Automated data transfer for digital twin applications: Two case studies.

Digital twins have been gaining an immense interest in various fields over the last decade. Bringing conventional process simulation models into (near) real time are thought to provide valuable insights for operators, decision makers, and stakeholders in many industries. The objective of this paper is to describe two methods for implementing digital twins at water resource recovery facilities and highlight and discuss their differences and preferable use situations, with focus on the automated data transfer from the real process. Case 1 uses a tailor-made infrastructure for automated data transfer between the facility and the digital twin. Case 2 uses edge computing for rapid automated data transfer. The data transfer lag from process to digital twin is low compared to the simulation frequency in both systems. The presented digital twin objectives can be achieved using either of the presented methods. The method of Case 1 is better suited for automatic recalibration of model parameters, although workarounds exist for the method in Case 2. The method of Case 2 is well suited for objectives such as soft sensors due to its integration with the SCADA system and low latency. The objective of the digital twin, and the required latency of the system, should guide the choice of method. PRACTITIONER POINTS: Various methods can be used for automated data transfer between the physical system and a digital twin. Delays in the data transfer differ depending on implementation method. The digital twin objective determines the required simulation frequency. Implementation method should be chosen based on the required simulation frequency.

A plant-wide model describing GHG emissions and nutrient recovery options for water resource recovery facilities.

In this study, a plant-wide model describing the fate of C, N and P compounds, upgraded to account for (on-site/off-site) greenhouse gas (GHG) emissions, was implemented within the International Water Association (IWA) Benchmarking Simulation Model No. 2 (BSM2) framework. The proposed approach includes the main biological N2O production pathways and mechanistically describes CO2 (biogenic/non-biogenic) emissions in the activated sludge reactors as well as the biogas production (CO2/CH4) from the anaerobic digester. Indirect GHG emissions for power generation, chemical usage, effluent disposal and sludge storage and reuse are also included using static factors for CO2, CH4 and N2O. Global and individual mass balances were quantified to investigate the fluxes of the different components. Novel strategies, such as the combination of different cascade controllers in the biological reactors and struvite precipitation in the sludge line, were proposed in order to obtain high plant performance as well as nutrient recovery and mitigation of the GHG emissions in a plant-wide context. The implemented control strategies led to an overall more sustainable and efficient plant performance in terms of better effluent quality, reduced operational cost and lower GHG emissions. The lowest N2O and overall GHG emissions were achieved when ammonium and soluble nitrous oxide in the aerobic reactors were controlled and struvite was recovered in the reject water stream, achieving a reduction of 27% for N2O and 9% for total GHG, compared to the open loop configuration.

Modelling gas-liquid mass transfer in wastewater treatment: when current knowledge needs to encounter engineering practice and vice versa.

Gas-liquid mass transfer in wastewater treatment processes has received considerable attention over the last decades from both academia and industry. Indeed, improvements in modelling gas-liquid mass transfer can bring huge benefits in terms of reaction rates, plant energy expenditure, acid-base equilibria and greenhouse gas emissions. Despite these efforts, there is still no universally valid correlation between the design and operating parameters of a wastewater treatment plant and the gas-liquid mass transfer coefficients. That is why the current practice for oxygen mass transfer modelling is to apply overly simplified models, which come with multiple assumptions that are not valid for most applications. To deal with these complexities, correction factors were introduced over time. The most uncertain of them is the α-factor. To build fundamental gas-liquid mass transfer knowledge more advanced modelling paradigms have been applied more recently. Yet these come with a high level of complexity making them impractical for rapid process design and optimisation in an industrial setting. However, the knowledge gained from these more advanced models can help in improving the way the α-factor and thus gas-liquid mass transfer coefficient should be applied. That is why the presented work aims at clarifying the current state-of-the-art in gas-liquid mass transfer modelling of oxygen and other gases, but also to direct academic research efforts towards the needs of the industrial practitioners.

Model-based analysis and optimization of a full-scale industrial high-rate anaerobic bioreactor.

