Experimental study on prediction model of wet gas pressure drop across single-or

Youfang Ma ,Youfu Ma,, *,Junfu Lyu ,Weiye Liu

1 Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering,School of Energy and Power Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China

2 Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Energy and Power Engineering,Tsinghua University,Beijing 100084,China

Keywords: Gas–liquid flow Two-phase flow Wet gas Orifice plate Pressure drop Model

ABSTRACT The pressure drop prediction of wet gas across single-orifice plate in horizontal pipes had been solved satisfactorily under an annular-mist flow in the upstream of orifice plates.However,this pressure drop prediction is still not clearly determined when the upstream is in an intermittent flow or stratified flow,which is corresponding to a region of low FrG(gas phase Froude number)in the flow pattern map of wet gases.In this study,the wet gas pressure drop across a single-orifice plate was experimentally investigated in the low FrG region.By the experiment,the flow pattern transition in the downstream of single-orifice plates,as well as the effects of FrG and FrL (liquid phase Froude number) on ΦG (gas phase multiplier),were determined and compared when the upstream is in the flow pattern transition and the stratified flow region,respectively.Prediction performances were examined on the available pressure drop models.It was found that no model could be capable of jointly predicting the wet gas pressure drop in the low FrG region with an acceptable accuracy.With a new method of correlating FrG and FrL simultaneously,new correlations were proposed for the low FrG region.Among which the modified Chisholm model shows the best prediction accuracies,with the prediction deviations of ΦG being within 7% and 3% when the upstream is in flow pattern transition and stratified flow region,respectively.

1.Introduction

In the oil and gas industry,gas–liquid flow with a gas volume fraction greater than 90% are often considered as wet gases [1,2].Generally,wet gases flow in the pipe with an annular or annularmist flow [3,4].Hence,the pressure drop of wet gas across single-orifice plates under an annular-mist flow upstream had been well established.In the flow pattern map of wet gases,annular-mist flows are corresponding to a region of high gas phase Froude numberFrG.However,with the continuous exploitation of natural gas,the gas production of gas wells gradually decreases,making the intermittent flow and stratified flow become common in the wet gas pipeline [5].In the flow pattern map of wet gases,intermittent flows and stratified flows are located in the lowFrGregion.In contrast to the annular-mist flow,the pressure drop of wet gas across single-orifice plates is still not solved satisfactorily when the upstream is in the lowFrGregion.

Orifice plates are often used as a meter of wet gas flow rates due to its advantages of simple structure and low cost,which perform the measurement of flow rates through the relationship between the orifice plate pressure drop and the flowrate [6,7].Meikapet al.[8–14]have done researches on the hydrodynamic characteristics of multi-phase flow in bubble column and fluidized bed,including the pressure drop experiment of gas–liquid two-phase flow across orifice plate.To correlate the pressure drop with the fluid flow rate,many pressure drop models had been proposed for gas–liquid flows (such as the well-known models by Chisholm[15,16],Murdock[17],Lin[18]and James[19]).These models usually aim to obtain the gas(or liquid)phase multiplier ΦG,reflecting the two-phase flow pressure drop of orifice plates based on the known single-phase flow pressure drop [20–22].

For wet gases,a kind of gas–liquid flow featured by a low liquid content,these well-known models must be modified further to predict the fluid flow rate based on the pressure drop accurately.For example,xinget al.[23] and Genget al.[24] recommended a modified Murdock model,usingFrGand β (equivalent diameter ratio) to correct the model,based on their experimental studies on wet gas pressure drop across a slotted multi-orifice plate in the stratified flow and annular-mist flow region.Here a very important change is the introduction of a new parameterFrGinto the traditional models to consider the pressure loss variation caused by gas turbulence on phase interface.This idea was originally reported by De Leeuw [25] in his study of wet gas pressure drop of Venturi,wherein a modified Chisholm model was suggested and the parameterFrGwas used to correct the powernof gas–liquid density ratio in the model.Briefly speaking,for annular-mist flows (highFrGregion)nincreases with the increase ofFrGwhile for stratified flows(lowFrGregion)nis independent ofFrGi.e.keeps constant.Afterwards,Steven and Hall[26]performed a similar modification in their study on wet gas pressure drop of single-orifice plates,and the correlation by Steven and Hall [26]was recommended for use in the standard ISO/TR 11583:2012[27].

