Estimation and Analysis of Carbon Dioxide Friction Loss in Wellbore During Liquid/Supercritical Carbon Dioxide Fracturing
- Xiaojiang Li (China University of Petroleum, Beijing, and Sinopec Research Institute of Petroleum Engineering) | Gensheng Li (China University of Petroleum, Beijing) | Kamy Sepehrnoori (University of Texas at Austin) | Wei Yu (Texas A&M University) | Haizhu Wang (China University of Petroleum, Beijing) | Qingling Liu (China University of Petroleum, Beijing) | Hongyuan Zhang (China University of Petroleum, Beijing) | Zhiming Chen (China University of Petroleum, Beijing)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Operations
- Publication Date
- February 2019
- Document Type
- Journal Paper
- 244 - 259
- 2019.Society of Petroleum Engineers
- Darcy friction factor, CO2 fracturing, Pressure and temperature, Friction loss, Empirical correlation
- 25 in the last 30 days
- 134 since 2007
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The push to extend fracturing to arid regions is drawing attention to water-free techniques, such as liquid/supercritical carbon dioxide (CO2) fracturing. It is important to understand CO2 flow behavior and thus to estimate the friction loss accurately in CO2 fracturing, but no focus on CO2 friction loss in large-scale tubulars has been made until now. Because of the difficulty in conducting field-scale experiments, we develop a computational-fluid-dynamics (CFD) model to simulate CO2 flow in circular pipes in this paper. The realizable k-e turbulence model is used to simulate the large-Reynolds-number fully turbulent flow. An accurate equation of state (EOS) and transport models of CO2 are used to account for CO2-properties variations with pressure and temperature. The roughness of the pipe wall also is considered. Our model is verified by comparing the simulation results with the experimental data of liquid CO2 and correlations developed for water-based fluid. It is confirmed that the friction loss of CO2 follows the phenomenological Darcy-Weisbach equation, regardless of the sensitivity of CO2 properties to pressure and temperature. The commonly used correlations also can give good predictions of the Darcy friction factor of CO2 within an acceptable tolerance of 4.5%, where the pressure range is 8 to 80 MPa, the temperature range is 250 to 400 K, the tubular-diameter range is 25.4 to 222.4 mm, and the Reynolds-number range is 105–108. Of all correlations used in this paper, the ones proposed by Colebrook and White (1937), Swamee and Jain (1976), Churchill (1977), and Haaland (1983) are recommended for field use. Finally, we investigate the influence of flowing pressure and temperature on Reynolds number, Darcy friction factor, and friction loss of CO2, and compare the difference between friction loss of water and of CO2 at different pressure, temperature, and flow-rate conditions.
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Brkíc, D. 2011. Review of Explicit Approximations to the Colebrook Relation for Flow Friction. Journal of Petroleum Science and Engineering 77 (1): 34–48. https://doi.org/10.1016/j.petrol.2011.02.006.
Buzzelli, D. 2008. Calculating Friction in One Step. Machine Design 80 (12): 54–55.
Cengel, Y. A. and, Cimbala, J. M. 2006. Fluid Mechanics: Fundamentals and Applications, third edition. McGraw-Hill Education.
Chen, N. H. 1979. An Explicit Equation for Friction Factor in Pipe. Industrial & Engineering Chemistry Fundamentals 18 (3): 296–297. https://doi.org/10.1021/i160071a019.
Chen, Z., Liao, X., Zhao, X. et al. 2015a. A New Analytical Method Based on Pressure Transient Analysis To Estimate Carbon Storage Capacity of Depleted Shales: A Case Study. International Journal of Greenhouse Gas Control 42: 46–58. https://doi.org/10.1016/j.ijggc.2015.07.030.
Chen, Y., Nagaya, Y., and Ishida, T. 2015b. Observations of Fractures Induced by Hydraulic Fracturing in Anisotropic Granite. Rock Mechanics and Rock Engineering 48 (4): 1455–1461. https://doi.org/10.1007/s00603-015-0727-9.
Chung, H. C., Hu, T., Ye, X. et al. 2014. A Friction Reducer: Self-Cleaning to Enhance Conductivity for Hydraulic Fracturing. Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170602-MS. https://doi.org/10.2118/170602-MS.
Churchill, S. W. 1977. Friction-Factor Equation Spans All Fluid-Flow Regimes. Chemical Engineering 84 (24): 91–92.
Colebrook, C. F. and White, C. M. 1937. Experiments With Fluid Friction in Roughened Pipes. Proc. of the Royal Society of London. Series A. Mathematical and Physical Sciences 367–381. https://doi.org/10.1098/rspa.1937.0150.
Desai, M. G. 2018. Specifying Carbon Dioxide Centrifugal Compressor. SPE Prod & Oper 33 (2): 313–319. SPE-182992-PA. https://doi.org/10.2118/182992-PA.
Feng, Y., Li, X., and Gray, K. E. 2017. Development of a 3D Numerical Model for Quantifying Fluid-Driven Interface Debonding of an Injector Well. International Journal of Greenhouse Gas Control 62: 76–90. https://doi.org/10.1016/j.ijggc.2017.04.008.
