PROBLEM$1$

A thick, subsurface formation contains an oil accumulation above an aquifer. A core sample $($porosity$=0\mathrm{.}12$ and k$=80$ mD$)$ from Well#$1$ in the formation has the capillary pressure curve shown in the figure below. Well logs and core analysis establish the WOC at $5,023$ ft below sea level. The following additional data at formation conditions are available:

Oil density: $43\mathrm{.}5$ lb$/$ft$^3$

Water density: $64\mathrm{.}1$ lb$/$ft$^3$

Oil$/$water interfacial tension $($IFT$)$: $50$ dynes$/$cm

Oil$/$water$/$rock contact angle: $55\backslash$deg

Calculate:

a$.$ The connate water saturation $($S$\_$wc$).$

b$.$ Depth of the Free Water Level $($FWL$).$

c$.$ Thickness of the transition zone.

d$.$ Depth to reach $50\%$ oil saturation. $(($SOLVE ALL PARTS AND CALCULATE TO FIND FINAL ANSWERS$))$

PROBLEM $2$

The formation in Problem #$1$ has a porosity$-$permeability transform of k$=3\mathrm{.}649*^1\mathrm{.}8($k in Darcys$).$ A core sample from Well#$2$ in the same formation shows a porosity of $0\mathrm{.}06.$ Assuming the same depth of the FWL$,$ what is the depth of the $50\%$ oil saturation in Well#$2?($SOLVE$)$