Department of Chemical Engineering and Analytical Chemistry, University of Barcelona, 08028, Barcelona, Spain.
Department of Chemical Engineering and Analytical Chemistry, University of Barcelona, 08028, Barcelona, Spain; Department of Chemistry and Bioscience, Centre for Microbial Communities, Aalborg University, 9220, Aalborg, Denmark.
Chemosphere. 2022 Nov;306:135579. doi: 10.1016/j.chemosphere.2022.135579. Epub 2022 Jul 2.
The Gamma model is a novel approach to characterise the complex degradation dynamics taking place during anaerobic digestion. This three parameters model results from combining the first-order kinetic model and the Gamma distribution function. In contrast to conventional models, where the kinetic constant is considered invariant, the Gamma model allows analysing the variability of the kinetic constant using a probability density function. The kinetic constant of mono-digestion and co-digestion batch tests of different wastes were modelled using the Gamma model and two common first-order models: one-step one-fraction model and one-step two-fraction model. The Gamma distribution function approximates three distinct probability density functions, i.e. exponential, log-normal, and delta Dirac. Specifically, (i) cattle paunch and pig manure approximated a log-normal distribution; (ii) cattle manure and microalgae approximated an exponential distribution, and (iii) primary sludge and cellulose approximated a delta Dirac distribution. The Gamma model was able to characterise two distinct waste activated sludge, one approximated to a log-normal distribution and the other to an exponential distribution. The same cellulose was tested with two different inocula; in both tests, the Gamma distribution function approximated a delta Dirac function but with a different kinetic value. The potential and consistency of Gamma model were also evident when analysing pig manure and microalgae co-digestion batch tests since (i) the mean k of the co-digestion tests were within the values of the mono-digestion tests, and (ii) the profile of the density function transitioned from log-normal to exponential distribution as the percentage of microalgae in the mixture increased.
Gamma 模型是一种新颖的方法，用于描述厌氧消化过程中发生的复杂降解动态。该三参数模型是通过将一级动力学模型和 Gamma 分布函数相结合而得出的。与传统模型不同，传统模型中认为动力学常数是不变的，而 Gamma 模型允许使用概率密度函数分析动力学常数的可变性。使用 Gamma 模型和两种常见的一级模型（单步单分数模型和单步双分数模型）对不同废物的单消化和共消化批量测试的动力学常数进行了建模。Gamma 分布函数近似三个不同的概率密度函数，即指数、对数正态和 delta Dirac。具体来说，（i）牛胃和猪粪近似于对数正态分布；（ii）牛粪和微藻近似于指数分布，（iii）初沉污泥和纤维素近似于 delta Dirac 分布。Gamma 模型能够描述两种不同的活性污泥，一种近似于对数正态分布，另一种近似于指数分布。同一种纤维素用两种不同的接种物进行了测试；在这两种测试中，Gamma 分布函数近似于 delta Dirac 函数，但动力学值不同。当分析猪粪和微藻共消化批量测试时，Gamma 模型的潜力和一致性也很明显，因为（i）共消化测试的平均 k 值在单消化测试的范围内，（ii）随着混合物中微藻百分比的增加，密度函数的分布从对数正态分布转变为指数分布。
