The pressure at the top of a gas bubble at any point in the annulus while circulating it out using the “wait and weight” method can be calculated as follows:
By calculating the expected annular pressures at the top of the influx at specific points along the wellbore together with the associated influx volumes at these points, comparisons can be made with actual values observed during circulating out the influx. This information can play an important role in the decision making process during well control operations.
Px = A/2 + {(A/2)2 + [Po - hinf.o x rinf.o)] x r2 x (Vinf.o /AV.cap.x) x (Z2T2/Z1T1)} ½
Where:
A = Po - (D - X) r2 + D1 (r2 - r1) - (hinf.o x rinf.o) x (AV.cap.o/AV.cap.x)
Px = pressure at the top of the gas point X
Po = formation pressure
hinf.o = height of gas column at the bottom of the hole
rinf.o = original influx gradient
r1 = original mud gradient
r2 = kill/mud gradient
Vinf.o = original influx volume
AV.cap.x = average annular capacity of influx volume at point X
AV.cap.o = average annular capacity of influx volume at bottom
Z1 = initial compressibility factor of gas
Z2 = compressibility factor of gas at point X
T1 = absolute initial temperature of the gas
T2 = absolute temperature of the gas at point X
D = depth of the hole
D1 = height of the r1 mud in the annulus after it has been displaced from the
drillstring.
X = depth of point X
Note: If there is no r2 mud in the annulus, us r1 instead.
We can assume Z2T2 / Z1T1= 1, if there is no other information available.
The influx volume at point X can be calculated as follows:
Vinf.x = Po - (hinf.o x rinf.o) x Vinf.o x Z2T2
Px Z1T1