Analysis of two phase critical flow with a non-equilibrium model

Critical (choked) flow is a highly concerning phenomenon in safety analysis for nuclear energy. The discharge mass flow rate prediction is crucial for engineering design and emergency response in case of nuclear accidents. Unfortunately, the critical flow is difficult to predict especially when the two-phase flow exists. The accuracy is based on a deeper understanding of the complex phenomenon of critical flow. The influence of virtual mass force on the two-phase critical flow was seldom concentrated on owing to the lack of suitable critical flow models for studies in detail. This study is based on a developed 6-equation two-phase critical flow model. It is confirmed that the virtual mass force contributes to the stability and convergence of the critical flow simulation and it will impact not only the critical mass flux but also the thermal hydraulic parameters along the discharge duct. The magnitude depends on the geometry of the discharge duct and the upstream condition. It is larger when the duct is longer and the pressure is lower. Furthermore, the virtual mass force for each flow regime was studied in detail with a sensitivity study. The results show that the most sensible condition for the virtual mass force is annular flow along a long tube under relatively low pressure. The future work is to develop a correlation of virtual mass force for critical flow specifically since the correlations in the literature were developed under general two-phase flow process conditions.

In recent years, the effort put forth toward the advancement of steamflood technology for improved heavy oil - recovery has seen considerable growth. A significant portion of the costs associated with a steamflood operation may be attributed to the generation of the steam required for injection. It is extremely important, therefore, that a high degree of accuracy is maintained in the measurement and control of the resulting steam-water mixture at each individual well. In fields where the required injection pressures are relatively low, the most common method of controlling the flow rate utilizes critical flow static chokes. New data are presented for the flow of steam-water through critical flow static chokes at conditions representative of a typical steam flood operation. The experimental data are a result of testing in Texaco’s new Steam Flow Research Facility. The experimental data covers a wide range of inlet qualities (20 to 100%) and inlet pressures (400 to 800 psig) for static choke bean diameters of 24/64 and 28/64 inch. The Thornhill-Craver empirical correlation predicts all of the experimentally measured values of critical mass flow rate within ± 10%. For inlet qualities ≥ 40%, all data is predicted within ±5%; below 40%, the equation over-predicts the critical flow data. The Napier equation modified for wet steam by King and Crocker over-predicts the critical mass flow rate at the present range of operating conditions.

Critical flows are widely used in power engineering. Such flows are characterized by non-stationary processes, active vaporization due to a sharp drop in pressure when the mixture flows from a high-pressure medium to an atmospheric pressure medium, which especially necessitates the study of the parameters of such flows in emergency situations, such as an emergency depressurization of a pipeline or cooling system. Due to the presence of two phases and the transiency of the processes, it is necessary to develop methods for numerical simulation of this process. The energy apparatus with a granular layer adds an additional level of complexity to the study of critical flows, namely, the effect of granular backfill on the characteristics of a two-phase flow. A new model for numerical simulation of the critical outflow of a vapor-liquid flow from a channel with a granular backfill has been created. The values of the mass flow rate of the mixture, the effect of vapor content on the critical flow rate, and the effect of geometric parameters of the granular backfill on the critical mass flow rate are obtained. The calculated data were compared with the experiment, and new data were obtained in a wider range of mass vapor content compared to experimental study.

A new statistical approach to identify critical mass flow rate in CO2 nozzles near saturation conditions

Although HFC-134a is a common refrigerant for residential and mobile refrigeration systems, investigators are dealing with replacing it with new alternatives because of its harmful environmental and global warming effects. Recently HFO-1234yf and HFO-1234ze have been introduced as suitable alternative refrigerants because they have zero ozone depletion potential (ODP) and low global warming potential (GWP) and possess thermophysical properties similar to those of HFC-134a. Because there is no experimental data on the performance of these new refrigerants in capillary tubes and short-tube orifices, a recently developed numerical model for analysis of critical two-phase flow through these tubes is used to predict the critical mass flow rate and pressure distribution of HFO-1234yf and HFO-1234ze under various operating conditions. The applied numerical model is based on a comprehensive two-fluid model including the effects of two-phase flow patterns and liquid-phase metastability. The numerical method has been validated by comparing numerical results of the critical flows of HFC-134a, R-410A, and HCFC-22 with available experimental data. The developed numerical simulation is applied in order to develop comparison and selection charts for short-tube orifices based on the common refrigerant HFC-134a and the alternative new refrigerants HFO-1234yf and HFO-1234ze.

A mechanistic, nonequilibrium model is presented, addressing the flashing and critical channel flow of initially subcooled water containing dissolved noncondensable gas. The model, which is based on the iterative numerical solution of, and the imposition of critical flow conditions on, one-dimensional two-fluid conservation equations, accounts for thermal, mechanical, and noncondensable species concentration nonequilibrium between the two phases. A two-phase flow regime map including bubbly, churn /slug, and annular patterns is applied, and flow regime-dependent heat, mass, momentum, and mass species transfer correlations are used for representing the interfacial transfer processes. The developed model is validated against experimental data. Parametric calculations assessing the significance of dissolved noncondensables in critical flow are then presented. It is shown that, for flashing and critical flow of subcooled water, the desorption of dissolved noncondensables reduces the critical mass flux slightly.

