Flow rate metering has less-than-satisfactory track record in the industry; modern sensors offer solution to this vexing problem. This paper offers two methods for estimating flow rates, predominantly from temperature data to complement rate measurements. One approach consists of modeling the entire wellbore and requires both wellhead pressure and temperature, whereas the other uses transient temperature formulation at a single point in the wellbore to compute the total production rate.
In the entire-wellbore approach, we use a wellbore model handling steady flow of fluids but unsteady-state heat transfer to estimate production rate, given wellhead pressure and temperature. The model rigorously accounts various thermal properties of the fluid and the formation, including Joule-Thompson heating and/or cooling. In the single-point approach, a single point temperature measurement made anywhere in the wellbore, including at the wellhead, is needed to estimate the mass rate at a given timestep. The method entails full transient treatment of the coupled fluid and heat flow problem at hand.
Examples from both gas and oil wells are shown to illustrate the application of the proposed methodology. Good correspondence between the measured and calculated results demonstrates the robustness of the proposed methods. These methods provide important rate information in various settings. For instance, in mature assets they can fill in the information void between tests or replace suspect rate data. Even well-instrumented wells can benefit because the methods can act as a verification tool, particularly in assets where integrated asset models are used to fine-tune rate allocation. In addition, the single-point approach can provide the much needed rate information during pressure-transient tests.