# M-ALBA: A modelling framework to guide the optimization of membrane-assisted algae-bacteria systems

François Crouchett-Catalán, Jineth Arango, Olivier Bernard, Carlos Martínez, Francesca Casagli, David Jeison

► To cite this version:

François Crouchett-Catalán, Jineth Arango, Olivier Bernard, Carlos Martínez, Francesca Casagli, et al. M-ALBA: A modelling framework to guide the optimization of membrane-assisted algae-bacteria systems. Science of the Total Environment, 2025, 971, pp.179061. 10.1016/j.scitotenv.2025.179061. hal-05458229

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# M-ALBA: A modelling framework to guide the optimization of membrane-assisted algae-bacteria systems

François Crouchett-Catalánª, Jineth Arango Oviedoª, Olivier Bernard b, Carlos Martínezª, Francesca Casagli b, David Jeison a*

*Corresponding author:

david.jeison@pucv.cl

**Abstract:**

Biological systems combining microalgae and bacteria have been identified as a system with great potential to provide sustainable sanitation solutions. This consortium has been conceived to be normally implemented in the form of high-rate algal-bacteria

<footnote>ª Escuela de Ingeniería Bioquímica, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2085, Valparaíso, Chile.</footnote>

<footnote>jineth.arango.o@mail.pucv.cl, david.jeison@pucv.cl,</footnote>

<footnote>francois.crouchett.c@mail.pucv.cl, carlos.martinez.v@pucv.cl</footnote>

<footnote>b Centre de recherche INRIA Sophia-Antipolis Méditerranée, France.</footnote>

<footnote>olivier.bernard@inria.fr, francesca.casagli@inria.fr</footnote>
ponds (HRABP). However, these systems face limitations, associated with effluent
clarification and limited loads. Application of membrane filtration to induce biomass
retention and effluent clarification have been identified as way to overcome such
constraints. However, the effects of decoupling solid retention time (SRT) from hydraulic
retention time (HRT) are complex and sometimes difficult to determine or predict. In
this study, a model (M-ALBA) was used to predict the performance of a membrane-
assisted HRABP. M-ALBA represents an extension of the previously validated ALBA
model, by incorporating a compartment providing membrane separation. M-ALBA
considers the action of microalgae, heterotrophic bacteria, and nitrifying bacteria
(ammonium oxidizers and nitrite oxidizers), including 34 state variables, 19 biological
processes and gas-liquid mass transfer of O₂, CO₂, and NH₃. Experimental data from
previous study were used to evaluate the model accuracy. Different scenarios were
simulated and analysed, using mass balances, considering SRT and HRT in the ranges
4.5-22.5 and 0.5-4.5 days, respectively. Results show how decoupling SRT from HRT
improves effluent quality, by increasing nitrogen removal, while avoiding ammonia
volatilization. Additionally, it allows operation at lower HRT values, achieving the best
performance at HRT 1.5 days. The results obtained in this study contributed to a better
understanding of the complex microalgae-bacteria dynamics in membrane assisted
HRABPs.

Keywords:

modelling, wastewater, microalgae, membrane, simulation
# NOMENCLATURE

## Wastewater systems

MBC: microalgae-bacteria consortia.

HRABP: high-rate algal-bacteria ponds.

MBR: membrane bioreactor.

MBR-MBC: MBC in membrane bioreactor (MBR).

HRT: hydraulic retention time.

SRT: solid retention time.

## Modelling

ALBA: Algae-Bacteria model proposed by Casagli et al. (2021b).

M-ALBA: ALBA model for uncoupling hydraulic and solid retention time.

$X_i$: Particulate component $i$.

$S_j$: Soluble component $j$.

ALG: microalgae.

HB: heterotrophic bacteria.

NB: nitrifying bacteria.

AOB: ammonium oxidizing bacteria.

NOB: nitrite-oxidizing bacteria.

## System's flow configuration

$Q_{in}$: influent flow of wastewater.

$Q_w$: wasted biomass flow existing in the system directly from the reactor.

$Q_{out}$: reactor outflow entering the membrane tank.

$Q_{ev}$: evaporation rate.

$Q_p$: permeate flow.

$Q_R$: retentate flow.

$V_r$: reactor of constant volume.

$V_m$: membrane tank volume

$K_L$: Volumetric oxygen mass transfer coefficient

## Model testing

NRR: nitrogen removal rate.

BPR: biomass production rate.

RMSE: root mean square error.

$R^2$: Pearson coefficient of correlation.

## Carbon balance

C-ORG,P: Particulate organic carbon (the sum of carbon in $X_s$ and $X_i$).

C-ORG,S: Soluble organic carbon (the carbon content in $S_s$ and $S_i$).

C-ALG, C-HB and C-NB: Carbon in algae, heterotrophic bacteria, and nitrifying bacteria, respectively.

C-INORG: Soluble inorganic carbon.

C-CO₂r and C-CO₂m: The inorganic carbon in the form of CO₂ gas, in the reactor and the membrane compartments, respectively.

## Nitrogen balance

N-ORG: Nitrogen in organic matter other than biomass (i.e. $X_s$, $S_s$, $X_i$, and $S_i$) and soluble nitrogen ($S_{ND}$).

N-ALG, N-HB and N-NB: Nitrogen in algae, heterotrophic bacteria, and nitrifying bacteria, respectively.

N-TAN: Total ammonia nitrogen, $S_{NH}$.
N-NO₂ and N-NO₃: Nitrous nitrogen and nitric nitrogen, respectively.

N-NH₃r and N-NH₃m: Ammonia gas, in the reactor and the membrane compartments, respectively.

N-N₂: Nitrogen gas.

## Oxygen balance

OUR_ALG, OUR_HB, OUR_NB: oxygen uptake rate of microalgae, heterotrophs and nitrifiers, respectively.

OPR_ALG: oxygen production rate of algae from photooxygenation.

OTRr and OTRm: oxygen transfer rate from gas to liquid, in the reactor and the membrane compartments, respectively.

CTRr and CTRm: CO₂ transfer rate from gas to liquid, in the reactor and the membrane compartments, respectively.

DO_AVE: dissolved oxygen in the liquid phase.
# 1. INTRODUCTION

Emerging biological wastewater treatment systems integrating microalgae and bacteria cultivation offers an eco-friendly alternative to reduce greenhouse gases emissions and energy consumption (Molazadeh et al., 2019; Vuppaladadiyam et al., 2018). Photosynthetic algae fix CO₂ while oxygen is produced, reducing the need for mechanical aeration and therefore the energy demand. Life cycle assessment studies have shown a reduction of 55% in CO₂ emissions, when compared with conventional activated sludge systems (Arashiro et al., 2018; Garfi et al., 2017). Furthermore, the synergistic interactions facilitated by the co-cultivation of algae and bacteria foster nutrient removal efficiency, especially nitrogen and phosphorus, and facilitates organic matter degradation (Amini et al., 2020; Ji et al., 2018; Unnithan et al., 2014; Wang et al., 2015).

