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 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

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)

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 Note that the range of values for SwD is from 0 to 1

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

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

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

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 Shifting the data plot on a log-log scale is the same as multiplying the axis value by a factor (horizontal shift for x-axis factor, vertical shift for y-axis factor). This “shift means multiply” comes from: log(a*b)=log(a)+log(b) Note that you cannot shift valid data points to the right past SwD=1, as this would give us negative Sw* (Sw<Swi). Data points that are shifted past 1 in your final analysis, must be concluded to be bad data.

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 The match point (1,1) described above is the “best” because it makes the continuation of Step 3 easier (shown on next slide). However, the match point is totally arbitrary and you should expect to get the same solution for any match point. 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: 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”