DrillHole Data:

Depth: $\backslash (12,200\backslash$mathrm$\{$ft$\}\backslash )$

Casing: $\backslash (103/4\backslash$mathrm$\{$inc$\}\backslash$times $10\backslash$mathrm$\{$in$\}\backslash ).$ set at $4000$ ft $.$

Mud Weight: $12$ ppg $.$

Open Hole Diameter: $\backslash (81/2\backslash$mathrm$\{$in$\}\backslash )$

Reduced Speed Pump Circulating Rate : $200$ gpm$.$

Parasitic $($or Frictional$)$ Pressure Losses at $\backslash (200\backslash$mathrm$\{$gpm$\}.\backslash$mathrm$\{750\}\backslash$mathrm$\{$psi$\}\backslash ).$

Total Volume of Mud in Tanks: $1000$ bbl$.$

Surface Temperature: $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$

Temperature @ $12,200$ ft: $\backslash (160^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$

Drill String Data:

Length of Drill Pipe: $11,600$ ft

Length of Drill Collars: $600$ ft $.$

Capacity of Drillpipe: $\backslash (0\mathrm{.}014\backslash$mathrm$\{$bbl$/$ft$\}\backslash )$

Capacity of Drill Collar: $0\mathrm{.}0087$ bbl$/$ft

Capacity of Drill collar$-$Openhole annulus: $\backslash (0\mathrm{.}035\backslash$mathrm$\{$bbl$\}/\backslash$mathrm$\{$ft$\}\backslash )$

Capacity of Drillpipe$-$Openhole annulus: $0\mathrm{.}0775$ bbl$/$ft

Capacity of Drillpipe casing annulus: $0\mathrm{.}1215$ bbl$/$ft

Initial Kick Data:

Pit Gain: $15$ Bbl$.$ Methane Kick

Shut$-$in Casing Pressure: $400$ psi $.$

Shut$-$in Drill Pipe Pressure: $200$ psi

Problem$-1(70$ Points$)$

It was decided to circulate the kick out of the well using Drillers method. When the top of the kick zone reaches to surface, determine the following parameters;

a$-)$ Length of kick zone, ft$.$

b$-)$ Casing pressure at the surface

c$-)$ Equivalent mud density at the casing shoe, ppg$.$

d$-)$ Mud volume pumped, bbl

e$-)$ Determine the drill pipe pressure schedule $($drill pipe pressure vs$.$ time$)$ as the kill mud is being pumped down the well.