The objective of this paper is to present the model-based optimization results of an anaerobic granular sludge internal circulation reactor. The International Water Association Anaerobic Digestion Model No. 1 extended with phosphorus (P), sulfur (S), and ethanol is used to describe the main biological and physico-chemical processes. The high-rate conditions within the reactor are simulated using a flow + reactor model comprised of a series of continuous stirred tank reactors followed by an ideal total suspended solids separation unit. Following parameter estimation by least squares on the measured data, the model had a relative mean error of 13 and 15% for data set #1 and data set #2, respectively. Response surfaces show that the reactor performance index (a metric combining energy recovery in the form of heat and electricity, as well as chemicals needed for pH control) could be improved by 45% when reactor pH is reduced down to 6.8. Model-based results reveal that influent S does not impose sufficient negative impacts on energy recovery (+5.7%, in MWh/day,+0.20 M€/year when influent S is removed) to warrant the cost of its removal (3.58 M€/year). In fact, the process could handle even higher S loads (ensuring the same degree of conversion) as long as the pH is maintained above 6.8. Nevertheless, a higher S load substantially increases the amount of added NaOH to maintain the desired operational pH (>25%) due to the acidic behavior of HS - . CO 2 stripping decreases the buffer capacity of the system and hence use of chemicals for pH control. Finally, the paper discusses the possibilities and limitations of the proposed approach, and how the results of this study will be put into practice.

Modelling phosphorus (P), sulfur (S) and iron (Fe) interactions for dynamic simulations of anaerobic digestion processes.

This paper proposes a series of extensions to functionally upgrade the IWA Anaerobic Digestion Model No. 1 (ADM1) to allow for plant-wide phosphorus (P) simulation. The close interplay between the P, sulfur (S) and iron (Fe) cycles requires a substantial (and unavoidable) increase in model complexity due to the involved three-phase physico-chemical and biological transformations. The ADM1 version, implemented in the plant-wide context provided by the Benchmark Simulation Model No. 2 (BSM2), is used as the basic platform (A0). Three different model extensions (A1, A2, A3) are implemented, simulated and evaluated. The first extension (A1) considers P transformations by accounting for the kinetic decay of polyphosphates (XPP) and potential uptake of volatile fatty acids (VFA) to produce polyhydroxyalkanoates (XPHA) by phosphorus accumulating organisms (XPAO). Two variant extensions (A2,1/A2,2) describe biological production of sulfides (SIS) by means of sulfate reducing bacteria (XSRB) utilising hydrogen only (autolithotrophically) or hydrogen plus organic acids (heterorganotrophically) as electron sources, respectively. These two approaches also consider a potential hydrogen sulfide ( [Formula: see text] inhibition effect and stripping to the gas phase ( [Formula: see text] ). The third extension (A3) accounts for chemical iron (III) ( [Formula: see text] ) reduction to iron (II) ( [Formula: see text] ) using hydrogen ( [Formula: see text] ) and sulfides (SIS) as electron donors. A set of pre/post interfaces between the Activated Sludge Model No. 2d (ASM2d) and ADM1 are furthermore proposed in order to allow for plant-wide (model-based) analysis and study of the interactions between the water and sludge lines. Simulation (A1 - A3) results show that the ratio between soluble/particulate P compounds strongly depends on the pH and cationic load, which determines the capacity to form (or not) precipitation products. Implementations A1 and A2,1/A2,2 lead to a reduction in the predicted methane/biogas production (and potential energy recovery) compared to reference ADM1 predictions (A0). This reduction is attributed to two factors: (1) loss of electron equivalents due to sulfate [Formula: see text] reduction by XSRB and storage of XPHA by XPAO; and, (2) decrease of acetoclastic and hydrogenotrophic methanogenesis due to [Formula: see text] inhibition. Model A3 shows the potential for iron to remove free SIS (and consequently inhibition) and instead promote iron sulfide (XFeS) precipitation. It also reduces the quantities of struvite ( [Formula: see text] ) and calcium phosphate ( [Formula: see text] ) that are formed due to its higher affinity for phosphate anions. This study provides a detailed analysis of the different model assumptions, the effect that operational/design conditions have on the model predictions and the practical implications of the proposed model extensions in view of plant-wide modelling/development of resource recovery strategies.

Modelling anaerobic co-digestion in Benchmark Simulation Model No. 2: Parameter estimation, substrate characterisation and plant-wide integration.