Microalgae-bacteria consortia (MBC) are often applied for sanitation in high-rate algal-bacteria ponds (HRABP), whose construction expenses are 70% lower than conventional activated sludge systems (Nguyen et al., 2021; Young et al., 2017). Thus, algae-bacteria systems are progressively seen as an affordable and sustainable solution with the potential to target the future challenges of sanitation (Qiao et al., 2020). MBC for wastewater treatment is often operated in continuous mode, to achieve better treatment capabilities and nutrient removal efficiencies (Amini et al., 2020; Castellanos, 2013; Muñoz and Guieysse, 2006).

Microalgae-based systems still present drawbacks that need to be addressed, such as low volumetric capacity and low biomass settleability, which can affect effluent clarification (Olguín, 2012). Both problems can be addressed using membrane separation systems. Membrane systems have been reported as efficient tools for microalgae separation (Pavez et al., 2015; Saidane et al., 2021), providing an effluent free of suspended solids. Moreover, biomass retention can be used to increase conversion rate, improving volumetric capacity. Application of membrane bioreactor (MBR) concept to MBC systems (MBR-MBC) have been only recently explored (Robles et al., 2020; Sun et al., 2018; Casagli et al. 2023). MBR technology promotes biomass retention by decoupling hydraulic from solid retention time (HRT and SRT) (Solmaz and Mustafa, 2019). As a result, SRT becomes a key parameter, shaping the dynamics of
microbial species (Barbera et al., 2020; Arashiro et al., 2017; Arango et al., 2022; Rada-Ariza et al., 2019).

Determination of an optimal value of SRT for wastewater treatment by MBR-MBC systems is not straightforward (Arango et al., 2022). Many factors can affect wastewater treatment such as wastewater characteristics and environmental conditions, including light intensity and temperature. For instance, balancing biomass concentration to avoid self-shading while maximizing growth rate is complex (Foladori et al., 2020; Luo et al., 2017; Sepehri et al., 2020; Yang et al., 2018).

Mathematical modelling offers a systematic approach to understand and optimize operations and processes. As for other processes in wastewater treatment (Batstone, et al. 2002; Henze et al. 2006), numerical tools can guide and optimize the design and operation of Algae-Bacteria systems. While several models exist for microalgal systems (Shoener et al., 2019; Arango et al., 2022), only a few works have addressed microalgae-bacteria systems (Nordio et al., 2024; Rossi et al., 2020; Solimeno et al., 2019). Furthermore, the modelling of membrane assisted MBC systems remains almost unexplored (Barbera et al., 2020). Recently, Casagli et al. (2021) developed the ALBA model (ALgae-BActeria), designed to describe an MBC within an HRAP system. The ALBA model was validated using over 630 days of pilot-scale data from two HRABP pilot plants operated under different feeding and climatic conditions. It accurately predicted daily and seasonal behaviors, including winter responses, which previous models failed to describe effectively. Casagli et al. (2023) later introduced a retention factor in the hydraulic balance for all particulate variables, to study the role of SRT and HRT in the optimization of microalgae productivity. Despite evident advances in the field, there are still great challenges when studying modelling of MBR-MBC systems. Some of them related with the effect of SRT and HRT on carbon and ammonia emissions, the impact of an aerated membrane tank on gases absorption or desorption, and the capacity of membrane retention to increase system capacity.

In this study, a model describing MBR-MBC systems was constructed, based on ALBA model. This model, named M-ALBA, involves the combination of a raceway reactor with an aerated membrane tank. Contribution of both compartments were considered for overall gases absorption and desorption. The M-ALBA model was then used to simulate
various scenarios involving different *HRT* and *SRT* values, in order to explore system dynamics, such as nitrogen removal, ammonia volatilization and biomass productivity. The generated information is expected to offer deeper insights into system performance and optimization.

## 2. MATERIALS AND METHODS

### 2.1. ALBA overview

The ALBA model was developed by Casagli et al., (2021b) to evaluate wastewater treatment performance in a HRABP. The model includes 17 state variables, representing both particulate ($X_i$) and soluble ($S_j$) components (summarized in Table 1), 19 biological processes and 3 gas-liquid mass transfer processes. The biological consortium involves microalgae (ALG), heterotrophic bacteria (HB), and nitrifying bacteria (NB). NB include ammonium oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB).

In the ALBA model, microalgae grow using ammonium ($NH_4^+$) or nitrate ($NO_3^-$), phosphate, inorganic carbon in the form of carbon dioxide ($CO_2$) and bicarbonate ($HCO_3^-$), and light as an energy source. During growth, microalgae produce oxygen ($O_2$). HB grow on organic compounds, aerobically and consuming $NH_4^+$ over $NO_3^-$.

However, when $O_2$ is unavailable, shift to anoxic growth with both nitrite ($NO_2^-$) and $NO_3^-$ as electron acceptors. HB are also responsible for the hydrolysis of slowly biodegradable organic matter and urea (ammonification). As for nitrifiers, AOB convert ammonia ($NH_3$) into nitrite, while NOB complete nitrification process by oxidizing nitrite into nitrate. Both grow aerobically, using inorganic carbon as a carbon source. For all microorganisms, growth rate is determined by the limiting factor among multiple substrates (carbon, nitrogen, oxygen and phosphorus) following Liebig's law of the minimum (de Baar, 1994).

The model includes respiration process for all types of microorganisms, resulting in biomass loss, subsequent oxygen consumption, and $CO_2$ release. Furthermore, decay processes are considered for all microorganisms, involving no oxygen consumption and resulting in the release of nutrients and organic matter.
Biological growth and respiration rates are temperature-dependent, as described by the Cardinal Temperature Model with Inflection (CTMI) proposed by Rosso et al. (1993), while decay rates follow an Arrhenius formula. Additionally, pH dependence is incorporated using the Cardinal pH Model (CPM) proposed by Rosso et al. (1995) and includes a charge balance for all cationic and anionic chemical species. For microalgae, growth also depends on light, which is modelled using a Haldane-type expression. This function is integrated across the reactor's liquid depth, with light penetration calculated based on Lambert-Beer's law, accounting for both depth and algal biomass concentration. Finally,

In terms of physical processes, the model incorporates the desorption/absorption of CO₂, NH₃, and O₂ between atmosphere and liquid phase. Saturation values for these processes vary with temperature according to Henry's law.

