Transformations of some growth models widely used in gas production measurements

Mehmet Korkmaz
2016 Journal of Scientific and Engineering Research   unpublished
A mathematical model is a tool used to obtain information about the behavior of a system. The mathematical models can be used to have a preliminary knowledge about the functioning of a system, reducing the product costs and improving the performance. In this study, the modified models of several existing models, Gompertz, Orskov, Logistic and Monomolecular were developed that basically divided gas production into two fractions, one arising from rapidly fermentable feed components and the other
more » ... rom slowly fermentable feed components. The aim of this study is related to how originally used models are converted into two fractions mentioned above. For this purpose, all steps of the transformations were given step by step. Introduction A mathematical model is a powerful tool used to get valuable knowledge about the behavior of a system by using a mathematical technique. However, the main purpose of using the mathematical models is to obtain a preliminary knowledge about the functioning of a system, reducing the product costs and improving the performance [1-2]. However, the mathematical models are collected under two classes: empirical and mechanistic models [3-4]. Empirical models contain with the parameters a, b, c, etc. Therefore, these models do not give an idea about the behavior of system, but they are used only to fit data points. Therefore, since the parameters of the empirical models do not contain any biological meaning. It is difficult to estimate their initial values. In other words, it is difficult to estimate start values for the parameters if they have no biological meaning. Since it is easy to estimate the initial values of the parameters of mechanistic model and it is possible to calculate in 95% confidence intervals. Therefore, the researchers prefer mechanistic models in their studies [3, 5]. Whereas mechanistic models describe the behavior of a system that also contain the parameters with
fatcat:psnvtpnntfhufi32lcixa4nmoe