A New Model for Studying Oilwell Pumping Installations
by J.E. Chacin U., INTEVEP S.A., and J.C. Purcupile, U. of Oklahoma
Engineers at the 62mi Annual Techmcal Conference and Exhmmon ot the Society ok Petroleum Engineers held m
TfIIs paper was prepared for pre.eentatmn Oallas. TX September 27-20. 19S7
Th,a pepef was selected forpreaentalrm by an SPE Program Commtttea Iollowmg review of mlormatmn contained m an abalractsubmmadby the author(a)Contentaof the paper. aa preeented. have no! been rewewed by the BOCIOIY of Pelroteum Engmaars and are subjacl 10 corract!an by the a aufhor(s) Tha material, a presented.does not neceaaarJyreftactany t=tlon of the Scciety of PetroteumEm#nears,es officers.or members Papers
to COPY Iepraaanwdat SPE maetmgaare sub@ 10pubficafon reww by Editorial ommmeeeof Iha Somafyof PetroleumEngmaere Permiamon C may restricted to anebatrart more 300 01 nol than WWOS lBu61r0fZmS not be copd The ebafracIaIwfsf confamccmap+wws acknowfe8gmenlof Tetex. 7W48D SPEDAL where qnd by whom the paperISPfeaantao write Pubtcatona Manager.SPE, P O Box633636. RIcfwaaon,Tx 75003S36 ABSTRACT
A digital discretemodel, similsr to the analog model investigated by Midwest Research, has been f developed to etudy pusapof, pumping with anchored tubing, and gas interference downhole conditions. The calculated surface dynagraphs are presented for unanchored tubing, anchored tubing, 60% gas interference, 20 gaa interference, and 80% pumpoff.
Gibba6*7). In the formulation of the solution, the damping coefficientIn the wave equation is treated as an empirical constant which varys between 0.1 to 0.5 see-’. More recently, Doty and Scttmidt* hwve formulated a pumping model that includes the dynmics of the fluid motion and uses experimental correlation, obtained by Valeev snd Repin,g to establish the frictional damping forces between the rods and the fluid. In this inveetigstion, a discrete model for rodpumping systems, similar to Midwest Research’s analog computer model, is discussed. The model can simulate any surface beam pumping unit type and sccounts for prime mover speed-torque characteristics (i.e., slip). The versatility of the approact. presented allows the modeling of Coulomb damping (produced when the rod string ruba sgainst the tubing) or viscous damping. Using a viscous friction model, aviecoue damping factor is obtained as a function of crude viscoeity and.rod-tubing atrf.ng size, This eliminate the need ~or empirical da~ping constants. The high frequency limitation of the proposed model (which are also the limitation of API RP1lL) are discussed. MATHEMATICAL MODEL —— Accurate prediction of the behavior of sucker rod pumping ayatems requlrea careful attention to the modeling ofthe (1) model’s boundar> condition at tbe polished rod, (2) sucker rod string dynamic behavior and, (3) model’s dowthole boundary condition. Beam Pumping Action -— TO start our formulation, consider the polished rod motion. T%e polished rod diaplacemcnt la a function of the crank arm angle O(t) as shown in Fig. 1. It can be calculated from the expression (ace GraYIO for details)
This model issimilsr to the analog model pioneered by Howe and Midwest Research. Howwer, because it uses a digital simulation, a wide variety of downhole conditions can be modeled. The upper limit on the frequency of this model (which also applies to RP1lL calculation) is also presented. INTRODUCTION Until the 1950’s, the oil industry relied almost completely on empirical correlations and trial and errormethods to design and analyze oil well pumping installations, In the mid 1950’s, Midwest Research Istc.(see Ref. 3) attempted to study sucker-rod pumping systems using the lumped psrameter approach with a mechanical model designed to incorporate all the important well varisbles. This approach was very difficult to use and control and they settled for analog computer simulation. Their result waa later...