(212f) Feedback Control of Two-Phase Flow in (Secondary) Enhanced Oil Recovery

In secondary enhanced oil recovery water is injected to push oil through the field to improve the rate of production as well as the overall amount of oil produced during the life of the field. The injection process works as long as the oil is actually displaced and moved towards the production wells. The process stops and the well is shut down when a significant amount of water is produced.

In practice it is difficult to achieve good recovery because the dynamic behavior of the oil field is often very uncertain, very few on-line measurements are available and it is often difficult to coordinate seismic data, results from high order models like ECLIPSE and massive amounts of historical data with low order network models used for on-line optimization and control.

In the current paper we describe a novel framework for the modeling and analysis of complex reservoir simulation and water injection control using irreversible thermodynamics and network theory. We show that conservation laws for the two phase oil-water system in porous rock and sand formations together with continuity (due to the second law) and sector conditions for the constitutive equations lead naturally to stability and optimality conditions which can be used to design nonlinear observers and better feedback control laws for dynamic water injection. The model we study (develop by TU Delft and Shell) represents the reservoir as an interconnected network of grid cells. The flow between the cells is given by a modified Darcy law with resistivity determined by the oil/water fraction in each grid cell. Flow is induced through potential gradients between the grid cells. The flow dependency is very nonlinear, but the sector conditions are satisfied. Our analysis suggests that the petroleum reservoir optimizes a natural objective during the water flooding process. This objective function is based on the dissipated energy and it is minimized for a given set of boundary and initial conditions.

The optimization principle is illustrated in a simulation example for the water-flooding of a typical petroleum field case study in which the oil recovery of a petroleum reservoir is analyzed during its life-cycle. A heterogeneous, horizontal, 2D, two-phase (oil and water) reservoir is considered, with injection wells and production wells at opposite sides. Dynamic and static feedback control strategies are compared. It is demonstrated that dynamic control yield higher recovery. The results will be demonstrated through a sequence of 2D simulation experiments with parameters motivated by a real oil field system.