Migration is natural behavior of gas. It means that when you shut the well in, gas will migrate from bottom to top of the well.
We can estimate the gas migration rate in a shut-in well with this following equation.
Where: Vg is gas migration rate in ft/sec
Current mud weight in ppg
e is the base of the nature logarithm which has a value of 2.71828182845904.
Note: This is an empirical equation. It may be different from the actual but it can give you good idea regarding how fast the gas can migrate up hole.
Please follow this example to understand how to use the formula.
Determine the gas migration rate with 12.0 ppg mud.
Vg = 0.142 ft/sec
We can convert unit from ft/sec to ft/hr by multiplied by 3600.
Vg = 0.142 x 3600 = 510 ft/hr
Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition