An Introduction To PeTra Pål Hedne Statoil F&U

An Introduction To

PeTra

Pål Hedne

Statoil F&U

An Introduction To PeTra

Background: Application

Three-phase flow simulator with tracking of individual slugs and pigs.

Computation of•Pressure•Temperature•Phase fractions•Slug lengths and velocities


Background: Code History1983 Olga IFE-SINTEF Multiphase Flow Laboratory

1988 Olga w/water1986 Wolga

1985 Comp.Olga

1989 Olga 1.0 com.

1998 Olga2000.x com.

1994 PeTra 0.1

1999 PeTra 2.x NDP

2001 PeTra 3.x com.?

1997 Olga97


Background: Experimental Foundation

Laboratory Experiments•SINTEF Large Scale Flow Loop•Small Scale High Density•Atmospheric data

Field Data•Gas/condensate •Oil Field•Three Phase Flow

Physical Model: Conservation Equations

Mass •gas•oil film•water film•oil droplets•water droplets

Momentum•gas+oil droplets+water droplets•oil film•water film

Energy•Mixture temperature

Pressure (volume)

Three phase flow model.Separate conservation equations for:


Sggwghggg GUAzAt

)(1)(Gas

Sodoeooo

ogoooooo GUA

zAt

)(1)(Oil film

Sdodoeooo

ogoooooo GUA

zAt

)(1)(Oil droplets

Slwdwewwwwww GUAzAt

)(1)(Water film

Sdwdwewwwwww GUAzAt

)(1)(Water droplets


0)(1

LWWL

tLkakb

kkIntegral form of mass equation for phase k for a moving control volume

where ZxZkkkx VuW k )(

Va Vb

Za Zb


Moving Control Volume


lSllelddl

lkkclk

lklklkilcll

shhllc

llll

UGUURUUU

Fgzp

zpUL

tL

)(

cos)(1

glSgwol

lcglwhl

lkgligcgg

shhggc

ggagb

ggg

UGUUU

Fgzp

zp

LFF

ULtL

,,

cos)(1 Gas

Liquid

Droplets

wollSl

wol

dldl

wol

lel

wolkSdldlkdidld

shhlwol

l

cwol

l

wol

lll

UGUURUGUU

Fgzp

zpUL

tL

,)(

cos1

,,,

,,,

Where: l=o,w k=g,l,w

and ZxZkkkkx VuuF k )(

Momentum equationsPhysical Model: Conservation Equations

wol l

Sdl

wogk k

Sk

wol

dladlb

lwogk

kakb

k

GGLWW

LWW

tL

Ltp

,,,,,,

111

Combination of mass equation and equation of state

ZxZkkkx VuW k )(Mass flux term

wol

l

l

l

wogk

l

k

k

pp ,,,

Compressibility

Volume equation



Energy equation

kwallk

akkkbkkkk

kk HQtpVuhmVuhm

LhLm

tL

))(())((11

( 1 )

Where:

kkkpeh Internal specific entalphy is given by

kH Enthalpy of an external mass source per section volume

Qwall Rate of heat loss to the wall per section volume.


Physical Model: Flow Regimes

Stratified Annular when 60°

Dispersed Slug


Physical Model: Closure Relationships

General parameters:•Wall friction•Interfacial friction•Entrainment/deposition rates

Slug parameters:•Bubble nose velocity•Gas entrained in slug body


Numerical Model: Formulation

One-dimensionalUpwind in spacePartly implicit in time.

The equations are discretized on a staggered grid:•The velocities and fluxes are defined on the section boundaries •Pressure, masses and temperature in the grid sections.

Upwind values are used in the convective terms.


Numerical Model: Dynamical Grid

zn12/

zn121

/

zjn1 zj

n zjn1 zN

n12/

zjn11 zj

n1 zjn11 zN

n121/

1,

1,1

12/1

12/1,

12/1

12/1,

1

1

)(ˆ)(ˆ

)()(1

njSk

njkn

j

njk

njk

njk

njk

njk

njk

nj

Gz

VumVum

tzmzm

z

Discretization on a moving grid for the mass equations


a)

b) c)

one mass point(normal control volume)

two mass points(discontinuity control volume)

Numerical Model: Discontinuities


Numerical Model: Solving Procedure

nt1 nt

U p d a t e g r i d p o s i t i o n s

C a l c u l a t e f l o w r e g i m e s a n d f r i c t i o n f a c t o r s

M o m e n t u m a n d v o l u m e e q u a t i o n s

F l u i d p r o p e r t i e s w i t h n e w p r e s s u r eM a s s t r a n s f e r r a t e sD r o p l e t e n t r a i n m e n t / d e p o s i t i o n

M a s s e q u a t i o n s

T e m p e r a t u r e e q u a t i o n

F l u i d p r o p e r t i e s w i t h n e w t e m pM a s s t r a n s f e r , e n t r a i n m e n t / d e p o s i t i o n

U p d a t e g r i d : - i n s e r t a n d r e m o v e s l u g a n d p i g s - a d a p t g r i d ( r e f i n e / c o a r s e n g r i d ) - u p d a t e d i s c o n t . v e l o c i t i e s - u p d a t e g r i d v e l o c i t i e s

U p d a t e t i m e s t e p ,1nt

11 , nnk pu

1 nk

111

111

,,

,,

ne

nd

nk

nk

nk

nk

1nkm

1nT

C a l c u l a t e v o l u m e f r a c t i o n s

'''

'''

,,

,,n

en

dn

k

nk

nk

nk

1nk

1

11 ,

n

nf

nB

V

uu

1 nt

nnnn Vtzz 1


Implementation: Code Layout

• Solver engine written in C++.• Graphical user interface written in G (LabVIEW). • Can be linked to existing code, i.e. Fortran, C, etc.

Numerical EnginenetPeTra.exe

Graphical User InterfacePeTraGUI.exe

Communicates throughTCP/IP


Implementation: Classes and Inheritance

•General code is separated from special•Reuse of code•Easy to add new models


Implementation: Linked Lists

Flexible, general, easy to maintain


Year 2000• PeTra will be tested and verified against available data set.• PeTra will be delivered to the NDP partners in the form of a

binary executable program for the Win32 operating system.

Year 2000+• Scandpower will provide PeTra services to the NDP

companies after the completion of the NDP work in 2000 on a commercial basis.

• Further development of the PeTra code after 2000 will be carried out within the SSH (Statoil-Shell-Hydro) collaboration.

• PeTra will be commercialized to 3rd parties at a later stage.

Delivery

Documents

An Introduction To PeTra Pål Hedne Statoil F&U