Fenghour, A., Wakeham, W. A., and Vesovic, V. 1998. The Viscosity of Carbon Dioxide. Journal of Physical and Chemical Reference Data 27: 31–44. https://doi.org/10.1063/1.556013.
Goel, R. K., Singh, B., and Zhao, J. 2012. Underground Infrastructures: Planning, Design, and Construction. Butterworth-Heinemann.
Gupta, D. and Bobier, D. M. 1998. The History and Success of Liquid CO2 and CO2/N2 Fracturing System. Presented at the SPE Gas Technology Symposium, Calgary, 15–18 March. SPE-40016-MS. https://doi.org/10.2118/40016-MS.
Haaland, S. E. 1983. Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow. Journal of Fluids Engineering 105 (1): 89–90. https://doi.org/10.1115/1.3240948.
Harris, Jr., R. P., Ammer, J. R., Pekot, L. J. et al. 1998. Liquid Carbon Dioxide Fracturing for Increasing Gas Storage Deliverability. Presented at the SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, 9–11 November. SPE-51066-MS. https://doi.org/10.2118/51066-MS.
Harris, P. C. and Heath, S. J. 2006. Friction Reducers for Fluids Comprising Carbon Dioxide and Methods of Using Friction Reducers in Fluids Comprising Carbon Dioxide. US Patent 7,117,943.
Inui, S., Ishida, T., Nagaya, Y. et al. 2014. AE Monitoring of Hydraulic Fracturing Experiments in Granite Blocks Using Supercritical CO2, Water and Viscous Oil. Presented at the 48th US Rock Mechanics/Geomechanics Symposium, Minneapolis, Minnesota, 1–4 June. ARMA-2014-7163. American Rock Mechanics Association.
Johnson, R. L., Walters, W. W., Conway, M. W. et al. 1998. CO2 Energized and Remedial 100% CO2 Treatments Improve Productivity in Wolfcamp Intervals, Val Verde Basin, West Texas. Presented at the SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 23–26 March. SPE-39778-MS. https://doi.org/10.2118/39778-MS.
Kaufman, P. B., Penny, G. S., and Paktinat, J. 2008. Critical Evaluation of Additives Used in Shale Slickwater Fracs. Presented at the SPE Shale Gas Production Conference, Fort Worth, Texas, 16–18 November. SPE-119900-MS. https://doi.org/10.2118/119900-MS.
Kim, S., Choudhury, D., and Patel, B. 1999. Computations of Complex Turbulent Flows Using the Commercial Code Fluent. Also, Modeling Complex Turbulent Flows, ed. Salas M. D., Hefner J. N., and Sakell L. Springer, pp. 259–276.
King, S. R. 1983. Liquid CO2 for the Stimulation of Low-Permeability Reservoirs. Presented at the SPE/DOE Low-Permeability Gas Reservoirs Symposium, Denver, 14–16 March. SPE-11616-MS. https://doi.org/10.2118/11616-MS.
Kizaki, A., Tanaka, H., Ohashi, K. et al. 2012. Hydraulic Fracturing in Inada Granite and Ogino Tuff With Super Critical Carbon Dioxide. Presented at the ISRM Regional Symposium-7th Asian Rock Mechanics Symposium, Seoul, Korea, 15–19 October. ISRM-ARMS7-2012-109.
Launder, B. E. and Spalding, D. B. 1974. The Numerical Computation of Turbulent Flows. Computer Methods in Applied Mechanics and Engineering 3 (2): 269–289. https://doi.org/10.1016/0045-7825(74)90029-2.
Li, G., Wang, H., Shen, Z. et al. 2013. Application Investigations and Prospects of Supercritical Carbon Dioxide Jet in Petroleum Engineering. Zhongguo Shiyou Daxue Xuebao 37 (5): 76–80.
Li, X., Li, G., Yu. W. et al. 2017a. Thermodynamic Behavior of Liquid-Supercritical CO2 Fracturing in Shale. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, Texas, 24–26 July. URTEC-2687198-MS. https://doi.org/10.15530/URTEC-2017-2687198.
Li, X., Li, G., Wang, H. et al. 2017b. A Unified Model for Wellbore Flow and Heat Transfer in Pure CO2 Injection for Geological Sequestration, EOR and Fracturing Operations. International Journal of Greenhouse Gas Control 57: 102–115. https://doi.org/10.1016/j.ijggc.2016.11.030.
Lillies, A. T. and King, S. R. 1982. Sand Fracturing With Liquid Carbon Dioxide. Presented at the SPE Production Technology Symposium, Hobbs, New Mexico, 8–9 November. SPE-11341-MS. https://doi.org/10.2118/11341-MS.
Manning, F. and Thompson, R. E. 1991. Oilfield Processing of Petroleum. Vol 1: Natural Gas. 1. PennWell Corp.
