The pressures discussed above relate exclusively to the pressure in the pore space of the formations. It is however also important to be able to quantify the vertical stress at any depth since this pressure will have a significant impact on the

pressure at which the borehole will fracture when exposed to high pressures. The vertical pressure at any point in the earth is known as the overburden pressure or geostatic pressure. The overburden pressure gradient is derived from a cross plot of overburden pressure versus depth (Figure below). The overburden pressure at any point is a function of the mass of rock and fluid above the point of interest. **In order to calculate the overburden pressure at any point, the average density of the material (rock and fluids) above the point of interest must be determined**. The average density of the rock and fluid in the pore space is known as the bulk density of the rock :

## Overburden Pressure Formulas

?b = ?f x ? +?m (1-? )

or

?b = ?m – (?m – ?f )?

where,

?b = bulk density of porous sediment

?m = density of rock matrix

?f = density of fluid in pore space

? = porosity

Since the matrix material (rock type), porosity, and fluid content vary with depth, the bulk density will also vary with depth. The overburden pressure at any point is therefore the integral of the bulk density from surface down to the point of interest.

The specific gravity of the rock matrix may vary from 2.1 (sandstone) to 2.4 (limestone). Therefore, using an average of 2.3 and converting to units of psi/ft, it can be seen that the overburden pressure gradient exerted by a typical rock, with

zero porosity would be :

### Overburden pressure gradient exerted by a typical rock

2.3 x 0.433 psi/ft = 0.9959 psi/ft

This figure is normally rounded up to 1 psi/ft and is commonly quoted as the maximum possible overburden pressure gradient, from which the maximum overburden pressure, at any depth, can be calculated. It is unlikely that the pore pressure could exceed the overburden pressure. However, it should be remembered that the overburden pressure may vary with depth, due to compaction and changing lithology, and so the gradient cannot be assumed to be constant.

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