# SPE Journal Volume 16, Number 2, June 2011, pp. 451-462

SPE-142294-PA

### Asymptotic Model of the 3D Flow in a Progressing-Cavity Pump

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DOI  10.2118/142294-PA http://dx.doi.org/10.2118/142294-PA

### Citation

• Andrade, S.F.A., Valério, J.V., and Carvalho, M.S. 2011. Asymptotic Model of the 3D Flow in a Progressing-Cavity Pump. SPE J.  16 (2): 451-462. SPE-142294-PA. doi: 10.2118/142294-PA.

### Discipline Categories

• 5.2.7 Progressing Cavity Pumps

### Keywords

• progressive cavity pump, flow model, petroleum artificial lift, lubrication theory, asymptotic model

### Summary

Fundamental understanding of the flow inside progressing-cavity pumps (PCPs) represents an important step in 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 because of 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 (CFD) as an engineering tool almost impossible. This work presents an asymptotic model to describe the single-phase flow inside PCPs using lubrication theory. The model was developed for Newtonian fluid, and lubrication theory was used to reduce the 3D Navier-Stokes equations in cylindrical coordinates to a 2D Poisson's equation for the pressure field at each timestep, 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 3D, 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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### History

• Original manuscript received: 23 December 2009
• Revised manuscript received: 16 August 2010
• Manuscript approved: 26 August 2010
• Published online: 23 February 2011
• Version of record: 17 June 2011