Water-Oil Pressure: Calculating Pressure at 2000m Depth

[slyman]

1Assume that below the surface of the Earth there is a connection between all of the ground water, and the water is static (the pressure profile is hydrostatic, you should know what this means in terms of water head). A hole is drilled (which fills with water) to a depth of 2000 m, where oil is found.
a) Call the surface of the Earth to be z=0 and assume this is the top of the water column. Find the water pressure (Pw) at a depth of 2000m.
b) Assume that at the reservoir, the water pressure is equal to the oil pressure (Po). Write down the oil pressure at z=2000 m.
c) Now assume that the well bore has its water displaced by the reservoir oil (density = 800 kg/m3), and then it is capped (we now have a column of static oil instead of a column of static water). Find the oil pressure at the top of the well bore (z= 0 m) and compare it to atmospheric pressure. (This is the simplest reason why there are gushers).

Homework Equations

Ptotal = Patmosphere + Pfluid

The Attempt at a Solution

for a) I got Ptotal= 1.01 * 10^5+ 1000*9.8*2000=1.9701*10^7 kpa = pw

b) I'm kind of confused here, so does this mean pw=poil so poil is the same answer as above

c) I don't have a clue.

I'm having a hard time understanding the question. Could somebody please clarify it for me? I'd appreciate your help. Thanks in advance.

 

[Dick]

b) yes, it's the same. c) do the same thing you did in a) but use the density of oil instead of the density of water. Note that atmospheric pressure is much smaller than the other two. You can probably ignore it.

 

[piercas]

I would first clarify the question and make sure I fully understand what is being asked. It seems like the question is asking about the pressure at different depths in a well that contains both water and oil. Here is my attempt at a solution:

a) To find the water pressure at a depth of 2000m, we can use the equation Ptotal = Patmosphere + Pfluid, where Ptotal is the total pressure, Patmosphere is the atmospheric pressure, and Pfluid is the pressure of the fluid (in this case, water). Since we are assuming a hydrostatic pressure profile, the pressure of the water at a depth of 2000m would be equal to the weight of the water column above it. Using the density of water (1000 kg/m3) and the acceleration due to gravity (9.8 m/s2), we can calculate the pressure as Pw = 1000 * 9.8 * 2000 = 1.96 * 107 Pa.

b) The question states that at the reservoir, the water pressure is equal to the oil pressure. This means that at a depth of 2000m, the oil pressure (Po) would also be 1.96 * 107 Pa.

c) Now, let's consider what happens when the well bore is filled with oil. Since the density of oil is given as 800 kg/m3, the pressure at the top of the well bore (z=0 m) would be Ptotal = Patmosphere + Pfluid = 1.01 * 105 + 800 * 9.8 * 2000 = 1.97 * 107 Pa. This is the same pressure as in part a), which makes sense since we are assuming the same pressure at the reservoir. The pressure at the top of the well bore is the same as atmospheric pressure (1.01 * 105 Pa), meaning there is no pressure difference to push the oil out. This is why gushers can occur - if the pressure at the reservoir is higher than atmospheric pressure, the oil will flow out of the well bore.

I hope this helps clarify the question and provides a satisfactory solution.