Buckley Leverett Pattern Flooding1 Gate

7/25/2019 Buckley Leverett Pattern Flooding1 Gate

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www.gateinpetroleum.com

Immiscible displacement

Buckley-leverett theory:

Frontal advance theory is application of conservation of mass. Assume flow through small element with

length

and cross-sectional area A,

Total flow-rate= Flow of oil + flow of water

= +

Water flow rate is,

=

Flow of oil rate is,

= = 1

Using darcys law,

=

=

Fractional flow of water is given as,

= + =

+

=

+

= 11 +


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Relative permeability (kro/krw) can be plotted on log scale of semi-log paper. As on semi-log paper

central portion of curve is linear and as a straight line on semi-log paper, relative permeability expresses

as function of water saturation by,

=

Semi-log plot of relative permeability versus water saturation

Plot of fw versus Sw (water saturation),


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Mass balance across control volume:

Assume mass conservation across control volume,

=

=

= +

= +

=

Re-arranging the terms and taking limits 0 & 0 =

Water saturation reservoir is also a function of Sw(x, t),

Then,

=

+

= +

Sw is constant thus dSw=0,

=


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Final equation of fractional flow can be given as,

=

Buckley-Leverett equation

= .

Additional tips to on why we use log-log & semi-log graph paper?

Article is taken from http://mathonweb.com/help_ebook/html/expoapps_3.htm &

http://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-

charts-and-graphs/

As per article discussed on forbes magazine there are two main reasons to use log scale on graph paper.

First is to respond skewness towards large values and second one is to show percent change or

multiplicative factors.

Logs are just another way of writing exponential function equation. Y = log

means Y is power or

exponent that b is raised to in order to get X. We can plot X itself on logarithmic graph paper ratherthan plotting log(x) on linear graph paper. By this we avoid taking logarithm on calculator.

A straight line on semi-log graph paper y versus x exponential function can be given as,

= . A straight line on log-log paper y versus x exponential function can be give as,

= .

Reference- http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-

immiscible-displacement/buckley-leverett-theory/
http://mathonweb.com/help_ebook/html/expoapps_3.htmhttp://mathonweb.com/help_ebook/html/expoapps_3.htmhttp://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/http://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/http://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-immiscible-displacement/buckley-leverett-theory/http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-immiscible-displacement/buckley-leverett-theory/http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-immiscible-displacement/buckley-leverett-theory/http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-immiscible-displacement/buckley-leverett-theory/http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-4-immiscible-displacement/buckley-leverett-theory/http://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/http://www.forbes.com/sites/naomirobbins/2012/01/19/when-should-i-use-logarithmic-scales-in-my-charts-and-graphs/http://mathonweb.com/help_ebook/html/expoapps_3.htm


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Pattern flooding

Central and peripheral flooding:

Central or pattern flooding is preferred in,

1. Anticlinal reservoir with large gas cap where gas is being injected into the reservoir.

2. Anticlinal reservoir with large aquifer under the reservoir where water is being injected

into the reservoir.

3. Monoclonal reservoir (dipping reservoir) in which water is injected at the bottom of

wellbore and if gas is injected at the top of the reservoir.

Production

well

Injection well


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Pattern flooding

a.

Direct line drive

Production wells and injection wells are directly opposite to each other.

b.

Staggered line drive

Here wells are still in line as in direct line drive, but comparatively displaced by some distance.

c.

Five spot

Injection well is located at the centre of square defined pattern of four production wells. Thepattern is called inverted five spot if the condition of five spot pattern is reversed i.e. four

injection wells and one production wells. (Injection/Production well ratio =1 )

Production

well

Injection well

Production

well

Injection well

a = distance between two similar wells

d= distance between injection and production well

a = distance between two similar wells

d= distance between injection and production well

Production

well

Injection well

d = perpendicular distance between injection

and production wells

a= distance between two same wells

d

L

a


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d.

Seven spot pattern

In seven spot pattern, injection wells are located at the corner of hexagon while production well is

located at the centre. (Injection to production wells ratio =2)

e. Nine spot pattern

Injection wells to production wells ration is three times.

Production

well

Injection well




Production

well

Injection well

d = perpendicular distance between injectionand production wells


Production

well

Injection well




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Buckley Leverett Pattern Flooding1 Gate