$100\%$ water saturated core sample was first applied to water injection with the rate of $0\mathrm{.}5c\frac{m^3}{s}$ for determination of absolute permeability. Second of all, the steady$-$state method was used, and finally oil flooding rate of $0\mathrm{.}38c\frac{m^3}{s}$ was injected in order to reach initial conditions of $(S_{wi},S_{oi}).$ Drainage curves of relative permeability data were presented at the table.

Cross$-$sectional area of core, $A=5c{m}^2,$ core length, $L=3cm$

Viscosity of water, ${}_w=1\mathrm{.}0cp,$ viscosity of oil, ${}_o=1\mathrm{.}25cp$

Pressure at inlet and outlet face of core, $P_1=2$atm and $P_2=1$atm, respectively.

Effective permeability data

$\backslash$table$[[S_w,\%,{30}^{**},40,60,80,90,100],[k_w,md,0\mathrm{.}0,6,18,90,180,300],[k_o,md,285,187\mathrm{.}5,75,7\mathrm{.}5,3,0]]$

Critical value $)=(0\mathrm{.}30$

a$)$ Calculate effective brine permeability at $)=(1\mathrm{.}0.$

b$)$ Calculate effective oil permeability at $)=(0\mathrm{.}30.$

c$)$ Plot the graph of effective permeabilities with respect to water saturation $(k_w,k_o)-S_w.$

d$)$ Calculate the relative permeability values and plot the graph $(k_{rw},k_{ro})-S_w$ if $)=(1\mathrm{.}0$ is taken as absolute permeability.