Basin modelling - calibration

Measured temperatures from drill stem tests (DST) are regarded as the most reliable temperature dataset as they reflect true formation temperatures. However, temperatures measured during logging operations are lower than undisturbed, true formation temperatures, mainly because of the cooling effect of mud circulation.

Many methods that have been proposed to correct measured log-derived temperatures for the cooling effects of mud circulation.

The most widely used methods in the petroleum industry are methods that try to extrapolate the undisturbed temperature from a time-series of logging temperatures (i.e. Horner-type corrections). However, time-series of logging temperatures are often not available, and attempts have been made to develop methods to correct single bottom hole temperatures (i.e. single-point corrections). For a review of published temperature correction methods see e.g. Goutorbe et al., 2007, Hermanrud et al., 1990 and Peters and Nelson, 2012.

Horner-type corrections utilise a time-series of at least three down-hole temperatures from a single depth. The technique was originally developed by Horner, 1951 to predict pressure build-up in a closed-in well, using an equation that extrapolates to infinite time. Dowdle and Cobb, 1975 presented an empirical method (1) utilising a modified Horner-plot to calculate true formation temperatures from logging temperatures.

\text{(1) } T=T_i-C \cdot log \frac{(t+\Delta t)}{\Delta t}

Where:

T=\text{true formation temperature}

T_i=\text{measured logging temperature at time } t+\Delta t

C=\text{Horner plot slope}

t=\text{circulation time}

∆t=\text{time since circulation}

However, various studies showed that Horner-plots systematically underestimate true formation temperatures (e.g. Goutorbe et al., 2007; Hermanrud et al., 1990) and methods have been developed to account for that issue. Hermanrud et al., 1990 showed that Horner-corrected temperatures in the Norwegian North Sea are on average 8°C to low compared to DST temperatures and based on that he proposed a simple correction of Horner-corrected temperatures (2).

\text{(2) } T=(T_i-C \cdot log \frac{(t+\Delta t)}{\Delta t})+8

Correction method (3) from Waples and Pedersen, 2004 is based on a data set from the Danish Central Graben.

\text{(3) } T=(T_i-C \cdot log \frac{(t+\Delta t)}{\Delta t})+26^{-0.0052 \cdot C}

In cases where a time-series of down-hole temperatures from a single depth do not exist, single-point corrections can be applied.

In general, single-point corrections apply a correction factor to the measured down-hole temperature to come up with an estimate of the true formation temperature. The applied correction factors are often depended on the time since circulation and the depth of the temperature measurement. Method (4) proposed by Waples and Ramly, 2001 was developed and calibrated using a data set from the Malay Basin.

\text{(4) } T=T_S+f \cdot (T_m-T_S)

Where:

T=\text{true formation temperature}

T_S=\text{surface temperature}

f=\text{correction factor}

T_m=\text{measured logging temperature}

∆t=\text{time since circulation}

Z=\text{measurement depth}

and

f=\frac{(-0.1462 \cdot ln \Delta t+1.699)}{0.572 \cdot Z^{0.075}}

Waples and co-authors tested the workflow for single-point temperature corrections on further data sets from different geological basins worldwide. The work resulted in the publication of a new formula and correction factor (5) based on a temperature data set from the Mexican Gulf of Mexico (Waples et al., 2004a).

\text{(5) } T=T_S+f \cdot (T_m-T_S)-0.001391 \cdot (Z-4498)

With:

f=1.32866^{-0.005289 \cdot \Delta t}

Another proposed temperature correction (6) by Waples et al., 2004b is based on a dataset from the Danish Central Graben

\text{(6) } T=T_S+f \cdot (T_m-T_S)

With:

f=\frac {3.07 \cdot \Delta t^{-0.09}}{0.47 \cdot Z^{0.175}}

The last presented single-point correction method (7) was proposed by Zare-Reisabadi et al., 2015 for wells from the Persian Gulf.

\text{(7) } T=T_S+f \cdot (T_m-T_S)

With:

f=1.012-0.0057 \cdot ln \Delta t + \frac{375.42}{Z}

Allen, P.A., Allen, J.R., 2005. Basin Analysis - Principles and Applications, 2nd ed. Blackwell Publishing.

Burnham, A.K., 2017. Global Chemical Kinetics of Fossil Fuels. Springer Nature.

Burnham, A.K., Peters, K.E., Schenk, O., 2016. Evolution of Vitrinite Reflectance Models, in: AAPG 2016 Annual Convention and Exhibition.

Burnham, A.K., Sweeney, J.J., 1989. A chemical kinetic model of vitrinite maturation and reflectance. Geochimica et Cosmochimica Acta 53, 2649–2657.

Cardott, B.J., 2012. Introduction to Vitrinite Reflectance as a Thermal Maturity Indicator. Tulsa Geological Society luncheon. doi:10.1520/D7708-11

Dembicki Jr., H., 2017. Practical Petroleum Geochemistry for Exploration and Production. Elsevier, p. 342.

Dowdle, W.L., Cobb, W.M., 1975. Static Formation Temperature from Well Logs - An Empirical Method. Journal of Petroleum Technology 27, 1326–1330.

Falvey, D.A., Middlelon, M.F., 1981. Passive continental margins: evidence for a prebreakup deep crustal metamorphic subsidence mechanism. Oceanologica Acta 103–114.

Goutorbe, B., Drab, L., Loubet, N., Lucazeau, F., 2007. Heat flow of the eastern Canadian rifted continental margin revisited. Terra Nova 19, 381–386.

Hermanrud, C., Cao, S., Lerche, I., 1990. Estimates of virgin rock temperature derived from BHT measurements: Bias and error. Geophysics 55, 924–931.

Horner, D.R., 1951. Pressure Build-Up in Wells, in: Third World Petroleum Congress. The Hague, pp. 503–521.

Nielsen, S.B., Clausen, O.R., McGregor, E., 2017. basin%Ro: A vitrinite reflectance model derived from basin and laboratory data. Basin Research 29, 515–536.

Peters, K.E., Nelson, P.H., 2012. Criteria to determine borehole formation temperatures for calibration of basin models. SEPM Special Publication 5–15.

Sweeney, J.J., Burnham, A.K., 1990. Evaluation of a Simple Model of Vitrinite Reflectance Based on Chemical Kinetics. AAPG Bulletin 74, 1559–1570.

Waples, D.W., Pacheco, J., Vera, A., 2004a. A method for correcting log-derived temperatures in deep wells, calibrated in the Gulf of Mexico. Petroleum Geoscience 10, 239–245.

Waples, D.W., Pedersen, M.R., 2004. Evaluation of Horner plot-corrected log-derived temperatures in the Danish Central Graben, North Sea. Natural Resources Research 13, 223–227.

Waples, D.W., Pedersen, M.R., Kuijpers, P., 2004b. Correction of Single Log-Derived Temperatures in the Danish Central Graben, North Sea. Natural Resources Research 13, 229–239.

Waples, D.W., Ramly, M., 2001. A statistical method for correcting log-derived temperatures. Petroleum Geoscience 7, 231–240.

Zare-Reisabadi, M.R., Kamali, M.R., Mohammadnia, M., Shabani, F., 2015. Estimation of True Formation Temperature from Well Logs for Basin Modeling in Persian Gulf. Journal of Petroleum Science and Engineering 125, 13–22.