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This does not actually qualifies this production as Pressure Control and the well is still under Liquid Control conditions and once bottomhole pressure raises above minimal the pump returns to producing the target liquid rate 

LaTeX Math Inline
bodyq^{\uparrow}_L(t) = q^{\uparrow}_{LL} = \rm const


See also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Dynamic Flow Modelling / Reservoir Flow Model (DFM)Modelling / Well control Control (Reservoir Flow Modelling)

Petroleum Industry / Upstream /  Production / Subsurface Production Operations / Well Control Pressure Control