A computational model for the flow within rigid stator progressing cavity pumps Emilio E. Paladino ⁎, João A. Lima, Paulo A.S. Pessoa, Rairam F.C. Almeida Graduate Program in Mechanical Engineering, Federal University of Rio Grande do Norte, 59072-970 Natal, RN, Brazil abstract article info Article history: Received 22 October 2010 Accepted 1 May 2011 Available online xxxx Keywords: Progressing Cavity Pump 3D Model transient Model moving Mesh This work presents the development of a novel computational model for the 3D-transient flow in a Progressing Cavity Pump (PCP) that includes the relative motion between the rotor and stator. The governing equations are solved using an Element-based Finite Volume Method in a moving mesh. The model im- plementation is only possible due to the meticulous mesh generation and motion algorithm described herein, which is considered to be one of the main contributions of the present work. The model developed in this study is capable of precisely predicting volumetric efficiency and viscous loses in addition to providing detailed information about the pressure and velocity fields inside the device. Turbulence effects are accurately treated with advanced turbulence models. In addition, although the presented results are for single phase flow, the model can be extended to account for multiphase flows using models available in CFD software. In addition, some aspects related to inertial effects that are not captured by simplified models are analyzed using this model. The results presented herein consider a rigid stator pump. The model was validated against experimental results from literature. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Progressing Cavity Pumps (PCP) are positive displacement pumps with an operation principle based on the eccentric motion of a single rotor, which displaces the fluid contained in cavities from low to high pressure regions. Hydraulic seals are required between moving and static parts to avoid counter-flow (from high to low pressure regions), which depletes the pump efficiency. These seals are promoted in two ways: 1) by generating inter- ference between the rotor and stator, in which case the stator must be deformable (elastomeric), or 2) by leaving a small clearance between them, where the sealing is dynamically accomplished through the viscous pressure drop along the clearance. Even in the case of inter- ference between the rotor and stator, because the stator is deform- able, a clearance could eventually appear as the pressure increases, as will be explained later. Since their invention by Moineau (1930), PCPs have been successfully used for pumping high viscosity fluids or slurries, mainly in food and cosmetic industry, but it was the growth of the application of these pumps for oil artificial lifts in low to medium depth oil wells since the 1970s (in several cases substituting for traditional recip- rocating pumps) that lead to the development of more detailed flow models and experimental studies within these devices in recent years. Among the main advantages of this system for artificial lifts are its ability to pump heavy oils, tolerate high percentages of free gas and high efficiency can be quoted (Revard, 1995, Cholet, 1997). This work presents a computational model for unsteady 3D flow in single lobe progressing cavity pumps (Paladino et al., 2008; Lima et al., 2009; Paladino et al., 2009; Pessoa, 2009; Almeida, 2010), which includes the relative motion between the rotor and stator using an Element-based Finite Volume Method (Baliga and Patankar, 1980; Raw, 1985). Full 3D transient velocity fields are obtained from the model together with pressure fields. Therefore, all flow variables, including the flow rate, hydraulic torque, and efficiency, can be evaluated. Turbulence effects are properly treated through the use of advanced turbulence models. The model can be extended for heat transfer calculations and multiphase flows, which are common in artificial lift applications as long as adequate interfacial transfer rela- tions are included. All available multiphase closure models in CFD packages can be used. The detailed understanding of the flow behavior within progressing cavity pumps is of fundamental importance for designing, optimizing and operating PCP artificial lift systems. This model intends to be an additional tool for PCP systems design and operation and not a substitute for experimentation or pilot/in-field testing. Nevertheless, experimentation is expensive, and obtaining local measurements of pressure, velocity or tempera- ture fields is difficult. In addition, real operational conditions, such as downhole pressures and temperatures are difficult (if not impossible) to reproduce in laboratory tests, but can be readily simulated through the computational model presented in this paper. Once the model is validated through experiments developed under realizable laboratory conditions, it can be used as a prediction upscale tool under real op- erational conditions. Journal of Petroleum Science and Engineering 78 (2011) 178–192 ⁎ Corresponding author, currently at: SINMEC Lab, Federal University of Santa Catarina, Brazil. Tel.: + 55 48 3721 9562. E-mail address: eepaladino@gmail.com (E.E. Paladino). 0920-4105/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2011.05.008 Contents lists available at ScienceDirect Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol