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The Transient Multiphase Flow Simulator

Contents • Introduction • Physical models and numerical solutions • Network topology • How to make fluids flow • Fluid properties • Heat transfer • Process equipment and modules • File structure and execution

Fundamental features • OLGA is – transient ( df/dt # 0 ) – one-dimensional (along pipe axis) – “complete” – a modified “two-fluid” model – realised with a semi-implicit numerical solution • staggered grid – made for (relatively) slow mass transients

The dynamic three phase flow simulator 8 Conserv. Equations mass (5) momentum (2) energy (1)

Closure Laws Fluid Properties

mass transfer momentum transfer energy transfer

Initial Conditions

Boundary Conditions

OLGA

The OLGA three phase flow model • Mass conservation – Gas – Hydrocarbon bulk – Hydrocarbon droplets – Water bulk – Water droplets • Momentum conservation – Gas + droplets – Liquid bulk • Energy conservation – Mixture • Constitutive equations

Variables • Primary variables – – – –

5 mass fractions (specific mass) 2 velocities 1 pressure 1 temperature

• Secondary variables – – – –

Volume fractions Velocities Flow rates Fluid properties

Conservation of mass

Conservation of energy

energy = mass (thermal energy + kinetic energy + potential energy)spec energy flow + work = mass flow (enthalpy + kinetic energy + potential energy)

Force balance equation (Conservation of momentum) Pj

Pj+1 gas liquid

j

dM /dt =

dZj

j+1

((M·V )j - (M·V )j+1) /dzj - S j + G j + F j + F j+1+ MT

M - Momentum V - Velocity m - Mass M = m ·V

S =

Shear

G= F = MT =

Gravity = m · gravity acceleration Force = pressure · flow area Momentum Transfer = mass transfer - entrainment + deposition

= wall shear + interfacial shear

The OLGA volume equation Pi i

Qi

i

Qi+1

i+1

source / sink

The OLGA volume equation for all sections the local fluid volume time variations

Combine all mass conservation equations

Net change of total fluid volume in a section = 0 T and RS constant

0= CdP/dt = Qin - Qout + volume change by mass transfer + volume change by mass sources + Volume Correction temperature change is assumed to be zero in this step : [m3/s]

(V / T)(T / t ) 0 C = “compressibility” i.e. dVfluid/dP

[m3/Pa]

Calculation sequence for each time step: a) solve model relations to give friction factors etc.

b) solve momentum - and volume equation simultaneously U and P c) perform flash d) solve mass equations first for gas then for oil film and oil droplets and then for water film and water droplets e) solve energy equation T f) perform flash

Sources of numerical errors in general •

Linearisation of strongly non-linear models – Iteration is not performed • Thermal expansion or contraction – Temperature decoupled from pressure may give volume errors • Local changes of total composition neglected in standard OLGA – taken into account in CompTrack

Volume error At each time step when all equations have been solved the net fluid volume change in each section usually is 0 and the volume error can be expressed as VOLi = 1- Vi f / Vsectioni 0 f Vi f = Vi f = m if =

mif / i f fluid volume in section no i mass in pipe section no i

i f =

density of fluid in section no i

(f indicates liquid , gas and droplets)

Volume error

cont.

The main source of high volume error peaks is change of phase velocity direction from one time step to the next (i.e. from time step tn to tn+1).The volume flow at tn+1 is based on massflows from tn and thus the volume flow and velocities may have opposite directions.

The volume error is corrected by “adding or subtracting fluid volume” over several time steps (not by iteration). This correction may also cause unphysical pressure and/or temperature peaks. (VOL is an output variable which should be plotted together with phase velocities during fast transients)

Modeling the pipeline profile in OLGA The assumption

OLGA topology

• GEOMETRY is a sequence of PIPES – a PIPE is defined by its • LENGTH • INCLINATION • INNER DIAMETER • ROUGHNESS and • WALL

OLGA topology cont.

