Mathematical Modeling of Steam Injection in Vertical Wells

  • F. Aguilar-Gastelum
  • O. Cazarez-CandiaEmail author
Conference paper
Part of the Environmental Science and Engineering book series (ESE)


In this work, a steady-state hydrodynamic model for steam injection vertical wells and a transient thermal model (2D energy diffusion equation) for the heat losses from a well towards the porous medium are presented. The hydrodynamic model is formed by mass, momentum and energy conservation equations (drift-flux model) for a steam-water two-phase flow. The steady-state drift-flux model was resolved using the finite differences method and the explicit Godunov scheme, while the thermal model solution was found with an implicit Godunov scheme. Models allow predicting the next parameters: pressure, temperature, steam quality, heat losses and flow patterns along the well. The parameter predictions presented good agreement against field data and simulations reported in literature. For the conditions simulated, it was found that: (1) the thermal model reaches its steady state at 500 h, (2) due to few steam condensation, pressure drop due to gravity is smaller than the friction and acceleration contributions, and (3) temperature gradients are large at the beginning of steam injection, but they diminish along time.


Porous Medium Heat Transfer Coefficient Injection Well Grid Block Annular Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Ali SMF (1981) A comprehensive wellbore stream/water flow model for steam injection and geothermal applications. SPE J Pet Technol 21(5):527–534. SPE-7966-PA. doi: 10.7910.2118/7966-PA
  2. Bahonar M, Azaiez J, Chen Z (2009) A semi-unsteady-state wellbore steam/water flow model for prediction of sandface conditions in steam injection wells. J Can Pet Technol 49(9):13–21CrossRefGoogle Scholar
  3. Durrant AJ, Thambynayagam RKM (1986) Wellbore heat transmission and pressure drop for steam/water injection and geothermal production: a simple solution technique. SPE, BP Petroleum Dev. CoGoogle Scholar
  4. Fontanilla JP, Aziz K (1982) Prediction of bottom-hole conditions for wet steam injection wells. J Can Pet Technol 21(2):82–88CrossRefGoogle Scholar
  5. Hasan AR, Kabir CS (1994) Aspects of wellbore heat transfer during two-phase flow. Society of petroleum engineersGoogle Scholar
  6. Hasan AR, Kabir CS, Sayarpour M (2007) A basic approach to wellbore two-phase flow modeling. In: Paper SPE 109868 presented at the SPE annual technical conference and exhibition, Anaheim, 11–14 November. doi: 10.2118/109868-MS
  7. Mozaffari S, Ehsani MR, Nikookar M, Sahranavard L (2011) Heat and mass transfer modeling in wellbore during steam injection process. Can J Chem Eng Technol 2(1):74–104Google Scholar
  8. Pacheco EF, Ali SMF (1972) Wellbore heat losses and pressure drop in steam injection. SPE J Pet Technol 24(2):139–144. SPE-3428-PA. doi: 10.3410.2118/3428-PA
  9. Ramey HJ (1962) Wellbore heat transmission. SPE J Pet Technol 14(4):427–435. SPE-496-PA. doi: 10.410.2118/2196-PA

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Instituto Mexicano del Petróleo (IMP)MexicoMexico

Personalised recommendations