Comparison of guideline- and model-based WWTP design for uncertain influent conditions

Dynamic models are suggested as the modern tool for refined wastewater treatment plant (WWTP) design (Jimenez et al. 2018). Additionally, uncertainties must be considered during design (Belia et al. 2021) and multiple uncertainty (UA) and sensitivity analysis (SA) methods for model assessment are available (Razavi et al. 2021). Yet, these technologies have not reached adoption in practice. Instead, current state-of-the-art design is based on guidelines and textbooks (e.g. ATV 2000; Tchobanoglous et al. 2003; Grady et al. 2011; Jimenez et al. 2018), which typically are based on a combination of physical knowledge, experience and rules of thumb. This approach leaves room for subjective interpretation, commonly conducted by the process design consultant, and might lead to non-transparent and sub-optimal designs.

Several publications have proposed methods for assessing, complementing, and verifying guideline-based designs with dynamic simulation (Corominas et al. 2010; Belia et al. 2021). Although creating added value, these methods do require additional effort since two calculation tools (guidelines and dynamic models) must be implemented and evaluated. Dynamic WWTP models can be, and are, applied in most stages of the WWTP life cycle (Rieger et al. 2012) and due to the reasons mentioned above it would be practical (decreasing the necessary number of digital tools), and possibly result in more efficient WWTPs, if the models were used in the design phase as well. Then, in a long-term perspective, current design, guidelines might even be redundant.

To enable acceptance among users of a new WWTP design methodology, the merits and pitfalls of either design technique must be further assessed by understanding and clarifying their differences. In this study, a design guideline-type calculation (DC, engineering spreadsheet) and a model-based design approach (MDL), subject to similar input data values and design pre-requirements, were therefore compared.

A real-life design task was identified from the preliminary phase of a WWTP upgrade project in Uppsala, Sweden, and a realistic DC was defined based on a combination of the available information in the preliminary design report and experience from other design projects in Sweden. The MDL approach included steady-state results generated with a commercial WWTP simulator.

Both design methods are sensitive to the selection of input data (Sin et al. 2011; Flores-Alsina et al. 2012) and the results of the two methods were therefore compared using uncertainty and sensitivity analysis. Thereby, it was assessed how input uncertainties were propagated to output uncertainties. The model parameters of both methods were fixed with ‘typical’ values in the DC approach and the default parameter set in the MDL approach. This was motivated as follows: (1) the early project phase of the design task at hand meant that historical data motivating any parameter value adjustment were scarce, (2) for future applications of the MDL approach in practice it is foreseen that a majority of the model parameters will need to be kept at their default values and (3) the model parameters of the two methods are very different involving that it is difficult to vary them in a fair and comparable way.

Instead of considering model parameter uncertainty, the two methods were assessed by comparing their design results for uncertain influent concentrations of chemical oxygen demand (COD), biological oxygen demand (BOD₇) and total nitrogen (TN). The choice of defining these input data as uncertain benefits from the facts that (1) there are commonly historical data available for determining and motivating the input distributions and (2) they represent basic input data that always needs to be specified in design projects.

The following realistic operational settings were selected based on operational experience and to keep the case study manageable:

• a Q_RAS/Q_C ratio of 1.7,

• a sludge loading rate to the secondary clarifier (including Q_RAS) of 3.8 kg TSS m⁻² h⁻¹,

• a distribution of pre-settled wastewater to the three cascades (f_C1-3) of 36.5/32/31.5%,

• a methanol (MeOH) flow rate to C2 (Q_MeOH,2) of 0.5 m³ d⁻¹. Q_MeOH,3 was allowed to be adjusted without constraints to fulfil the effluent TN requirement.

In this study, two general difficulties were recognised for defining a typical conventional design methodology:

• 1.

  Details about the applied equations were not readily available in the preliminary design documents. Documentation on how the process was historically designed was lacking as well.

• 2.

  The design guideline equations were not presented in a closed-form expression and required manual iterations to converge to the final design.

Facing difficulty 1, the DC was defined taking inspiration from Swedish practice and available information in the WWTP's preliminary design report as presented by the process design consultants. It must be emphasised, however, that, although being realistic, the DC developed in this study was unlikely to match the one used by the consultants exactly. To enable automatic iterations, the DC equations were implemented in MATLAB. Below, the DC equations are conceptually introduced. In the results section the model parameters and the applied values, of the DC are shown (Table 1), which provides further explanation of the included calculations.

