This is a classic example demonstrating how bottom hole pressure will be due to gas migration in a shut in well. This is very important concept in well control.
Assumption: For this example, since the volume of the well does not change, and assuming that no mud or fluid is lost to the formation.
This example will demonstrate the gas behavior in a shut in well. The well is shut-in without pipe in hole. 5 bbl of gas kick is taken and initial shut in casing pressure is equal to 400 psi. Hydrostatic head on top of gas is 4000 psi (see figure below).
Even though the well is shut in, the gas influx is able to move upward due to gas migration.
In this case, we will not allow any gas expansion and let the gas gradually migrate.
The well is shut in and gas is allowed to migrate up hole until hydrostatic pressure underneath gas is 2000 psi (see the figure below).
What will happen to bottom hole pressure and casing pressure?
With Bolye’s Law concept, we will apply it see how much gas bubble should be.
According to this example,
Pressure of gas (P1) is 4400 which equates to the bottom hole pressure.
Volume of gas at beginning (V1) is 5 bbl
P1 x V1 = P2 x V2
4400 x 5 = P2 x 5
P2 = 4400 psi ->Gas pressure remains constant.
You have total of hydrostatic pressure of 4,000 psi at the beginning. Currently, you have 2000 psi of hydrostatic at the bottom therefore you have 2000 psi of hydrostatic on top of gas. See the figure below.
Let’s see how much casing pressure will be.
Apply hydrostatic pressure concept to solve this problem.
Gas influx pressure = hydrostatic pressure above the gas influx + casing pressure
4400 = 2000 + casing pressure
Casing pressure = 2400 psi
Moreover, you can find the bottom hole pressure by applying the same concept.
Bottom hole pressure = hydrostatic pressure of mud + casing pressure
Bottom hole pressure = 4,000 + 2,400
Bottom hole pressure = 6,400 psi.
If the well is shut in and the gas influx is allowed to migrate, gas pressure will remain constant; however, bottom hole pressure and casing pressure will increase. If you let casing pressure (surface pressure) increase too much, you can break formation or damage surface equipment.
Reference book: Well Control Books