imbibition assisted recovery orkhan h pashayev petroleum engineering department texas a&m...

Imbibition Assisted Recovery

Orkhan H PashayevPetroleum Engineering

DepartmentTexas A&M University

February 2004Masters Division

Presentation Outline

February 2004Imbibition Assisted Recovery

IntroductionProblem StatementBackground and Literature ReviewObjectives

Numerical ModelingGrid SensitivityMatching Experimental ResultsNumerical Analyses of Spontaneous Imbibition

Imbibition Upscaling

Conclusions

Problem Statement

February 2004Imbibition Assisted Recovery

An understanding the role of imbibition in Naturally Fractured Reservoirs in order to achieve maximum recovery

Lack of knowledge in upscaling laboratory imbibition experiments to field dimensions

February 2004Imbibition Assisted Recovery

Two methods of modeling Naturally Fractured ReservoirsNumerical model with sufficiently

refined grid to adequately represent matrix/fracture geometry

Dual Porosity Model (Warren and Root, 1963)

Background and Literature Review

VUGS MATRIX

FRACTURE

MATRIX FRACTURE

ACTUAL RESERVOIR MODEL RESERVOIR

VUGS MATRIX

FRACTURE

VUGS MATRIX

FRACTURE

MATRIX FRACTUREMATRIX FRACTURE

ACTUAL RESERVOIR MODEL RESERVOIR

February 2004Imbibition Assisted Recovery

Expulsion of oil from matrix block to the surrounding fractures by capillary imbibition of water is the most important oil recovery in Naturally Fractured Reservoirs

Background and Literature Review

February 2004Imbibition Assisted Recovery

Transfer Functions:

Transfer functions that use Darcy’s Law

Diffusivity transfer functions

Empirical transfer functions

Scaling transfer functions

Background and Literature Review

February 2004Imbibition Assisted Recovery

Scaling transfer functions: Rapoport (1952)

Graham and Richardson (1959), Mattax and Kyte (1962)

Hamon and Vidal (1986), Bourblaux and Kalaidjian (1995), Akin and Kovsek (1998), etc

Du Prey (1978), Kazemi (1992), Ma et.al (1996), etc

blockmatrixw

c

welw

c

w dS

dP

L

tk

dS

dP

L

tk

2

mod

2

2

1

L

ktt

W

mD

Background and Literature Review

February 2004Imbibition Assisted Recovery

Conduct numerical studies with matrix block surrounded by fractures to better understand the characteristic of spontaneous imbibition

Evaluate dimensionless time tD and investigate the limitations of the upscaling laboratory imbibition experiments to field dimensions

Objectives

Presentation Outline

February 2004Imbibition Assisted Recovery

IntroductionProblem StatementBackground and Literature ReviewObjectives

Numerical ModelingGrid SensitivityMatching Experimental ResultsNumerical Analyses of Spontaneous Imbibition

Imbibition Upscaling

Conclusions

February 2004Imbibition Assisted Recovery

Two phase black-oil commercial simulator, CMG™

Core = 3.2cm x 3.2cm x 4.9cmK = 74.7SWi = 41.61%Φ = 15.91%μOIL = 3.52 cpμWATER = 0.68 cpAPIOIL = 31°

Simulation Parameters

February 2004Imbibition Assisted Recovery

Cartesian grid system

Grid Sensitivity Analyses

SimulationRun

No. of gridblocks in I, J and K directionsTotal No. of

gridblocks

I - Direction J - Direction K - Direction

1 7 7 7 343

2 12 12 12 1,728

3 16 16 16 4,096

4 20 20 20 8,000

5 20 20 25 10,000

February 2004Imbibition Assisted Recovery

Grid Sensitivity AnalysesOil Recovery Curves

0

5

10

15

20

25

30

35

40

45

50

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Time, min

Re

co

ve

ry,

%

7x7x7 - 343

12x12x12 - 1728

16x16x16 - 4096

20x20x20 - 8000

20x20x25 - 10000

February 2004Imbibition Assisted Recovery

Grid Sensitivity Analyses

Water Saturation Profile

0

1

2

3

4

5

6

65 65.5 66 66.5 67 67.5 68 68.5 69

Water Saturation (%)

