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.

Ultrasonic method for measuring water holdup of low velocity and high-water-cut oil-water two-phase flow

Oil reservoirs with low permeability and porosity that are in the middle and late exploitation periods in China＇s onshore oil fields are mostly in the high-water-cut production stage.This stage is associated with severely non-uniform local-velocity flow profiles and dispersed-phase concentration（of oil droplets） in oil-water two-phase flow,which makes it difficult to measure water holdup in oil wells.In this study,we use an ultrasonic method based on a transmission-type sensor in oil-water two-phase flow to measure water holdup in lowvelocity and high water-cut conditions.First,we optimize the excitation frequency of the ultrasonic sensor by calculating the sensitivity of the ultrasonic field using the finite element method for multiphysics coupling.Then we calculate the change trend of sound pressure level attenuation ratio with the increase in oil holdup to verify the feasibility of the employed diameter for the ultrasonic sensor.Based on the results,we then investigate the effects of oildroplet diameter and distribution on the ultrasonic field.To further understand the measurement characteristics of the ultrasonic sensor,we perform a flow loop test on vertical upward oilwater two-phase flow and measure the responses of the optimized ultrasonic sensor.The results show that the ultrasonic sensor yields poor resolution for a dispersed oil slug in water flow（D OS/W flow）,but the resolution is favorable for dispersed oil in water flow（D O/W flow） and very fine dispersed oil in water flow（VFD O/W flow）.This research demonstrates the potential application of a pulsed-transmission ultrasonic method for measuring the fraction of individual components in oil-water two-phase flow with a low mixture velocity and high water cut.

Variation law of gas holdup in an autoclave during the pressure leaching process by using a mixed-flow agitator

The multiphase reaction process of pressure leaching is mainly carried out in the liquid phase. Therefore, gas holdup is essential for the gas–liquid–solid phase reaction and the extraction rate of valuable metals. In this paper, a transparent quartz autoclave, a six blades disc turbine-type agitator, and a high-speed camera were used to investigate the gas holdup of the pressure leaching process. Furthermore, experiments determining the effects of agitation rate, temperature, and oxygen partial pressure on gas holdup were carried out. The results showed that when the agitation rate increased from 350 to 600 r/min, the gas holdup increased from 0.10% to 0.64%. When the temperature increased from 363 to 423 K, the gas holdup increased from 0.14% to 0.20%. When the oxygen partial pressure increased from 0.1 to 0.8 MPa, the gas holdup increased from 0.13% to 0.19%. A similar criteria relationship was established by Homogeneous Principle and Buckingham's theorem. Comprehensively, empirical equation of gas holdup was deduced on the basis of experimental data and the similarity theory, where the criterion equation was determined as ε=4.54×10^(-11)n^(3.65)T^(2.08)P_g^(0.18). It can be seen from the formula that agitation rate made the most important impact on gas holdup in the pressure leaching process using the mixed-flow agitator.

Numerical Simulation of Gas Holdup Distribution in a Standard Rushton Stirred Tank Using Discrete Particle Method

The discrete particle method was used to simulate the distribution of gas holdup in a gas-liquid standard Rushton stirred tank. The gas phase was treated as a large number of bubbles and their trajectories were tracked with the results of motion equations. The two-way approach was performed to couple the interphase momentum exchange. The turbulent dispersion of bubbles with a size distribution was modeled using a stochastic tracking model, and the added mass force was involved to account for the effect of bubble acceleration on the surrounding fluid. The predicted gas holdup distribution showed that this method could give reasonable prediction comparable to the reported experimental data when the effect of turbulence was took into account in modification for drag coefficient.

The Operation of Draining Column Holdup for Slop Cut Withdrawal in Batch Distillation

The new mode of operation for slop cut withdrawal in batch distillation, i.e., draining Column liquid holdup at the end of slop cut period, was proposed. And the stopping criterion for the operation was investigated, Experiments were carded out with isopropanol-n-propanol binary system and isopropanol-n-propanol-n-butanol ternary system in a distillation column with a liquid collector installed between the reboiler and the column section, Experimental results in a Ф 45mm batch column show that the proposed policy can overcome the flywheel effect caused by column liquid holdup and thus cut down operation time and energy consumption 31%-61%.

