Drilling Engineering: A well is drilled down to a depth of $10,000$ feet using a mud that

weighs $9\mathrm{.}6ppg,$ circulated at $8\mathrm{.}5bb\frac{l}{m}in.$ During this process, the well

unexpectedly starts flowing, leading to a gain of $20bbls$ of mud in just $3$ minutes.

Following this, the pump is shut off and the blowout preventers are activated.

Once the pressures stabilize, the shut$-$in pressure in the drillpipe measures $520$

psig and that in the casing is $720g.$ The annular capacity between the casing

and drillpipe can hold $12\mathrm{.}9f\frac{t}{b}bl,$ while the one against the $900$ feet of drill

collars is $28\mathrm{.}6f\frac{t}{b}bl.$ The entire drillstring has a capacity of $130$ barrels.

Determine:

a$.$ The density of the required kill$-$mud

b$.$ The equivalent density at the casing seat $($i$.$e$.,$ at $3,500$ ft$)$ for the shut$-$in

well conditions.

c$.$ The equivalent density at the casing seat after introducing $300$ barrels of

kill mud while keeping the bottomhole pressure $50$ above the

formation pressure using an adjustable surface choke. Assume that the

kick consists of $CH4,$ wellbore temperature is constant and equal to $140F,$

and that the gas is ideal.