Improved Pressure Drop Modeling During Regeneration of Particulate Filters Using Soot Cake with Variable Porosity

Previous models of regeneration in a diesel particulate filter (DPF) assume that the porosity of the soot cake remains constant throughout the process and the pressure drop contribution from the soot cake is proportional to its mass/thickness. In several recent studies, it was shown that the constant porosity model was not able to capture the pressure drop trend during soot oxidation. At the beginning of regeneration, the experimental pressure drop curves exhibit a convex shape which may be interpreted as the soot cake becoming denser due to compaction. Due to the changing density, traditional models underpredict the pressure drop during this early phase of regeneration. Experimental results have also shown that, at a later phase of regeneration, the pressure drop approaches the clean-filter value before the soot mass is completely consumed, possibly due to the opening of pores in the soot cake. A pressure drop contribution from the soot cake that is negligible while significant mass remains in the soot cake violates the proportionality between pressure drop and mass/thickness that the conventional model upholds as the soot depletes. This work seeks to address these physical observations by introducing a new model incorporating variable soot cake porosity and a replacement of the Kuwabara function for improved performance in predicting pressure drop during both phases of regeneration. In the new model, porosity is a function of the relative mass in the soot cake and decreases during the initial phase to capture the compaction of the soot cake. The function to replace the Kuwabara function is a power law that breaks the proportionality between pressure drop and mass allowing for the clean-filter pressure drop to be reached before the soot cake is fully consumed. In this study, it will be shown that the new interpretation of the regeneration mechanism is highly effective in improving the correlation between the observed pressure drop and its predictions.