Abstract
A model describing the two-dimensional transient heat transfer in and around a wellbore is developed. The model considers the fluid flowing down a drill string and returning up the annulus. Calculated results show that the use of steady-state solutions previously published give good estimates of previously published give good estimates of circulating mud temperatures. The transient solution presented here is more suited for matching presented here is more suited for matching temperature logs. The viscous flow energy, rotational energy, and drill bit energy were found to be significant items in the energy balance and are included in the model.
Calculated vertical temperature distributions in the innermost casing string permit the determination of the average temperature increase in that pipe. This quantity may then be used to compute thermal stresses and to predict casing stability.
Introduction
In drilling deep wells (15,000 to 30,000 ft) the geothermal temperatures encountered can cause problems with drilling fluids, drill pipe, and casing. problems with drilling fluids, drill pipe, and casing. To evaluate the effects of these high temperatures on the drill pipe and casing, it is necessary to know the temperature distributions in these pipe strings.
Previous work includes the approximate model described by Edwardson et al. for estimating formation temperature disturbances resulting from mud circulation. This work formed the basis for the calculation method that Crawford et al. proposed for estimating mud temperatures. Ramey proposed a model for solution of the wellbore heat transmission problem. He assumed that heat transfer in the problem. He assumed that heat transfer in the wellbore is steady-state while heat transfer in the earth is due to transient radial heat conduction. Ramey's model gave results comparable to the more exact method of Squier et al. and formed the basis for the solution of other wellbore circulation problems. problems. Two recent treatments of the mud circulation problem are based on models that assume steady-state problem are based on models that assume steady-state conditions in both the wellbore and the surrounding earth. The treatment of this problem by Raymond is very good with the exception that he neglected the presence of the casing strings and the effects of presence of the casing strings and the effects of energy sources in the system.
The prediction of these temperature distributions can best be accomplished with a two-dimensional thermal model that accounts for the dynamic flow, of mud down the drill pipe and back up through the annulus around the drill pipe, with appropriate heat interchange by convection and conduction. Such a model is described in this paper.
DESCRIPTION OF THE PROBLEM
This problem consists of determining the temperature distribution and around a wellbore during the drilling operations on that well. Drilling fluids are pumped down the drill pipe and recirculated up the annulus surrounding the drill pipe. Energy is added to the fluid columns by the frictional flow losses in the drill pipe and annulus, the shear work done in rotating the drill string, and frictional work at the drill bit.
Since the temperature in the earth's crust increases with depth, the drill fluids encounter increasingly higher temperatures with increased depth. This heated fluid then flows to the surface and tends to heat the casing as it passes through it. In deep wells this casing heating can be sufficient to cause excessive thermal stresses and result in pipe buckling. Casing stability predictions can be made if the average temperature increase in the pipe is know. A method for calculating this quantity is presented here.
Fig. 1 is a representation of the system considered in this model. We assume that fluid enters the drill string at the surface at a constant rate and known temperature. The fluid flowing down the drill pipe has a vertical temperature distribution resulting from convective heat transfer within the fluid, heat generated by fluid friction, and heat exchange with the drill pipe. A vertical temperature distribution is calculated for the drill pipe by accounting for the vertical conduction of heat in the pipe and the convective heat exchange between the pipe and the fluid columns surrounding it.
SPEJ
P. 23
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