New Approach for Modeling Progressive Cavity Pumps Performance

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractProgressive Cavity Pump (PCP) performance has been traditionally modeled as a composition of Couette flow and Poiseuille flow, represented by pump displacement and internal slip respectively. Pump displacement can be easily calculated from pump components geometry, but calculating internal slip is not a trivial problem. Previous studies have proposed to use Hagen-Poiseuille equation for modeling internal slip flow, assuming a constant interference value. In these studies slippage gap area is not clearly defined, so great results have not been reached.This study introduces a new approach for modeling single lobe PCP performance. Slip flow is modeled as the result of two components, one of them due to the movement of the rotor and the other one due to the differential pressure between cavities, assuming that slippage gap area depends on the stator material. This assumption is based on the analysis of metallic, elastomer and PTFE stator PCP characteristic curves, obtained from experimental data of previous works.The existence of a strong relationship between slippage gap area and differential pressure, related to mechanical properties of stator material, is demonstrated. Thus, internal deformation of stator is identified as the main parameter to be understood before predicting PCP performance. For a polymer stator PCP this relationship approximates to a quadratic form, while in a metallic stator PCP a constant gap area can be assumed.Although the proposed model is not able to fit data for any PCP models, its results agree with the ideas proposed above and documented PCP performance theory. In order to obtain a definitive model, future investigation is needed to improve expressions for calculating friction factor inside the pump and also to define a procedure for obtaining gap area relationships for any type of stator material.

A computational model for the flow within rigid stator progressing cavity pumps

“…The usual flow models based on the ideas of the PCP creator, Rene Moineau (Moineau, 1930), attempt to establish relations between differential pressure and flow rate by subtracting the counter-flow leaked through the seals from the displaced flow rate (Gamboa et al, 2003;Pessoa et al, 2009). Because the displaced flow rate depends only on the pump geometry and kinematics, fluid models usually attempt to calculate the leakage, or "slippage" 1 , fluid properties and the differential pressure along the pump.…”

“…Recognizing those limitations, Gamboa et al (2003) presented a simplified model for single-phase flow by considering the possibility of variable gap due to elastomeric stator deformation. In this way, his model was able to reproduce the characteristic non-linear behavior of volumetric flow versus differential pressure in PCPs with elastomeric stators.…”

Analytical Model for the Flow in Progressing Cavity Pump with the Metallic Stator and Rotor in Clearance Fit

“…These meshing lines also play as sealing lines between cavities during the PCP operating in clearance fit. The transversal slippage flows through the sealing lines formed at straight sections of the stator, while the longitudinal slippage flows through the sealing lines at fixed positions corresponding to semicircular sections of the stator [24]. Figure 4 shows the two-dimensional coordinate system of the pump cross-section, in which the center of the stator is the origin.…”

“…Olivet et al [22] and Gamboa et al [23] had performed extensive experiments to study the performance of a metallic stator PCP prototype, and the transient pressure profiles along consecutive cavities were also obtained. Based on the experimental study, Gamboa et al [24] made the first attempt to propose an analytical model for the flow, in which the slippage was the result of two components due to the differential pressure and the rotor movement. However, a definitive model still needs to be established by further studies on the calculation of the friction factor and the clearance geometry between the stator and rotor.…”

Experimental and numerical studies on pumping viscoplastic fluids

“…Graham et al (2009) experimentally investigated the performance of a centrifugal pump for lifting a power-law fluid and a Herschel-Bulkley fluid. The performance of PCP system was analyzed and modelled by Moreno and Romero (2007) and Gamboa et al (2003). Numerical analysis was also presented by Li et al (1999) for extrusion process of viscoelastic cementatious flows in a shallow flight screw extruder, which is similar to a PCP system.…”