Estimation of fluid temperature in both flow conduits (drillpipe or tubing and the annulus) is required to ascertain the fluid density and viscosity, and in turn to calculate the pressure-drop or the maximum allowable pumping rate for a number of operations. These operations include drilling, workover, and well control. During circulation, the inlet fluid temperature at the drillpipe/tubing is generally much lower than the bottomhole formation temperature. Consequently, in flowing down the drillpipe/tubing and up the annulus, the fluid continues to gain heat, thereby precipitating an unsteady-state heat transfer problem. The heat transfer rate for the fluid in the annulus depends upon the formation temperature from which it gains heat, as well as on the drillpipe/tubing fluid temperature to which it loses heat. Thus, the fluid temperature estimation becomes critical for high-temperature or geothermal reservoirs where significant heat exchange occurs or when fluid properties are temperature sensitive, such as for a non-Newtonian fluid.
In this work, we present an analytical model for the flowing fluid temperature in the drillpipe/tubing and in the annulus as a function of well depth and circulation time. The model is based on an energy balance between the formation and the fluid in the drillpipe/tubing and annulus. Steady-state heat transfer is assumed in the wellbore while transient heat transfer takes place in the formation. Solutions are obtained for two possible scenarios: first, the fluid flows down the annulus and up the drillpipe/tubing; second, the fluid flows down the tubing and up the annulus. The analytic model so developed is cast in a set of simple algebraic equations for rapid implementation. We also show that the maximum temperature occurs not at the well bottom, but at some distance higher from the bottom, for flow up the annulus.
The solution approach is flexible enough to use the formation temperature distribution function (T D) developed by various authors. A limited sensitivity study shows that all the T D models give comparable solutions, with the exception of line-source solution at early times.