This article presents a mathematical model to describe High-Rate Algal Ponds (HRAPs). The hydrodynamic behavior of the reactor is described as completely mixed tanks in series with recirculation. The hydrodynamic pattern is combined with a subset of River Water Quality Model 1 (RWQM1), including the main processes in liquid phase. Our aim is to develop models for WSPs and aerated lagoons, too, but we focused on HRAPs first for several reasons: Sediments are usually less abundant in HRAP and can be neglected, Stratification is not observed and state variables are constant in a reactor cross section, Due to the system's geometry, the reactor is quite similar to a plugflow type reactor with recirculation, with a simple advection term. The model is based on mass balances and includes the following processes: *Phytoplankton growth with NO3-, NO2- and death, *Aerobic growth of heterotrophs with NO3-, NH4+ and respiration, *Anoxic growth of heterotrophs with NO3-, NO2- and anoxic respiration, *Growth of nitrifiers (two stages) and respiration. The differences with regard to RWQM1 are that we included a limiting term associated with inorganic carbon on the growth rate of algae and nitrifiers, gas transfers are taken into account by the familiar Adeney equation, and a subroutine calculates light intensity at the water surface. This article presents our first simulations.

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We previously suggested a method to characterize the oxygen balance in High-Rate Algal Ponds (HRAPs). The method was based on a hydrodynamic study of the reactor combined with a tracer gas method to measure the oxygen transfer coefficient. From such a method diurnal variations of photosynthesis and respiration can be quantified and the net oxygen production rate determined. In this paper we propose a similar approach to obtain carbon dioxide balances in HRAPs. Then oxygen and carbon dioxide balances can be compared.