3.3 Capillary Pressure

8/3/2019 3.3 Capillary Pressure

1/78

.rocks

1 Rise of fluid in Capillaries

2 Additional pressure of arbitrary curvature

3 Ca illar Pressure effect in Porous Media

4 Capillary Pressure Hysteresis

5 measurement of Capillary Pressure

6 Application of Capillary Pressure


2/78

1 Rise of fluid in Capillaries

1) Capillary pressure of gas-liquid system

If a Capillary tube is placed in

a large open vessel continuingliquid , liquid will rise in the

tube above the height of the

.

This rise in height is duo to the

attractive force (adhesion

tension) between the tube and

-

e qu an e sma we g

of the column of liquid in the tube..


3/78

cos2

= r

Definition: The ressure difference betweennon-wet phase and wet phase is called capillary

ressure.expressed by Pc.

- .


4/78

2 Ca illar ressure in oil-water s stem

pc=

2 cos

( )r

=

Fig.3-21 Pressure relations in Capillary tube


5/78

3)Property of capillary pressure

A. The capillary pressure exists in capillaryu e a up n any rec on

Fig.3-22 displacement of oil by water in Horizontal capillary


6/78

3)Property of capillary pressure

PC is proportional to cos, and inverse

proportional to r;


7/78

Figure 7.8 Capillary rise experiments for two porous

media of different grain sizes.


8/78


9/78

,

is driving force of displacing oil by water;

If rock surface is oil-wet , capillary pressure

If rock surface is water-wet water can

automatically enter rock ; but if rock surface

- ,

rock .


10/78

Drainage :A process displacing the-

wetting phase is known as drainage.

the non-wetting phase from a porous medium with

.


11/78

Question: Why does the oil-water contact is atransitional zone?


12/78

2. Additional pressure of arbitrary curvature

1) Derived equation (

Laplace equation can be derived by consideringthe mechanical equilibrium of the interface.

The work done in expanding the surface, by

,

work against the surface tension.


13/78

'D

2p + += dRRBCdRRBDCBfA 21

11

'A'

CD

dR

++=RR

21

'B

C

1p

2R

1

AB=

B

11

BC= dRpBCABdRfABCDpW ==

2R

21 pppc =WZ =

BCABfABCD = +==11

21

RR


14/78

2) Equation simplification in Several

spec a cases

.

R R R= =r

cos =

cP =

radius and the curvature radius


15/78

If curved surface is cylindrical surface

1 2,R R r= =

1 1P

= + = =

1 2 2R R R r


16/78

c. Ca illar ressure in conical ca illar

R1

=r1

/COS(+)

R2=r2/COS(-)

so:

cip

=

cos2

i


17/78

D. ca illar ressure in cracks

2

2/cos

W=

1

cos2

== WRc

1


18/78

F. The capillary pressure in packing of uniform

sp eres

+=

11pC

21

111 +=m

cp

=

m


19/78

3 capillary effect in capillary tube

1) When the droplet (or bubble) is at the static state

cos22'

rRp

c==

cylindrical interface

rp

cz=''

2cos2

e cap ary pressure e ec :

.==rrr


20/78

tube of constant diameter

'

'p =

''

''p =

'''''' 211 ''' =

==rRR

C


21/78

3 When the dro let asses throu h

a throat of a pore

= '''2p C


22/78

am n ec :

to a capillary tube of decreasing size ,a higherpressure drop is required to move the drop into

.

='''

2p C


23/78

Capillary Pressure Hysteresis

Capillary Pressure Hysteresis by Contact

Fig.3-51 contact angle hysteresis


24/78

Ca illar Pressure H steresis b the

sudden change in diameter

Fig3-52. the change in diameter


25/78

Ca illar Pressure H steresis b the

gradual change in diameter

( ) +=

cos2

pr

( )tp

=

cos2

tr


26/78

capillary hysteresis in actual rock

angle: 1A

Visual recedin= 2R

angle:

( )Rp == 2

cos2cos2

ttrr

( )A

+== 1

cos2cos2

PP

m

rr


27/78

Semi-permeable Disk Method

Mercury injection method

Centrifuge method

The dynamic capillary-pressure method

The evaporation method


28/78

Definition :

Capillary Pressure curve: The relationship

curve between ca illar ressure of reservoirrock and the wetting- phase saturation is called

.

sc =


29/78


30/78

1) Semipermeable Disk Method

A. Normal pressure Semipermeable Disk Method

-

wetting phase is water

the maximum capillary pressure

is about 1atm

1) S i bl Di k M h d


31/78


The bottom of the vessel

consists of a semi-

permeable plate, which

displaced from the sample

to pass through while

blocking the passage of

-


32/78


P W

w

V VS

= =

P


33/78

Principle and step of measurement:

placing the sample, initially saturated with awetting fluid, in a vessel filled with the non-wetting

fluid.

