The accuracy of a biofilm reactor model depends on the extent to which physical system conditions (particularly bulk-liquid hydrodynamics and their influence on biofilm dynamics) deviate from the ideal conditions upon which the model is based. It follows that an improved capacity to model a biofilm reactor does not necessarily rely on an improved biofilm model, but does rely on an improved mathematical description of the biofilm reactor and its components. Existing biofilm reactor models typically include a one-dimensional biofilm model, a process (biokinetic and stoichiometric) model, and a continuous flow stirred tank reactor (CFSTR) mass balance that [when organizing CFSTRs in series] creates a pseudo two-dimensional (2-D) model of bulk-liquid hydrodynamics approaching plug flow. In such a biofilm reactor model, the user-defined biofilm area is specified for each CFSTR; thereby, Xcarrier does not exit the boundaries of the CFSTR to which they are assigned or exchange boundaries with other CFSTRs in the series. The error introduced by this pseudo 2-D biofilm reactor modeling approach may adversely affect model results and limit model-user capacity to accurately calibrate a model. This paper presents a new sub-model that describes the migration of Xcarrier and associated biofilms, and evaluates the impact that Xcarrier migration and axial dispersion has on simulated system performance. Relevance of the new biofilm reactor model to engineering situations is discussed by applying it to known biofilm reactor types and operational conditions.
One-dimensional (1-D) biofilm models are accurate for simulating biofilm reactors (Morgenroth et al. 2000). Boltz et al. (2010) evaluated and summarized biofilm (reactor) models in existing wastewater treatment plant (WWTP) simulators. Typically, existing biofilm reactor models include a 1-D biofilm model, a biokinetic model, and a continuous flow stirred tank reactor (CFSTR) module that (when organized in series) creates a pseudo two-dimensional (2-D) model of bulk-liquid hydrodynamics approaching plug flow. In such an existing biofilm reactor model, a user-defined biofilm area (AF) is specified for each CFSTR, which is akin to the retention/isolation of free-moving submerged biofilm carriers (Xcarrier) in any CFSTR (i.e., Xcarrier does not exit the boundaries of the CFSTR to which they are assigned, or exchange boundaries with other CFSTRs in the series). Rittmann (1982) defined a well operating biofilm reactor with Xcarrier as having a hydrodynamic regime approaching plug flow while the Xcarrier population and associated biofilms are completely mixed despite L:W≫1 (i.e., the biofilm biomass distribution is equal throughout the reactor).
The accuracy of existing biofilm reactor models is largely defined by the extent to which physical system conditions – particularly, bulk-liquid hydrodynamics and biofilm dynamics – deviate from the ideal conditions upon which the model is based (Boltz & Daigger 2010). Boltz et al. (2011) systematically evaluated the ability of existing biofilm models to describe systems having Xcarrier while using a common modeling platform (i.e., AQUASIM), and assessed the identifiability of key model parameters. Boltz et al. (2012) outlined a Good Biofilm Reactor Modeling Practice (GBRMP). A component of GBRMP is the calibration protocol. Brockmann et al. (2013) reported evidence of modeling limitations when the GBRMP was applied to a nitrifying moving bed biofilm reactor (MBBR) that deviates from ideal completely mixed bulk-liquid hydrodynamics. An improved capacity to model a biofilm reactor does not necessarily rely on an improved biofilm model, but does rely on an improved mathematical description of the biofilm reactor and its components. This notion is particularly relevant when considering that biofilm reactors containing Xcarrier are presently the most widely applied biofilm-based system(s) for municipal and industrial wastewater treatment.
Existing biofilm reactor models, which require a user-defined AF in each CFSTR, simulate biofilm biomass distribution (in 1-D perpendicular to the growth medium) as a function of substrate availability and environmental conditions in each respective CFSTR. Isolating portions of an Xcarrier population and associated biofilms in different CFSTRs results in different simulated biofilm biomass compositions in each CFSTR, which can impact the simulated value of flux of any substrate i (JF,i). This results in the number of different biofilm biomass compositions and JF,i values for any simulated biofilm reactor being defined by the number of CFSTRs in series. The error introduced by this pseudo 2-D biofilm reactor modeling approach may adversely affect model results and limit a model user's capacity to accurately calibrate the model. This paper presents and evaluates a biofilm reactor sub-model that accounts for the movement of an Xcarrier population and associated biofilms through any number of CFSTRs in series, affiliated connection/recirculation stream(s), and the biofilm reactor coupled liquid-solid separation unit process. The objective of our investigation is to ascertain the sub-model's capacity for describing biofilm reactor performance when Xcarrier is present.
