Method for controlling production and downhole pressures of a well with multiple subsurface zones and/or branches

A method for controlling the influx of fluids into a multizone well in which each inflow zone is provided with an inflow control device, comprises: assessing the flux of oil, gas, water and other effluents from the well; monitoring production variables, including ICD position and/or fluid pressure in each inflow zone upstream of each ICD and/or downstream of each ICD; sequentially adjusting the position of each of the ICDs and assessing the flux of crude oil, natural gas and/or other well effluents; monitoring production variables; deriving a zonal production estimation model for each inflow zone of the well; and adjusting each ICD to control the influx of crude oil, natural gas and/or other effluents into each inflow zone on the basis of data derived from the zonal production estimation model for each inflow zone of the well.