Pore pressure gradient
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Pore pressure gradient is a dimensional petrophysical term used by drilling engineers during the design of drilling programs for drilling (constructing) oil and gas wells into the earth. It is the pressure gradient inside the pore space of the rock column from the surface of the ground down to total depth (TD), as compared to the pressure gradient of seawater in deep water.
Whereas in "pure math," the gradient of a scalar function expressed by the math notation grad(f) may not have physical units associated with it; in drilling engineering the pore pressure gradient is usually expressed in APItype International Association of Drilling Contractors (IADC) physical units of measurement, namely "psi per foot."
In the wellknown formula
 P = 0.052 * mud weight * total vertical depth
taught in almost all petroleum engineering courses worldwide, the mud weight (MW) is expressed in pounds per U.S. gallon, and the total vertical depth (TVD) is expressed in feet, and 0.052 is a conversion constant that can be derived by dimensional analysis later. This is pretty lazy considering\[\mathrm{1\; psi/ft = \frac{1\; ft}{12\; in}\times \frac{1\; lb/in^{2}}{1\; psi}\times \frac{231\; in^{3}}{1\; US\; Gal}=19.25000000\; lb/gal}\]
It would be more accurate to divide by 19.25.^{[clarification needed]}
Therefore, for a column of fresh water of 8.33 pounds per gallon (lb/U.S. gal) standing still hydrostatically in a 41,000 foot vertical cased wellbore from top to bottom (vertical hole), the pressure gradient would be
 grad(P) = pressure gradient = 0.052 * 8.33 = 0.433 psi/ft
and the hydrostatic bottom hole pressure (BHP) is then
 BHP = grad(P) * TVD = 0.43316 * 41,000 = 17,759 psi
However, the pore pressure is usually much greater than a column of fresh water, and can be as much as 19 lb/U.S. gal (e.g., in Iran). For an onshore vertical wellbore with an exposed open hole interval at 41,000 feet with a pore pressure gradient of 19 lb/U.S. gal, the BHP would be
 BHP = pore pres grad * TVD = 0.052 * 19 * 44,000 = 43,500 psi
These are the most important and basic math calculations in almost all well control courses taught worldwide, for the prevention of oil and gas well blowouts.
Simple Examples
Using the figures above, we can calculate the maximum pressure at various depths in an offshore oil well.
Saltwater is 0.444 psi/ft (2.5% higher than fresh water) Pore pressure in the rock could be as high as 1.0 psi/ft of depth (19 * .052)
A well with 5,000 feet of seawater and 15,000 feet of rock could have pressures at the bottom as high as 17Kpsi (5000 * 0.444 + 15000 * 1.0). That pressure is reduced at the surface by the weight of oil and gas the riser pipe, but this is only a small percentage of the total. It takes heavy mud inserted at the bottom to regain control when pressures are this high.
References