New Approach for Modeling Progressive Cavity Pumps Performance

Abstract

Abstract Progressive 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. Introduction Oil production completions with PCP are designed over the knowledge of characteristics curves of the pump. These curves are usually extracted from manufacturer catalogs and experimental tests pumping water or a lube oil. Previous studies with elastomer PCP have showed that several variables can affect their characteristic curves, even into the low slip region, where differential pressure is below the one obtained at a volumetric efficiency equal to 80% [1, 2]. These variables can produce changes in operating parameters, such as pump displacement and maximum recommended head. Recent studies have demonstrated that all these operating parameters are also strongly affected by gas handling [3]. For a metallic stator PCP, which works under permanent slip condition, is well known how characteristic curves change by viscosity effects and gas handling. Previous studies show that fluid viscosity can change the flow regimen inside the pump [4]. Analyzing all these results and on the basis of field experience, the following conclusion can be made: characteristic curves presented by PCP manufacturers and even those obtained in experimental tests, do not represent real pump performance at downhole conditions. This problem is the main reason why researching efforts are dedicated to model PCP performance. Moineau, Vetter, Saveth and Robles [5, 6, 7, 8] have worked in creating simplified models for predicting PCP performance, but any of them have related stator material behaviour with hydrodynamic phenomena inside the pump. A model to predict PCP performance must take into account this relationship and others effects such as: gas and liquid mixture, swelling and thermal expansion. Main goals followed with this study are analyze the performance of progressing cavity pumps whose stator are made from different materials and introduce a new approach for modeling internal slip in a single lobe PCP, based on a previous model proposed by Vetter et. al. for twin screw pumps [9, 10].