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L o g o Compositional Simulation

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Page 1: Compositional Simulation

L o g o

Compositional

Simulation

Page 2: 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

Page 3: Compositional Simulation

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

Page 4: Compositional Simulation

Compositional Models

• Fussell and Fussell (1978)

• Coats (1980) : Fully implicit

• Nghiem et al. (1981) : IMPES-type

• Young and Stephens (1983)

• Acs et al. (1985) : IMPES–type

• Watts (1986) : Sequential implicit

• Collins et al. (1986) : Adaptive implicit

Page 5: Compositional Simulation

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

Page 6: Compositional Simulation

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

Page 7: Compositional Simulation

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

Page 8: Compositional Simulation

Displacements

• Miscible

­ Two or more components flow within a

single phase

• Flow of oil by solvent

• Transport of salts

• Polymer

• Tracers

• Contaminant in water

Page 9: Compositional Simulation

Commercial Compositional Gas Reservoir Simulator

• VIP (Landmark Graphics)

• Eclipse 300 (Geoquest)

• CMG-GEM (Computer Modeling Group)

• Simbest (Formerly SSI and now Bakers)

Page 10: Compositional Simulation

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

Page 11: Compositional Simulation

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 CO2

rich phase

­ Under proper conditions CO2 becomes miscible with the original reservoir oil

Page 12: Compositional Simulation

Reservoir Simulators

• Compositional chemical models for

chemical flooding processes

• Thermal models for steam flooding and

in situ combustion

Page 13: Compositional Simulation

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 Fick’s 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

Page 14: Compositional Simulation

Mass Conservation Equation

termSourceR

FluxF

onAccumulatiW

RFt

W

i

i

i

iii

0

Page 15: Compositional Simulation

Mass Conservation Equation

jphaseinicomponentoffractionmolex

jphaseforsaturationS

jphasefordensitymolar

porosity

xSW

ij

j

j

ijj

n

jji

p

1

• Accumulation term

Page 16: Compositional Simulation

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

Page 17: Compositional Simulation

Mass Conservation Equation

• Phase Index

­ J = 1 water

­ J = 2 Oil

­ J = 3 Gas

Page 18: Compositional Simulation

Mass Conservation Equation

• Flux Term

ijijjjjij

n

jji xKSuxF

p

1

Convective Flux Dispersive Flux

Page 19: Compositional Simulation

Mass Conservation Equation

DepthD

jphaseofweightspecific

jphaseofitycosvis

typermeabilirelativek

mobilityrelative

tyPermeabiliK

DPku

j

j

rj

k

rj

jjrjj

j

rj

• Darcy's law

Page 20: Compositional Simulation

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

Page 21: Compositional Simulation

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

Page 22: Compositional Simulation

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

Page 23: Compositional Simulation

L o g o

Compositional

Simulation

Page 24: 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

Page 25: Compositional Simulation

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 f

ref

p

pcV

P

V

Page 26: Compositional Simulation

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

Page 27: Compositional Simulation

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

Page 28: Compositional Simulation

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

Page 29: Compositional Simulation

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

Page 30: Compositional Simulation

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

Page 31: Compositional Simulation

IMPES Computational Procedure

• Establish initial conditions

­ Phase saturation

­ Component moles

­ Viscosity

­ Density

­ Relative permeability

­ Capillary pressure

­ Original in place

­ Fluid volume

Page 32: Compositional Simulation

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

Page 33: Compositional Simulation

IMPES Computational Procedure

5. Compute phase densities

6. Calculate phase viscosities

7. Calculate phase relative

permeabilities

8. Compute capillary pressures

Page 34: Compositional Simulation

Special Case

• 2 hydrocarbon oil and gas phases

• No physical dispersion

• Use Darcy’s law

jrjj ku

Page 35: Compositional Simulation

Special Case

• Water equation is the same as

black oil model

w

www

w

w

B

S

tq

B

Page 36: Compositional Simulation

Mass balance for component i

ggiooiigggioooi SySxt

qyx

cowcoggw

wcoggwocow

coggoogcog

g

jjj

PPPP

PPPPPP

PPPPPP

PP

DPSubstitute

Reference phase

Special Case

Page 37: Compositional Simulation

Interfacial Tension

• Water and hydrocarbon phases = constant

• Hydrocarbon phases (Macleod –Sugden)

