### Abstract

Petroleum reservoirs are subsurface formations of porous rocks with hydrocarbons
trapped in the pores. Initially, the reservoir pressure may be sufficiently
large to push the fluids to the production facilities. However, as the fluids
are produced the pressure declines and production reduces over time. When
the natural pressure becomes insufficient, the pressure must be maintained artificially
by injection of water. Conventional technologies for recovery leaves
more than 50% of the oil in the reservoir. Wells with adjustable downhole flow
control devices coupled with modern control technology offer the potential to increase
the oil recovery significantly. In optimal control of smart wells, downhole
sensor equipment and remotely controlled valves are used in combination with
large-scale subsurface flow models and gradient based optimization methods in
a Nonlinear Model Predictive Control framework to increase the production and
economic value of an oil reservoir. Wether the objective is to maximize recovery
or some financial measure like Net Present Value, the increased production is
achieved by manipulation of the well rates and bottom-hole pressures of the injection
and production wells. The optimal water injection rates and production
well bottom-hole pressures are computed by solution of a large-scale constrained
optimal control problem.
The objective is to maximize production by manipulating the well rates and
bottom hole pressures of injection and production wells. Optimal control settings
of injection and production wells are computed by solution of a large scale
constrained optimal control problem. We describe a gradient based method to
compute the optimal control strategy of the water flooding process. An explicit
singly diagonally implicit Runge-Kutta (ESDIRK) method with adaptive
stepsize control is used for computationally efficient solution of the model. The
gradients are computed by the adjoint method. The adjoint equations associated
with the ESDIRK method are solved by integrating backwards in time.
The necessary information for the adjoint computation is calculated and stored
during the forward solution of the model. The backward adjoint computation
then only requires the assembly of this information to compute the gradients.

Original language | English |
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Title of host publication | Proceedings of the 17th Nordic Process Control Workshop |

Editors | John Bagterp Jørgensen, Jakob Kjøbsted Huusom, Gürkan Sin |

Place of Publication | Kogens Lyngby |

Publisher | Technical University of Denmark |

Publication date | 2012 |

Pages | 198 |

ISBN (Print) | 978-87-643-0946-1 |

Publication status | Published - 2012 |

Event | 17th Nordic Process Control Workshop - Kongens Lyngby, Denmark Duration: 25 Jan 2012 → 27 Jan 2012 Conference number: 17 http://npcw17.imm.dtu.dk/ |

### Conference

Conference | 17th Nordic Process Control Workshop |
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Number | 17 |

Country | Denmark |

City | Kongens Lyngby |

Period | 25/01/2012 → 27/01/2012 |

Internet address |

## Cite this

Völcker, C., Jørgensen, J. B., Thomsen, P. G., & Stenby, E. H. (2012). Production Optimization for Two-Phase Flow in an Oil Reservoir. In J. B. Jørgensen, J. K. Huusom, & G. Sin (Eds.),

*Proceedings of the 17th Nordic Process Control Workshop*(pp. 198). Technical University of Denmark. http://npcw17.imm.dtu.dk/