A New Approach in Permeability

and Hydraulic Flow Unit

Determination

Mohammad Izadi

Colorado State University

DWLS 1ST Student Day

February 2014

This work was published in SPE

Reservoir Evaluation and

Engineering Journal in August 2013

SPE-151576-PA

Mohammad Izadi- Colorado School of Mines

My coauthor was Dr Ali Ghalambor- Oil

Center Research Internaitonal

Objectives:

• To improve permeability estimation

• To enhance the prediction of the number of

Hydraulic Flow Units in a formation

• To provide a model to estimate the irreducible

water saturation using NMR logging

Approach:

• Inclusion of the irreducible water saturation

parameter in Kozeny-Carman equation

• Validated with data from Berea sandstone

• Demonstrated application to a low

permeability sandstone reservoir

• Introduced a new method to obtain the

irreducible water saturation ( not validated

yet!)

R r

2 2 2 2

2 2

water

wir

pore

V R L r L R rS

V R L R

π π

π

− −= = =

1wir

r R S= −

Approach:

Model Derivation:

• Hagen-Poiseuille equation: �

�

��

��=

�

�

�

�

��

�

• Solve with the new boundary condition

• Combine the Poiseuille and Darcy equations to obtain

the relation between porosity and permeability in porous

media

• Using the definition of porosity and tortuosity factor, one

can obtain the new permeability model:

k =1

2τS���

�

φ�

(1 − φ)�(1 − S���)

�

• Generalize the model :

� =�

� !"#$%& '

()

(�*()&' (1 − +,-.)

�

/. /1234

5' (2 − 6789) =

2

:;< ' 6=>9

'5

(2 − 5)' (2 − 6789)

?

Modified

Reservoir Quality

Index (MRQI)

Flow Zone

Indicator (FZI)

Normalized

Porosity

Model Verification:

Berea Sandstone

Sample Quartz,% Clay, % Others,%

sample 1 86 8 6

sample 2 87 8 5

sample 3 41 37 22

sample 4 97 3 0

sample 5 96 3 1

sample 6 95 4 1

sample 7 59 6 35 (calcite)

Model Comparison:

Normalized Porosity0.1 1

RQI0.1

1

10 Cluster 1Cluster 2Cluster 3Cluster 4Cluster 5

Plot of Reservoir Quality Index versus Normalized porosity for

two models to determine the number of flow units

Common HFU Modified Model

Porosity, fraction0.17 0.18 0.19 0.20 0.21 0.22

Per

mea

bil

ity,

md

0

20

40

60

80

100

Permeability = 1200.5 (Porosity) - 163.66 R-Squared = 0.937

Sw, Fraction0.0 0.2 0.4 0.6 0.8 1.0

J-Function0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Height from

FWL to OWC

Height of transition zone

7 ft transition zone

55 ft oil zone

Common HFU Model

Proposed

Model

Porosity, fraction

0.17 0.18 0.19 0.20 0.21 0.22

Perm

eabili

ty,

md

0

20

40

60

80

100

120

Permeability= 1344.26 (Porosity) - 193.56

R-Squard = 0.964

Sw, Fraction

0.0 0.2 0.4 0.6 0.8 1.0

J-F

unction

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Height of transition zone

Height from FWL to OWC

4 ft Transition zone

58 ft Oil zone

Low permeability sandstone

Silurian formations-Appalachian basin-Medina group –NW

Pennsylvania

Normalized Porosity

0.001 0.01 0.1 1

RQ

I

0.001

0.01

0.1

1

10

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Normalized Porosity x (1-Swir)^2

0.001 0.01 0.1 1

MR

QI

0.001

0.01

0.1

1

10

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

Perm = 4.6132Poro - 0.1828R² = 0.7607

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.02 0.04 0.06 0.08 0.1

Perm

eab

ilit

y,

md

Porosity

y = 6.6135x - 0.2444

R² = 0.879

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.02 0.04 0.06 0.08 0.1

Pe

rme

ab

ilit

y,

md

Porosity

New Model

Common HFU

Model

Question?

How to Obtain the Irreducible Water Saturation?

Approach:

Modified J-function

@∗ =BC

DEFGH

�I

J(1 − +,-.)

SDR model

�"K� = EJLM�NOP

Coates permeability

�QRLSTU = VWMQRLSTUP JL

1 − +,-. = V". JL*�. M�NOP 1 − +,-. = YW. JL*�. MQRLSTU

P

Summary

- Considered Swir in Kozeny-Carman equation

- Validated it with Berea and a low permeability formation

- Proposed a new method to estimate Swirfrom NMR