The mud pumps can be shut down after the total volume of the well has been displaced with kill mud. Practically, you need to check mud weight out several times to ensure that the mud weight out equates to the kill weight mud. Otherwise you may have misinterpretation once the well is shut in and flow checked.
Once shutting down the mud pumps, the choke should be gradually closed in order to hold casing pressure constant. The drill pipe pressure will be slowly dropped to zero as the pump speed is reduced. Please always remember every time that you either bring the pumps up to speed or slow down pump speed, you must hold casing pressure constant.
After the well is shut-in, both the drill pipe pressure and casing pressure should be reading zero. Typically, you may see any trapped pressure that you account for any pressure safety factor while circulating. You may consider trying to bleed off trapped pressure and observe if there is pressure built up. If there is no pressure built up, you must confirm that the well is dead by opening the choke and checking well via trip tank. At this stage, if the well is totally killed, you must not see any increases in the trip tank.
Once you confirm that the well is dead, the BOPs can be opened. I would like to remind you that a small gas volume may be trapped between the choke line and the BOP. Please make sure that everybody is cleared from the rig floor before opening up the BOP.
Once the BOP is opened, you probably need to circulate and condition the mud in order to obtain the desired mud properties. For example, if the yield point is too high, it will cause swabbing effect while pulling out of hole and it could lead to another kick. In order to prepare for a trip after conditioning the mud, you may raise the mud weight to an acceptable “trip margin”.
Note: This is just only guide line for well control. Before you do any well control operation, please contact your supervisor and make good agreement about the forward plan.
Reference book: Well Control Books