Using the oil and water relative permeability curves given below, determine the effective

permeabilities for oil and water at a water saturation of $50\%.$ Absolute permeability of the

rock is $214mD.$

Consider steady$-$state radial flow in an under$-$saturated oil reservoir with an active water

drive. A set of oil$-$water relative permeability curves were obtained from a core sample and

are given in Question $1.$ Other information are:

Reservoir thickness, $h$:$10ft$

Reservoir radius, $r_e$:$660ft$

Wellbore radius, $r_w$:$0\mathrm{.}5ft$

Pressure difference, $P$:$500$ psi

Oil viscosity, ${}_0$:$3cp$

Water viscosity, ${}_w$:$1cp$

Find:

a$)$ The oil and water flow rates at initial reservoir state @$S_{wi}$

b$)$ Over time the water encroaches as oil produced. At $S_w=S_0=50\%$ what is the oil and water

flow rates?