Modelamiento de Sistemas Multifasicos

 

PSIG 0403

The Modelin Modeling go off Multi phase Systems und under er Steady-S Steady-State tate a and nd Transient Conditions – A Tutorial Ivor R. Ellul, Geir Saether, Knowledge Reservoir, L.P., Mack E. Shippen, Schlumberger

© Copyright 2004, Pipeline Simulation Interest Interest Group This paper was prepared for presentation at the PSIG Annual Meeting held in Palm Springs, California, 20 October – 22 October 2004. This paper was selected for presentation by the PSIG Board of Directors following review of information contained in an abstract submitted by the author(s). The material, as presented, does not necessarily reflect any position of the Pipeline Simulation Interest Group, its officers, or members. Papers presented at PSIG meetings are subject to publication review by Editorial Committees of the Pipeline Simulation Interest Group. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of PSIG is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, Pipeline Simulation Interest Group, P.O. Box 22625, Houston, TX 77227, U.S.A., fax +1-713-586-5955.

THE STEADY STATE A PPROACH Two distinct approaches are available to the petroleum engineer in accounting for the behavior of multiphase flow systems. The first is a global approach that relies on empiricism in developing simplified models that contain parameters which are evaluated from experimental data. The second is a continuum approach in which more complex physically-based models are used to describe the flow  phenomena.

 A BSTRACT 

Empirical Methods

The search for oil and gas continues to progress towards increasingly hostile environments. Environments such as found in deepwater  preclude the ability to efficiently separate the fluid phases prior to export. As a result, multiphase transportation has become commonplace with systems being designed using integrated flow assurance techniques.

An empirical approach to the problem primarily aims to produce a correlation valid at least over the entire range of measured data (and hopefully beyond this range). The parameters of the model are derived from the measured data. The selection of correlating variables is often decided on the basis of dimensional analysis. For example, the pressure drop in two-phase flow may be expressed as a function of at least six dimensionless variables, one set of which includes:

Additionally, pipelines that had been designed for single phase flow are now expected to cope with the transport of multiple phases. With the continuous variation in production, these pipelines tend to operate under both steady-state and transient conditions. The requirement to model these systems is, therefore, critical for adequate field development planning.

Froude Number - N FFr r  

V  gl

Reynolds Number - Re This paper will present a tutorial focusing on the complex analysis of multiphase flow in pipelines with an emphasis on the tools currently available for modeling purposes.

The analysis of multiphase flow phenomena in pipeline systems is usually classified along two levels of complexity. The first is that associated with steady state flow where there are no major changes transgressing the pipeline network. The second related to transient or dynamic flows where the flow behavior is changing on a regular and significant basis. These situations will be dealt with in turn.

VD ρ 

µ  µ l

Viscosity Ratio

µ g

The tools selected for use during the tutorial include Pipesim and OLGA.

INTRODUCTION 

 

Weber  Number- N W Wee 

2 V l ρ 

Density Ratio

 ρ l

 

σ 

 

 

g

Flow rate Ratio

 

 ρ   M l  M g

 

The functional form of the two-phase friction factor, thus, may be expressed as follows:

⎛ ⎜ ⎝

 f n ⎜ N Fr , Re, N We ,

 ρl  ρ g

,

µ l  M l , µ g  M g

⎞ ⎟⎟ = 0  (1) ⎠

Empirical methods usually involve the prediction of mixture density  ρm and a representative r epresentative friction factor, f m. The mixture density may be defined in terms of the in-situ volume fraction fr action of liquid θ l as follows:

 ρ m

= ρlθ l + ρ g (1 − θ l )  

(2)

 

2

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

Some authors of empirical correlations select an appropriate functional form for equation 1, and proceed to back calculate a holdup function that best fits experimental data for two-phase  pressure drop. The Hagedorn and Brown, [1], correlation for flow in vertical pipes is based on such an approach. Other investigators such as Beggs and Brill, [2], and Dukler, [3], have correlated both variables (f m , θ l) as functions of gas and liquid flow rates, pipe geometry, fluid PVT and transport properties, among other variables.

For vertical flow, the stratified flow regime cannot exist as there is no  preferred direction for the liquid to settle. An empirical flow regime map developed by Aziz, et al, [6], for vertical upward flow is shown in Figure 3. The coordinates used in this vertical map are:  Nx = VsgXA  (5)

Empirical correlations have been successful in terms of:

 X A

1. 

Enabling models for particular flow conditions to be formulated quickly.

2. 

Being amenable to tuning to yield results of reasonable accuracy over well-defined ranges of operating conditions.

3. 

Being relatively easy to employ as design tools.

Table 1  lists some of the more successful and widely-used correlations with recommended areas of application. The limitations of empirical techniques stem from some or all of the following:

 

Individual equations tend not to apply with sufficient accuracy to the broad range of flow conditions usually encountered in  practice.

 

The use of a number of different correlations to predict the hydraulic conditions of the dominant flow regimes in a pipeline system can result in numerical difficulties and/or discontinuous  predictions.



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⎛  ρ g ⎞ = ⎜⎝  ρ a ⎠⎟

NY = VsLYA  (6)

0.333

⎛ ρ Lσ wa ⎞ = ⎜⎝  ρ wσ  ⎠⎟  

Y  A

Y A   (7)

0.25

  (8)

Pressure Pre ssure Drop Calculation of pressure drop in two-phase flow lends itself better to computer than hand calculation. A method suggested by the American Gas Association, [7], can serve as a basis for hand calculation generated by Dukler, [8], with elevation pressure drop correlation by Flanigan, [9].

Frictional Component Using the Dukler frictional pressure drop calculation method, the frictional pressure drop is given by the equation: 2



 



Because empirical techniques do not address the complex  physical phenomena that can can occur during multiphase flow, extrapolation beyond the specific conditions for which the correlations were developed may render them unreliable.

 f n f ttppr ρ kVm Lm

∆P f  = where

 ρ k 

=

 ρ L λ 2  H Ld

The generation of flow regime maps.

2. 

The development of regime-specific correlations for liquid holdup and pressure loss prediction.

+

 ρ g (1 − λ )

2

(1 − H Ld  )

  (10)

and

λ  =  =

Empirical techniques were an improvement on the earlier homogeneous methods, [4], in so far as they provided a basis for: 1. 

(0.14623)d    (9)

Q L Q L

+ Qg

  (11)

The single phase friction factor,  f n, can be obtained from the correlation:

 f n

= 0.0056 + 0.5 ( Re y )

−0.32

  (12)

The mixture Reynolds number, Rey, is calculated according to the

Flow Regime Determination Several empirical flow regime maps have been presented that determine vapor-liquid flow patterns as a function of fluid properties and flow rates. Figure 1 shows schematics of these flow patterns. One map commonly used was developed by Mandhane, et al, [5], Figure 2. The coordinates for the map are:

equation:

Re y

Care should be taken in the interpretation of these flow maps as the regime boundaries are strongly affected by pipe inclination. In  particular, horizontal flow regime maps must not be used for vertical flow and vice-versa.

