Lyapunov Approach For Stability Investigation Of Well - Production Model For Fluid Flow:- Ogbonna, Christopher O.

ABSTRACT

This research work presents Lyapunov approach for stability investigation of well - production model for fluid flow. It is established that a well production rate u(t) is essentially a controller used in the Lyapunov stability analysis. The physical relationships for the conservation of mass with an equation of motion and an equation of state of the mathematical models which describes the fluid flow in well – production model were combined, which leads to the diffusivity equation known as heat equation. The horizontal well model that describes the interaction between the well and the reservoir is cast into a boundary control problem of the porous medium equation with mixed boundary conditions. Finally, we arrived at a boundary control problem of the Boussinesq equation. Hence, a well rate controller u(t) for the boundary control problem is designed such that it exponentially stabilizes the system to an equilibrium state as t becomes large.