The objective of this work is the study of the procedure for flow rate measurement derived from temperature profiles. This method is deemed appropriate because of the inability to mount conventional flow meters in multiple-zone oil wells. In this work, a reduced-scale prototype well with horizontal geometry was developed to study and validate a method of flow profiling by temperature measurements in the well column based on a heat transfer mathematical model studied by Ramey in 1962. Flow sensors were installed at key points to provide validation data for the flow measurements derived from the temperature. The plant was automated and all the tests were managed from a workstation. It was possible to test different situations to provide a variability of evaluation scenarios. The initial experiments used injected fluid flow rates of 15 and 18 L/min in the well inlet. The results of the calculated flow values in different work conditions were compared with a relatively low error reference meter.

This article presents an analytical solution for calculating the flow rate in water injection wells based on the established thermal profile along the tubing. The intent is to minimize the intrinsic systematic error of classic quasi-static methodologies, which assume that all thermal transience on well completion has passed. When these techniques are applied during the initial hours of injection well operation, it can result in errors higher than $20\%$. To solve this limitation, the first law of thermodynamics was used to define a mathematical model and a thermal profile was established in the injection fluid, captured by using distributed temperature systems (DTSs) installed inside the tubing. The geothermal profile was also established naturally by a thermal source in the earth to determine the thermal gradient. A computational simulation of the injection well was developed to validate the mathematical solution. The simulation intended to generate the fluid’s thermal profile, for which data were not available for the desired time period. As a result, at the cost of greater complexity, the systematic error dropped to values below $1\%$ in the first two hours of well operation, as seen throughout this document. The code was developed in Phyton, version 1.7.0., from Anaconda Navigator.

Every simplification has the potential to add a systematic error to the measured value. Sometimes, the addition does not render the measurement useless. In the case of oil well flow measurements based on the thermal properties of the fluid in the well, the addition of a systematic error of up to 20% can occur if the variation in the internal energy of the fluid and, most importantly, the transient nature of heat transfer in the completion are not taken into account. This error is a mathematical consequence of the simplifications chosen. To work within the first hours of good operation, given the need for immediate application in a prototype water injection well developed and installed at the UFRN, this article presents an analytical solution for calculating the flow rate by solving the differential equations obtained by applying the principles of mass and heat transfer. As a result, at the cost of greater complexity, the systematic error drops to values of less than 1% in the first two hours of operation of the well, as seen throughout this document.