(124.0 ) ρ kVm d    µ n

  (13)

Calculation of this Reynolds number requires determination of a mixture velocity, Vm, and mixture viscosity  µn. These quantities can  be determined from:

VsL = superficial liquid velocity = Q L/A (3) Vsg = superficial liquid velocity = Qg/A (4)

=

Vm = VsL + VsG  (14)

µn

= µ L λ + µ g (1 − λ )  

(15)

The two-phase friction factor ratio,  f ttpr  pr   representing a two-phase frictional efficiency can be determined by reference to Figure 4 or by the equation:

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

⎡ ⎤  y  f tpr  = 1 + ⎢   (16) 2 3 4⎥ ⎣1.281 − 0.478 y + 0.444 y − 0.094 y + 0.00843 y ⎦

⎛   ρ L ⎞  N d  = 10.073   d ⎜ σ  ⎟ ⎝ ⎠

where y = - ln(λ  ln(λ )

 N  L

The remaining quantity to be calculated is an estimate of the liquid holdup, HLd. This holdup can be estimated using Figure 5. This figure gives liquid hold-up as a function of λ  and   and Rey. The Rey line can be used as a first estimate in the iteration process.

Elevation Component The elevation component of pressure drop can be found using the Flanigan method. In this method, the elevation component is calculated using the equation:

∆Pe =

 ρ  L H Lf  144

(17)

 H  Lf 

=

⎛ 1 ⎞     µ L ⎜ = 0.15726 3 ⎟ ⎝  ρ Lσ  ⎠

  (23)

0.25

  (24)

= (28.80) H Le d 2 Lm   (25)

As is the case with the pressure drop calculations, holdup fractions should be calculated on a segment-by-segment basis.

where HLf  is determined from Figure 6 or calculated according to the formula:

1

0.50

The liquid holdup fraction, HLe , is the fraction of the flow area of the  pipe occupied o ccupied by the liquid. To calculate the liquid inventory o off the  pipe, IL, the pipe internal volume is multiplied by this holdup fraction.

 I L

ΣZ e  

3

  (18)

Mechanistic Me chanistic Me Methods thods

The term Ze  is the vertical elevation rise of a hill. The rises are

The development and application of a phenomenological description of the individual phases constituting a multiphase mixture generally requires that a mechanistic transport equation be written for each of the phases within the system, [11]. Best estimate sub-models are used

summed, no elevation drops are considered. One should keep in mind that this may lead to errors in downhill sections of pipelines. The overall two-phase pressure drop is given by:

for parameters which are substituted into these equations. The number of sub-models differs for each flow regime, and the submodels may be mechanistic or correlational, [12].

1.006

1 + 0.3264 (V sg )

∆Pt = ∆Pe + ∆Pf   

(19)

The advantages claimed for this approach include:

Accuracy of calculation is improved if the above calculations are  performed on a segment-by-segment basis. basis.

Liquid Holdup The liquid holdup correlation given in Figure 5 is intended only for use in the Dukler friction pressure drop calculation. A correlation by Eaton et al, [10], is better suited for liquid holdup determination in liquid inventory calculations.

1. 

The transitions in flow regime maps have an analytical basis and are more successful in facilitating comparisons with a wide range of data.

2. 

Flow regime models are particularly useful for treating effects of  pipe inclination.

3. 

In general, mechanistic formulations provide a means to assess the uncertainty in the predictions of the analysis.

4. 

The models, being closer to first principles, are not only more widely applicable than the empirical correlations currently

The correlation is shown in Figure 7. In this figure, the holdup fraction, HLe , is plotted as a function of the dimensionless group, NE.

available but are also easier to upgrade/amend as, and when, improved sub-models (e.g., for wall-liquid, interfacial shear)  become available. available.

0.05

⎛ Pavg ⎞ 0.1 1.84 ( N Lv ) ⎜ P ⎟ ( N L ) ⎝ b ⎠  N  E  = 0.0277  N gv ( N d  ) 0  .575

5.    (20)

Mechanistic modeling can incorporate all of the significant variables identified via the observation, study, and mathematical modeling of the physical p hysical mechanisms governing multiphase flow in pipes.

The cost associated with the use of these methods is attributable to:

 N Lv

 N gv

  ⎛ ρ L ⎞ = 1.938   V sL ⎜ σ  ⎟ ⎝ ⎠   ⎛ ρ L

= 1.938   V sg ⎜ σ  ⎝

⎞ ⎟ ⎠

0.25

  (21)

0.25

 

The greater amount of understanding / knowledge needed n eeded to apply them.

 

The increased complexity of formulation and implementation and consequent implications for solution speed.





  (22)

The mechanistic formulation commonly proceeds along the following solution sequence:

 

4

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

1. 

Predict the flow regime corresponding to the expected / actual operating conditions of the pipeline.

2. 

Employ specific mechanistic models / sub-models to predict:

 

Liquid holdup

 

Interfacial friction factor

 

Slug/bubble characteristic characteristicss







3. 

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Combined Momentum Balance

τ wG

S G  AG

 

− τ wl

S L AL

⎛ 1 + τ i S i ⎜ + ⎝ AL

⎞ ⎟ AG ⎠ 1

(28)

+ ( ρ  L −  ρ      G  ) g sin α  = 0

Employ mechanistic model to predict total pressure gradient.

Flow Regime Determination

The shear stress terms may be evaluated using the following constituitive equations:

The prediction of flow regime transitions is a central element of the mechanistic modeling modeling approach. Taitel and Dukler[13] were the first to propose horizontal and near-horizontal flow regime transition criteria based on physical mechanisms governing the flow geometry. Their method involves the development of a series of dimensionless groups representing the force balances acting on each fluid phase. Mechanisms for transitions based on stability analysis coupled with closure relationships allows for the determination of flow regime in terms of these dimensionless groups.

Gas-Wall shear:

τ wG 

  ρ G vG2

=  f G

(29)

2

 Liquid-Wall Shear:

 

More recently, Zhang et al [14] proposed another approach based o on n the premise that slug flow incorporates and shares transition  boundaries with all other flow regimes. Transitions are determined hydrodynamically by treating the slug and filmcombined zone as the control volume when solving the continuity momentum equations. Table 2  summarizes a series of suggested mechanistic methods for flow regime determination Table 3  lists the individual flow regime transitions employed to identify any one of the four main flow regimes for the given range of inclination.

Liquid Holdup and Pressure Gradient The Taitel and Dukler model constructs momentum balances for the gas and liquid phases comprising stratified flow, incorporating shear stress terms based on the defined flow geometry in Figure 8. By equating the pressure gradient terms, a combined momentum balance can be formulated, yielding yielding an implicit model for li liquid quid holdup. The  pressure gradient may then be determined from the momentum  balance equation for either either phase.

 Liquid Phase Momentum Balance:

dP  ⎞   i +  ρ  L A L g sin α    =0 −  A L ⎛  ⎜ ⎟ − τ wl S  L +  τ i S  ⎝ dX  ⎠

(26) 

=  f  L

(30)

2  Interfacial Shear:

  ρ   (v − vi ) τ i =  fi G G 2

2

(31)

A number of methods have been proposed to evaluate the friction factor terms appearing in tthe he shear st stress ress equations. Taitel aand nd Dukler assumed the interfacial friction factor to be equal to the gaswall friction factor, though more recent models treat this term independently. Subsequent studies have expanded on the work of Taitel and Dukler to formulate models for calculating liquid holdup and  pressure losses for other flow regimes. While these models apply the same concept offor solving combinedand momentum balance,relationships. they require new definitions flow ageometry updated closure Such models are presented by Zhang et al [14] and Xiao, Shoham, and Brill [15]. The suggested mechanistic methods for the prediction of the  parameters of the liquid liquid holdup and pressure gradient models for each flow regime are summarized in Table 4.

