GAO Song,YOU Yun-xiang,LI Wei,YANG Chi

(1.State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China；2.Center for Computational Fluid Dynamics,College of Science,George Mason University Fairfax,Virginia,USA)

1 Introduction

The pipeline-riser system,including a downward inclined pipeline and a vertical riser,is needed to transport oil and associated gas from subsea wellheads up to offshore platform systems in the exploitation of offshore oil and gas[1].At low gas and liquid rates,one important problem experienced in such a pipeline-riser system is a severe slugging phenomenon that is defined as the buildup of liquid slug that equals to or exceeds the riser height[2-3].Severe slugging has obvious periodicity,and a cycle consists of four stages:slug generation,slug production,blowout and liquid fall back.This phenomenon,also called terrain-induced slugging,is a considerably harmful flow pattern in offshore petroleum production systems because of its high potential in causing sudden fluctuations of pressure and flow mass in the pipeline and overflow or interruption of the terminal gas-liquid separator[4].

Such a severe slugging has been studied experimentally in several flow laboratories.These experiments mainly focused on the formation mechanism,flow characteristics and elimination method for the severe slugging with a two-phase mixture of water and air[2,5-7].Some simplified models were also proposed for studying such a severe slugging in a pipeline-riser system[3,6].Due to limitations of instruments and safety reason,it is very difficult to obtain the effects of the gas-liquid physical parameters on severe slugging by experimental method,and simplified models are derived from the experiment,so it is still not clear for the relation between the gasliquid physical properties and the severe slugging.However,for different subsea wells,the quality of generated gas-liquid mixture is various,thus it is valuable to perform the research about the effects of gas-liquid physical parameters on the severe slugging.

In order to study the influence of gas-liquid physical parameters on severe slugging systematically,a CFD model is developed to simulate the gas-liquid severe slugging in a pipelineriser system.Based on the consistence principle of severe slugging formation,the 3D flow in a pipeline-riser system is simplified into a 2D flow.The gas-liquid severe slug flow in a pipelineriser system with a given pipeline declination angle is simulated numerically,in which water,crude oil and kerosene are selected as the liquid,while methane and air as the gas,and all cases have the same flow conditions.The effects of gas-liquid physical parameters on slug flow characteristics are studied and analyzed.Specifically,the effects of viscosity,density and surface tension of the liquid on the characteristics of severe slugging,including flow pattern,period,pressure fluctuation,void fraction and slug velocity are analyzed by comparing the results obtained from the CFD simulation.The present research is helpful to study the effect of physical parameters on severe slugging,and to evaluate the damage of the oil-gas severe slugging in different undersea oil fields,which can provide a useful reference for the design of pipeline-riser systems.

2 Numerical method

The presented numerical method adopts Reynolds time-averaged equations to solve the gas-liquid flow,in which the Brackbill model is applied to simulate surface tension and the VOF method is used to capture moving interfaces between gas-liquid phases.

2.1 Governing equations

Assuming that two-phase fluids are immiscible,the VOF method can be employed for tracking the gas-liquid interface where the volume fraction of the gas phase can be obtained by solving the transport equation[8]

where t denotes time,Reynolds time-averaged velocity vector is represented by v.

The volume fraction of the liquid phase is given by αl=1-αg.The density and dynamic viscosity in the computational cell can be determined as follows:

The Reynolds time-averaged equations and RNG k-ε two-equation turbulent model are applied to solve the gas-liquid severe slugging in the declined pipeline-riser system:

where p is the Reynolds time-averaged pressure,F is the body force,E is the internal energy,T is temperature,keffis the thermal conductivity.

The surface tension is considered as an extra body force in the momentum equation based on the Continuum Surface Force(CSF)model[9]

2.2 2D equivalent principle

Due to the fact that pipeline-riser systems are not axisymmetric and the gas-liquid flow law in the pipeline is different from that in the riser,three-dimensional CFD simulations should be performed.However,the 3D CFD simulation is very time-consuming since the pipeline and the riser have a very large length-diameter ratio.Thus,a 2D CFD model is developed to numerically simulate the gas-liquid severe slugging by means of transforming the 3D flow into a 2D one.

The mechanism of severe slugging formation can be described as follows:liquid accumulates in the pipeline and the riser bottom,forming the liquid slug and blocking the gas flow passage.The liquid slug continuously grows until the liquid level in the riser reaches the top,which results in a compression and pressure build-up in the gas phase.Therefore,the formation of severe slugging should meet two conditions:(a)Formation of liquid slug that traps gas;(b)Continuous increase of liquid slug length.

