Reaction extents: A Divide-and-Conquer Approach for Kinetic Model Identification

Obtaining reliable wastewater treatment process models is critical for the application of model-based design, operation, and automation. For example, Masic et al. (2014) explored the use of an observer designed for nonlinear processes to estimate nitrite in a biological urine nitrification process. In this process, anthropogenic urine is used as a resource for the production of a fertilizer (Udert & Wächter, 2012). Thanks to the separated collection and treatment of urine via NoMix toilets (Larsen et al., 2001), the majority of the nitrogen and phosphorus released via human excreta is captured. The urine nitrification step has two purposes: to prevent (i) volatilization of ammonia by reducing the pH and (ii) production of malodourous compounds. If successful, one can store nitrified urine for long periods of time. The urine nitrification process operates at fairly high conversion rates and is prone to three important failures. The first failure is caused by inhibition of the ammonia oxidizing bacteria (AOB) at high free ammonia concentrations and can lead to washout of AOB as well as the nitrite oxidizing bacteria (NOB). The second failure is caused by growth of acid-tolerant AOB and causes the pH to decrease to a level where the NOB are inhibited and undesired chemical reactions occur. The third failure appears when a temporary accumulation of nitrite causes NOB inhibition, thereby reducing their activity. Such a nitrite accumulation can lead to an irrecoverable failure if the nitrite is allowed to accumulate to high levels (above 50 mg N/L). The first and second failures are mitigated easily by maintaining a safe pH via manipulation of the urine feed flow rate. The third failure is more difficult to avoid and requires a timely detection of nitrite. Masic et al. (2014) provided successful preliminary tests with a model-based observer, which highly depends on the availability of a reliable model. It is unlikely that standard parameter values apply due to the high-strength nature of human urine. For this reason, a well-calibrated model is desired. In Masic et al. (2016b) parameters were estimated to global optimality for the nitrite oxidation by NOB. The applied method, however, allows only estimating parameters of a single reaction system. To apply the same optimization method to multivariate processes, an extent-based methodology was tested in silico in Masic et al. (2016a). By means of the computation of reaction extents, one can separate the estimation of the parameters for each individual reaction. This extent-based modelling method however requires as many measured variables as the number of reactions (Rodrigues et al., 2015). For this reason, Masic et al. (2016a) simplified the model identification problem by considering a constant biomass, i.e. a net biomass growth equal to zero for both AOB and NOB. In the present study, the extent-based model identification method is modified to avoid this simplification, while allowing