BUBBLE SIZES AND HOLDUP STRUCTURE IN BUBBLE COLUMNS DETERMINED BY DYNAMIC GAS DISENGAGEMENT

A new model for determining bubble size distributions in bubble columns by the dynamic gasdisengagement(DGD)technique is developed.It is based on an idea of non-uniform steady statedirstribution of bubble dispersion.Interpreting the axial non-uniformity,this model gives axial gasholdup distributions.If assuming an axially homogeneous dispersion,a radial gas holdup distributioncan be obtained.The Sauter mean diameters or specific interfacial areas for several systems areestimated by the technique.The results for an air-water system agree with those measured by afive-point conductivity probe technique.The obtained axial gas holdup distributions agree well withreported measurements and the radial gas holdup distributions are also reasonable.

Effects of internals on phase holdup and backmixing in a slightly-expanded-bed reactor with gas–liquid concurrent upflow

Five different internals were designed,and their effects on phase holdup and backmixing were investigated in a gas–liquid concurrent upflow reactor where the spherical alumina packing particles of three diameters(3.0,4.5 and6.0 mm)were slightly expanded under the conditions of varied superficial gas velocities(6.77×10-2-3.61×10-1 m·s-1)and superficial liquid velocities(9.47×10-4-2.17×10-3 m·s-1).The experimental results show that the gas holdup increases with the superficial gas velocity and particle size,opposite to the variational trend of liquid holdup.When an internal component is installed amid the upflow reactor,a higher gas holdup,a less liquid holdup and a larger Peclet number characterizing the weaker backmixing are obtained compared to those in the bed without internals under the same operating conditions.Additionally,the minimal backmixing is observed in the reactor equipped with the internals with a novel multi-step design.Finally,empirical correlations were proposed for estimating gas holdup,liquid holdup and Peclet number with the relative deviations within 11%,12%and 25%,respectively.

THEORETICAL AND EXPERIMENTAL STUDIES ON BUBBLE DIAMETER AND GAS HOLDUP IN AERATED STIRRED TANKS

Experiments were carried out in geometrically similar vessels with diameters of 0.287, 0.495 and 1.1m respectively. Bubble diameter distribution was measured with a dual electric conductivity probe placed in the tanks. Gas holdup was measured by spillover method. Considering the coalescence of bubbles in the upper circulation region of the aeration stirred tank, introducing the concepts of turbulence decay and effective viscosity of gas-liquid system into this work, and taking into account the equilibrium between the surface energy of the bubbles and the energy supplied by agitation, mathematical models for bubble diameter and mean gas holdup were derived. The mathematical models were confirmed by experimental data.

Prediction of dispersed phase holdup in pulsed disc and doughnut solvent extraction columns under different mass transfer conditions

Using experimental data from a number of pulsed disc and doughnut solvent extraction columns, a unified correla- tion for the prediction of dispersed phase holdup that considers the effects of mass transfer is presented. Pulsed disc and doughnut solvent extraction columns （PDDC） have been used for a range of important applications such as ura- nium extraction and nuclear fuel recycling. Although the dispersed phase holdup in a PDDC has been presented by some researchers, there is still the need to develop a robust correlation that can predict the experimental dispersed phase holdup over a range of operating conditions including the effects of mass transfer direction. In this study, dis- persed phase holdup data from different literature sources for a PDDC were used to refit constants for the correlation presented by Kumar and Hartland lind. Eng. Chem. Res.,27 （1988）,131-138] which did not consider the effect of col- umn geometry. In order to incorporate the characteristic length of the PDDC （i.e. the plate spacing）, the unified cor- relation for holdup proposed by Kumar and Hartland based on data from eight different types of columns [Ind. Eng. Chem. Res.,34 （1995） 3925-3940] was refitted to the PDDC data. New constants have been presented for each hold- up correlation for a PDDC based on regression analysis using published holdup data from PDDCs that cover a range of onerating conditions and nhwical nronerties and consider the direction of mass transfer.

