This work presents a novel computational model for the 3D flow in a rigid stator Progressing Cavity Pump (PCP), using an element based finite volume method, which includes the relative motion between rotor and stator. Usual flow models in PCPs consider a Poiseuille flow along the seal lines, i.e., along the positive clearance between cavities in order to predict the internal slip and then, the volumetric efficiency for different pressures, rotations and fluid viscosities. Furthermore, some attempts for more detailed models including computational solutions for the flow in simplified geometries can be encountered in literature. These approaches include, treating cavities as parallel plates or computing the flow between two static cavities, in all cases considering steady state flow, which is a strong hypothesis in this case. Nevertheless no models considering the solution for the full transient 3D Navier-Stokes equations and the relative motion between rotor and stator were encountered. The main challenge at this point was the imposition of the mesh motion and mesh generation process, mainly, because of the mesh quality control (element distortion) in regions near the seal lines, or in the clearance regions between rotor and stator.
The model developed is capable to predict accurately the volumetric efficiency and the viscous looses as well as provide detailed information of pressure and velocity fields inside this device. Furthermore, the present model could be used to predict the hydraulic performance of an elastomeric progressing cavity pump after stator wear or deformation and allow for the development of a computational model for the fluid-structure interaction which permits the analysis of the non-rigid stator case.
Progressing Cavity Pumping is being more and more used in oil production, mainly in heavy oil fields, due to its numerous technical advantages. Simplest models for PCP design, firstly presented by Moineau (1930), are based on calculating the slippage across the pump, considering a Hagen-Poiseuille flow in the sealing region, which is subtracted from the volume displaced, giving the volumetric flow pumped. As differential pressure increases, so does the slippage, and the relation between differential pressure across the pump and net volumetric flow pumped, can be calculated.
After Moineau's models, several attempts for more precise fluid dynamic and fluid-structure interaction models have been presented. For oil production applications works due to Robello Samuel & Saveth (1998), Olivet et al. (2002), Gamboa et al. (2002) and Gamboa et al. (2003) constitute the main references in this field of research. Robello Samuel & Saveth (1998) developed optimal relationships between the pitch and the diameter of the stator to achieve a maximum flowrate for multilobe pumps. Olivet et al. (2002) performed an experimental study and obtained characteristic curves and instantaneous pressure profiles along metal to metal pumps for single- and two-phase flow conditions.
Gamboa et al. (2002) presented some attempts of flow modeling within a PCP using Computational Fluid Dynamics with the aim of getting a better comprehension of the flow inside the pump. Nevertheless, attempts for developing a three-dimensional model including rotor motion were failed even for rigid stator (this means constant clearance) due to the complexity of the geometry, mesh motion and (may be) the inadequateness or limitations of the numerical approach used to solve the governing equations. In virtue of this, Gamboa et al. (2003) presented simplified models for single phase flow considering the possibility of variable gap due to elastomeric stator deformation. The basic approach does not differ too much from previous works based on metallic stator, but the slippage is calculated cavity by cavity and the possibility of a variation of the clearance as function of differential pressure is considered. In this way they were able to reproduce the characteristic non-linear behavior of volumetric flow versus differential pressure in a PCP with elastomeric stator.