Boundary control of two-phase fluid flow using the Laplace-space domain

In this paper, we introduce the Laplace-space approach to a linearized two-phase flow model governed by a set of hyperbolic-like partial differential equations (PDEs). Compared to the discretization approaches to PDEs, which result in a large number of ordinary differential equations (ODEs), the Laplace-space approach gives a set of functional relationships that describe the two-phase flow behavior with respect to space. The key element in our work is the Laplace space representation of the two-phase flow model that connects the two-phase flow regimes and causal input/output structures. The causal input/output structures need to be determined in order to design a boundary controller that can regulate the flow. The main advantage of the Laplace-space approach to the two phase flow and effectiveness of the proposed boundary control design are illustrated on a numerical example of a counter current two-phase flow in a vertical bubble column.