The DC take the design flow, BOD_7,In and TN_In as influent input variables. The first process unit, the primary clarifier load reduction was modelled by fixed removal percentages for BOD₇ and TN. Then, the main output of the DC is the dimensioned capacity, e.g., the maximum value of Q_C, for which the pre-requirements defined in the section above are met. To find Q_C, the flow was iteratively increased until either nitrification or denitrification limited the capacity of the existing volumes and configuration. For each flow rate a steady-state nitrogen mass balance was therefore calculated to check if the effluent requirements could be met without violating any of three design criteria, valid for the process temperature 9 °C:

• Crit. 1: The necessary amount of N to nitrify (N_Nit, kg N d⁻¹) is obtained without exceeding the maximum allowed nitrification rate (1.1 g NH₄-N (kg VSS)⁻¹ h⁻¹).

• Crit. 2: The necessary amount of N to denitrify (N_Dn, kg N d⁻¹) is obtained without exceeding the maximum allowed denitrification rate with methanol (2.6 g NO₃-N (kg VSS)⁻¹ h⁻¹) in C3.

• Crit. 3: The aerobic sludge age (SRT_Aer) exceeds the minimum allowed (9 d).

The maximum allowed concentration of mixed liquor suspended solids (MLSS) in Cascade 3 was determined from the influent flow rate and assumed maximum sludge loading rate to the secondary clarifier. The MLSS in Cascade 1 and Cascade 2, and the concentration of total suspended solids (TSS) in the RAS flow, were then calculated from a static solids mass balance assuming that TSS in presettled and secondary settled wastewater is negligible. The volatile (organic) part of the suspended solids (VSS) was assumed to be a fixed fraction of the TSS (0.75 g VSS (g TSS)⁻¹).

Nitrification: N_Nit was calculated as the mass balance difference between the total nitrogen load to the three cascades, and the nitrogen in the effluent and waste-activated sludge (WAS). More specifically, the effluent nitrogen was assumed to consist of inert soluble N (assumed to be 1 g N m⁻³), nitrogen in the effluent suspended solids (assumed to be 0.5 g N m⁻³), and the effluent NH₄-N and NO₃-N. The sludge was assumed to contain a constant nitrogen fraction (0.08 g N (g VSS)⁻¹).

The DC assumed (according to the design pre-requirements) complete nitrification and a residual concentration of 1 g NH₄-N m⁻³ in the cascades as well as in the effluent. The necessary nitrification rate was then calculated by dividing N_Nit with the mass of volatile suspended solids (VSS) in the aerobic volumes and compared to Crit. 1.

Denitrification: N_Dn was given by subtracting the load of effluent NO₃-N (allowed concentration 8.0 – 1.0 – 0.5 – 1.0 = 5.5 g N m⁻³) from N_Nit. It is thus assumed that there was no NO₃-N in the influent. The denitrification process in each of the three cascades was limited by either:

• the amount of organic matter in the inlet to the cascades, or

• the amount of NO₃-N in the inlet to the cascades, or

• the assumed maximum allowed denitrification rates.

The DC calculation assumed yield parameters determining the requirement of influent BOD₇ and added methanol for denitrification, see Table 1. The denitrification process was assumed to primarily oxidize the more easily degradable carbon source (in this case methanol). Only when methanol was fully oxidized, the influent BOD₇ was consumed. The maximum allowed denitrification rate in a certain volume was assumed to depend on the fraction of nitrogen that is denitrified with the easily degradable substrate. For example, in Cascade 1, denitrification was assumed to be with influent BOD₇ only and the resulting maximum rate at 9 °C was thus set to 1.20 g NO₃-N (kg VSS)⁻¹ h⁻¹, see Table 1. In Cascade 3, conversely, denitrification could potentially be with methanol only and the maximum rate was set to 2.60 g NO₃-N (kg VSS)⁻¹ h⁻¹. For a certain flow rate and influent TN and BOD₇ concentration, the DC calculates the actual amounts of N that is denitrified in Cascade 1 and Cascade 2. The necessary denitrification rate in Cascade 3 was then calculated by dividing the remaining amount of N_Dn with the mass of volatile suspended solids (VSS) in the anoxic volume in Cascade 3 and compared to Crit. 2. In this way it was verified whether the effluent requirements were met with methanol addition and the associated required dosage flow rate (Q_MeOH,3).

Sludge production: Despite the nitrification rate (Crit. 1) a necessary condition for complete nitrification according to the DC was a sufficient aerobic sludge age (SRT_Aer), which was calculated by dividing the mass of sludge into the aerobic volumes by the sludge production (SP, kg TSS d⁻¹) and then compared to Crit. 3. The sludge production was calculated as the sum of sludge produced due to the mass loading rate of BOD₇ in the effluent of the primary clarifier and the total amount of dosed external carbon (here methanol), assuming two fixed sludge production factors, depending on the type of carbon source only.

