Petroleum Engineering: Why is constant 0.052 used in the drilling mud hydrostatic pressure equation?
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Hello friends and followers of STEM content, especially engineering content lovers.
In this opportunity I want to share with all of you the reasons why the constant 0.052 is used in the drilling mud hydrostatic pressure equation, but before that let's get into context:
History and evolution of well drilling and the oil industry in general
When the United States began to drill oil wells, it was done with the percussion drilling technology, which consisted of dropping a heavy pointed drill bit from a height with the objective of building a hole, every so often a pause was taken to remove the cuttings and continue advancing.
The bad thing about the percussion drilling technology is that it was impossible to keep control of the pressures found at the bottom of the well, after these inconveniences to control the pressures at the bottom of the well is that another technology in well drilling called rotary drilling is originated.
Rotary drilling is a method where a well is drilled and where the drill string rotates and with its own weight pulls out the drill cuttings at the bottom of the well helped with the circulation of a drilling fluid called drilling mud.
This drilling fluid when circulating in the oil well generates a circulating pressure, and when the mud pumps are off it generates a hydrostatic pressure, i.e. a pressure where the drilling mud is static and does not circulate. This hydrostatic pressure is calculated with the following equation:
When the U.S. oil industry arrives to my country Venezuela and other Spanish speaking countries, they realize that they have to adapt the measurement models of units of the international system to the English system, since all these Spanish speaking countries learned from the U.S. oil industry everything concerning exploration, drilling and production of hydrocarbons from them.
Therefore parameters such as density and length would not be measured in units of the international system, so much so that within the English system of measurement, specifically in the drilling of wells, density is measured in Pounds / gallon, while the true vertical depth is measured in feet, in the case that we will use these units of the English system, there was an incompatibility for the pressure to be measured in pounds / square inches (PSI), which is why it was necessary to calculate a constant that would make it possible to calculate the hydrostatic pressure where the density was measured in pounds / gallon and the true vertical depth in feet.
Demonstration of why the constant 0.052 is used in the hydrostatic pressure equation
We start from the hydrostatic pressure equation:
We know that density will be measured in pounds/gallon and TVD in feet:
As can be seen in the above equation, in order to give us the hydrostatic pressure in pounds/square inches (PSI), it is necessary to convert the volume from gallons to cubic inches, and feet to inches, taking into account that:
1 galón = 231 inch3
1 pie = 12 pulgadas
Therefore:
Simplifying we are left with:
Therefore:
If we take into account that to arrive at the deduction that it is necessary to use the constant 0.052 was from multiplying density by true vertical depth, then the hydrostatic pressure equation is as follows:
Conclusion
It is necessary to take into account that only the constant of 0.052 is used as long as the density (𝜌) is entered into the equation in units of pounds/gallon, and also the same validity must be met as long as the TVD is entered in feet, the hydrostatic pressure calculated in units of pounds over square inches (PSI).
References