Besides stratified flows,intermittent flows are also in the lowFrGregion,which means the gas–liquid flow of lowFrGaccompanied by a relative high liquid content.Recently,Liuet al.[28]reported an experiment on the wet gas pressure drop of singleorifice plates in the flow pattern transition region(near the boundary of annular-mist,intermittent and stratified flow),and found that the Steven–Hall model [26] cannot predict accurately to this region.In [27],three new correlations,by modifying the homogenous flow model,Chisholm model,and Murdock model,respectively,were proposed for the flow pattern transition region,and they exhibited approximately the same prediction accuracy.

As can be seen,the Steven–Hall model [26] is applicable for annular-mist flows (highFrGregion) and stratified flows (a part of lowFrGregion).Meanwhile,the correlations proposed by Liuet al.[28] are applicable for intermittent flows (another lowFrGregion in addition to stratified flows).Therefore,it’s still an unclear question that if the wet gas pressure drop of orifice plates can be jointly predicted for the whole lowFrGregion with an acceptable accuracy.For this concern,we conducted a further experiment on the wet gas pressure drop of orifice plates in the stratified flow region after the experiment by Liuet al.[28].In order to establish a united prediction on the wet gas pressure drop of orifice plates in the lowFrGregion,in this paper the two groups of experimental data for stratified flows and intermittent flows were analyzed together.

2.Experiment Method

2.1.Experimental system and the testing single-orifice plate

The wet gas pressure drop across a single-orifice plate in horizontal pipes in the lowFrGregion were experimented using air and water as the two phases.The experimental system (as shown in Fig.1) is the same as those described in reference [28].Therefore,they are no longer repeated in this paper.In addition,the measuring instruments used for the experiment are also basically the same as those introduced in [28],besides an added rotameter,which has the range of 0.025–0.25 m3∙h-1with an accuracy of 4% ,was supplemented for measuring the water flow rate in the stratified flow region.

The inner diameter of the horizontal pipe where the orifice plate is located in the experiment isD=50 mm,a sharp-edged orifice plate with orifice diameterd=25 mm and orifice thicknesst=5 mm was used for the experiment.Thus,the orifice plate for the test has a diameter ratio β=0.50.

In addition,in order to observe the two-phase flow pattern before and after the orifice plate,plexiglass pipes of length 0.50 m and 1.5 m are installed upstream and downstream of the orifice plate,respectively.The pressure taps used for obtaining the pressure drop across orifice plates were located at 20Dupstream and 40Ddownstream of the orifice plate,respectively.

2.2.Experimental conditions and data processing methods

Referring to the flow pattern map of Shell[29],the testing conditions are designed in the flow pattern transition region and stratified flow region,which are shown in Table 1.The flow pattern transition region was designed with an air flow rate rangeQG=4 0–120 m3∙h-1(the corresponding superficial gas velocityJG=5.6 1–16.82 m∙s-1) and a water flow rate rangeQL=1–3 m3∙h-1(the corresponding superficial liquid velocityJL=0.141–0.423 m∙s-1),wherein the gas volume fractions is in the range of 93.05% –99.31% .The stratified flow region was designed with an air flow rate rangeQG=70–170 m3∙h-1(JG=9.89–24.06 m∙s-1)and a water flow rate rangeQL=0.05–0.15 m3∙h-1(JL=0.007–0.021 m∙s-1),in which the gas volume fractions is in the range of 99.79% –99.97% .The testing conditions are shown in Fig.2 with the flow pattern map of Shell.

Table 1 The testing condition of the flow pattern transition region and stratified flow region

The pressure drop of wet gas across orifice plates is characterized by the gas phase multiplier ΦGand the Lockhart–Martinelli parameterX.ΦGis determined by:

where ΔpTPand ΔpGOare the orifice pressure drops of the twophase flow and the gas phase only,respectively (kPa).ΔpTPis obtained directly from the experiment,and ΔpGOis determined by the correlation obtained from a prior experiment on the pressure drop of air across the orifice plate.

The LM parameterXis determined by:

where x is the gas quality,ρ is the density (kg∙m-3),and the subscripts G and L denote the gas phase and the liquid phase,respectively.

The gas and liquid phase flow rates in wet gas are expressed by Froude numberFrGandFrL,respectively.They are determined by:

wheregis the gravitational acceleration (9.81 m∙s-2),JGandJLare the superficial gas velocity and superficial liquid velocity,respectively (m∙s-1).

