Method of optimizing operation one or more tubing strings in a hydrocarbon well, apparatus and system for same

A method, performed by a processor of at least one apparatus, of optimizing operation of one or more tubing strings, each tubing string being located in a hydrocarbon well and having a plurality of valves, each valve being actuatable between a fully open position and a fully closed position, each valve being in communication with a respective zone of a formation defining a reservoir containing hydrocarbon material, the method comprising:

• for each injection string in the one or more tubing strings:
• (i) characterizing an injectivity of one or more zones of the formation in accordance with sensed characteristics of an injection fluid;
• (ii) determining an optimal operating schedule for the injection string in accordance with the characterization of the one or more zones of the formation and one or more performance objectives of the respective injection string, wherein the optimal operating schedule comprises one or more valve configurations and an operating duration for each of the one or more valve configurations, wherein each valve configuration is defined by a condition of the valves in which each valve in the plurality of valves is in either the fully open position or the fully closed position.