Anaerobic co-digestion is an emerging practice at wastewater treatment plants (WWTPs) to improve the energy balance and integrate waste management. Modelling of co-digestion in a plant-wide WWTP model is a powerful tool to assess the impact of co-substrate selection and dose strategy on digester performance and plant-wide effects. A feasible procedure to characterise and fractionate co-substrates COD for the Benchmark Simulation Model No. 2 (BSM2) was developed. This procedure is also applicable for the Anaerobic Digestion Model No. 1 (ADM1). Long chain fatty acid inhibition was included in the ADM1 model to allow for realistic modelling of lipid rich co-substrates. Sensitivity analysis revealed that, apart from the biodegradable fraction of COD, protein and lipid fractions are the most important fractions for methane production and digester stability, with at least two major failure modes identified through principal component analysis (PCA). The model and procedure were tested on bio-methane potential (BMP) tests on three substrates, each rich on carbohydrates, proteins or lipids with good predictive capability in all three cases. This model was then applied to a plant-wide simulation study which confirmed the positive effects of co-digestion on methane production and total operational cost. Simulations also revealed the importance of limiting the protein load to the anaerobic digester to avoid ammonia inhibition in the digester and overloading of the nitrogen removal processes in the water train. In contrast, the digester can treat relatively high loads of lipid rich substrates without prolonged disturbances.

A plant-wide aqueous phase chemistry module describing pH variations and ion speciation/pairing in wastewater treatment process models.

There is a growing interest within the Wastewater Treatment Plant (WWTP) modelling community to correctly describe physico-chemical processes after many years of mainly focusing on biokinetics. Indeed, future modelling needs, such as a plant-wide phosphorus (P) description, require a major, but unavoidable, additional degree of complexity when representing cationic/anionic behaviour in Activated Sludge (AS)/Anaerobic Digestion (AD) systems. In this paper, a plant-wide aqueous phase chemistry module describing pH variations plus ion speciation/pairing is presented and interfaced with industry standard models. The module accounts for extensive consideration of non-ideality, including ion activities instead of molar concentrations and complex ion pairing. The general equilibria are formulated as a set of Differential Algebraic Equations (DAEs) instead of Ordinary Differential Equations (ODEs) in order to reduce the overall stiffness of the system, thereby enhancing simulation speed. Additionally, a multi-dimensional version of the Newton-Raphson algorithm is applied to handle the existing multiple algebraic inter-dependencies. The latter is reinforced with the Simulated Annealing method to increase the robustness of the solver making the system not so dependent of the initial conditions. Simulation results show pH predictions when describing Biological Nutrient Removal (BNR) by the activated sludge models (ASM) 1, 2d and 3 comparing the performance of a nitrogen removal (WWTP1) and a combined nitrogen and phosphorus removal (WWTP2) treatment plant configuration under different anaerobic/anoxic/aerobic conditions. The same framework is implemented in the Benchmark Simulation Model No. 2 (BSM2) version of the Anaerobic Digestion Model No. 1 (ADM1) (WWTP3) as well, predicting pH values at different cationic/anionic loads. In this way, the general applicability/flexibility of the proposed approach is demonstrated, by implementing the aqueous phase chemistry module in some of the most frequently used WWTP process simulation models. Finally, it is shown how traditional wastewater modelling studies can be complemented with a rigorous description of aqueous phase and ion chemistry (pH, speciation, complexation).

Effects of influent fractionation, kinetics, stoichiometry and mass transfer on CH4, H2 and CO2 production for (plant-wide) modeling of anaerobic digesters.

This paper examines the importance of influent fractionation, kinetic, stoichiometric and mass transfer parameter uncertainties when modeling biogas production in wastewater treatment plants. The anaerobic digestion model no. 1 implemented in the plant-wide context provided by the benchmark simulation model no. 2 is used to quantify the generation of CH4, H2and CO2. A comprehensive global sensitivity analysis based on (i) standardized regression coefficients (SRC) and (ii) Morris' screening's (MS's) elementary effects reveals the set of parameters that influence the biogas production uncertainty the most. This analysis is repeated for (i) different temperature regimes and (ii) different solids retention times (SRTs) in the anaerobic digester. Results show that both SRC and MS are good measures of sensitivity unless the anaerobic digester is operating at low SRT and mesophilic conditions. In the latter situation, and due to the intrinsic nonlinearities of the system, SRC fails in decomposing the variance of the model predictions (R² < 0.7) making MS a more reliable method. At high SRT, influent fractionations are the most influential parameters for predictions of CH4and CO2emissions. Nevertheless, when the anaerobic digester volume is decreased (for the same load), the role of acetate degraders gains more importance under mesophilic conditions, while lipids and fatty acid metabolism is more influential under thermophilic conditions. The paper ends with a critical discussion of the results and their implications during model calibration and validation exercises.

