When a well is shut in due to well control operation, the casing pressure will increase due to gas migration and gas expansion. In water based mud, you are able to estimate the maximum surface pressure with this following formula.

Where;

Max surface pressure in psi.

P is expected formation pressure in psi.

V is pit volume gain in bbl.

KWM is kill weight mud in ppg.

An is an annular capacity in bbl/ft.

We can easily estimate surface pressure in water based mud because gas kick is not soluble in water based mud. On the other hand, with oil based mud, you will not be able to use this equation because you will not see the real volume of gas kick due to gas solubility in oil.

Determine the maximum surface pressure.

Drill well with water based mud.

Pit gain = 25 bbl

Stabilized casing pressure = 600 psi

Initial drill pipe pressure = 450 psi

Current mud weight = 12.0 ppg

Hole depth = 10,000’MD/9,500’TVD

Hole diameter = 8.5 inch

Drill pipe = 5 inch

**Determine kill weight mud with this equation**: KMW = current mud weight + (drill pipe pressure ÷ (0.052 x Hole TVD)).

KMW = 12.0 + (450 ÷ (0.052 x 9500)) = 12.91

You need to round the kill weight mud up; therefore, KMW is 13.0 ppg.

**Note: **Please read the following link about kill weight mud -> **well control formulas**

**Determine formation pressure.**

Formation pressure = surface pressure + hydrostatic pressure

Formation pressure = 450 + (0.052 x 12.0 x 9500) = 6378 psi

**Note: **Please read the following link about formation pressure -> Formation Pressure from Kick Analysis

Determine annular capacity: Annular capacity = (8.52 – 52) ÷ 1029.4 = 0.0459 bbl/ft

Note: if you would like to understand annular capacity, please check out the following links -> **Annular capacity**

Once you get all parameters you need, you can determine a figure.

Maximum surface pressure = 1344 psi.

**Ref book: ** **Formulas and Calculations for Drilling, Production and Workover, Second Edition**