Download - Capillary Pressure Brooks and Corey Type Curve. Review: S w * Power Law Model Power Law Model (log-log straight line) –“Best fit” of any data set with.

Capillary Pressure

Brooks and Corey Type Curve

Review: Sw* Power Law Model

• Power Law Model (log-log straight line)– “Best fit” of any data set with a straight line model can be used

to determine two unknown parameters. For this case:• slope gives • intercept gives Pd

– Swi must be determined independently

• it can be difficult to estimate the value of Swi from cartesian Pc vs. Sw plot, if the data set does not clearly show asymptotic behavior

1/λ*wdc SPP

wi

wiw*w S1

SSS

Type Curves• A Type Curve is a dimensionless solution or relationship

– Dimensionless means that it applies for any values of specific case parameters

– Petroleum Engineers often use type curves to determine model parameters

• well test analysis

• well log analysis

• production data analysis

• analysis of capillary pressure data

Type Curves• Process of type curve matching

– Step 1: observed data is plotted using an appropriate format• The data and type curve must be plotted using the same sized grid (ie. 1

log cycle = 1 log cycle)

– Step 2: a “match” is found between observed data and a dimensionless solution by sliding the data plot over the type curve plot (horizontal and vertical sliding only)

– Step 3: the “match” is used to determine model parameters for the observed data

• Often values are recorded from an arbitrary “match point” on both the data plot and type curve plot

Brooks and Corey Type Curve• Dimensionless variable definitions

– Dimensionless Capillary Pressure

– Dimensionless Wetting Phase Saturation

• Restating Sw* Model (Type Curve Plot)

d

ccD P

PP

wi

w*wwD S1

S1S1S

1/λwDcD S1P

Brooks and Corey Type Curve• Type Curve Plot

– By matching the type curve, we can solve for all three Sw* Model parameters: Pd , Swi , and

• curve matched gives, • vertical slide gives: Pd

• horizontal slide gives: Swi

Dimensionless Capillary Pressure Type Curve

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Brooks and Corey Type Curve• Data Plot, Pc vs. (1-Sw )

– Grid must be same size as Type Curve Plot

• 1 log cycle on type curve is the same size as one log cycle on data plot

– Any pressure unit can be used for plotting Pc

• Pd determined from analysis will be in same pressure unit used to plot Pc

Dimensionless Capillary Pressure Data Sheet

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Brooks and Corey Type Curve• Example Data, Cottage

Grove #5 Well• lithology: sandstone

• porosity: 0.28 fraction

• permeability: 127 md

• fluid system: brine/air wg: 72 dyne/cm


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Sw, fraction Pc, psia Sw, fraction Pc, psia0.237 56.57 0.487 6.070.263 40.23 0.519 5.020.279 30.83 0.567 4.480.311 22.53 0.599 4.050.343 15.94 0.647 3.540.359 13.30 0.712 3.250.391 10.82 0.744 2.880.407 9.04 0.824 2.640.439 4.43 0.888 2.30

Brooks and Corey Type Curve• Step 1: Plot data on same

sized grid– Plots are shown with grid

lines exactly overlayed• We often use tracing paper

without gridlines, and mark the location of gridlines from the type curve on the tracing paper


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SwD , Dimensionless

PcD

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• Step 2: Slide data plot to obtain the best match– Only horizontal and

vertical sliding is allowed

– Best match is near the =1.0 curve

• Value of is slightly less than 1.0


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SwD , Dimensionless

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Pc

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• Step 3: Pick an arbitrary match point and record values from both curves– For this particular type

curve, the “best” arbitrary match point is where PcD=1 and SwD=1

– At this match point, Pc=2.0 psia and (1–Sw)=0.77


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Match Point

Brooks and Corey Type Curve• Step 3: Continued

– Using dimensionless variable definitions• Dimensionless Capillary Pressure

– When PcD = 1.0, from match point Pc=2.0

– Since by definition, PcD=Pc/Pd , then Pd=2.0

• Dimensionless Wetting Phase Saturation– When SwD = 1.0, from match point (1-Sw)=0.77

– Since by definition, SwD=(1-Sw)/(1-Swi), then (1-Swi)=0.77

– Therefore, Swi=0.23

• Final Solution, for All Three Sw* Model Parameters: =1.0, Pd=2.0, Swi=0.23

– The Sw* log-log plot should be used to verify these values now that we know Swi

• This would allow a more precise determination of than “slightly less than 1.0”