Development and Application of a Mathematical Model for the Quantification of Induced Air and Its Extraction at Bulk Material Transfer Points

Abstract One of the most used methods to mitigate fugitive dust during bulk material transfers is the extraction of air generated by the falling material, where the airflow is defined by matching it to the calculation of induced air in a confined space. The motivation behind this study arises from the lack of a mathematical model to quantify the induced air in transfers with wide or no confinement, as well as the limitations identified in traditional theoretical-empirical formulations used for transfers with narrow confinement. These equations do not consider the material trajectory, rock beds, high velocity, high material flow, or the actual behavior of the airflow during the transfer process and after impact in the receiving area. This study shifts the focus towards developing a mathematical model that considers the material trajectory and the theoretical physical concept of induced airflow. The objective is to obtain, for the first time, a mathematical model to quantify the volume of induced air during the dynamic process of bulk material transfer in unconfined or widely confined spaces. This equation provides the upper limit of the induced area, allowing its applicability to be extended to scenarios with narrow confinement using one of the traditional equations. The model was validated through flow analysis and measurements in a transfer between conveyor belts. The results indicate a significant improvement in the accuracy of the estimated induced air volume compared to previous methods, demonstrating its applicability in various material transfer scenarios. Specifically, this model covers an area not previously addressed, such as the model for induced air without confinement or with wide confinement, which allows for the calculation of the upper induced area and the determination of recirculation efficiency in any transfer with narrow confinement. In other words, it allows for a more accurate determination of the air to be extracted. The underlying premise of the model is based on the principle that, during the free-fall of the material occurring in a defined lapsus of time, all the natural interstices of the material are occupied by the surrounding air, causing a difference between the initial volume of the material and the final volume due to expansion which, in turn, determines the volume of air induced per unit of time incorporated after the impact.