La Situación Política.

Parameter estimation is known to be a highly subjective procedure, as it relies on the modeller’s discretion and experience (Koch et al., 2010). The simplest approach would be to reference calibrated parameters from previous studies where similar substrate type is experimented; however such data is often neither available nor exactly applicable to the scenario at hand (Astals et al., 2014).

Batch tests have been used to study model parameters. For instance, a specific bacteria type could be isolated in a batch system together with a particular soluble substrate. Given the substrate-limited condition, it would allow one to determine the specific substrate uptake rate which is a parameter required by ADM1. Some modellers prefer estimating kinetic parameters through the use of a batch test called BMP (Biomethane Potential) test first and then applying the parameters for continuous modelling (Antonopoulou et al., 2012). BMP test involves introducing a calculated quantity of substrate into a known quantity of sludge based on a certain substrate to biomass ratio. Biogas production rate is continuously monitored whilst samples are extracted at fixed time intervals to monitor the evolution of specific constituents. Thereafter, kinetic parameters (e.g. hydrolysis rate, hydrogen and VFA uptake rates) can be approximated by fitting ADM1 against the batch experimental data using non-linear estimation methods.

Despite its popularity, Baltes et al. (1994) cautioned against estimating kinetic parameters of Monod growth kinetic model (which ADM1 uses) from batch systems, as the estimated parameters would fail under dynamic feed situations. Instead, the author suggested that the estimation should be applied to experiments with continuous, time-varying feed rates. Batstone, Tait and Starrenburg (2009) further pointed out that as a batch system the BMP testing is unable to conduct under the same conditions (except temperature) as the full-scale digester. Therefore, batch testing is deemed not entirely representative. Another drawback is that the test requires specialised experimental setup which is costly and time-consuming.

A major limitation of batch systems is the absence of inputs variance. The only model input is the initial conditions, which as a consequence, induces inadequate outputs sensitivity (Lokshina & Vavilin, 1999). Donoso-Bravo et al. (2011) concurred that experimental data from continuous systems are appropriate for kinetic parameter estimation, provided that the experiment ran at different dilution rates or where inputs are dynamic. Many publications have demonstrated estimation of ADM1 parameters using data obtained from continuous or semi-continuous systems on lab-scale (Blumensaat & Keller, 2005; Boubaker & Ridha, 2008); however only a few actually featured modelling of full-scale industrial plants (Batstone et al., 2009; Girault & Steyer, 2010; López & Borzacconi, 2009).

In a study by Batstone, Tait & Starrenburg (2009), a full-scale plant operating at variable flow and organic loading was modelled. The authors compared the modelling performance when using biodegradability extent and hydrolysis parameter (khyd) estimated separately from BMP test data and 1.5 years full-scale plant data. Parameters estimated from the BMP test were found to result in poorer modelling performance, supposedly due to the estimated hydrolysis rates being too low. Hydrolysis values estimated from continuous data were an order of magnitude higher.

high sensitivity towards the model outputs instead of the entire group of ADM1 parameters. By reducing the number of degrees of freedom and bias, it allows one to execute model fitting quicker and avoid parameter equifinality situations where more than one set of parameters have the same model fitting accuracy. For that reason, researchers often apply some sort of sensitivity analysis techniques to rank model parameters according to their sensitivities on model outputs.

Figure 3: Parameter estimation procedure typically followed in anaerobic digestion modelling (Donoso-Bravo et al., 2011)

A literature survey into the methods used in published ADM1 research was conducted (see Appendix, Table 20). The survey suggests that there is currently no protocol on parameter calibration, and in many cases, the method applied is not described explicitly. It is common practice that stoichiometric parameters are left uncalibrated and their default values (as suggested in the STR) retained unless sensitivity analysis suggests otherwise. For kinetic parameters, different approaches were noted:

• Only adjust kinetic parameters that are suggested in the STR as highly sensitive while parameters deemed less sensitive are left unchanged. e.g. Blumensaat & Keller (2005)

• Select kinetic parameters based on outcomes of a sensitivity analysis and only calibrate a few of the most sensitive ones. e.g. Jeong et al. (2005), Koch et al. (2010), Razaviarani & Buchanan (2015) • Calibrate a selected group of parameters based on expert knowledge about the substrate or its

degradation behaviour. e.g. Mairet et al. (2011)

• Calibrate parameters in groups in conjunction with digester design-related constants e.g. Bernard et al., (2001) decoupled the calibration process by first classifying parameters into three subsets then calibrate them sequentially: (1) kinetic parameters, (2) transfer coefficient kLa and (3) the yield coefficients. Modeling Objectives Model selection or development Model implementation Parameter sensitivity analysis

Experimental error assessment and selection of the cost function

Parameter estimation (Minimisation procedure)

Direct Validation (fit quality, parameter accuracy)

Cross Validation (different conditions) Prior knowledge,

experimental data collection

• Group parameters according to different level of sensitivity, then calibrate parameters in the high sensitivity subset first, followed by the next sensitivity subset if the objective function objective is not met e.g. Coelho et al. (2006) grouped the kinetic parameters into the 3 groups of sensitivities (High, Medium, Low) as suggested in the STR, and calibrate each group sequentially.

In an alternative approach, Girault & Steyer (2010) aimed at balancing total nitrogen, ammonium and COD whilst keeping the model parameters as default. To achieve nitrogen and ammonium balance, the nitrogen contents of composite particulate (Xc), protein (XPr) and soluble and particulate inerts (SI, XI) were calibrated. COD balance is achieved by adjusting the proportion of SI and XI relative to the total COD. These constants are normally fixed values by default.

In conclusion, it can be said that there is currently no consensus or common framework for sensitivity analysis and which parameters subset to be calibrated.