MATERIALS AND METHODS
Formulating a larger, more widely functional model using a combination of focused models, or sub-models, to describe a unit process is commonly employed when modeling municipal and industrial wastewater treatment processes. Biofilm reactor models typically include the following sub-models: (1) process, kinetic, and stoichiometric model (e.g., ASM3 and ASM2d); (2) pseudo-analytical, analytical, or numerical 1-D biofilm model; and (3) bulk-liquid hydrodynamic model. A biofilm reactor model also typically includes user-defined streams that account for internal recirculation, biomass wasting, and constituent introduction from external tanks (e.g., nutrients or flows from other unit processes).
This paper presents a sub-model that simulates Xcarrier population and associated biofilms' heterogeneity throughout a biofilm reactor. Accurate implementation of this sub-model depends on the model user understanding the difference between Xcarrier (and associated biofilm) movement and migration. Biofilm reactors with Xcarriermovement is defined here as mixing conditions that result in the even distribution of an Xcarrier population and associated biofilms, throughout, whereby the AF is uniformly exposed to substrates in the bulk liquid of a CFSTR. Migration is defined here as an Xcarrier population and associated biofilms flowing through any number of CFSTRs in series and affiliated connection/recirculation stream(s) used to simulate a biofilm reactor (and coupled liquid-solid separation unit process, if applicable). Migration of Xcarrier results in the AF being uniformly exposed to substrates in the bulk-liquid of each CFSTR through which Xcarrier passes during the simulation specific, user-defined Xcarrier residence time in each respective CFSTR.
To further evaluate the migration of an Xcarrier population and associated biofilms, the reader should consider a rectangular (plan view) biofilm reactor having L:W ≫1, and a hydrodynamic condition that approaches ideal plug flow. The biofilm reactor is coupled with a liquid-solids separation unit process (e.g., sedimentation basin). By definition, Xcarrier can be retained in a specific bioreactor zone, move throughout the entire biofilm reactor, or move throughout the entire biofilm reactor and its coupled liquid-solids separation unit process. If retained in the biofilm reactor (or a specific zone of the biofilm reactor), the tank is equipped with an Xcarrier retention construct (e.g., screens in an MBBR) or relies on gravity acting against the Xcarrier in an upward flowing liquid field (e.g., fluidized bed biofilm reactor or granule reactors). Kagawa et al. (2016) presented an aerobic granule reactor model that accounts for a mechanistic mathematical description of the biofilm coupled with a sequencing batch reactor model to evaluate both micro- and macro-scale system observations. An Xcarrier population and associated biofilms can be classified as one of the following four conditions or as a transient state:
Configuration A: The biofilm reactor (or zone thereof) plan L:W ≤ 1, Xcarrier is retained in the biofilm reactor, and – provided sufficient mixing energy – Xcarrier is evenly distributed throughout the biofilm reactor (or zone thereof). The hydrodynamic regime and Xcarrier population is completely mixed.
Configuration B: The biofilm reactor (or zone thereof) plan L:W ≫ 1, Xcarrier is retained in the biofilm reactor (or zone thereof), and Xcarrier is evenly distributed throughout the biofilm reactor (or zone thereof) (i.e., Xcarrier, inlet=Xcarrier, effluent). The hydrodynamic regime is plug flow.
Configuration C: The biofilm reactor (or zone thereof) plan L:W ≫ 1, Xcarrier is retained in the biofilm reactor (or zone thereof), and Xcarrier is unevenly distributed throughout the biofilm reactor (or zone thereof) (i.e., Xcarrier, inlet ≠ Xcarrier, effluent). Hydrodynamic regime is plug flow with a large extent of axial dispersion.
Configuration D: The biofilm reactor (or zone thereof) plan L:W ≫ 1, Xcarrier is not retained in the biofilm reactor (or zone thereof), and Xcarrier is evenly distributed throughout the biofilm reactor (or zone thereof). The hydrodynamic regime is plug flow. Xcarrier migrates throughout the secondary process (i.e., bioreactor and liquid-solids separation unit process), and Xcarrier egress is either with clarified effluent due to non-ideal liquid-solid separation, or with wasted biomass.