NODE-1

a BRANCH consists of one GEOMETRY and two NODES

a BRANCH has flow direction

NODE-2

OLGA topology cont. a NODE is either TERMINAL or MERGE or SPLIT 1)

1)

v 4.00

An OLGA network consists of a number of BRANCHES

OLGA topology cont. PIPE_1 3

PIPE SECTIONS

2

1

1

2

2

3

3

4

PIPE SECTION BOUNDARIES

4

1 5

OLGA topology cont. OLGA calculates different types of output variables: VOLUME VARIABLES e.g. pressure (PT), temperature (TM) and volume fractions (e.g. HOL) are calculated in the midpoints of the pipe sections. BOUNDARY VARIABLES e.g. velocities, flowrates and flow patterns which are calculated on section boundaries. e.g. a VALVE is always positioned on a section boundary.

OLGA topology cont.

BOUNDARY of type ”CLOSED” –i.e. no flow across boundary

BOUNDARY of type ”PRESSURE” –i.e. flow across boundary.

OLGA topology cont. Pressure boundary

- Pressure, - Temperature, - Gas Mass Fraction - Water Mass Fraction

Analogy Pressure boundary; gas mass fraction Gas fraction = 1 P,T

Gas fraction = 0.5 P,T

Gas fraction = 0 P,T

How to make fluids flow • a mass SOURCE • pressure boundaries • the standard WELL

a mass SOURCE BOUNDARY TYPE = CLOSED OLGA calc. this P and T BOUNDARY TYPE = PRESSURE SOURCE-1 a mass source into the pipe Total mass rate T Gas mass fraction Water fraction

mass SOURCE cont. • a SOURCE feeds its mass regardless of the pressure in the pipe • a SOURCE can be positioned anywhere • one pipe section can have several SOURCES • a SOURCE can be negative

a negative SOURCE

BOUNDARY TYPE = PRESSURE

BOUNDARY TYPE = CLOSED

OLGA calc. this P

a mass source out of the pipe

SOURCE-out

two PRESSURE BOUNDARIES BOUNDARY TYPE = PRESSURE

BOUNDARY TYPE = PRESSURE Pin

Pout Pin > Pout

Pin

Pout Pin < Pout

a WELL BOUNDARY

BOUNDARY

TYPE = CLOSED

TYPE = PRESSURE

WELL-1 Pres

Reservoir P & T PI (productivity index) Injection index Gas mass fraction Water fraction

a WELL cont. • a WELL is essentially a pressure boundary

• fluid flows into the well when the bottom hole pressure is less than the reservoir pressure • a WELL can be positioned anywhere along a pipe • a pipe can have several WELLs • the Advanced Well Module provides numerous additional options.

Starting the dynamic calculation sequence conditions at t = 0 can either be calculated from user given Initial Conditions: calculated by the or be i.e. profiles of T, P, steady state mass flow, pre-processor gas volume fraction, water cut

Steady state pre-processor • Activated when setting STEADYSTATE = ON in mainkey OPTIONS • Gives a full steady state solution at time 0 (when STARTTIME = ENDTIME = 0 in INTEGRATION) • The subsequent dynamic simulation will tell you if the system is stable or not

0

time

Wall heat transfer • Standard heat transfer correlations • Averaged fluid properties • Radial heat conduction in pipe walls

Pipe wall discretisation How OLGA represents walls

Calculated by OLGA: Heat transfer coefficient gas

Need to input: Heat transfer coefficient

Need to input: liquid

Conductivity

Heat capacity Density

Fluid properties General • The fluid properties are pre-calculated tables as a function of P and T and for one fluid composition – It follows that the total composition is constant throughout a fluid table1)

• The exact value of a property for a given P and T is found by interpolating in the relevant property table

1)

Compositional tracking available with OLGA 2000 v3.00

Properties in the fluid tables

More on Rs: the gas mass fraction Rs =

mass of gas at P and T mass of gas + HC-liquid at P and T

• the mass transfer between gas and liquid as a function of variations in P and T is determined by a rate of mass transfer (it takes time) • the change of Rs w.r. to P and T determines this rate • thus: Rs (P,T) = constant gives no mass transfer

Restrictions - limitations • Table based fluid properties – Total composition is constant for one fluid table. • the solution is thus approximate due to slip, phase separation, network systems and varying sources of different compositions Flowline has Well A has

fluid properties ?

