Water injection into a low-permeability rock - 2: Control model

Dmitriy B. Silin*, Tad W. Patzek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In Part 1, we have demonstrated the inevitable growth of the fluid injection hydrofractures in low-permeability rocks. Thus, a smart controller that manages fluid injection in the presence of hydrofracture extension is highly desirable. Such a controller will be an essential part of automated waterflood project surveillance and control. Here we design an optimal injection controller using methods of optimal control theory. The controller inputs 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 control objective is the injection rate. We demonstrate that the optimal injection pressure depends not only on the instantaneous measurements, but it is determined by the whole history of the injection and of the fracture area growth. We show the controller robustness when the inputs are delayed and noisy and when the fracture undergoes abrupt extensions. Finally, we propose a procedure that allows estimation of the hydrofracture size at no additional cost.

Original languageEnglish (US)
Pages (from-to)557-580
Number of pages24
JournalTransport in Porous Media
Issue number3
StatePublished - Jun 2001
Externally publishedYes


  • Controller
  • Hydrofracture
  • Optimal injection
  • Quadratic optimization
  • Waterflood

ASJC Scopus subject areas

  • Catalysis
  • General Chemical Engineering


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