Modeling aerobic carbon source degradation processes using titrimetric data and combined respirometric-titrimetric data: structural and practical identifiability

Abstract

The structural and practical identifiability of a model for description of respirometric-titrimetric data derived from aerobic batch substrate degradation experiments of a C(x)H(y)O(z) carbon source with activated sludge was evaluated. The model processes needed to describe titrimetric data included substrate uptake, CO(2) production, and NH(3) uptake for biomass growth. The structural identifiability was studied using the Taylor series method and a recently proposed generalization method. It showed that combining respirometric and titrimetric data allows structural identifiability of one extra parameter combination, the biomass yield, Y(H), compared to estimation on separate data sets, on condition that the nitrogen fraction in biomass (i(XB)) is known. However, data from short-term batch substrate degradation experiments were not sufficiently informative to allow practical identification of all structurally identifiable parameters. Combining respirometry and titrimetry resulted in improvements of parameter confidence intervals compared to estimation on separate respirometric or titrimetric data sets. However, the level of the improvement seems to be substrate dependent: parameter confidence intervals improved considerably more for dextrose than for acetate degradation models. Noteworthy is the finding that the half-saturation substrate concentrations can be different depending on whether they are estimated from respirometric or titrimetric data. Moreover, this difference appears to be dependent on the carbon source considered: for dextrose, titrimetry-based K(S) values are higher than respirometry-based values while for acetate the opposite was found. It was hypothesized that this can be explained by the different point in cell metabolism where the proton production or consumption takes place, leading to a corresponding difference in timing between pH effect and oxygen consumption. Finally, the biomass yield Y(H) and the nitrogen content of the biomass i(XB) could be estimated from combined respirometric-titrimetric data obtained with addition of a known amount of carbon source. Y(H) can also be estimated from r(O) data when the initial substrate concentration S(S)(0) is known. The values found correspond to values reported in literature, but, interestingly, also seem able to reflect the occurrence of storage processes when pulses of acetate and dextrose are added.