Investigation of influential factors on well temperature for gas-liquid two-phase flow in under-balanced drilling operation

Document Type : Research Paper


1 Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Mechanical Engineering, Yasouj University, Yasouj, Iran


Analysis of the drilling fluid temperature due to heat transfer of drilling fluid with the formation in under-balanced drilling operation is the main objective of this study. Gas-liquid two-phase flow model considering thermal interaction with the formation is used to numerically simulate a well with real dimensions. In the present study, the continuity, momentum, and energy equations are developed to compute the wellbore temperature profile. In this simulation, the effects of oil and gas production from the reservoir into the annulus and heat generated by viscous dissipation within the drilling fluid, heat generated by friction between the rotating drill string and the wellbore wall, and heat generated by the drill bit were included in the model. The results are validated with actual field data and also with two-phase flow model using the geothermal temperature gradient given in the literature. Comparisons of the present results show that two-phase flow numerical simulation with thermal consideration gives more accurate results compared to other models for the prediction of the bottom-hole pressure. Results show that the fluid temperature at the bottom-hole increases with increasing well depth, the flow rate of gas, and source terms consideration. Whereas the fluid temperature at the bottom-hole decreases with increasing liquid flow rate and specific heat of liquid and gas.


[1]           H. J. Ramey, Jr., Wellbore Heat Transmission, 1962/4/1/, 1962.
[2]           C. S. Holmes, S. C. Swift, Calculation of Circulating Mud Temperatures, 1970/6/1/, 1970. 
[3]           F. C. Arnold, Temperature Variation in a Circulating Wellbore Fluid, Journal of Energy Resources Technology, Vol. 112, No. 2, pp. 79-83, 1990.
[4]           F. C. Arnold, Temperature Profile During Heated Liquid Injection, Int. Comm. Heat Mass Transfer, Vol. 16, pp. 763-72.
[5]           C. S. Kabir, A. R. Hasan, G.E. Koubs, M.M. Ameen, Determining Circulating Fluid Temperature in drilling, workover, and well-control operation, SPEDC (June 1996) 74.
[6]           L. R. Raymond, Temperature Distribution in a Circulating Drilling Fluid, 1969/3/1/, 1969.  
[7]           T.R. Marshal, O.H. Lie, A Thermal Transient Model of Circulating Wells: 1. Model Development, SPE 24290, Stavanger, Norway, May 25-227, 1992.
[8]           X. Song, Z. Guan, Coupled modeling circulating temperature and pressure of gas–liquid two phase flow in deep water wells, Journal of Petroleum Science and Engineering, Vol. 92-93, pp. 124-131, 2012/08/01/, 2012.
[9]           C. Perez-Tellez, Improved bottom hole pressure control for underbalanced drilling operations, 2003.
[10]         C. Perez-Tellez, J. R. Smith, J. K. Edwards, A New Comprehensive, Mechanistic Model for Underbalanced Drilling Improves Wellbore Pressure Predictions, in SPE International Petroleum Conference and Exhibition in Mexico, Villahermosa, Mexico, 2002.  
[11]         Khezrian, M., Hajidavalloo, E., Shekari, Y., 2015. Modeling and simulation of under-balanced drilling operation using two-fluid model of two-phase flow. Chemical Engineering Research and Design 93, 30-37.
[12]         Shekari, Y., Hajidavalloo, E., Behbahani-Nejad, M., Reduced order modeling of transient two-phase flows and its application to upward two-phase flows in the under-balanced drilling, Applied Mathematics and Computation 224, 775–790, 2013.
[13]         S. Ghobadpouri, Hajidavalloo, E., Noghrehabadi, A., Shekari, Y., Khezrian, Numerical simulation of under-balanced drilling operations with oil and gas production from reservoir using single pressure two-fluid model, Modares Mechanical Engineering, Vol. 16, No. 6, pp. 291-302, 2016 (in Persian)
[14]         A. R. Hasan, C. S. Kabir, A mechanistic Model For Circulating Fluid Temperature, SPEJ (June 1996) 133.
[15]         A. R. Hasan, C. S. Kabir, Two-phase flow in vertical and inclined annuli, International Journal of Multiphase Flow, Vol. 18, No. 2, pp. 279-293, 1992/03/01/, 1992.
[16]         S. Evje, T. Flåtten, Hybrid flux-splitting schemes for a common two-fluid model, Journal of Computational Physics, Vol. 192, No. 1, pp. 175-210, 2003.
[17]         M. Ishii, K. Mishima, Two-fluid model and hydrodynamic constitutive relations, Nuclear Engineering and design, Vol. 82, No. 2-3, pp. 107-126, 1984.
[18]         N. Hatta, H. Fujimoto, M. Isobe, J.-S. Kang, Theoretical analysis of flow characteristics of multiphase mixtures in a vertical pipe, International Journal of Multiphase Flow, Vol. 24, No. 4, pp. 539-561, 1998.
[19]         D. Drew, L. Cheng, R. Lahey Jr, The analysis of virtual mass effects in two-phase flow, International Journal of Multiphase Flow, Vol. 5, No. 4, pp. 233-242, 1979.
[20]         D. Bestion, The physical closure laws in the CATHARE code, Nuclear Engineering and design, Vol. 124, No. 3, pp. 229-245, 1990.
[21]         P. Dranchuk, H. Abou-Kassem, Calculation of Z factors for natural gases using equations of state, Journal of Canadian Petroleum Technology, Vol. 14, No. 03, 1975.
[22]         O. O. Harris, Evaluation of equivalent circulating density of drilling fluids under high pressure-high temperature conditions,  Thesis, University of Oklahoma, 2004.
[23]         D. Kim, Improved convective heat transfer correlations for two-phase two-component pipe flow, KSME international Journal, Vol. 16, No. 3, pp. 403-422, 2002.
[24]         M. Li, G. Liu, J. Li, T. Zhang, M. He, Thermal performance analysis of drilling horizontal wells in high temperature formations, Applied Thermal Engineering, Vol. 78, pp. 217-227, 2015.
[25]         D. Gao, Down-hole tubular mechanics and its applications, China University of Petroleum Press, Dongying, China, pp. 80-87, 2006.
[26]         O. Bratland, Pipe flow 2: multi-phase flow assurance, Ove Bratland Flow Assurance Consulting, Chonburi, Thailand, 2010.
[27]         E. Hajidavalloo, A. Falavand Jozaei, A. Azimi, Shekari, Y., S. Ghobadpouri, Thermal simulation of gas-liquid two-phase flow in under-balanced drilling operation with oil and gas production, Journal of Computational Applied Mechanics, Vol. 16, No. 6, pp. 291-302, 2018.
Volume 50, Issue 2
December 2019
Pages 210-218
  • Receive Date: 26 August 2018
  • Revise Date: 05 September 2018
  • Accept Date: 13 September 2018