Kinetic Parameter Identification for a DOC Catalyst Using SGB test and Advanced Optimization Algorithms

Kinetic Parameter Identification for a DOC Catalyst Using SGB test and Advanced Optimization Algorithms Mahsa RAFIGH - Politecnico di Torino Federico MILLO - Politecnico di Torino Paolo FERRERI General Motors Global Propulsion Systems Eduardo Jose BARRIENTOS BETANCOURT - General Motors Global Propulsion Systems Marcello RIMONDI - General Motors Global Propulsion Systems NA GT-Conference Plymouth, MI, United States November 6 th, 2017

Introduction: Need for Aftertreatment Modelling In order to develop simulation models capable of reliably predicting performance and emissions of innovative diesel powertrain systems, the following steps are required for aftertreatment systems modelling: Definition of suitable Synthetic Gas Bench (SGB) test protocols Development and calibration of kinetic mechanisms based on SGB data using optimization tools Validation of the model on full scale component data using engine-out emissions over driving cycles Sample Extraction Reactor-scale Tests Simulation Model Model Calibration Validation of the model from roller bench data

Test case: DOC with zone coating Characteristic Unit Front Zone Rear Zone Core size: diameter x length in x in 1 x 3 1 x 3 Washcoat loading - 1.2 x REF REF PGM - Pt and Pd Pt Cells density [cpsi] 400 400 Wall thickness [mil] 4.5 4.5 Substrate material [-] cordierite cordierite Zeolite coating [-] 3

Synthetic Gas Bench (SGB) tests SGB test protocols are defined with the aim to decouple the effects of different mechanisms, by feeding the catalyst sample with controlled species concentrations, flow rates and temperatures, thus facilitating the model calibration process. Cylindrical reactor-size components are extracted from full-scale monolith maintaining the length of the sample. Gas concentration were measured with a multicomponent FTIR, 1 Hz sampling frequency. Scale: 1 inch Gas are sampled upstream and downstream of the sample. Temp probes at sample inlet and outlet

Synthetic Gas Bench (SGB) tests SGB test protocols include HC storage tests and light-off tests Heavy HC Storage tests (TPD) (4 tests) Light-off tests (2x24 = 48 tests for each core) Base feed: 4.5% H 2 O, 4.5% CO 2, Balanced N 2 400 and 800 ppmc 1 C 10 H 22 Inlet T ramp 90/120 C 400 C, rate = 5 C/min Base feed: 12% O 2, 4.5% H 2 O, 4.5% CO 2, Balanced N 2 Inlet T ramp 80 C 400 C, rate = 5 C/min SV: 30 and 60 k/hr @ T = 273 K, p = 1 atm Standard SV: 30 k/hr @ T = 273 K, p = 1 atm

1D Simulation Model Assumptions A 1D-CFD model using GT-SUITE is built based on the following assumptions: Neglect non-homogeneity and non-uniformity of flow and thermal field in a cross-section Only variations along the catalyst length (x) Governing equations: continuity, momentum, solid and gas energy balances Quasi-steady approximation Global kinetic mechanism Reaction rates: Arrhenius form: Objective function defined for the calibration of kinetic parameters to be minimized by means of suitable calibration method

Models for zone coating Due to differences in formulation of each core (front and rear) in terms of washcoat, zeolite coating, PGM loading and PGM ratio, 2 separate kinetic models were built for each core with different calibration and optimization runs. DOC front The model of the full-size component used for the engine-scale simulation is then built by combining the models of the two catalyst zones Full-scale Model DOC rear

Simulation model: reaction schemes The following 11 reactions are considered in a DOC model: The following parameters have to be identified: 21 pre-exponent multiplier and activ. energy 2 site densities (zeolite and PGM) 7 exponent of inhibition terms 16 parameters for inhibition terms 46 parameters for front core and 42 parameters for rear core 8

Kinetic Scheme and Calibration Guideline Overall 46 parameters are unknown for the front core with zeolite coating Thanks to suitable definition of test protocols, a stepby-step guideline for the calibration of kinetic parameters is defined such that in each step a reduced number of unknowns are optimized: 1 2 3 HC storage reactions using TPD tests Oxidation reactions using single species light-off tests Inhibition terms for oxidation reactions using 2 species light-off tests 4 HC reactions with NO x

Calibration Approaches 10 For the identification of the optimal values for the kinetics parameters the following approaches were evaluated: Manual/ Trial and Error Time consuming May results in local minimum Requires deep knowledge of kinetics DoE Numerical Methods Direct Search Methods Explorative Methods Includes an initial exploration of the variables domain in their routines Running full test matrix not smart Time consuming When the analytical expression of the function to be optimized is known, numerical methods can be used. Linear or quadratic programming Some examples: Brent method, Newton Method Based on iterative algorithms moving along a certain direction to reach minimum Used for smooth and continuous objective functions Possibility to be trapped in a local minimum Some examples: Hooke-Jeeves Direct Search, Discrete-grid bisection, Implies a systematic exploration of the variables domain Used for complex and non-linear systems Reaching global minimum Some examples: Genetic Algorithm, selected for the DOC model