## 2.2. M-ALBA model

The M-ALBA model is proposed as an extension of ALBA model to include the uncoupling of SRT from HRT. M-ALBA considers a two-compartment system: a HRABP and a membrane tank, with a flow between the two systems (Figure 1). M-ALBA involves 17 state variables for each compartment, 34 in total (see Table 1). The reactor compartment is characterized by 19 biological processes and the gas/liquid transfers of O₂, CO₂, and NH₃, as is the case of ALBA model. Biological activity within the membrane compartment is neglected, only occurring gas/liquid mass transfer of O₂, CO₂, and NH₃. This hypothesis is justified by the considerably lower HRT of the membrane compartment in comparison to that of the reactor.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Schematic diagram of the studied MBR-MBC. The volume of the reactor and the membrane compartment are denoted as $V_r$ and $V_m$, respectively. $Q_{in}$, $Q_{ev}$, $Q_w$, $Q_{out}$, $Q_p$ and $Q_R$ represent the flows associated with influent, evaporation, purge, effluent, permeate and recirculation, respectively.</figcaption></figure>
<table><caption>**Table 1.** State variables of the M-ALBA model</caption><thead><tr><th colspan="2"></th><th colspan="3">State variables</th></tr><tr><th colspan="2"></th><th>Symbol</th><th>Description</th><th>Unit</th></tr></thead><tbody><tr><th rowspan="10">Substrate and products</th><th rowspan="5">Biomass</th><th rowspan="2">X<sub>ALG,r</sub></th><td>X<sub>ALG,m</sub></td><td>Phototrophic algae</td><td>g COD m<sup>-3</sup></td></tr><tr><td>X<sub>AOB,r</sub></td><td>X<sub>AOB,m</sub></td><td>Ammonium Oxidizing Bacteria (AOB)</td><td>g COD m<sup>-3</sup></td></tr><tr><th rowspan="2">X<sub>NOB,r</sub></th><td>X<sub>NOB,m</sub></td><td>Nitrite Oxidizing Bacteria (AOB)</td><td>g COD m<sup>-3</sup></td></tr><tr><td>X<sub>H,r</sub></td><td>X<sub>H,m</sub></td><td>Heterotrophic Bacteria (HB)</td><td>g COD m<sup>-3</sup></td></tr><tr><th rowspan="2">X<sub>S,r</sub></th><td>X<sub>S,m</sub></td><td>Slowly biodegradable organic matter</td><td>g COD m<sup>-3</sup></td></tr><tr><td>X<sub>I,r</sub></td><td>X<sub>I,m</sub></td><td>Inert particulate organic matter</td><td>g COD m<sup>-3</sup></td></tr><tr><th rowspan="2">S<sub>S,r</sub></th><td>S<sub>S,m</sub></td><td>Readily biodegradable organic matter</td><td>g COD m<sup>-3</sup></td></tr><tr><td>S<sub>I,r</sub></td><td>S<sub>I,m</sub></td><td>Inert soluble organic matter</td><td>g COD m<sup>-3</sup></td></tr><tr><th rowspan="6">Soluble (S)</th><th rowspan="2">S<sub>IC,r</sub></th><td>S<sub>IC,m</sub></td><td>Total inorganic carbon</td><td>g C m<sup>-3</sup></td></tr><tr><td>S<sub>ND,r</sub></td><td>Organic nitrogen</td><td>g N m<sup>-3</sup></td></tr><tr><th rowspan="2">S<sub>NH,r</sub></td><td>S<sub>NH,m</sub></td><td>Total Ammoniacal Nitrogen (TAN)</td><td>g N m<sup>-3</sup></td></tr><tr><td>S<sub>NO2,r</sub></td><td>S<sub>NO2,m</sub></td><td>Nitrous nitrogen</td><td>g N m<sup>-3</sup></td></tr><tr><th rowspan="2">S<sub>NO3,r</sub></th><td>S<sub>NO3,m</sub></td><td>Nitric nitrogen</td><td>g N m<sup>-3</sup></td></tr><tr><td>S<sub>N2,r</sub></td><td>S<sub>N2,m</sub></td><td>Nitrogen gas</td><td>g N m<sup>-3</sup></td></tr><tr><th rowspan="2">S<sub>PO4,r</sub></th><td>S<sub>PO4,m</sub></td><td>Total inorganic phosphorus</td><td>g P m<sup>-3</sup></td></tr><tr><td>S<sub>O2,r</sub></td><td>S<sub>O2,m</sub></td><td>Dissolved Oxygen</td><td>g O<sub>2</sub> m<sup>-3</sup></td></tr><tr><th rowspan="2"></th><th rowspan="2"></th><th rowspan="2"></th><td>Water</td><td>g H m<sup>-3</sup></td></tr><tr><td></td><td></td></tr></tbody></table>
The influent wastewater flow ($Q_{in}$) enters the reactor of constant volume $V_r$ where it is treated. A biomass outflow ($Q_w$) directly leaves the reactor, while another outflow ($Q_{out}$) enters the membrane compartment of volume $V_m$. The water mass flow resulting from water evaporation is considered ($Q_{ev}$). Inside the membrane tank, the membrane separation provides complete retention of suspended solids. Then, a permeate flow leaves the membrane compartment ($Q_p$) and the retentate flow ($Q_R$) is recycled to the reactor. All flow rates can be calculated as a function of applied HRT and SRT, according to Equations 1 to 5.

$$Q_{in} = \frac{V_r}{HRT} \qquad \text{Eq. 1}$$

$$Q_w = \frac{V_r}{SRT} \qquad \text{Eq. 2}$$

$$Q_p = Q_{in} - Q_{ev} - Q_w \qquad \text{Eq. 3}$$

$$Q_R = RQ_{in} \qquad \text{Eq. 4}$$

$$Q_{out} = Q_p + Q_R \qquad \text{Eq. 5}$$

$Q_R$ is assumed to be proportional to $Q_{in}$, where the proportionality constant $R$ is chosen to ensure that particulate concentrations inside the membrane compartment do not exceed 10% of that inside the MBR, to prevent excessive membrane fouling. Equations (3) and (5) result from constant compartments volumes.

The evolution of the state variables in the reactor of the particulate ($X_{j,r}$) and soluble ($S_{j,r}$) species are described by the following expressions:

$$\frac{dX_{j,r}}{dt} = \frac{Q_{in}}{V_r} X_{j,in} + \frac{Q_R}{V_r} X_{j,m} - \frac{Q_{out}}{V_r} X_{j,r} - \frac{Q_w}{V_r} X_{j,r} \pm \sum_i k_{i,j} \rho_i \qquad \text{Eq. 6}$$

$$\frac{dS_{j,r}}{dt} = \frac{Q_{in}}{V_r} S_{j,in} + \frac{Q_R}{V_r} S_{j,m} - \frac{Q_{out}}{V_r} S_{j,r} - \frac{Q_w}{V_r} S_{j,r} \pm \sum_i k_{i,j} \rho_i \pm Q_j \qquad \text{Eq. 7}$$

In the same way, membrane compartment dynamics for particulate ($X_{j,m}$) and soluble ($S_{j,m}$) components are:

$$\frac{dX_{j,m}}{dt} = \frac{Q_{out}}{V_m} X_{j,r} - \frac{Q_R}{V_m} X_{j,m} \qquad \text{Eq. 8}$$

$$\frac{dS_{j,m}}{dt} = \frac{Q_{out}}{V_m} S_{j,r} - \frac{(Q_R+Q_p)}{V_m} S_{j,m} \pm Q_j \qquad \text{Eq. 9}$$
where the term $p_i$ represents the biological reaction rate [g m⁻³ d⁻¹] and $k_{i,j}$ is the stoichiometric coefficients associated to the state variable j. On the other hand, $Q_j$ denotes the gas/liquid transfer rate of O₂, CO₂, and NH₃.

