Abstract.  In Part 11 of the present paper we have demonstrated that an injection hydrofracture inevitably grows.  It implies that a smart injection controller that accounts for the changes caused by fracture extension has to be designed.  Such a controller is a component of an automated system of waterflooding surveillance and control system operating on field scale.  We discuss the controller design in the present paper.

We design an optimal injector controller using methods of optimal control theory.  The controller input parameters are the history of the injection pressure and the cumulative injection along with the fracture size.  The output parameter is the injection pressure and the objective of control is a given injection rate.  It is demonstrated that the optimal injection pressure depends not only on the instantaneous measurements, but on all the history of injection.  We propose a procedure allowing estimation of the hydrofracture size at no additional cost.