In-storage-psychrophilic-anaerobic-digestion (ISPAD) is a treatment system applicable to wastewaters stored for a period of over 100 days, such as livestock wastes and municipal sludge. The ISPAD system consists of a storage tank covered by an airtight geo-membrane, filled as a sequentially batch fed system and emptied when full except for a 0.3 m depth to inoculate the next batch. Thus, ISPAD operates at a temperature fluctuating with ambient, and its microbial community is acclimated to low temperatures. Taking advantage of existing structures and requiring little technical supervision because of its low operating temperatures, ISPAD is an anaerobic digestion (AD) system feasibly accessible to operations producing limited amount of organic wastewaters. Since ISPAD operates under conditions which are totally different as compared to conventional AD reactors, optimal management practices need to be developed through microbial kinetic estimation and process modelling. The first objective was to evaluate the microbial behaviour of the ISPAD system by estimating its kinetic coefficients. The second and third objectives were to develop and validate a mathematical model to simulate the ISPAD process, such as the volatile fatty acid (VFA) concentration and pH of its content and its CH4 production, based on its specific microbial kinetics. The final project objective was to predict and experimentally test conditions which lead to ISPAD content acidification to limit ammonia (NH3) volatilization from the digestate. The first part of the project consisted of determining microbial kinetic values by fitting the Monod model to results obtained from laboratory substrate activity test (SAT) using ISPAD inoculum and for temperatures of 8, 18 and 35 ºC. The fitting process consisted of: applying the decomposition principle to prioritize the determination of kinetic parameters, and then using the statistical least square error procedure to minimize the sum of squared errors between the measured ISPAD experimental data and the Monod model results. The results produce microbial kinetic values specific to the ISPAD system and associated with two groups of microbial population, one acclimated to cold and another to the mesophilic conditions. The second part of the project consisted of developing a mathematical model based on that of Keshtkar et al. (2001). Simulation of ISPAD was achieved using the Simulink/Matlab software to predict glucose, VFAs degradation, pH and CH4 production. To predict the pH of the ISPAD content, a function was introduced based on optimized dissociation constants () for the major ions found in organic wastewaters under AD. Finally, a temperature function was added for most kinetic values to simulate the ISPAD process for temperatures ranging from 4 to 35 ºC. For this purpose, the Arrhenius and Square-Root Equations were compared. For the maximum microbial growth rate (), the Square Root Equation better represented acidogens and propionate degrading acetogens, while the Arrhenius Equation better represented the methanogens and butyrate degrading acetogens. The model was calibrated using experimental data, where ISPAD content and glucose was used as inoculum and substrate, respectively. The proposed model showed good agreement with the experimental data in predicting biogas generation, substrate consumption and pH at a temperature range of 4 to 35 ºC. Although microbial activity at 4 °C was much less than that at 18 and 35 ºC, it showed acclimation to lower temperature. The third part of the project validated the ISPAD model using condition, which differed from those used for calibration, such as a different concentration of substrate. The model accuracy was checked mathematically by determining the coefficient of determination. The ISPAD model was able to predict glucose degradation, VFAs, pH, and methane. However, the model weakly predicts CO2 production for the first 2 days likely because of its water solubility. The final portion of the method dealt with ISPAD content acidification, to reduce NH3 volatilization from the digestate upon removal from the system. Acidification was based on quickly increasing the sequential organic load (OL), under specific temperatures to favour acidogen growth and VFA accumulation. A mathematical equation was applied to the ISPAD model to optimize different OL strategies, where glucose was fed to simulate the hydrolysis of sugar rich wastes. By comparing with laboratory experiments, ISPAD model prediction was found adequate in selecting optimal acidification OL strategies, but did not predict accumulation of intermediate substrates, which produced a lag in pH drop, and generates a pH drop below 6.0, because of set values for its pH inhibition function. Nevertheless, sequentially feeding 13 kg glucose/m3 of ISPAD content over 4 days was found to drop the pH of the ISPAD content to 6.0 by day 7. Such OL competes favorably against present acidification techniques such as that using concentrated sulfuric acid. The contribution to knowledge of this work was introducing the decomposition method to determine AD microbial kinetics; for ISPAD, establishing microbial kinetics, ion dissociation constants for pH prediction, and parameter variation with temperature producing an accurate model to predict and optimize the ISPAD process, and determination of sequential OL strategies to feasibly acidify the ISPAD content to lower NH3 volatilization from its digestate upon system removal.