4th Latin American CFD Workshop

Applied to the Oil and Gas Industry

July 12-13, 2010 - Rio de Janeiro - Brazil

Organization: Support:

A CFD Model for a Progressing Cavity Pump

Emilio E. Paladino*, João Alves de Lima

†

PPGEM - Graduate Program in Mechanical Engineering,

Federal University of Rio Grande do Norte, CEP 59072-970- Natal - RN

*e-mail: emilio@ct.ufrn.br

†e-mail:jalima@dem.ufrn.br

ABSTRACT

The growth of Progressing Cavity Pump as artificial lift system in the last years lead to the development of

models for the flow behavior within these devices. Based on the ideas of the system creator, Rene Moineau, usual

flow models attempt to establish relations between differential pressure and flow rate by considering a Poiseuille

flow along the seal lines between cavities in order to predict the internal slip which is subtracted from the

displaced volumetric flow rate. In addition, some attempts for more detailed models including computational

solutions for the flow in static simplified geometries can be encountered in previous works. Nevertheless no models considering the solution for the full transient 3D Navier-Stokes equations and relative motion rotor and

stator were found in literature. This work presents a computational model for the unsteady 3D flow, using an

element based finite volume method, which includes the relative motion between rotor and stator, in a Progressing Cavity Pumps. The computational model for the flow in a Progressing Cavity Pump was

implemented in CFX11 [1]. This software is based on a discretization of the governing equations using and

Element Based Finite Volume Method ([2]; [3]; [4]) and a coupled approach for solving the pressure-velocity

decoupling ([5]).

The numerical flow computation within positive displacement pumps is, in general, a challenging task as it

normally requires moving mesh simulations. Furthermore, depending on the pump type, the need of discretization

of small clearances between rotor and stator introduces serious difficulties into the mesh generation process. In

addition, for the specific case of PCPs, the pump kinematics are very complex (when compared with a

reciprocating pump, for instance). , the main challenge in this work was the imposition of the mesh motion and mesh generation process, mainly, because of the need of mesh quality control (element distortion) in regions near

the seal lines

The model developed is capable of the accurate prediction of volumetric efficiency and viscous looses as well as provide detailed information of pressure and velocity field inside this device. This could allow, for example, the

prediction of local stator deformation in order to predict how this influences on slip, the accurate treatment of

turbulence effects, by using advanced turbulence models, and the model extension for the case of multiphase flows, which is a common case in artificial lift.

The model was validated against experimental results from literature, as can be seen in Figure 1. The model

successfully predicts the performance for high (oil 42 cP) and low (Water) viscosity fluids. For the caso of low

viscosity fluids, simplified models based on Pouseuille flow in seal regions, use to fail [6]. Some aspects related

to the dynamic behavior of the flow, not captured by the simplified models, are analyzed using this model. In

Figure 2, the pressure distribution along the pump stator is showed. This information, no available in simplified

models, allows the calculation of the stator deformation, in the case of elastomeric stators.

4th Latin American CFD Workshop

Applied to the Oil and Gas Industry

July 12-13, 2010 - Rio de Janeiro - Brazil

Organization: Support:

0 25 50 75 100 125 150 175 200

∆P [psig]

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QNET [bpd]

Present Work: Model

Gamboa et al. (2003): Exper

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Figure 1 - Comparison of model results with experimental results from [7]

Figure 2 - Pressure distibution along the stator for different rotor positions

References

[1] ANSYS CFX 11 Theory Manual , ANSYS Inc., Cannonsbourg, PA, USA (2008)

[2] Baliga, B. R. and Patankar, S. V., A New Finite Element Formulation for Convection-

Diffusion Problems, Numerical Heat Tranfer, 3, (1980) 393-409.

[3] Ferziger, J. H. & Peric, M., Computational Methods for Fluid Dynamics, Springer-Verlag Telos, (2001).

[4] Maliska, C. R., Transferência De Calor e Mecânica Dos Fluidos Computacional (in

Portuguese), LTC Editora, (2004). [5] Raw, M. J., A New Control-Volume-Based Finite Element Procedure for Numerical

Solution of the Fluid Flow and Scalar Transport Equations , University of Waterloo,

Canada (1985). [6] Gamboa, J.; Olivet, J.; Espin, S.. New Approach for Modelling Progressive Cavity Pumps

Performance, Proceedings of SPE Annual Technical Conference and Exhibition, Denver,

Colorado, USA, (2003).

[7] Olivet, J.; Gamboa, J.; Kenyery, F.. Experimental Study of Two-Phase Pumping in a

Progressive Cavity Pump Metal to Metal, Proceedings of SPE Annual Technical

Conference and Exhibition, San Antonio, Texas, SPE 77730 (2002).