Fluid Table 1 Well B has Fluid Table 2

Process equipment with OLGA 2000 basic • Separators • Compressors • Heat exchangers • Chokes and Valves (CV) - critical, sub-critical • Check valves • Controllers PID,PSV,ESD etc. • Controlled sources and leaks • Pig/plug • Heated walls

OLGA 2000 Modules • Slugtracking

– with pigging • Water

– three-phase flow • FEM -Therm

– conductive 2-D (“radial”) heat transfer – finite elements – integrated with OLGA bundle – grid generator

OLGA 2000 Modules • Comptrack – compositional tracking • MEG-track • UBitTS – Under Balanced interactive transient Training Simulator • Advanced Well • Multiphase Pumps – positive displacement – rotodynamic • Corrosion • Wax

OLGA 2000 file structure Input File .inp Fluid Properties File .tab

ASCII file

OLGA 2000

.out .rsw reflex of the Input File + results from OUTPUT

.tpl

Trend Plot File results from TREND

.ppl Restart File (binary) Profile Plot File results from PROFILE

Principles of OLGA 2000 execution Input File .inp

OLGA 2000 GUI

OLGA 2000

Fluid Properties File .tab

.tpl PVTsim

.ppl .out

.rsw

OLGA 2000 Support • [email protected] – OLGA 2000 Helpdesk mail address

• http://www.olga2000.com – The OLGA 2000 web site

• [email protected] – OLGA 2000 News Network (ONN): Mailbox at Scandpower for sending news and important messages to the OLGA users that have signed on.

View more...
Contents • Introduction • Physical models and numerical solutions • Network topology • How to make fluids flow • Fluid properties • Heat transfer • Process equipment and modules • File structure and execution

Fundamental features • OLGA is – transient ( df/dt # 0 ) – one-dimensional (along pipe axis) – “complete” – a modified “two-fluid” model – realised with a semi-implicit numerical solution • staggered grid – made for (relatively) slow mass transients

The dynamic three phase flow simulator 8 Conserv. Equations mass (5) momentum (2) energy (1)

Closure Laws Fluid Properties

mass transfer momentum transfer energy transfer

Initial Conditions

Boundary Conditions

OLGA

The OLGA three phase flow model • Mass conservation – Gas – Hydrocarbon bulk – Hydrocarbon droplets – Water bulk – Water droplets • Momentum conservation – Gas + droplets – Liquid bulk • Energy conservation – Mixture • Constitutive equations

Variables • Primary variables – – – –

5 mass fractions (specific mass) 2 velocities 1 pressure 1 temperature

• Secondary variables – – – –

Volume fractions Velocities Flow rates Fluid properties

Conservation of mass

Conservation of energy

energy = mass (thermal energy + kinetic energy + potential energy)spec energy flow + work = mass flow (enthalpy + kinetic energy + potential energy)

Force balance equation (Conservation of momentum) Pj

Pj+1 gas liquid

j

dM /dt =

dZj

j+1

((M·V )j - (M·V )j+1) /dzj - S j + G j + F j + F j+1+ MT

M - Momentum V - Velocity m - Mass M = m ·V

S =

Shear

G= F = MT =

Gravity = m · gravity acceleration Force = pressure · flow area Momentum Transfer = mass transfer - entrainment + deposition