Effects of ionic strength and ion pairing on (plant-wide) modelling of anaerobic digestion.

Plant-wide models of wastewater treatment (such as the Benchmark Simulation Model No. 2 or BSM2) are gaining popularity for use in holistic virtual studies of treatment plant control and operations. The objective of this study is to show the influence of ionic strength (as activity corrections) and ion pairing on modelling of anaerobic digestion processes in such plant-wide models of wastewater treatment. Using the BSM2 as a case study with a number of model variants and cationic load scenarios, this paper presents the effects of an improved physico-chemical description on model predictions and overall plant performance indicators, namely effluent quality index (EQI) and operational cost index (OCI). The acid-base equilibria implemented in the Anaerobic Digestion Model No. 1 (ADM1) are modified to account for non-ideal aqueous-phase chemistry. The model corrects for ionic strength via the Davies approach to consider chemical activities instead of molar concentrations. A speciation sub-routine based on a multi-dimensional Newton-Raphson (NR) iteration method is developed to address algebraic interdependencies. The model also includes ion pairs that play an important role in wastewater treatment. The paper describes: 1) how the anaerobic digester performance is affected by physico-chemical corrections; 2) the effect on pH and the anaerobic digestion products (CO2, CH4 and H2); and, 3) how these variations are propagated from the sludge treatment to the water line. Results at high ionic strength demonstrate that corrections to account for non-ideal conditions lead to significant differences in predicted process performance (up to 18% for effluent quality and 7% for operational cost) but that for pH prediction, activity corrections are more important than ion pairing effects. Both are likely to be required when precipitation is to be modelled.

Calibration and validation of a phenomenological influent pollutant disturbance scenario generator using full-scale data.

The objective of this paper is to demonstrate the full-scale feasibility of the phenomenological dynamic influent pollutant disturbance scenario generator (DIPDSG) that was originally used to create the influent data of the International Water Association (IWA) Benchmark Simulation Model No. 2 (BSM2). In this study, the influent characteristics of two large Scandinavian treatment facilities are studied for a period of two years. A step-wise procedure based on adjusting the most sensitive parameters at different time scales is followed to calibrate/validate the DIPDSG model blocks for: 1) flow rate; 2) pollutants (carbon, nitrogen); 3) temperature; and, 4) transport. Simulation results show that the model successfully describes daily/weekly and seasonal variations and the effect of rainfall and snow melting on the influent flow rate, pollutant concentrations and temperature profiles. Furthermore, additional phenomena such as size and accumulation/flush of particulates of/in the upstream catchment and sewer system are incorporated in the simulated time series. Finally, this study is complemented with: 1) the generation of additional future scenarios showing the effects of different rainfall patterns (climate change) or influent biodegradability (process uncertainty) on the generated time series; 2) a demonstration of how to reduce the cost/workload of measuring campaigns by filling the gaps due to missing data in the influent profiles; and, 3) a critical discussion of the presented results balancing model structure/calibration procedure complexity and prediction capabilities.

Balancing effluent quality, economic cost and greenhouse gas emissions during the evaluation of (plant-wide) control/operational strategies in WWTPs.

The objective of this paper was to show the potential additional insight that result from adding greenhouse gas (GHG) emissions to plant performance evaluation criteria, such as effluent quality (EQI) and operational cost (OCI) indices, when evaluating (plant-wide) control/operational strategies in wastewater treatment plants (WWTPs). The proposed GHG evaluation is based on a set of comprehensive dynamic models that estimate the most significant potential on-site and off-site sources of CO2, CH4 and N2O. The study calculates and discusses the changes in EQI, OCI and the emission of GHGs as a consequence of varying the following four process variables: (i) the set point of aeration control in the activated sludge section; (ii) the removal efficiency of total suspended solids (TSS) in the primary clarifier; (iii) the temperature in the anaerobic digester; and (iv) the control of the flow of anaerobic digester supernatants coming from sludge treatment. Based upon the assumptions built into the model structures, simulation results highlight the potential undesirable effects of increased GHG production when carrying out local energy optimization of the aeration system in the activated sludge section and energy recovery from the AD. Although off-site CO2 emissions may decrease, the effect is counterbalanced by increased N2O emissions, especially since N2O has a 300-fold stronger greenhouse effect than CO2. The reported results emphasize the importance and usefulness of using multiple evaluation criteria to compare and evaluate (plant-wide) control strategies in a WWTP for more informed operational decision making.

