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Model-Based Optimization of Ammonia Dosing in NH3-SCR of NO x for Transient Driving Cycle: Model Development and Simulation

  • SPECIAL ISSUE: 2017 MODEGAT SEPTEMBER 3-5, BAD HERRENALB, GERMANY
  • Published:
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Abstract

The ability to catalytically reduce NO x efficiently with ammonia (NH3) has made the selective catalytic reduction (SCR) technology indispensable in diesel after-treatment systems. Ammonia is dosed periodically in the form of urea which decomposes to ammonia and reacts with NO x . During the application of real-world driving cycles, owing to fast transients of the emissions, it is not efficient to dose constant amount of ammonia. An efficient optimized dosing strategy is quite essential to improve the efficiency and contain the NH3 excursions within the permissible limits. Development of such an optimized dosing solution requires the usage of simple yet powerful mathematical models capable of simulating the process with reasonable accuracy and robust optimization schemes, which can ensure optimal solutions in spite of having high number of parameters to be optimized. Several efficient model reduction techniques presented in the literature have been used to obtain a grey-box model which can effectively simulate the process. Direct collocation method based on Orthogonal Collocation over Finite Elements (OCFE) is used to transform the Differential Algebraic Equation-constrained optimization problem into a nonlinear program. The developed model is applied to the World Harmonic Transient Driving cycle to optimize NH3 dosing for each second of the driving cycle. The obtained optimal dosing solution not only improved the efficiency of the process but also maintained the NH3 excursions below 10 ppm over the entire driving cycle. The developed methodology is applicable to other systems to obtain such large-scale optimal solutions efficiently.

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Abbreviations

A if :

Forward kinetic pre-exponential, [mol/m2 s]

A ib :

Backward kinetic pre-exponential, [mol/m2 s]

c p :

Specific heat capacity of the mixture, [J/kg K]

c s :

Specific heat capacity of the solid phase, [J/kg K]

c T :

Total concentration, [mol/m3]

D eff :

Vector of effective diffusivity coefficient, [m2/s]

d h :

Hydraulic diameter, [m]

E if :

Forward activation energy, [J/mol]

E ib :

Backward activation energy, [J/mol]

k me :

Vector of external mass transfer coefficient of species, [m/s]

k mi :

Vector of internal mass transfer coefficient of species, [m/s]

k mo :

Vector of overall mass transfer coefficient of species, [m/s]

k if :

Forward rate constant, []

k ib :

Backward rate constant, []

l :

Lagrange polynomial, [–]

L:

Channel length, [m]

n c :

Number of collocation points, [–]

n e :

Number of finite elements, [–]

P :

Pressure, [Pa]

u :

Time-dependent control parameters, [–]

PP :

Vector of dimensionless constants, [–]

R :

Vector of reaction rates, [mol/m2 s]

S :

Vector of the rate of production of the species, [mol/m2 s]

Sh :

Sherwood number, [–]

Sh int :

Internal Sherwood number, [–]

Sh int , ∞ :

Asymptotic Sherwood number, [–]

SS :

Vector of dimensionless constants, [–]

T f :

Gas-phase temperature, [K]

T f , 0 :

Inlet gas-phase temperature, [K]

u :

Velocity, [m/s]

X :

Conversion, [–]

X f :

Vector of species mole fraction in gas phase, [–]

X s :

Vector of species mole fraction in solid phase, [–]

\( {X}_{{\mathrm{NO}}_x} \) :

NO x conversion, [–]

y :

Vector of algebraic variables, [–]

z :

Vector of state variables, [–]

β :

Vector of independent variables, [–]

δ wc :

Washcoat thickness, [m]

ε g :

Volume fraction of the channel, [–]

ε wc :

Washcoat porosity, [–]

\( {\theta}_{{\mathrm{NH}}_3} \) :

Surface coverage of adsorbed ammonia, [–]

Λ :

Geometric constant, [–]

τ :

Normalized time, [–]

\( {\varOmega}_{{\mathrm{NH}}_3} \) :

Adsorption capacity of ammonia, [mol/m3]

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Acknowledgements

This work was funded by the German Ministry of Education and Research in the framework of the ReffKat project (grant number 03X3563B). Especially we would like to thank our project partner Martin Votsmeier (Umicore) for coordination and discussion.

Author information

Authors and Affiliations

  1. Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany

    Sivaram Kannepalli & Olaf Deutschmann

  2. Faculty of Management Science and Engineering, Karlsruhe University of Applied Sciences, Karlsruhe, Germany

    Adrian Bürger

  3. Department of Microsystems Engineering, University of Freiburg, Freiburg im Breisgau, Germany

    Adrian Bürger

  4. Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany

    Steffen Tischer & Olaf Deutschmann

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Correspondence to Steffen Tischer.

