REVIEW OF MULTIPHASE FLOW MODELS FOR...

IV Journeys in Multiphase Flows (JEM2017)March 27-31, 2017 - São Paulo, Brazil

Copyright c© 2017 by ABCMPaperID: JEM-2017-0041

REVIEW OF MULTIPHASE FLOW MODELS FOR CHOKE VALVESFernando Kenig [email protected] Luis Baliñ[email protected] de Engenharia Mecânica, Escola Politécnica, Universidade de São Paulo, São Paulo, SP, Brazil

Abstract. Choke valves are widely used at the wellhead as a safety device in order to maintain a high pressure upstreamthe valve, avoiding the killing of the well, and can be operated as a closing device to isolate one well from the productionpipeline. Pioneer authors used empirical correlations to predict the flow, based in fitting curves obtained from experi-mental data: representative examples are the correlations proposed by Gilbert (1954), Ros (1961) and Ashford (1974).Later, more accurate approaches were developed based on mass, momentum and energy conservation equations, seekingto solve them with some simplifications: the models from Sachdeva et al. (1986), Perkins (1993), Al-Safran and Kelkar(2009) and Schüller et al. (2003, 2006) can be cited as references. This paper reviews some of the models for predictingthe flow rate of a gas and liquid mixture through a choke valve, widely applied at gas wells and petroleum industry. Thebasic assumptions are reviewed, such as the thermodynamical gas evolution, slippage between the phases and consider-ation of the upstream kinetic energy and diameter ratio. Two models are chosen to be reviewed: the homogeneous flowmodel proposed by Sachdeva et al. (1986) and the model proposed by Al-Safran and Kelkar (2009). The input parametersto compare the solutions when applying each model are based on the experimental data published by Schüller et al. (2003,2006). Considerations for developing a general expression to predict the flow through the valve and discussions regardingthe discharge coefficient are presented.Keywords: Choke valve, Multiphase Flow

1. INTRODUCTION

Chokes valves are widely applied at gas well head as a safety device in order to maintain a high pressure upstreamthe valve, avoiding the killing of the well. These valves can be operated as a closing device to isolate one well from theproduction pipeline. In some cases these valves are parameterized to measure the upstream and the downstream valvepressure and with this measurements plus some numerical models is possible to predict the flow that pass through thevalve.

A choke valve can be considered similar of an orifice plate, or a venturi pipe, that is, the valve can be consideredas a restriction in the pipeline. Several authors had been studied this application and proposed different approaches topredict the flow through the valve. The firsts authors applied empirical models to predict the flow; this models were basedin fitting curves obtained from experimental data, as the relations proposed by Gilbert (1954), Ros (1961) and Ashford(1974). The other, more accurate approach, considers the mass, momentum and energy conservation equations with somesimplifications; as references the models from Sachdeva et al. (1986), Perkins (1993), Al-Safran and Kelkar (2009) andSchüller et al. (2003, 2006) can be cited.

Basically the models divide the flow in two parts: the first part comprises the upstream condition up to the contractionarea, while the second part comprises the expansion area. The analysis is completed by considering a suitable dischargecoefficient, relating the predicted and real mass flows.

Different physical effects can be considered for the different models in the converging section: a) Heat transfer betweenthe phases can be analyzed by considering the limit cases of phases evolving in an adiabatic condition or in thermalequilibrium, b) Mass transfer between the phases can be analyzed by considering the limiting cases of no mass transfer(frozen model) or equilibrium concentration and c) Slippage between the phases.

The mainly aim of this paper is to present the models applied nowadays and the inconsistencies that each modelpresent. This inconsistencies comes from the physical model development, where some physical and mathematical ap-proaches were developed in a wrong way.

2. BASIC RELATIONS

In order to review and analyze the models expressions, it is necessary to present the relations in a general way, fromwhich different approximations can be made in order to get analytical expressions.