## 2.3. Simulating large-scale MBR-MBC systems

The M-ALBA model was used to predict the performance of full-scale MBR-MBC and to provide insights of the large-scale mechanisms responsible for organic matter and nitrogen removals. We considered a 5,000 m² HRABP, with depth 0.3 m meaning a volume of 1,500 m³. We assumed that an appropriate mixing system such as paddle wheels ensures perfect reactor homogeneity. Immediately after the reactor, a membrane filtration compartment is positioned. Based on the recommendations for the ZeeWeed hollow fibre membranes, the membrane compartment volume was adapted for each *HRT* as a function of the required membrane area, assuming a constant permeate flux of 20 [L m⁻² h⁻¹]. This adjustment resulted in membrane volumes ranging from 20 to 68 [m³]. For clarity, it is important to note that the system *HRT* is defined in terms of reactor volume (see Equation 1), excluding the membrane compartment volume.

Different operational conditions were simulated, considering various *SRT* (4.5, 9, 13.5, 18 and 22.5 days) and *HRT* values (0.5, 1.5, 2.5, 3.5, and 4.5 days). Operations involving equal *SRT* and *HRT* were simulated using the standard ALBA model, i.e., without a membrane compartment. Two different climatological conditions were considered, representing typical conditions for winter and summer in the south of France (Narbonne). Each climatological condition was defined by a periodic daily pattern of light, temperature, and evaporation rate (see Figure 2). The corresponding average, maximum and minimum value of each parameter are detailed in Table 2. The
wastewater characteristics of the influent were the same as in Casagli et al. (2021b) (see Table 2).

Simulations were conducted using the ode15s solver in MATLAB 2020b, which is well-suited for addressing the stiffness arising from the coupled biological and physical processes in the M-ALBA model (Shampine and Reichelt 1997).

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Typical average daily patterns of (A) Incident photosynthetically active radiation (PAR), (B) Temperature, and (C) Evaporation in summer (blue line) and winter (red line) (Casagli et al., 2021b).</figcaption></figure>
<table><caption>**Table 2.** Influent values of the state variables included in the M-ALBA model and environmental conditions (Casagli et al., 2021b).</caption><thead><tr><th colspan="8">Influent characteristics</th></tr><tr><th></th><th>X<sub>ALG</sub>; X<sub>H</sub>; X<sub>AOB</sub>; X<sub>NOB</sub></th><th>X<sub>S</sub></th><th>X<sub>I</sub></th><th>S<sub>S</sub></th><th>S<sub>I</sub></th><th>S<sub>IC</sub></th><th>S<sub>NH</sub></th></tr></thead><tbody><tr><td>Unit</td><td>g COD m<sup>-3</sup></td><td>g COD m<sup>-3</sup></td><td>g COD m<sup>-3</sup></td><td>g COD m<sup>-3</sup></td><td>g COD m<sup>-3</sup></td><td>g C m<sup>-3</sup></td><td>g N m<sup>-3</sup></td></tr><tr><td>Value</td><td>0</td><td>133</td><td>3</td><td>224</td><td>18</td><td>65</td><td>8</td></tr><tr><td></td><td>S<sub>NO2</sub></td><td>S<sub>NO3</sub></td><td>S<sub>N2</sub></td><td>S<sub>ND</sub></td><td>S<sub>PO4</sub></td><td>S<sub>O2</sub></td><td>S<sub>H2O</sub></td></tr><tr><td>Unit</td><td>g N m<sup>-3</sup></td><td>g N m<sup>-3</sup></td><td>g N m<sup>-3</sup></td><td>g N m<sup>-3</sup></td><td>g P m<sup>-3</sup></td><td>g O<sub>2</sub> m<sup>-3</sup></td><td>g H m<sup>-3</sup></td></tr><tr><td>Value</td><td>0.03</td><td>0.05</td><td>0</td><td>55</td><td>13</td><td>8</td><td>10000</td></tr><tr><th colspan="8">Environmental conditions (average; maximum)</th></tr><tr><td></td><td></td><td>Summer</td><td></td><td>Winter</td><td></td><td></td><td></td></tr><tr><td>Incident irradiance [µE m<sup>-2</sup> s<sup>-1</sup>]</td><td></td><td>584; 1697</td><td></td><td>196; 807</td><td></td><td></td><td></td></tr><tr><td>Temperature [°C]</td><td></td><td>26.8; 30.8</td><td></td><td>8.1; 10.0</td><td></td><td></td><td></td></tr><tr><td>Evaporation rate [m<sup>3</sup> m<sup>-2</sup> h<sup>-1</sup>]</td><td></td><td>2.40; 4.77</td><td></td><td>0.69; 1.65</td><td></td><td></td><td></td></tr></tbody></table>

Global volumetric mass transfer coefficient $K_{La}$ was set at 20 [d⁻¹] for the reactor base on El Ouarghi et al. (2003). A conservative value of 200 [d⁻¹] inside the membrane tank was considered (Germain et al., 2007; Henkel et al., 2009), resulting from the intense gas sparging normally used to prevent membrane fouling in hollow-fibre membranes.

Finally, for each operational and climatological condition, the M-ALBA model was run until a periodic regime on the state variables was reached. Average estimations of biomass productivity, oxygen and CO₂ fluxes were then assessed, together with carbon and nitrogen balances.

## 2.4. M-ALBA model validation

To assess the model accuracy, data collected by Robles et al. (2020) were used. These data comprise nitrogen removal rate (NRR), biomass production rate (BPR), irradiance, and temperature. The data were obtained through an experimental campaign performed in Narbonne, France, on the same outdoor HRABP of 16.8 m³ (56 m²) on
which the ALBA model was calibrated and validated. The reactor was coupled to a
hypothetical external microfiltration membrane and fed with synthetic municipal
wastewater, similar to that used in the study by Casagli et al. 2021b. NRR and BPR were
estimated at three different operational conditions with the same SRT = 6 [d], but
different HRTs: (i) HRT = 2.5 [d], autumn; (ii) HRT = 4 [d], autumn; and (iii) HRT = 2.5 [d],
during summer.