Sufficient Xcarrier migration towards the retention construct, or point of egress, results in Xcarrier accumulation in this location. Configuration A may be accurately simulated with existing biofilm reactor models, but is applied in this study to compare results from existing biofilm reactor models with results from an expanded biofilm reactor model that accounts for Xcarrier migration. Configurations B and C facilitate an evaluation of simulation results when Xcarrier migration is constrained inside the [physical] biofilm reactor (i.e., Xcarrier moves amongst CFSTRs, but does not enter the liquid-solids separation unit process). Configuration D is simulated as a Modified Ludzack Ettinger (MLE) process, and facilitates an evaluation of the impact that unimpeded Xcarrier migration throughout the bioreactor and liquid-solids separation unit process has on simulated system performance. A return activated sludge (RAS) stream is applied for Xcarrier accumulation since Xcarrier is not retained in the bioreactor. Solid-state variables (i.e., Xcarrier and suspended growth) have the same residence time if (1) a modeling device is not included to separate suspended growth from Xcarrier and (2) the rate of Xcarrier and suspended growth attrition (either due to non-ideal liquid-solid separation or with wasted biomass) is equivalent.
A description of the Xcarrier migration model and related mathematical treatments is presented as supplemental information (available with the online version of this paper). Migration of an Xcarrier population and associated biofilms has been modeled by recirculating Xcarrier (along with the biofilm, bulk liquid, and all constituents suspended in the bulk of the liquid). The Xcarrier recirculation stream may originate from any CFSTR (i = 1, 2, …, n− 1, n) and be directed to any CFSTR in the series. Migration modeling introduces the solid-state variable Xcarrier. Simulation of Configuration B allows Xcarrier to pass through a recirculation stream from CFSTR_n = 3 to CFSTR_n = 1. Simulation of Configuration C allows Xcarrier back mixing to describe axial dispersion and allow the model user to account for an uneven distribution of the Xcarrier population and associated biofilms along the bioreactor length. Simulation of Configuration D describes Xcarrier recirculation in the RAS stream, and no Xcarrier attrition (with wasted biomass or in the liquid-solid separation unit process effluent stream). The 1-D biofilm model is described by Wanner & Reichert (1996). ASM3 was applied when simulating Configurations A, B, and C; the model and parameter values described by Henze et al. (2000) were used unless defined herein. A modified ASM2d was the biological process model applied when simulating Configuration D; the model and parameter values described by Boltz et al. (2009) were used unless defined herein. The simulated 1-D biofilm was discretized as a series of 10 layers, plus a mass transfer boundary layer for modeling resistance to mass transfer external to the biofilm surface while linking the bulk liquid with the biofilm. The relevance of our proposed biofilm reactor model was evaluated by application to engineering scenarios and a comparison of model results. Dynamic simulations were executed using SUMO (Dynamita, Nyons, France; Kovács et al. 2013) or Pro2D2 (CH2M HILL, Colorado, USA). The WWTP simulator used allows for the configuration of elements (e.g., CFSTR module, flow connector) to establish a user-defined process configuration.
Modeling the impact that Xcarrier location/migration has on biofilm reactor performance (quantified here as the simulated JF,i) is approached differently with each process configuration. In Configuration A, Xcarrier is retained in each individual CFSTR; therefore, the AF value in each CFSTR is input by the model user. In Configuration B, Xcarrier migrates and is uniformly distributed throughout the series of CFSTRs (i.e., the AF value in each CFSTR is equal and is established by the Xcarrier specific surface area (AS [=] m2/m3) defined by the model user). In Configuration C, Xcarrier migrates and accounts for uneven AF distribution throughout the CFSTR series; therefore, the value of AF in each CFSTR can be modified by the model user through manipulation of each back-mixing stream flow rate. In Configuration D, Xcarrier migrates throughout the CFSTR series and liquid-solid separation unit, which allows for Xcarrier and suspended biomass accumulation, Xcarrier is uniformly distributed throughout the series of CFSTRs (i.e., the value of AF is equal in each CFSTR). Each of these modeling approaches requires a user-defined AF or AS, and recirculation stream flow rate (R) when appropriate.
