After kick has been circulated out of the well, the mud pumps can be shut down and the well must be secured. While shutting down the pumps, it is a good practice to gradually close the choke instead of suddenly shut in.
You must keep in mind that while shutting down pumps, you must keep casing pressure constant achieved by manipulating the choke. This procedure is to ensure that constant bottom hole pressure is maintained during the shutdown.
The shut-in casing pressure and the shut-in drill pipe pressure should be equal after complete the first circulation of the driller’s method. After shutdown pumps, the Shut In Casing Pressure (SICP) and the Shut In Drill pipe Pressure (SIDP) should be equal to the initial shut-in drill pipe pressure observed at the first time. If SICP and SIDP are the same but they are more than the initial shut-in drill pipe pressure, there is possibly trapped pressure on top of SICP.
If you see that the casing pressure is still higher than the drillpipe pressure, this situation means there is still some kick in the annulus or another kick was possibly taken while circulating. If you see this situation, you must do an additional circulation to ensure that there is no influx left in the well before kill weight fluid is mixed and pumped.
After you ensure that there is no influx in the well, you need to weight up the active pits to desired kill weight fluid.
Kill weight fluid is calculated by the following equation.
Kill mud weight = original mud weight + (Initial Shut In Drill Pipe Pressure ÷ (0.052 x TVD of the well)
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The ideal condition is to maintain a reasonably low active volume because when the mud is circulated out of the hole, you will have room to weight up without having to stop circulating. At least, you should have enough volume to displace entire volume with kill weight mud.
Reference book: Well Control Books