Accurate prediction of bottomhole circulating temperatures (BHCT) and bottomhole static temperatures (BHST) is important during drilling and completion of oil and gas wells.
These downhole temperatures affect cement thickening time, rheological properties, compressive strength development, and set time.
Accurate estimation of BHCT and BHST becomes particularly challenging, however, for deep offshore wells that have cold seabed temperatures and unknown formation temperatures.
Several techniques, when combined, simplify the task. Examples will demonstrate how to combine the use of American Petroleum Institute (API) temperature correlations, an API equivalent well (API-EW) method, an empirical formula, and an analytical equation to determine BHCT, BHST, and the averaged temperature gradient (Γ).
The technique requires that the rig measure and record the stabilized circulating (or shut in) mud temperature, while drilling at some current total TVD.
API correlations
The API developed new temperature correlations for estimating circulating temperatures for cementing.1 2
Current API test schedules assume 80° F. surface formation temperature (T0).
Workers must know the average static temperature gradient to design cement-slurry thickening time with the current API bottomhole temperature circulation correlations.
Many drilling operators have observed that the API method overestimates circulating mud temperatures for deep wells.3
A recently developed API-EW method allows workers to use the API temperature correlations for any deep well, both onshore and offshore, and for any values of surface formation temperature.4
The wellbore temperature during drilling is a complex function of wellbore geometry, wellbore depth, penetration rate, mud circulation rate, shut-in period durations, pump and rotary inputs, fluid and formation properties, and geothermal gradients.
Once the drilling engineer determines static formation temperature, shut-in temperature, downhole circulating temperature, mud density, and hydrostatic pressure, workers should be able to combine computer models, approximate analytical solutions, and field-data-based empirical relationships for future modeling.
Temperature logs while drilling, or at short shut-in intervals, could provide the needed data input economically.
In many cases, for design of a mud-density program, the literature can provide valuable information such as regional heat-flow density, geothermal gradient, seabed or mud-line temperature, thermal properties of formations, and formation pore pressure.
API-EW method
The API-EW method transforms a real wellbore into an API equivalent wellbore by treating the real well's 80° F. isotherm as the surface temperature.4 As example, consider a well with the following parameters:
- Total TVD (H) = 20,000 ft.
- Water depth (Hw) = 4,000 ft.
- Average temperature gradient, Γ = 0.020° F./ft.
- Mud line temperature, T0 = 40° F.
Since the API temperature correlations assume 80° F. surface temperature, the 80° F. isotherm of the example well would be (80° F. - 40° F.)/G, which is 2,000 ft below the mud line or 6,000 ft from surface.
The total TVD (H*) of the API equivalent wellbore would be 20,000 ft less 6,000 ft, or 14,000 ft. Equation 1 presents the general form to determine the API equivalent wellbore for an offshore well (see accompanying box).
A function of seabed temperature and well depth below the mud line (H - Hw), Equations 2 and 3 calculate the average temperature gradient (Γ) or the BHST (Tfb), depending on the known value.
In the absence of direct mud-line-temperature measurements, the US National Oceanic and Atmospheric Administration's World Ocean Atlas contains seabed temperatures, T0. At depths below 3,000 ft, the temperature is about 40° F. (Fig. 1).
Empirical formula
Table 1 presents the most recent temperature correlations reported in API's recommended practice for testing well cements, API RP 10B. These temperatures, combined with an empirical formula, will yield the average temperature gradient (Γ).
An empirical Kutasov-Targhi equation, Equation 4, calculates bottomhole-circulating temperature as a function of two independent variables: the averaged static temperature gradient and BHST (Tfb).6
Equations 2 and 4 combine to give Equation 5. Solving the quadratic equation for Γ yields Equation 6, where Equations 7 and 8 give the required coefficients, B1 and B0.
Table 2 presents the average temperature gradients, calculated from Equation 6, for seven wells. Comparison of the calculated values with the actual measured temperature gradients shows that the method yields satisfactory accuracy.
With use of Equation 6, the authors calculated average temperature gradients from the API temperature correlations of Table 1 (T0 = 80° F.). Table 3 presents the results that show satisfactory agreement between calculated and API values of the average temperature gradients.
This work demonstrates that both Table 1 and Equation 6 will provide accurate temperature gradients, given stabilized BHCT values recorded at any current vertical depth during drilling operations.
Workers can also use Table 1 to forecast BHCT values at deeper depths within the well, as Example 1 will demonstrate.
Bottomhole static temperature
To calculate the averaged temperature gradient and determine the rate of cement strength development, engineers must know the BHST.
The authors earlier obtained an approximate analytical solution for dimensionless bottomhole shut-in temperature (Equation 9).8 9
The dimensionless bottomhole shut-in temperature is a function of two parameters, which in turn are functions of drilling-fluid-circulation time, shut-in time, wellbore radius, dimensionless circulation time, dimensionless shut-in time, and formation thermal diffusivity (Equation 10).