F. Kenig & J. L. BaliñoReview of multiphase flow models for choke valves

2.1 Momentum equation

The momentum equation considering one-dimensional flow and neglecting volume and friction forces is:

W 2

A

∂

∂s

[1

A

(x+

1− xS

)(x

ρg+

1− xρl

S

)]= −∂P

∂s(1)

where A is the flow passage area, P is the pressure, S is the slip ratio, s is the axial position, W is the mass flow rate, xis the mass quality and ρg and ρl are respectively the gas and liquid density. Defining the effective density ρe as:

1

ρe=

(x+

1− xS

)(x

ρg+

1− xρl

S

)(2)

Equation (1) reduces to:

W 2

A

∂

∂s

(1

ρeA

)= −∂P

∂s(3)

Defining an effective velocity ue such as G =W

A= ρe ue, where G is the mass flux, it results:

−dPρe

= ue due (4)

For barotropic flow, that is ρe = ρe (P ), Eq. (4) can be integrated between location l (upstream) and 2 (throat) as:

−∫ P2

P1

dP

ρe (P )=

1

2

G22

ρ2e2

[1−

(A2

A1

)2(ρe2ρe1

)2]

(5)

Considering a circular cross section and defining β = D2

D1, it results:

G22 =

−2 ρ2e2∫ P2

P1

dP

ρe (P )

1− β4

(ρe2ρe1

)2 (6)

2.2 Critical condition

From Eq. (3) and assuming barotropic flow, it results:

W 2

A

[1

A

d

dP

(1

ρe

)∂P

∂s+

1

ρe

d

ds

(1

A

)]= −∂P

∂s(7)

Isolating the pressure gradient, it can be obtained:

−∂P∂s

=

W 2

ρe

d

ds

(1

A2

)1 +

W 2

A2

d

dP

(1

ρe

) (8)

From Eq. (8), the necessary condition for existence of critical flow occurs at the throat and results:

1 +G2c

d

dP

(1

ρe

)= 0 (9)


G2c = −

[d

dP

(1

ρe

)]−1

(10)

Neglecting the liquid compressibility and mass transfer between the phases (constant mass quality or frozen model) itcan be obtained from Eq. (2):

d

dP

(1

ρe

)= x2

(1 +

1− xxS

)d

dP

(1

ρg

)(11)

Substituting Eq. (11) into Eq. (10), it results:

G2c = −

[d

dP

(1

ρg

)]−1

x2(1 +

1− xxS

) (12)

2.3 Isentropic evolutions

For the frozen model, neglecting compressibility of the liquid phase, the isentropic evolution for the mixture mustsatisfy:

x dsg + (1− x) dsl = 0 (13)

where sg and sl are respectively the gas and liquid specific entropies. The entropy differential for the gas phase, consid-ering an ideal gas (P = ρg RT ) and mechanical equilibrium, can be written as:

dsg = cpgdTgTg−R dP

P(14)

R = cpg − cpv (15)

where cpg , cpv , R and Tg are respectively the gas specific heat at constant pressure, gas specific heat at constant volume,gas constant and gas absolute temperature. The entropy differential for the liquid phase, neglecting compressibility effects,results:

dsl = cvldTlTl

(16)

where cvl and Tl are respectively the liquid specific heat at constant volume and the liquid absolute temperature. Weconsider two limiting cases in which the isentropic mixture evolution of Eq. (13) is satisfied:

a) The gas and liquid phases evolve individually at constant entropy, without heat exchange between them. In this case,Tg = T and Tl = const. Notice that in this case the mixture is not at thermal equilibrium. For this case, Eq. (14) canbe readily integrated, resulting the polytropic relation:

P

(1

ρg

)n

= P1

(1

ρg1

)n

= const (17)

n = γ =cpgcpv

(18)

where ρg1 is the upstream gas density and γ is the gas heat capacity ratio.


b) The gas and liquid phases evolve at thermal equilibrium, exchanging the necessary heat power to satisfy this condition.In this case Tg = Tl = T and Eq. (13) can be written as:

[x cpg + (1− x) cvl]dT

T− xR dP

P= 0 (19)

Integrating Eq. (19) and considering an ideal gas, it results the polytropic relation of Eq. (17), where:

n = 1 +x (γ − 1)

x+ (1− x) cvlcvg

(20)

Coefficient from Eq. (20) was derived by Ros (1961).

