD test for CO2 diffusion into bitumen at 80°C and approximately 700 psi.
- A robust inversion technique for parameter estimation is presented for exponentially decaying late-transient data, which can be used with any PD model used in the literature.
- The validity and applicability of the inversion technique is demonstrated against numerical data that are generated for a PD system by solving a diffusion model with continuity in the state variable (using Henry’s constant) and molar flux at the gas/oil interface.
- Most importantly, the issues with the nonlinear-regression technique are resolved using the linearized technique. The inversion technique presented in the work is dependent on a combination of linear regression and numerical integration using a modified, more-convenient form of the fundamental equations rather than a nonlinear regression on the fundamental equations as derived. This integral-based linear representation avoids the multiple solutions and can be used with limited data sets and/or when noise in the experimental data is significant, especially in industrial-grade experiments.
|File Size||842 KB||Number of Pages||22|
Adelstein, S. J. and Manning, F. J. ed. 1995. Isotopes for Medicine and the Life Sciences. Washington, DC: National Academic Press.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N. 2001. Transport Phenomena, second edition. New York City: John Wiley & Sons.
Bosse, D. and Bart, H.-J. 2006. Prediction of Diffusion Coefficients in Liquid Systems. Ind. Eng. Chem. Res. 45 (5): 1822–1828. https://doi.org/10.1021/ie0487989.
Boustani, A. and Maini, B. B. 2001. The Role of Diffusion and Convective Dispersion in Vapor Extraction Process. J Can Pet Technol 40 (4): 68–77. PETSOC-01-04-05. https://doi.org/10.2118/01-04-05.
Campbell, B. T. and Orr, F. M. Jr. 1985. Flow Visualization for CO2/Crude-Oil Displacements. SPE J. 25 (5): 665–678. SPE-11958-PA. https://doi.org/10.2118/11958-PA.
Civan, F. and Rasmussen, M. L. 2001. Accurate Measurement of Gas Diffusivity in Oil and Brine Under Reservoir Conditions. Presented at the SPE Production and Operations Symposium, Oklahoma City, Oklahoma, 24–27 March. SPE-67319-MS. https://doi.org/10.2118/67319-MS.
Civan, F. and Rasmussen, M. L. 2002. Improved Measurement of Gas Diffusivity for Miscible Gas Flooding Under Nonequilibrium vs. Equilibrium Conditions. Presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 13–17 April. SPE-75135-MS. https://doi.org/10.2118/75135-MS.
Civan, F. and Rasmussen, M. L. 2003. Analysis and Interpretation of Gas Diffusion in Quiescent Reservoir, Drilling, and Completion Fluids: Equilibrium vs. Non-Equilibrium Models. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October. SPE-84072-MS. https://doi.org/10.2118/84072-MS.
Civan, F. and Rasmussen, M. L. 2006. Determination of Gas Diffusion and Interface-Mass Transfer Coefficients for Quiescent Reservoir Liquids. SPE J. 11 (1): 71–79. SPE-84072-PA. https://doi.org/10.2118/84072-PA.
Crank, J. 1956. The Mathematics of Diffusion. London: Oxford University Press.
Creux, P., Meyer, V., Cordelier, P. R. et al. 2005. Diffusivity in Heavy Oils. Presented at the SPE International Thermal Operations and Heavy Oil Symposium, Calgary, 1–3 November. SPE-97798-MS. https://doi.org/10.2118/97798-MS.
Dill, K. A. and Bromberg, S. 2003. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology. New York City: Garland Science.
Etminan, S. R, Maini, B. B., Hassanzadeh, H. et al. 2009. Determination of Concentration Dependent Diffusivity Coefficient in Solvent Gas Heavy Oil Systems. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October. SPE-124832-MS. https://doi.org/10.2118/124832-MS.
Etminan, S. R., Maini, B. B., and Chen, Z. 2014. Determination of Mass Transfer Parameters in Solvent-Based Oil Recovery Techniques Using a Non-Equilibrium Boundary Condition at the Interface. Fuel 120 (15 March): 218–232. https://doi.org/10.1016/j.fuel.2013.11.027.
Froment, G. F. and Bischoff, K. B. 1990. Chemical Reactor Analysis and Design, second edition. Hoboken, New Jersey: John Wiley & Sons.
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.
Harstad, K. and Bellan, J. 2004. High-Pressure Binary Mass Diffusion Coefficients for Combustion Applications. Ind. Eng. Chem. Res. 43 (2): 645–654. https://doi.org/10.1021/ie0304558.
