Annulus pressure at depth is a primary requirement of any gas lift design. There are several methods of determining annulus pressure including reference to a monograph, density equation used to full depth with average pressure and temperature, and density equation used in small depth increments with average temperature and pressure within the increment. The choice of which method to use comes with limitations on the accuracy of the predicted pressure at depth. When the annulus pressure at depth is calculated by use of a computer program, the choice of which correlation to use to model the critical properties of the gas and which compressibility factor correlation also affects the accuracy of the calculated pressure at depth. As a gas lift well transitions from a geothermal temperature profile to a flowing temperature profile during the unloading and lifting process, the annulus pressure at depth will decrease even though the surface injection pressure remains unchanged. Finally, the change in annulus pressure during the unloading process is governed by the volume of gas present in the annulus. A decrease in pressure is due to a reduction in gas volume. Traditional design techniques ignore this reality and substitute a theory of valve performance to explain annulus pressure changes during unloading. This simplified analogy of valve performance made it easy to design a gas lift well but incurred errors and misconceptions about how the annulus pressure changes during unloading. This paper will address all of the above issues and provide advice on which method of annulus pressure prediction at depth is most appropriate for specific conditions, advise on the accuracy of the combination of different critical properties and compressibility correlations, offer an alternative design technique to account for changing annulus temperature during the unloading process, and finally, provide guidelines on how to accurately and realistically model the changes in annulus pressure during the unloading process.
This study presents a methodology for the use of parametric Reduced Order Modeling (ROM) techniques to generate predictive models of hypersonic aerodynamic flow fields. The goal of this study is to synthesize a methodology for the development of these field surrogate models using techniques and procedures from the literature. This methodology is applied to two analytical test problems and one CFD application to demonstrate the functionality of the methodology and quantify the performance of models generated using various ROM techniques. The models compared in this study were generated using Proper Orthogonal Decomposition (POD) as a representative linear dimensionality reduction method, along with ISOMAP and Locally Linear Embedding (LLE) as representative Nonlinear Dimensionality Reduction (NLDR) methods. Based on the results of study, it is observed that the NLDR-based ROMs provide better predictions in the regions of fields near shocks, while linear methods are found to outperform non-linear methods when predicting steady-state behaviors far from shocks. Furthermore, nonlinear ROMs generated models of lower dimension than their linear counterparts, which resulted in significantly lower evaluation cost and could have significant ramifications if these predictive models are applied to coupled systems analyses. NOMENCLATURE
Summary Although gas lift design has been practiced for many years with the use of the Thornhill Craver (TC) equation (Cook and Dotterweich 1946) to predict the rate of gas passage through a gas-lift-valve port, the equation and charts were never intended for use with live gas lift valves. It is now possible to obtain tested valve-gas-passage-performance data for any pressure and temperature conditions. To date, a method has not been provided for the use of this information during the design stage. This paper will show how tested valve-performance data can be used in the design of 1-in. (25.4-mm) injection-pressure-operated (IPO) gas-lift valves. Introduction The American Petroleum Institute (API's) recommended method of spacing and sizing gas-lift-valve ports is published in API, s Recommended Practice (RP) 11V6 (RP 11V6, Recommended Practice for Design of Continuous Flow Gas Lift Installations Using Injection Pressure Operated Valves. 1992). This RP describes the design technique that has been used for many years with considerable success and uses the TC equations and charts as the principal methods of sizing gas-lift-valve ports. There are several commensurate assumptions with the use of the TC chart. First, it assumes that the valve port is fully open, and second, it assumes an unobstructed flow path through the valve. Both of these assumptions could be incorrect, depending on the type of gas lift valve used and the pressure being applied to the bellows. Every IPO gas lift valve has a property called loadrate. This property refers to the amount of opening a valve will achieve for a given annulus and tubing pressure. In most cases, a gas lift valve is rarely fully open when passing gas. Secondly, the valve and/or stem, downstream restrictions, and the reverse-flow check usually obstruct the flow passage through a gas lift valve. As a consequence of these exceptions, the flow rate through the gas lift valve is considerably less than that of the TC predictions. In many cases, the design engineer will apply a "safety" factor to the TC predictions. The value of the safety factor is a result of experience, but it usually varies from 50 to 80% of the value given by the TC correlation. It is now possible to predict accurately the rate of gas passage through a gas lift valve for any pressure and temperature conditions. This is possible as a result of correlations developed from actual tests of the valves at pressures similar to those encountered in service, correlations made available by license through the Valve Performance Clearinghouse™ (VPC™). Background The purpose of gas lift is to lighten the flowing-production gradient by injecting gas into the production string. There are two phases to a gas lift operation:unloading andoperating. The objective of unloading is to leverage the injection pressure by sequentially injecting gas through deeper unloading valves until the operating valve is reached. The operating phase should be a single-point injection through the operating valve over a range of injection rates. The API design method recommends that each lower unloading valve should use an injection pressure that is approximately 138 to 345 kPa (20 to 50 psi) lower than the upper valve. The theory is that as each lower valve is uncovered and begins injecting, the injection pressure would drop by this amount. This technique helped to close upper valves and also gave the operator a mechanism (wellhead-injection pressure) to determine which valve was open. This theory is based on the assumption that the amount of gas being injected at the surface is equal to approximately 50 to 80% of the combined total of the injecting valve and the next lower valve when it uncovers. If this is true, the wellhead injection pressure will drop 138 to 345 kPa (20 to 50 psi) as each lower valve is uncovered. If the amount of gas injected at the surface is greater than the combined total of the upper valve and the next lower valve, the injection pressure will not drop but will continue to increase. This paper will suggest a modification to RP 11V6 (1992). The modification will involve the use of tested valve-gas-flow rates to determine port sizes. The valve-performance predictions will be supplied by the VPC™ correlation. These correlations provide gas-passage-flow-rate predictions that are within 15% of actual flow for any pressure and temperature conditions.
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