Pressure Buildup at CO2 Injection Wells

Sally M. BensonLawrence Berkeley National Laboratory

Berkeley, California 94720

Second Annual Conference on Carbon SequestrationMay 5-8, 2003

Abstract

An approximate analytical solution for calculating pressure buildup at CO2 injection wells has been developed. It can be used to rapidly calculate the pressure buildup during injection, as well as, the rate of pressure falloff once injection stops. The solution includes the influence of the advancing CO2 front, changes in the permeability of the near-well region due to chemical reactions between the CO2 and reservoir rock, and temperature dependent viscosity. The approximate solution can be used for both open and closed systems. In addition, it can be used as the basis for designing and interpreting pressure tests as a method of monitoring the progress of CO2 injection operations.

Applications

• Estimation of injection pressures at CO2injection wells

• Pressure transient analysis at CO2 injection wells

• Evaluation of the influence of CO2/water/rock interactions on formation permeability

• Characterization and monitoring of CO2sequestration processes and progress

Physical Processes During Injectionof CO2 into Water

• Immiscible displacement of water by CO2• Relative permeability effects• Capillary pressure effects• Adverse mobility ratio

µwater >>µCO2

• Pressure and temperature dependent CO2 viscosity and density

• Partitioning of CO2 into the water phase

• Partitioning of water into the CO2 phase

Relative Permeablity

0

0.2

0.4

0.6

0.8

1

0 0.25 0.5 0.75 1

sw

0

0.2

0.4

0.6

0.8

1krCO2

krw

Relative Permeablity

0

0.2

0.4

0.6

0.8

1

0 0.25 0.5 0.75 1

sw

0

0.2

0.4

0.6

0.8

1krCO2

krw

Implications for Pressure BuildupDuring CO2 Injection

⇒ Relative permeability of CO2and water will vary in the region behind the CO2-front

Saturation of CO2 and water will vary in the region

behind the CO2- front

Saturation Distribution

00.20.40.60.8

1

0 50 100 150 200r (m)

Saturation Distribution

00.20.40.60.8

1

0 50 100 150 200r (m)

Sharp Front

Relative Pemeability

00.20.40.60.8

1

0 50 100 150 200r (m)

Relative Pemeability

00.20.40.60.8

1

0 50 100 150 200r (m)

A New Approximate Analytical Solution For Pressure Buildup

• Assumptions• Buckley-Leverett type

displacement• Vertical equilibrium

Horizontal reservoir• Homogeneous reservoir• Neglect capillary pressure

(not required)• Slightly compressible fluid

• Based on technique developed by Benson (1984, 1987)

rw rf

qCO2

hk,ct,φ

∞

New Pressure Buildup Solution

• Solution consists of two components• Steady state pressure buildup behind the CO2

front (∆ps.s.)• Pressure transient buildup outside of the front

(∆pt)

)4

(4

),(

),(),(

),(),(

2),(

),(),(),(

2

..

..

2

2

2

2

2

22

ktcr

Eikhq

trp

rdr

trktr

trtrf

khq

trp

trptrptrp

twf

CO

wCOft

r

COr

r CO

COCOwss

ftwssw

CO

f

w

φµρπµ

µρπ

=∆

=∆

∆+∆=∆

∫

Evaluating ∆p s.s.

rdr

trktr

trtrf

khq

trpCO

f

w r

COr

r CO

COCOwss ),(

),(),(),(

2),(

2

2

2

22..

µρπ ∫=∆

Density DistributionAfter 30 Days of Injection

700725750775800

0 50 100 150r (m)

CO

2< 10% variation

Density DistributionAfter 30 Days of Injection

700725750775800

0 50 100 150r (m)

CO

2< 10% variation

Viscosity DistributionAfter 30 Days of Injection

6.0E-056.5E-057.0E-057.5E-058.0E-05

0 50 100 150r (m)

CO

2

< 10% variation

Viscosity DistributionAfter 30 Days of Injection

6.0E-056.5E-057.0E-057.5E-058.0E-05

0 50 100 150r (m)

