Q$1$:

$(45$ Points$)$

A well consists of $8,500ft,\frac{85}{8}-in.$ casing $($ID $=8\mathrm{.}00)$ and $1500ft,\frac{77}{8}-in.$ open hole. The drill string consists of $9,300ft,\frac{51}{2}-in.$ drill pipe $($ID $=4\mathrm{.}778-in.,21\mathrm{.}9l\frac{b}{f}t)$ and $700ft,7-in.$ drill collar $($ID $=3-in.,150l\frac{b}{f}t).$ A duplex pump of $6\mathrm{.}5-in.$ liner, $1\mathrm{.}6-in.$ rod size, $16-in.$ stroke length and $60$ SPM with a volumetric efficiency of $0\mathrm{.}96$ are used to circulate the $(13$ ppg $)$ mud. If there are $250$ bbls of mud in mud pits at surface, determine:

Available WOB

Water, barite, and clay $(22l\frac{b}{b}bl)$ to mix mud

Displacement volume

Fluid velocities in pipe and annulus

Bottom up time

Hole cycle time

Mud cycle time

Time for cutting to reach surface, if cutting settling velocity $=60fpm$