Analysis of Warm-Back Data After Cold-Fluid Injection Into Multilayer Reservoirs
- Refaat G. Hashish (Louisiana State University) | Mehdi Zeidouni (Louisiana State University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2020
- Document Type
- Journal Paper
- 212 - 229
- 2020.Society of Petroleum Engineers
- warm-back temperature analysis, injection profiling, multilayer reservoir
- 7 in the last 30 days
- 238 since 2007
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Determining the rate distribution over multilayer injection zones (i.e., injection profiling) is critical to the optimization of injection operations. With the recent advancements in deployment of fiber-optic distributed-temperature-sensing (DTS) technology, temperature data can be achieved at high resolution and at relatively low cost along the wellbore length. During injection of cooler fluids into a higher-temperature injection zone, the temperature at the wellbore and near-wellbore region decreases. During a shut-in period when the injection operation is paused, the temperature at the wellbore sandface and near-wellbore region experiences “warm back” that is caused by the heat flux from the warmer inswept region of the injection zone. A slower warm back is observed for a layer that admits larger amount of cooler fluid during injection. As a result, the sandface warm-back temperature can be analyzed to determine the injection rate per layer, and hence the thermal-front extent per layer.
In this work, we develop an analytical model to determine the temporal and spatial temperature variation for a single-phase reservoir during a warm-back period following a constant-rate-injection period. The analytical solution is developed for a single-layer reservoir and extended to multilayer reservoirs. The solution considers heat transfer by conduction and convection during the injection period and conduction during the shut-in warm-back period. The solution is verified by comparison with synthetic numerical-simulation results obtained using a thermally coupled numerical simulator for single-layer and multilayer cases. Graphical interpretation techniques are introduced by recasting the analytical solution into desirable forms. The graphical techniques are applied to synthetic warm-back data to illustrate their application and accuracy in obtaining the injection rate, thermal-front extent, and initial geothermal temperature per each layer.
|File Size||2 MB||Number of Pages||18|
Abramowitz, M. and Stegun, I. A. ed. 1965. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. New York City: Dover Publications.
Allan, M. E., Rahman, M., and Reed, D. A. 2013. The Challenges of Full Field Implementation of Fiber-Optic DTS for Monitoring Injection Profile in Belridge Field, California. Presented at the SPE Digital Energy Conference, The Woodlands, Texas, 5–7 March. SPE-163694-MS. https://doi.org/10.2118/163694-MS.
App, J. and Yoshioka, K. 2013. Impact of Reservoir Permeability on Flowing Sandface Temperatures: Dimensionless Analysis. SPE J. 18 (4): 685–694. SPE-146951-PA. https://doi.org/10.2118/146951-PA.
App, J. F. 2010. Nonisothermal and Productivity Behavior of High-Pressure Reservoirs. SPE J. 15 (1): 50–63. SPE-114705-PA. https://doi.org/10.2118/114705-PA.
App, J. F. 2016. Influence of Flow Geometry on Sandface Temperatures During Single-Phase Oil Production: Dimensionless Analysis. SPE J. 21 (3): 928–937. SPE-166298-PA. https://doi.org/10.2118/166298-PA.
Avdonin, N. A. 1964. Some Formulas for Calculating the Temperature Field of a Stratum Subject to Thermal Injection. Neft’i Gaz 3: 37–41.
Brown, G., Carvalho, V., Wray, A. et al. 2004. Monitoring Alternating CO2 and Water Injection and Its Effect on Production in a Carbonate Reservoir Using Permanent Fiber-Optic Distributed Temperature Systems. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 26–29 September. SPE-90248-MS. https://doi.org/10.2118/90248-MS.
Chen, C.-S. and Reddell, D. L. 1983. Temperature Distribution Around a Well During Thermal Injection and a Graphical Technique for Evaluating Aquifer Thermal Properties. Water Resour Res 19 (2): 351–363. https://doi.org/10.1029/WR019i002p00351.
Computer Modelling Group (CMG). 2016. CMG-STARS, Advanced Process and Thermal Reservoir Simulator. Calgary: CMG.
Debnath, L. and Bhatta, D. 2006. Integral Transforms and Their Applications, second edition. Boca Raton, Florida: Chapman & Hall/CRC.
Duru, O. O. and Horne, R. N. 2010. Modeling Reservoir Temperature Transients and Reservoir-Parameter Estimation Constrained to the Model. SPE Res Eval & Eng 13 (6): 873–883. SPE-115791-PA. https://doi.org/10.2118/115791-PA.
Duru, O. O. and Horne, R. N. 2011a. Simultaneous Interpretation of Pressure, Temperature, and Flow-Rate Data Using Bayesian Inversion Methods. SPE Res Eval & Eng 14 (2): 225–238. SPE-124827-PA. https://doi.org/10.2118/124827-PA.
