# compositional simulation

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L o g o

Compositional

Simulation

Applications

Black oil models

Immiscible flow

Hydrocarbon phase has fixed composition of two component oil and gas

Fluid properties are a function of pressure

Fluid properties are a function of pressure and solution gas

Applications

Compositional gas models

Significant mass transfer between oil and gas phases

Fluid properties are dependent on pressure and composition

Examples processes Volatile oil reservoir depletion

Gas condensate reservoir depletion

Gas cycling

Miscible flooding by CO2 or enriched gas

injection

Compositional Models

Fussell and Fussell (1978)

Coats (1980) : Fully implicit

Nghiem et al. (1981) : IMPES-type

Young and Stephens (1983)

Acs et al. (1985) : IMPEStype

Watts (1986) : Sequential implicit

Collins et al. (1986) : Adaptive implicit

Formulations

IMPES Type

Solve pressure and saturation separately

Adaptive implicit

In each time step solve few gridblocks implicitly and the rest explicitly

Fully implicit

Solve for pressure, saturation, and composition simultaneously

Applications

Compositional chemical models

Injection of of liquid chemicals to displace oil

Phase behavior

Reduction in interfacial tension between oil

and liquid

Example processes are

Surfactant/polymer

Surfactant/alkaline/polymer

Surfactant/foam

Displacements

Immiscible flow under reservoir conditions

fluids with different properties mix

Displacement of oil by miscible or partially

miscible fluids

Displacement using chemicals that can

affect fluid properties

Non isothermal flow or combustion reaction

Displacements

Miscible

Two or more components flow within a

single phase

Flow of oil by solvent

Transport of salts

Polymer

Tracers

Contaminant in water

Commercial Compositional Gas Reservoir Simulator

VIP (Landmark Graphics)

Eclipse 300 (Geoquest)

CMG-GEM (Computer Modeling Group)

Simbest (Formerly SSI and now Bakers)

Oil Reservoir Simulator

Black oil model for immiscible

processes

Miscible black oil model for first

contact miscible process where

injected fluid is directly miscible with

oil at reservoir pressure and

temperature

Reservoir Simulators

Compositional gas models for multiple contact miscible displacements

Inject CO2 to mobilize and displace residual oil saturation through multiple contacts

between oil and CO2 phases

Intermediate and higher molecular weight hydrocarbons are contacted into the CO2rich phase

Under proper conditions CO2 becomes miscible with the original reservoir oil

Reservoir Simulators

Compositional chemical models for

chemical flooding processes

Thermal models for steam flooding and

in situ combustion

Mathematical Models Isothermal conditions

No flow boundary

Permeability tensor is orthogonal and aligned with the coordinate system

No precipitation or chemical reaction

Negligible adsorption

Physical dispersion follows Ficks law Water is treated as a separate component present

only is water

No mass transfer between water and oil or gas phases

Hydrocarbon phase compose of nc hydrocarbon components which may include nonhydrocarbons such as CO2, N2, or H2S

Assume instantaneous thermodynamic equilibrium between hydrocarbon phases

Mass Conservation Equation

termSourceR

FluxF

onAccumulatiW

RFt

W

i

i

i

iii

0

Mass Conservation Equation

jphaseinicomponentoffractionmolex

jphaseforsaturationS

jphasefordensitymolar

porosity

xSW

ij

j

j

ijj

n

jji

p

1

Accumulation term

Mass Conservation Equation

111

2

,........1

SW

and

nhydrocarbonixSW

c

p

n

c

n

jijjji

Since there is no hydrocarbon component in the water phase

Accumulation term

Mass Conservation Equation

Phase Index

J = 1 water

J = 2 Oil

J = 3 Gas

Mass Conservation Equation

Flux Term

ijijjjjij

n

jji xKSuxF

p

1

Convective Flux Dispersive Flux

Mass Conservation Equation

DepthD

jphaseofweightspecific

jphaseofitycosvis

typermeabilirelativek

mobilityrelative

tyPermeabiliK

DPku

j

j

rj

k

rj

jjrjj

j

rj

Darcy's law

Mass Conservation Equation

1ccb

ii n,n,.....1i

V

qR

Source term:

Vb= Bulk volume

qi = Molar flow rate of component i

producer : negative value

Injector : Positive value

Physical Dispersion

Diagonal terms

zzij

yyij

j

2zj

j

Tj

j

2yj

j

Tj

j

2xj

j

Ljijxxij

KandKfortermsSimilar

u

u

Su

u

Su

u

S

DK

zzzyzx

yzyyyx

xzxyxx

ij

KKK

KKK

KKK

K

tydispersiviTransverse

tydispersiviallongitudin

tortuosity

dispersionmolecularD

T

L

ij

Physical Dispersion

Off Diagonal terms

2zj

2yj

2xjj

zyij

yzij

zxij

xzij

yxij

xyij

j

yjxj

j

TjLjxyij

uuuu

where

KK

KK

KK

u

uu

SK

L o g o

Compositional

Simulation

Mass Conservation Equation

Set of coupled, nonlinear, partial differential

equations with ncnp+6np+2 variables

1,,.........1

011

cc

b

in

jijijjjjijj

n

jijjj

nni

V

qxKSuxxS

t

pp

Pressure Equation

Acs et al. formulation where total fluid volume is equal to the pore volume

)(),( PVNPV pt

t

P

P

V

t

N

N

V

t

P

P

V pn

i

i

ikNPi

t

N

tc

ki

1

1)(,

reffref PPc 1 frefpp cVPV

Pressure EquationFrom mass conservation equation, we have

ij

n

1jjjbi

cc

i

n

1jijijjjjijjb

i

xSVNwhere

1n,n,.........1i

0qxKSuxVt

N

p

p

Define partial molar volume as

)(, ikNPi

tti

k

N

VV

Pressure Equation

Neglect physical dispersion and cjj PPP

1

1

1

1 1

c

c p

n

iiti

n

i

n

jjcjijjrjtib

tf

ref

p

qV

DPxkVVt

P

P

VcV

Initial conditions: known pressure and known no. of moles

for each component

Boundary conditions : No flow boundary

Variables No. of variables

1

Sj np

ij np

xij (np-1)nc

Krj np

j np

Pj np

j np

qi nc+1

Total nc np+6 np+2

List of Variables

Equations Name No. Of Eq.

Mass conservation nc+1

fij = fil Phase equilibrium nc(np-2)

Saturation constraint 1

Phase composition

constraint

np-1

Formation porosity 1

Equation of State np

Equation of State np

Viscosity np

11

pn

jjS

11

cn

iijx

P

),(

)(11

jjj xP

P

),(

)(11

jjj xP

P

),(

)(11

jjj xP

P

Number of Equations

Equations Name No. Of Eq.

Phase

Relative permeability np

Phase pressure np-1

Well model nc+1

Totalnc np+6 np+2

),,( xSPkk rjrj

),( xSPP jj

),,( xSPqq ii

Number of Equations

IMPES Computational Procedure

Establish initial conditions

Phase saturation

Component moles

Viscosity

Density

Relative permeability

Capillary pressure

Original in place

Fluid volume

IMPES Computational Procedure

1. Solve pressure equation implicitly using

explicit saturation and phase composition

dependent properties

2. Compute flow rate and bottomhole pressure

for wells

3. Solve mass balance equation explicitly for

component mole number and overall

hydrocarbon composition

4. Solve for phase equilibrium and hydrocarbon

phase saturation

IMPES Computational Procedure

5. Compute phase densities

6. Calculate phase viscosities

7. Calculate phase relative

permeabilities

8. Compute capillary pressures

Special Case

2 hydrocarbon oil and gas phases

No physical dispersion

Use Darcys law

jrjj ku

Special Case

Water equation is the same as

black oil model

w

www

w

w

B

S

tq

B

Mass balance for component i

ggiooiigggioooi SySxt

qyx

cowcogg

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