When 3D severe slugging flow is transformed into 2D flow,Conditions(a)and(b)should be in agreement for the two kinds of pipeline systems respectively.Condition(a)implies that the geometry and gas-liquid inlet Froude Number are similar.So,the 2D system is obtained by lateral projection of the 3D pipeline-riser system,and gas-liquid inflow superficial velocities of 2D system should be equal to those of the 3D

Subscripts 1 and 2 denote 3D and 2D systems,respectively,vsgand vsldenote gas and liquid superficial velocities,respectively.

The criterion number of severe slugging is defined as[10]

where g is acceleration of gravity,Tgis gas temperature,R is gas constant,Mgis average gas molecular,L and αpipedenote the length of the declined pipeline and the volume fraction,respectively.For Condition(b),the criterion number of the 3D flow should be the same as that of the 2D flow[10],which means Πs1=Πs2.

According to the Mukherjee-Brill correlation[11],αpipeis only associated with the angle of the declined pipeline and the gas-liquid physical properties,hence the αpipein the 2D model should be the same as that in the 3D model,this means αpipe1=αpipe2.Based on Eqs.(7)and(8),equivalence principle for transforming 3D severe slugging flow into 2D flow can be expressed as

2.3 Method validation

To validate the numerical method,simulations are conducted for the severe slugging in a declination pipeline-riser system according to the experimental cases presented in the reference[5],as shown in Fig.1.The diameter of the pipeline considered in this study is 0.051 m,and the declined pipe is 10.8 m-long with an inclination angle of β=-4°,and the length of the vertical pipe is 4.1 m.The result comparison between simulation and experiment is given in Tab.1.In Tab.1,T,Pampand tpdenote the severe slugging flow period,pressure fluctuation amplitude and blowout time,respectively,which are characteristic parameters of the severe slugging[5].According to Tab.1,the 2D equivalent method successfully simulates the 3D severe slugging with reasonable accuracy in the pipeline-riser system.

Fig.1 Sketch of the numerical model

Tab.1 Comparison of results between experiment and simulation

continue Tab.1

In Eqs.(1)-(9),various gas-liquid physical parameters,including density,surface tension,viscosity,specific heat and thermal conductivities,can be regarded as variable inputs.Therefore,the method can be applied for not only the air and water,but also any other gas-liquid mediums.

3 Influence of gas-liquid physical parameters on severe slugging

To study the influence of physical parameters on severe slugging,six cases considered are shown in Tab.2,where all cases are simulated with the same superficial velocities of 0.054 4 m/s and 0.136 m/s for gas and liquid respectively.The temperature is set to 298 K,and the environment pressure is 1 atm.

Tab.2 Simulation cases

3.1 The flow characteristics of the severe slugging

(a)Pipeline flow characteristics

The simulation results show that when severe slugging flow occurs,the flow in the pipeline is steadily stratified with the gas being above the liquid,as shown in Fig.2,where black and white represent liquid and gas respectively,and the dotted lines stand for the pipeline section that is not plotted.All six cases share the same gas-liquid flow pattern,but the void fractions are different.The across-sectional void fractions αsectionof all cases are shown in Fig.3,in which the chosen section is 5 m away from the pipeline entrance.

It can be seen from Fig.3 that the values of αsectionchange very little for different gases when the same liquid is considered,which implies that the properties of gas have little effects on αsection.However,they change significantly when different liquids are considered.αsectionfor the crude oil cases(Case C and Case D),the kerosene cases(Case E and Case F),and the water cases(Case A and Case B)show the maximum value,middle value,and minimum value,respectively.The reason is that the liquid viscosity and surface tension make big differences[11]in the values of αsection.

Fig.2 The stratified flow in the pipeline

Fig.3 αsectionfor Case A-Case F

(b)Riser flow characteristics

In the riser,the flow exhibits apparent periodicity,and each cycle consists of four stages:slug generation,slug production,blowout and liquid falling back,as shown in Fig.4(a)-(d).

