13th international conference multiphase flow in

17/09/2014 1

13th International Conference MULTIPHASE FLOW IN INDUSTRIAL

PLANTS 17-19 September, 2014, Sestri Levante (GE) , Italy

Full Compositional Simulation of Two-Phase Flow

Author: Luigi Raimondi Process Simulation Services – Italy www.xpsimworld.com

Process Simulation Services 2


Perspective This paper presents a development in the simulation of single-phase and multi-phase flow for the transportation of gas and liquids in pipelines. The approach used can be defined as

‘full compositional’ since the vapour and liquid phases are described taking into account the chemical composition



Summary The following main points are discussed: • A general introduction • Fluid dynamic models and equations • Equation of state and temperature calculations • Example 1 - Pipeline pressurization • Example 2 – Pipeline depressurizations • Conclusion



The simulation of multiphase flow in pipelines has become a very important topic in research and engineering along the past 20 years.

This fact has been promoted mainly by the exploitation of oil and gas reservoirs in off-shore fields and the transportation to onshore treatment facilities

The term flow-assurance has been introduced to define the technology applied for the design of pipeline systems, prevention and the solution of problems related to fluid flow that can arise during their operations



Along the years, a number of simulation programs and tools have been developed starting from nuclear industry where LOCA simulations have assumed a pre-eminent aspect. From these needs some simulation tools (e.g. RELAP, CATHARE) have been developed for the evaluation of mixed steam-water flows.



With the scope of solving the problems faced by the oil and gas industry particularly for the development of offshore fields, new two-phase flow simulators have been developed on the basis of the experience gained in the nuclear industry. Today commercial tools such as Olga, Tacite and LedaFlow are well known and are probably the most used simulators for steady state and transient multi-phase flow modelling..



Notwithstanding the enormous amount of published papers in the field of fluid flow in pipelines, practically all experimental data and simulated cases deal with fluid of constant composition. Most experiments use very simple and safe two-component systems such as: • air-water, • nitrogen-water, • nitrogen-naphtha and very few more..



These two-components systems have almost no resemblance to real cases faced by the oil&gas industry where the oil-gas mixture is described by tens of: hydrocarbon components (from C1 to C80)

light gases (N2, CO2, H2S, mercaptanes)

water, often as a separated second liquid phase.



Mass balance

Momentum balance

kkkkkk mu

t=∇+

∂∂

)( ραρα

ikkkkkkkkkk

kkk MgPPuut

u++∇=+∇+

∂∂ ϑραααραρα sin)(



Sum of phase volumes

Energy conservation

( ) ( )LL

VV

L

L

LV

V

V uz

uztt

αρρ

αρρ

ρραρ

ρα

∂∂

−∂∂

−=∂∂

+∂∂ 11

kkkk

kkkk

kkk uPquuEuEt

⋅∇+−∇=

+∇+

+

∂∂

22

22

ραρα



Chemical component i-th mass balance

( ) 0=∇+∂∂

kik

ik um

tm

Diffusivity effects related to chemical components are not considered



When the differential equations are integrated, by assuming the temperature is constant across one time step Δt, then the change of the phase density can be associated to the change of pressure. The volume conservation equation can be rewritten as:

( ) ( )LL

VV

L

L

LV

V

V uz

uzt

PPP

αρρ

αρρ

ρραρ

ρα

∂∂

−∂∂

−=∂∂

∂∂

+∂∂ 11



• The complete set of the Navier-Stokes equations are solved using a mixed implicit-explicit integration scheme.

• The material and momentum balance equations are integrated using an implicit scheme.

• The energy balance equations are combined and solved using an explicit Euler integration.

• Details of the applied integration method are not given and a valuable reference is the text of Ferziger and Peric.

• The component balance equation is integrated based on the new phase velocities and densities obtained in the previous time step.



Cubic equations of state which are a standard for oil&gas thermodynamic calculation are applied. So either the Soave-Redlich-Kwong equation (SRK)

or the Peng-Robinson equation are used.

( )( )

( )bVVTa

bVRTP

−−

−=

( )( )

( ) ( )bVbbVVTa

bVRTP

−++−

−=



Here the a and b parameter are function of the actual vapor and liquid compositions:

i

NC

iibzb ∑= )1(

,ijii

NC

jiji kaazza −=∑

So the calculation of amount of gas and liquid phases, their composition is the result of the solution of the highly non-linear ‘flash’ equations based on the k-value relations:

),,,( yxPTKxy

ii

i = where i=1,NC



If we consider a given time integration step Δt, the calculated new temperature and pressure must satisfy the Navier-Stokes equations and the thermodynamic equilibrium equations. This represents a difficult and critical point in the numerical solutions of the equations.



Some help can be obtained through the application of the Clausius-Clapeyron equation which can be used to connect the change of pressure and temperature.

VTH

dTdP

∆∆

=

However it should be kept in mind that this equation is exact only when one-component fluids are considered and is approximated for binary and multicomponent fluids.



The model summarized by the previous pages has been implemented in XPSIM (eXtended Process SIMulator) a software for process simulation and flow-assurance studies. The following examples have been simulated using this tool.



Example 1 - Pipeline pressurization

• internal diameter 0.2679 m • length 500 m • initially filled with N2 at 20 bar at ambient

temperature Filling fluid: • hydrocarbon mixture at 80 bar by opening an inlet

control valve



Hydrocarbon fluid composition No Component Molar Fraction, % 1 H2O 0.0172 2 N2 0.6984 3 CO2 4.5054 4 H2S 6.6298 5 C1 39.1120 6 C2 23.4063 7 C3 22.2626 8 IC4 0.8409 9 NC4 1.4369 10 IC5 0.3492 11 NC5 0.3753 12 C6 0.2604 13 C7 0.0716 14 C8 0.0263 15 C9 0.0063 16 C10 0.0013



Pipeline pressurization



Example 2 - Pipeline de-pressurization • internal diameter 0.154 m • length 1000 m • Initial status: 120 bar and 20 °C Depressurized through a valve, diameter 50 mm

No Component Molar Fraction, %

1 C1 50

2 NC4 40

3 NC8 10

Hydrocarbon fluid composition



Pipeline de-pressurization



Conclusion The development of algorithms for the simulation of vapour-liquid two-phase flow through pipelines taking into account the chemical composition of the fluid is an important topic for the analysis of multiphase transport The validity of this approach is demonstrated by two cases taken from flow-assurance design practices in the on-shore and off-shore engineering .

13th international conference multiphase flow in

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