From Eq. (2) it can be verified that the isentropic coefficients from Eq. (17) and (20) lead to barotropic flows.

3. Particular solutions

In this Section particular solutions for Eq. (6) and (12), as well as the critical condition are determined, considering aconstant slip ratio and a polytropic gas evolution. From Eq. (17) it can be written:

ρlρg

= y−1nρlρg1

(21)

where y =P

P1is the pressure ratio. From Eq. (2) the effective density can be written as:

1

ρe=

x2

ρg1

(1 +

1− xxS

)(ω S + y−

1n

)(22)

where:

ω =1− xx

ρg1ρl

(23)

Calculating different terms appearing in Eq. (6) it can be obtained:

ρe2ρe1

=ω S + 1

ω S + y− 1n

2

(24)

∫ P2

P1

dP

ρe (P )= P1

∫ y2

1

dy

ρe (y)= −P1 x

2

ρg1

(1 +

1− xxS

)[ω S (1− y2) +

n

n− 1

(1− y

n−1n

2

)](25)

Substituting Eq. (22), (24) and (25) in Eq. (6), the mass flux at the throat finally results:

G2 =

2P1 ρg1x2

[ω S (1− y2) +

n

n− 1

(1− y

n−1n

2

)](1 +

1− xxS

)(y− 1n

2 + ω S)2 1− β4

(1 + ω S

y− 1n

2 + ω S

)2

12

(26)

In order to calculate the critical mass flux, Eq. (21) is differentiated, resulting:

d

dP

(1

ρg

)=

1

P1

d

dy

(1

ρg

)= − 1

nP1 ρg1y−

n+1n (27)


Substituting Eq. (27) in Eq. (12) and rearranging, the critical flux results:

G2c =

nP1 ρg1x2

yn+1n

2(1 +

1− xxS

)

12

(28)

Equalizing Eq. (26) and (28) the critical pressure ratio at the throat yc results:

yc =

ω S (1− yc) +

n

n− 1

(1− y

n−1n

c

)n

2

(1 + ω S y

1nc

)2 1− β4

(ω S + 1

ωS + y− 1n

c

)2

nn−1

(29)

3.1 Sachdeva’s model

The model proposed by Sachdeva et al. (1986) considers a simple approach, neglecting the slippage between the phases(S = 1, homogeneous model) and the upstream kinetic energy (β = 0). With this additional assumptions, Sachdeva’sexpression for the critical mass flux is:

G2c =

(nP1 ρg1

xy2ρg2ρg1

) 12

(30)

where n is given by Eq. (20). However, there is an inconsistency when integrating the momentum equation by assumingthat the gas evolution is isentropic, resulting:

G2 =

2P1 ρg1

x

[ω (1− y2) +

γ

γ − 1

(1− y

γ−1γ

2

)](y− 1γ

2 + ω

)2

12

(31)

Equation (31) is coincident with Eq. (26) in which S = 1, n = γ and β = 0; however, it is inconsistent with Eq. (30).After substituting the gas density ratio from the isentropic relation in Eq. (30) and equaling to Eq. (31) both polytropiccoefficients appear in the determination of the critical pressure ratio, resulting:

yc =

ω (1− yc) +γ

γ − 1γ

γ − 1+n

2

(1 + ω y

1nc

)2

kk−1

(32)

Based on the experimental data it was defined a discharge coefficient for the valve with a proposed value of 0.75 whenthe choke is in a housing (close to an elbow upstream of it) or 0.85 when the choke is installed in a condition without anyflow disturb upstream the choke.