tensionerfacialintgas/oil

icomponentofParachor

yx016018.0

og

i

n

1i

igioiog

c

Page 38: Compositional Simulation

Physical Properties

• Relative permeability

­ Function of phase saturation

and interfacial tension

• Capillary pressure

­ Function of phase saturation

and interfacial tension

jljcjl SfP ,

jljrjl Sfk ,

Page 39: Compositional Simulation

Physical Properties

• Molar density

RTZ

P

v

1

jjj

• Mass density

gasoroiljWxcn

1itiijjj

Where Wti is the molecular weight of component i

waterref

PPc

111

111

Page 40: Compositional Simulation

Physical Properties

• Phase viscosity using linear mixing rule

gasoroiljx i

n

iijj

c

~1

Where i~ is the pure component viscosity

Page 41: Compositional Simulation

Phase Behavior

• Peng-Robinson Equation of State

bvbbvv

)T(a

bv

RTP

a and b are constants computed as a function of

critical properties.

Compressibility factor: RT

PVz

RT

bPB

RT

aPA

0BBABZB2B3AZB1Z

2

32223

Page 42: Compositional Simulation

Critical Properties

Comp. Composition P

(psi)

T

(R)

V

ft3/lbmole

MW Accentric

factor

Parachor

CO20.05 1073 547 1.5 44 0.23 49

C3-617.8 476 848 5.0 73 0.25 60

C715.5 453 985 6.0 96 0.28 100

C832.35 430 1040 8.8 102 0.30 300

Page 43: Compositional Simulation

Binary Interaction Coefficients

CO2 C3-6 C7 C8

CO2 0.0

C3-6 0.12 0.0

C7 0.12 0.0 0.0

C8 0.12 0.0 0.0 0.0

Page 44: Compositional Simulation

Phase Behavior

100% bubble

point curve

Bubble

point

Dew point

Liquid + vapor

Vapor

T

P

PC

TC

Page 45: Compositional Simulation

Phase Behavior

2 phase

1 phase

Methane

C7+ C2-C6

Tie line

Plait point

Binodal curve

T, P = constant

Page 46: Compositional Simulation

Ternary Diagram

Plait point

Binodal curve

Tie line

CO2

C13+ C5-12

Page 47: Compositional Simulation

L o g o

Three and Four Phase Flow

Compositional Gas Simulations

Page 48: Compositional Simulation

Phase Diagram

Liquid/

Liquid/

Vapor0

500

1000

1500

2000

2500

3000

0.0 0.2 0.4 0.6 0.8 1.0

Mole Fraction of CO2/NGL

Pre

ssu

re (

psi) Liquid

Liquid/Liquid

Liquid/Vapor

Page 49: Compositional Simulation

Permeability Field

100 200 300 400 500 600 700 800 900 1000

Length (ft)

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Ele

va

tio

n (

ft)

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

Permeability(md)

Injector Producer

Page 50: Compositional Simulation

Phase Viscosities

0.01

0.1

1

10

100

1000

0 200 400 600 800 1000Length, ft

Vis

co

sit

y,

cp

Oil Viscosity (4-Phase Flow)Gas Viscosity (4-Phase Flow)Second HC Liquid Viscosity (4-Phase Flow)Oil Viscosity (3-Phase Flow)Gas Viscosity (3-Phase Flow)

Page 51: Compositional Simulation

Phase Densities

0

10

20

30

40

50

60

0 200 400 600 800 1000Length, ft

De

ns

ity

, lb

m/c

uft

Oil Density (4-Phase Flow)

Gas Density (4-Phase Flow)

Second HC Liquid Density (4-Phase Flow)

Oil Density (3-Phase Flow)

Gas Density (3-Phase Flow)

Page 52: Compositional Simulation

Number of Phases

0 100 200 300 400 500 600 700 800 900 1000

Length,ft

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Ele

va

tio

n,f

t

2

3

4

Page 53: Compositional Simulation

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 182.5 365 547.5 730

Total Injection Time (Days)

Cu

mu

lati

ve O

il R

eco

very

(F

racti

on

of

OO

IP)

4-phase flow (Run 4p2dh3b4)

3-phase flow (Run 3p2dh3b4)

Comparison of three and four phase flow results

Page 54: Compositional Simulation

SPE 89343

Reservoir Simulation of CO2 Storage in

Deep Saline Aquifers

A. Kumar, M. Noh, G.A. Pope, K. Sepehrnoori,

S.L. Bryant and L.W. Lake.