7x7x7 - 343

12x12x12 - 1728

16x16x16 - 4096

20x20x20 - 8000

20x20x25 - 10000

February 2004Imbibition Assisted Recovery

Grid Sensitivity Analyses

Computer Time

0

20

40

60

80

100

120

140

160

180

200

0 2,000 4,000 6,000 8,000 10,000 12,000

Total No. of Gridblocks

CP

U T

ime,

sec

1728 4096

8000

10000

February 2004Imbibition Assisted Recovery

Reservoir Grid

I = 20, J = 20, K = 20

No. of gridblocks = 8000

Grid dimensionsI: 1x0.01cm 18x0.178cm 1x0.01cmJ:1x0.01cm 18x0.178cm 1x0.01cmK:1x0.01cm 19x0.259cm

February 2004Imbibition Assisted Recovery

Matching Experimental Results

Simulation vs. Experiment

0

5

10

15

20

25

30

35

40

45

50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

Time, min

Oil

Re

co

ver

y, %

Simulation

Experiment

February 2004Imbibition Assisted Recovery

Matching Experimental Results

The following logarithmic capillary pressure relationship was used

)ln(SwPP occ

PC° - threshold capillary pressureSW – water saturation

Simulation vs. Experiment

0

5

10

15

20

25

30

35

40

45

50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

Time, min

Oil R

ec

ov

ery

, %

Simulation

Experiment

February 2004Imbibition Assisted Recovery

Matching Experimental Results

2ocP

February 2004Imbibition Assisted Recovery

Gravity Effect

Bond number

ρWATER = 1 g/cc

ρOIL = 0.8635 g/cc

ρWATER = ρOIL = 0.8635 g/cc

221 Lg

Bo

February 2004Imbibition Assisted Recovery

Different Boundary Conditions

All Faces Open

Two Ends Closed

Two Ends Open

One End Open

No Flow Surfaces

February 2004Imbibition Assisted Recovery

Different Boundary Conditions

Oil Recovery Curves

0

10

20

30

40

50

60

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

Time, min

Oil

Rec

over

y, %

Recovery_AFO

Recovery_TEO

Recovery_TEC

Recovery_OEO

February 2004Imbibition Assisted Recovery

Different Boundary Conditions

Absolute Time for Imbibition as a Function of Faces Available for Imbibition

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7Number of Open Faces

To

tal T

ime

of

Imb

ibit

ion

to

g

et C

ore

60%

Wat

er

Sat

ura

ted

, (m

in)

February 2004Imbibition Assisted Recovery

Heterogeneities

K1

K2

K3

K4

One End Open

Case 1: K1 > K2 > K3 > K4

Case 2: K1 < K2 < K3 < K4

water

February 2004Imbibition Assisted Recovery

Oil Recovery Curves

0

5

10

15

20

25

30

35

40

45

50

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

Time, min

Oil

Re

co

ve

ry, %

K1>K2>K3>K4

K1<K2<K3<K4

Heterogeneities

Presentation Outline

February 2004Imbibition Assisted Recovery

IntroductionProblem StatementBackground and Literature ReviewObjectives

Numerical ModelingGrid SensitivityMatching Experimental ResultsNumerical Analyses of Spontaneous Imbibition

Imbibition Upscaling

Conclusions

2

1

L

ktt

W

mD

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition UpscalingTheory

Recovery behavior for a large reservoir matrix block could be predicted from lab experiments