3.2 Al-Safran’s model

The model proposed by Al-Safran and Kelkar (2009) based on the Sachdeva et al. (1986) and Perkins (1993) models,adding a constant slip between the phases and including the upstream kinetic energy. The slip ratio depends of the flowtype (critical or sub-critical), valid range of the flow quality relation and the phase viscosity ratio. The slip relationproposed by Schüller et al. (2003, 2006) was applied for critical flow and the relation from Grolmes and Leung (1985)with the constants values presented by Simpson et al. (1983) was applied for sub-critical flows. One of the objectives ofthis model is correcting the inconsistence appearing in Sachdeva’s model; the gas evolution is polytropic, with the samecoefficient given by Eq. (20).


Al-Safran and Kelkar (2009) applied at his study several slip models and the conclusion was that the model with thehigher accuracy for his load cases was the model proposed by Schüller et al. (2003, 2006) for the critical condition withthe following equation:

S =

√1 + x

(ρlρg− 1

)[1 + 0.6 exp (−5.0x)] (33)

For subcritical flows Al-Safran and Kelkar (2009) considered the approach proposed by Grolmes and Leung (1985)with the constants values presented by Simpson et al. (1983) with the following equation:

S = a0

(1− xx

)(a1−1)(ρlρg

)(a2+1)(µl

µg

)a3

(34)

where a0 = 1, a1 = 1, a2 = -0.83 and a3 = 0.The present model considers the slip ratio constant during all the flow development. The author cites that at critical

condition, the slip ratio is between 3 and 4 and this condition is reliable in his opinion.For the model expressions, the assumptions are the same as in Section 3., the mass flux relation are the same as Eq. (26).

The critical pressure ratio, was determined by zeroing the derivative of the mass flux with respect to the pressure ratio andthe following expression is presented:

yc =

ω S (1− yc) +

n

n− 1

n

n− 1+n

2

(1 + ω S y

1nc

)2 1− β4

(ω S + 1

ωS + y− 1n

c

)2

nn−1

(35)

Equation (35) is not correct and does not represent the critical pressure ratio (local maximum mass flux) for β 6= 0,whereas Eq. (29) does. It is worth noticing that Eq. (35) and (29) are coincident for β = 0; as the upstream kinetic energyis usually small, de error committed by using Eq. (35) is also small, but for β ratios close to unity the error is noticeable.Unfortunately, in Al-Safran and Kelkar (2009) it is not shown an analytical expression for the critical mass flux.

It is recommended to apply a discharge coefficient with the value between 0.7 and 0.75 "to calibrate for model imper-fections and irreversible losses".

4. SENSITIVITY TO PHYSICAL EFFECTS

Based on the explanation done in the previous section, the models can be divided in two groups based on the as-sumption for the phases velocity: the homogeneous model considers the same velocity for both phases, while slip modelconsider that the phases have different velocities. Sachdeva’s model considers the homogeneous approach, while Al-Safran’s model considers the slip approach.

The models can also be divided regarding the thermodynamical gas evolution inside the mixture: the adiabatic modelassumes that there is no heat exchange between the phases, while the thermal equilibrium model assumes that the phasesexchange heat in order to have locally the same temperature. The real evolution is between these two limiting cases, andshould be closer to the adiabatic model as the mass fluxes are higher.

Regarding the consideration of the upstream kinetic energy, this effect becomes important for high beta factors, occur-ring when the valve is near the fully open condition.

In order to show the differences between the physical effects, the mass flux G as a function of the pressure ratio y ispresented in Fig. 1 to 3. The expressions used are the ones described at Section 3..

