The prospect of treating wastewater and at the same time producing microalgae biomass is receiving increasing attention. Mechanistic models for microalgae growth in wastewater are currently being developed for new systems design as well as to improve the understanding of the involved biokinetic processes. However, mathematical models able to describe the complexity of microalgal cultures are still not a common practice. The aim of the present study is to present and calibrate a new mechanistic model built in COMSOL MultiphysicsTM platform for the description of microalgae growth. Carbon-limited algal growth, transfer of gases to the atmosphere; and photorespiration, photosynthesis kinetics and photoinhibition are included. The model considers the growth of microalgae as a function of light intensity and temperature, as well as availability of nitrogen and other nutrients. The model was calibrated using experimental data from a case study based on the cultivation of microalgae species in synthetic culture medium. The model was able to reproduce experimental data. Simulations results show the potential of the model to predict microalgae growth and production, nutrient uptake, and the influence of temperature, light intensity and pH on biokinetic processes of microalgae. New mechanistic model to simulate microalgae growth 7E-mail address: joan.garcia@upc.edu (J. García). 9 Abstract 10The prospect of treating wastewater and at the same time producing microalgae biomass 11 is receiving increasing attention. Mechanistic models for microalgae growth in wastewater are 12 currently being developed for new systems design as well as to improve the understanding of 13 the involved biokinetic processes. However, mathematical models able to describe the 14 complexity of microalgal cultures are still not a common practice. The aim of the present study 15 is to present and calibrate a new mechanistic modelbuilt in COMSOL Multiphysics TM 16 platformfor the description of microalgae growth. Carbon-limited algal growth, transfer of gases 17 to the atmosphere;and photorespiration,photosynthesis kinetics and photoinhibitionare included. 18The model considersthe growth of microalgae as a function of light intensity and temperature, 19 as well as availability of nitrogen and other nutrients. The model was calibrated using 20 experimental data froma case study based on the cultivation of microalgae species in 21 syntheticculture medium.The model was able to reproduce experimental data. Simulations 22 results show the potential of the model to predict microalgae growth and production, nutrient 23 uptake, and the influence of temperature, light intensity and pH on biokinetic processes of 24 microalgae. 25

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Horizontal subsurface Flow Constructed Wetlands (HF CWs) are biofilters planted with aquatic macrophytes within which wastewater is treated mostly through contact with bacterial biofilms. The high concentrations of organic carbon and nutrients being transported leads to high bacterial biomass production, which decreases the flow capacity of the porous material (bioclogging). In severe bioclogging scenarios, overland flow may take place, reducing overall treatment performance. In this work we developed a mathematical model using COMSOL Multiphysics™ and MATLAB(®) to simulate bioclogging effects in HF CWs. Variably saturated subsurface flow and overland flow were described using the Richards equation. To simplify the inherent complexity of the processes involved in bioclogging development, only one bacterial group was considered, and its growth was described using a Monod equation. Bioclogging effects on the hydrodynamics were taken into account by using a conceptual model that affects the value of Mualem's unsaturated relative permeability. Simulation results with and without bioclogging were compared to showcase the impact of this process on the overall functioning of CWs. The two scenarios rendered visually different bacteria distributions, flow and transport patterns, showing the necessity of including bioclogging effects on CWs models. This work represents one of the few studies available on bioclogging in variably saturated conditions, and the presented model allows simulating the interaction between overland and subsurface flow occurring in most HF CWs. Hence, this work gets us a step closer to being able to describe CWs functioning in an integrated way using mathematical models.

In this paper, sensitivity analysis is applied to a mechanistic model developed to simulate microalgae growth. The Morris method of Elementary Effects (EEs) is applied to evaluate the sensitivity of model outputs with respect to a subset of key input parameters. For an easier interpretation, results were plotted as distributions of elementary effects means and standard deviations for each input parameter. The model outputs were very sensitive with respect to the maximum specific growth rate of microalgae (μALG). Results of the sensitivity analysis indicate that the transfer of ammonia (Ka,NH3) and carbon dioxide (Ka,CO2) have a non-linear relation with nitrogen uptake and carbonate concentrations, respectively. This analysis helped identify the parameters with the greatest impact on simulation outputs. The results indicated that maximum specific growth rate of microalgae (μALG) was the most critical parameter to calibrate properly. Tables Table 1. List of model outputs. Model outputs Description X ALGConcentration of microalgae biomass. It increases with growth processes and decreases by endogenous respiration and inactivation. S NH3 +S NH4Concentration of nitrogen present in the water as ammonium and ammonia. Nitrogen as ammonium (S NH4 ) is produced through the processes of endogenous respiration and through inactivation of microalgae. It is consumed through the growth of microalgae. Nitrogen in form of ammonia (S NH3 ) is in chemical equilibrium with ammonium (S NH4 ). Its concentration decreases by volatilization to the atmosphere. S NO3Nitrogen available as nitrate. It is consumed by microalgae (X ALG ). S HCO3 +S CO2Concentration of carbon as carbon dioxide and bicarbonate. Carbon as carbon dioxide (S CO2 ) is consumed by microalgae and is produced through the processes of endogenous respiration and inactivation. Carbon as bicarbonate (S HCO3 ) is in chemical equilibrium with carbon dioxide (S CO2 ) and carbonate (S CO3 ). S CO3Carbon in the form of dissolved carbonate. It is in chemical equilibrium with bicarbonate (S HCO3 ) and carbon dioxide (S CO2 ). Carbonate is not used by microalgae as carbon source.