Haugen, K. B. and Firoozabadi, A. 2009a. Mixing of Two Binary Nonequilibrium Phases in One Dimension. AIChE J. 55 (8): 1930–1936. https://doi.org/10.1002/aic.11814.
Haugen, K. B. and Firoozabadi, A. 2009b. Composition at the Interface Between Multicomponent Nonequilibrium Fluid Phases. J. Chem. Phys. 130 (6): 064707. https://doi.org/10.1063/1.3072793.
Hayduk, W. and Minhas, B. S. 1982. Correlations for Predictions of Molecular Diffusivities in Liquids. Can. J. Chem. Eng. 60 (April): 295. https://doi.org/10.1002/cjce.5450600213.
Heck, R. M., Farrauto, R. J., and Gulati, S. T. 2009. Catalytic Air Pollution Control: Commercial Technology. Hoboken, New Jersey: John Wiley and Sons.
Horne, R. N. 1995. Modern Well Test Analysis: A Computer-Aided Approach, second edition. Dallas: Petro Way.
Huang, E. T. S. and Tracht, J. H. 1974. The Displacement of Residual Oil by Carbon Dioxide. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 22–24 April. SPE-4735-MS. https://doi.org/10.2118/4735-MS.
Jackson, R. 1977. Transport in Porous Catalysts, Chemical Engineering Monographs, Vol. 4. New York City: Elsevier.
Jamialahmadi, M., Emadi, M., and Mu¨ller-Steinhagen, H. 2006. Diffusion Coefficients of Methane in Liquid Hydrocarbons at High Pressure and Temperature. J. Pet. Sci. Eng. 53 (1–2): 47–60. https://doi.org/10.1016/j.petrol.2006.01.011.
Kumar, P., Gu, T., Grigoriadis, K. et al. 2014. Spatio-Temporal Dynamics of Oxygen Storage and Release in a Three-Way Catalytic Converter. Chem. Eng. Sci. 111 (24 May): 180–190. https://doi.org/10.1016/j.ces.2014.02.014.
Li, X. and Yortsos, Y. C. 1995. Theory of Multiple Bubble Growth in Porous Media by Solute Diffusion. Chem. Eng. Sci. 50 (8): 1247–1271. https://doi.org/10.1016/0009-2509(95)98839-7.
Maton, A., Lahart, D., Hopkins, J. et al. 1997. Cells: Building Blocks of Life. Upper Saddle River, New Jersey: Prentice Hall.
Neogi, P. 1996. Diffusion in Polymers. New York City: Marcel Dekker.
Policarpo, N. A. and Ribeiro, P. R. 2011. Experimental Measurement of Gas-Liquid Diffusivity. Brazil. J. Petrol. Gas 5 (3): 171–188. https://doi.org/10.5419/bjpg2011-0017.
Ratnakar, R. R. and Balakotaiah, V. 2014. Coarse-Graining of Diffusion–Reaction Models With Catalyst Archipelagos. Chem. Eng. Sci. 110 (3 May): 44–54. https://doi.org/10.1016/j.ces.2013.08.011.
Ratnakar, R. R. and Balakotaiah, V. 2015a. Reduced-Order Transient Models for Describing Thermal Gradients in Catalytic Monoliths. Ind. Eng. Chem. Res. 54 (42): 10260–10274. https://doi.org/10.1021/acs.iecr.5b01377.
Ratnakar, R. R. and Balakotaiah, V. 2015b. Reduced Order Multimode Transient Models for Catalytic Monoliths With Micro-Kinetics. Chem. Eng. J. 260 (15 January): 557–572. https://doi.org/10.1016/j.cej.2014.09.008.
Ratnakar, R. R. and Dindoruk, B. 2015. Measurement of Gas Diffusivity in Heavy Oils and Bitumens by Use of Pressure-Decay Test and Establishment of Minimum Time Criteria for Experiments. SPE J. 20 (5): 1167–1180. SPE-170931-PA. https://doi.org/10.2118/170931-PA.
Ratnakar, R. R., Bhattacharya, M., and Balakotaiah, V. 2012a. Reduced Order Models for Describing Dispersion and Reaction in Monoliths. Chem. Eng. Sci. 83 (3 December): 77–92. https://doi.org/10.1016/j.ces.2011.09.056.
Ratnakar, R. R., Kalia, N., and Balakotaiah, V. 2012b. Carbonate Matrix Acidizing With Gelled Acids: An Experiment-Based Modeling Study. Presented at the SPE International Production and Operations Conference and Exhibition, Doha, 14–16 May. SPE-154936-MS. https://doi.org/10.2118/154936-MS.
