The pressure at the top of a gas bubble at any point in the annulus while circulating it out using the Driller’s 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 r1 x Vinf.o     x    Z2T2} ½

         2    {4                                          AV.cap.x      Z1T1}

Where:

A = Po - (D - X) 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

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

X = depth of point X

Note:

We can assume Z2T2 = 1, if there is no other information available.

                        Z1T1

 

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