EMPIRICAL EQUATION ESTIMATES GEOTHERMAL GRADIENTS

Jan. 2, 1995
I.M. Kutasov MultiSpectrum Technologies Santa Monica, Calif. An empirical equation can estimate geothermal (natural) temperature profiles in new exploration areas. These gradients are useful for cement slurry and mud design and for improving electrical and temperature log interpretation. Downhole circulating temperature logs and surface outlet temperatures are used for predicting the geothermal gradients. With Equation 1, one can estimate the bottom hole circulating temperature: 1 (1) T bc = a
I.M. Kutasov
MultiSpectrum Technologies
Santa Monica, Calif.

An empirical equation can estimate geothermal (natural) temperature profiles in new exploration areas. These gradients are useful for cement slurry and mud design and for improving electrical and temperature log interpretation.

Downhole circulating temperature logs and surface outlet temperatures are used for predicting the geothermal gradients.

With Equation 1, one can estimate the bottom hole circulating temperature:1 (1) T bc = a 1 + a 2G + (a 3 - a 4G)T bs where: T bc = Bottom hole circulating temperature, F. T bs = Bottom hole static (undisturbed) temperature, F. G = Geothermal gradient, F./ft a 1 = -102.1F. a 2 = 3,354 ft a 3 = 1.342 a 4 = 22.28 ft/F. These coefficients were obtained for 0.83F./100 ft < G < 2.44F./100 ft and 166F. < Tbs < 414F.

One can also express the bottom hole static temperature as a function of average surface temperature and true vertical depth.

(2) T bs = T o + GH where: T o = Average surface temperature, F. H = True vertical depth, ft

From Equations 1 and 2, one obtains:

(3) G 2 + B 1G + B o = 0 where: B 1 = (a 4T o - a 2 - a 3H)/a 4H B o = (T bc - a 1 - a 3T o)/a 4H

The solution of Equation 3 is:

(4) G = -B 1/2 - (B 12/4 - B o) 1/2 In Equation 1, Tbc is the stabilized bottom hole circulating temperature. The time of the downhole temperature stabilization, ts, can be estimated from routinely recorded mud temperature logs. As an example, assume that the mud pump starts operating when t = 0. In this case to obtain stabilized values of the outlet mud temperature, one must take readings at t greater than ts. The following empirical equation can be used to obtain ts:2 (5) t s = b o + b 1H where: b o and b 1 are constants time (t s) is in hours The ts1 is obtained from the recorded outlet mud temperature, Tmo, during mud circulation without penetration. After ts1, Tmo remains practically constant (Fig. 1) (8790 bytes). Hence, for H = H1: (6) t s1 = b o + b 1H 1 Similarly at depth H = H2: (7) t s2 = b o + b 1H 2

From Equations 6 and 7 the following relationships are obtain:

b 1 = (t s2 - t s1)/(H 2 - H 1); b o = t s1 - b 1H 1 More than 10 deep wells, including two offshore wells, indicated that results from Equation 5 are satisfactory.3 For deep wells, 16,000-24,000 ft, the suggested empirical formula is:3 (8) t s = 0.77 + 0.000145H

EXAMPLE

Two examples (Table 1) (7763 bytes) show how Equation 4 predicts the geothermal gradient.

In the first part of Table 1 (7763 bytes) are field temperature surveys Of tbc, and G* for Well No. 16.4 The comparison shows that the calculated geothermal gradient, G, agrees well with the surveyed values, G*. In the Gulf of Mexico example, only records of the bottom hole circulating temperatures were available for the well.5 One should note that for onshore wells To is the undisturbed formation temperature at a depth of 50-60 ft. In many cases, this temperature can be obtained from literature.6 For offshore wells, To can be assumed to be the temperature of the sea bottom sediments.

Fig. 2 (8683 bytes) shows that the geothermal gradient prediction (Equation 4) is very dependent on the estimated average surface temperature.

REFERENCES

  1. Kutasov, I.M., and Targhi, A.K., "Better BHCT estimations possible," OGJ, May 25, 1987, pp. 71-73.

  2. Kuliev, S.M., Esman, B.I., and Gabuzov, G.G., "Temperature regime of the drilling wells," Nedra, Moscow, 1968.

  3. Kutasov, I.M., Caruthers, R.M., Targhi, A.K., and Chaaban, H.M., "Prediction of downhole circulating and shut-in temperatures," Geothermics, Vol. 17, 1988, pp. 607-618.

  4. Shell, F., and Tragesser, A.F., "API is seeking more accurate bottom hole temperature," OGJ, July 10, 1972.

  5. Holes, C.S., and Swift, S.C., "Calculation of circulating mud temperature," JPT, June 1970, pp. 670-674.

  6. Jorden, J.R., and Campbell, F.L., "Well logging 1-Rock properties, borehole environment, mud and temperature logging," SPE, 1984.

THE AUTHOR

I.M. Kutasov is senior research engineer with Multi-Spectrum Technologies Inc, Santa Monica, Calif. He was a graduate faculty member in the petroleum engineering and geosciences department at Louisiana Tech University and worked for Shell Development Co., Houston, as a senior research physicist.

Kutasov's research interests include the temperature regime of deep wells, transient pressure flow analysis, and drilling in permafrost areas. He holds an MS in physics from the Yakutsk State University and a PhD in physics from O. Schmidt Earth Physics Institute in Moscow. Kutasov is a member of SPE.

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