= wall shear + interfacial shear

The OLGA volume equation Pi i

Qi

i

Qi+1

i+1

source / sink

The OLGA volume equation for all sections the local fluid volume time variations

Combine all mass conservation equations

Net change of total fluid volume in a section = 0 T and RS constant

0= CdP/dt = Qin - Qout + volume change by mass transfer + volume change by mass sources + Volume Correction temperature change is assumed to be zero in this step : [m3/s]

(V / T)(T / t ) 0 C = “compressibility” i.e. dVfluid/dP

[m3/Pa]

Calculation sequence for each time step: a) solve model relations to give friction factors etc.

b) solve momentum - and volume equation simultaneously U and P c) perform flash d) solve mass equations first for gas then for oil film and oil droplets and then for water film and water droplets e) solve energy equation T f) perform flash

Sources of numerical errors in general •

Linearisation of strongly non-linear models – Iteration is not performed • Thermal expansion or contraction – Temperature decoupled from pressure may give volume errors • Local changes of total composition neglected in standard OLGA – taken into account in CompTrack

Volume error At each time step when all equations have been solved the net fluid volume change in each section usually is 0 and the volume error can be expressed as VOLi = 1- Vi f / Vsectioni 0 f Vi f = Vi f = m if =

mif / i f fluid volume in section no i mass in pipe section no i

i f =

density of fluid in section no i

(f indicates liquid , gas and droplets)

Volume error

cont.

The main source of high volume error peaks is change of phase velocity direction from one time step to the next (i.e. from time step tn to tn+1).The volume flow at tn+1 is based on massflows from tn and thus the volume flow and velocities may have opposite directions.

The volume error is corrected by “adding or subtracting fluid volume” over several time steps (not by iteration). This correction may also cause unphysical pressure and/or temperature peaks. (VOL is an output variable which should be plotted together with phase velocities during fast transients)

Modeling the pipeline profile in OLGA The assumption

OLGA topology

• GEOMETRY is a sequence of PIPES – a PIPE is defined by its • LENGTH • INCLINATION • INNER DIAMETER • ROUGHNESS and • WALL

OLGA topology cont.

NODE-1

a BRANCH consists of one GEOMETRY and two NODES

a BRANCH has flow direction

NODE-2

OLGA topology cont. a NODE is either TERMINAL or MERGE or SPLIT 1)

1)

v 4.00

An OLGA network consists of a number of BRANCHES

OLGA topology cont. PIPE_1 3

PIPE SECTIONS

2

1

1

2

2

3

3

4

PIPE SECTION BOUNDARIES

4

1 5

OLGA topology cont. OLGA calculates different types of output variables: VOLUME VARIABLES e.g. pressure (PT), temperature (TM) and volume fractions (e.g. HOL) are calculated in the midpoints of the pipe sections. BOUNDARY VARIABLES e.g. velocities, flowrates and flow patterns which are calculated on section boundaries. e.g. a VALVE is always positioned on a section boundary.

OLGA topology cont.

BOUNDARY of type ”CLOSED” –i.e. no flow across boundary

BOUNDARY of type ”PRESSURE” –i.e. flow across boundary.

OLGA topology cont. Pressure boundary

- Pressure, - Temperature, - Gas Mass Fraction - Water Mass Fraction

Analogy Pressure boundary; gas mass fraction Gas fraction = 1 P,T

Gas fraction = 0.5 P,T

Gas fraction = 0 P,T

How to make fluids flow • a mass SOURCE • pressure boundaries • the standard WELL

a mass SOURCE BOUNDARY TYPE = CLOSED OLGA calc. this P and T BOUNDARY TYPE = PRESSURE SOURCE-1 a mass source into the pipe Total mass rate T Gas mass fraction Water fraction

mass SOURCE cont. • a SOURCE feeds its mass regardless of the pressure in the pipe • a SOURCE can be positioned anywhere • one pipe section can have several SOURCES • a SOURCE can be negative