With the sample on the porous plate, thepressure of the non-wetting fluid is increased in

steps and the system is allowed to achieve

equilibrium after each pressure change. The volume of wettin hase dis laced at each

pressure is measured.

determined from the volume of wetting phase

pressure versus saturation relationship.


34/78


35/78

typical curve

cP

%

20

12

4

(%)w

S

r, m

4.2 9 18 27 54

Fig.-1 capillary pressure curveFig. -2 pore size distribution curve

%

r

Fig.-3 pore volume accumulate distribution curve



36/78


A. High pressure Semipermeable Disk Method


37/78

Principle and step of measurement:

p ac ng e samp e, n a y sa ura e w awetting fluid, in a vessel filled with the non-wetting

u .

With the sample on the porous plate, thepressure of the non-wetting fluid is increased in

steps and the system is allowed to achieve

equilibrium after each pressure change. The volume of wettin hase dis laced at each

pressure is measured.

determined from the volume of wetting phase

pressure versus saturation relationship.


38/78

This method use oil and water therefore more

nearly approaching actual wetting conditions.

The method gives a reliable estimate of the

irreducible wetting phase saturation.

Disadvantage:

The porous plate limits the maximum capillary

It takes too long to obtain the entire capillary

pressure curve y s me o .


39/78


40/78


41/78

non-wetting phase mercury;

wetting phase air

mercury injection equipment

The sample chamber is evacuated, and

the pressure required for injection of each increment

.


42/78

Princi le of measurement:

2

543

1 Nitrogen pressure; 2 pressure gauge;

mercury n ec on pump; samp e ce ;

5 vacuum system


43/78

. . -


44/78

Advantage of mercury injection method :.

The range of pressure is large.

Disadvantage of mercury injection method:

Core can no longer be used for other tests aftermercury injection.

The method also cannot be used to determine

mercury vapor is toxic, so strict safety precautions

.

3) Centrifuge method


45/78

3) Centrifuge method

Measuring Principle and step:

e samp e sa ura e w a we ng u s p ace

in a centrifuge cup containing the non-wetting fluid

The sample is rotated at a series of constant

displaced at equilibrium at each velocity is measured

when the rotational velocity is increased.


46/78

3 the centrifu e method


47/78


48/78

2

=2 2 2P w r r =

2


49/78

The centrifuge method is fast

The method is good for determining the

irreducible water saturation.

It can simulate the process of water or gas

Disadvantage:.

. .

inability to obtain spontaneous imbibition

ca illar ressure curve.

the calculated water saturation at the core inlet is

an approximation,

4) Converting the laboratory data


50/78

4) Converting the laboratory data

to reservoir conditions

p LLcL

cos= LLr

cos=

rpcR=

cR

RR

pr =

cLcRpp

cos=

The conversion between semi permeable disk method


51/78

The conversion between semi-permeable disk method

and oil-water capillary pressure under reservoirconditions.

wgwgwg

wgwg

owow

owpppp

30cos72

cos

cos

cos=

==


52/78

Swiirreducible saturation

of wetting fluidPt threshold displacement

,

onset of invasion of the

P median ressure,characteristic

of

corresponds to the nonwetting

hase saturation of 50% .


53/78

E = Hgmax Hgmin Hgmax

WE: Mercury injection efficiency;

Hgmax

: max mum mercury sa ura on;

gm n

the oil recovery in a strongly water-wet oil reservoir

typical capillary pressure curve


54/78

yp p y p


55/78

typical capillary pressure curve

(a) Well sorted sample, with medium-size pores;(b) Nonsorted sample;

(c) Well sorted sample, with large pores;

,

(e) Poorly sorted sample, with more fine pores;

(f) Poorly sorted sample, with more large pores.

6 Application of Capillary Pressure curves


56/78

6 Application of Capillary Pressure curves

1) Determining rock wettability

A. Determining by Wettability number

cos Two ogwo PW

= =

cos og Tog woP

W=1 complete wetting by water;

W=0 complete wetting by oil;


57/78

B. Determining by apparent contact angle

P P cos arccoswo wo

To wo To woP P

= =

=00 complete wetting by water;wo

wo =90ocomplete wetting by oil;


58/78

. e erm n ng y ona son s me o

Principle of Determination

by the curve of water displacing oil with the area

unclosed the curve of oil displacing water.