Global sensitivity analysis of the BSM2 dynamic influent disturbance scenario generator.

This paper presents the results of a global sensitivity analysis (GSA) of a phenomenological model that generates dynamic wastewater treatment plant (WWTP) influent disturbance scenarios. This influent model is part of the Benchmark Simulation Model (BSM) family and creates realistic dry/wet weather files describing diurnal, weekend and seasonal variations through the combination of different generic model blocks, i.e. households, industry, rainfall and infiltration. The GSA is carried out by combining Monte Carlo simulations and standardized regression coefficients (SRC). Cluster analysis is then applied, classifying the influence of the model parameters into strong, medium and weak. The results show that the method is able to decompose the variance of the model predictions (R(2)> 0.9) satisfactorily, thus identifying the model parameters with strongest impact on several flow rate descriptors calculated at different time resolutions. Catchment size (PE) and the production of wastewater per person equivalent (QperPE) are two parameters that strongly influence the yearly average dry weather flow rate and its variability. Wet weather conditions are mainly affected by three parameters: (1) the probability of occurrence of a rain event (Llrain); (2) the catchment size, incorporated in the model as a parameter representing the conversion from mm rain · day(-1) to m(3) · day(-1) (Qpermm); and, (3) the quantity of rain falling on permeable areas (aH). The case study also shows that in both dry and wet weather conditions the SRC ranking changes when the time scale of the analysis is modified, thus demonstrating the potential to identify the effect of the model parameters on the fast/medium/slow dynamics of the flow rate. The paper ends with a discussion on the interpretation of GSA results and of the advantages of using synthetic dynamic flow rate data for WWTP influent scenario generation. This section also includes general suggestions on how to use the proposed methodology to any influent generator to adapt the created time series to a modeller's demands.

Benchmarking biological nutrient removal in wastewater treatment plants: influence of mathematical model assumptions.

This paper examines the effect of different model assumptions when describing biological nutrient removal (BNR) by the activated sludge models (ASM) 1, 2d & 3. The performance of a nitrogen removal (WWTP1) and a combined nitrogen and phosphorus removal (WWTP2) benchmark wastewater treatment plant was compared for a series of model assumptions. Three different model approaches describing BNR are considered. In the reference case, the original model implementations are used to simulate WWTP1 (ASM1 & 3) and WWTP2 (ASM2d). The second set of models includes a reactive settler, which extends the description of the non-reactive TSS sedimentation and transport in the reference case with the full set of ASM processes. Finally, the third set of models is based on including electron acceptor dependency of biomass decay rates for ASM1 (WWTP1) and ASM2d (WWTP2). The results show that incorporation of a reactive settler: (1) increases the hydrolysis of particulates; (2) increases the overall plant's denitrification efficiency by reducing the S(NOx) concentration at the bottom of the clarifier; (3) increases the oxidation of COD compounds; (4) increases X(OHO) and X(ANO) decay; and, finally, (5) increases the growth of X(PAO) and formation of X(PHA,Stor) for ASM2d, which has a major impact on the whole P removal system. Introduction of electron acceptor dependent decay leads to a substantial increase of the concentration of X(ANO), X(OHO) and X(PAO) in the bottom of the clarifier. The paper ends with a critical discussion of the influence of the different model assumptions, and emphasizes the need for a model user to understand the significant differences in simulation results that are obtained when applying different combinations of 'standard' models.

Evaluation of plant-wide WWTP control strategies including the effects of filamentous bulking sludge.

The main objective of this paper is to evaluate the effect of filamentous bulking sludge on the predicted performance of simulated plant-wide WWTP control strategies. First, as a reference case, several control strategies are implemented, simulated and evaluated using the IWA Benchmark Simulation Model No. 2 (BSM2). In a second series of simulations the parameters of the secondary settler model in the BSM2 are automatically changed on the basis of an on-line calculated risk of filamentous bulking, in order to mimic the effect of growth of filamentous bacteria in the plant. The results are presented using multivariate analysis. Including the effects of filamentous bulking in the simulation model gives a-more realistic-deterioration of the plant performance during periods when the conditions for development of filamentous bulking sludge are favourable: compared to the reference case where bulking effects are not considered. Thus, there is a decrease of the overall settling velocity, an accumulation of the total suspended solids (TSS) in the middle layers of the settler with a consequent reduction of their degree of compaction in the bottom. As a consequence there is a lower TSS concentration in both return and waste flow, less biomass in the bioreactors and a reduction of the TSS removal efficiency. The control alternatives using a TSS controller substantially increase the food to microorganisms (F/M) ratio in the bioreactor, thereby reducing both risk and effects of bulking sludge. The effects of ammonium (NH(4)(+)), nitrate (NO(3)(-)) and reject water control strategies are rather poor when it comes to handling solids separation problems.