Fig.4 Flow patterns of four stages for the severe slugging

The first stage is slug generation,during which the liquid slug increases in both the pipeline and the riser.The flow pattern of the riser comprises the liquid column and the gas column without mixing,as shown in Fig.4(a).Results show that the liquid viscosity has remarkable influence on the slug level in the riser,while the gas phase has little influence.In general,the larger the liquid viscosity is,the higher the slug level in the riser is.The reason is that the larger viscosity corresponds to the smaller αsection,which represents the smaller gas compression space in the pipeline,leading to the shorter slug in the pipeline instead of the longer slug in the riser.At the same time,crude oil has the highest level in the riser,while water has the lowest,and kerosene is in the middle.

The slug length reaches its maximum at the moment when the liquid level reaches the riser outlet,and the severe slugging steps into the second stage which is called as the slug production,as shown in Fig.4(b).At this stage,the pressure at the bottom of the riser reaches a maximum,while the gas space in the pipeline begins to expand and push the liquid slug to outflow from the outlet of the riser.In addition,for Cases C and D,high viscosity and small surface tension make the crude oil unable to completely block the pipeline,leaving a very narrow gap between the slug and the upper wall and allowing a little gas to flow into the riser in the form of small bubbles.

The blowout stage begins at the moment when the gas penetrates into the riser,which includes two processes called as liquid slug blowout and gas-liquid slug blowout respectively,as shown in Fig.4(c).The liquid slug blowout starts at the moment when the gas enters the riser and ends at the moment when the gas reaches the outlet of the riser.During this process,only liquid flows out from the outlet of the riser,and there exist both the liquid slug and the gas-liquid mixture in the riser.During the process of the gas-liquid slug blowout,the intermittent gas-liquid flow occurs at the riser outlet,and the riser is filled with the gas-liquid mixture.It can be observed from Fig.4(c)that flow patterns in the riser for all cases are slug flow with different levels,which means different blowout velocities.Under the condition of identical gas,the blowout velocity depends on the volume of gas space in the pipeline,as larger gas space leads to more gas entering,which results in faster blowout velocity.Therefore,the level of gasliquid mixture in the riser is in proportion to αsection.For the same liquid,the drift velocity of methane is larger due to its smaller surface tension and smaller density than those of air,which gives rise to higher bubble velocity.

The last stage corresponds to the liquid falling back.At a moment when the gas pressure in the pipeline is insufficient to push the liquid to flow out of the riser,the liquid starts to fall downward due to its gravity and eventually blocks the entrance of the riser.This stage has a short duration,as shown in Fig.4(d).After falling back,the liquid levels for the crude oil and kerosene are almost the same,and higher than that of the water due to the fact that the riser void fraction of the crude oil is nearly the same as that of the kerosene,while higher than that of the water at the end of the blowout stage.The deeper discussion about the riser void fraction lies in the following section.

3.2 Characteristics of pressure and cycle period

The results of the pressure fluctuation Prat the bottom of the riser are shown in Fig.5.It could be seen that Prchanges periodically,and the characteristics of Prin the four stages of the severe slugging are different.In addition,the liquid properties have remarkable effects on the pressure characteristics rather than the gas properties.

Fig.5 Pressure characteristics of the severe slugging

During the slug generation stage,the pressure almost increases linearly with the increase of the liquid level in the riser.The rate of the pressure change can be expressed aswhere ρldenotes the liquid density,denotes the rate of liquid level in the riser.In terms of ρlandthe descending order of the values foras follows respectively:water,crude oil,and kerosene under the condition of the same gas.However,under the same liquid condition,depends on the gas compressibility.Due to the smaller compressibility of the methane than that of the air,the value offor the methane is smaller than that for the air.

At the slug production stage,the riser is filled with the liquid,causing Prto maintain the maximum value Pmaxwhich corresponds to the hydrostatic head of the liquid column.The liquid densities of the water,crude oil and kerosene are in descending order,and so are the corresponding Pmax.In addition,the gas penetrations in Cases C and D show the fact that Prslightly descends.

When gas bubbles enter the riser,the blowout stage starts.This stage is characterized by a rapid decrease in the pressure.In the liquid slug blowout process,the gas enters the riser from pipeline,causing Prto decrease.Therefore,much gas flows into the riser as a result of continuous pressure decreasing.In the gas-liquid slug blowout process,the decreasing tendency of Prbecomes gentle until the blowout ends.depends on the volume of the gas space VGand ρl.The lager VGand ρlare,the more rapidly Prdecreases.Assuming that the gas is identical,both VGand ρlwill be the largest in Case A,so that itsis also maximum.VGof Case C is less than that of Case E,but the ρlof Case C is greater,as a result,theof Case C is greater than that of Case E.The gas has very little effect on

During the process of falling back,the falling liquid leads to a slight increase in the pressure in a short time,however the increase could be neglected since it has very little effect on the severe slugging.

