MODELLING AND CONTROL OF TWO-PHASE SYSTEMS Daniel R. Lewin", Miriam Faigon, Avraham Fuchs and Raphael Semiat Department of Chemical Engineering, Technion I.I.T., Haifa 32000, Israel ABSTRACT This paper outlines a linear model-based control design procedure, suitable for processes involving two- phase phenomena, where the transient response is often subject to nonminimum phase characteristics: inverse response and time delays. We show that in order to capture these features in the process models implicit in the control scheme, it may be necessary to model the transients in each phase separately, thus precluding simple homogeneous approaches. Furthermore, as shown by two examples, combina- tions of nonminimum phase characteristics can be accurately modelled by the Parallel Linear Structure, introduced here, which can be the basis for improved linear control design. KEYWORDS: Process Dynamics, Two-Phase Systems, Inverse Response, Evaporators, Boiling, Feedback Control 1. INTRODUCTION Inverse response phenomena are commonly found in chemical processing equipment. They may occur when a single input perturbation affects the process output in two opposing directions, with one direction being the dominant steady state effect, and the other being the dominant transient effect. Consider the simple example of a liquid flowing in a heated pipe. Since the thermal expansion coeffi- cient is usually positive, a sudden temperature increase at the inlet will soon cause the first part of the pipe contents to heat up and also to expand. Therefore, the residence time of the fluid will progressively decrease, so that the outlet temperature will also decrease before the expected (positive) thermal wave reaches the outlet (Fuchs et al, 1991). Since the mean density of a two-phase mixture is usually a very sensitive function of intensive variables, one would expect that inverse response phenomena should be common in two-phase systems. Selected examples amongst the many reported cases in the literature are: 1) Distillation Column Tray Dynamics: Luyben (1969), analyzed the response of a binary distillation column to a step increase in the internal vapor flow rate. This change affects the transient of the light component concentration on a given column tray through two mechanisms. The first, dominated by the tray hydrodynamic time constant, will cause the concentration to rise because the additional vapor, rising through the tray and rich in the lighter component, will displace fluid held on the tray, previously richer in the heavier component. The long-term effect is controlled by thermodynamics and will therefore reflect the overall tray steady state gain: as the temperature increases, the concentration of the lighter component will decrease. The overall transient therefore exhibits inverse response. 2) Azeotropic Distillation Column Dynamics: Andersen et al (1991) analyzed the dynamics of homogeneous azeotropic distillation, and found that the effect of internal flows in the azeotropic column affect the overall separation in two directions, each dominated by different time constants. Thus, depending on the chosen operating point, both overshoot and inverse response phenomena are possible. 3) Two-phase Reactor Dynamics: Tsai and Tsao (1991) describe the dynamics of a solid-catalyzed, liquid-phase reaction in a CSTR. The existence of inverse response in the bulk fluid concentration transient for such a system is shown to be caused by an appropriate temporal balance between reactant supply rate to the bulk fluid and the mass transfer rate to the solid catalyst. SI49