A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Liquid holdup measurement with double helix capacitance sensor in horizontal oil-water two-phase flow pipes

This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil–water two-phase flow. The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented. Then, a horizontal oil–water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor, in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes. The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

Investigation on Liquid Holdup in Vertical Zero Net-Liquid Flow

Zero net-liquid flow (ZNLF) is a special case of upward gas-liquid two-phase flow. It is a phenomenon observed as a gas-liquid mixture flows in a conduit but the net liquid flow rate is zero. Investigation on the liquid holdup of ZNLF is conducted in a vertical ten-meter tube with diameter of 76 mm, both for Newtonian and nonNewtonian fluids. The gas phase is air. The Newtonian fluid is water and the non-Newtonian fluids are water-based guar gel solutions. The correlations developed for predicting liquid holdup on the basis of Lockhart-Martinelli parameter are not suitable to ZNLF. A constitutive correlation for the liquid holdup of vertical ZNLF was put forward by using the mass balance. It is found that the liquid holdup in ZNLF is dependent on both the gas flow rate and the flow distribution coefficient.

A Dynamic Modeling For Cyclic Total Reflux Batch Distillation

Cyclic total reflux(CTR) batch distillation is a promising mode of the process but lacking of appropriate modeling for the period of filling the reflux drum.A new dynamic modeling method for the simulation of CTR batch distillation is proposed in this work,in which the changes in column holdup and liquid flow rate during the filling of the drum,and the consequent change in valid number of theoretical plates are considered.The effect of drum holdup on operation time is investigated and the optimal drum holdup is obtained from the simulation.The dynamic modeling is compared to the conventional modeling without consideration of change in liquid flow rate. The experimental result shows that the present modeling is more reliable and more accurate,especially for the column with large liquid holdup.

Slug Flow Characteristics in Inclined and Vertical Channels

Horizontal well production technology gradually occupies a dominant position in the petroleum field.With the rise in water production in the later stage of exploitation,slug flow phenomena will exist in horizontal,inclined and even vertical sections of gas wells.To grasp the flow law of slug flow and guide engineering practice,the flow law of slug flow at various inclination angles(30°~90°)is studied by means of the combination of laboratory experiments(including high frequency pressure data acquisition system)and finite element numerical simulation.The results reveal that because of the delay of pressure variation at the corresponding position of pipeline resulting from gas expansion,the highest point of pressure change curve corresponds not to the highest point of liquid holdup curve(pressure change lags behind 0.125 s of liquid holdup change).Thus,the delay of pressure should be highlighted in predicting slug flow using pressure parameter change;otherwise the accuracy of prediction will be affected when slug flow occurs.It is generally known that liquid holdup and pressure drop are the major factors affecting the pressure variation and stable operation of pipelines.Accordingly,the results of finite element numerical simulation and Beggs-Brill model calculation are compared with those of laboratory experiments.The numerical simulation method is applicable to predicting the pressure drop of the pipeline,while the Beggs-Brill model is more suitable for predicting the liquid holdup variation of the pipeline.The research conclusion helps reveal the slug flow law,and it is of a scientific guiding implication to the prediction method of flow parameters under slug flow pattern in the process of gas well exploitation.

Numerical study of macroscopical drainage process in fabricating foamed aluminum using microscopical method

The velocity field in a single Plateau border（PB） of the aluminum foam in the drainage process is studied using a mathematical model for the flow inside a microchannel.We show that the liquid/gas interface mobility characterized by the Newtonian surface viscosity has a substantial effect on the velocity inside the single PB.With the same liquid/gas interfacial mobility and the same radius of the curvature,the maximum velocity inside an exterior PB is about 6～8 times as large as that inside an interior PB.We also find a critical value of the interfacial mobility in the interior PB.For the values greater and less than this critical value,the effects of the film thickness on the velocity in the PB show opposite tendencies.Based on the multiscale methodology,with the coupling between the microscale and the macroscale and the results obtained from the microscopical model,a simplified macroscopical drainage model is presented for the aluminum foams.The comparisons among the computational results obtained from the present model,the experimental data quoted in the literature,and the results of the classical drainage equation show a reasonable agreement.The computational results reveal that the liquid holdup of the foams is strongly dependent on the value of the mobility and the bubble radius.

Error Analysis of Liquid Holdup Measurement in Gas-Liquid Annular Flow Through Circular Pipes Using High-Speed Camera Method

Accurate measurement of gas-liquid phase fraction is essential for the proper modelling of the pressure drop, heat transfer coefficient, mass transfer rate and interfacial area in two-phase flows. In this paper, taking the issue of optical distortion into account, an analytical model was proposed to estimate and correct the liquid holdup in gas-liquid annular flow through a circular pipe using high-speed camera method. The error in the liquid holdup measurement generated from different refractive indices among transparent circular pipe, liquid film and air core was firstly theoretically analyzed based on the geometric optics. Experimental tests were then carried out to identify the difference as well as to validate the proposed model. Results indicated that the prediction of the liquid holdup has a good performance with the experimental data(i.e., mean relative error is 4.1%) and the measured liquid holdup is larger than the real one. It was found that the measured liquid holdup is larger than the real one. Generally, when the real liquid holdup gets smaller, the discrepancy between the measured liquid holdup by image and the real liquid holdup becomes more significant. Thus, after measuring the liquid holdup from the images, the value of the measured liquid holdup must be corrected by the present model in order to obtain the real liquid holdup.

Behavior of liquid passing through deadman:influence of slag/iron ratio and unburned pulverized coal

The ability of a blast furnace hearth liquid(iron and slag)passing through deadman characterizes the activity of the blast furnace hearth.To explore the influence of various factors on the static holdup rate of liquid in the process of passing through the deadman,a physical transport model of liquid passing through the deadman was firstly established.Then,a self-designed experimental device was used to simulate the process,and the influences of slag/iron ratios(250–450 kg/t)and unburned coal content(0%–9%)on the static holdup rate were studied.The experimental results indicate that with the slag/iron ratio increasing,the behavior of liquid passing through the coke packed bed gets much more difficult,and the static holdup rate increases.As the content of unburned pulverized coal(UPC)increases,the static holdup rate decreases first and then rises.This is caused by the dual effects of UPC.On the one hand,UPC can promote the carburizing reaction of unsaturated molten iron,thereby improving the fluidity of molten iron and reducing the static holdup rate.On the other hand,when the content of UPC rises to a certain level,it will be regarded as a kind of solid particle which will increase the liquid viscosity,causing an increase in the static holdup rate.Moreover,the liquid and coke will present interfacial chemical reactions when the liquid flows through the coke packed bed.And the Si-containing iron droplets at the slag–coke interface,generated by the reaction of SiO_(2)with C in the coke,can improve the interface wettability by reducing the interface wetting angle and increase the basicity of slag by consuming SiO_(2),thus improving the fluidity of the liquid and reducing the static holdup rate.

A modified wake model in bubble-induced three-phase inverse fluidized bed(BIFB)

A modified wake model was proposed for the newly developed bubble-induced three-phase inverse fluidized bed(BIFB),by combining the generalized wake model and the gas-perturbed liquid model.On the basis of the modified wake model,the solids and liquid holdups and the complete fluidization gas velocity in BIFB system have been successfully predicted with two established correlations.The predictions achieved very good agreements with the experimental data.