Capillary Pressure Brooks and Corey Type Curve

1. Capillary Pressure Brooks and Corey Type Curve

2. 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 l • 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

3. 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

4. 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

5. Brooks and Corey Type Curve • Dimensionless variable definitions • Dimensionless Capillary Pressure • Dimensionless Wetting Phase Saturation • Restating Sw* Model (Type Curve Plot)

6. 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 l • curve matched gives, l • vertical slide gives: Pd • horizontal slide gives: Swi

7. 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

8. Brooks and Corey Type Curve • Example Data, Cottage Grove #5 Well • lithology: sandstone • porosity: 0.28 fraction • permeability: 127 md • fluid system: brine/air • swg: 72 dyne/cm

9. 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

10. 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 l=1.0 curve • Value of l is slightly less than 1.0

11. 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 Match Point

12. 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: l=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 l than “slightly less than 1.0”