The detailed modeling of temperature and friction for coiled tubing (CT) operations is especially important in extended-reach wells. Although the fluid flow through the CT and annulus, downhole temperature, and the CT mechanical friction inside the well are crucial during CT operations, a mathematical model that captures all these effects does not currently exist.

In a separate study, we propose a new temperature-dependent coefficient of friction correlation, based on an extensive in-house experimental data set. In the current study we implement this correlation in a thermal well flow model. The model includes transient single-phase mass, momentum, and energy balance equations for the CT and annulus. Heat exchange between tubing and annulus and between annulus and formation as well as heat generated by CT mechanical friction while sliding inside the well are included in the model. Frictional pressure drops due to the fluid flowing downwards through the tubing and upwards through the annulus are also included in the momentum equations. The formation temperature is assumed to be geothermal. Although the model is aimed specifically at CT operations, it can easily be extended to other applications where thermal multiphase well flow in tubing and annulus is important.

We proceed by first presenting two analytical solutions for tubing and annulus temperature under various assumptions (similar solutions have been previously obtained for drilling operations). We then describe the use of one of these solutions, which allows for space-dependent fluid density and velocity and time- and space-dependent temperature inside the tubing and the annulus. The analytical model is verified against the corresponding numerical model that solves the full mass, momentum, and energy conservation equations and is validated against a Distributed Temperature Sensing (DTS) field case. Close agreement is obtained for the cases presented. A synthetic case that shows the effect of several key downhole parameters on tubular and annular temperature is also presented. We show that temperature distribution inside the well is important for best prediction of an average coefficient of friction for the entire well. For instance, the generic coefficient of friction of 0.24 that is currently used in the planning of CT operations does not apply for similar CT strings in wells with different downhole temperatures. The overall procedure is therefore very well suited for use in thermal simulation of CT operations.