Study of the effect of viscosity on the head and flow rate degradation in different multistage electric submersible pumps using dimensional analysis

Multistage Electrical Submersible Pumps (ESPs) undergo performance degradation when operating with highly viscous fluids. Several studies on this subject seek to provide models to predict the pump performance under such conditions. However, some of those models require knowledge of geometric parameters or are only designated for radial-type pumps. In this article, dimensional analysis is used as an alternative to analyse head and flow rate degradation of different pumps without the need of any major geometric parameters. To accomplish this task, head curves for two multistage, mixed-flow type ESPs are obtained through a computational fluid dynamics (CFD) program for a wide range of viscosities and different rotational speeds. The numerical head curves were compared with experimental data under equivalent operating conditions and a good agreement was found. When adequate normalisations are used together with relevant dimensionless numbers, the head values obtained from the different ESPs proved to match quite well along curves of constant specific speeds. Experimental head values from literature for a radial-type centrifugal pump with volute operating with different fluid viscosities were used to extend the present analysis for a different pump geometry. Results from this procedure turned out to match the ESPs data well. A straightforward expression to correlate head and flow rate correction factors due to viscosity follows from the present approach, thus yielding a useful tool that might help in proposing a general method to estimate performance degradation.