GISCOD: general integrated solid waste co-digestion model.

This paper views waste as a resource and anaerobic digestion (AD) as an established biological process for waste treatment, methane production and energy generation. A powerful simulation tool was developed for the optimization and the assessment of co-digestion of any combination of solid waste streams. Optimization was aimed to determine the optimal ratio between different waste streams and hydraulic retention time by changing the digester feed rates to maximize the biogas production rate. Different model nodes based on the ADM1 were integrated and implemented on the Matlab-Simulink simulation platform. Transformer model nodes were developed to generate detailed input for ADM1, estimating the particulate waste fractions of carbohydrates, proteins, lipids and inerts. Hydrolysis nodes were modeled separately for each waste stream. The fluxes from the hydrolysis nodes were combined and generated a detailed input vector to the ADM1. The integrated model was applied to a co-digestion case study of diluted dairy manure and kitchen wastes. The integrated model demonstrated reliable results in terms of calibration and optimization of this case study. The hydrolysis kinetics were calibrated for each waste fraction, and led to accurate simulation results of the process and prediction of the biogas production. The optimization simulated 200,000 days of virtual experimental time in 8 h and determined the feedstock ratio and retention time to set the digester operation for maximum biogas production rate.

An ASM/ADM model interface for dynamic plant-wide simulation.

Mathematical modelling has proven to be very useful in process design, operation and optimisation. A recent trend in WWTP modelling is to include the different subunits in so-called plant-wide models rather than focusing on parts of the entire process. One example of a typical plant-wide model is the coupling of an upstream activated sludge plant (including primary settler, and secondary clarifier) to an anaerobic digester for sludge digestion. One of the key challenges when coupling these processes has been the definition of an interface between the well accepted activated sludge model (ASM1) and anaerobic digestion model (ADM1). Current characterisation and interface models have key limitations, the most critical of which is the over-use of X(c) (or lumped complex) variable as a main input to the ADM1. Over-use of X(c) does not allow for variation of degradability, carbon oxidation state or nitrogen content. In addition, achieving a target influent pH through the proper definition of the ionic system can be difficult. In this paper, we define an interface and characterisation model that maps degradable components directly to carbohydrates, proteins and lipids (and their soluble analogues), as well as organic acids, rather than using X(c). While this interface has been designed for use with the Benchmark Simulation Model No. 2 (BSM2), it is widely applicable to ADM1 input characterisation in general. We have demonstrated the model both hypothetically (BSM2), and practically on a full-scale anaerobic digester treating sewage sludge.

Comparison of environmental effects and resource consumption for different wastewater and organic waste management systems in a new city area in Sweden.

An analysis of the environmental effects and resource consumption by four systems for management of wastewater and organic household waste in a new city area have been performed, as follows: (1) conventional system complemented with advanced sludge treatment for phosphorus recovery, (2) blackwater system with urine diversion and food waste disposers, (3) blackwater system with food waste disposers and reverse osmosis, and (4) local wastewater treatment plant with nutrient recovery by using reverse osmosis. Substance-flow analysis and energy/exergy calculations were performed by using the software tool URWARE/ORWARE. Emissions were calculated and classified based on the impact categories global warming potential, acidification, and eutrophication, according to ISO 14042 (2000). The analysis also included nutrient recovery (i.e., the potential to use nutrients as a fertilizer). Depending on which aspects are prioritized, different systems can be considered to be the most advantageous.

Continuity-based interfacing of models for wastewater systems described by Petersen matrices.

In this paper the Petersen and composition matrices that modellers are now familiar with are used as a basis to construct interfacing models between subsystems considered in wastewater treatment. Starting from continuity considerations and a set of transformation reactions between components used in the two models of the subsystems to be interfaced, a set of linear algebraic equations needs to be solved. The theoretical development is illustrated using a simplified integrated model of an activated sludge system coupled to an anaerobic digester. Continuity-guaranteed interfacing of subsystems will facilitate optimization studies of the within-the-fence process units of a wastewater treatment plant or of the integrated urban wastewater system.