Modeling and Design of Jet Pumps

Abstract

Summary Models for jet pumps currently are derived under the assumption that thepower and well fluids are incompressible liquids that, in many cases, areassumed to have equal densities. When either the well or the power fluidcontains gas, current design practices still use the equations power fluidcontains gas, current design practices still use the equations forincompressible liquids and account for the presence of gas by modifying themass-flow-rate ratio and the friction-loss coefficients. This paper proposes anew approach to modeling pumps operating under multiphase-flow proposes a newapproach to modeling pumps operating under multiphase-flow conditions. Introduction Jet pumps were initially used in the oil industry for artificial lift. onlyrecently have these pumps been used in BOR processes whenever lowering thebottomhole pressure (BHP), extending the production stage, and limitingcavitation and/or sand erosion problems are desired. The concept ofjet-pumpoperation is simple. Power fluid enters the nozzle at high pressure and leavesas a high-velocity jet (the nozzle acts as a converter of potential intokinetic energy) that is directed into a constant-area mixing tube or throatfilled with stagnant or slowly moving well fluid. As the high-velocity jetpenetrates the well fluid in the throat, momentum is transferred frompenetrates the well fluid in the throat, momentum is transferred from the fast-to the slow-moving fluid elements, and mixing between the two fluids occurs. The mixture stream of the power-fluid jet and the entrained well-fluid elementsspreads, while the undisturbed well-fluid core gradually decreases as the flowprogresses. At the throat exit, the mixture stream occupies the entirecross-sectional area of the throat and has substantial kinetic energy. It issubsequently directed into an expanding area diffuser, where part of itskinetic energy is converted into potential and its pressure rises to a levelsufficient to lift the mixture of the two fluids to the surface. Cunninghamproposed comprehensive mathematical models for liquid/liquid jet pumps in thelate 1950's. Although his early models address systems of equal-densityliquids, they have been adopted in their exact form by some designers not onlyfor liquid/liquid systems of different densities but also for systems with freegas. For the latter, slight modifications of the volumetric-flow-rate ratio andthe friction-loss coefficients have been suggested. Re cent derivations of theliquid/liquid pump model account for density differences between power and wellfluids. In addition to his liquid/liquid pump model, Cunningham proposed in theearly 1970's a complete model for a jet pump used to pressurize anoncondensable gas. No model is available for a jet pump that uses gas as thepower fluid. Although it is recognized that both power and well fluidsgenerally can be multiphase mixtures, the design of jet pumps for oil wells isbased totally on a model for single-phase, incompressible liquids. Governing Equations In the work presented here, Cunningham's nomenclature from his liquid/gasmodel (i, n = the power fluid at the nozzle inlet and exit, respectively; s =well-fluid intake, 0 = throat or mixing-tube inlet; and 1,2 = power and wellfluids, respectively) is retained. Liquid/Liquid Pump. The following assumptions are made.1D flow conditions apply.Power and well fluids are incompressible.The pump operates isothermally and under steady-state conditions.Thekinetic energies at the inlet and outlet of the jet pump are negligible.Thefluids are perfectly mixed at the throat outlet.The average jet velocity ismaintained between the nozzle outlet and the throat inlet.