The parameters (input and calculated), taken from the data presented in Schüller et al. (2003, 2006), are shown in Table1. As water was also used in the experiments and the densities of the liquid phases are not so different, it was decidedto homogenize the liquid phases considering that they have the same velocity. The resulting expressions to calculate theliquid density and specific heat are:

1− xρl

=xoρo

+xwρw

(36)

(1− x) cvl = xo cvo + xw cvw (37)


Parameter Symbol Value UnitGas specific heat at constat pressure cpg 2.254 kJ/ (kg K)Gas specific heat at constat volume cvg 1.7352 kJ/ (kg K)

Liquid specific heat (*) cvl 4.224 kJ/ (kg K)Oil specific heat cvo 4.7424 kJ/ (kg K)

Water specific heat cvw 4.1855 kJ/ (kg K)Polytropic gas coefficient (*) n 1.0009 −

Upstream Pressure P1 741000 PaChoke Pressure (*) P2 640307 Pa

Downstream Pressure P3 643000 PaSlip (*) S 2.1562 −

Upstream Temperature T1 324.05 KGas flow quality x 0.0083 −Oil flow quality xo 0.862 −

Water flow quality xw 0.13 −Upstream diameter D 77.9 mm

Downstream diameter d 11 mmDiameter ratio (*) β 0.1412 −

Gas heat capacity ratio (*) γ 1.299 −Gas density ρg 7.7 kg/m3

Liquid density (*) ρl 817.44 kg/m3

Oil density ρo 796 kg/m3

Water density ρw 998 kg/m3

Nondimensional parameter (*) ω 1.1255 −

Table 1. Parameters used in the sensitivity studies; parameters with (*) are calculated.

Case Gc

[kg/

(sm2

)]yc [−]

Adiabatic, slip model 18402.2 0.376850Adiabatic, homogeneous model 14469.6 0.440953Thermal equilibrium, slip model 17021.0 0.444136

Thermal equilibrium, homogeneous model 13293.2 0.506953

Table 2. Critical values for different flow models.

As only the upstream and downstream pressures were measured, the choke Pressure P2 was calculated consideringthe expression proposed by Perry (1950), also used by Sachdeva et al. (1986), Perkins (1993) and Al-Safran and Kelkar(2009):

P2 = P1 −(P1 − P3

1− β1.85

)(38)

Figures 1 and 2 show the mass flux as a function of the pressure ratio respectively for the adiabatic and thermalequilibrium model; in each figure, the influence of the slip is accounted for. It can be seen that the adiabatic modelpredicts higher mass fluxes than the thermal equilibrium model; the differences in mass flux between these limiting casescan be used as an estimation of the uncertainty due to the influence of heat transfer between the phases. Besides, thehomogeneous model predicts lower mass fluxes, constituting an important systematic error that should be corrected formore reliable calculations; this behavior was also found in Campos et al. (2014) when correlating nearly incompressiblemultiphase flow data through orifice plates. It can also be observed that the critical pressure ratio shift to lower values: a)when slip is taken into account, and b) when the adiabatic model is chosen. The numerical values for critical mass fluxand critical pressure ratio for the different models are shown in Table 2.

As stated before, the upstream kinetic energy modifies the results of the critical mass flux and pressure ratio. Thedifferences are negligible for low values of β; however for higher values there can be a significant influence. As anexample, considering the same parameters shown in Table 1 with the exception of the choke diameter, which was adjustedto give β = 0.6, Fig. 3 shows the performance for the slip, thermal equilibrium model. The numerical results are shown


Figure 1. Slip influence on mass flux as a function of pressure ratio, adiabatic model.

Figure 2. Slip influence on mass flux as a function of pressure ratio, thermal equilibrium model.


0

5

10

15

20

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

G[1

03kg

/(s

m²)

]

y [-]

Upstream kinetic energy

No upstream kinetic energy

Gc

Gc

Figure 3. Upstream kinetic energy influence on mass flux as a function of pressure ratio, thermal equilibrium, slip model(β = 0.6).

