$($a$)$ A rock $10$ long and $2!$ in cross$-$section flows $0\mathrm{.}0080"$#$!$ $$\%"$&$\text{'}($

of a $2\mathrm{.}5$ oil under a

$1\mathrm{.}5$ pressure drop. If the oil saturates the rock $100\%,$ what is its absolute permeability?

$($b$)$ What will be the flow rate of $0\mathrm{.}75$ brine in the same core under a $2\mathrm{.}5$ pressure drop

if the brine saturates the rock $100\%.$

$($c$)$ Is the rock more permeable to the oil at $100\%$ oil saturation or to the brine at $100\%$ brine

saturation?

$($d$)$ The same core is maintained $40\%$ water saturation and $60\%$ oil saturation. Under a $2\mathrm{.}0$

pressure drop, the oil flow is $0\mathrm{.}0030)/$ and the water flow is $0\mathrm{.}004)/.$ What

are the effective permeabilities to water and to oil at these saturations.

$($e$)$ Explain why the sum of the two effective permeabilities is less than the absolute

permeability.