Center for Petroleum & Geosystems Engineering,

The University of Texas at Austin.

Carbon Sequestration

Page 55: Compositional Simulation

CO2

Deep Saline Aquifer

Aquifer/Depleted

Oil or Gas Reservoir

Oil/Gas Producing Reservoir

Unmineable Coal

CO2

Deep Saline Aquifer

Aquifer/Depleted

Oil or Gas Reservoir

Oil/Gas Producing Reservoir

Unmineable Coal

Evaluate Storage Potential of Aquifers

CO2

Page 56: Compositional Simulation

Brine Dissolution Traps Significant CO2 Volume

1000 Years50 Years

CO2 mole fraction in

aqueous phase

Page 57: Compositional Simulation

0

20

40

60

80

100

0 200 400 600 800 1000

Time, years

CO

2 S

tore

d i

n V

ari

ou

s P

ha

se

s,

%CO2 Capture

Percentage CO2

as Residual Gas

Percentage CO2 in

Aqueous Phase

Percentage CO2

as Free Gas

Injection

ends

Page 58: Compositional Simulation

L o g o

SPE 80253

Effect of Dispersion on Transport and

Precipitation of Barium and Sulfate In Oil

Reservoirs

2003 SPE International

Symposium on Oilfield

Chemistry

February 5-7, 2003

Houston, Texas

Page 59: Compositional Simulation

Objectives

• Determine sensitivity to sulfate concentration

in injected seawater for 150-300 ppm barium

concentration in formation brine

• Estimate how much sulfate will need to be

removed from injected water

• Determine sensitivity to dispersion and mixing

in reservoir

• Determine how much solid precipitates in

reservoir and in wellbore

Page 60: Compositional Simulation

Reservoir Model Description

• Three - dimensional

22x40x22 (19,360 gridblocks)

• Pore volume

123 million m3 (774 million bbls)

• OOIP

6 million m3 (38 million bbls)

• 4 vertical injectors, 3 slanted producers

• 10-year simulation

Page 61: Compositional Simulation

Water Analysis

Ion Formation Water, Mg/L Injected Seawater, Mg/L

Na+ 37,400 11,400

K+ 329 400

Ca++ 3,067 435

Mg++ 1,114 1,370

HCO3- 1,029 0

Cl- 62,380 20,500

Li+ 3.4 0

Sr++ 153 0

Ba++ 151 0

Fe 1.7 0

B 41 0

Br- 325 0

SO4-- 0 2,800

Page 62: Compositional Simulation

Simulation Variables

• Initial Barium ion concentration (ppm)

­ 151 and 300

• Physical longitudinal dispersivity (m)

­ 100, 12, 0 (only numerical dispersion)

• Injected sulfate ion in water (ppm)

­ 2800 ( seawater), 200, 120, 80, 40, 20

Page 63: Compositional Simulation

Simulation Grid

Vertical exaggeration = 3

Page 64: Compositional Simulation

Permeability Distribution150 m

Permeability, md

1 50 100+25 75

Permeabilities from 100 to 3720: red

Permeabilities below 20: transparent

Page 65: Compositional Simulation

Barium, mole/L

0.0000 0.0010 0.00200.0005 0.0015

Barium Ion Concentration

Barium ion concentrations less than 0.0007 are transparent

After One Year of

Seawater Flooding

After Ten Years of

Seawater Flooding

Initial Ba++ = 300 ppm

Dispersivity = 12 m

Page 66: Compositional Simulation

2800200

120

80

40

20100

12

00

50

100

150

200

250

300

350

400

Initial Barium

Concentration = 300 ppm

Total Barium Sulfate Precipitated in Wells

Page 67: Compositional Simulation

Mass of Barium Sulfate Precipitated in Formation

0

500

1000

1500

2000

2500

3000

3500

4000

0 1000 2000 3000 4000

Time, days

Ma

ss

of

Pre

cip

ita

te, to

ns

0 m

12 m

100 m

Dispersivity

120 ppm SO4

--and 151 ppm Ba

++