CO

2

< 10% variation

Assign average values for ρ and µ behind the front

Multi-phase Flow Behind the CO2 Front

22

2

2

2

2

CO

CO

sCO

CO

CO

COs s

fhtq

r∂∂

ρπφ=

)()(

1

1)(

22

22

2

22

COrw

wrCOCOw

COCOCO

skskqq

qsf

CO

w

µµ

+=

+=

Fractional Flow of CO2

0.00

0.20

0.40

0.60

0.80

1.00

0 0.2 0.4 0.6sCO2

sf

Fractional Flow of CO2

0.00

0.20

0.40

0.60

0.80

1.00

0 0.2 0.4 0.6sCO2

sf

Buckley-Leverett Solution

Saturation Distribution

00.20.40.60.8

1

0 50 100 150 200r (m)

Saturation Distribution

00.20.40.60.8

1

0 50 100 150 200r (m)

Buckley-Leverett Solution

Evaluating ∆p s.s.

rdr

trktrf

khq

trpf

w CO

r

r r

CO

CO

COCOwss ∫=∆

),(),(

2),(

2

2

2

22.. ρπ

µ

CO2 Saturation After 30 Days

0.0

0.5

1.0

0 50 100 150r (m)

Numerical

Buckley Leverett

CO2 Saturation After 30 Days

0.0

0.5

1.0

0 50 100 150r (m)

Numerical

Buckley Leverett

fCO2/krCO2 30 Days

0.0010.0020.0030.0040.00

0 50 100 150r (m)

fCO2/krCO2 30 Days

0.0010.0020.0030.0040.00

0 50 100 150r (m)

Assign a linear variation for fCO2/krCO2 behind the front

Approximate Analytical Solution),(),(),( .. trptrptrp ftwssw ∆+∆=∆

+=∆

−−⋅

−+=∆

80907.ln4

),(

ln11ln2

),(

2

..

2

2

2

2

2

22

ftwCO

wCOft

w

f

wf

w

rr

CO

w

f

CO

COCOwss

rckt

khq

trp

rr

rrr

kf

rr

khq

trpf

CO

φµρπµ

ρπµ

rsCO2 =Qtπφh

∂fCO2∂sCO2 sCO2

Fractional Flow of CO2

0.00

0.25

0.50

0.75

1.00

0 0.2 0.4 0.6

sCO2

sf

Fractional Flow of CO2

0.00

0.25

0.50

0.75

1.00

0 0.2 0.4 0.6

sCO2

sf

Typical Pressure Buildup

195

197

199

201

203

0 30 60 90 120 150 180time (days)

Pres

sure

(bar

s)

k = 100 mDh = 20 mqCO2 = 15.86 kg/sinitial pressure = 150 barsµCO2 = 6.5 e-5 Pa-sρCO2 = 715 kg/m3

porosity = 0.12195

197

199

201

203

0 30 60 90 120 150 180time (days)

Pres

sure

(bar

s)

k = 100 mDh = 20 mqCO2 = 15.86 kg/sinitial pressure = 150 barsµCO2 = 6.5 e-5 Pa-sρCO2 = 715 kg/m3

porosity = 0.12

Semi-log Plot

195

197

199

201

203

0.10 1.00 10.00 100.00 1000.00time (days)

Pres

sure

(bar

s)

0.5

0.7

0.9

1.1

1.3

1.5

Slop

e (b

ars)

Pressure BuildupSlope

195

197

199

201

203

0.10 1.00 10.00 100.00 1000.00time (days)

Pres

sure

(bar

s)

0.5

0.7

0.9

1.1

1.3

1.5

Slop

e (b

ars)

Pressure BuildupSlope

khq

mCO

COCO

2

22

4 ρπµ

=

How Good Is the Approximate Solution?

• Comparison to numerical simulation generated using TOUGH2 (Pruess et al., 2001)

Pressure Buildup

190

195

200

205

210

0.01 0.10 1.00 10.00 100.00time (days)

Pres

sure

(bar

s)

Numericalsf=0.225sf=0.23

Pressure Buildup

190

195

200

205

210

0.01 0.10 1.00 10.00 100.00time (days)

Pres

sure

(bar

s)

Numericalsf=0.225sf=0.23

Summary• A new approximate analytical solution for

predicting pressure buildup during CO2 injection into brine formations has been developed

• Comparison to numerical simulations verifies the applicability of this solution to typical CO2sequestration scenarios

• Pressure transient analysis may provide a useful tool for monitoring CO2 sequestration operations, including:• Validation of multiphase flow processes• Front tracking• Detection of permeability changes from CO2 injection