2.4 Rock Permeability

7/31/2019 2.4 Rock Permeability

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2.4 Permeabili t y of reservoir rock

2 The unit of permeability

3 The conditions of measuring absolutepermeability

4 Applicable condition of Darcy's law

as ermea y an ec o as ppage

on Permeabilityra ua on o orma on n permea y


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2.4 Permeability of reservoir rock

7 Factors af fect in the ma nitude of

permeabil ity

9 Flow Syst ems of Sim ple Geomet ry

10 Average perm eabilit y of combinat ion

layers11 The relat ionship of permeabilit y and

ot her ro ert of rock


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rock

In 1856, Darcy investigated the flow ofwa er roug san ers .

s exper men a appara us s s ownin Fig

Darcy interpreted his observations soas to y e resu ts essent a y as g ven n

equation.


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hhK

upstream pressure

21

L

of rockexperimental apparatus


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Definition of ermeabilit

Permeability is the ability of fluids to

pass roug a porous ma er a .

3

1 Darcy =

( ) ( )cmatmcm 112

1 Darcy = 0.987 x 10-8 cm2


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ere,

cylindrical sand pack of cross-sectional area A

P is pressures drop across the cylindrical

sand pack .

s v scos y o e u

, ,

characteristic of the sand pack.


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2 The unit of permeability

Darc CGS PERM SI

L cm cm ft cm

A cm2 cm2 ft2 cm2

P atm dyn/cm2 psia MPa cp p cp mpa.s

Q cm3/s cm3/s bbl/day cm3/s

Kdarcy cm

2

perm m

2


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Physical significance of one Darcy

One Darcy is defined as the permeability that

to flowat a rate of 1 cm3/s through a cross

sectional area of 1 cm2 when the pressure

gradient is 1 atm/cm.

1 Darcy (d)=1000 millidarcy (md)


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permeability

The orous medium must be 100 er centsaturated with the flowing fluid.

No interaction between the fluid and theporous media

Laminar flow .


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EXAMPLE 4

If the length of a core sample is 3cm ,and the

cross-sec on area s cm . n er a pressure

difference of 2atm, the core sample will bepermit a fluid of 1 cp (centipoise ) viscosity to

flow at a rate of 0.5cm3/s throu h.

Calculate permeability of core sample .

:

.0.375K D= = = ( )


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,be permit a fluid of 3 cp (centipoise ) viscosity

to flow at a rate of 0.167cm3/s through,

n er t e same pressure erence.

0.167 3 3L

.

2 2

K D

A P

= = =


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Characteristic of absolute permeability:

The permeability is a property of rockalone,dependent on the porous media size and

s r u on o roa on y, no on e uused.


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'

1) Mid-high permeability

3 23.5u=

c

K

2) Low permeabilityFig.1 relations between velocity and

pressure gradient


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2). Klinkenberg Effect

Klinkenberg Effect Effect of Gas Slippage

expressed that the flow rate of gas at solid

surface of pore is not zero.


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is greater than liquid Permeability

It has been found that gas permeabilitiessometimes vary with the pressure of gas,

and that gas permeability is greater than

.

ca illar tubes.


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3). Effect of gas slippage on Permeability

Measurements

800

001um2

1

200

400

0.

2

3

0

0 2 4 6 8 10 co2

p,

the reciprocal of the mean pressure


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or eac gas a s ra g ne s o a ne or eobserved permeability as a function of the reciprocal

o e mean pressure o e es .

- -gas yield the straight line with the greatest slope

, .

All the lines when extra olated to infinite meanpressure ( ) intercept the permeability axis

at a common oint.

1 0p

=

This point is designated kL or the equivalent liquidpermea ty.


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The linear relationship between the observed

permea y an e rec proca o mean pressuremay be expressed as follows:

K = K 1+ b /

=

permeability,

b=constant for a given gas in a given medium

g=measure permea y us ng e arcy equa on

for gas flow.

= mean flowing pressure of the gasp


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)b

1(K KgKp

K

P

1r

b 22 d n=


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permeability

grade permeability evaluation

2u m

3 210 um

> 1 >1000 Very good

10.1 1000100 good

. .

0.010.001 101 fair

- .


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ac ors a ec ng e magn u e opermeability

(a) Shape and size of sand grains(b) Grain packing and Cementation

(c) Fracturing and solution

ore ze an onnec v y


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1) The experimental laboratory determinations

A . determinations on small samples of

Apparatus for measuring of permeability with liquid


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0 02Q P u L2 2

1 2

( )P P

Apparatus for measuring of permeability with gas


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310K =


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a

C b

w iS

=

. . ,

of the fluid and the porous medium


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9 Flow S stems of Sim le Geometr

Horizontal Flow.

Horizontal rectilinear( steady-state flow is

.

1 2( )kA P P

L


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.

A radial-flow system, analogous

, .

e wQ

=

e w

e eis measured

rw the radius at which Pwis measured.


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10 Average permeability of combination

1 . Consider the case where the flow s stem islayers

comprised of layers of porous rock separated

from each other b infinitel thin im ermeablebarriers as shown in Fig. Parallel combination

n

k h

1j

nk

=

=jh

=


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Radial flow

Qt = Q1+ Q2 + Q3

t = 1 2 3

j jk hn

k=

=

1

j

j =


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2 Another ossible combination for flow

systems is to have the beds of different

shown in Fig. series combination

Linear flowP1- P2 = P1+P2+P3

Qt = Q1= Q2 = Q3

n

k =

/j j

L k


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Radial flow

- = + +Qt = Q1= Q2 = Q3

ln

e wQu R R

=e w

ln e

wRRadial flow- series combination

1ln i

R

1i i


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11 The relationship of permeability and

other property of rock

Fig. parallel bundle of capillary tubes pack


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Consider a system comprised of a bundle of

cap ary u es o e same ra us an eng ;The e uation for flow of fluids in circular conduits:

4

0 1 2( )r P P

8uLq e vo ume ra e o ow, cm s

fluid viscosit mPa.s(P1-P2)pressure loss over length L,

ro ra us o cap ary u e , cm,


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2)The relationship of permeability and pore radius

If the fluid-conducting channels in a porous medium

tubes of same diameters, then the flow rate through

4

nA r P

8uL=nnumber of capillary tubes per unit cross-

rradius of capillary tube

A total cross-sectional area


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From Darcys law it is also known that :

' K A P

u L

=

Equating Darcys and Poiseuilles equation:

'Q Q=4 4

KA P nA r P n r = = (1)8 8uL uL


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,

2PV n A r L

n r

= = =(2)

b

r

K r= =(3)


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3)The relationship of permeability and specific

sur acesurface area S is the total area exposed within

the pore space per unit of bulk volume .

22a n r

S n r n r

= = = = =

b

2 322 4

S S

= = = 28 KK


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Let Sp be the internal surface area per unit of pore

volume ,Ss be the total area exposed within thepore space per unit of grain volume

a=

PV

(1 )P SS S S = =

1 1S

S = =


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Gaocaini-Equation

3 3

3 2 2 22 2 2 (1 )P SK

S S S = = =

LLL

2 2 2 2K = = =

S P


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EXAMPLE 1

A core sample from a uniform sandstone formation-3 2

of 0.17

(b) Specific surface areas Sp and Ss.


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.conditions that should be met when measuring

.

to measure permeability of reservoir rock? How

.

2.4 Rock Permeability

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