Duru, O. O. and Horne, R. N. 2011b. Combined Temperature and Pressure Data Interpretation: Applications to Characterization of Near-Wellbore Reservoir Structures. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-146614-MS. https://doi.org/10.2118/146614-MS.
Erdelyi, A. (ed.) 1954. Tables of Integral Transforms, Vols. I & II, Bateman Manuscript Project. New York City: McGraw-Hill Book Company.
Ganguly, S. and Kumar, M. S. M. 2014. Analytical Solutions for Transient Temperature Distribution in a Geothermal Reservoir Due to Cold Water Injection. Hydrogeol J 22 (2): 351–369. https://doi.org/10.1007/s10040-013-1048-2.
Ganguly, S., Seetha, N., and Mohan, K. M. S. 2012. Numerical Simulation and Analytical Validation for Transient Temperature Distribution in an Aquifer Thermal Energy Storage System. Oral presentation given at the 8th International Symposiumon Lowland Technology, Bali, Indonesia, 11–13 September.
Holley, E. H., Molenaar, M. M., Fidan, E. et al. 2013. Interpreting Uncemented Multistage Hydraulic-Fracturing Completion Effectiveness By Use of Fiber-Optic DTS Injection Data. SPE Drill & Compl 28 (3): 243–253. SPE-153131-PA. https://doi.org/10.2118/153131-PA.
Horner, D. R. 1951. Pressure Build-Up in Wells. Presented at the 3rd World Petroleum Congress, The Hague, 28 May–6 June. WPC-4135.
Huckabee, P. T. 2009. Optic Fiber Distributed Temperature for Fracture Stimulation Diagnostics and Well Performance Evaluation. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19–21 January. SPE-118831-MS. https://doi.org/10.2118/118831-MS.
Lauwerier, H. A. 1955. The Transport of Heat in an Oil Layer Caused by the Injection of Hot Fluid. Appl Sci Res Sec A 5 (2–3): 145–150. https://doi.org/10.1007/BF03184614.
Li, K.-Y., Yang, S.-Y., and Yeh, H.-D. 2010. An Analytical Solution for Describing the Transient Temperature Distribution in an Aquifer Thermal Energy Storage System. Hydrol Process 24 (25): 3676–3688. https://doi.org/10.1002/hyp.7779.
Malofeev, G. E. 1959. Simulation of the Formation-Heating Process During the Injection of Hot Fluid Into a Well. Neft’i Gaz 2 (9): 49–55.
Malofeev, G. E. 1960. Calculation of the Temperature Distribution in a Formation When Pumping Hot Fluid Into a Well. Neft’i Gaz 3 (7): 59–64.
Mao, Y. and Zeidouni, M. 2017a. Analytical Solutions for Temperature Transient Analysis and Near Wellbore Damaged Zone Characterization. Presented at the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, 8–10 May. SPE-185990-MS. https://doi.org/10.2118/185990-MS.
Mao, Y. and Zeidouni, M. 2017b. Temperature Transient Analysis for Characterization of Multilayer Reservoirs With Crossflow. Presented at the SPE Western Regional Meeting, Bakersfield, California, 23–27 April. SPE-185654-MS. https://doi.org/10.2118/185654-MS.
Onur, M. and Çinar, M. 2016. Temperature Transient Analysis of Slightly Compressible, Single-Phase Reservoirs. Presented at SPE Europec featured at the 78th EAGE Conference and Exhibition, Vienna, Austria, 30 May–2 June. SPE-180074-MS. https://doi.org/10.2118/180074-MS.
Onur, M. and Palabiyik, Y. 2015. Nonlinear Parameter Estimation Based on History Matching of Temperature Measurements for Single-Phase Liquid-Water Geothermal Reservoirs. Oral presentation given at the World Geothermal Congress, Melbourne, Australia, 19–25 April.
Onur, M., Palabiyik, Y., Tureyen, O. I. et al. 2016. Transient Temperature Behavior and Analysis of Single-Phase Liquid-Water Geothermal Reservoirs During Drawdown and Buildup Tests: Part II. Interpretation and Analysis Methodology With Applications. J Pet Sci Eng 146 (October): 657–669. https://doi.org/10.1016/j.petrol.2016.08.002.
Palabiyik, Y., Onur, M., Tureyen, O. I. et al. 2016. Transient Temperature Behavior and Analysis of Single-Phase Liquid-Water Geothermal Reservoirs During Drawdown and Buildup Tests: Part I. Theory, New Analytical and Approximate Solutions. J Pet Sci Eng 146 (October): 637–656. https://doi.org/10.1016/j.petrol.2016.08.003.