THE TRANSIENT A PPROACH 

Gas Phase Momentum Balance:

dP  ⎞   i +  ρ G AG g sin α    =0 − AG ⎛  ⎜ ⎟ − τ wg S G +  τ i S  dX  ⎝   ⎠

τ wL 

2  ρ    L v L

Formulation (27) 

The dynamic modeling of two-phase flow systems has, over recent years, become commonplace. This has been a direct resul resultt of stringent requirements to adopt the latest technology in health, safety,

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

and pipeline integrity analysis [16] and [17], as well as the emergence of complex operational situations that demand such technology [18]. The more widely accepted route to the derivation of the averaged multiphase equations is that taken by such workers as Ishii, [19], Banerjee and Chan, [20], and Drew and Lahey [21], where the field equations for the individual phases within the two-phase mixture are obtained by averaging of the respective local instantaneous equations for each phase – Figure 9. As a consequence of the averaging of terms relating to the instantaneous conditions across the interface between the phases – Figure 10, new expressions that lack formal description are introduced. Closure models for such terms thus become necessary. Once these terms are established the derivation of the individual  phase conservation is complete. complete.

The Multifluid Model

 present, liquid droplets, and a separate one for the liquid film. One energy conservation equation is employed.

Conservation of Mass: Gas Phase

1 ∂ ∂ ( fG ρG ) = − [ AfG ρG vG ] + ψ G + GG   A ∂z ∂t

 

the gas phase

 

the liquid film phase

 

the liquid droplets





Two momentum equations are, however, implemented:

 

A combined one for the gas and liquid droplet phase

 

A separate one for the liquid film.





A mixture energy conservation equation is written for the overall mixture. The system is, therefore, represented by – Figure 11:

 



Cross sectional area, A

 

Void fraction, α 

 

Liquid film fraction, β 

 

Liquid droplet fraction, γ 







Interphase mass transfer – Figure 12  – is incorporated within the system of equations:

 



Droplet entrainment, ψe 

∂ 1 ∂ ( f L ρ L ) = − [ Af L ρ  LvL ] −ψ G ∂t A ∂z

−ψ e + ψ d + GL    

(33)

 f D f L

+

fD

+ ψ e − ψ d + GD    

(34)

Combined Gas/Droplets  Gas/Droplets 

∂ ⎛ ∂ p ⎞ 1 ∂ ( f  ρ v + f ρ v ) = − ( f G + f D) ⎜ ⎟ −   ⎡⎣ Af Gρ Gv2G+ Af ∂t G G G D L D ⎝ ∂z ⎠ A ∂z −λG

1

+ψ G

2

ρ G vG v G  f  L

 f L + f D

SG

4 A

− λi

1 2

ρG vR v R

S i

4A

+ [ f Gρ G + f Dρ L] g cosα

ρ  Lv2D⎤⎦

D

 

(35)

va + ψ e vi −ψ d v D

 

 Liquid Film

∂ ⎛ ∂ p ⎞ 1 ∂ ( f L ρ L vL ) = − ( f L ) ⎜ ⎟ −   ⎡⎣ Af L ρ L vL2 ⎤⎦ ∂t ⎝ ∂z ⎠ A ∂z

Mass transfer (flashing), ψg 

−ψ G

Mass sources, Gl , Gg 

fD

Conservation Conserva tion o f Momentum:

 

 

+

where f G, f L, f D  are the gas, liquid film, and liquid droplet volume fractions, ρ, v, p are the density, velocity, and pressure, and A is the  pipe cross-section. Subscripts G, L, i, and D indicate gas, liquid, interface and droplets respectively. ψG  is the mass transfer rate  between the phases, ψe, and ψd  are the entrainment and deposition rates and Gx relates to a source for phase x, if present.

Droplet deposition, ψd 



f L

1 ∂ ∂ ( f D ρ D ) = − [ Af D ρ  L vD ] −ψ G t A z ∂ ∂

 



 f L

 Liquid Droplets

−λ L



(32)

 Liquid Film at the Wall

The OLGA model, [22, 23] is based on an extension to the traditional two-phase model. Separate continuity equations are written for: 

5

1 2

ρ L vL v L  f L

 f L

+

fD

va

S  L

4 A

−

+ λi

1 2

ρ G vR vR

S i

+

 

f L ρ L g cos α

4A ∂f  f L d ( ρ L − ρ G ) g L sin α − ψ e vi ∂z

 

+ ψ d vD  

The conservation equations that comprise the OLGA model are derived in two-fluid format. Separate (three) continuity equations are written for the gas, liquid bulk, and liquid droplets. Two momentum

where α  is   is the pipe inclination to the vertical. S G, S  L, and S i are the wetted perimeters for the gas, the liquid and the interface respectively. The velocity, va, is equal to the liquid, droplet or gas velocity depending on whether evaporation or condensation occurs.

equations are implemented; one combined equation for the gas and, if

The relative velocity, vR , is defined by a distribution slip formula

(36)

 

6

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

given in reference [23]. The interphase velocity, vi, is approximated  by v L.

PSIG 0403

Interfacial Mass Transfer Phase transfer is a function of pressure and temperature:

The Pressure Equation

ψG

The properties of the fluid traversing the pipeline are assumed to  behave in accordance with with an equation of state state::

 ρ f

=

ρ f ( p,T , Rs )  

=

⎡⎛ ∂ Rs ⎞ ∂ p ⎛ ∂Rs ⎞ ∂p ∂z ⎤ ⎢⎢⎜⎝ ∂ p ⎟⎠T ∂t + ⎜⎝ ∂p ⎟⎠T  ∂z ∂t  ⎥⎥   ψ G = ⎢ (mG + mL + mD ) ⎥ ⎢ + ⎜⎛ ∂ Rs ⎟⎞ ∂T  + ⎜⎛ ∂Rs ⎟⎞ ∂T ∂z ⎥ ⎢⎣ ⎝ ∂ p ⎠ p ∂t ⎝ ∂T ⎠ p ∂z ∂t ⎥⎦

(37)

mG mG

+ mL + mD

 

(41)

ψ G may be expanded by a Taylor series in p, T , and Rs:

where the gas mass fraction, R s, is defined by:

 Rs

= ψ G ( p, T , Rs )  

(38)

The term

⎛ ∂ Rs  ⎞   ∂p ⎜⎝ ∂ p ⎟⎠ ∂t    represents T 

(42)

the mass transfer from a mass

 present in a section due to pressure change in that section. The term

mG, m L, and m D are the specific mass of gas, liquid film, and liquid droplets respectively.

⎛ ∂ Rs  ⎞   ∂p ∂z ⎜⎝ ∂ p ⎟⎠ ∂z ∂t    represents mass transfer due to mass flowing from T 

Using the continuity equations (32) to (34) together with equations (37) and (38), one derives a single equation for pressure for the

one section to the next.

system.

The interface mass transfer model takes into account condensation, evaporation as well as retrograde condensation.

