Petroleum Engineering Education: Bottom-of-Well Pressure When the Well Is Filled with Two Fluids of Different Specific Gravities
Hello, friends and followers of my blog. Today I’d like to share with you a very special example of how to calculate the pressure at the bottom of a well when it is filled with two fluids that have different specific gravities.
Taking into account the mechanical diagram of the well shown in the cover image, we have the following:
Consider a well with a depth of 9,000 feet, which is filled with 28 API gravity crude oil from the surface down to a depth of 5,000 feet; below the oil is salt water with a specific gravity of 1.12 at depths ranging from 5,000 to 9,000 feet. We are asked to calculate the pressure at the bottom of the well.
To calculate the bottom-hole pressure—assuming the well is sealed and atmospheric pressure is not acting on the bottom-hole pressure— we simply need to know that the bottom-hole pressure is the sum of the pressure exerted by the column of oil from the surface to 5,000 feet plus the pressure exerted by the column of saltwater from 5,000 feet to 9,000 feet (that is, a 4,000-foot column of saltwater).
We will now calculate the pressure exerted by the oil.
First, we must calculate the density of the oil at 28 degrees API.
To calculate the density, we use the equation for calculating the specific gravity of a fluid:
We solve for the density of oil in the equation:
The density of water in pounds per cubic foot is 62.4 pounds per cubic foot; therefore, all we need to calculate is the specific gravity of oil using the following equation:
We simply substitute the API grades into the equation and perform the calculations:
We already have the specific gravity of the oil, which is 0.88714. To find the density of this oil, we simply need to multiply the specific gravity by the density of water, which is 62.4 pounds per cubic foot:
The density of 28 API gravity crude oil is 55.35 pounds per cubic foot.
The next step is to convert that density value to a pressure gradient. To do this, we divide the density by 144, which gives us the pressure gradient in PSI/FT:
Since the well is full of oil from the surface down to 5,000 feet, we multiply the pressure gradient by the depth of 5,000 feet:
Now we'll calculate the density of saltwater:
We convert this density to a pressure gradient by dividing the density by 144; this will also give us a result in PSI/FT:
To determine the pressure exerted by the saltwater, we multiply the pressure gradient by 4,000 feet, which is the height of the saltwater column in the well:
The pressure exerted by the brine is 1941 PSI.
The pressure at the bottom of the well is the oil pressure plus the brine pressure: (1922 + 1941) PSI, for a total bottom-hole pressure of 3863 PSI.
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