Palabiyik, Y., Tureyen, O. I., and Onur, M. 2015. Pressure and Temperature Behaviors of Single-Phase Liquid Water Geothermal Reservoirs Under Various Production/Injection Schemes. Oral presentation given at the World Geothermal Congress, Melbourne, Australia, 19–25 April.
Palabiyik, Y., Tureyen, O. I., Onur, M. et al. 2013. A Study on Pressure and Temperature Behaviors of Geothermal Wells in Single-Phase Liquid Reservoirs. Oral presentation given at the Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 11–13 February.
Pimenov, V., Brown, G. A., Tertychnyi, V. V. et al. 2005. Injectivity Profiling in Horizontal Wells via Distributed Temperature Monitoring. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October. SPE-97023-MS. https://doi.org/10.2118/97023-MS.
Platenkamp, R. J. 1985. Temperature Distribution Around Water Injectors: Effects on Injection Performance. Presented at the Middle East Oil Technical Conference and Exhibition, Manama, Bahrain, 11–14 March. SPE-13746-MS. https://doi.org/10.2118/13746-MS.
Ramazanov, A. S. and Nagimov, V. M. 2007. Analytical Model for the Calculation of Temperature Distribution in the Oil Reservoir During Unsteady Fluid Inflow. Oil Gas Business 1 (1), 8 pages.
Ramazanov, A., Valiullin, R. A., Shako, V. et al. 2010. Thermal Modeling for Characterization of Near Wellbore Zone and Zonal Allocation. Presented at the SPE Russian Oil and Gas Conference and Exhibition, Moscow, 26–28 October. SPE-136256-MS. https://doi.org/10.2118/136256-MS.
Rubinshtein, L. I. 1959. The Total Heat Losses in Injection of a Hot Liquid Into a Stratum. Neft’i Gaz 2 (9): 41.
Rubinshtein, L. I. 1960. A Contact Thermal Conduction Problem. Dan SSSR 135 (4): 805–808.
Rubinshtein, L. I. 1962. An Asymptotic Solution of an Axially Symmetric Contact Problem in Thermal Convection for Higher Values of the Convection Parameter. Dan SSSR 146 (5): 1043–1046.
Shaw-Yang, Y. and Hund-Der, Y. 2008. An Analytical Solution for Modeling Thermal Energy Transfer in a Confined Aquifer System. Hydrogeol J 16 (8): 1507–1515. https://doi.org/10.1007/s10040-008-0327-9.
Sidorova, M., Shako, V., Pimenov, V. et al. 2015. The Value of Transient Temperature Responses in Testing Operations. Presented at the SPE Middle East Oil & Gas Show and Conference, Manama, Bahrain, 8–11 March. SPE-172758-MS. https://doi.org/10.2118/172758-MS.
Stopa, J. and Wojnarowski, P. 2006. Analytical Model of Cold Water Front Movement in a Geothermal Reservoir. Geothermics 35 (1): 59–69. https://doi.org/10.1016/j.geothermics.2005.11.002.
Sui, W., Ehlig-Economides, C., Zhu, D. et al. 2012. Determining Multilayer Formation Properties From Transient Temperature and Pressure Measurements. Pet Sci Technol 30 (7): 672–684. https://doi.org/10.1080/10916466.2010.514581.
Sui, W., Ehlig-Economides, C. A., Zhu, D. et al. 2010. Determining Multilayer Formation Properties From Transient Temperature and Pressure Measurements in Commingled Gas Wells. Presented at the International Oil and Gas Conference and Exhibition in China, Beijing, 8–10 June. SPE-131150-MS. https://doi.org/10.2118/131150-MS.
Sui, W., Zhu, D., Hill, A. D. et al. 2008. Model for Transient Temperature and Pressure Behavior in Commingled Vertical Wells. Presented at the SPE Russian Oil and Gas Technical Conference and Exhibition, Moscow, 28–30 October. SPE-115200-MS. https://doi.org/10.2118/115200-MS.
Thomas, G. W. 1967. Approximate Methods for Calculating the Temperature Distribution During Hot Fluid Injection. J Can Pet Technol 6 (4): 123–129. PETSOC-67-04-02. https://doi.org/10.2118/67-04-02.
van der Horst, J. 2015. Recent Advances in Fiber Optic Technology for In-Well Production and Injection Profiling. Presented at the International Petroleum Technology Conference, Doha, 6–9 December. IPTC-18563-MS. https://doi.org/10.2523/IPTC-18563-MS.
Xu, B., Kabir, S., and Hasan, A. R. 2018. Modeling Coupled Nonisothermal Reservoir/Wellbore Flow Behavior in Gas Reservoir Systems. Presented at the SPE Western Regional Meeting, Garden Grove, California, 22–26 April. SPE-190067-MS. https://doi.org/10.2118/190067-MS.