Viscoelastic Representation of the Operation of Sucker Rod Pumps

Sheldon Wang,Carrie Anne Taylor,Lynn Rowlan,Sean T Aleman,Trent Creacy,Abbey Henderson

doi:10.3390/fluids7020070

Abstract

The issues of leakage with respect to the clearance between the pump plunger outer surface and the pump barrel inner surface and other operational conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to explore the possibility of representing the entire downhole pump system with a simple viscoelastic model. We have explored both Kelvin and Maxwell viscoelastic models along with the dynamic behaviors of a mass point attached to the viscoelastic model. By using the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic models, we have obtained the displacement responses, which match closely with the actual measurements in experiments and operations. Further study and experiments have been planned and partially implemented in the McCoy School of Engineering at Midwestern State University, a member of the Texas Tech University System.

Highlights

Throughout a typical petroleum reservoir’s productive life, natural lift force due to fluid pressure tends to decay and diminish
The full-fledged computational fluid dynamics results have been documented in references [5,6] with a well-established commercial code ADINA for the annulus region using measured pressure differential and plunger velocity as boundary conditions
The effects of the eccentricity have been established analytically with the perturbation method and have been directly verified with the flow rates passing through the annulus region with various eccentricities calculated with the full-fledged computational fluid dynamics

Summary

Introduction

Throughout a typical petroleum reservoir’s productive life, natural lift force due to fluid pressure tends to decay and diminish. The quasi-static nature of the flow within annulus regions in typical sucker rod pump systems has been confirmed with both analytical and computational studies. The full-fledged computational fluid dynamics results have been documented in references [5,6] with a well-established commercial code ADINA for the annulus region using measured pressure differential and plunger velocity as boundary conditions. These sets of computations have yielded nearly identical flow rates through the annulus region directly matching with the analytical formulas for quasi-static Poiseuille and Couette viscous flows respectively as documented in references [5,6]. In this paper we have attempted to replace the entire downhole sucker rod pump system with a simple viscoelastic model to mimic sucker rod pump units behavior, in particular the piston-like motions between the plunger and the barrel

Theory and Experimental Setup

Conclusions