Controlled　mud-cap　(CMD)　drilling　is　an　advanced　deepwater　drilling　technology.　When　the　surface　pump　is　shut　down,　the　CMD　system　causes　unsteady　flow　that　may　create　control　problems.　A　new　mathematical　model　has　been　developed　to　simulate　unsteady　flow　in　CMD　systems.　The　model　predicts　the　transient　flow,　the　equilibrium　time,　and　the　change　in　bottomhole　pressure　during　the　unsteady　flow.　The　simulation　results　show　that　the　flow　parameters　change　rapidly　during　the　first　10　min　and　that　unsteady　flow　leads　to　fluctuations　in　bottomhole　pressure.　In　combination　with　measured　data,　the　transient　flow　behavior　computed　by　the　model　can　be　used　for　early　detection　of　well　kick　after　shutdown　of　the　mud　pump.