Thermal Profiles in Water InjectionWells: Reduction of the Systematic Error in the Flow Measurement during the Transient Regime

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.