Ratnakar, R. R., Kalia, N., and Balakotaiah, V. 2013. Modeling, Analysis and Simulation of Wormhole Formation in Carbonate Rocks With In Situ Cross-Linked Acids. Chem. Eng. Sci. 90 (7 March): 179–199. https://doi.org/10.1016/j.ces.2012.12.019.
Riazi, M. R. 1996. A New Method for Experimental Measurement of Diffusion Coefficients in Reservoir Fluids. J. Pet. Sci. Eng. 14 (3–4): 235–250. https://doi.org/10.1016/0920-4105(95)00035-6.
Riazi, M. R. and Whitson, C. H. 1993. Estimating Diffusion Coefficients of Dense Fluids. Ind. Eng. Chem. Res. 32 (12): 3081–3088. https://doi.org/10.1021/ie00024a018.
Rongy, L., Haugen, K. B., and Firoozabadi, A. 2012. Mixing From Fickian Diffusion and Natural Convection in Binary Non-Equilibrium Fluid Phases. AIChE J. 58 (5): 1336–1345. https://doi.org/10.1002/aic.12685.
Sachs, W. 1998. The Diffusional Transport Methane in Liquid Water: Method and Result of Experimental Investigation at Elevated Pressure. J. Pet. Sci. Eng. 21 (3–4): 153–164. https://doi.org/10.1016/S0920-4105(98)00048-5.
Sheikha, H., Pooladi-Darvish, M., and Mehrotra, A. K. 2005. Development of Graphical Methods for Estimating the Diffusivity Coefficient of Gases in Bitumen From Pressure-Decay Data. Energy Fuels 19 (5): 2041–2049. https://doi.org/10.1021/ef050057c.
Sheikha, H., Mehrotra, A. K., and Pooladi-Darvish, M. 2006. An Inverse Solution Methodology for Estimating the Diffusion Coefficient of Gases in Athabasca Bitumen From Pressure-Decay Data. J. Pet. Sci. Eng. 53 (3–4): 189–202. https://doi.org/10.1016/j.petrol.2006.06.003.
Shelton, J. L. and Schneider, F. N. 1975. The Effects of Water Injection on Miscible Flooding Methods Using Hydrocarbons and Carbon Dioxide. SPE J. 15 (3) 217–226. SPE-4580-PA. https://doi.org/10.2118/4580-PA.
Sigmund, P. M. 1976. Prediction of Molecular Diffusion at Reservoir Conditions. Part 1—Measurement and Prediction of Binary Dense Gas Diffusion Coefficients. J Can Pet Technol 15 (2): 48–57. PETSOC-76-02-05. https://doi.org/10.2118/76-02-05.
Stalkup, F. I. 1970. Displacement of Oil by Solvent at High Water Saturation. SPE J. 10 (4): 337–348. SPE-2419-PA. https://doi.org/10.2118/2419-PA.
Tharanivasan, A. K., Yang, C., and Gu, Y. 2006. Measurements of Molecular Diffusion Coefficients of Carbon Dioxide, Methane, and Propane in Heavy Oil Under Reservoir Conditions. Energy Fuels 20 (6): 2509–2517. https://doi.org/10.1021/ef060080d.
Vignes, A. 1966. Diffusion in Binary Solutions. Variation of Diffusion Coefficient With Composition. Ind. Eng. Chem. Fundamen. 5 (2): 189–199. https://doi.org/10.1021/i160018a007.
Yang, C. and Gu, Y. 2006. Diffusion Coefficients and Oil Swelling Factors of Carbon Dioxide, Methane, Ethane, Propane, and Their Mixtures in Heavy Oil. Fluid Phase Equilibr. 243 (1–2): 64–73. https://doi.org/10.1016/j.fluid.2006.02.020.
Yanze, Y. and Clemens, T. 2012. The Role of Diffusion for Nonequilibrium Gas Injection Into a Fractured Reservoir. SPE Res Eval & Eng 15 (1): 60–71. SPE-142724-PA. https://doi.org/10.2118/142724-PA.
Zamanian, E., Hemmati, M., and Beiranvand, M. S. 2012. Determination of Gas-Diffusion and Interface-Mass-Transfer Coefficients in Fracture-Heavy Oil Saturated Porous Matrix System. Nafta 63 (11–12): 351–358. https://hrcak.srce.hr/95410.
Zhang, Y. P., Hyndman, C. L., and Maini, B. B. 2000. Measurement of Gas Diffusivity in Heavy Oils. J. Pet. Sci. Eng. 25 (1–2): 37–47. https://doi.org/10.1016/S0920-4105(99)00031-5.