A polymer flood is being designed that uses $1200ppm$ of a polymer solution $(=1\mathrm{.}173g\frac{m}{c}c.$ The polymer solution will be iniected into a sandstone oil reservoir $)=(2\mathrm{.}65g\frac{m}{c}c.$ A five$-$spot pattern is planned on $40-$acre spacing. At the beginning of the polymer flood, the reservoir is at $S_{wi}.$ The concentration due to polymer retention and inaccessible $PV$ was $220$ ppm$.$ Two thousand bb of polymer solution have been injected for a period of $4$ days. The average reservoir pressure at the effective radius $(r_e)$ of the $5-$spot pattern is $390.$

Other data are: $k=170md,\frac{O}{?}=0\mathrm{.}21,K_{rw}=0\mathrm{.}31,h=45ft.,S_{oi}=0\mathrm{.}7$ and $S_{or}=0\mathrm{.}32,r_w$inj.$=3\mathrm{.}25in.,n{c}_1=0\mathrm{.}509,{}_0=3\mathrm{.}62cp,{}_w=1\mathrm{.}0cp.$

It is required to:

$1-$ List the assumptions of the applied polymer injection model.

$2-$ Determine the effective radius of the flood pattern.

$3-$ Determine the radius of polymer front.

$4-$ Calculate the expected injection rate of the polymer solution.

$5-$ Find the bottom hole injection pressure.