**Pressure and depth:**

“Pressure and Depth” is the FUNDAMENTAL relationship in the oil industry. Your understanding of the concept is crucial. The easiest way to calculate pressure from depth is to use the *pressure gradient* of the given fluid.

Pressure gradients for incompressible fluids have units of pressure/depth. For example, psi/ft, bar/m.

Pressure gradient seems difficult, but it is simply using the density of the fluid and converting units:

The density of pure water is 1000 kg/m3. To convert to gradient:

- 1 kg = 2.2 pounds
- 1 m = 39.37 inches
- 1 m = 3.28 feet

**0.433** is the gradient for pure water (SG = 1) in Imperial units, remember it.

NB:Specific Gravity is always relative to pure water.

**Calculating Pressure Gradient:**

Most of the time you will not be given a fluid gradient or an average specific gravity, you will need to calculate it.

First calculate your average specific gravity:

**Average SG = SG of water x Water Cut + SG of oil x (1-Water Cut)**

Then calculate your Gradient:

**Average Gradient = 0.433 x Average SG**

If you are given the API gravity of oil instead of the SG, then use this formula:

__Example:__

WC = 70%

Water SG = 1.04

Oil Gravity = 36 °API

Calculate the average Gradient:

- Oil density = 141.5 / (131.5 + 36) = 0.845
- Average density = 1.04×0.7 + 0.845×0.3 = 0.9815
- Average Gradient = 0.433 x 0.9815 =
**0.425 psi/ft.**

**Pressure-Depth Plot:**

To find a pressure at a given depth, simply multiply the **VERTICAL** depth by the given fluid gradient.

Pressure = Density x Gradient

Assuming that the fluid is incompressible, this is *a linear relationship*.

We can draw this on a graph that we call the *pressure-depth plot*.

Obviously, denser fluids, and therefore higher fluid gradients result in higher pressure.

For example, if my depth is 2000 ft. and my gradient is 0.425 psi/ft, then my pressure is 2000 ft. x 0.425psi/ft = **850 psi.**

If the pressure at surface isn’t zero, then the whole line shifts over according to the surface pressure.

__Example:__

From the previous example, a gradient of 0.425 psi/ft at 2000 ft. resulted in 850 psi pressure.

If my surface pressure was 150 psi, then the pressure at depth would increase by the same amount:

Pressure @ depth = 850 psi + 150 psi = **1000 psi.**

If the fluid doesn’t reach the surface, then there is some ‘fluid level’, or depth, where the pressure is zero and then the pressure increases according to the gradient.

__Example:__

Our total depth (2000 ft.) and gradient (0.425 psi/ft.) are the same as before. The fluid level, however, is below the surface (zero) at 500 ft. What is the pressure at 2000 ft.?

P = (2000 ft. – 500 ft.) x (0.425 psi/ft.) = **637.5 psi.**

**Calculating the Fluid Height or Column:**

Similarly, if we know the pressure and the gradient, we can calculate the equivalent fluid column resulting from that pressure.

**Fluid Height = Pressure / Gradient**

Here the effect of increasing gradient is reversed, and denser fluid results in a shorter fluid column for a given pressure.

__Example:__

Pressure = 2500 psi @ depth (pressure zero at surface).

Gradient = 0.402 psi/ft.

Fluid Height = (2500 psi.) / (0.402-psi/ft.) = **6218.9 ft.**