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Appendix

Appendix

The gas-phase NO species balance Eq. (19) from Sect. 2.3 can be written as Eqs. (42) and (43)

$$ \frac{u}{\varDelta z}\left({X}_{\mathrm{f},\mathrm{NO}}-{X}_{\mathrm{f},\mathrm{NO}}^{\mathrm{in}}\right)=\frac{-4{k}_{\mathrm{mo},\mathrm{NO}}}{\varepsilon_{\mathrm{g}}}\left({X}_{\mathrm{f},\mathrm{NO}}-{X}_{\mathrm{s},\mathrm{NO}}\right) $$
(42)
$$ {P}_{\mathrm{NO}}\left({X}_{\mathrm{f},\mathrm{NO}}-{X}_{\mathrm{f},\mathrm{NO}}^{\mathrm{in}}\right)=-\left({X}_{\mathrm{f},\mathrm{NO}}-{X}_{\mathrm{s},\mathrm{NO}}\right) $$
(43)

And upon further simplification, outlet composition of NO in gas phase can be written as a function of inlet NO composition and NO composition in the solid phase.

$$ {X}_{\mathrm{f},\mathrm{NO}}=\frac{P_{\mathrm{NO}}\cdot {X}_{\mathrm{f},\mathrm{NO}}^{\mathrm{in}}+{X}_{\mathrm{s},\mathrm{NO}}}{1+{P}_{\mathrm{NO}}} $$
(44)

Analogously similar Eqs. (44) and (45) can be obtained for NO2 and NH3

$$ {X}_{\mathrm{g},{\mathrm{NO}}_2}=\frac{P_{{\mathrm{NO}}_2}\cdot {X}_{{\mathrm{NO}}_2}^{\mathrm{in}}+{X}_{\mathrm{s},{\mathrm{NO}}_2}}{1+{P}_{{\mathrm{NO}}_2}} $$
(45)
$$ {X}_{\mathrm{g},{\mathrm{NH}}_3}=\frac{P_{{\mathrm{NH}}_3}\cdot {X}_{{\mathrm{NH}}_3}^{\mathrm{in}}+{X}_{\mathrm{s},{\mathrm{NH}}_3}}{1+{P}_{{\mathrm{NH}}_3}} $$
(46)

From the species conservation Eq. (20) in the solid phase for NO, NO2, and NH3 can be expressed as Eqs. (47), (48), and (49).

$$ {\displaystyle \begin{array}{c}\hfill \frac{-{c}_{\mathrm{T}}\cdot {k}_{\mathrm{mo},\mathrm{NO}}}{\delta_{\mathrm{wc}}}\left({X}_{\mathrm{f},\mathrm{NO}}-{X}_{\mathrm{s},\mathrm{NO}}\right)=-{k}_{3f}\cdot {X}_{\mathrm{s},{\mathrm{O}}_2}^{0.5}\cdot {X}_{\mathrm{s},\mathrm{NO}}-4{k}_{4f}\cdot {X}_{\mathrm{s},\mathrm{NO}}\cdot \theta \hfill \\ {}\hfill -{k}_{5f}\cdot {X}_{\mathrm{s},\mathrm{NO}}\cdot {X}_{\mathrm{s},{\mathrm{NO}}_2}\cdot \theta +{k}_{3b}\cdot {X}_{\mathrm{s},{\mathrm{NO}}_2}\hfill \end{array}} $$
(47)

Substituting (43) in (46) and upon simplification, we obtain Eq. (26). Similarly for NO2 substituting (43) and (44) in (47), we obtain Eq. (24), and by following the same procedure and substituting (45) in (48), we obtain Eq. (22).

$$ {\displaystyle \begin{array}{c}\hfill \frac{-{c}_{\mathrm{T}}\cdot {k}_{\mathrm{mo},{\mathrm{NO}}_2}}{\delta_{\mathrm{wc}}}\left({X}_{\mathrm{f},{\mathrm{NO}}_2}-{X}_{\mathrm{s},{\mathrm{NO}}_2}\right)={k}_{3f}\cdot {X}_{\mathrm{s},{\mathrm{O}}_2}^{0.5}\cdot {X}_{\mathrm{s},\mathrm{NO}}-{k}_{3b}\cdot {X}_{\mathrm{s},{\mathrm{NO}}_2}\hfill \\ {}\hfill -4{k}_{4f}\cdot {X}_{\mathrm{s},\mathrm{NO}}\cdot \theta -{k}_{5f}\cdot {X}_{\mathrm{s},\mathrm{NO}}\cdot {X}_{\mathrm{s},{\mathrm{NO}}_2}\cdot \theta -3{k}_{6f}\cdot {X}_{\mathrm{s},{\mathrm{NO}}_2}\cdot \theta \hfill \end{array}} $$
(48)
$$ \frac{-{c}_{\mathrm{T}}\cdot {k}_{\mathrm{mo},{\mathrm{NH}}_3}}{\delta_{\mathrm{wc}}}\left({X}_{\mathrm{f},{\mathrm{NH}}_3}-{X}_{\mathrm{s},{\mathrm{NH}}_3}\right)=-{k}_{1\mathrm{f}}\cdot {X}_{\mathrm{s},{\mathrm{NH}}_3}\cdot \left(1-\theta \right)+{k}_{1\mathrm{b}}\cdot \theta $$
(49)

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Kannepalli, S., Bürger, A., Tischer, S. et al. Model-Based Optimization of Ammonia Dosing in NH3-SCR of NO x for Transient Driving Cycle: Model Development and Simulation. Emiss. Control Sci. Technol. 3, 249–262 (2017). https://doi.org/10.1007/s40825-017-0072-4

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