Emission Control Science and Technology

, Volume 3, Issue 2, pp 171–201 | Cite as

Predicting Pressure Drop, Temperature, and Particulate Matter Distribution of a Catalyzed Diesel Particulate Filter Using a Multi-Zone Model Including Cake Permeability

  • Boopathi S. MahadevanEmail author
  • John H. Johnson
  • Mahdi Shahbakhti


A multi-zone particulate filter (MPF) model was developed to predict pressure drop and PM oxidation of a catalyzed diesel particulate filter (CPF). The MPF model builds upon our previous work (Mahadevan et al., J Emiss Control Sci Technol 1:183–202, 2015; Mahadevan et al., J Emiss Control Sci Technol 1:255–283, 2015) by adding a new multi-zone version of a classical 1-D filtration model (Konstandopoulos and Johnson, 1989) to account for PM filtration within the substrate wall and PM cake of a CPF. In addition, pressure drop (∆P) simulation capability was also developed for the MPF model in order to simulate the pressure drop across the substrate wall and PM cake of the CPF. A cake permeability model was developed based on fundamental research findings in the literature. The PM cake and wall pressure drop simulation accounts for the wall and cake permeability variation during loading, PM oxidation, and an additional post-loading after oxidation. This extended MPF model was calibrated using 18 runs of experimental data from a Cummins ISL engine that consisted of passive and active regeneration data sets for ULSD, B10, and B20 fuels. The validation results show that the new MPF model can predict PM loading with a maximum root mean square (RMS) error of 7.4% and predict (∆P) across the filter with an RMS error of within 7.2%. It is found that the permeability of the PM cake layer increases rapidly during PM oxidation. The increase in permeability was attributed to the damage in the PM cake and was simulated using the newly developed cake permeability model. The increased permeability of the damaged PM cake layer and oxidation of cake PM leads to near zero cake PM pressure drop during PM oxidation for the passive and active regeneration experiments.


Diesel particulate filter model Particulate matter oxidation Pressure drop Cake permeability modeling Substrate wall permeability modeling 



Active regeneration


Diesel blend (ULSD) with 10% biodiesel


Diesel blend (ULSD) with 20% biodiesel


Catalyzed particulate filter


Carbon dioxide


Diesel oxidation catalyst


Diesel particulate filter


Electronic control unit




Multi-zone particulate filter


Michigan Technological University


Nitrogen dioxide


Nitrogen monoxide




On-board diagnostics


Passive oxidation


Particulate matter


Root mean square


Ramp up


Selective catalytic reduction


Ultra-low-sulfur diesel


Pressure drop







The authors would like to thank Kenneth Shiel and James Pidgeon of Michigan Technological University for collecting the temperature distribution data presented in this work and Dr. Kiran Premchand for assistance in understanding his 1-D model simulation of the data presented in this work. We would like to extend our appreciation to the reviewers, whose comments helped us to significantly improve the content.

Compliance with Ethical Standards

Competing Interests

The authors declare that they have no competing interests.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Boopathi S. Mahadevan
    • 1
    Email author
  • John H. Johnson
    • 1
  • Mahdi Shahbakhti
    • 1
  1. 1.Michigan Technological UniversityHoughtonUSA

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