Study on solid-liquid transition behaviors of cohesive powders and predict the critical arch-breaking gas flow rate

A fully analytical model for virtual mass force in mixture flows

An accurate prediction of a critical flow discharged from a pressurized pipe system is of most importance in such a safety analysis of nuclear power plants, since it provides the transient boundary conditions during the depressurization transients initiated by a pipe break in primary or secondary systems and during the over-pressurization transients resulting in a relief of coolant through valves. Mass and energy discharge through the opening of pressure boundary affects the system thermal hydraulic responses, that is, phase changes and flow distribution in the system, and the mass inventory remaining in the system necessary to remove core decay heat of a nuclear reactor. Therefore, the safety significance relating to the critical flow led to a development of various empirical and mechanistic critical flow models. However, the accuracies of these models are still in question especially during two-phase critical flow condition. A good example of that is a homogeneous equilibrium model (HEM). The HEM is the basis of several system codes, such as early versions of RELAP, for nuclear loss-of-coolant accident (LOCA). The major non-equilibrium phenomena that are ignored in the HEM are vapor bubble nucleation and interface heat, mass, and momentum transfer. Henry & Fauske empirically handled non-equilibrium vapor generation by introducing a non-equilibrium parameter that allows only a fraction of the equilibrium vapor generation to occur. This approach boils down in essence to a correlation of the deviation between the measured flow rate and the prediction from the HEM: The details of the flow path do not have to be worked out and only needs to know the upstream conditions. However, if we treat non-equilibrium phenomena with this model, it requires an empirical database of the non-equilibrium parameters or their correlations that are so far unknown. Further, because the coefficients have not been applied separately to the subcooled liquid and two-phase mixture, we have not been able to treat the non-equilibrium phenomena with the phase change properly. For this reason, we propose the non-equilibrium parameters for subcooled liquid and two-phase mixture, respectively, and then we adopt their combinations according to the flow conditions through the phase change process using the RELAP5/MOD3 code. In addition, we discuss the assessment results of Marviken LBLOCA tests using these non-equilibrium parameter sets with those from the non-equilibrium model by Trapp & Ransom and Chung et al.

Evaluation of metal foam based thermoelectric generators for automobile waste heat recovery

The inability of the gas to lift liquid to the surface causes liquid to accumulate in the downhole, this event is called liquid loading, and sand deposits at the bottom of the well are caused to be swept away by the gas flow. If a well has liquid loading and sandification, well production will decrease and even the well will die. For this reason, it is necessary to carry out a predictive analysis of the well and a method to overcome the problem of liquid loading and sandiness using a plunger lift.Liquid loading is not always easy to identify, because the well is still producing significantly. The method used in the petroleum world to identify liquid loading is the "Turner et al" method. The plunger is a piston-type device that moves freely in the tubing and according to the inside diameter of the pipe, rising when the well pressure is sufficient to lift it and moving back down due to the force of gravity. The plunger lifting system uses gas pressure buildup in the well to lift the accumulated liquid column out of the well. The researcher conducted a liquid loading analysis on well A1 and well A2. From the results of the study it was identified that well A1 did not experience liquid loading, because the calculation results showed that the well's critical gas flow rate was 3.3 MMSCFPD which was less than the actual gas flow rate of 5 MMSCFPD. Well A2 is experiencing liquid loading, because the results of the calculation of the well's critical gas flow rate are 3.6 MMSCFPD, while the actual gas flow rate in the field is 3MMSCFPD.After removal of fluid and sand from the bottom of the well, the production rate of the A2 gas well increased to 5 MMSCFPD.

The ejector is a process equipment frequently used in refrigeration processes. There is currently a knowledge gap on the efficiency of ejectors operating with mixtures. To address this knowledge gap, we present a one-dimensional ejector model for mixtures, defined by spatially distributed mass-, energy- and momentum-balances for different zones, which together constitute the full ejector geometry. The recently developed delayed homogeneous relaxation model is used to describe the two-phase transition in the motive and suction nozzles. For evaporation of pure CO 2 in the throat of the motive nozzle, the model yields an average error of 2.6% in the critical mass flow rate, which is significantly lower than the homogeneous equilibrium model that has an average error of 8.4%. A comparison to new experimental data shows that both models give excellent predictions of critical mass flow rates where condensation occurs in the throat, with an average error below 0.9%. New experimental data with CO 2 are presented, which are used to regress two parameters in correlations that describe the momentum transfer between the primary and secondary stream in the mixer and diffuser sections. This leads to accurate reproduction of the pressure lift in five different ejector geometries, with a mean error of 2.3%. By using nonequilibrium thermodynamics, we derive formulae for the local exergy destruction in the ejector. The largest exergy destruction is located in the mixer, and originates in transfer of momentum between the primary and secondary streams. The local exergy destruction profiles through the mixer and diffuser are highly non-uniform, and deviate from the established guidelines for energy-efficient design characterized by equipartition of exergy destruction. This reveals a potential to increase the performance of ejectors by suitable adjustments to their geometric design. The mathematical model validated for pure CO 2 is assumed to also be valid for mixtures rich in CO 2 . We show that minute concentrations of a second component can have a significant influence on the ejector performance. When fixing the inlet conditions and ejector geometry, we demonstrate that adding 2% H 2 to a mixture of CO 2 decreases the critical mass flow rate by 20%, while adding 2% SO 2 increases the pressure lift by 1 bar. • A state-of-the-art, one-dimensional ejector model for mixtures is presented. • New experimental data for ejector operation with CO2 improves the model. • Critical mass flow rates and pressure lifts from experiments reproduced within 3%. • Local mapping of exergy destruction with nonequilibrium thermodynamics. • Minute concentrations of a second component alter the ejector performance.

