- Fluids and their interesting properties
- Calculation of pressure
- How to calculate the pressure gradient?
- Density conversion factor
- References
The pressure gradient consists of the variations or differences in pressure in a given direction, which can occur inside or at the border of a fluid. In turn, pressure is the force per unit area exerted by a fluid (liquid or gas) on the walls or border that contains it.
For example, in a pool filled with water there is a positive pressure gradient in the downward vertical direction, because pressure increases with depth. Every meter (or centimeter, foot, inch) of depth, the pressure grows linearly.
In oil extraction, the pressure gradient is a very important quantity. Source: pixabay.com
However, at all points located at the same level, the pressure is the same. Therefore, in a swimming pool the pressure gradient is null (zero) in the horizontal direction.
In the oil industry, the pressure gradient is very important. If the pressure at the bottom of the hole is higher than at the surface, then the oil will come out easily. Otherwise, the pressure difference would have to be created artificially, either by pumping or injecting steam.
Fluids and their interesting properties
A fluid is any material whose molecular structure allows it to flow. The bonds that hold the molecules of the fluid together are not as strong as in the case of solids. This allows them to oppose less resistance to traction and therefore flow.
This circumstance can be seen by observing that solids maintain a fixed shape, while fluids, as already mentioned, adopt to a greater or lesser degree that of the container that contains them.
Gases and liquids are considered fluids because they behave in this way. A gas expands completely to fill the volume of the container.
Liquids, on the other hand, do not reach that much, since they have a certain volume. The difference is that liquids can be considered incompressible, while gases cannot.
Under pressure, a gas compresses and adapts easily, occupying all the available volume. When the pressure increases, its volume decreases. In the case of a liquid, its density - given by the quotient between its mass and its volume - remains constant over a wide range of pressure and temperature.
This last limitation is important since in reality, almost any substance can behave like a fluid under certain conditions of extreme temperature and pressure.
In the interior of the earth where conditions can be considered extreme, rocks that would be solid on the surface, melt into magma and can flow to the surface, in the form of lava.
Calculation of pressure
To find the pressure exerted by a column of water or any other fluid, on the floor of the container, the fluid will be considered to have the following characteristics:
- Its density is constant
- Is incompressible
- It is in conditions of static equilibrium (rest)
A column of fluid in these conditions exerts a force on the bottom of the container that contains it. This force is equivalent to its weight W:
Density is normally measured in kilograms / cubic meters (kg / m 3) or pounds per gallon (ppg)
The hydrostatic pressure P is defined as the quotient between the force exerted perpendicularly on a surface and its area A:
Pressure = Force / Area
By substituting the volume of the fluid column V = area of the base x height of the column = Az, the pressure equation becomes:
Pressure is a scalar quantity, whose units in the international measurement system are Newton / meter 2 or Pascals (Pa). Units of the British system are widely used, especially in the oil industry: pounds per square inch (psi).
The above equation shows that denser liquids will exert greater pressure. And that the pressure is greater the smaller the surface on which it is exerted.
By substituting the volume of the fluid column V = area of base x height of column = Az, the pressure equation is simplified:
The above equation shows that denser liquids will exert greater pressure. And that the pressure is greater the smaller the surface on which it is exerted.
How to calculate the pressure gradient?
The equation P = ρgz indicates that the pressure P of the fluid column increases linearly with depth z. Therefore, a variation ΔP in pressure will be related to a variation in depth Δz in the following way:
Density conversion factor
Units of the English system are widely used in the oil industry. In this system the units of the pressure gradient are psi / ft or psi / ft. Other convenient units are bar / meter. Pound per gallon or ppg is widely used for density.
The density and specific gravity values of any fluid have been determined experimentally for various conditions of temperature and pressure. They are available in tables of values
To find the numerical value of the pressure gradient between different systems of units, one must use conversion factors that lead from the density directly to the gradient.
The conversion factor 0.052 is used in the oil industry to go from a density in ppg to a pressure gradient in psi / ft. In this way, the pressure gradient is calculated like this:
References
- Serway, R., Jewett, J. (2008). Physics for Science and Engineering. Volume 2. Mexico. Cengage Learning Editors. 367-372.
- Well Control School Manual. Chapter 01 Principles of pressure.