Abstract— As an alternative or addition to complex physical modeling, in this paper transfer function models of the disinfection process in annular photoreactors under different flow conditions are derived. These transfer function models allow an analytical evaluation of the system dynamics and the control strategies to gain further insight while preserving the physical process parameters. For diffusive flow conditions a dead-time/Padé approximation is proposed to find a low-order linear system description. Given the (approximate) transfer functions with their physical process parameters, an analytical feed-forward – feedback law is further worked out. I. INTRODUCTION VER the years chlorination has been the most preferred disinfection process for water treatment. However, several investigations have proved that chlorine residuals are toxic to the aquatic life [1], while at the same time some by-products of chlorination have proved to be mutagenic. Therefore, the use of other disinfection techniques which are friendlier to the environment and do not arise health concerns is increasing. It is known to scientists for nearly a century that ultraviolet (UV) light is an effective germicidal agent at certain wavelengths. However, the production cost of UV light was high. With the development of high intensity, long life lamps, interest in the use of UV as disinfection agent was renewed. Precise modeling of the disinfection process in a UV photoreactor requires complex analysis of the radiation field [2]. This analysis needs to be linked to the modeling of the flow dynamics and the reaction kinetics. The models obtained are composed of very complicated differential equations which require demanding numerical computations (see e.g. [3]). Consequently, modeling of the disinfection process in a photoreactor is a quite complicated task. Moreover, phenomena such as reactivation of disinfected microorganisms make the situation even less straightforward. On the other hand, in practice simple Manuscript received October 13, 2006. This work was supported by the Dutch organization for Scientific Research NWO, the Dutch Ministry of Economic Affairs and the technology foundation STW under the project number WWI.6345. K. J. Keesman and D. Vries are with the Systems and Control Group, Wageningen University, Bornsesteeg 59, 6708 PD Wageningen, The Netherlands (corresponding author: K. J. Keesman, phone +31 317 483780; fax +31 317 484957; e-mail: karel.keesman@wur.nl ). S. van Mourik and H. Zwart are with the Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. models that preferably preserve prior knowledge are needed for fast online calculations. The methods that have been used so far for the design of water disinfection systems are based on either complex physical models or empirical models. In this study our approach is to build relatively simple mathematical models based on the prior knowledge of the system. After setting up basic equations for the irradiation field, the effect of the type of flow is examined. Models are obtained for ideal plug flow as well as for diffusive flow. The ultimate goal of this paper is to show how to develop these relatively simple mathematical models that are suitable for dynamical analysis and control. Consequently, transfer functions are derived that connect the output of the system (bacteria load after disinfection) with the disturbance of system (initial load of bacteria) and the control inputs (light intensity and/or flow velocity). In section 2 the UV disinfection process is described in some more detail. The modeling procedure of the disinfection process is presented in section 3. Section 4 presents two model approximation techniques. The resulting approximate models are used in section 5 to further derive an analytical feed-forward – feedback control law that explicitly depends on the physical process parameters. II. UV DISINFECTION A UV disinfection system transfers electromagnetic energy from a UV lamp to the genetic material of microorganisms. The absorption of light causes photochemical reactions that alters molecular components essential to cell function. There is scientific evidence to conclude that if sufficient dosages of UV energy reach the organisms, UV can disinfect water to whatever degree is required. In [4], the experimental data for UV inactivation of micro organisms have been extensively reviewed and furthermore they tabled the UV dose required to achieve the inactivation of bacteria, viruses and protozoa. Predominantly, there are two types of UV sources that are used for water treatment, low pressure (LP) and medium pressure (MP) mercury lamps. The UV dose is the product of UV intensity (mW/cm2) and the average exposure time (s) of the water to be disinfected. In theory using a low intensity lamp for a longer period of time should give the same microbial inactivation as when a high intensity lamp is used for a shorter period. However, in [5] it is shown that preferably high intensity lamps should be used. Modeling and control of water disinfection process in annular photoreactors K. J. Keesman, D. Vries, S. van Mourik and H. Zwart O