Asymptotic Approach for Modelling Progressive Cavity Pumps Performance

Selma F. Andrade, Juliana V. Valério, Márcio S. Carvalho


The fundamental understanding of the flow inside Progressive Cavities Pumps (PCP) represents an important step on the optimization of the efficiency of these pumps, which are largely used in artificial lift processes in the petroleum industry. The computation of the flow inside a PCP is extremely complex due to the transient character of the flow, the moving boundaries and the difference in length scale of the channel height between the stator and rotor. This complexity makes the use of computational fluid dynamics as an engineering tool almost impossible. This work presents an asymptotic model to describe the single phase flow inside progressive cavities pumps using lubrication theory. The model was developed for Newtonian fluid and lubrication theory was used to reduce the three-dimensional NavierStokes equations in cylindrical coordinates to a two-dimensional Poisson’s equation for the pressure field at each time step, which is solved numerically by a second order finite difference method. The predictions are close to the experimental data and the results obtained by solving the complete three-dimensional, transient Navier-Stokes equations with moving boundaries, available in the literature. Although the accuracy is similar to the complete 3D model, the computing time of the presented model is orders of magnitude smaller. The model was used to study the effect of geometry, fluid properties and operating parameters in the pump performance curves and can be used in the design of new pumping processes.

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