4) In a vertical-well hydraulic fracture test, the $P_{BD}$ (bottom-hole breakdown pressure) and the $P_{ISIP}$ (instantaneous bottom-hole shut-in pressure) for a number of pressurisation cycles when the fracture was being episodically extended are given in this Table.
CYCLE NUMBER $P_{BD}$ $P_{ISIP}$
1 57 MPa 39 MPa
2 50 MPa 38 MPa
3 50 MPa 37 MPa
4 49 MPa 37 MPa
5 49 MPa 36 MPa
a. The equation for the breakdown pressure in terms of the maximum and minimum horizontal stresses, and the "tensile rupture resistance $T_o$", is:
$P_{BD} = 3 \cdot \sigma_{hmin} - \sigma_{HMAX} + T_o$
If the formation pore pressure was measured to be 20 MPa, estimate the minor and major principal effective and total stresses. The fracture test took place at a depth of 2 km and the mean overburden density was 2.40 g/cm³. (State clearly any assumptions you must make)
