A 3-D model to predict the temperature of liquid manure within storage tanks
Rennie, T.J., Baldé, H., Gordon, R.J., Smith, W.N., VanderZaag, A.C. (2017). A 3-D model to predict the temperature of liquid manure within storage tanks. Biosystems Engineering, [online] 163 50-65. http://dx.doi.org/10.1016/j.biosystemseng.2017.08.014
Plain language summary
Manure storage systems are a key contributor to greenhouse gas emissions. It is important to model the temperature of manure storage tanks to be able to accurately model greenhouse gas emissions, which are temperature dependent. A 3-D model was developed to determine the temperature distribution in liquid manure storages throughout the year. Several factors were taken into consideration to develop the temperature model, including radiation, heat transfer through walls and floors, as well as heat lost and gained through evaporation and manure loading. Testing was implemented and validated through a study with a circular concrete storage tank in Ontario, Canada, measuring 40 meters in diameter and 2.5 meters deep. On an annual basis, the model estimates were close to the measured temperature, having an average bias of 0.12°C. The model performed best in the summer and autumn, which are the most important seasons for modelling temperature. This is because both the temperature manure and volume are the highest, meaning there is the greatest potential for high greenhouse gas emissions. Through a sensitivity analysis, some of the most significant parts of the model are solar absorptivity, manure depth, the incoming manure temperature, and wind speed. The least significant parameters of the model are the amount of solids in the manure, and thermal conductivity of soil around the bottom and sides of the tank. Results of the study show that heat transfer is primarily 1-dimensional, and a simplified 1-D model would be sufficient for future applications.
A numerical model was developed to determine the year-round temperature distribution within liquid manure storages, which is relevant for modelling temperature-dependent greenhouse gas and ammonia emissions. The model considers net short and long-wave radiation, heat conduction through walls and floor, surface convective heat transfer, evaporative heat loss, and manure loading. The model was implemented and validated for a circular concrete storage tank (40 m diameter; 2.5 m depth) on a dairy farm in Ontario, Canada, where it is assumed that heat transfer occurs in horizontal and vertical directions, and is symmetric in the angular direction. Annual root mean square error (RMSE), Nash–Sutcliffe model efficiency, coefficient of determination, and average bias between model estimates and measured values were 2.4 °C, 0.91, 0.95, and 0.12 °C, respectively. The model performed best in summer and autumn (lowest RMSE), which are the most important seasons for modelling temperature, as both temperature and manure volume are highest, leading to the greatest opportunity for gaseous emissions. A sensitivity analysis indicated that the most significant parameters were solar absorptivity, manure depth, incoming manure temperature, emissivity, and wind-speed. For every unit increase in depth (m), incoming manure temperature (°C), or wind-speed (m s−1), the peak summer temperature changed by −7.3, 0.3, or −2.4 °C, respectively. Parameters with little effect on temperature were the manure solids content and thermal conductivity of soil around the sides and the bottom of the tank. Results show that heat transfer is primarily 1-dimensional, and a simplified 1-D model would be sufficient for future applications.