Towards a standardised analysis of experimental Threshold Of Flocculation (TOF) curves

In activated sludge (AS) processes, solid/liquid separation based on settling is one of the key steps in organic matter removal and capture. Settling can be defined in four regimes: discrete non-flocculent and discrete flocculent settling, driven by Stokes' law and thus grouped under the name ‘Stokesian settling’, and hindered and compression settling, grouped under ‘non-Stokesian settling’ (Ekama et al. 1997). Conventional characterisation methods such as Sludge Volumetric Index (SVI) and zone or hindered settling velocity assess non-Stokesian settling. However, organic matter removal or capture in secondary settlers is essentially driven by Stokesian settling and especially flocculent settling (Torfs et al. 2016). Flocculent settling is not easily characterised due to a lack of existing methodologies (Van Dierdonck et al. 2012). Therefore, better understanding flocculent settling mechanisms represent one of the main challenges to optimise wastewater treatment plants (WWTPs).

Flocculent settling is based on sludge capacity to flocculate (Mancell-Egala et al. 2017), referring in this study to the capacity to form flocs, by aggregation and enmeshment of particulate matter, which are able to settle quickly enough to be separated in the settling unit (at around 1 m/h in AS). Flocculation in a biological process is generally assessed indirectly, through the measurement of the clarifier Effluent Suspended Solid (ESS). However, this analysis alone does not enable to characterise and understand how bioflocculation exactly works (Van Dierdonck et al. 2012). In 2017, Mancell-Egala et al. introduced another promising parameter: the Threshold Of Flocculation (TOF). TOF reflects the collision capacity of a sludge and corresponds to the minimum Total Suspended Solid (TSS) concentration required to obtain flocs that settle with a velocity larger than 1.5 m/h. In practice, AS samples are diluted and settled for 2 min corresponding to a settling velocity of 1.5 m/h. TOF curves are obtained by plotting the ratio of supernatant/initial TSS concentrations as a function of the initial TSS concentration. TOF is graphically determined as the deflection point with a minimal differential of 10%. TOF enables the characterisation of the flocculation capacities of a sludge and has been positively correlated to ESS (Ngo et al. 2021). TOF is increasingly used, particularly in studies on High-Rate Activated Sludge (HRAS) processes where bioflocculation represents a key parameter (Rahman et al. 2019; Van Winckel et al. 2019; Ngo et al. 2021). However, analysing TOF curves can be challenging. The identification of the threshold is not supported by a clear published methodology and the visual approach to identify TOF values may lead to different results depending on the person analysing the curve. Additionally, the ratio of low TSS concentration values is more sensitive to the uncertainties that affect their experimental determination, which may induce bias in the general trend and, consequently, in TOF determination. Thus, results obtained in different studies are difficult to compare and the robustness of the method is questioned. Therefore, there is an interest to improve TOF curves analysis using a systematic, accurate and robust identification method of the threshold and to widen its application to different AS processes.

In this context, a new method to estimate TOF values is proposed, based on mathematical modelling of TOF curves combined with a mechanistic interpretation of the observed trends. A systematic detection is performed using a regression method coded on R, the script of which is available in the supplementary material. By comparing the method proposed in this paper and the one published by Mancell-Egala et al. (2017), the objective is to assess the improvement of the proposed method in terms of (1) curve interpretation, (2) associated uncertainties, and (3) applicability of the method to a wide panel of AS processes.

To this aim, both methods are first compared on two datasets: (1) the first one was obtained using an AS sample from a conventional activated sludge (CAS) system (Sludge Retention Time (SRT) of 5 days) and (2) the second one was one of the examples presented in Mancell-Egala et al. (2017) for which no TOF value could not be determined using the original method. The new method is applied to different types of AS systems (HRAS, CAS, and densified sludge (DAS) to assess its applicability.

The methods described below were applied to sludge from eight AS full-scale processes and three pilot plants for three different systems, operated over a wide range of sludge retention times (see Table 1): conventional AS operated under low loaded conditions (CAS), HRAS, and DAS. As presented in Table 1, the influent characteristics may also differ (raw or settled wastewater). Samples from the biological reactors were collected during dry weather conditions, outside of any filamentous event (T° = 17 − 21 °C), one to four times per reactor. One dataset from Mancell-Egala et al. (2017) was also analyzed in this work to check the consistency of the method.

TOF measurements were performed at the WWTP directly after sampling. TOF data were obtained using an experimental setup based on Mancell-Egala et al. (2017). A plexiglas column with a volume of 1.7 L, a diameter of 9 cm and a sample port located at 5 cm from the water surface was used. Between 6 and 8 dilutions of AS were prepared and poured into the column with a funnel to avoid any vortex formation. A 100 mL of sample was taken to determine the initial TSS concentration. Sludge was allowed to settle for 2 min in order to obtain a critical velocity test at 1.5 m/h and the supernatant above the sample port was withdrawn to measure the supernatant TSS concentration. TSSs were measured according to the standard method (APHA 2005). The critical velocity of 1.5 m/h was set according to Mancell-Egala et al. (2017) at 15% lower than the surface overflow rate (SOR) of 1.7 m/h at which clarifier failure can occur. Lowering this critical velocity may result in greater measurement error, as the TSS concentration of the supernatant would decrease.

Data from Mancell-Egala et al. (2017) have been extracted from the paper and numerical values recalculated when necessary.

Mancell-Egala et al. (2017) determine TOF as the deflection point (a minimum differential of 10%) in the curve plotting the normalised supernatant TSS (supernatant/initial TSS concentration ratio) as a function of the initial TSS concentration.