Case Gc

[kg/

(sm2

)]yc [−]

Upstream kinetic energy 17667.4946 0.4607No upstream kinetic energy 17030.4001 0.4441Al-Safran’s model, Eq. (35) 17665.9325 0.4668

Table 3. Influence of upstream kinetic energy in the critical values for β = 0.6, thermal equilibrium, slip model.

in the Table 3, where it is also shown the critical values calculated with Al-Safran’s critical pressure ratio, Eq. (35). It canbe seen that the critical values are slightly different.

In order to test the performance of the different models in predicting the experimental, the predicted mass flowscorresponding to the adiabatic and thermal equilibrium model are plotted against the experimental data of Schüller et al.(2003, 2006) respectively in Fig. 4 and 5. In these figures, a discharge coefficient CD = 1 was considered.

A source of uncertainty in building Fig. 4 and 5 is the determination of the choke pressure P2, which is not measuredand is determined indirectly from the measured downstream pressure P3. As Eq. (38), relating the choke and downstreampressures, depends only on the parameter beta, it is expected some uncertainty from this simplified model . It can beobserved that the choice of flow model modifies the predicted operational condition for an individual data point. Amongthe 67 experimental points considered, the adiabatic model predicts that 40 of them are in subcritical condition, while thethermal equilibrium model predicts 30 subcritical data points.

In order to improve the correlation between the experimental and predicted mass flows, a discharge coefficient isdefined as the ratio of the measured to predicted mass flows. As the predicted mass flow comes from a model with ananalytical (or master) equation, the discharge coefficient is dependent on the physical assumptions made in the model.

The discharge coefficient is well studied for compressible single-phase flow. However, there is a considerable dis-persion in the discharge coefficients for multiphase flows, resulting parameters that can not be used to correlate otherexperimental data; for instance, in Guo et al. (2002, 2007) values as high as 1.5 were calculated in order to compensatethe systematic error appearing in the Sachdeva’s model. As the number of parameters in the multiphase problem is higherthan in single phase flow, the assumption of a constant discharge coefficient is not reasonable from a physical point ofview. An expression to determine the discharge coefficient value based on the available data for single phase, compress-ible flow would be very useful, as done in Campos et al. (2014) to correlate nearly incompressible multiphase flow data


Figure 4. Comparison between predicted (adiabatic, slip model) and measured mass flow (data from Schüller et al. (2003,2006)).

Figure 5. Comparison between predicted (thermal equilibrium, slip model) and measured mass flow (data from Schülleret al. (2003, 2006)).


through orifice plates.

5. CONCLUSIONS AND COMMENTS

This paper reviews some of the models for predicting the flow rate of a gas and liquid mixture through a choke valve.The basic assumptions are reviewed, such as the thermodynamical gas evolution, slippage between the phases and consid-eration of the upstream kinetic energy and diameter ratio. Two models are chosen to be reviewed: the homogeneous flowmodel proposed by Sachdeva et al. (1986) and the model proposed by Al-Safran and Kelkar (2009). The input parametersto compare the solutions when applying each model are based on the experimental data published by Schüller et al. (2003,2006). Considerations for developing a general expression to predict the flow through the valve and discussions regardingthe discharge coefficient are presented.

It was found that the no slip (homogeneous) model introduces a considerable systematic error, underestimating themass flow; consequently, the slip model should be chosen as more accurate.

Regarding the gas evolution, the adiabatic and thermal equilibrium models should bound the real gas evolution, beingthis a source of uncertainty. As the mass flux is higher, gas evolution is closer to adiabatic.

Evaluating the effect of the upstream kinetic energy, it can be stated that it is usually negligible except for beta factorsclose to unity (valve near the fully open condition).

Finally, the different approaches to calculate the discharge coefficient, as well as the choke pressure based on themeasured downstream pressure, are considered too simplistic and there are room to develop more realistic expressions forthem. This is a task underway.

