Improved Two-Phase Model for Hydraulic Jet Pumps
Authors: Noronha F.A.F. , Franca F.A. , Alhanati F.J.S. 
Published: December 2007

Abstract
A new model is proposed to predict the performance of hydraulic jet pumps, HJP, when pumping two-phase gas-liquid mixtures. The model performance is compared with Petrie et al. (World Oil, Nov. 83) and Jiao et al.'s (SPEPE, Nov. 90) model, using as input data the set of measurements taken by Jiao (1988) when experiencing an industrial HJP.
The present model results from the application of the one dimensional conservation law of mass, momentum and energy to the gas-liquid flow throughout the HJP. It differs from the previous published ones because it takes into account the flow of the two-phase compressible homogeneous mixture along the different parts of the device. It is not just an adaptation of a model originally developed for single phase flows, as the existent ones. Until now, most models representing the flow of a gas-liquid mixture in a HJP were adapted from models developed for incompressible single phase flows. The gas compressibility, for instance, is fully considered, as in Cunningham's paper (J. Fluids Eng., Sep. 74), when modeling a jet pump driven by a gas.
The solution of the proposed model requires the knowledge of two constant energy dissipation factors, for the flow inside the nozzle and throat. Best values for these factors were obtained performing a regression analysis over Jiao's data. The results showed a consistently better agreement with the experimental data than those delivered by the existing models, over the full range of the operational variables.

Introduction
Hydraulic jet pumping is an artificial lift method to be considered when difficult applications, such as remote sites (including offshore), crooked holes, or heavy oil production, exist.
It presents important characteristics such as simplicity, flexibility and easiness of maintenance. The downhole equipment has no moving parts, and can be removed or installed by fluid circulation or wireline. On the other hand, the hydraulic jet pump is a low efficiency device: just a small fraction of the power fluid energy, around 30%, is actually transferred to the suctioned fluids.
Fig. 1 shows the main components of a HJP: the nozzle, suction, throat and diffuser sections. Fig. 2 depicts a schematic of the pressure distribution of the mixture flow along the device. Power fluid, at an injection pressure pi, is forced through the nozzle. As the fluid accelerates due to the area reduction, its kinetic energy increases and the pressure reduces. The pressure gradient (pi - ps), established between the nozzle exit section, n, and the pump suction chamber at pressure pi, is the flow driving force. The power and produced fluids enter the throat, where a mixing process occurs and the pressure increases from p1 to ps. When the produced fluid is a gas-liquid mixture, the main characteristics of this process, usually referred to as a mixing shock, are:the momentum transfer from the power to the produced fluid andthe flow regime transition taking place within a short finite length.
The mixing shock process apparently determines the energetic efficiency of the pump. In the diffuser, kinetic energy is again converted into pressure. The gas-liquid mixture leaves the diffuser at a pressure pd.
There are thousands of jet pumps installed in oil wells, most of them suctioning two-phase gas-liquid mixtures. However, some models developed to predict the pump performance when the produced fluid is a gas-liquid mixture are mere adaptations of single-phase flow models. The gas compressibility effect is not taken into account, and some of the proposed adjustments have no theoretical support. An exception is Alhanati's model, which requires a demanding numerical solution, and it is not suitable for inclusion in computer programs that carry out the overall design of the installation. P. 333