This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The computer modelling and simulation of wastewater treatment plant and their specific technologies, such as membrane bioreactors (MBRs), are becoming increasingly useful to consultant engineers when designing, upgrading, retrofitting, operating and controlling these plant. This research uses traditional phenomenological mechanistic models based on MBR filtration and biochemical processes to measure the effectiveness of alternative and novel time series models based upon input–output system identification methods. Both model types are calibrated and validated using similar plant layouts and data sets derived for this purpose. Results prove that although both approaches have their advantages, they also have specific disadvantages as well. In conclusion, the MBR plant designer and/or operator who wishes to use good quality, calibrated models to gain a better understanding of their process, should carefully consider which model type is selected based upon on what their initial modelling objectives are. Each situation usually proves unique.

A phenomenological dead-end filtration model [_{t}

This initial model was extensively modified and added to by Paul ^{©}.

Most current researchers model the membrane fouling process using a phenomenological mechanistic approach that obeys the fundamental laws of physics. This is the traditional approach used to model MBR systems that treat wastewater. However it has been found that it does suffer from the following disadvantages:

Membrane fouling is in reality highly complex and currently poorly understood as a process. Hence any mechanistic fouling model, either simple or complex, cannot hope to adequately address all aspects involved in the fouling procedure;

Usually a mechanistic fouling model needs to be made bespoke for each individual filtration system so that it accurately depicts the specific hydrodynamics of the process and the membrane operational regime;

These models are normally highly dimensional and contain several parameters requiring determination by real life plant data sets (e.g., flux stepping trials, extended specialist laboratory experiments,

Parameter estimation and optimisation require expert knowledge and proves to be complex as most models of this type are over-parameterised with too many degrees of freedom;

For many applications insufficient quality data is usually available to allow a full model calibration and validation, and thus any verified model is not accurate for every situation;

The general application of such complex models means their take up for process control and the development of future operational strategies will always prove limited [

In a bid to overcome the distinct disadvantages of a traditional mechanistic approach, it has been suggested that a non-traditional approach can be used to describe the membrane filtration and fouling process for a MBR system. The non-traditional approach which was used in this study is based on time series system identification methods [

System identification is an iterative process in which models with different structures are identified from data, and the individual model performance compared. The normal start point is by estimating the parameters of very simple model structures. If the performance still proves poor, then the model structure is gradually increased in complexity. Ultimately the simplest of all model structures tested is eventually selected that best describes the dynamics of the system under scrutiny. In this iterative process, which can be automated, the system identification procedure commences by initially using linear continuous input-output (IO) model structures. This followed by using more complex non-linear structures. The best fit structure is then chosen as the optimal model formulation.

Historically speaking the first real instance of using a times series approach to analyse wastewater treatment data was carried out by Berthouex

In this study a linear continuous IO state-space model structure is tested using the supplied times series data. The state space model structure is a good choice for quick estimation because it requires only two parameters, namely the model order and one or more input delays. These model formulations are usually solved using iterative optimisation techniques and algorithms like the least squares method. However, this requires a lot of computing power and they are prone to inherent inaccuracies. A much more attractive model formulation is the sub-space one which does not need to be solved using iterative optimisation techniques and algorithms, but by only using algebraic calculations [

Both fouling model types have been tested on data obtained from flux stepping tests performed on an ITT Sanitaire Ltd. (Colwick, Nottingham, UK) pilot membrane filtration unit depicted in

ITT Sanitaire membrane filtration unit (depicted with bioreactor).

Operational data for pilot membrane filtration unit.

ITT Sanitaire membrane filtration unit (without bioreactor) | |
---|---|

Membrane type and area | Horizontal “Kolon” fibres; PVDF 0.1 μm pore size; 20 m^{2} |

Feed flow; permeate flow; backwash | 1 to 2.4 m^{3}/h; 0.6 to 1 m^{3}/h; 1.2 to 1.8 m^{3}/h |

Backwash interval & duration | Every 4 min with 30 s ON |

TMP | 300 to 500 mbar |

Aeration rate | 13 Nm^{3}/h from coarse bubble tube diffuser |

Cleaning regime | hypochlorite dosed 4 times daily into permeate tank |

Feed flow biological data | COD concentration 50 mg O_{2}/L; TSS concentration 25 mg/L |

Indicative feed flow SMP data | Measured glucose concentration 5 mg/L; measured protein concentration 100 mg/L |

After various assumptions and simplifications of the plant data, the eight best flux steps were used to test the modified phenomenological model.

Modified phenomenological model—best model fit for 8 flux steps.

After various assumptions and simplifications of the plant data, the eight best flux steps were used to test the proposed multi-input single output (MISO) model structure. As the plant layout for this unit is very simple with no bioreactor to complicate matters, the selected MISO model structure should give a very high degree of accuracy. In this case the permeate flux, the measured SMP levels, and the measured bulk mixed liquor concentration into the membrane were used as variables in the input model vector with the TMP being the single variable in the output model vector. Firstly an IO model based on a standard iterative state-space formulation was tested. This was followed by using a quicker single-shot algebraic sub-space method as a comparison. Results are described below.

Best model fit for 8 flux steps (4 for validation) for standard state-space formulation.

Best model fit for 8 flux steps (4 for validation) for sub-space method.

The standard state-space formulation, whose equations are not given here for the sake of brevity, gave a workable fit, albeit not a very good one of 8.5% as shown in

When this MISO model structure is run as a subspace formulation, the best fit is for a 6th order model with an algorithm block size of 4. This fit is carried out by using the last four flux stepping cycles as the validation data set. Again for simplicities sake, the subspace model equations are not given here. The result as shown in

Overall it is clear that the phenomenological model performed very well even though it took a considerable time to be developed into a useful format, and the model had to be calibrated using complex genetic algorithm procedures. Conversely, the subspace method gave consistent results for the IO models used, and was very easy to set up and calibrate.

It initially looks like this novel approach has many advantages over traditional mechanistic models while giving comparable results for some IO structures. Early simulation results described in this study prove this, especially for subspace methods. However these methods can prove very fragile and prone to crashing. Additionally a comprehensive “Model Conceptualisation Procedure” is required to tie it into reality which needs expert know-how to set up. They also require very large data sets to produce accurate formulations, and these linear models are only useful around a very narrow operating range or operating point. Non-linear model versions can improve the predictive accuracy but are even more fragile.

In conclusion, it may prove advantageous to use these methods for model prediction under most circumstances apart from the following instances:

Not for design of new plant (particularly for processes with long time constants), and the biological operation of plant (

No good as research tools to investigate membrane fouling. Cannot predict one-off fouling events, only generalised scenarios.

The situation, in which they may particularly prove themselves superior to traditional model structures, is for model predictive control (possibly in real time) for processes with very short time constants (

_{b}

Bulk concentration (g/L)

Fractional amount of total foulant contributing to deposit growth

_{0}

Initial flux rate of clean membrane (m/s)

_{t}

Total volumetric flow rate (m^{3}/s)

_{0}

Initial volumetric flow rate (m^{3}/s)

_{m}

Resistance of the clean membrane (m^{−1})

_{p0}

Original resistance of the deposit (m^{−1})

Specific protein layer resistance (m/kg)

Filtration time (s)

_{p}

Filtration time after initial membrane blocking occurs (s)

Constant total membrane pressure (Pa)

Pore blockage parameter (m^{2}/kg)

Pore constriction parameter (kg)

The author would like to thank and acknowledge the assistance received especially in terms of data collation from ITT Sanitaire Limited (UK).