It is required to balance $200$ sacks of Class $G$ neat cement in $9\frac{7}{8}$ open hole by use of a $4\frac{1}{2}$ in OD$/3\mathrm{.}92-$in$.$ ID$,13\mathrm{.}5l\frac{b}{f}t$ tubing. The hole depth is $9,000ft$ and $20bbl$ of water is to be used as preflush ahead of the cement slurry.

Calculate:

a$.$ Total slurry volume, annular volume and tubing volume

b$.$ Height of the balanced plug

c$.$ Volume of water to be used as a spacer behind the cement

d$.$ Volume of mud chase $($or displacement volume$)$

e$.$ Number of strokes required to displace cement to just below the drillpipe shoe, assuming that the pump capacity is $0\mathrm{.}1bbl$ per stroke

f$.$ Volume of cement and number of sacks required if the height of the plug is $500ft.$

Tubing capacity $=0\mathrm{.}0838f\frac{t^3}{f}t.$

Total slurry volume $=230f{t}^3$

Annular volume of cement $=0\mathrm{.}422455=192cu.ft$

Tubing volume of cement $=0\mathrm{.}0838455=38cu.ft$

Height of plug, $H=\frac{230}{0\mathrm{.}532}=432\mathrm{.}3ft$

Volume of water $=3\mathrm{.}97bbl$

Displacement Volume $=695f{t}^3=123\mathrm{.}8bbl$

Number of pump strokes to displace cement $=1277$

Volume of cement for $500ft$ plug $=253f{t}^3$

Number of sacks $=\frac{253}{1\mathrm{.}15}=220$ sacks