⎡  fG ⎛ ∂ ρG ⎞ ⎞ ⎤ ∂p 1 − fG ⎛ ∂   ρ L + ⎢ ⎜ ⎟ ⎜ ⎟ ⎥ = ρ L ⎝ ∂p ⎠T , R ⎥ ∂t  ⎢⎣ ρG ⎝ ∂ p ⎠T , R ⎦  1   ∂ ( Af L ρ L vL )   1 ∂ ( AfG ρ G vG  ) − −    A ρG Aρ L ∂z ∂z s

+GG

1  ρG

+ GL

C ASE STUDY 

s

1 ρL

+ GD

(39)

System Descriptio Descriptio n

1

Located in a water depth of 500 ft., a host platform is to receive gas from three remote platforms and export the mixture 100 mi. to shore. Figure 13 provides a schematic of the pipeline system with Figures  14 to 17 depicting the profiles of each branch in the pipeline system. The contract delivery pressure for the onshore terminal is set at 1000  psia and the Maximum Allowable Operating Pressure in the export line is 1500 psia. All compression will occur at the remote platforms with a maximum discharge pressure of 2000 psia. A brief description

ρ L

Equation (39) together with the momentum equations (35) and (36) are discretized and solved simultaneously for pressure and phase velocity. This is done sequentially allowing for step-wise time integration.

of the 3 source platforms is given 6. in Table 5  with expected gas compositions presented in Table

The Energy Equation An energy conservation equation for the mixture is derived as follows:

∂⎡ ⎛ 1 1 1 ⎞ ⎛ ⎞ ⎛ ⎞⎤ m E + v2 + gh gh⎟ + mL ⎜ EL + vL2 + gh gh⎟ + mD ⎜ ED + vD2 + gh⎟⎥ = ∂t ⎣⎢   G ⎝⎜ G 2 G 2 2 ⎠ ⎝ ⎠ ⎝ ⎠⎦ ∂⎡ ⎤ 1 1 1 − ⎢mGvG ⎛⎜ HG + vG2 + gh⎞⎟ + mLvL ⎛⎜ HL + vL2 + gh⎞⎟ + mDvD ⎛⎜ HD + vD2 + gh⎞⎟⎥ ∂ z ⎣   ⎝ 2 2 2 ⎠ ⎝ ⎠ ⎝ ⎠⎦ + HS  + Q  

Where  E  is   is the internal energy per unit mass,  H  is   is the enthalpy, h is S  is the enthalpy from mass sources, and Q is the heat the elevation, H S  transfer from the pipe walls.

(40)

During Phase 1 of the development, the host platform will receive fluids from Platform C, with Platforms A and B coming online in the future. Since the gas arriving from Platform C ha hass the highest condensate yield, and the initial phase of development will entail the lowest gas rates in the export line, the liquids handling capacity on the onshore receiving plant will be most constrained during the initial  phase. Thus, the design of the slug catcher will consider only fluids  produced through the export line originating from Platform C. The required export pipeline size will, however, need to consider the anticipated gas rates during phase 2 of the development, when Platforms B and C are brought online. o nline.

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

Steady State Analysis

7

The average liquid rate during the transition period can be determined as follows:

 Export Line Sizing The required export pipeline diameter was evaluated with several multiphase flow models for a gas flowrate of 1000 mmscfd, representing a combined fluid mixture mixture from the three platforms. The design is based on a delivery pressure of 1000 psia and a maximum allowable line operating pressure of 1500 psia. As illustrated in Figure 18  and Table 7, assuming homogeneous flow (no-slip model), the required pipeline pipeline diameter is 32”. The OLGA-S and Xiao mechanistic models also indicate that a pipeline ID of 32” is sufficient, while the empirical methods suggest larger  pipe sizes are required. The larger line size suggested by the empirical correlations can be attributed to a higher predicted degree of gas-liquid slip, resulting in higher liquid holdup and increased  pressure drop.

Tieback Line Sizing The required pipeline sizes for the 3 pipelines flowing to the host  platform are calculated using the OLGA-S model. The OLGA-S calculated pressure at the host platform is 1478 psia for 32 inch export pipeline, which serves as the delivery pressure for each of the lines flowing to the host platform assuming no pressure losses to

Q Lt = Q Lf +(HL t r = HL

tot-F

/Q

Lf

tot-i

 

- HL

tot-F

)/ t r    

(43) (44) 

Where: QLt  QLf   HL tot- ii   HL tot-F  tr  

average liquid rate during the transition period final liquid rate total liquid holdup volume in line at initial gas rate total liquid holdup volume in line at final gas rate transition time ~ liquid residence time at final flowrate

As shown in Figure 19  the total liquid holdup in both the Tieback connecting platform C to the host platform and the export line is 51,340 BBL at 300 mmscfd and 24,340 BBL for a gas rate of 500 mmscfd. The difference (27,000 BBL) will repre represent sent the total surge volume associated with the ramp-up. Figure 20  displays the initial liquid flowrate at the receiving facility, followed by the average liquid flowrate during the transition period, and finally stabilized flow at the higher gas rate. The transition period is calculated calculated to last approx. 53 hours during which the average liquid rate is estimated to  be 19,150 STBD. Figure 21 shows the slug catcher inventory during the transition period period assuming a draina drainage ge rate of 12,500 STB STBD. D. The

occur at the host platform. platform. The required line siz sizes es as shown in Table 8  represent the smallest possible diameter that results in a source  pressure of less than 2000 psia. psia.

 peak inventory occurs at the end of the transition period and indicates that a slug catcher volume of approx. 23,530 BBL (19,530 STB liquid) is required to handle the ramp-up surge.

 Ramp- Up

 Pigging

During Phase 1, the steady-state liquid rate at the receiving terminal will be 9,080 STBPD based on a gas production rate of 500 mmscfd from platform C. For Phase 2, the st steady-state eady-state liquid rate at the receiving terminal increases to 10,000 STBPD based on a gas  production rate of 1000 mmscfd from all all 3 incoming pipelines. pipelines.

The volume of liquid expelled at the receiving terminal as a result of  pigging the export line can be estimated estimated using steady-state analysis analysis as a first order approximation.

It is anticipated that the gas rate from Platform C may occasionally be reduced to 300 mmscfd with a corresponding liquid rate of 5430 STBPD. Therefore, the onshore faci facility lity will be si sized zed to accommodate a ramp-up scenario using Cunliffe’s method [24] based on the results from steady-state simulation. This approximation iiss later compared to the more rigorous calculation of surge rate  performed with transient simulation. simulation. Cunliffe’s method applies a simple material balance to predict the liquid surge rate due to an overall gas rate change for condensate  pipelines. For ramp-up cases, as the gas rate increases, the total liquid holdup in the line will drop owing to less slippage between the gas and liquid phases. phases. The liquid residing in the line is th therefore erefore accelerated to the equilibrium velocity at the final gas rate and thus expelled at a rate higher than the final equilibrium liquid rate for the duration of the transition transition period. The transition period is assumed to  be equal to the residence time at the final gas rate, that is, the time it takes the liquid to travel from one end of the line to the other. Calculations are performed in terms of actual volumetric flowrates, while the results results are pres presented ented in term termss of standard conditions. In this example, approx. 20% of the liquid volume at onshore terminal conditions (1000 psia and 65F) will flash to the gaseous phase at standard conditions.

