Problem

A fracture treatment consists of injecting a fluid $(=0\mathrm{.}05k\frac{g}{m}-sec,=1250k\frac{g}{m^3})$ at a rate of $0\mathrm{.}03$

$\frac{m^3}{sec}.$ The fracture length of the vertical fracture is calculated to be $100$ m and the average fracture

width measured at the wellbore is calculated to be $8{10}^{-3}m$ at a time of $2200$ sec after starting the

treatment. These calculations are all based on the assumption that the fracture height is $30$ m $.$

Now, the actual fracture height created by the fracture treatment appeared to be $40$ m rather than

the $30$ m used in the original calculation. Assuming the long$-$time approximation to be valid, answer

the following:

What is the actual fracture length and average fracture width measured at the wellbore after $2200$

sec$?$

Estimate the bottomhole pressure after $2200$ sec$.$ The instantaneous shut$-$in pressure is $25,000$

kPa $.$