In order to analyze the deviation between the prediction results of the available models and the experimental results of this study,the relative deviationERis determined by:

For a homogeneous flow model:

For a separated flow model:

where ΔpTP,Eand ΔpTP,Care the pressure drops of the gas–liquid flow obtained by the experiment and the prediction model,respectively(kPa);ΦG,Eand ΦG,Care the gas phase multipliers obtained by the experiment and by the prediction model,respectively.

2.3.Uncertainty analysis of the experimental result

Fig.1.Experimental system for the pressure drop of wet gas across single-orifice plates.

Fig.2.Distributions of the testing conditions in the flow pattern map of Shell.

In the experiment,ΔpTPand ΔpGOwere obtained directly by differential pressure transmitters.Therefore,their uncertainties can be determined by the measuring value and the range,accuracy of the transmitters.Then,the uncertainty of ΦGcan be obtained by uncertainty propagation principle with its definition as Eq.(1).As the dimensionless parameters,FrGandFrLare often used to indicate the influences of superficial gas and liquid velocity,respectively,on the pressure drop of wet gas flow.Therefore,their uncertainties were also determined according to their definitions as Eq.(3).Specifically,uncertainties ofFrGandFrLmainly depend on the uncertainties of measuring gas and liquid flow rates,and the uncertainties of ρGthat are derived from the measurements of temperature and pressure of the gas,while the uncertainties of ρLare not considered because it does not change much in the experiment.The uncertainty analysis results are listed in Table 2,in which the uncertainty of a parameterYis expressed byU(Y).

Table 2 Uncertainty analysis results (%) of the experimental result

3.Experimental Results

3.1.Results of flow patterns

In the flow pattern transition region,the upstream flow patterns of the orifice plate can be divided into three types:stratified,intermittent and annular-mist flow.Meanwhile,the downstream presents an annular-mist flow only.This result is exhibited in Fig.3 by taking the testing condition points A,B and C,seen from Fig.2,as examples.Under condition A (QG=40 m3∙h-1,QL=1 m3-∙h-1),the upstream of the orifice plate is a stratified flow,the downstream region near the orifice plate presents a dispersed annular-mist flow,and the flow pattern returns to a stratified flow at approximately 2Dbehind the orifice plate.Under condition B(QG=80 m3∙h-1,QL=2 m3∙h-1),the upstream of the orifice plate presents an intermittent flow,while the downstream is an annular-mist flow.Compared with condition A,in condition B the distance of the mist flow behind the orifice plate is significantly increased,and the flow pattern returns to an intermittent flow at approximately 6Dbehind the orifice plate.Under condition C,the upstream of the orifice plate presents annular-mist flow,the downstream is also in the form of mist flow;compared with the upstream,the mist flow in the downstream behaves more uniformly.

In the stratified flow region,the upstream of the orifice plate presents stratified flow at all testing conditions.However,the downstream flow pattern of the orifice plate can be divided into stratified flow and annular-mist flow.Compared with the horizontal empty pipe,the boundary of forming annular-mist flows,at approximatelyFrG=0.60,become earlier in the downstream of the orifice plate.This result is exhibited in Fig.4 by taking the test-ing condition points D and E,seen from Fig.2,as examples.Under condition D(QG=70 m3∙h-1,QL=0.15 m3∙h-1),both the upstream and downstream of the orifice plate are stratified flows;nevertheless,the downstream shows a decreased liquid layer and an increased gas phase volume fraction.Under condition E(QG=90 m3-∙h-1,QL=0.15 m3∙h-1),the upstream presents stratified flow,while the downstream behaves a dispersed annular-mist flow near the orifice plate,with the flow pattern returning to a stratified flow at approximately 4Dbehind the orifice plate.When the downstream presents annular-mist flows,which are corresponding to the conditions ofQG=90–170 m3∙h-1andQL=0.05–0.15 m3∙h-1,the flow pattern recovery distanceSincreases with the increase ofQGorQL,varying from 1Dto 14D.

Fig.3.Upstream and downstream flow patterns of single-orifice plates in the flow pattern transition region.

Fig.4.Upstream and downstream flow patterns of single-orifice plates in the stratified flow region.

