Calculation of Circulating Mud Temperatures
Authors: Holmes Charles S. , Swift Samuel C. 
Published: December 2007

The mud circulation temperatures obtained by this simple analytical method can be used to predict logged bottom-hole mud temperatures, they can be used also as initial temperatures in predicting mud column temperature buildup after circulation is stopped.

Introduction
A thorough knowledge of the mud temperature profiles developed during well drilling and profiles developed during well drilling and subsequent periods of well logging is helpful. Complete temperature profiles for the fluid in both the pipe and the annulus may aid in revealing information about downhole conditions. Accurate prediction of maximum temperatures to be encountered prediction of maximum temperatures to be encountered during drilling allows for precise mud selection and preparation. The mud profiles also give indication of formation characteristics of the rock contacted during drilling. The object of this investigation was to develop an analytical mathematical model that could be used to predict the mud temperature in the drill pipe and annulus during drilling at any depth in the well.
The model is a solution of the steady-state equation for the heat transfer between the fluids in the annulus and the fluids in the drill pipe. This is combined with an approximate equation for the transient heat transfer between the fluid in the annulus and in the formation. The approximate method is adequate since the total heat transfer between the two fluids is much greater than that between the annulus fluid and the formation. The low heat transfer between the annulus fluid and the formation is a result of the relatively low thermal conductivity of the formation and the film resistance to beat transfer formed at the interface of the mud and the rock. Temperatures can be calculated as a function of well depth, mud circulation rate, circulating fluid characteristics, reservoir properties, and wellbore and drill-pipe size. properties, and wellbore and drill-pipe size. Previous Studies Previous Studies Farris has developed charts that depict the bottomhole temperature during cementing periods. These charts represent a commonly used basis for choosing oil-well cements and for predicting bottom-hole cementing temperatures. Crawford et al. has developed a method based upon the work of Edwardson et al. to calculate the bottom-hole circulating temperature as a function of well depth, casing and hole size, pumping rate and time, fluid characteristics, reservoir physical properties and the thermal status of the well. properties and the thermal status of the well. Their method represents a numerical solution for the transient beat transfer at a given depth.

Basic Assumptions and Equations
The model in this study is based upon the assumption that the heat transfer between the annular fluid and the formation can be approximated by steady-state linear heat transfer. The work of Edwardson et al. has shown that the temperature is relatively constant at any point sufficiently removed from the drill bit. This effect shows that the steady-state assumption appears to be a close enough approximation of this phenomenon. Other simplifying assumptions are that phenomenon. Other simplifying assumptions are that the heat generated by the drill bit is negligible and that a linear geothermal profile exists.
The development of the model is depicted in Fig. 1.
JPT
P. 670