Temperature Distribution in a Circulating Drilling Fluid
Authors: Raymond L.R. 
Published: December 2007

A technique for calculating drilling temperature as a function of position and time shows that circulation lowers considerably the position and time shows that circulation lowers considerably the temperatures of both the bottom-hole fluid and the rock and that the maximum circulating fluid temperature occurs a fourth to a third of the way up the annulus.

Introduction
With the trend toward deeper and consequently hotter holes, measurements of drilling mud properties at atmospheric temperatures are becoming increasingly inadequate. Both the prediction and control of downhole mud properties depend in part upon our knowledge of temperatures in the wellbore. Consequently, a better understanding of factors that affect temperatures during circulation and trips could improve drilling operations. It was toward the goal of obtaining this understanding that this study was directed.
Other investigators have studied the response of fluid temperature in the borehole during trips. However, all of these studies have used an assumed formation temperature profile at the conclusion of circulation and have provided no means to calculate this profile directly. In this study, the formation profile during circulation was calculated. Other profile during circulation was calculated. Other investigators have also studied bottom-hole temperature during circulation. However, they have developed neither general techniques for calculating the entire temperature profile in the system nor generalized methods for predicting bottom-hole fluid temperatures during circulation. Such techniques and methods have been developed and are discussed briefly in the following pages.

Temperature Behavior During Circulation
Circulation of fluid during the drilling operation is represented schematically in Fig. 1. The process of circulation has three distinct phases:
fluid enters the drill pipe at the surface and passes down the drill pipe; fluid exits the drill pipe through the bit and pipe; fluid exits the drill pipe through the bit and enters the annulus at the bottom; and fluid passes up the annulus and exits the annulus at the surface.
To simulate the thermal behavior of the fluid in the system, each of the phases of circulation must be described mathematically.
In Phase 1, the fluid enters the drill pipe at a specified temperature, TDo. As the fluid passes down the pipe, its temperature is determined by the rate of heat convection down the drill pipe, the rate of heat exchange between the drill pipe and the annulus, and time. Phase 2 of the circulating process merely requires that the fluid temperature at the exit of the drill pipe be the same as the fluid temperature at the entrance of the annulus; i.e., TD(L, t) = TA(L, t). Thus in Phase 3, the fluid enters the annulus at TD(L, t). As the fluid flows up the annulus, its temperature is determined by the rate of heat convection up the annulus, the rate of heat exchange between the annulus and the drill pipe, the rate of heat exchange between the formation adjacent to the annulus and the fluid in the annulus, and time. These rates of heat exchange and the time dependency of mud temperature are described by well known heat-flow equations.
JPT
P. 333