| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn><mo>%</mo></mrow></semantics></math></inline-formula>. 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> 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.
|
|---|