When a sphere (pig) is introduced into the line, it will gather in front of itself a liquid slug comprised of the liquid that is flowing slower than the mean fluid flowrate in the pipeline at any given point. Thus the crucial value that determines Sphere Generated Liquid Volume (SGLV) is the Slip Ratio (SR), which is the average velocity of the fluid divided by the velocity of the liquid. If the liquid and gas move at the same velocity, the slip ratio will be 1, i.e. there is 'no slip'  between the phases. In this situation the sphere will not collect any liquid, so the SGLV will be zero. Since the liquid flows slower than the gas, i.e. the slip ratio is greater than 1, some of the liquid in the  pipeline will collect in front of the sphere to form the SGLV. The amount of liquid that accumulates is summed for each segment of  pipe, and the duration of the liquid expulsion can be calculated assuming that the liquid velocity ahead of the pig is equal to the steady-state mixture velocity at the outlet. This steady-state approach is based on two key assumptions: 1) The sphere travels at the mixture velocity of the fluid, and 2) no leakage of liquid occurs behind the sphere (ie. Liquid displacement is 100% efficient). These assumptions w will ill tend to overestimate th thee SGLV, yielding a conservative prediction. In the current example, the SGLV is calculated for the phase 1 turndown rate of 300 mmscfd with the sphere introduced at the host  platform. The velocity of the sphere is nearly constant thoughout the export line at approx. 8 ft/s. ft/s. The total volume of liquid swept by the

 

8

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

sphere is 24,690 STB corresponding to a surge time of 52 min. at the slug catcher. Given a drainage rate of 12,500 STBD at the slug catcher, the required volume at flowing conditions is 24,315 bbl (20,178 STB).

Transient Tra nsient simulations The system described in the current case study will be investigated from a transient perspective. Two cases will be presented:

1.  Flow is deriving from Platform C at 300 mmscfd and on through the export line. After a long period of steady flow, the flow is ramped up to the design flowrate of 500 mmscfd.

2.  The export flowline is pigged after it has been flowing at 300 mmscfd with fluid from Platform C only The network is designed for a gas flowrate of 1000 mmscfd, and 10,000 STBD of condensate. The slug catcher liquid handling is 25% over the condensate design flowrate, i.e. 12,500 STBD. Parameter sensitivity analysis was performed to study the influence on the slug catcher size of varying liquid off take flowrates.

 Ramp up

This exercise is performed mainly to determine the size of the slug catcher at the land terminal, and the sensitivity of this size to some of the main operational variables. As seen in Figure  22, when the gas flowrate is increased, the higher gas velocity will sweep the lines for excess liquid content. As a result, a total of approx. 31,500 BBLS of liquid will be expelled from the flowline. Figure 23 shows the total liquid contents of the flowline from Platform C, and the export flowline. In Figure 24 the resulting liquid flowrate into the slug catcher is shown. The peak flowrate is approx. 38,000 STBD. With a design flowrate of 12,500 STBD, the liquids must be stored in the slug catcher for a period of time before they can be processed in the downstream process plant. Based on the simulator results, the slug catcher must have a minimum working volume of approx. 21,100 STB. If the liquid off take flowrate was different, it is expected that the slug catcher size will be different as well. To investigate, two additional off take flowrates were run, one at 10,000 STBD and one at 20,000 STBD. The required slug catcher sizes based on the maximum liquid volumes shown in Figure 26 are plotted as a function of the off take flowrate in Figure 27. As seen in these figures, the required slug catcher is approximately 26,000 STB for the off take flowrate of 10,000 STBPD, and approximately 10,500 STB for the off take flowrate of 20,000 STBPD. Another parameter sensitivity that was studied relates to the slug catcher size for various ramp-up scenarios. The case shown above is  based on an instantaneous ramp-up from 300 to 500 mmscfd at Platform A. Two additional cases were run: 1. 

One where the ramp-up was over 12 hours, and

2. 

One where the ramp-up was executed over 24 hours

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As expected, the required slug catcher size is dependent on the manner in which the flow is ramped-up. The faster the flow is increased, the larger the slug catcher needs to be. The results from this analysis are shown in Figures 28 to 31. As seen in these figures, the required slug catcher iiss approximately 20,700 STB for the rampup time of 12 hours, and approximately 19,900 STB for the ramp-up time of 24 hours.

 Pigging Pigging is performed on the export flowline. Prior to pigging, the export flowline has been flowing with gas from Platform C at 300 mmscfd. The pig is inserted at 12 hours, and the gas flowrate is kept steady at 300mscfd. The liquid drainage flowrate from the slug catcher is 12,500 STBD. Figures 32  to 34  depict such dynamic elements as gas and liquid flow rate into the slug catcher during the  pigging cycle as well as the actual pigging velocity. Figure 35 shows the total liquid content in the export flowline. As seen in Figure 36, the slug catcher needs to have a working volume of 30,700 STB or more to handle the liquid pushed out by the  pig when the pig is arriving.

DISCUSSION  In analyses involving multiphase flow calculations one has to be highly cognizant of the tools and methodology adopted and ensure that they are fit-for purpose. For example, let us consider the calculation of slug catcher size using a number of steady-state methods. Figure 37  shows the calculated slug catcher size requirement expressed in terms terms of STB of condensa condensate. te. The OLGA-S correla correlation tion  predicts a volume requirement for the ramp-up of about 19,530 STBD and 19,450 for the pigging p igging case, whereas the Xiao mechanistic model suggests a smaller slug catcher volum volumee requirement. The Beggs-Brill correlation indicates a required slug catcher volume of approx 37,800 STBD for the pigging case, but does not predict that the surge associated with the ramp-up is beyond the drainage capacity of the separator. Similar results are suggested by the Dukler-AGAFlanigan method using the Eaton holdup correlation; a slug catcher size of approx. 23,260 STBD is calculated for the pigging case, but

the surge resulting from ramp-up is minimal. These results suggest that the empirical methods predict higher amounts of slip, resulting in higher total holdup volumes in the  pipeline, and thus higher pigging volumes. However, the liquid holdup predictions made by the empirical methods are less sensitive to changes in gas rate than the mechanistic models, and therefore do not predict high high surge rates for ramp-up scenarios scenarios.. This example illustrates the difficulty in modeling slip effects for low-liquid loading situations (no-slip liq. Vol ~ 1% in this case) as observed by  previous investigators [25]. A more rigorous transient analysis predicts a required slug catcher volume of 21,100 STBD for the ramp-up case, which is approximately 8% larger than that predicted using Cunliffe’s method applied to the OLGA-S OLGA-S model. However, the required volume from transient pigging analysis suggests that a slug catcher volume of 30,700 STB is required, which is 58% larger than the 19,450 STB calculated using a steady-state approach.

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

Steady-state analysis can provide a first order approximation for estimating liquids handling capacity under various operating scenarios. This is parti particularly cularly useful for evaluating a numbe numberr of field development options with parametric studies and identifying future situations where capacity constraints will be most limiting. However, a more rigorous transient analysis is required to more accurately ascertain capacity requirements and account for timedependent operating practices practices used to manage liquids. For example, transient analysis is needed to quantify the reduction in the required slug catcher size resulting from a graduated, rather than instantaneous, ramp-up of production. Figure 38 illustrates the sensitivity of flowline size as a function of LGR expressed in terms of the ratio of calculated pipe diameter using a 2-phase correlation to the caculated pipe diameter for no-slip (D/Dns). The design rate 1000 mmscfd for the export line is considered as the basis for the gas flowrate. Even for low LGR’s, the required line size increases significantly when 2-phase slip effects are considered.

