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.