Use of Genetic Algorithm for Model Calibration An automatic and smart optimization procedure is adopted with the aim to find the optimized independent variables (unknowns) such that the objective function defined based on the error between simulated and measured concentration of each species, using suitable weighting factor, is minimized. Genetic Algorithm (GA) embedded in GT-SUITE is an appropriate approach, since the final results do not depend on the initial guess and therefore global minimum can be achieved. Depending on the number of independent variables optimization settings can be defined as follows: Mutation rate: 1/(# independent variables) Generations: starting from 20 and increasing up 35 (depending on the convergence) tt eeeeee OOOOOOOOOOOOOOOOOO FFFFFFFFFFFFFFFF = CC mmmmmmmmmmmmmmmm CC ssssssssssssssssss 00 dddd

Example: C 10 H 22 and NO x reactions Calibration of C 10 H 22 and NO x reactions on the basis of SGB tests # 16 & 17 4 kinetic parameters + 5 inhibition parameters 9 parameters The objective function is defined using suitable weighting factors for each specie: tt eeeeeeww11 OOOOOOOOOOOOOOOOOO FFFFFFFFFFFFFFFF = CC mmmmmmmmmmmmmmmm CC ssssssssssssssssss + WW NNOOxx 22 CC mmmmmmmmmmmmmmmm CC ssssssssssssssssss NN22OO + WW 33 CC mmmmmmmmmmmmmmmm CC ssssssssssssssssss dddd CC1111HH2222 00 12

Example: C 10 H 22 and NO x reactions Optimization Settings Value Mutation Rate 0.1 Population Size 80 Number of Generations 20 (increased up to 30) Total Number of Iterations Simulation Run Time 80 x 20 =1600 (increased up to 2400) ~ 26 hours * number of cases optimized/ number of licenses used at a time Mutation rate: 1/(# independent variables) Population size: > 50 for # ind var greater than 5 Generations: starting from 20 and increasing up 35 on a processor: Intel (R)Core(TM) i7 4600U CPU @2.10GHz 2.70 GHz 13

Results An example of results for a validation point (not included in the calibration) for the rear core and the front core samples.

Scaling from Reactor-Scale to Full-Size: Limitations and Assumptions The calibrated model based on SGB data can be transferred to full-size component for validation over driving cycles, paying attention to the issues listed here below. References [1]P. Kočí, V. Novák, F. Štěpánek, M. Marek, M. Kubíček, Multi-scale modelling of reaction and transport in porous catalysts, Chem. Eng. Sci. 65 (2010) 412 419. doi:10.1016/j.ces.2009.06.068. [2] D. Kryl, P. Koc, Kryl - Catalytic converters for automobile diesel engines with adsorption of hydrocarbons on zeolites.pdf, (2005) 9524 9534. [3] T. Gu, V. Balakotaiah, Impact of heat and mass dispersion and thermal effects on the scale-up of monolith reactors, Chem. Eng. J. 284 (2016) 513 535. doi:10.1016/j.cej.2015.09.005. Possible sources of different results between reactor-size and full-scale model: Absence of pore diffusion model in washcoat layer may lead to higher conversions [1,2] Non-uniformity of flow and temperature field in full-size component [3] affecting kinetics [4] J. Sjöblom, Bridging the gap between lab scale and full scale catalysis experimentation, Top. Catal. 56 (2013) 287 292. doi:10.1007/s11244-013-9968-6. [5] C.S. Sampara, E.J. Bissett, M. Chmielewski, D. Assanis, Global kinetics for platinum diesel oxidation catalysts, Ind. Eng. Chem. Res. 46 (2007) 7993 8003. doi:10.1021/ie070642w. The engine exhaust gas includes a mixture of different gas species, expecially for HC [4] Presence of external heat transfer in the full-size component [4] Different ageing status of the catalyst components [5]

Conclusions A methodology for the kinetic parameter identification for a DOC catalyst using SGB tests and advanced optimization algorithms was developed and successfully applied to a zone coated DOC. Two different SGB test protocols were used including HC storage tests (only for cores with zeolite coating) and light-off tests for a total of about 50 tests for each catalyst. From 42 to 46 kinetic parameters needed to be identified for the 11 reactions used in the model. The kinetic parameters were identified in the following sequence, by means of GA optimization algorithms, targeting the minimization of error functions comparing measured and simulated concentrations of the main chemical species: 1.HC storage reactions using TPD tests 2.Oxidation reactions using single species light-off tests 3.Exponents of inhibition terms for oxidation reactions using 2 species light-off tests 4.HC reactions with NO x Finally, caveats & guidelines were provided for the up-scaling of the calibrated model based on SGB data to the fullsize component for validation over driving cycles.

Aknowledgments This work has been carried out as part of the PhD thesis Exhaust Aftertreatment Modeling for Efficient Calibration in Diesel Passenger Car Applications defended at Politecnico di Torino on June, 27 th 2017 by Mahsa Rafigh, and of the Research Project GT-Power 1-D kinetics modeling improvements of LNT systems, both funded by General Motors Global Propulsion Systems, which is gratefully acknowledged for the financial support and for providing the experimental data for models calibration and validation. The authors would also like to gratefully acknowledge Gamma Technologies for the valuable support provided, and in particular Syed Wahiduzzaman and Ryan Dudgeon for their precious suggestions and remarks.