Matching Gompertz and Logistic models to Monod single substrate model

In anaerobic digestion, many experimental results are represented by traditional form of kinetic models such as Gompertz and Logistic equations. They are derived to use as empirical representation of biogas/methane/hydrogen accumulation data. These models normally fit the anaerobic biogas evolution (ABE) curve very well. However, these parameters cannot be used directly for design operation and optimisation of the processes. Most researchers and biochemical engineers prefer to use the Monod approach to deal with designed problems because of its flexibility and well-proven industrial practices. The purpose of this work is to utilise large amount of biogas data which has been represented in Gompertz-type models for design, operation and optimisation purposes. However, it is difficult to match Gompertz or Logistic models to Monod single substrate model because their parameters have complicated interpretation and each parameter can affect more than one shape characteristic of the curve. Secondly, fitting the ABE data to the original or modified form of Gompertz and Logistic models will create initial value error that is at zero-time biogas is not zero. Thirdly, although we can avoid initial value error by using their corresponding corrected forms, the fitting process becomes more complicated because of extra-model parameter. The problem can be solved by using the corrected form of unified Gompertz (U-Gompertz) model or unified Logistic (U-Logistic) model. Therefore, in this work we propose to use U-Gompertz and U-Logistic models, and match them to a Monod-type models so that Gompertz-type parameters are converted to Monod-type parameters. We illustrated that U-Gompertz and U-Logistic models facilitate parameters matching because each parameter in these unified models affects only one shape characteristic of the curve. In this way, it is easy to choose four fixed points based on these U-form parameters and the curve fitting process is simplified. We illustrated the matching process with some published data successfully. This article shows that it is possible to use large amount of ABE data published in the literatures by this matching approach.