In the MDL approach, the iterations of the DC approach were replaced by a steady-state simulation, e.g., by solving the model mass balances for constant design influent concentrations. The variables Q_C and Q_MeOH,3 were first manipulated by PI control loops to maintain the effluent requirements (effluent concentration of NH₄-N and TN, respectively). In case the denitrification capacity was limited (e.g. compliant values of NH₄-N but too high TN), the Q_C controller was switched from measuring NH₄-N to TN, leading to a decreased flow rate. The requirement of the secondary clarifier sludge loading rate was maintained by controlling the Q_WAS flow rate, i.e. while Q_C increases, the MLSS of Cascade 3 is automatically lowered (recall that the Q_RAS/Q_C ratio was considered to be fixed). In this way, the maximum capacity Q_C, conditioned by the influent concentrations, was established.

To run the steady-state simulations, the configuration (Figure 1) was implemented in the software Simba^# 5.0 (ifak, Germany) using the built-in biokinetic process model ASM_inCtrl (inCTRL Solutions Inc., Canada). This model is, although significantly extended, based on the same principles as the activated sludge models described in Henze et al. (2000). For the application in this paper, the significant processes of the model are the growth of ammonia and nitrite-oxidizing bacteria (two-step nitrification), growth of ordinary heterotrophs (resulting in denitrification in the absence of oxygen) and the growth of methylotrophs (resulting in denitrification with methanol in the absence of oxygen). The applied primary clarifier model is based on Otterpohl & Freund (1992) and the secondary clarifier on the three-layer model described in Alex (2011). For the simulated conditions in this paper, the effluent TSS were always close to 6 g m⁻³. Thus, any change in clarifier performance due to changes in the design flow rate was not seen. With few exceptions, as discussed in the following, the parameter values of the Simba# WWTP model were kept at their default values.

A main difference between the MDL and DC approaches is that in the MDL, COD is used as an input variable for the total concentration of organic matter while BOD₇ (used in the DC) is a calculated model output. In Simba#, BOD₇ is calculated from the COD state variables and several decay, yield and empirical parameters. These parameters, which are specific for the BOD calculation, were kept at their default values and the MDL influent concentration of inert particulate COD was modified to match the design figures for influent TSS and BOD₇.

The TSS removal of the primary clarifier was adjusted to obtain the design value (80%), while the fraction of soluble influent COD was modified to obtain a fit with the design primary clarifier BOD₇ removal (53%). Eventually, the influent fractionation and primary clarifier parameter values involved that the MDL (with COD as main input) produced the same BOD₇ concentrations in influent and pre-settled wastewater compared to the DC. The observed TN removal in MDL was used as the design figure and inserted in the DC in this case study. A validated methodology for dealing with influent fractionation and pre-treatment during an MDL approach for WWTP dimensioning is regarded to be an important and challenging topic for future research.

In total, 1,000 Monte Carlo samples were sampled from the multivariate Gaussian distribution, in which each sample was independently and identically distributed. Each sample was then thought to represent a realization of a future (daily) concentration and load. Since the concentration samples were derived with data from the entire year, while the design was done for a fixed cold temperature scenario (9 °C), it was assumed that the variability in influent concentrations was independent of the temperature. The samples were used as inputs to the uncertainty and sensitivity analysis, where Q_C was the output. A so-called random sampling with binning approach (estimates of the conditional variance and expectations from Monte Carlo data) was used for the sensitivity analysis to estimate the main effects of the variance (commonly abbreviated S_i). Random sampling with binning was used instead of the more common standardized regression coefficients due to the strong correlations in influent data. The sensitivity analysis was executed in MATLAB with code kindly provided by Gürkan Sin (DTU, Denmark).

The (initially assumed) simple task of automating the DC iterations was time-consuming but necessary since manual tweaking of the DC to fulfil one new design scenario could take up to one hour. Having automated the DC calculations, both design approaches were fast to simulate, and in the order of seconds on a desktop computer. Thus, the bottleneck in time was to manually set up and configure the methods. Our experience from this study is that it was both faster and less error prone to conduct uncertainty analysis and the Monte Carlo simulations with commercial software including validated model libraries, compared to the DC approach using spreadsheets. This challenges the common perception of models being complicated and time-consuming.

We interpret the difference between the DC and the MDL capacity as the total effect of all accumulated safety factors in the DC, i.e., the built-in resilience towards influent load and concentration variations with respect to Q_C. As expected, the DC was more restrictive than the model, which does not include safety factors.