CLOSURE  This paper paper presents a summary of the technology behind the simulation of multiphase flow in pipelines. This technology is classified into steady state and transient approaches and the underlying methodology has been presented for both. A case study is selected to illustrate the approach to the simulation of  both steady state and transient phenomena in a pipeline network system and the appropriate industry tools are used in the process.

 A UTHOR B IOGRAPHIES  Dr. Ivor R. Ellul   began his career in the oil and gas industry in 1980, in West Germany, as a design engineer on pipeline and storage tank systems. After specializing iin n the modeling of multiphase flow in pipelines, he worked for a number of years in the area of numerical modeling of single and multi-phase pipelines under steady-state and transient conditions. He has been involved in various pipeline simulation studies for clients worldwide. Recent experience includes various executive positions in the upstream area of the oil and gas industry. Dr. Ellul is industry lecturer to the Petroleum Engineering Department of Imperial College, University of engineering. London where lectures the M.S. course on pipeline and process He he is also a member of the advisory board of the Faculty of Petroleum Engineering of the University of Houston. Dr. Ellul holds a BS in Mechancal Engineering from the University of Malta and MS, and PhD degrees in Petroleum Engineering from the University of London. Dr. Ellul is a registered Chartered Engineer in the United Kingdom and a registered Professional Engineer in the state of Texas.

Geir Saether  has  has been involved in Flow Assurance Engineering in the petroleum industry for over 17 years. His background includes  planning and development of oil and and gas fields in the Gulf of Mexico, Mexico,  North Sea, Barents Sea, at Grand Banks, offshore Malaysia, and off the West African coast. coast. He is a speciali specialist st in the charact characteristics eristics of multiphase flow related problems. His experience includes significant work in the area of research and simulation of multiphase flow in pipelines as well as developing multiphase flow simulators. He has served as project manager and systems engineer, analyzing risk and assessing operational constraints in large oil and gas field

9

studies and developments. developments. He has knowledge and skills in process simulation with a strong understanding of PVT behavior.

Mack E. Shippen  Shippen   is a senior petroleum engineer with Schlumberger Information Solutions in Houston, where he provides user support, training, and consulting services for PIPESIM. He holds BS and MS degrees in petroleum engineering from Texas A&M University where his research focused on multiphase flow modeling. He has performed a number of well and surface network simulation studies, including dynamic coupling of reservoir and surface simulation models. An active SPE member, he is currently serving as an editor of the SPE Reprint Series on Offshore Multiphase Production Operations. 

 

10

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

REFERENCES  1. 

2.  3.  4.  5. 

6.  7.  8. 

9. 

10. 

11. 

12. 

13. 

14. 

Hagedorn, A.R., Brown, K.E., “Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small Diameter Vertical Conduits, J. Pet. Tech., April, 1965. Beggs, H.D., Brill, J.P., “A Study of Two-Phase Flow in Inclined Pipes”, J. Pet. Tech., May, 1973. Dukler, A.E., “Gas-Liquid Flow in Pipelines Research Results”, Project NX-28, AGA, May, 1969. Brill, J.P., “Multiphase Flow in Wells”, J. Pet. Tech., January, 1987. Mandhane, J.M., Gregory, G.A., Aziz, K., “A Flow Pattern Map for Gas-Liquid Flow in Horizontal Pipes”, Int. J. Multiphase Flow, Vol. 1, 1974, pp. 537 – 553. Aziz, K., Govier, G.W., Fogarasi, M., “Pressure Drop in Wells Producing Oil and Gas”, J. Cdn. Pet. Tech., July-Sept, 1972. Baker, O., “Gas-Liquid Flow in Pipelines, II. Design Manual”, AGA-API Project NX-28, October, 1970. Dukler, A.E., Wicks, M., Cleveland, R.G., “Frictional Pressure Drop in Two-Phase Flow: B. An Approach through Similarity Analysis”, AIChE Journal, Vol. 10, No. 1, January, 1964. Flanigan, O., “Effect of Uphill Flow on Pressure Drop in Design of Two-Phase Gathering Systems”, Oil and Gas Journal, March 10, 1958. Eaton, B.A., Andrews, D.E., Knowles, C.R., Silberberg, I.H., Brown, K.E., “The Prediction of Flow Patterns, Liquid Holdup and Pressure Losses Occurring During Continuous Two-Phase Flow in Horizontal Pipelines”, J. Pet. Tech., June 1967, pp 815 – 828. Ellul, I.R., “The Prediction of Dispersed Gas-Liquid Flow in Complex Pipe Geometries”, Ph.D. Thesis, University of London, 1989. Finch, L., Ellul, I., Gochnour, R., “Implementation of Mechanistic Flow Models in a Practical Multiphase Flow Simulator”, Twenty-third Annual meeting of PSIG, October, 1991. Taitel, Y. & Dukler, A.E.: “A Mechanistic Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Journal, 22 (Jan. 1976), 47-55. Gas-Liquid Flow,” AIChE Journal, Zhang, H.Q., Wang, Q., Sarica, C., Brill, J.P.: “Unified Model for Gas-Liquid Pipe Flow Via Slug Dynamics - Part 1: Model Development,” ASME  Journal of Energy Resources Technology , Vol.125 (December 2003) 274.

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15.  Xiao. J.J., Shoham, O., Brill, J. P.: “A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines,” paper SPE 20631 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, LA., 23-25 Sept . 16.  The Honorary Lord Cullen, “The Public Enquiry into the Piper Alpha Disaster.” Report presented to the Parliament of the United Kingdom of Great Britain, November 1990. 17.  Rygg, O.B., Ellul, I.R., “The Dynamic Two-Phase Modeling of Offshore Live Crude Lines Under Rupture Conditions.” OTC6747, 1991. 18.  Ellul, I.R., King, P.E., Findlay, W.A., Delacroix, M.P., “The Use of Dynamic Simulation in Offshore Multiphase Pipeline Design.” 5th International Conference on Multiphase Production, Cannes, June 1991. 19.  Ishii, M., “Thermo-fluid Dynamic Theory of Two-Phase Flow”, Eyrolles, Paris, 1975. 20.  Banerjee, S., Chan, A.M.C., “Separated Flow Models I – Analysis of the Averaged and Local Instantaneous Formulations”, Int. Journal of Multiphase Flow, Vol. 6, pp. 124, 1980. 21.  Drew, D.A., Lahey, R.T., “Application of General Constitutive Principles to the Derivation of Multidimensional Two-Phase Flow Equations”, Int. Journal of Multiphase Flow, Vol. 5, pp. 243-264, 1979. 22.  Bendiksen, K., Malnes, D., Moe, R., Nuland, S., “The Dynamic Two-Fluid Model OLGA: Theory and Application.” SPE-19451, 1989. 23.  Bendiksen, K., Espedal, M., Malnes, D., “Physical and  Numerical Simulation of Dynamic Two-Phase Flow Flow in Pipelines with Application to Existing Oil-Gas Field Lines.” Conference on Multiphase Flow in Industrial Plants, Bologna, September 1988. 24.  Cunliffe, R., “Prediction of Condensate Flow Rates in Large Diameter High Pressure Wet Gas Pipelines”,  APEA Journal  (1978), 171-177. 25.  Asante, B., “Two-Phase Flow: Accounting For The Presence Of Liquids In Gas Pipeline Simulation”, Thirty-fourth Annual meeting of PSIG, October, 2002.