Following the work of Casagli et al. (2023), the NRR and BPR were simulated using M-ALBA and then compared to the actual values using the root mean square error (RMSE) and the Pearson correlation coefficient (R²). It is important to note that when HRT equals SRT, the M-ALBA model corresponds to ALBA model, which has been validated in previous works (Casagli et al., 2021; Casagli et al., 2023). This alignment reinforces confidence in the parameters used in the simulations.

**3. RESULTS AND DISCUSSIONS**

**3.1. M-ALBA accuracy on nitrogen removal and biomass productivity**

Figures 3.A and 3.B present NRR and BPR, with a comparison between the experimental data by Robles et al. (2020) and the M-ALBA model predictions. Overall, the M-ALBA showed a good performance for predicting the BPR and NRR. Average simulated values of BPR ranged from 16.8 to 22.8 [g VSS m⁻² d⁻¹], showing a small model underestimation (below 20%). Analysis revealed an RMSE of 3.7 [g VSS m⁻² d⁻¹] and R² coefficient equal to 0.90. On the other hand, the average NRR ranging from 2.0 to 3.4 [g N⁻¹ m⁻² d⁻¹] with no clear trend. RMSE for nitrogen removal was 0.3 [g N⁻¹ m⁻² d⁻¹] whereas R² was 0.71. Predicting more accurately the system behaviour is challenging due to the inherent operative difficulties expected for an open pilot plant installation. Also, the initial conditions, in terms of the various populations initially present were not measured. Despite all these approximations, the model predictions well predict the experimental records.
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Comparison between experimental data (Robles et al., 2020b) and simulations with the M-ALBA model. A) Biomass productivity in [g VSS m⁻² d⁻¹], B) Nitrogen removal rate [g N m⁻² d⁻¹].</figcaption></figure>
## 3.2. Behaviour of a large-scale MBR-MBC system

### 3.2.1. Biomass composition

The simulated biomass compositions are presented in Figure 4, together with the average biomass productivities (Px). We observe that the concentration of algae was mainly affected by SRT, while the concentration of HB was mainly affected by the HRT. Uncoupling SRT from HRT seems an efficient strategy to prevent the washout of the nitrifying biomass in the MBC for HRT larger than 0.5 [d]. Figure 4 also shows that increasing SRT from 4.5 to 22.5 [d] almost doubled the total biomass concentration in all scenarios, due to the enhancement of the biomass retention. On the other hand, a reduction of HRT from 4.5 to 1.5 [d] was triggering a total biomass concentration raise from 36 to 62 % for winter scenarios, and from 9 to 17 %, for summer scenarios. This is the direct consequence of the higher nutrient loading rate. A further reduction of HRT from 1.5 down to 0.5 [d] has even a more marked effect, with a 1.6 and 2.2-fold increase, for summer and winter respectively.

Figure 4 shows that in most scenarios, especially during summer, microalgae are expected to dominate the microbial populations, followed by heterotrophs. Only during winter and at specific conditions, HB became dominant. For HRT of 1.5 [d] and SRT larger than 4.5 [d], the concentrations of HB and ALG were very similar, whatever the SRTs. In summer, HB concentrations were approximately 42 % to 65 % lower than for winter, whereas microalgae concentrations were around 1.5 to 2 times higher. Seasonal differences in predicted HB concentrations are mainly attributed to temperature, since the model predicts that the impact of this parameter on decay rates is comparatively higher than its influence on growth rates. In addition, model predicts higher temperatures scenarios (summer) affect negatively the ratio between aerobic and anoxic growth rates, because of higher microbial activity. Therefore, the oxygen consumption was higher during night. Finally, simulations analysis revealed that the limiting factor for microalgae growth was irradiance, and not nutrients as for heterotrophic organisms.

Figure 4 also predicts that an increase in SRT results in a rise of biomass concentration but a decrease in biomass productivity. In fact, uncoupling SRT from HRT promotes
higher biomass concentrations in the system, resulting in higher respiration rates. This
shifts the fate of incoming carbon from contributing to biomass production towards
generating biogenic emissions of CO2, as addressed in the following section. For
example, during the summer and at HRT = 1.5 [d], productivity decreased from 26.4 to
8.0 [g TSS m-2 d-1], when increasing SRT from 1.5 [d] to 22.5 [d]. On the other hand,
decreasing HRT resulted in higher overall biomass productivity at any tested SRT (except
at 0.5 [d]), mainly because of the growth of heterotrophs.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Average concentration and productivity of biomass during summer (A) and winter (B) at different conditions of *HRT* and *SRT*. *X*<sub>H</sub> is the concentration of the heterotrophic bacteria, *X*<sub>ALG</sub> is the microalgae concentration, and *X*<sub>NB</sub> is the concentration of nitrifying bacteria. In the secondary axis of the graph, the average biomass productivity *Px* is shown with black dots.</figcaption></figure>
### 3.2.2. Carbon mass balances

Carbon mass balances were evaluated for each scenario, and the results are presented in Figure 5, identifying the distribution (in %) of each carbon flow. To simplify the representation of carbon flows, some model components were grouped as follows:

* C-ORG,P: Particulate organic carbon (the sum of carbon in $X_S$ and $X_I$).

* C-ORG,S: Soluble organic carbon (the carbon content in $S_S$ and $S_I$).

* C-ALG: Carbon in algae; C-NB: Carbon in nitrifying bacteria; and C-HB: Carbon in heterotrophic bacteria.

* C-INORG: Soluble inorganic carbon.

* C-CO₂r and C-CO₂m: The inorganic carbon stripped from the system in the form of CO₂ gas, from the reactor and the membrane compartment, respectively.

Figure 5 shows that biomass-associated carbon flows (C-ALG, C-NB and C-HB) presented the most important variations among the evaluated scenarios. These relative contributions were reduced when increasing the SRT, following the trends of biomass productivity as shown in Figure 4.