In the MDL, the influent concentration of organic matter (expressed as COD) has the highest sensitivity (compare Figure 4(a) and 4(c)). For a given COD_In of 600 g m⁻³, for example, the capacity was about 27,500 m³ d⁻¹ when TN_In was varied between 50 and 70 g m⁻³ (recall Figure 2). A reasonable explanation is that the COD of the methanol dosage to Cascade 3, used to compensate for the impact of the influent nitrogen to COD ratio, gives a quite different model response compared to the COD of the influent (e.g. a lower sludge production per denitrified nitrogen), which do not significantly impact the capacity. However, in this case, the equation structure is significantly more complex compared to the DC and the UA/SA of this study do not directly provide an answer to why the influent COD concentration is the limiting factor. Although all equations are available, it requires time and deep model understanding to understand the root-cause effect, which is a challenge and drawback of using models for design.

Finally, the magnitude of the sensitivity indices did not directly match the corresponding variance in the corresponding slopes in Figure 4, i.e., the standardized regression coefficients (data not shown). The reason is that the input data were correlated, and therefore overestimated the impact of each input factor if the correlations were disregarded. The applied random sampling with the binning method coped with this issue for the estimation of the main effects. However, the total effects (including interactions) are critical when more influent parameters are considered. For this situation, methods such as the one described by Kucherenko et al. (2012) are needed and will be a topic for future research.

In Table 1, assumptions and results of the DC and MDL approach for this case study are summarised. As described in the methods section, the removal in the primary clarifier was set by fixed percentages (design pre-requirements) in the DC while in the MDL, the influent fractionation and TSS removal were adjusted to mimic these. A consequence of this was that the MDL removal of nitrogen varied between 13.3 and 23.6% in the Monte Carlo runs depending on the influent COD/TN ratio. With a higher ratio, more COD and nitrogen are in particulate form, which increases the TN removal. This exemplifies the fact that it may sometimes be difficult to exactly match pre-defined design requirements with a model-based approach.

As mentioned, the nitrification rate in the DC limited a further increase of Q_C for all influent concentrations. The assumed maximum nitrification rate (1.1 gNH₄-N (kg VSS)⁻¹ h⁻¹) in the DC was restrictive, but not unrealistic, for the combination of low design temperature (9 °C) and a strict effluent ammonia requirement (<1 g NH₄-N m⁻³). Note that the MDL, on average, had a higher nitrification rate than the DC (Table 1). The observed aerobic sludge retention times for both the DC and the MDL were well above (12–23 d) the set criterion (>9 d). Accordingly, manual simulations (results not shown) showed that the maximum effluent NH₄-N (and not denitrification) limited an increase in Q_C in the MDL.

The DC results from Cascade 1 (no addition of methanol) showed that the assumed maximum denitrification rate (1.2 g NO₃-N (kg VSS)⁻¹ h⁻¹) was reached at all times, indicating that the denitrification rate, and not the inlet BOD₇ load, was a limitation in Cascade 1. In the MDL, a similar ‘maximum rate’ was not seen, and the observed rates were higher (1.46–2.09 g NO₃-N (kg VSS)⁻¹ h⁻¹). The denitrification rate in the MDL was instead limited by the actual BOD₇ load, fed to Cascade 1.

Finally, the conceptual two-substrate-denitrification model used in the DC shows a high impact on the calculated sludge production (Figure 5(c)). In both methods, the specific sludge production per kg denitrified N increased with the influent BOD₇/TN ratio. In the MDL, this is due to the higher yield parameter values for wastewater COD compared to methanol COD. This is also true in the DC approach (3.2 and 1.7 kg TSS/kg NO₃-N denitrified with BOD₇ and methanol, respectively) but the resulting dependence on BOD₇/TN was, in this case, higher. Overall, the DC predicts a significantly higher sludge production compared to the MDL. For many dimensioning projects, the sludge production plays a crucial role, and the differing behaviour of the approaches is therefore important to consider.

The capacity of the existing process for future conditions depends on uncertainties in influent concentrations, which emphasises the importance of uncertainty analysis during design. The results show that model-based design can simplify and reduce the time required for uncertainty and sensitivity analysis compared to a conventional design approach, in which the equations are solved manually and iteratively. A benefit with the conventional design approach is the simple interpretation regarding which factors limit the design capacity. However, the validity of these observations should be questioned since they differ from the mechanistic model output. Sensitivity analysis is effective in quantifying how correlated influent variations affect the capacity and more research is needed on how to quantify interactions for correlated input data. In the end, this study shows the potential, as well as the need for, model-based design of WWTPs.

We gratefully acknowledge the review of anonymous reviewers and Ulf Jeppsson (Lund University, Sweden). The project was financially supported by the Foundation for IVL (SIVL), Svenskt Vatten, Uppsala Vatten och Avfall, and Stockholm Vatten och Avfall.

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

The authors declare there is no conflict.