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

11

TABLES Correlation Correlation Eaton Eaton

For Liquid Holdup Pressure Gradient

Based Upon Water-gas data (2”, 4” pipe sizes) Water-gas and distillate data (2”, 4”,

Comments  Correlation is free from abrupt discontinuities  Valid only for horizontal pipes  May produce unreliable results for very low or very high volume fractions

 





 May be unreliable for liquid viscosities above 12-15 cP.  Neglects pipe roughness effects  Valid only for horizontal pipes

17” pipe sizes)

 

Hughmark Dukler

Liquid Holdup Pressure Gradient

 Air-liquid data (0.63”, 2.5” pipe sizes) Field data

 Developed for vertical up flow systems  Over predicts liquid holdup at low liquid volume fractions

 

 Similarity analysis employed to develop correlation  Makes no distinction between flow regimes  Best results obtained for pipelines with moderate to high liquid volume fractions and limited elevation changes

  

Flanigan

Liquid Holdup

Flanigan

Beggs Brill

Field data (16” pipe size)



Pressure

Field data (16” pipe



Gradient

size)

and Pressure Gradient

 Applies only to uphill inclined pipe pip e segments  Liquid holdup (uphill sections) correlated with superficial gas velocity  Applies only to uphill inclined pipe pip e segments





 Applies only to gravitational component of pressure gradient  Pressure recovery in downhill sections is neglected  Pressure  Original correlation based on smooth friction factors  Applicable to all ranges of pipe inclination  Flow regimes considered: segregated, intermittent, distributed  Predictions for downhill sections frequently too low



Laboratory data (1”, 1.5” pipe sizes)

   

Hagedorn and Brown

Liquid Holdup and Experimental Pressure (1500’) Gradient

well

 Applies only to vertical upward flow  Makes no distinction between flow regimes  Liquid holdup merely a correlating factor  Pressure gradient predictions not accurate for bubble flow  Gives best results for wellbores with high gas-liquid ratios and relatively high mixture velocities  Hybrid method which uses three different correlations for

   



Orkiszewski

Liquid Holdup and



Pressure Gradient



vertical upflow  Convergence problems owing to discontinuities across flow regime boundaries

Table 1

 

12

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

Range of Inclination

Stratified Stratifie d - Slug

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FLOW REGIME TRANSITIONS Slug - Annular

o

o

A or G

B or A

Slug - Bubbly  A

o

o

No transition

C

C

+60  to +90  

o

o

No transition

C or D

D or C

-90o to -80o 

No transition

F

F or H

-10  to +15   +15  to +60  

o

o

E

B

B

o

o

A

B

B

-80  to -70   -70  to -10  

Table 2  Key:

A: B: C: D: E: F: G:

Taitel-Dukler (1976a) Barnea et al (1980) Taitel et al (1980) Mishima et al (1984) Barnea et al (1982a) Barnea et al (1982b) Ferschneider et al (1985)

H: Martin (1973)

Range of Inclination o

o

o

o

o

o

-10  to +15  

+15  to +60   +60  to +90  

FLOW REGIME TRANSITIONS USED TO TO DETERMINE ACTUAL FLOW FL OW REGIME Stratified Regime Ann ular Regime Slug Regime Bub bly Regime ST - SL ST – SL ST – SL ST – SL SL – ANN SL - ANN SL – ANN SL - BUB SL - BUB -

SL – BUB

SL – BUB

SL – ANN

SL – ANN

SL – BUB

SL – BUB

SL – ANN

SL – ANN

SL – BUB SL – BUB

o

o

-

SL – ANN

SL – BUB

SL – BUB

o

o

SL – BUB

SL – BUB

SL – BUB

SL – BUB

ST – SL

ST – SL

ST – SL

SL - ANN

SL - ANN

SL – BUB

SL – BUB

SL – BUB

ST – SL

ST – SL

ST – SL

SL - ANN

SL - ANN

-90  to -80   -80  to -70  

o

o

-70  to -10  

Table 3 

SL – BUB

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

Submodel for: Stratified Stratifie d

13

FLOW REGIME Pressure Pre ssure Gradient and Liquid Holdup Methods Annular Slug Slug Horizontal/Inclined Vertical

Bubbly

Wall – Gas Shear

A or B

-

-

-

-

Wall – Liquid Shear

B or C

D

-

-

-

Interfacial Shear

A or B

B or F

-

-

-

Interfacial Friction Factor

-

B or F

-

-

-

Wall – Liquid Friction Factor

-

-

Blasius

Blasius

Blasius

Liquid Droplet Entrainment

-

G

-

-

-

Liquid Holdup

A

F

-

-

K or M

Liquid Holdup in Liquid Slug

-

-

H or I

-

-

Slug Frequency

-

-

G or J

-

-

Slug Velocity

-

-

G or K

-

-

Carpet Velocity Gas Bubble  – Slug Length

-

-

G or L

-

-

Liquid Holdup Correction

-

-

-

F

-

 Acceleration Effects

F

F

F

F

F

Table 4  Key: 

A: B: C: D: E: F:

Taitel-Dukler Taitel-Dukler (1976b) Laurinat-Hanratty (1984) Chermisisnoff and Davis (1979) Hewitt (1982) Oliemans (1986) Wallis (1969)

G: H: I: J: K: L: M:

Creare, Inc. (1986) Gregory et al (1978) Fabre et al (1983) Gregory-Scott (1969) Zuber and Findlay (1965) Dukler and Hubbard (1975) Mishima and Ishii (1984)

Fluid type water depth (ft.) Distance to host (mi) Gas rate (mmscfd)

Pl at f o r m A dry gas 600 20 200

Pl at f o r m B wet gas 1000 30 300

Table 5: Description of Source Platforms

Pl at f o r m C wet gas 5000 50 500

 

14

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

Compon ent N2 CO2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10+ C10+ Molwt Condensate yield (BBL/mmscf)

Pl at f o r m A Mole % 0.1 0.1 99.5 0.25 0.03 0.02

none

Pl at f o r m B Mole % 0.19 0.05 98.59 0.41 0.21 0.04 0.11 0.04 0.04 0.05 0.038 0.032 0.028 0.172 221.585 3.8

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Pl at f o r m C Mole % 0.19 0.05 97.86 0.41 0.21 0.04 0.11 0.04 0.04 0.05 0.12 0.10 0.09 0.70 241.67 18.1

Ex p o r t Mole % 0.17 0.06 98.40 0.38 0.17 0.04 0.09 0.03 0.03 0.04 0.07 0.06 0.05 0.40 9.9

Table 6: Gas Com Compositions positions

Method no-slip OLGA-S Xiao (Taitel-Dukler model) Beggs & Brill Dukler, AGA & Flanigan (Eaton holdup)

Required Re quired pipe size 32" 32" 32" 34" 36"

 Av e Li qu id  Ave Holdup (%) 1.0 5.9 3.4 10.3 7.0

Table 7: Selected export pipeline diameter by various methods  

Lin e Platform A tieback Platform B tieback Platform C tieback

Required pipe size 12" 16" 24"

Table 8: Selected tieback pipeline diameter using OLGA-S

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

FIGURES

Figure 1 – Horizontal Flow Regimes Figure 3 – Vertical Flow Regime Map

Figure 4

Figure 2 – Horizontal Flow Regime Map

Figure 5 

15

 

