An Introduction To PeTra Pål Hedne Statoil F&U
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Transcript of An Introduction To PeTra Pål Hedne Statoil F&U
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An Introduction To
PeTra
Pål Hedne
Statoil F&U
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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
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An Introduction To PeTra
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
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An Introduction To PeTra
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
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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:
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Physical Model: Conservation Equations
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
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An Introduction To PeTra
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
Physical Model: Conservation Equations
Moving Control Volume
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An Introduction To PeTra
lSllelddl
lkkclk
lklklkilcll
shhllc
llll
UGUURUUU
Fgzp
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tL
)(
cos)(1
glSgwol
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,,
cos)(1 Gas
Liquid
Droplets
wollSl
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,)(
cos1
,,,
,,,
Where: l=o,w k=g,l,w
and ZxZkkkkx VuuF k )(
Momentum equationsPhysical Model: Conservation Equations
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wol l
Sdl
wogk k
Sk
wol
dladlb
lwogk
kakb
k
GGLWW
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tL
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,,,,,,
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
Physical Model: Conservation Equations
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Physical Model: Conservation Equations
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.
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An Introduction To PeTra
Physical Model: Flow Regimes
Stratified Annular when 60°
Dispersed Slug
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An Introduction To PeTra
Physical Model: Closure Relationships
General parameters:•Wall friction•Interfacial friction•Entrainment/deposition rates
Slug parameters:•Bubble nose velocity•Gas entrained in slug body
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An Introduction To PeTra
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.
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An Introduction To PeTra
Numerical Model: Dynamical Grid
zn12/
zn121
/
zjn1 zj
n zjn1 zN
n12/
zjn11 zj
n1 zjn11 zN
n121/
1,
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12/1,
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)(ˆ)(ˆ
)()(1
njSk
njkn
j
njk
njk
njk
njk
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njk
nj
Gz
VumVum
tzmzm
z
Discretization on a moving grid for the mass equations
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An Introduction To PeTra
a)
b) c)
one mass point(normal control volume)
two mass points(discontinuity control volume)
Numerical Model: Discontinuities
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An Introduction To PeTra
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
'''
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,,
,,n
en
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n
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uu
1 nt
nnnn Vtzz 1
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An Introduction To PeTra
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
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An Introduction To PeTra
Implementation: Classes and Inheritance
•General code is separated from special•Reuse of code•Easy to add new models
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An Introduction To PeTra
Implementation: Linked Lists
Flexible, general, easy to maintain
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An Introduction To PeTra
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