Task $2$: Loads on casing

W$$ now turn to the problem of calculating loads on a casing string, and consider a vertical well with the current section drilled to $2400m$ using a mud with density $1120k\frac{g}{m^3}.$ A $\frac{95}{8}-$in production casing will be run to the bottom of the section. The formation pressure at the bottom of the section $($at a depth of $2400m)$ is estimated to be $530$ bar. After running and cementing the casing, we plan to drill the next section with a mud of density $1225k\frac{g}{m^3}.$

It is estimated that the loss of mud to a possible low$-$pressure zone will empty maximum $45\%$ of the casing. The required safety factors are $1\mathrm{.}8$ for tear$-$off, $1\mathrm{.}5$ against bursting, and $1\mathrm{.}2$ against collapse. Density of any gas in annulus is assumed to be $240k\frac{g}{m^3}.$ When mud is still for a long period of time it can degenerate into a density of $1030k\frac{g}{m^3}($the weight material falls out of the mud, but not the salt$).$

a$)$ Find the maximum burst pressure in a possible gas kick situation. At which depth is the strain $($bursting pressure$)$ on the casing maximum? Explain your answer.

b$)$ Find the maximum collapse pressure in case of mud losses to the low$-$pressure zone. At which depth is the strain on the casing maximum? Explain your answer.

When cementing the $945/8-$in production casing, a cement slurry with a density of $1960k\frac{g}{m^3}$ is to be used. The fluid used to pump$/$push the cement down the casing has a density $1225k\frac{g}{m^3}($which is the mud to be used for further drilling$).$ The top of the cement should be at $300m$ above the bottom $($casing shoe$)$ of the previous casing, which goes down to a depth of $1640m.$ We assume a "worst case" scenario, with the cement slurry completely filling the casing during injection. The critical fracture pressure for the cementing operation is $\frac{328}{b}ar$ at a depth of $2180m.$ If this pressure is exceeded, we need to repair it by a second stage cementing operation.

c$)$ Calculate the maximum burst pressure and maximum collapse pressure when cementing. At which depth is the strain on the casing maximum? Do we have to repair and perform a second stage cementing operation? Explain your answers!M