Height of influx will increase when the drillstring penetrates a kick; therefore, hydrostatic pressure decreases and casing pressure increases in order to compensate this situation.
If the casing is maintained constant while penetrating the kick, you will have high chance to take more influx because of underbalance situation (Figure 1). This article will teach you about how to determine pressure increment while penetrating into the kick, what to look for, etc.
Figure 1 – Height of Influx increases when the drillstring penetrates into it.
However, if the constant surface pressure is utilized for the stripping operation, you must account for pressure increment due to height of influx change. The equation below is for calculating the increase in casing pressure.
∆CP = ∆H x (MG – KG)
Where: ∆CP = Increase in casing pressure, psi
∆H = Change in length of influx, ft
MG = Mud Gradient, psi/ft
KG = Kick Gradient, psi/ft
The example below demonstrates how to calculate casing pressure increase.
Hole TD = 12,000’MD/12,000’TVD
Hole size =11.75”
Drill pipe = 5”
Drill collar = 6.5”
Drill collar length = 800 ft
Pit gain = 35 bbl
Mud weight = 12.0 ppg
Kick gradient = 0.3 psi/ft
Figure 2 – Calculation Example for This Situation
Hole capacity = 11.752 ÷ 1029.4 = 0.134 bbl/ft
Kick Height in open hole =35 ÷ 0.134 = 261 ft
Hole and 6.5” drill collar capacity = (11.752 -6.52) ÷ 1029.4 = 0.0931 bbl/ft
Kick Height in annulus between hole and DC = 35 ÷ 0.0931 = 376 ft
Mud gradient = 12.0 x 0.052 = 0.624 psi/ft
Kick gradient = 0.3 psi/ft
∆CP = ∆H x (MG – IG)
∆CP = (376 – 261) x (0.624 – 0.3)
∆CP = 37 psi
Figure 3 – Casing Pressure Increase Due To Kick Penetration
The increase in casing pressure required for this scenario is 37 psi. This figure tells you that you need to let casing pressure increase by 37 psi in order to compensate to hydrostatic loss.
Practically, you should have the safety factor which is greater than casing pressure increase required for kick penetration and for this case, the safety factor must be more than 37 psi. This will prevent the underbalance situation when the influx is penetrated and you don’t need to worry about the time when the influx penetration will actually happens.
For gas kick, it is impossible to use either the constant pressure method or the volume accounting method because gas will migrate. You must have the method to control the bottom hole pressure and deal with increase in surface pressure due to gas migration. For gas kick, the volumetric control stripping technique must be used. This technique will account for volume of pipe bled back and surface pressure increase. We will discuss this technique separately in a next topic.
Reference books: 
Well Control Books