• U. Olea-González Instituto Mexicano del Petróleo. Competencia de Perforación de Pozos
  • A. Vázquez-Rodríguez Universidad Autónoma Metropolitana –Iztapalapa. Depto. de Ingeniería de Procesos e Hidráulica
  • A. García-Gutiérrez Insitituto de Investigaciones Eléctricas. Unidad Geotermia.
  • P. Anguiano-Rojas Coordinación de Administración del Conocimiento y Propiedad Intelectual. Instituto Mexicano del Petróleo
Keywords: Formation temperature, inverse problem, heat conduction,, circulation time, shut-in time


We describe a numerical procedure based on the inverse method to model the thermal stabilization in both, an oil well and a geothermal well, after the drilling mud circulation has stopped. The formation temperature and the drilling mud temperature are estimated. For the model we use the temperature in shut-in time taken at a fixed depth, the mud temperature in the surface and the time when the circulation stopped. We also consider the borehole radius, the density and the specific heat of the drilling mud and of the formation, where the measurement of temperature is known.
The application of a Marquardt type method as an inverse method and the use of field data showed that the formation temperature and the simulated mud temperature are in agreement to the geothermal gradient and the measured information, respectively. The results indicate that the transitory temperature in shut-in period is a function of the mud circulation, of the shut-in time, of the formation temperature and the radius of the borehole. The sensitivity of the values predicted for the formation temperature are shown. Two examples of calculation are presented.


Alifanov, O. M. (1974). Solution of an inverse problem of heat conduction by iterative methods. Journal of Engineering Physics 26(4), 471-476.

Alifanov, O. M. (1994). Inverse heat transfer problems. Springer-Verlag, New York.

Beck, J. V. (1962). Calculation of surface heat flux from an internal temperature history. ASME paper 62-HT-46.

Beck, J. V.; Blackwell, B. y St. Clair, C. R. (1985). Inverse heat conduction: Ill-posed problems. Wiley Interscience, New York.

Bullard, E. C. (1947). The time taken for a borehole to attain temperature equilibrium: Monthly Notices of the Royal Astronomical Society, Geophysics Supplement 5, 127-130.

Cao, S., Lerche, I. y Hermanrud, C. (1988). Formation temperature estimation by inversion of borehole measurements. Geophysics 53(7), 979-988.

Dennis, J. y Schnablel, R., 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall.

Dowdle, W.L. y Cobb, W.M. (1975). Static formation temperature from well logs, and empirical method. Journal of Petroleum Technology, November, 1326-1330.

Edwardson, M.J., Girner, H.M., Parkinson, H.R., Williamson, C.D. y Matthews, C.S. (1962). Calculation of formation temperature disturbances caused by mud circulating. Journal of Petroleum Technology, April, 416-426.

Espinosa-Paredes, G., García, A., Santoyo E. y Hernández, I. (2001). TEMLOPI/V.2: a computer program for estimation of fully transient temperatures in geothermal wells during circulation and shut-in. Computer & Geosciences 27, 327-344.

Espinosa-Paredes G. y García-Gutiérrez A. (2004). Thermal behavior of geothermal wells using mud and air-water mixtures as drilling fluids. Energy Conversion & Management 45, 1513-1527.

García, A., Hernández I. Espinosa G. y Santoyo, E. (1998a), TEMLOPI: A thermal simulator for estimation of drilling mud and formation temperatures during drilling of geothermal wells. Computers & Geosciencies 24(5), 465-477.

Holmes, C.S. y Swift, S.C. (1970). Calculation of circulating mud temperatures. Journal of Petroleum Technology, June, 670-674.

Jaeger, J.C. (1961). The effect of the drilling on temperatures measurements in boreholes. Journal of Geophysical Research 66 (2) February. 563-569.

Keller, H. H. y Couch, E. J. (1973). Temperature distribution in circulating mud columns. Society of Petroleum Engineers Journal, February, 23-30.

Laureano-Cruces, A. y Espinosa-Paredes, G. (2005). Behavior design to model a reactive decision of an expert in geothermal wells. International Journal of Approximate Reasoning 39,1-28.

Lachenbruch, H. A. y Brewer, C. M. (1959). Dissipation of the temperature effect of drilling a well in Artic Alaska. Geological and theoretical geophysics. Geological Survey Bulletin 1083-C, 73-109.

Leblanc, Y., Pascoe, L. J. y Jones, F. W. (1981). The temperature stabilization of a borehole. Geophysics 46 (9) 1301-1303.

Luheshi, M. N. (1983). Estimation of formation temperature from borehole measurements. Geophysical Journal of the Royal Astronomical Society 74, 747-776.

Marquardt, W.D. (1963). An algoritm for least squares estimation of non linear parameters. Journal Society Industrial Applied Mathematics 11 (2), June, USA, 431-441.

Martínez-Méndez E. J., R. Vazquez-Rodríguez, E. Torijano-Cabrera y Hernández-Escoto, H. (2006). Análisis en pequeña escala longitudinal del proceso de transporte de calor en una región semi-porosa de un pozo geotérmico. Revista Mexicana de Ingeniería Química 5, 59-70.

Middleton, M. F. (1982). Bottom-hole temperatura stabilization with continued circulation of drilling mud. Geophysics 47 (2), 1716-1723.

Monde, M. y Mitsutake, Y. (2001). A new estimation method of thermal diffusivity using analytical inverse solution for one dimensional heat conduction. International Journal of Heat and Mass Transfer 44 (16) 3169-3177.

Nicolas, R., 1998. Análisis térmico de la perforación de pozos geométricos direccionales. Cenidet. Tesis de maestría. Cuernavaca, México. P. 56

Osato K., Ujo S. y White S. (2003). Prediction of formation equilibrium temperature while drilling based on drilling mud temperature: Inverse problem using Tough and wellbore thermal model. Proceedings, Though Symposium. Lawrence Berkeley National Laboratory. Berkeley California, May 12-14.

Ösizik M. Necati y H. Orlande, (2000). Inverse Heat Transfer: fundamentals and applications. Taylor & Francis. New York.

UONE, Reporte del programa de perforación, 2004. Pozo 3007, Pemex, Campeche. México.

Santoyo-Gutiérrez, E. R. (1997). Transient numerical simulation of heat transfer processes during drilling of geothermal wells. University of Salford, UK. Ph. D. Thesis.

Santoyo E., García, A., Espinosa-Paredes, G., Santoyo-Gutiérrez, S., González-Partida, E. (2003). Convective heat transfer of nonNewtonian geothermal driiling fluids. Journal of Geochemical Exploration 78/79, 249-255

Shen, P.Y. y Beck, A.E. (1986). Stabilization of bottomhole temperature with finite circulation time and fluid flow. Geophysics Journal of Royal Astronomical Society 86, 63-90.

Takahashi W., Osato K., Takasugi S. y White S. (1997). Estimation of the formation temperature from the inlet and outlet mud temperatures while drilling. Proceedings, Twenty Second Workshop on Geothermal Reservoir Engineering. Stanford University, California, January 27-29.

Thikonov, A. N. (1975). Inverse problems in heat conduction. Journal of Engineering Physics 29(1), 816-820.

Thikonov, A. N. y Arsein, V. Y. (1977). Solution of Ill-Posed Problems. Winston & Sons, Washington, DC.

Wooley, G.R. (1980). Computing downhole temperatures in a circulation, inyection and production wells. Journal of Petroleum Technology, September, 1509-1522.
How to Cite
Olea-González, U., Vázquez-Rodríguez, A., García-Gutiérrez, A., & Anguiano-Rojas, P. (2020). ESTIMATION OF FORMATION TEMPERATURES IN RESERVOIRS: INVERSE METHOD. Revista Mexicana De Ingeniería Química, 6(1), 65-74. Retrieved from