Waterflooding BL PETE482 SP 14

5/27/2018 Waterflooding BL PETE482 SP 14

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Efficiency of Oil Displacement by Water

By: Fathi H. Boukadi


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1/19/2011 Waterflooding/Introduction 2

Shock front theory

implies that front saturation is ought to be located at

position x where two shaded areas A and B of Figure 12 must cancel.Virtualline

represents position of shock front saturation .

Following profile is obtained;

wfS

PROCEDURE FOR BUCKLEY-LEVERETT

0 Lx1 x2

Swc

1-Sor

Swf

x

Sw

Sw

Saturation profile

at t < tbt

0 Lx1 x2

Swc

1-Sor

Swf

x

Sw

Sw

Saturation profile

at t < tbt

Figure 13: Saturation profile before breakthroughindicating shock front saturation


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Figure 13 shows a saturation profile before breakthrough. Water is injected forsometime. At position , water saturation of plane is maximum, while atwater saturation is shock front saturation.

Need to determine location

and value of saturation at front. We also need

to estimate average water saturation behind front.

0 Lx1 x2

Swc

1-Sor

Swf

x

Sw

Sw

Saturation profileat t < tbt

0 Lx1 x2

Swc

1-Sor

Swf

x

Sw

Sw

Saturation profileat t < tbt

Figure 13: Saturation profile before breakthroughindicating shock front saturation

AVERAGE WATER SATURATION BEHIND FRONT

x1 x2


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Material balance for injected water gives:{ }

{ }iW volume swept

average water saturation - connate water saturation

= (31)

wf

i wi w wc w wc

w S

W dfW A x S S A S SA dS = = 2 (32)

Replacing using Buckley-Leverett yields;x2

wf

w wc

w

w S

S S

dfdS

= 1 (33)

Average saturation behind front

is also obtained by integrating saturation

profiles.



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Tangent to fractional flow curve from is at .

Extrapolated tangent must intercept line at point .

w wc wS S ,f = 0 wfw w wf Sf f f=wf = 1 w w wS S ; f = 1

Plot w wf vs S , obtain derivative (inflection point indicates saturation at front).

wf

f1

w wfS S 1 0

w wcS S

wSwcS wfS

w wff f

wf = 1

wf = 0

wf

f1

w wfS S 1 0

w wcS S

wSwcS wfS

w wff f

wf = 1

wf = 0Figure 14: Slope of fractional flow curve



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Oil recovery Equation

Based on overall material balance, general oil equation writes as:

where N is initial oil in place expressed as:

Recovery factor (RF), is product of microscopic displacement efficiency (ED) and

volumetric sweep efficiency (Evol);

where,

N*EfficiencyNp=

o

poi

B

VSN=

N

NEEE p

VolDR =

volumeoilcontactedvolumeoilmobilizedED= OIIP volumeoilcontactedEVol=

DISPLACEMENT FUNDAMENTALS

(46)

(45)

(47)


7/621/19/2011 Waterflooding/Introduction 7

Oil recovery Equation

Typical values of ER* are;

Waterflooding 30-40% (EVxED=0.6x0.6=.36)Steam injection 30-50%

Polymer injection 30-55%

CO2 injection 30-65%

Solvent injection 35-63%

*depends on ER from primary and reservoir and fluid properties (Carcoana, 92)

Volumetric sweep (Evol) is product of areal (EA) and vertical sweep (Ever);

where,

VAvol EEE =


areatotalareacontactedEA=

(48)




Figure: Sketch of areal (top) and vertical sweep

Figure 15: Sketch of areal sweep efficiency

Therefore, using all definitions, oil recovery equation becomes;

= o poivADp BVSEEEN (49)




To determine recovery, we need to estimate EA, ED, and EV from:1. correlations

2. scaled laboratory experiments

3. numerical simulation

Areal sweep efficiency

data is obtained from Craig (1980). Correlations are

for displacements in homogeneous, confined patterns.




EA , is a function of mobility ratio (M) and injected volumes (Vd);

From curve, we can conclude that EA

:

1. increases

with increasing

throughput (Vd

), injection volumes

2. increases

with decreasing

mobility ratio (M)




Mobility ratio (M) is defined as ratio of pressure gradients behind and aheadof displacement front (Prats, 1982):Also defined as ratio of mobilities of displacing (ing) and displaced (ed) phases,

with;

ing= water=krw/w and ed= oil=kro/o

Mobility ratio (M) writes as:

Debate about krw value; krw

for water-contacted portion of reservoir

kro

in oil bank; 2 different saturations

w

o

ro

rw

oro

wrw

oil

water

k

k

/k

/kM

==

= (50)




Mobility ratio (M) is:

where,krw( ); evaluated at average water saturation behind front at BT,

kro(Swc); evaluated in oil bank ahead of front, Swc

Mobility ratio characterizes stability of displacement front;

1. M is constant before breakthrough.

2. M increases after breakthrough.

3. if M < 1, displacement is stable.4. if M >

1, displacement

is unstable.

5. if M >

1, viscous fingering and early breakthrough.

(50)

wS

wS

w

o

wcro

wrw

owcro

wwrw

)S(k

)S(k

/)S(k

/)S(kM ==




Viscous fingering also results in prolonged injection to achieve sweep out.

Need to optimize injection rate, qw, and number of injectors by using voidagereplacement.

water

w

o

wcro

wrw

owcro

wwrw

)S(k

)S(k

/)S(k

/)S(kM ==




M, end-point mobility ratio,

is:

where,krw is end-point relative permeability at Sorwkro is end-point relative permeability at Swc

If M

Waterflooding BL PETE482 SP 14

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