Furthermore,the cycle period can be obtained from the Fig.5.Results show that gas prop-erties have little effect on cycle period compared with the liquid.Under the condition of the same gas,the cycle periods of the water,crude oil and kerosene are in descending order.The difference of period mainly comes from slug generation,slug production and blowout stages.During the slug generation,the liquid levels of the water,crude oil and kerosene are in ascending order,so that the time consumptions at this stage are in the reverse order.The slug production time relies on the slug length in the pipeline,and the blowout time depends on the blowout velocity,hence the total time consumptions in the two stages of the water,crude oil and kerosene are in a descending order.

3.3 Characteristics of void fraction

The void fractions of the riser is denoted by αriser,which is an important parameter for severe slugging.The characteristics of αriserin the riser are shown in Fig.6.Results show that αriserhas different characteristics at the four sages of the severe slugging.

During slug generation,Lsrgrows gradually,as a result αriserdecreases.Because gas and liquid are not mixed then,the formula αriser=1-Lsr/H can be obtained,in which H denotes the height of the riser.Thus,αriseris inversely proportional to Lsr.

During slug production,for the cases with water or kerosene as liquid,the value of αriseris zero,while for the cases with crude oil as liquid,αriserincreases slowly with small amplitude due to the gas leaking.

Fig.6 Characteristics of αriserfor the severe slugging

When the flow steps into blowout stage,the value of αriserincreases with an accelerating trend.Under the condition of same liquid and different gas,the difference of αriseris small;but under reversed situation,αriservaries remarkably.The differences in αrisercome from the differences in liquid density and gas space,and the smaller density and larger gas space make more gas entering the riser.Therefore,at the end of blowout,the αriservalues of Case A,Case C and Case E are in a descending order.

At the falling back stage,the remnant gas can still flow out through the falling liquid,which causes αriserto decrease until the next cycle.For all cases,the variance of αriseris small since remnant gas is very little.

3.4 Characteristics of liquid velocity

voutis defined as the outlet average velocity of the riser in this paper,referring to the areaweighted average velocity of all grid nodes,and equals to the slug outflow velocity.Fig.7 provides the voutgraphs of all cases and shows that all the voutshare the same trend of change.Under the condition of the same gas,voutdiffers greatly.During slug generation,voutcan be expressed asand the rule is the same asAt slug production stage,the value of voutincreases rapidly,then oscillates around some value until it becomes stable.The stable value of voutdepends on the expansion rate of gas space,and there isAccording to the ideal gas state equation,can be concluded,hence the values of voutdepend on Pmax.At blowout stage,voutdepends on blowout velocity.Consequently,vouthas the same change rule as that of VG.For liquid falling back,voutrepresents the velocity of the remnant gas,and it is not analyzed in detail in this paper due to its less importance.

Fig.7 Liquid slug velocities for Case A-Case F

4 Conclusions

Based on the consistence principle for the severe slugging formation condition,a 2D CFD method is proposed for numerically simulating the gas-liquid severe slugging in a pipelineriser system.Furthermore,the method is applied to study the influence of gas-liquid physical parameters on severe slugging,with the combinations of liquid phase chosen from water,crude oil and kerosene,and gas phase chosen from air and methane.The conclusions can be summarized as follows:

(1)The liquid viscosity has large influence on the flow characteristics of the severe slugging.The increase in the liquid viscosity will decrease the volume of the gas space by reducing the void fraction of the pipeline,which leads to the decline in the cycle period,pressure fluctuation,the riser void fraction and slug velocity.

(2)The increase in the surface tension will lead to a little increase in the volume of the gas space so that the effect of the flow parameters on the severe slugging is not significant.However,under the condition of small surface tension,the liquid slug will not fill the whole pipeline section,and hence the gas can permeate into the riser,making it more difficult to form liquid slug.

(3)The liquid density mainly affects the amplitude of the pressure fluctuation.The compressibility and the density of gas phase have a little influence on the flow characteristics of the severe slugging.However,the effect of the gas properties is not as obvious as that of the liquid properties.

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