NOMENCLATURE

A : cross sectional area, m2

CD : discharge coefficient, (nondimensional)cp : specific heat at constant pressure, J/ (kgK)cv : specific heat at constant volume, J/ (kg K)d : choke diameter, mD : pipe diameter, mγ : gas heat capacity ratio, (nondimensional)n : polytropic gas expansion coefficient (nondimensional)P : pressure, Pas : axial position, ms : specific entropy, J/ (kg K)S : slip ratio (nondimensional)x : mass quality (nondimensional)W : mass flow rate, kg/sy : pressure ratio, (nondimensional)β : diameter ratio, (nondimensional)ρ : density, kg/m3

ω : nondimensional coefficient

Subscriptsc : criticale : effectiveg : gasi : elemental data pointl : liquidm : measuredo : oilp : predictedw : water1 : upstream2 : at choke throat3 : downstream


ACKNOWLEDGEMENTS

This work was supported by Petróleo Brasileiro S. A. (Petrobras). The authors wish to thank Conselho Nacional deDesenvolvimento Científico e Tecnológico (CNPq, Brazil).

REFERENCES

Al-Safran, E.M. and Kelkar, M., 2009. “Predictions of two-phase critical-flow boundary and mass-flow rate acrosschokes”. SPE Production & Operations, Vol. 24, No. 2, pp. 249–256.

Ashford, F.E., 1974. “An evaluation of critical multiphase flow performance through wellhead chokes”. Journal ofPetroleum Technology, Vol. 26.

Campos, S.R.V., no, J.L.B., Slobodcicov, I., Filho, D.F. and Paz, E.F., 2014. “Orifice plate meter field performance:Formulation and validation in multiphase flow conditions”. Experimental Thermal and Fluid Science, Vol. 58, pp.93–104.

Gilbert, W.E., 1954. “Flowing and gas-lift well performance”. Drilling and production practice, Vol. 143, pp. 127–157.Grolmes, M.A. and Leung, J.C., 1985. Chemical Engineering Progress, Vol. 81, No. 8, p. 47.Guo, P., Al-Bemani, A.S. and Ghalambor, A., 2002. “Applicability of sachdeva’s choke flow model in southwest louisiana

gas condensate wells”. In 2002 SPE Gas Technology Symposium, Paper SPE 75507. SPE, p. 11p.Guo, P., Al-Bemani, A.S. and Ghalambor, A., 2007. “Improvement in sachdeva’s multiphase choke flow model using

field data”. Journal of Canadian Petroleum Technology, Vol. 46, No. 5, p. 22.Perkins, T.K., 1993. “Critical and subcritical flow of multiphase mixtures through chokes”. SPE Drilling & Completion,

Vol. 8, No. 4, pp. 271–276.Perry, R.H., 1950. Chemical Engineers’ Handbook. McGraw-Hill.Ros, N.C.J., 1961. “An analisys of critical simultaneous gas/liquid flow through a restriction and its application to flow

metering”. Applied Science Research.Sachdeva, R., Schmidt, Z., Brill, J.P. and Blais, R.M., 1986. “Two-phase flows through chokes”. SPE 61st Annual

Technical Conference and Exhibition, paper SPE 15657.Schüller, R.B., Solbakken, T. and Selmer-Olsen, S., 2003. “Evaluation of multiphase flow rate models for chokes under

subcritical oil/gas/water flow conditions”. SPE Production & Facilities, Vol. 18, No. 3, pp. 170–181.Schüller, R.B., Solbakken, T. and Selmer-Olsen, S., 2006. “Critical and subcritical oil/gas/water mass flow rate experi-

ments and predictions for chokes”. SPE Production & Facilities, Vol. 21, No. 3, pp. 372–380.Simpson, H., Rooney, D. and Grattan, E., 1983. “Two-phase flow through gate valves and orifice plates”. Coventry, UK.

RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.

REVIEW OF MULTIPHASE FLOW MODELS FOR...

Documents

Transcript of REVIEW OF MULTIPHASE FLOW MODELS FOR...