At HRT values between 1.5 and 4.5 [d], and $SRT > HRT$, the sum of organic particulate (C-ORG,P) and organic soluble carbon (C-ORG,S) stayed in the range 22-18 %. In those scenarios, heterotrophic bacteria consumed almost entirely the biodegradable organic matter ($S_S \sim 0$ [g m⁻³]). Hence C-ORG,S was mainly associated to inert soluble carbon ($S_I$). In contrast, in scenarios where HRT was set at 0.5 [d] the consumption of biodegradable organic matter was incomplete, so the C-ORG,S were much higher. Regarding C-ORG,P, the values did not undergo significant variations with respect to SRT, even though the concentration of inert organic particulates ($X_I$) increased significantly, because the wasted solids flow ($Q_w$) compensated the variation. For instance, for the summer scenario, the concentration of $X_I$ for SRT = 22.5 [d] at HRT = 1.5 [d] was 6-fold the value at SRT = 4.5 [d] (514.5 and 81.5 [g m⁻³], respectively), but the mass carbon flux of the former was only 1.3 times of the latter (12.4 and 9.8 [kg C d⁻¹], respectively).
Figure 5 also shows how the contribution of C-CO₂r and C-CO₂m to overall carbon balance increases as SRT increases, for the HRT scenarios between 1.5 and 4.5 [d]. This is the result of the reduction of the systems capability to assimilate inorganic carbon, associated with a lower biomass productivity. For example, at HRT = 1.5 [d] during summer, increasing the SRT from 4.5 to 22.5 [d] raised the sum of C-CO₂r and C-CO₂m from 32.0 to 42.0 %. It is important to emphasize that Figure 5 represents contributions rather than actual carbon flows. For example, variations in hydraulic retention time (HRT) alter the influent flow rate, leading to significant changes in the absolute values of both influent and effluent carbon flows. The proportion of CO₂ emitted from the membrane compartment, C-CO₂m, increased when HRT decreased. Indeed, a higher inflow requires a larger membrane area, associated with a larger membrane compartment, and as a result a larger CO₂ stripping. Nevertheless, the contribution of the membrane tank to the overall CO₂ stripping stays relatively low for the tested working conditions. More precisely, the relation between the CO₂ transfer rates (absorption or desorption) in the reactor (CTRr) and the membrane tank (CTRm) depends on the KLa values, the compartment volumes (Vr and Vm) the CO₂ concentrations (SCO₂,R and SCO₂,m) and the CO₂ partial pressures in both compartments (i.e. S*CO₂,R and S*CO₂,m):

$$ \frac{CTRr}{CTRm} = \frac{KLa \cdot a_r (S_{CO2,R}^* - S_{CO2,R}) V_r}{KLa \cdot a_m (S_{CO2,m}^* - S_{CO2,m}) V_m} \qquad \text{Eq. 10} $$

If we assume similar concentrations in the reactor and in the membrane modules, then the contribution of the membrane tank to CO₂ stripping is determined by the ratio of KLa and volumes of each compartment. If the volume ratio largely exceeds the ratio of KLa, then the membrane tank should not contribute largely to the desorption of CO₂. This is true for the system in most of the cases examined. For instance, when HRT = 2.5, 3.5 or 4.5 [d], only about 12 % of CO₂ desorption would be attributed to membrane tank. This conclusion is also applicable to the mass transfer of other gases such as oxygen, as it will be discussed below.

Direct CO₂ emissions from wastewater treatment plants are conventionally excluded from the greenhouse gas emission inventory, as proposed by the International Panel on Climate Change (Bartram et al., 2019). However, some authors have highlighted the
importance to consider such emissions, since some of them are coming from the
decomposition of organic matter present in carbon-based fossil pollutants, like
detergents, cosmetics, and pharmaceuticals (Bao et al., 2015). Monteith et al. (2005)
estimated that the on-site direct CO₂ emissions associated with removal of organic
matter for Canadian conventional wastewater treatment plants was around 1.4 g CO₂
per g COD removed which is superior to the estimated emissions of membrane assisted
MBC that was lower than 1.27 g CO₂ g COD⁻¹, depending on the applied condition.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Carbon flux percentages of the influent and effluent under different scenarios of SRT (1.5, 4.5, 9,13.5, 18, 22.5 [d]) and HRT (0.5, 1.5, 4.5 [d]), for summer (A) and winter (B) conditions. C-ORG,P corresponds to the carbon presented in $X_s$, $X_i$; C-ORG,S corresponds to the soluble carbon fraction in $S_s$ and $S_i$; C-INORG,S is the soluble inorganic carbon modelled as $S_{iC}$; C-ALG, C-NB, and C-HB correspond to the fraction of carbon into the algal, NB (AOB and NOB) and HB biomass, respectively. C-CO2r and C-CO2m are the inorganic carbon fraction in the form of CO2 gas, in the reactor and the membrane compartments, respectively.</figcaption></figure>
### 3.2.3. Nitrogen mass balances

The distribution of the nitrogen fluxes as predicted by M-ALBA is shown in Figure 6. As for carbon balance, the nitrogen fluxes are grouped in the following forms:

* N-ORG: Nitrogen in organic matter other than biomass (i.e. $X_s$, $S_s$, $X_i$, and $S_i$) and soluble nitrogen ($S_{ND}$).

* N-ALG: Nitrogen in algae; N-HB: Nitrogen in heterotrophic bacteria; and N-NB: Nitrogen in nitrifying bacteria.

* N-TAN: Total ammoniacal nitrogen, $S_{NH}$.

* N-$NO_2$ and N-$NO_3$: Nitrous nitrogen and nitric nitrogen, respectively.

* N-$NH_3$r and N-$NH_3$m: Ammonia gas, in the reactor and the membrane compartments, respectively.

* N-$N_2$: Nitrogen gas.

Contribution of nitrogen fluxes associated with biomass exhibit similar trends as those for carbon for the SRT and HRT range explored: at higher SRTs the nitrogen fluxes associated to microorganisms are lower. Notably, the maximum contribution of algal biomass to nitrogen outflow was less than 20 %, at HRT 4.5 [d] for the summer scenario.

During summer, the consumption of organic nitrogen N-ORG (i.e. urea hydrolysis or ammonification and the conversion of slow-biodegradable COD into easily biodegradable) are strongly enhanced at higher temperatures. This appears clearly in Figure 6, when comparing summer and winter scenarios. For instance, at HRT = 4.5 [d] and SRT = 13.5 [d], the predicted ammonification rates were approximately 1.5 times higher in summer than in winter, despite a population of heterotrophs divided by two in summer. Higher ammonification rates lead to an increase in ammoniacal nitrogen (N-TAN) available for bacteria and algae.

As observed in Figure 6, the ammonia stripping, N-$NH_3$r and N-$NH_3$m, occurs mainly for summer scenarios, because of the higher temperatures, and only when HRT = 0.5 [d] or SRT equal to HRT. Those scenarios are characterized by very low concentrations of NB (see Figure 4) as to guarantee the full oxidation of ammonia into nitrite and nitrate. pH
was not relevant in ammonia stripping since the values barely exceeded 9. For instance, when SRT ≥ 4.5, HRT = 0.5 [d], in summer, about 35% of the incoming nitrogen (24 % as N-NH₃r and 11 % as N-NH₃m) was released into the atmosphere as ammonia and around 50 % as N-TAN. In contrast, in all the other scenarios when HRT > 0.5 [d] and SRT > HRT, NB stayed in the system and N-TAN constituted less than 10 % (below 1 % in most cases) of the produced nitrogen, avoiding the ammonia stripping. This is a positive outcome, since atmospheric NH₃ is very damageable for the environment, playing a significant role in acid rains, nucleating fine particulates, and eutrophicating sensitive ecosystems (Behera et al., 2013).