Mazza, R. L. 2001. Liquid-Free CO2/Sand Stimulations: An Overlooked Technology-Production Update. Presented at the SPE Eastern Regional Meeting, Canton, Ohio, 17–19 October. SPE-72383-MS. https://doi.org/10.2118/72383-MS.
Middleton. R. S., Carey, J. W., Currier, R. P. et al. 2015. Shale Gas and Non-Aqueous Fracturing Fluids: Opportunities and Challenges for Supercritical CO2. Applied Energy 147: 500–509. https://doi.org/10.1016/j.apenergy.2015.03.023.
Moody, L. F. 1944. Friction Factors for Pipe Flow. Trans., ASME 66 (8): 671–678.
Nikuradse, J. 1933. Laws of Flow in Rough Pipes. VDI Forschungsheft.
Nwachukwu, A., Min, B., and Srinivasan, S. 2017. Model Selection for CO2 Sequestration Using Surface Deformation and Injection Data. International Journal of Greenhouse Gas Control 56: 67–92. https://doi.org/10.1016/j.ijggc.2016.11.019.
Ribeiro, L. H., Li, H., Bryant, J. E. et al. 2017. Use of a CO2-Hybrid Fracturing Design to Enhance Production From Unpropped-Fracture Networks. SPE Prod & Oper 32 (1): 28–40. SPE-173380-PA. https://doi.org/10.2118/173380-PA.
Sayed, M. A. and Al-Muntasheri, G. A. 2016. Mitigation of the Effects of Condensate Banking: A Critical Review. SPE Prod & Oper 31 (2): 85–102. SPE-168153-PA. https://doi.org/10.2118/168153-PA.
Serghides, T. K. 1984. Estimate Friction Factor Accurately. Chemical Engineering 91 (5): 63–64.
Shih, T., Liou, W. W., Shabbir A. et al. 1995. A New K-_ Eddy Viscosity Model for High Reynolds Number Turbulent Flows. Computers & Fluids 24 (3): 227–238. https://doi.org/10.1016/0045-7930(94)00032-T.
Span, R. and Wagner, W. 1996. A New Equation of State for Carbon Dioxide Covering the Fluid Region From the Triple-Point Temperature to 1100 K at Pressures Up to 800 MPa. Journal of Physical and Chemical Reference Data 25 (6): 1509–1596. https://doi.org/10.1063/1.555991.
Span, R. 2000. Multiparameter Equations of State: An Accurate Source of Thermodynamic Property Data. Springer Science & Business Media.
Swamee, P. K. and Jain, A. K. 1976. Explicit Equations for Pipeflow Problems. Journal of the Hydraulics Division 102 (5): 657–664.
Vesovic, V., Wakeham, W. A., Olchowy, G. A. et al. 1990. The Transport Properties of Carbon Dioxide. Journal of Physical and Chemical Reference Data 19 (3): 763–808. https://doi.org/10.1063/1.555875.
Wang, F. 2004. Computational Fluid Dynamics Analysis. Bejing: Tsinghua University Press.
Wang, H., Li, G., and Shen, Z. 2012. A Feasibility Analysis on Shale Gas Exploitation With Supercritical Carbon Dioxide. Energy Sources: Part A 34 (15): 1426–1435. https://doi.org/10.1080/15567036.2010.529570.
Wood, D. J. 1966. An Explicit Friction Factor Relationship. Civil Eng. 36 (12): 60–61.
Wu, J. Q., Sun, X., Wang, X. Z. et al. 2015. Experimental Study on Pipe Friction Characteristics of Liquid CO2. Applied Chemical Industry 44 (10): 1796–1798, 1802.
Yost, A. B. I., Mazza, R. L., and Gehr, J. B. 1993. CO2/Sand Fracturing in Devonian Shales. Presented at the SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, 2–4 November, pp. 353–362. SPE-26925-MS. https://doi.org/10.2118/26925-MS.
Yost, A. B. I., Mazza, R. L., and Remington, R. E. I. 1994. Analysis of Production Response to CO2/Sand Fracturing: A Case Study. Presented at the SPE Eastern Regional Meeting, Charleston, West Virginia, 8–10 November. SPE-29191-MS. https://doi.org/10.2118/29191-MS.
Yu, W., Lashgari, H. R., Wu, K. et al. 2015. CO2 Injection for Enhanced Oil Recovery in Bakken Tight Oil Reservoirs. Fuel 159: 354–363. https://doi.org/10.1016/j.fuel.2015.06.092.
Zahid, U., Al Rowaili, F. N., Ayodeji, M. K. et al. 2017. Simulation and Parametric Analysis of CO2 Capture From Natural Gas Using Diglycolamine. International Journal of Greenhouse Gas Control 57: 42–51. https://doi.org/10.1016/j.ijggc.2016.12.016.
Zigrang, D. J. and Sylvester, N. D. 1982. Explicit Approximations to the Solution of Colebrook’s Friction Factor Equation. AIChE Journal 28 (3): 514–515. https://doi.org/10.1002/aic.690280323.