An anchor module has an inner mandrel having a through bore, a slips device, upper and lower slips supports, and a spring device radially outside of the inner mandrel. The slips device is biased to a run state. A fluid actuation system counteracts the biasing force and includes a lower piston axially displaceable within a lower fluid chamber, an upper piston axially displaceable within an upper fluid chamber, and a fluid restriction provided in the bore. A lower fluid line is provided between the bore and the lower fluid chamber. The upper and lower pistons are connected to the lower slips device. An upper fluid line is between the bore and the upper fluid chamber. A cross sectional area of the fluid bore at the entrance of the upper fluid line smaller than the cross sectional area of the fluid bore at the entrance of the lower fluid line.