Mattax and Kyte

Ma et.al

OWg

n

i A

i

bc

ilA

VL

1

2

1

cg

mD

L

ktt

February 2004Imbibition Assisted Recovery

All Faces Open, Two Ends Closed, Two Ends Open and One End Open

Semi-log plot:Normalized Recovery vs. Dimensionless

Time

Spontaneous Imbibition Upscaling

R

RR imb

n

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0

Dimensionless time, td

No

rmal

ized

Rec

ov

ery

AFO

TEC

TEO

OEO

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition UpscalingComparison

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0 1000000.0

Dimensionless time, td

Nor

mal

ized

Rec

over

y

AFO

TEC

TEO

OEO

2

1

L

ktt

W

mD

2

1

cg

mD

L

ktt

AFO

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00 1000000.00

Dimensionless time, td

No

rma

lize

d R

ec

ov

ery

M=1.15

M=6.54

M=13.07

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling

wro

orw

k

kM

*

*

Varying Mobility Ratio

2

1

cg

mD

L

ktt

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition UpscalingVarying Mobility Ratio

Mobility Ratio - not included

Need to include mobility ratio into the formulation of dimensionless time

*

*

**2 1

1

MML

ktt rorw

cD

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition UpscalingVarying Mobility Ratio

AFO

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

Dimensionless time, td

No

rmal

ized

Rec

ove

ry

M=1.15

M=6.54M=13.07

TEO TEO

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

Dimensionless time, tdNo

rmal

ized

Reco

very

M=1.15

M=6.54

M=13.07

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling

TEO

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

Dimensionless time, td

Nor

mal

ized

Rec

over

y

M=1.15

M=6.54

M=13.07

*

*

**2 1

1

MML

ktt rorw

cD

2

1

cg

mD

L

ktt

TEC

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling

*

*

**2 1

1

MML

ktt rorw

cD

2

1

cg

mD

L

ktt

TEC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00 1000000.00Dimensionless time, td

No

rmal

ized

Rec

ove

ry

M=1.15

M=6.54

M=13.07

TEC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

Dimensionless time, td

Nor

mal

ized

Rec

over

y

M=1.15

M=6.54

M=13.07

February 2004Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling

K1

K2

K3

K4

One End Open

Case 1: K1 > K2 > K3 > K4

Case 2: K1 < K2 < K3 < K4

water

Heterogeneous Core

February 2004Imbibition Assisted Recovery

OEO

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

Dimensionless time,td

No

rmal

ized

Rec

ove

ry

K1>K2>K3>K4

K1<K2<K3<K4

Spontaneous Imbibition UpscalingHeterogeneous Core

Presentation Outline

February 2004Imbibition Assisted Recovery

IntroductionProblem StatementBackground and Literature ReviewObjectives

Numerical ModelingGrid SensitivityMatching Experimental ResultsNumerical Analyses of Spontaneous Imbibition

Imbibition Upscaling

Conclusions

Conclusions

February 2004Imbibition Assisted Recovery

It was observed that time required to saturate core to Sw=60% increases

exponentially as the number of faces available for imbibition decrease

Results proved that using characteristic length in the equation of dimensionless

time, instead of length of the core improves upscaling of spontaneous

imbibition

Conclusions

February 2004Imbibition Assisted Recovery

Further investigation revealed that upscaling correlations could be

significantly improved by taking into account end-point mobilities and mobility

ratio

Spontaneous imbibition recovery is higher for a flow in the direction of decreasing

permeability than in the case of a flow in the direction of increasing permeability

Conclusions

February 2004Imbibition Assisted Recovery

Some discrepancy observed in correlations, while upscaling heterogeneous core,

indicated that existing transfer functions can not precisely account for heterogeneities in

the core

Acknowledgement

February 2004Imbibition Assisted Recovery

Finally I would like to express my sincere gratitude and appreciation to my advisor Dr. David Schechter and Dr. Erwin Putra.

Imbibition Assisted Recovery

Orkhan H PashayevPetroleum Engineering

DepartmentTexas A&M University

February 2004Masters Division