Minimisation of the above criterion was performed using the constrOptim function on R software (version 3.6.1), to integrate the above-mentioned constraints on the parameters (corresponding script available in supplementary material). A preliminary visual identification of and was required to initialise the algorithm in order to identify the ‘best’ solution to the optimisation problem and not a local minimum.

Uncertainty propagation was performed through Monte Carlo simulations. Uncertainties on each TSS measurement were modelled by a normal distribution with a standard deviation of 5 mg/L based on repeatability analyses reported in the standard APHA (2005). TODF and TOF values were therefore obtained from 1,000 simulations, and their variability was characterised by a 90% coverage interval associated with boxplot visualisations (representing the median, the first and the third quartiles and the minimum and maximum values). It was checked that the number of simulations allowed for numerical convergence of the statistical indicators within ±1 mg/L.

For several sludge samples, TOF curves present only one threshold. A second script was developed and is available for these scenarios (available in Supplementary material).

The proposed method has been compared to the one from Mancell-Egala et al. (2017) on the dataset obtained on CAS1 and on the ‘sidestream dataset’ (Section 3.1). Contrary to Mancell-Egala et al. (2017), data analysis did not rely on relative data (% supernatant TSS/initial TSS) but absolute concentrations (supernatant TSS) to gain precision as explained in Section 3.1.4. In Section 3.2, the method was applied to different sludge types to assess its generalisation potential.

The same dataset analyzed using the method described in Mancell-Egala et al. (2017) (Figure 2(b)) presented a decrease in normalised supernatant TSS with an increase in initial TSS concentration. Normalised supernatant TSS concentration decreased almost linearly from 100% to below 40% for an increase in initial TSS concentration from 0 to 810 mg/L. The deflection point and associated mechanisms were difficult to identify. TOF would certainly have been detected rather arbitrarily at a value of 240 mg/L, corresponding to the third experimental measured value.

With the proposed method using absolute data (Figure 5(a)), the uncertainty in x and y values was the same regardless the initial TSS concentration. Uncertainties did not impact the curve shape.

With the Mancell-Egala et al. (2017) method (Figure 5(b)), normalised supernatant TSS concentrations (i.e., supernatant/initial concentration ratios) showed a larger uncertainty, especially for initial TSS concentrations below 250 mg/L. For a measured initial TSS concentration of 80 mg/L, the normalised supernatant TSS concentration varied between 80 and 120%. This may explain the value of the normalised supernatant TSS from Mancell-Egala et al. (2017) higher than 100%, which is physically impossible. Uncertainties on each determined TSS value had a significant impact, especially at low initial TSS concentration, leading to a significant effect on the curve shape. Given the distribution of values, the experimental trend can take significantly different shapes, and the deflection point is not always visible or identified at the same concentration.

The apparent higher dispersion obtained for the TODF value may be related to the low number of data points below the first slope break and their arrangement (Figure 3). This may call for increasing the number of measurement points in the low range of initial concentration.

For densified sludge, the three parts detailed in Section 3.1 are visible on the experimental curves obtained (Figure 8(a)). However, the lowest experimental points were systematically below the 1:1 line even at very low initial concentrations (i.e., supernatant TSS concentrations are lower than initial concentrations). This can be explained by the presence of granules that settle almost instantaneously and do not need and participate to the flocculation mechanisms. This observation corresponds to the discrete non-flocculent settling described by Torfs et al. (2016). Considering only the floc fraction (i.e., removing the fraction of granules (experimentally measured) from the initial TSS concentration) enabled TOF curves to be analyzed in the same way as for CAS systems, as seen in Figure 8(b).

In conclusion, the proposed method is adapted to analyse Stokesian settling of AS samples from CAS systems. The method is also applicable to estimate flocculation capacity of the floc fraction of densified sludge, considering an offset that corresponds to the granular sludge fraction. Sludge sampled in HRAS systems with very low SRT show a different behaviour, which calls for an adaptation of the protocol. In addition, increasing the number of measurement points, especially around TOF values, would be beneficial to gain in accuracy. On-line measurement of the supernatant TSS concentration could also be envisaged as a further improvement of the method.

TOFs are interesting indicators of the ability of AS to settle following Stokesian settling mechanisms. In this work, the method originally proposed by Mancell-Egala et al. (2017) to determine TOF has been improved to gain accuracy and reproducibility. An R-code was developed to mathematically analyse TOF curves using a piecewise linear function with two slope breaks. This new method:

• provides a more accurate identification of TOF values displayed using a boxplot;

• allows to identify another threshold value, corresponding to the apparition of discrete flocculent settling and thus flocculation, which can also be used to assess flocculation capacities of a specific sludge;

• relates the shape of the experimental curves to the mechanisms occurring in the setup which compensates for the limited number of data points and reinforces results;

• takes into account the analytical uncertainties.

The method was then successfully applied to sludge sampled in CAS and DAS processes. For HRAS processes, further investigations are required to better assess bioflocculation mechanisms and to see whether adapting the protocols (increased settling time, initial mixing) would lead to more consistent results. Combining visual analysis (images and microscopy) and size distribution analysis would also be relevant to improve the understanding of the bioflocculation mechanisms and to optimise the operation and performances of HRAS systems in particular.

This work has been partly supported by the EUR H2O'Lyon (ANR-17-EURE-0018) of Université de Lyon (UdL), within the programme ‘Investissements d'Avenir’ operated by the French National Research Agency (ANR). The authors are also grateful to the technicians and Master students involved in the laboratory measurements, in particular Etienne PLE and Lise NGNANGWE WAGHA.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.