a negative SOURCE

BOUNDARY TYPE = PRESSURE

BOUNDARY TYPE = CLOSED

OLGA calc. this P

a mass source out of the pipe

SOURCE-out

two PRESSURE BOUNDARIES BOUNDARY TYPE = PRESSURE

BOUNDARY TYPE = PRESSURE Pin

Pout Pin > Pout

Pin

Pout Pin < Pout

a WELL BOUNDARY

BOUNDARY

TYPE = CLOSED

TYPE = PRESSURE

WELL-1 Pres

Reservoir P & T PI (productivity index) Injection index Gas mass fraction Water fraction

a WELL cont. • a WELL is essentially a pressure boundary

• fluid flows into the well when the bottom hole pressure is less than the reservoir pressure • a WELL can be positioned anywhere along a pipe • a pipe can have several WELLs • the Advanced Well Module provides numerous additional options.

Starting the dynamic calculation sequence conditions at t = 0 can either be calculated from user given Initial Conditions: calculated by the or be i.e. profiles of T, P, steady state mass flow, pre-processor gas volume fraction, water cut

Steady state pre-processor • Activated when setting STEADYSTATE = ON in mainkey OPTIONS • Gives a full steady state solution at time 0 (when STARTTIME = ENDTIME = 0 in INTEGRATION) • The subsequent dynamic simulation will tell you if the system is stable or not

0

time

Wall heat transfer • Standard heat transfer correlations • Averaged fluid properties • Radial heat conduction in pipe walls

Pipe wall discretisation How OLGA represents walls

Calculated by OLGA: Heat transfer coefficient gas

Need to input: Heat transfer coefficient

Need to input: liquid

Conductivity

Heat capacity Density

Fluid properties General • The fluid properties are pre-calculated tables as a function of P and T and for one fluid composition – It follows that the total composition is constant throughout a fluid table1)

• The exact value of a property for a given P and T is found by interpolating in the relevant property table

1)

Compositional tracking available with OLGA 2000 v3.00

Properties in the fluid tables

More on Rs: the gas mass fraction Rs =

mass of gas at P and T mass of gas + HC-liquid at P and T

• the mass transfer between gas and liquid as a function of variations in P and T is determined by a rate of mass transfer (it takes time) • the change of Rs w.r. to P and T determines this rate • thus: Rs (P,T) = constant gives no mass transfer

Restrictions - limitations • Table based fluid properties – Total composition is constant for one fluid table. • the solution is thus approximate due to slip, phase separation, network systems and varying sources of different compositions Flowline has Well A has

fluid properties ?

Fluid Table 1 Well B has Fluid Table 2

Process equipment with OLGA 2000 basic • Separators • Compressors • Heat exchangers • Chokes and Valves (CV) - critical, sub-critical • Check valves • Controllers PID,PSV,ESD etc. • Controlled sources and leaks • Pig/plug • Heated walls

OLGA 2000 Modules • Slugtracking

– with pigging • Water

– three-phase flow • FEM -Therm

– conductive 2-D (“radial”) heat transfer – finite elements – integrated with OLGA bundle – grid generator

OLGA 2000 Modules • Comptrack – compositional tracking • MEG-track • UBitTS – Under Balanced interactive transient Training Simulator • Advanced Well • Multiphase Pumps – positive displacement – rotodynamic • Corrosion • Wax

OLGA 2000 file structure Input File .inp Fluid Properties File .tab

ASCII file

OLGA 2000

.out .rsw reflex of the Input File + results from OUTPUT

.tpl

Trend Plot File results from TREND

.ppl Restart File (binary) Profile Plot File results from PROFILE

Principles of OLGA 2000 execution Input File .inp

OLGA 2000 GUI

OLGA 2000

Fluid Properties File .tab

.tpl PVTsim

.ppl .out

.rsw

OLGA 2000 Support • [email protected] – OLGA 2000 Helpdesk mail address

• http://www.olga2000.com – The OLGA 2000 web site

• [email protected] – OLGA 2000 News Network (ONN): Mailbox at Scandpower for sending news and important messages to the OLGA users that have signed on.

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