Understanding Factors Affecting the Balance Point (and Rate of Balance Point Approach) of a Diesel Particulate Filter: an Analytical Expression for the Balance Point Soot Loading

Diesel particulate filters (DPF) are commonly used to remove harmful particulate matter (PM) from the exhaust of diesel engines. If the DPF is subjected to a constant inlet condition, under favourable conditions, the soot loading will eventually stabilise at a constant value, when the rate of soot accumulation is matched by the rate of soot oxidation by NO₂; this is known as the balance point. The balance point soot loading (BPSL) is commonly used as a measure of the effectiveness of passive soot oxidation. Generally, the DPF will take a long time to reach the balance point, making determining BPSLs, experimentally or using a 1-dimensional model, extremely time-consuming. This paper offers an alternative. By making some assumptions (constant temperature and through-wall gas velocity along the DPF), an equation allowing instantaneous BPSL prediction is derived, as is an equation predicting the variation in soot loading with time. Both give comparable predictions to a 1-dimensional model. The equation predicts that the BPSL is independent of the substrate, is proportional to the space velocity (but independent of DPF size) and is dependent on NO₂/PM ratio (but independent of NO₂ concentration). Finally, this approximate approach is applied to the prediction of BPSL and evolution of soot loading for a DPF subjected to a repeated transient drive cycle. In this case, it is no longer possible to obtain a simple equation, but still the prediction is obtained much more quickly than with a 1-dimensional model. The prediction is in excellent agreement with the 1-dimensional model.