3.2.Results of pressure drops

The experimental result of pressure drops of the single-orifice plate is shown in Fig.5.It can be seen that bothJGandJLhave obvious influence on ΔpTPwhen the upstream is in the region of flow pattern transition and stratified flows,i.e.ΔpTPincreases with the increase ofJGorJL.

For wet gases,gas phase multiplier ΦG,see Eq.(1),is widely used to express the pressure drop of orifice plates.Then,the pressure drop results of the single-orifice plate,expressed by ΦG,are shown in Fig.6.In order to determine the effect of flow pattern variation on the pressure drop of single-orifice plates,in Fig.6,ΦGare shown by the classification of flow pattern transition region,stratified flow region and annular-mist flow region according to the two-phase flow upstream.Among them,ΦGfor the flow pattern transition and stratified flow region are obtained by the experiment of this study,while ΦGof the annular-mist flow region are calculated by Steven–Hall model in the Standard ISO/TR 11583:2012 [27].According to the flow pattern map of Shell,the annular-mist flow region was selected in the range ofFrG=2.0–5.0 thus ensuring the condition of an annular-mist flow;meanwhile,FrLwas selected in the range ofFrL=0.20–0.60,which is the same as the range of the flow pattern transition region experimented.

Fig.6 clearly shows that the flow pattern in pipes has a significant influence on the pressure drop response of single-orifice plates.This can be demonstrated by the different response of ΦGonFrGandFrLunder the different flow pattern regions.For the annular-mist flow region,ΦGis almost independent ofFrG,while slightly increases withFrLincreasing.It means that in the highFrGregion,i.e.in the annular-mist flow region,ΦGof singleorifice plates basically keeps a stable value under the different gas flow rate,though the liquid content has a limited influence on ΦGin such cases.

Fig.5.The experimental result of pressure drops of the single-orifice plate for:(a) the flow pattern transition region and (b) the stratified flow region.

Fig.6.Gas phase multiplier ΦG of the single-orifice plate for different flow pattern regions.

With the decrease ofFrG,the two-phase flow will transit to an intermittent flow or stratified flow,depending on the amount of the liquid content (i.e.FrL).In the lowFrGregion,corresponding to the range ofFrL=0.20–0.60,the two-phase flow in the pipe behaves a transition between stratified flows and intermittent flows.It can be seen from Fig.6 that,in this flow pattern transition region,bothFrGandFrLpresent significant influences on ΦG,which markedly increases with the decrease ofFrGand the increase ofFrL.In comparison with the highFrGregion,FrLpresents a more pronounced effect on ΦGin the lowFrGregion.For example,asFrLincreases from 0.20 to 0.60,ΦGincreases approximately 0.50 in the annular-mist flow region,while it increases by approximately 2.0 in the flow pattern transition region.This indicates thatFrLis an important parameter that cannot be ignored in the prediction of ΦGin the lowFrGregion.

For the effect ofFrGon ΦGin the lowFrGregion,as seen from Fig.6,it is dependent on the value ofFrL.With the decrease ofFrL,the effectFrGon ΦGtends to decrease.That is,in the pure stratified flow with lowFrL,FrGis independent of ΦG,like that in the annular-mist flow.However,for relatively highFrLin the lowFrGregion,which denotes the intermittent flow and a part of stratified flow,ΦGincreases with the decrease ofFrG.This means that ΦGwill no longer keep stable and will gradually reach a very large value with the increase of liquid content in the two-phase flow.

4.Summary and Evaluation of the Available Models

4.1.Summary of the available pressure drop models

The models in literatures used for predicting the pressure drop of gas–liquid flow across orifice plates were summarized in Table 3.

4.2.Evaluation of the available pressure drop models

To evaluate the prediction accuracies of the available pressure drop models for the wet gas across a single-orifice plate in the lowFrGregion,the prediction results of the models listed in Table 3 were compared with the experimental result of this study.The comparison results,namely the prediction deviations of these models,were given in Table 4.

It can be observed from Table 4 that the homogeneous flow models largely overestimate the wet gas pressure drop in the lowFrGregion.Taking the James model as an example,the prediction deviations are further illustrated by Fig.7.It can be seen that in the flow pattern transition region,the deviation of the James model is mainly dependent onFrL,increasing with the decrease ofFrL.Meanwhile,under a certainFrL,the deviation of the James model is inclined to decreasing with the increase ofFrG.In the lowFrGregion,the flow pattern transits from intermittent flows to stratified flows with the decrease ofFrL,and tend to be annular-mist flows asFrGincreasing.Therefore,it indicates that the James model,as a homogeneous flow model,shows low prediction deviation for a uniform dispersed flow such as the annularmist flow,while produces high prediction deviation for a pure separated flow such as the stratified flow.

