First derivative of Gompertz equation: Identification of substrate fractions in psychrophilic anaerobic digestion

Abstract

The biochemical methane potential (BMP) test is widely used to model methane production from organic wastes during anaerobic digestion (AD), often with the Modified Gompertz (MG) kinetic model. Further analysis of the MG model can provide critical insights into the hydrolysis and methanogenic stages of AD. While BMP tests are traditionally conducted at mesophilic temperatures, conducting them at the inoculum source temperature has been recommended. This study evaluated the BMP of waste activated sludge (WAS), organic kitchen waste (OKW), and two co-digestion ratios (Co-D1: 65/35 % OKW/WAS; Co-D2: 35/65 % OKW/WAS) at a psychrophilic temperature of 20 °C. A novel spreadsheet-based approach utilizing the first derivative of the Gompertz equation identified substrate fractions, kinetic constants and AD stages insights. Co-digestion prevented media acidification and enhanced methane yields, with Co-D2 producing 261.0 mLCH₄/g-VSadd—significantly higher than WAS (192.8) and OKW (81.2). These yields are comparable to those from similar substrates under mesophilic conditions (35–37 °C), underscoring the energy potential of psychrophilic co-digestion. The kinetic constants achieved coefficients of determination exceeding 0.90. The first derivative method identified two substrate fractions: readily and slowly biodegradable organic matter. This research provides new insights into anaerobic microbial dynamics and substrate degradation pathways, demonstrating the effectiveness of psychrophilic co-digestion for methane production.