59/78

.

0.7

2

ogA

> water-wet;A1

1log 0A < Oil-wet; A2

2

1log 0A

= intermediatewetting

-0.70 100

2 determinin the ore size distribution


60/78


of porous materials(

20

%

16

8

4

4.2 9 18 27 54

r, m



61/78


of porous materials(

r = 2cosPT

Tpr .max =

Rmax: the largest pore size


62/78

drainage capillary pressure curve

A. Calculation ofabsolute ermeabilit

B. Calculation of relative permeability


63/78

u y ng o recovery

SS

max

=Hg

w

S

5) Studying initial static fluid distribution in


64/78

5) Studying initial static fluid distribution in


65/78

the oil water contact level 100% water

saturation lever) PT

the free water level PC=0

connate water saturation levelS

between 100% water saturation lever and

conna e wa er sa ura on eve


66/78

level of fw=100% oractual transition zonethe height

=saturation level

1.0

0.8


67/78

0.6

.

0.2

0

20 40 60 80 100Sw %

Pc(R)

HSwi

B

0 20 40 60 80 100

%

To convert capillary pressure data to

e g a ove ree wa er sur ace


68/78

e g a ove ree wa er sur ace

cRh =

ca illar ressure at some articular

,

saturation for reservoir conditions,MPa

w,o ens ty o water an o at reservo rconditions of water and oilg/cm3)

xamp e : e cap ary orce curve as een


69/78

xamp e : e cap ary orce curve as een

obtained from laboratory. if the water saturation is

, an e cap ary pressure s . a,

calculate the height of water saturation of 35%

p ane a ove ree wa er eve .

e a reservo r con ons ,

wo = 24 mN/m,

w = . g cm ,

o = 0.848 g / cm3,

a a mosp er c pressurewg= 72 mN/m.

Example 2: The air water capillary pressure curve isobtained by semi permeable diaphragm method in the


70/78

obtained by semi-permeable diaphragm method in the

laboratory. When the water saturation is 50%, the capillary

cL . .

of water is 72 mN/m in surface conditions. While in the

reservoir conditions ,the interfacial tension between waterand oil is 24 mN/m.The water density is w = 1.088 g / cm3

and oil density is o = 0.848 g / cm3 .The altitude of free

wa er eve s - m. e reservo r roc s wa er-we , an e

contact angle between water and reservoir rock is assumed.

Calculate:

50% to the free water level.

50%.

e erm na ng c ness o o -wa er


71/78

e erm na ng c ness o o -wa er

production

Pc1

2 2or cS P h

Pc2 1 1cw cS P h

Scw Sor

6.Avera in ca illar - ressure data


72/78

The definition of J-function :

1

2( ) ( )cos

cW

J S

=

-

media that have the same pore structure but

di erent permeability and porosity will have

the same Leverett J-function.

Formula Derivation:


73/78

1

==

cr r =

1 1

Kc cos2

2

=

2

2 = Kpc

c

( )2

=Kp

sJ cw

The characteristic of J-function :


74/78

a b cd e

Water-gas system in laboratory: 70mN/m, =0 p J


75/78

70mN/m, 0

-3

cp J

number

C

(50)

,

m2

. . . .

2 2.5 34.0 0.174 0.50

. . .

4 0.85 569 0.275 0.55 23

5.0

K

=Jc

%w

S

.

At reservoir conditions:= 2


76/78

average porosity is 0.208Sw% J(sw) Pc(sw)

100 0.35 0.35

70 0.40 0.40

54 0.45 0.45

c

J44 0.60 0.59

30 1.45 1.43

20 3.15 3.12

%w

S

JJ 1028cos

( )Kpc .

208.0166

5.05.0 ===


77/78

200/cm)

100

ure

k

1ryPres I displacement

0.1Capilla displacement trap hysteresis

Inhaledt

0.001

W

or

Mercury saturation (%)

1.0

0.8


78/78

0.6

.

0.2

0

20 40 60 80 100Water saturation Sw %

Pc(R)

H

irreducible water saturation )Swi

B Producing oil and water( )100 producing water surf

(100 )

Pure water producing areasirreducible oil )

Sw=1-Sor

0 20 40 60 80 100

Water saturation %

Free water level

Date post:	07-Apr-2018
Category:	Documents
Upload:	hind-lionne
View:	222 times
Download:	1 times

3.3 Capillary Pressure

Documents