In contrast to the large deviation of the homogeneous flow models,Table 4 shows that the deviations of the separated flow models are relatively small.Compared with the experimental pressure drop of the stratified flow region,each separated flow model included in Table 4 presents a good prediction performance.However,their prediction deviations are still high when the upstream in the flow pattern transition region.For instance,the prediction deviations of the model by Steven and Hall [26],i.e.the Standard ISO/TR 11583:2012 [27],are further illustrated by Fig.8.It can be seen that this model exhibits a very good prediction accuracy(4%) whenFrLis low enough,while produces a large deviation(up to 45%) whenFrLis increased even though the upstream flow pattern is a stratified flow(for example,whenFrL=0.20).This indicates that the Steven–Hall model [26] cannot be capable of accu-rately predicting the pressure drop of wet gas across orifice plates in the whole lowFrGregion.Besides,the upperFrLlimitation of the Steven–Hall model is not clear yet,which make it difficult to judge the applicability of the Steven–Hall model when wet gases are in the lowFrGregion.Therefore,it is meaningful to establish a united prediction model for the wet gas pressure drop of single-orifice plates in the lowFrGregion.

Table 3 The available models of the pressure drop of gas–liquid flow across orifice plates

Table 4 Prediction deviations of the available pressure drop models

Fig.7.Prediction deviations of the James model.

5.New Models and Correlations

By evaluating the available pressure drop models with the experimental result of this study,it was found that no model could be capable of jointly predicting the wet gas pressure drop in the lowFrGregion with an acceptable accuracy.In order to establish a united prediction on the wet gas pressure drop of single-orifice plates in the lowFrGregion,hereinafter the three typical models such as the homogenous flow model,Chisholm model and Murdock model were modified with a new method of correlatingFrGandFrLsimultaneously.

Fig.8.Prediction deviations of the Steven–Hall model.

5.1.Modification of the homogenous flow model

To consider the effect of the complex factors in real two-phase flow that cannot be included in the theoretical homogeneous flow model,the powernof quality x in the formula was often correlated with those factors,such as James [19].In the theoretical homogeneous flow modeln=1.0;in the James modeln=1.5.By the equation of the theoretical homogeneous flow model (see Table 3),the relationship between the powernandFrG,FrLcan be deduced based on the experimental result of this study,which is shown in Fig.9.Then,the correlation of powerncan be obtained by surface-fitting method.Accordingly,the new correlation based on the modified homogeneous flow model is given by Eq.(6).

The prediction accuracies of Eq.(6)are shown in Fig.10.As can be seen,the prediction deviations of pressure drops are within ± 10% and ± 6% for the flow pattern transition region and stratified flow region,respectively.

5.2.Modification of the Chisholm model

Fig.9.Effects of FrG and FrL on the power n of the theoretical homogenous flow model.

Fig.10.Prediction accuracies of the modified homogenous flow model.

Fig.11.Effects of FrG and FrL on the power n of the Chisholm model.

Based on the Chisholm model (see Table 3,whereinn=0.25),Steven and Hall [26] further considered the influence ofFrGon the wet gas pressure drop across orifice plates by correlating the powernof gas–liquid density ratio in the Chisholm model withFrG.They suggested such a modification onnwhenFrG>1.5,but advisednkeeping constant whenFrG≤1.5.Their correlation is recommended in the Standard ISO/TR 11583:2012[27]for predicting the wet gas pressure drop across orifice plates.The experimental result of this study shows that,in the lowFrGregion,bothFrGandFrLare closely related with the pressure drop of wet gas across single-orifice plates,especially whenFrLis relatively high.Thus,by the equation of the Chisholm model,the relationship between the powernandFrG,FrLcan be deduced based on the experimental result of this study,which is shown in Fig.11.Then,the correlation of powernwas acquired by surface-fitting method.Accordingly,the new correlation based on the Chisholm model is developed by Eq.(7).

The prediction accuracies of Eq.(7)are shown in Fig.12.As can be seen,the prediction deviations of gas phase multipliers are within ± 7% and ± 3% for the flow pattern transition region and stratified flow region,respectively.

