For this case, we will consider the shoe pressure when the gas kick is passing the casing shoe. See the image below.
Let’s apply the hydrostatic pressure concept.
The formula for the bottom hole pressure is listed below:
Bottom Hole Pressure = Pressure at casing shoe + Hydrostatic Pressure in the open hole underneath the shoe
While circulating kick, we keep the BHP constant therefore the equation will look like this
Bottom Hole Pressure (constant while circulating) = Pressure at casing shoe + Hydrostatic Pressure in the open hole underneath the shoe
While the gas kick is passing the shoe, the hydrostatic pressure in the open hole will increase because mud column underneath the shoe increases. According to the equation above, in order to maintain bottom hole pressure constant, the shoe pressure will decrease.
Conclusion: Pressure at shoe will decrease when gas bubble passing the shoe.
Ps – assumptions : water base mud is used and kick is gas.
Reference book: Well Control Books