References 8 and 9 present an expression for the TsD function of Equation 9. A Fortran computer program called SHUTEMP will also calculate the value.9
Once workers determined static formation temperature, industry practice has been to assume that the thermal properties of the well and surrounding formations were identical.
From physical considerations it follows that, at short mud circulation times, this assumption may introduce errors in formation temperature predictions.
The authors did not make this assumption during the creation of Equation 9, leading to the bottomhole static temperature expression (Equation 11).
When workers record the temperature of the drilling fluid at a given depth (Tbot), they require only one value of shut-in temperature to calculate the static formation temperature.
Determination of formation temperature requires at least two shut-in temperatures if the value of Tbot is unknown. The authors recommend placing the temperature probe at a distance of about 10 well diameters from the bottom of the well.
Only one mud-circulation period will cause thermal disturbance of formations in this case and workers can consider the wellbore as an infinite cylindrical source with constant wall temperature.
Fortunately, the TsD function is not very sensitive to variations in the formations' thermal diffusivity (a).
An averaged value of this parameter is appropriate. For example, for dolomite and limestone, thermal diffusivity is about 48X10-3 sq ft/hr, and for sandstone, thermal diffusivity is about 38X10-3 sq ft/hr.
Example 1, BHCT
The first example estimates BHCTs at 21,000 ft total TVD for two offshore wells (Table 4).
Assume that the average temperature gradient is known for Well A. For Well B the temperature gradient is not known and only the value of stabilized BHCT of 201° F. at 15,000 ft TVD was recorded.
The example assumes that the formation's thermal diffusivity would be 0.04 sq ft/hr. To avoid interpolation, the example assumes that the measured value of BHCT at H* of 12,000 ft is 201° F. (Table 1).
A three-step procedure calculates the BHCT for Well A and a four-step procedure calculates BHCT for Well B (see accompanying box). Table 4 lists the BHCT calculation results from the Kutasov-Targhi formula (Equation 4).
Example 2, BHCT, BHST
The second example estimates BHCT and BHST for an offshore well at 20,000 ft total TVD (Table 5).
Workers do not know the average Well C temperature gradient and only one value of the shut-in temperature and stabilized BHCT were recorded at 16,000 ft TVD.
The bit diameter at 20,000 ft is 8.75 in. and the formation's thermal diffusivity is 0.04 sq ft/hr.
Some parameters were selected to avoid interpolation. A seven-step procedure calculates BHCT and BHST (see accompanying box).
Table 6 and Fig. 2 present the temperatures for various shut-in times. The well requires 56 hr for shut-in temperature (Ts) to approach BHST, at 20,000 ft TVD, to within an accuracy of 5° F (Table 6).
Acknowledgments
The authors thank J. Zajaczkowski for his assistance in preparing this paper.
References
- Cowan, M., and Sabins, F., "New correlations improve temperature predictions for cementing and squeezing," OGJ, Aug. 21, 1995, p. 53.
- API RP 10B, Recommended Practice for Testing Well Cements, Washington, 22nd Edition, December 1997.
- Calvert, D.G., and Griffin, T.J., Jr., "Determination of Temperatures for Cementing in Wells Drilled in Deep Water," SPE paper 39315, presented at the 1998 IADC and SPE Drilling Conference, Dallas, Mar. 3-6, 1998.
- Kutasov, I.M., "Method corrects API bottomhole circulating-temperature correlation," OGJ, July 15, 2002, p. 47.
- Romero, J., and Loizzo, M., "The Importance of Hydration Heat on Cement Strength Development for Deep Water Wells," SPE paper 62894, presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, Oct. 1-4, 2000.
- Kutasov, I.M., and Targhi, A.K., "Better deep-hole BHCT estimations possible," OGJ, May 25, 1987, p. 71.
- Sump, G.D., and Williams, B.B., "Prediction of Wellbore Temperatures During Mud Circulation and Cementing Operations," ASME J. of Eng. for Industry, 1973, p. 1083.
- Kutasov, I.M., "Tables simplify determining temperature around a shut-in well," OGJ, July 26, 1993, p. 85.
- Kutasov, I.M., Applied Geothermics for Petroleum Engineers, Elsevier Science Publisher, 1999.
The authors
I. Kutasov is a senior research engineer for Pajarito Enterprises, Los Alamos, NM. Prior to his current position, he was a senior lecturer in the school of petroleum engineering at University of New South Wales, Sydney, and a graduate faculty member in the department of petroleum engineering and geosciences at Louisiana Tech University, Ruston. He also worked for Shell Development Co., Houston, as a senior research physicist. Kutasov holds an MS in physics from the Yakutsk State University and a PhD in physics from O. Schmidt Earth Physics Institute in Moscow. He is a member of SPE.
Michael Kagan is a research scientist in the school of petroleum engineering at University of New South Wales, Sydney, with interests in hydrodynamics of ferrofluids, capillary phenomena, and thermal conductivity. He has a BS in mathematical physics from Leningrad State University (currently Saint-Petersburg State University), Russia, and an MS in physical chemistry from Macquarie University, Sydney.