Gas Holdups of Small and Large Bubbles in a Large-scale Bubble Column with Elevated Pressure

Gas holdups of large bubbles and small bubbles were measured by means of dynamic gas disengagement approach in the pressured bubble column with a diameter of 0.3 m and a height of 6.6 m. The effects of superficial gas velocity, liquid surface tension, liquid viscosity and system pressure on gas holdups of small bubbles and large bubbles were investigated. The holdup of large bubbles increases and the holdup of small bubbles decreases with an increase of liquid viscosity. Meanwhile, the holdup of large bubbles decreases with increasing the system pressure. A correlation for the holdup of small bubbles was obtained from the experimental data.

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.

Simple Model for Gas Holdup and Liquid Velocity of Annular Photocatalytic External-Loop Airlift Reactor Under both Bubble and Developing Slug Flow

Based on the momentum conservation approach, a theoretical model was developed to predict the superficial liquid velocity, and a correlation equation was established to calculate the gas holdup of an annular external-loop airlift reactor(AELAR)in the bubble flow and developing slug flow pattern. Experiments were performed by using tap-water and silicone oil with the viscosity of 2.0 mm^2/s(2cs-SiO)and 5.0 mm^2/s(5cs-SiO)as liquid phases. The effects of liquid viscosity and flow pattern on the AELAR performance were investigated. The predictions of the proposed model were in good agreement with the experimental results of the AELAR. In addition, the comparison of the experimental results shows that the proposed model has good accuracy and could be used to predict the gas holdup and liquid velocity of an AELAR operating in bubble and developing flow pattern.

Experimental determination of gas holdup and volumetric mass transfer coefficient in a jet bubbling reactor

The hydrodynamics and mass transfer characteristics of a lab-scale jet bubbling reactor(JBR)including the gas holdup,volumetric mass transfer coefficient and specific interfacial area were assessed experimentally investigating the influence of temperature,pH and superficial gas velocity.The reactor diameter and height were 11 and 30 cm,respectively.It was equipped with a single sparger,operating at atmospheric pressure,20 and 40℃,and two pH values of 3 and 6.The height of the liquid was 23 cm,while the superficial gas velocity changed within 0.010-0.040 m·s^(-1)range.Experiments were conducted with pure oxygen as the gas phase and saturated lime solution as the liquid phase.The liquid-side volumetric mass transfer coefficient was determined under unsteady-state oxygen absorption in a saturated lime solution.The gas holdup was calculated based on the liquid height change,while the specific interfacial area was obtained by a physical method based on the bubble size distribution(BSD)in different superficial gas velocities.The results indicated that at the same temperature but different pH,the gas holdup variation was negligible,while the liquid-side volumetric mass transfer coefficient at the pH value of 6 was higher than that at the pH=3.At a constant pH but different temperatures,the gas holdup and the liquid-side volumetric mass transfer coefficients at 40℃were higher than that of the same at 20℃.A reasonable and appropriate estimation of the liquid-side volumetric mass transfer coefficient(kla)in a pilot-scale JBR was provided which can be applied to the design and scale-up of JBRs.

Study on the Holdup and Mass Transfer Performances for Gas-Liquid-Liquid System in a Screen Plate Column

The gas and dispersed phase holdups and mass transfer coefficients of liquid-iquid were determined for gas-liquid-liquid three phase system in a screen plate column. The flow pattern of gas-liquid-liquid three phase system was studied under different gas velocities. The shape factors showed the geometric properties of screen plates and the corrected drop characteristic velocities were introduced. The phase holdup in two phases was correlated. The research results indicated that mass transfer coefficient for liquid-liquid system in a column with screen plates and gas agitation was found to increase apparently.

Prediction of Gas Holdup in Bubble Columns Using Artificial Neural Network

A new correlation for the prediction of gas hold up in bubble columns was proposed based on an extensive experimental database set up from the literature published over last 30 years. The updated estimation method relying on artificial neural network, dimensional analysis and phenomenological approaches was used and the model prediction agreed with the experimental data with average relative error less than 10%.