M-ALBA predicts active denitrification at HRT = 1.5 [d], with a further enhancement when increasing SRT. According to Figure 6, at low HRT (0.5 [d]), the washout of nitrifiers resulted in the absence of nitrate or nitrite, while at higher HRT (4.5 [d]), complete nitrification occurs, with large concentrations of N-NO₃ and the absence of N-NO₂. At an HRT of 1.5 [d], the predicted presence of nitrite revealed partial nitrification, resulting from oxygen limitation, as discussed in the next section. However, a great part of nitrogen was converted into nitrogen gas N-N₂, especially when increasing SRTs, given the limiting dissolved oxygen concentration in these scenarios. N-N₂ ranged from 39 to 74 % of the total outflow of nitrogen for summer scenarios and from 18 to 60 % for winter.

Nitrate must therefore be present in the effluent, and additional stages or processes for its removal may be needed. Notably, several studies reported the addition of an external carbon source during the night, as an efficient way to enhance the denitrification process rate in MBC wastewater treatment systems. These steps are currently included in activated sludge processes (Arun et al., 2019; Liu et al., 2022; Wang et al., 2015).
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Nitrogen fluxes as percentage of the influent and effluent for different scenarios of SRT (1.5, 4.5, 9,13.5, 18, 22.5 [d]) and HRT (0.5, 1.5, 4.5 [d]), for Summer (A) and Winter (B) conditions. N-ORG is the organic nitrogen in Xs, Ss, Xi, Xs, and as organic nitrogen (modelled as variable SND). N-ALG, N-HB, and N-NB are the fraction of algal, NB (AOB and NOB), and HB biomass, respectively. N-TAN is the ammoniacal nitrogen fraction (SNH), and N-NO2⁻ and N-NO3⁻ are the fraction of nitrogen as nitrite and nitrate, respectively. N-NH3r and N-NH3m are the fluxes of ammonia gas, in the reactor and the membrane compartments, respectively. N-N2 is the flux of nitrogen gas.</figcaption></figure>
### 3.2.4. Effect of HRT and SRT on dissolved oxygen dynamics

Dissolved oxygen concentration is a crucial factor for MBC since it supports aerobic bacterial growth and nitrification. Figure 7 presents the oxygen fluxes, that were evaluated with the following considerations:

* OUR_ALG, OUR_HB and OUR_NB: Oxygen uptake rate of microalgae, heterotrophs and nitrifiers, respectively. Since it is a consumption rate, it appears as negative values.

* OPR_ALG: Oxygen production rate of algae during photosynthesis, with positive values.

* OTRr and OTRm: Gas-liquid oxygen transfer rate from gas to liquid, in the reactor and the membrane compartments, respectively. These values can be negative or positive, depending on oxygen desorption and absorption dynamics.

In addition, a distinction was made between light and dark phases, and the predicted average oxygen concentrations (DO_AVE) are also reported (black dots).

As expected, higher biological oxygen demands, OUR_ALG, OUR_HB and OUR_NB, resulted from higher biomass concentrations due its retention (see Figure 4 and Figure 7). Despite the small proportion of nitrifiers, the associated oxygen consumption was marked (OUR_NB).

Environmental conditions, such as temperature and irradiance, are expected to play a key role on oxygen dynamics, as confirmed by the simulations presented in Figure 7. Oxygen uptake rate was higher during summer, especially due to microalgae and nitrifiers. In fact, warmer scenarios involve higher bacterial and algal respiration rates, thus increasing oxygen demand. An increase in temperature also decreases oxygen solubility, affecting gas/liquid mass transfer. Indeed, the estimated average oxygen saturation in summer was 30 % lower than in winter. Figure 7 shows that during the light phase, for HRT = 4.5 [d], microalgae were able to fully meet the oxygen demand of bacteria. However, in the dark phase, the conditions were completely different, and DO levels dropped down drastically, leading to oxygen limitation.
As already discussed, the importance of the membrane tank on gas/liquid mass transfer depends on the relation between $K_L$ and the system compartment volumes (reactor and membrane). In the standard configuration where the membrane compartment is much smaller than the reactor, the gaseous transfer in the membrane compartment is much lower than in the reactor. This can be seen clearly in Figure 7 for the case of oxygen dynamics. Simulations revealed the importance of the combined OTR (OTRr + OTRm) on the oxygen dynamics, especially at low HRTs (when oxygen requirements are higher), and during the dark phases when photosynthesis does not occur. For example, at $HRT = 1.5$ [d] and $SRT = 22.5$ [d], OTR was similar to the oxygen produced by algae (OPR_ALG) during summer. It was much higher during winter, while oxygen saturation concentration is higher at lower temperature. During the dark phase OTR due to the mixing system was the only supply of oxygen, supporting a moderated activity of heterotrophs and nitrifiers. Over the full cycle of 24 hours, OTR provided 2/3 of the oxygen for $HRT = 1.5$ [d] and 1/2 for $HRT = 4.5$ [d], while algae provided the remaining fractions.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 7.** Oxygen uptake rate (OUR), oxygen production rate (OPR) and oxygen transfer rate (OTR) under different scenarios of SRT (1.5, 4.5, 9, 13.5, 18, 22.5 [d]) and HRT (0.5, 1.5, 2.5, 3.4, 4.5 [d]), for summer (A) and winter (B) conditions. OPR_ALG is the oxygen production rate of algae; OUR_ALG, OUR_HB, and OUR_NB are the oxygen uptake rate of algae, heterotrophs, and nitrifiers, respectively. OTRr and OTRm are the transfer rate of oxygen of the reactor and the membrane compartments, respectively. Black dots indicate the dissolved oxygen (DO_AVE) in the liquid phase.</figcaption></figure>
### 3.2.5. Efficiency of the wastewater remediation system.

The M-ALBA model was also used to predict the COD and nitrogen concentrations in the effluent, as indicators of the remediation system efficiency. The average effluent (permeate) concentrations of total soluble nitrogen and COD are shown in Figures 8 and 9. The discharge limits for treated domestic wastewater imposed by the European directive 91/271/EEC are presented for comparison purposes. The scenarios where $SRT = HRT$, i.e. without the membrane module, is presented to highlight the advantages of the separation system.

Figure 8 shows that the nitrogen content in the effluent decreased with longer $SRT$ and shorter $HRT$. Figure 8 reveals a minimum of total soluble nitrogen concentration for $HRT$ around 1.5 [d] and $SRT$ greater than 9 [d]. For this condition, the overall nitrogen removal was in average 61.5% for winter and 78.5% for summer. Summer scenarios exhibited better results, thanks to the higher temperature, allowing larger removal rate capacity. Improvement of nitrogen removal for lower $HRTs$ is the result of oxygen limitation at higher biomasses. Such conditions are typically favourable for denitrification. Oxygen limitation during the night, can be a desired operational mode, in order to promote denitrification enhancing overall nitrogen removal.

