Development of a mathematical model for predicting bio-slurry temperature and subsequent gas production rate for underground brick-built biogas digester using ambient air temperature forecast

Abstract

Background: Heat energy is essential for the anaerobic digestion of organic materials such as household, human or agricultural waste. Many developing countries have witnessed efforts to implement anaerobic digestion technology for biogas production as a strategy to enhance energy supply and poverty eradication in rural communities. Underground, brick, and mortar built fixed dome type digesters are the most deployed small-scale biogas technology in sub-Saharan Africa (SSA) countries such as Rwanda, Ethiopia, Tanzania, Kenya, Uganda, Burkino Faso, Cameroon, Benin, Senegal, and South Africa despite their relatively high initial costs. They have a long lifespan and no moving or rusting parts involved. The basic design is compact, saves space, is well insulated, and does not need additional heating, hence suitable for developing countries. The technology is labour-intensive that involves digging the pit and constructing the structure from underground, thus creating local employment. Unlike prefabricated biogas digesters, underground, brick, and mortar-built fixed dome type digesters are more robust than the latter, with minimal gas pipes corrosion experienced. However, little literature on this type of digesters' actual field operation and performance within the SSA context is available. The end-user must know what needs to be done and what the system's outcome is supposed to be. Besides determining parameters like total solids, volatile solids, carbon-nitrogen ratio, hydrolysis rate, organic loading rate, and hydraulic retention time, the temperature inside the digester becomes one of the metrics to evaluate the anaerobic digestion process. The digestion temperature critically affects the biogas yield, considering all other conditions unchanged. Knowing the operational temperature, one can estimate the maximum specific growth rate of the microorganisms and the biogas production rate. Prediction models for the internal operating temperature of these digesters under local conditions typical of Limpopo province of South Africa, where most of these digesters have been installed, are still lacking. To ordinary users in rural areas, the prediction of the possible 'duration of use,' for example, the duration of continuous cooking, is essential. However, regardless of fulfilling all other operational requirements to predict daily gas production, internal digester temperature remains the missing link to having a complete set for a quick and easy gas yield estimation. Aim of the study: The overall objective was to develop a locally applicable model for predicting the bio-slurry operating temperature of underground brick-built domestic size biogas digesters. The work established a correlation of ambient air temperature with the slurry temperature inside the digester using a heat transfer mechanism through the media between the fermenting slurry and the ambient air. Methodology: A thermodynamic study of a small-scale fixed-dome Deenbandhu biogas digester model was performed by monitoring the digester's temperature and surroundings. The K-type chromium-nickel temperature sensors with a sensitivity of 41 μV/°C and a response time of 0.8 s in liquids were positioned at the centre of the digester to measure the slurry temperature. Another temperature sensor was placed 2.0 m above the ground to measure ambient air temperature. The sensors were connected to the data logger and programmed to record temperature readings every second, automatically averaged hourly and daily. The soil surface heat flux was computed using Fourier's law of heat conduction to strengthen the model. Results: The average daily bio-slurry temperature of the digesters ranged between psychrophilic and mesophilic ranges. The results show a strong correlation between bio-slurry and ambient air temperature. A strong correlation was obtained between the measured and predicted temperature of the fermenting slurry inside the digester with a ()Pr|t|>value less than 2e-16 ***, showing that the model is most significant. A Q-Q plot was also used to measure the importance of each observation to the regression. Conclusion: The developed models can accurately estimate the bio-slurry temperature inside the digester using local ambient air temperature data. The set equation adds value as input to the research of small-scale household biogas digesters. Furthermore, the biogas production rate was calculated using data on predicted slurry temperature. It was found that the biogas production rate is satisfactory, given the condition of the study area. The biogas production rate varies from as low as 0.18 m3m-3d-1 during the cold month to 0.48 m3m-3d-1 during the warmest month. Temperatures above 20 ℃ were more conducive to a high biogas production rate.