Capillary Pressure Brooks and Corey Type Curve. Review: S w * Power Law Model Power Law Model...
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Transcript of Capillary Pressure Brooks and Corey Type Curve. Review: S w * Power Law Model Power Law Model...
![Page 1: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/1.jpg)
Capillary Pressure
Brooks and Corey Type Curve
![Page 2: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/6.jpg)
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
1
10
100
1000
0.01 0.1 1
SwD , Dimensionless
PcD
, D
imen
sio
nle
ss
![Page 7: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/7.jpg)
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
1
10
100
1000
0.01 0.1 1
1-Sw , Fraction
Pc
, Sam
e P
ress
ure
un
it a
s P
d
![Page 8: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/8.jpg)
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
Dimensionless Capillary Pressure Data Sheet
1
10
100
1000
0.01 0.1 1
1-Sw , Fraction
Pc
, Sam
e P
ress
ure
un
it a
s P
d
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
![Page 9: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/9.jpg)
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
Dimensionless Capillary Pressure Type Curve
1
10
100
1000
0.01 0.1 1
SwD , Dimensionless
PcD
, D
imen
sio
nle
ss
Dimensionless Capillary Pressure Data Sheet
1
10
100
1000
0.01 0.1 1
1-Sw , Fraction
Pc
, Sam
e P
ress
ure
un
it a
s P
d
![Page 10: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/10.jpg)
Brooks and Corey Type Curve
• 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
Dimensionless Capillary Pressure Type Curve
1
10
100
1000
0.01 0.1 1
SwD , Dimensionless
PcD
, D
imen
sio
nle
ss
Dimensionless Capillary Pressure Data Sheet
1
10
100
1000
0.01 0.1 1
1-Sw , Fraction
Pc
, Sam
e P
ress
ure
un
it a
s P
d
![Page 11: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/11.jpg)
Brooks and Corey Type Curve
• 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
Dimensionless Capillary Pressure Type Curve
1
10
100
1000
0.01 0.1 1
SwD , Dimensionless
PcD
, D
imen
sio
nle
ss
Dimensionless Capillary Pressure Data Sheet
1
10
100
1000
0.01 0.1 1
1-Sw , Fraction
Pc
, Sam
e P
ress
ure
un
it a
s P
d
Match Point
![Page 12: 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.](https://reader036.fdocuments.net/reader036/viewer/2022072006/56649f565503460f94c7b067/html5/thumbnails/12.jpg)
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”