Prediction of Pressure Gradient and Holdup in Small Eoetvoes Number Liquid-Liquid Segregated Flow

The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combinations of phase superficial velocities ranging from 0.05 m.s^-1 to 0,96 m.s^-1. For the current small Eoetvoes number liquid-liquid system （EOD=4.77）, the dominant effect of interfacial tension and wall-wetting properties of the liquids over the gravity is considered. The approach introduces the closure relationship for the case of turbulent flow m a rough pipe, and attempts to modify the two-fluid model to account for the curved interface. In present flow rates range, wave amplitudes were found small, while interfacial mixing was observed. An adjustable definition for hydraulic diame- ters of two fluids and interfacial friction factor is adopted. The predicted pressure gradient and in situ phase distribution data have been compared with present experimental data and those reported in the literature.

Measurement of water holdup in oil-in-water emulsions in wellbores using microwave resonance sensor

In this study,we propose a new method for water holdup measurement of oil-in-water emulsions with a microwave resonance sensor(MRS).The angle and length of the electrode plate are optimized by HFSS simulation software.Using a vector network analyzer(VNA),a static calibration experiment is conducted,and the resonant frequency distribution of oil-in-water emulsions is analyzed within an 80%–100%water holdup range.In addition,we observe and analyze the micron-sized oil bubble structure in the emulsifi ed state with an optical microscope.On this basis,a dynamic experiment of oil-in-water emulsions with high water cut and low velocity in a vertical upward pipe is conducted.S_(21) response curves of the MRS are obtained by the VNA under diff erent working conditions in real time.Finally,we analyze the relationship between the resonant frequency and water cut.Experimental results show that the MRS has an average resolution of 0.096%water cut for high water cut oil-in-water emulsions within the frequency range of 2.2–2.8 GHz.

Primary study on holdup measurement of ^(235)U in pipe using γ-ray spectrometry and Monte Carlo simulation

The pipe holdup measurement is very important for decommissioning nuclear facilities and nu- clear-material control and accounting. The absolute detection efficiencies (εsp) of full-energy γ rays peak under dif- ferent source density distribution function have been simulated using the Monte Carlo (MC) software, and the counting rates (n0) of the characteristic γ rays have been measured using the γ spectrometer followed by the calculation of the holdup. The holdup is affected by the energy of γ rays, distance at which they are detected, pipe material, thickness, and source distribution of pipe, especially source distribution at a short distance. The comparative test of 235U refer- ence materials on the inner wall of Fe and Al pipes (the total mass of 235U is 44.6 mg and 222.8 mg, respectively) have been accomplished using this method. The determined result of 235U is 43.2 mg (U0.95rel = 5.4%) and 216.2 mg (U0.95rel = 3.2%), respectively, which are in accordance with the reference values.

PHASE HOLDUP AND LIQUID DISPERSION IN GAS-LIQUID-SOLID CIRCULATING FLUIDIZED BEDS

Axial and radial profiles of gas and solids holdups have been studied in agas-liquid-solid circulating fluidized bed at 140mm i.d..Experimental results indicate that the axialand radial profiles of gas and solids holdups are more uniform than those in a conventionalfluidized bed.Axial and radial liquid dispersion coefficients in the gas-liquid-solid circulating fluidizedbed are investigated for the first time.It is found that axial and radial liquid dispersioncoefficients increases with increaes in gas velocity and solids holdup.The liquid velocity has littleinfluence on the axial liquid dispersion coefficient,but would adversely affect the redial liquiddispersion coefficient.It can be concluded that the gas-liquid-solid circulating fluidized bed hasadvantages such as better interphase contact and lower liquid dispersion along the axial directionover the expanded bed.

The Operation of Draining Column Holdup for Slop Cut Withdrawal in Batch Distillation

The new mode of operation for slop cut withdrawal in batch distillation, i.e., draining column liquid holdup at the end of slop cut period, was proposed. And the stopping criterion for the operation was investigated. Experiments were carried out with isopropanol-n-propanol binary system and isopropanol-n-propanol-n-butanol ternary system in a distillation column with a liquid collector installed between the reboiler and the column section. Experimental results in a 45mm batch column show that the proposed policy can overcome the flywheel effect caused by column liquid holdup and thus cut down operation time and energy consumption 31%—61%.