16

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

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Figure 6

Figure 9

Figure 7

SG  V G 

 V L 

 A G Si

D h L

 A L SL

Figure 8

Figure 10

 

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The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

Figure 11 Figure 14: Tieback A pi pipeline peline profile 

Figure 12 Figure 15: Tieback B pi pipeline peline profile

Figure 13: Schematic of System  

Figure 16: Tieback C pi pipeline peline profile

17

 

18

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

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25000

20000    )    d    /    B    T 15000    S    (   e    t   a    R 10000    d    i   u   q    i    L 5000

0 0. 0

0. 5

1. 0

1. 5

2. 0

2. 5

3. 0

3. 5

4. 0

4. 5

5. 0

Time (days)

  Figure 20: Liquid rate at plant vs. Time used for ramp-up scenario (steady-state approach) 

Figure 17: Export pipeli pipeline ne profile

25000

   )    B    T    S    (   e   m   u    l   o    V    d    i   u   q    i    L

20000

15000

10000

5000

0 0. 0

0 .5

1 .0

1.5

2 .0

2. 5

3 .0

3 .5

4. 0

4. 5

5 .0

Time (days)

  Figure 21: Slug Catcher Inventory vs. Time for ramp-up scenario (steady-state approach) 

Figure 18: Export line deliverability as a function of flow correlation and pipe diameter 55000

Trend data GAS VOLUME FLOW AT STOCK TANK CONDITION EXPORT,PIPE-24,2 [MMscf/d]

50000    )    L    B 45000    B    (   p 40000   u    d    l   o 35000    H    l   a 30000    t   o    T 25000

550

500

450    d    /    f   c   s 400    M    M

350

300

20000 300

350

4 00

450

500 250

Gas Rate (mmscfd)

0

  Figure 19: Total Holdup vs. gas rate for Tieback C and Export line during phase 1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time [d] PSIG 2004 - Ramp-up

Figure 22: Gas flowrate into the land terminal

 

 

PSIG 0403

The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

Trend data

19

Slug catcher liquid inventory Different liquid offtake flowrates

TOTAL LIQUID CONTENT IN A BRANCH PLAT A [bbl] TOTAL LIQUID CONTENT IN A BRANCH EXPORT [bbl]

30000

60000 55000

25000

50000 20000

   )    B    T    S    (   e   m   u 15000    l   o   v    d    i   u   q    i    L

45000 40000    l    b 35000    b

Offtake=10,500 STB/d Offtake=12,500 STB/d Offtake=20,000 STB/d

10000

30000 25000

5000

20000 0 0

15000

0 .5

1

1.5

2

2.5

3

3.5

4

4. 5

Time (d)

10000 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time [d] PSIG 2004 - Ramp-up

 

Figure 26. Slug catcher inventory for different liquid off take rates

5

 

Figure 23: Liquid content in the two flowline branches Required slug catcher size for various offtake flowrates 30000

Trend data LIQUID VOLUME FLOW AT STOCK TANK CONDITION EXPORT,PIPE-24,2 [STB/d]

25000

40000

20000

35000

   )    B    T    S    (   e

25000

   i   z   s   r   e 15000    h   c    t   a   c   g   u    l    S

   d    /    B20000    T    S

5000

30000

10000

15000 0 0

10000

5000

10000

15000

20000

25000

Liquid offtake flowrate (STB/d)

5000

 

Figure 27. Slug catcher size for different drainage flowrates

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time [d] PSIG 2004 - Ramp-up

 

Trend data Instantaneous ramp-up

Figure 24. Liquid flowrate into the land terminal

Ramp-up over 12 hrs Ramp-up over 24 hrs

550

500

Slug catcher liquid inventory 25000

450      d      /      f     c     s 400      M      M

20000

   ) 15000    B    T    S    (   e   m   u    l   o   v    d    i   u   q    i    L10000

350

300

250 0

5000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Time [d]

0 0

0.5

1

1.5

2

2.5 Time (d)

Figure 25. Slug catcher inventory

3

3.5

4

4.5

 

Figure 28. Gas flowrate into the slug catcher for different ramp-up times

6

 

 

20

ELLUL, I.R., SAETHER, G., SHIPPEN, M.E.

PSIG 0403

Trend data

Trend data Instantaneous ramp-up

GAS VOLUME FLOW AT STOCK TANK COND ITION EXPORT,PIPE-24,2 [MMscf/d]

600

Ramp-up over 12 hrs Ramp-up over 24 hrs

550

40000

500 35000

450 30000

400

25000

   d    /    f   c   s 300    M    M

350

   d    /    B20000    T    S

250 200

15000

150 10000

100 5000

50 0

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Time [d]

0

6

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Time [d]

 

PSIG 2004 - Pigging

Figure 29. Liquid flowrate into slug catcher for different ramp-ups

 

Figure 32. Gas flowrate at slug catcher Trend data PIG/PLUG VELOCITY PLUG-1 [ft/s]

Slug catcher liquid inventory Different ramp-up rates

15

25000

20000

10    )    B    T 15000    S    (   e   m   u    l   o   v    d    i   u   q 10000    i    L

  s    /    t    f

Instantaneous ramp-up Ramp-up over 12 hrs Ramp-up over 24 hrs

5 5000

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0

Time (d)

0

 

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Time [d]

PSIG 2004 - Pigging

Figure 30. Slug catcher inventory for different ramp-up rates

 

Figure 33. Pigging velocity

Required slug catcher size for various ramp-up rates 22000

Trend data LIQUID VOLUME FLOW AT STOCK TANK CONDITION EXPORT,PIPE-24,2 [STB/d]

21500

1.5e6 21000

   )    B    T    S    (   e   z    i   s   r   e 20500    h   c    t   a   c   g   u    l    S

1e6

20000

   d    /    B    T    S

19500

500000

19000 0

5

10

15

20

25

Ramp-up time (hrs)

30

 

Figure 31. Slug catcher size for different ramp-up rates 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Time [d] PSIG 2004 - Pigging

Figure 34. Liquid flowrate into slug catcher

 

 

PSIG 0403

The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial

21

Trend data

1.25

TOTAL LIQUID CONTENT IN A BRANCH EXPORT [bbl]

OLGA-S

40000

BBR 35000

DAF (Eaton) 1.20

30000

25000

1.15

   l    b 20000    b

  s   n    D    /    D

15000

1.10

10000

5000

1.05

0 0

50

100

150

Time [h] PSIG 2004 - Pigging

  1.00

Figure 35. Liquid content in export flowline

0

20

40

60

80

100

LGR (STB/mmscfd)

 

Slug catcher liquid inventory during pigging

Figure 38. Line size as a function of LGR and correlation

35000

30000

25000    )    B    T    S    ( 20000   e   m   u    l   o   v    d    i 15000   u   q    i    L

10000

5000

0 0

1

2

3

4

5

6

Time (d)

 

Figure 36. Slug catcher liquid inventory during pigging 40000 35000    )    B 30000    T    S    (   e 25000   m   u    l   o 20000    V    d   e 15000   r    i   u   q   e 10000    R

 

Ramp-up Pigging

5000 0 Beggs & Brill

Dukler,  AGA & Flanigan (Eaton holdup)

Xiao

OLGASteady State

OLGA Transient

  Figure 37. Slug catcher sizing using various methods