Simulations: Configurations A, B, and C
Simulated Configurations A, B, and C consist of three CFSTRs in series designated MBBR_1, MBBR_2, and MBBR_3. The simulated processes are defined as a tertiary nitrifying biofilm reactor according to McQuarrie & Boltz (2011): BOD5:TKN ≤ 1.0 and soluble BOD5 ≤ 12 g/m3 (BOD5: biochemical oxygen demand; TKN: total Kjeldahl nitrogen). The dissolved oxygen concentration is rate-limiting inside the biofilm compartment of each simulated CFSTR. Simulated biofilm reactor influent wastewater constituent concentrations, physical characteristics of Xcarrier, and biofilm model parameter values are listed as supplemental information. Each of the three CFSTRs has a 90 m3 volume (V). The influent wastewater flow rate is (Q=) 3,785 m3/d, and the bulk-liquid temperature was 17 °C for each simulation. Configurations A and B were modeled with (AF=) 52,650 m2 in each of the three CFSTRs. Configuration B was modeled with an Xcarrier recirculation rate set to 200% of the influent wastewater flow rate (i.e., QRCY = 2 × 3,785 m3/d = 7,570 m3/d) which was adequate for Xcarrier to approach an ideal completely mixed condition. The total AF of (3 × 52,650 m2=) 157,950 m2 was evenly distributed throughout the biofilm reactor when simulating Configurations A and B. The individual recirculation streams surrounding each CFSTR were adjusted when modeling Configuration C. The recirculation stream flow rates were manipulated until the Xcarrier distribution resulted in AF being 10-30-60 percentage of the total. The resulting AF in each CFSTR (n = 1, 2, and 3) of Configuration C was 15,795 m2, 47,385 m2, and 94,770 m2, respectively.
Simulations: Configuration D
A MLE process with a 250% internal mixed liquor recirculation flow rate including a suspended growth compartment, a biofilm compartment, or combined suspended growth and biofilm compartments (i.e., integrated fixed film activated sludge, IFAS) was simulated as Configuration D. The simulated process consists of three CFSTRs in series designated ANOXIC_1, AEROBIC_1, and AEROBIC_2. Physical characteristics of Xcarrier and biofilm model parameter values are listed as supplemental information. The influent wastewater flow rate was (Q=) 3,785 m3/d, and the bulk-liquid temperature was 17 °C for each simulation. Total bioreactor volume was 1,420 and 473 m3 for the suspended growth and IFAS/migrating Xcarrier simulations, respectively. The total AF was 118,250-m2, and was evenly distributed throughout CFSTRs in series. Suspended growth solids residence time was 9.1 and 2.3 days for the suspended growth and IFAS simulations, respectively. The mixed liquor total suspended solids concentration (XTSS) was 2,350 and 2,280 g/m3 for the suspended growth and IFAS simulations, respectively. Bulk-liquid dissolved oxygen concentration(s) were set to 4 g O2/m3 in aerobic zones. Dynamic simulations were executed using a diurnally varying influent that was equal on a day-to-day basis, and were run for 100 days. Normalized diurnal profiles for flow rate and pollutant loads were applied to average day values for steady-state simulations to quantify diurnal flow rate and pollutant load profiles. The assumed peak hydraulic load was 140% of the average day value (1.4 × 3,785 = 5,299 m3/day), and the assumed peak pollutant load was 170% of the average day value. The average day influent chemical oxygen demand (COD) concentration was 292 g/m3, and the average influent ammonia-nitrogen concentration (SB,A=) 30 g/m3.
RESULTS AND DISCUSSION
Simulated dissolved oxygen flux values also vary when Xcarrier is isolated in respective CFSTRs. Figure 2 illustrates nearly equivalent values of obtained when simulating Xcarrier migration throughout Configuration B. Such model output can potentially offer significant implications for air diffuser grid design. An air-diffuser grid designed to accommodate Configuration A would require substantial tapering while the air-diffuser grid for Configuration B would be nearly uniform.