The computation of mass flow rates through crack-like defects in piping systems of light water reactors requires typically the description of two-phase flow conditions. The computed discharge rate depends on the crack opening area, the thermal-hydraulic modeling of the flow, and the flow resistance of the crack. Several models have been proposed to characterize the critical flow through crack-like defects. An evaluation of advantages and shortcomings of the different models with regard to the interaction of the three different parts (crack opening area, thermal-hydraulic modeling, flow resistance) has been performed. In this paper, the flow resistance modeling from several approaches is discussed, and compared with a database from eight different testing programs. Five different flow models are applied to analyze a database of more than 800 leak rate measurements for subcooled water from twelve different experimental programs. It is shown that the correct modeling of the flow resistance is crucial for a best estimate reproduction of the measured data. It turns out that generally, equilibrium models are about as good as non-equilibrium models. The data were processed with the GRS software WinLeck which includes different analytical approaches for the calculation of crack sizes and leak rates in piping components. The most reliable results within the model selection are produced by the CDR model (Critical Discharge Rate) of the ATHLET code (Analysis of Thermal-hydraulics of Leaks and Transients) developed by GRS. As a conclusion, the accurate modeling of form losses and frictional pressure losses for critical discharge flow rates through crack-like leaks are essential for a reliable prediction of flow rates. Uncertainties in leak rate computations results arise due to the lack of information about the flow geometry and its associated drag. The assumed flow resistance of a through-wall crack influences the computed leak rate as significant as the phase-change- and flow-models. The manifest difference between equilibrium models (Pana, Estorf) and non-equilibrium models (Henry, ATHLET-CDR) seems to be less significant than the pressure loss issue. One can conjecture that, for crack-like through-wall defects, friction effects play a more important role than non-equilibrium effects.

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 100590, "The Tools, Techniques, and Advantages Involved in Combining Compression and Plunger Lift in Low-Rate Gas Wells," by R.A. Schmitz, SPE, and G.D. Steele, SPE, VaporTech Energy Services Inc., prepared for the 2006 SPE Gas Technology Symposium, Calgary, 15–17 May. Plunger lift and gas injection are two common methods used in gas wells to unload liquids. As the productivity of gas wells in the western Canadian sedimentary basin continues to decline, these methods used alone are no longer sufficient for many wells. Combining plunger lift with gas injection by use of newly developed and innovative tools and techniques can provide a solution for many low-rate gas wells that otherwise could not be cost-effectively produced. Introduction The maturing of the western Canadian sedimentary basin and the decline in average gas-well production rates, combined with strong demand and high commodity prices for natural gas, has led to a need to find ways to produce gas wells at lower and lower rates before they are shut in and abandoned. As a result, tools and techniques to remove liquids from these gas wells have become increasingly important. Both plunger lift and gas injection are techniques that have been used for many years to remove liquids from gas wells. Although there are several synergistic effects that occur when plunger lift and compression are combined, there also are a number of operational issues that make it challenging to combine the two technologies. Liquid Loading Liquid loading in a gas well is caused by the inability of the produced gas to remove the produced liquids from the wellbore. The point at which liquid loading will begin to occur in a producing well can be estimated by calculating the critical gas velocity, which can be translated into a critical gas flow rate. Various methods are available to estimate the critical gas flow rate, but the most important variables that determine the critical gas flow rate are gas production rate, inside diameter of the tubulars through which the gas is flowing, and the pressure and temperature of the gas. If the produced gas is flowing at a rate less than the critical rate at any point in the wellbore, liquid loading will occur. The produced liquid will start to accumulate in the wellbore, which often leads to erratic slugging flow and to decreased production. Eventually, the liquid buildup will cause the well to cease production entirely. Plunger Lift Fig. 1 shows a basic plunger-lift system. The primary function of the plunger is to provide a semisealing interface between the gas and the liquid, enabling the gas to lift the plunger along with a slug of liquid. The gas flow rate required for a plunger-lift system to function effectively depends on many of the same factors as the critical rate, but it also is affected by other factors such as the amount of liquid produced, the depth of the well, and the sealing efficiency of the plunger. As a result, prediction of gas-well performance with plunger lift is not an exact science.

Alternative determination of critical mass flow rate for the photovoltaic solar thermal collector in forced fluid mode