Fig.12.Prediction accuracies of the modified Chisholm model.

5.3.Modification of the Murdock model

According to the Murdock model (see Table 3),ΦGis linearly related toX,slopekand interceptbare the coefficients to be determined by experiments.As can be seen from Table 3,Lin [18] further developed the model by considering the effect of gas–liquid density ratio on the slopekwith an additional correlation.For the wet gas flow,Xinget al.[23] also made a further modification on the model by correlatingkandbwithFrGand β.

Table 5 Prediction accuracies of the three modified models proposed

In reference to the Murdock model,if the experimental result of this study was expressed by the way of ΦGversus X,which are shown by Fig.13.By comparison,it was found that sorting the data with differentFrLcould let the result more in line with the laws of the Murdock model.It can be observed from Fig.13 that,under the sameFrL,ΦGhas a linear relationship withX.kare approximately constant (k≈1.22 for the flow pattern transition region andk≈3.27 for the stratified flow region),whilebincrease with the increase ofFrL.Therefore,it is more suitable to correlatekandbwithFrL.By the equation of the Murdock model,kandbunder differentFrLcan be deduced based on the experimental result of this study,which is shown in Fig.14.Then,the correlations ofkandbwere achieved with a quadratic polynomial and linear expression,respectively.Accordingly,the new correlation based on the Murdock model is advanced by Eq.(8).

The prediction accuracies of Eq.(8)are shown in Fig.15.As can be seen,the prediction deviations of gas phase multipliers are within ± 12% and ± 4% for the flow pattern transition region and stratified flow region,respectively.

Fig.13.Expressing the experimental result with ΦG versus X for:(a) the flow pattern transition region and (b) the stratified flow region.

Fig.14.Relationship between k, b and FrL based on the Murdock model:(a) between slope k and FrL,(b) between intercept b and FrL.

Fig.15.Prediction accuracies of the modified Murdock model.

The prediction accuracies of the three modified models are shown in Table 5.As can be seen,the prediction accuracy of each model is significantly improved in comparison with those of the available models listed in Table 4.Therefore,it is completely feasible to jointly predicting the wet gas pressure drop in the lowFrGregion with an acceptable accuracy.Among the three modified models,the modified Chisholm model shows the best prediction accuracy.It might be acting asa supplement to the Standard ISO/TR 11583:2012 [27] for the prediction of wet gas pressure drop across orifice plates in the lowFrGregion.

6.Conclusions

(1) The results of flow pattern show that there is annular-mist flow downstream of the single-orifice plate when the upstream is in the flow pattern transition region.There are annular-mist flow and stratified flow downstream of the single-orifice plate when the upstream is in the stratified flow region.The boundary of forming annular-mist flow behind the single-orifice plate,which is nearFrG=0.60,is much earlier than that ofin the horizontal empty pipe.

(2) In the flow pattern transition region,ΦGincreases significantly with the increase ofFrGor the decrease ofFrL.In the stratified flow region,ΦGis almost independent of theFrG,and slightly increases with the increase ofFrL.This indicates that bothFrGandFrLare important parameters that affect the wet gas pressure drop of single-orifice plates;the influences ofFrGandFrLon the pressure drop characteristics are obvious in the flow pattern transition region,while are slight in the stratified flow region.

(3) Compared with the experimental result of this study,the available homogeneous flow models for pressure drop of orifice plates show a large overestimation in the two flow pattern regions.The available separated flow models present a good accuracy in the stratified flow region,while generally exhibit an underestimation in the flow pattern transition region.Typically,the Steven–Hall model shows a prediction accuracy 3% in the stratified flow region,while the prediction deviations can be up to 45% in the flow pattern transition region.It is concluded that the Steven–Hall model,as well as the other available models,cannot accurately predict the wet gas pressure drop across single-orifice plate in the whole lowFrGregion.

(4) Based on the experimental result,the available pressure drop models were modified by a new method of correlatingFrGandFrLsimultaneously.Accordingly,new correlations were proposed for predicting the wet gas pressure drop across singleorifice plate in the lowFrGregion.Among them,the corrected Chisholm model shows the best prediction accuracies,with the prediction deviations of ΦGbeing within 7% and 3% for the upstream in flow pattern transition region and stratified flow region,respectively.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the Major Science and Technology Special Projects in Shanxi Province,China (20181102001).