A leak off test has been carried out just below the casing shoe set at $5200$ feet. The density of the water$-$based mud weight used for the test was $12\mathrm{.}0$ ppg$.$ Leak off test data is given in the below figure.

a$.$ Construct a plot of surface pressure vs$.$ volume of pumped drilling fluids.

b$.$ Determine on the plot the leak$-$off pressure and the formation break down pressure.

c$.$ Calculate the fracture pressure and the fracture gradient.

d$.$ Calculate the formation breakdown gradient.

e$.$ Calculate the maximum allowable annular surface pressure $($MAASP$).$

$\backslash$table$[[$Surface Pressure, psi,Pumped Volume, bbl$],[125,0\mathrm{.}5],[225,1],[375,1\mathrm{.}5],[500,2],[625,2\mathrm{.}5],[750,3],[875,3\mathrm{.}5],[975,4],[1050,4\mathrm{.}5],[1125,5],[1175,5\mathrm{.}5]]$