Even though simulations do not predict nitrogen level coping with discharge standards for sensitive areas, it is observed that adding a membrane to decouple $SRT$ from $HRT$ increases the water flow that can be effectively treated. This allows operation at lower $HRT$ values and surface requirement than commonly required (Chen et al., 2003; Kim et al., 2014; Solimeno and García, 2019), without compromising the effluent quality.
<figure><img src="image_12.png" /><figcaption>**Figure 8.** Soluble nitrogen concentration in the effluent different scenarios of SRT (1.5, 4.5, 9,13.5, 18, 22.5 [d]) and HRT (0.5, 1.5, 2.5, 3.4, 4.5 [d]), for Summer (A) and Winter (B) conditions. The dashed lines represent the discharge limit concentration in European directive 91/271/EEC (15 [g N m⁻³]).</figcaption></figure>

The effluent soluble COD (accounted as the sum of *S*<sub>s,m</sub> and *S*<sub>l,m</sub> in the permeate) is presented in Figure 9 for all the analysed scenarios. The model predicts concentrations below the European discharge standard values (125 [g COD m⁻³]) for all the SRT and HRT, except at *HRT* = 0.5 [d], where the influent flow exceeds the system's treatment capacity. Soluble COD removal efficiencies were higher in winter scenarios (over 75%) compared to summer scenarios (above 62%), because of the negative impact of higher temperatures on HB growth rates. Finally, similar to nitrogen removal, optimal COD removal was obtained for *HRT* of at least 1.5 [d].
<figure><img src="image_13.png" /><figcaption>**Figure 9.** Soluble COD concentration ($S_S$ and $S_I$) in the effluent for the different scenarios: SRT (1.5, 4.5, 9,13.5, 18, 22.5 [d]) and HRT (1.5, 4.5 [d]), for summer and winter conditions. The dashed lines represent the discharge limit concentration in European directive 91/271/EEC (125 [g COD m⁻³]).</figcaption></figure>

**3.3. General Discussion**

Mathematical modelling and simulation are useful tools to provide insights about the behaviour of complex systems, when responses to operational conditions are difficult to predict due to the nonlinear interactions within the players of the ecosystem, submitted to permanent light and temperature fluctuations. Exploring the behaviour and performances of this system under a variety of scenarios revealed the benefits of adding a membrane-assisted biomass retention step. Results show how different levels of biomass retention and wastewater load (determined by *HRT*) must be optimized and adapted to the climatic conditions to maintain efficient performance.

Even though hollow fibre membranes require intense aeration to reduce biofouling, the reduced relative volume of the membrane tank should not significantly impact the gas/liquid mass transfer.

The biomass retention triggered by the membrane has been demonstrated to deeply impact the carbon dynamics and distribution. It is generally claimed that the advantage
of using microalgae is the fixation of anthropogenic CO2. However, as a consequence of
biomass retention the carbon dioxide production increases, and the access to light for
phototrophic organisms decreases, resulting in systems that release more carbon
dioxide than what they absorb. The second advantage which is also claimed for this
system is the reduction of the energy requirements by the use of algae producing the
oxygen. Simulation show that this point of view should be moderated, since the mixing
system is still the source of oxygen during the night. More refined computations,
involving Life Cycle Assessment (Morales et al. 2019), should therefore be carried out to
better quantify the gain in carbon footprint compared to the traditional processes.

The main advantages of membrane assisted biomass retention are probably at another
level. First, the complete clarification of the effluent (permeate), and this is even true
for emerging contaminants. Microalgae have the potential to address emerging
contaminants through mechanisms like bioadsorption, bioaccumulation, and metabolic
degradation (Rempel et al. 2021). The M-ALBA model predicted oxygen concentrations
in the medium that can peak up above 20 mgO2/L during the day, triggering strong
oxidative stress driving molecular degradation (Matamoros et al. 2015). This specificity
of microalgae-based process is probably understated yet and would need more work to
be better appreciated.

Finally, the modelling analysis predicts that *HRT* can be substantially reduced, without potentially affecting the systems performance in terms of organic matter and nitrogen removal. Indeed, since *SRT* and *HRT* moderately impact the removal of organic matter, the decision on the operating conditions could be primarily determined by nitrogen removal and installation size (depending on *HRT*). An optimized approach will involve selecting operational settings with *SRT* exceeding *HRT* to mitigate ammonia volatilization, coupled with low *HRT* values to enhance nitrogen removal in the form of *N*₂. Specifically, optimal parameter values are envisaged to be an *HRT* of approximately 1.5 [d] and an *SRT* greater than or equal to 9 [d].

Furthermore, if we compare the wastewater treatment capacity between operating at
an *HRT* of 1.5 [d] and a baseline scenario with *HRT* = 8 [d], it increases by 4.3 times the
treatment capacity. This would allow processing wastewater generated by 6,670
population equivalents, instead of 1,250. In other words, the HRAP area requirement per square meter would decrease from 4 to 1.3 [m² p.e.⁻¹] (Arashiro et al., 2018).

## 4. CONCLUSIONS

The M-ALBA model was proposed as an extension of the validated ALBA model to represent biomass retention in HRABP systems coupled to membrane filtration. Experimental data were used to successfully validate the model prediction capability. Model predictions demonstrated the effectiveness of uncoupling *SRT* from *HRT* in a MBC based system, providing the following main outcomes:

* Biomass retention increases biomass respiration rate, which results in lower net biomass productivity and the release of more biogenic CO₂.

* Retention of slow growing nitrifying bacteria enables total nitrification, therefore reducing consistently ammonia stripping.

* Biomass retention allows operation at low *HRT*, which increase oxygen requirements. Under certain conditions, such limitation during the night promotes denitrification, favouring the overall nitrogen removal.

* Even though intense mixing and air sparging is expected in the membrane compartment, for fouling control of the membrane, the contribution of this compartment to overall gas-liquid mass transfer stays moderated.

* The increase of the treatment capacity resulting from biomass retention, enables the reduction of the area and volume required. This may contribute to significantly reduce the resources and cost requirements, favouring real-scale application.

Based on these results obtained from a modelling study, adding a filtration unit for biomass recirculation to the reactor represents a significant opportunity to quantitative improve domestic wastewater treatment, particularly in terms of nitrogen compound removal and, more significantly, volumetric treatment capacity.
## Acknowledgment

This work was financed by ANID Chile through FONDECYT Project 1230660. Authors also acknowledge the support provided by ANID through project Anillo ACT240022 and CRHIAM center (ANID/FONDAP/15130015 and ANID/FONDAP/1523A0001). F. Casagli and O. Bernard benefited from the support of the ADEME BioMSA project.

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