Configuration C was modeled to evaluate the impact that uneven Xcarrier distribution has on a model-user's ability to describe biofilm reactor performance. This scenario may occur when an elevated approach velocity (e.g., due to a rapid increase in flow rate resulting from peak hydraulic loading conditions or wet-weather) ‘pushes’ Xcarrier towards the retention apparatus located at the effluent discharge or point of egress. Mechanically, the model accounts for Xcarrier migration, but this model does not account for potential diminished oxygen transfer efficiency and the resulting reduction in ammonia-nitrogen uptake (i.e., JF,A) when a majority of Xcarrier has accumulated at the point of egress.
The bulk liquid and its constituents are recycled with Xcarrier when simulating migration using the method described in this paper. A sufficient recirculation rate through the CFSTR series (which is intended to simulate plug flow) approaches a completely mixed state. However, a suitable difference exists between liquid, solids, and Xcarrier residence times that allows a model user to account for a homogeneous Xcarrier distribution while retaining liquid and solid substrate gradients consistent with those observed in a physical system. Simulations quantify the impact of recirculation on biofilm biomass composition for a recirculation rate of (R=) 2. Reviewing Figure 3(a) indicates 50% change in XF,N between CFSTRs designated MBBR_1 (n = 1) and MBBR_3 (n = 3) without simulating Xcarrier migration. Simulation of Xcarrier migration results (Figure 3(b)) in less than 8% change in XF,N between CFSTRs designated MBBR_1 (n = 1) and MBBR_3 (n = 3) for a recirculation rate of (R=) 2. Simulation of Xcarrier migration as Configuration B resulted in a 78% SB,A conversion (with a quantifiable reduction in SB,A across each CFSTR in series), which indicates that the series of (n = 3) CFSTRs does not have completely mixed contents as a result of the internal recirculation stream flow rate.
|.||Conventional .||IFAS .||MC .|
|Ammonia, mg NH4-N/L||0.9||2.6||4.1|
|Nitrate, mg NO3-N/L||10.9||14.2||13.3|
|Phosphate, mg PO4-P/L||4.6||3.6||4.0|
|.||Conventional .||IFAS .||MC .|
|Ammonia, mg NH4-N/L||0.9||2.6||4.1|
|Nitrate, mg NO3-N/L||10.9||14.2||13.3|
|Phosphate, mg PO4-P/L||4.6||3.6||4.0|
A biofilm reactor modeling approach accounting for Xcarrier migration is presented and evaluated. The proposed model is aimed toward overcoming limitations inherent to existing biofilm reactor models. Simulating Xcarrier migration provides a model user with flexibility to account for the heterogeneity of an Xcarrier population and associated biofilms throughout a biofilm reactor. The relevance of the proposed biofilm reactor model to engineering situations was evaluated by applying it to scenarios and comparing model results. Simulation of Configurations A, B, and C demonstrates that failure to account for physically present Xcarrier migration can result in an inaccurate representation of biofilm reactor performance and biofilm biomass distribution. Model results are consistent with the expected influence of Xcarrier migration, but the model does not account for physical system anomalies such as reduced oxygen transfer efficiency and, therefore, reduced JF,A due to poor air flow and mixing when Xcarrier concentration exceeds any system-specific acceptable tolerance.
Simulating Xcarrier migration through anoxic and aerobic zones of an MLE configured bioreactor and a coupled liquid-solids separation unit process showed differences in process performance for IFAS and migrating Xcarrier systems. The migrating Xcarrier biofilm system showed less simulated ammonia-nitrogen conversion when compared to an equivalently-sized IFAS process. Model results indicate a decrease in ammonia-nitrogen conversion when the biofilm thickness was arbitrarily increased in a migrating Xcarrier system. Simulating varying availability of bulk-liquid dissolved oxygen concentration quantified its impact on ammonia-nitrogen removal in systems having a biofilm compartment. Model results suggest that a migrating Xcarrier system is a viable alternative to IFAS. However, while model results are consistent with the expected influence of Xcarrier migration, the model does not account for physical system anomalies such as the impact of recirculation pumping on biofilm accumulation/detachment.
This material was presented during the 5th International Water Association (IWA)/Water Environment Federation (WEF) conference Wastewater Treatment Modeling 2016 (WWTmod2016), Annecy, France, and was a named component of the session entitled ‘Best of WWTmod2016’ at the Water Environment Federation Technical Exhibition and Conference (WEFTEC), New Orleans, Louisiana, USA (2016).