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Machine learning-aided modeling of dry pressure drop in rotating packed bed reactors

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Abstract

The challenge of reducing the carbon footprint of many chemical processes and bringing down their development costs can be achieved through process intensification (PI). Different PI technologies have been investigated over the years with rotating packed bed (RPB) technology receiving much of the attention for its potential of significant intensification in terms of hardware size, capital expenditure and operating costs. In this study, we present a complete derivation of the dry pressure drop in RPB that differs from the published models in considering the radial distribution of the gas tangential velocity as well as the viscous shear stress between gas layers. Aorous media approach is adopted to model the viscous and inertial packing resistance forces. The inertial resistance coefficient is derived using machine learning (ML) techniques based on a part of the published data on RPB dry pressure drop (training set). The data learning step relies on the minimization of the absolute error between the pressure drop evaluated from a one-dimensional mathematical model and experimental data to determine the optimum inertial resistance coefficient. Then, an artificial neural network (ANN) is implemented to relate the inertial resistance coefficient to gas flow rate and rotating speed. Finally, the other part of the published data is used to test and validate the proposed approach based on the total pressure drop. The results show that the error in predicting RPB dry pressure drop using the semiempirical model can be reduced from 25 to 2% when a machine learning algorithm is used to estimate the resistance coefficients instead of relying on Ergun's model.

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Abbreviations

ANN:

Artificial neural network

\({C}_{2}\) :

Inertial resistance coefficient, \(1/\mathrm{m}\)

\(D\) :

Viscous resistance coefficient, \(1/{\mathrm{m}}^{2}\)

\({D}_{h}\) :

Hydraulic diameter, \(\mathrm{m}\)

\(E\) :

Error matrix

\(I\) :

Turbulent intensity, \(\left[-\right]\)

\(J\) :

Jacobian matrix of error

ML:

Machine learning

\(P\) :

Pressure, \(\mathrm{Pa}\)

\(Q\) :

Volume flow rate, \({\mathrm{m}}^{3}/\mathrm{s}\)

\(\text{Re}\) :

Reynolds number, \(\left[-\right]\)

RMSE:

Root mean square error

\(\overline{U }\) :

Total velocity magnitude, \(\mathrm{m}/\mathrm{s}\)

\({a}_{p}\) :

Area density, \({\mathrm{m}}^{2}/{\mathrm{m}}^{3}\)

\(g\) :

Gravitational acceleration, \(\mathrm{m}/{\mathrm{s}}^{2}\)

\(h\) :

Packing height, \(\mathrm{m}\)

\(k\) :

Turbulent kinetic energy, \({\mathrm{m}}^{2}/{\mathrm{s}}^{2}\)

\(l\) :

Characteristic length, \(\mathrm{m}\)

\(r\) :

Radial coordinate, \(\mathrm{m}\)

\(t\) :

Time, \(\mathrm{s}\)

\(u\) :

Absolute velocity, \(\mathrm{m}/\mathrm{s}\)

\(\ddot{u}\) :

Slip velocity, \(\mathrm{m}/\mathrm{s}\)

\(z\) :

Axial coordinate, \(\mathrm{m}\)

\(\epsilon\) :

Turbulent kinetic Energy dissipation, \({\mathrm{m}}^{2}/{\mathrm{s}}^{2}\)

\(\alpha\) :

Permeability, \({\mathrm{m}}^{2}\)

\(\varepsilon\) :

Porosity, \({\mathrm{m}}^{3}/{\mathrm{m}}^{3}\)

\(\gamma\) :

Regularization factor

\(\lambda\) :

Coefficient parameter

\(\mu\) :

Laminar/dynamic viscosity, \(\mathrm{Pa}.\mathrm{s}\)

\({\mu }_{e}\) :

Effective viscosity, \(\mathrm{Pa}.\mathrm{s}\)

\({\mu }_{t}\) :

Eddy viscosity, \(\mathrm{Pa}.\mathrm{s}\)

\(\vartheta\) :

Kinematic viscosity, \({\mathrm{m}}^{2}/\mathrm{s}\)

\(\theta\) :

Output parameter matrix

\(\theta\) :

Angle, \(\mathrm{degree}\)

\(\rho\) :

Density, \(\mathrm{kg}/{\mathrm{m}}^{3}\)

\(\omega\) :

Angular velocity, \(\mathrm{rad}/\mathrm{s}\)

\(\Omega\) :

Rotating speed, rpm

\(ie\) :

Inner edge

\(oe\) :

Outer edge

\(r\) :

Radial direction

\(z\) :

Axial direction

\(\theta\) :

Tangential direction

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Acknowledgements

The authors acknowledge the financial support from Khalifa University of Science and Technology through the grant No. CIRA-2019-031 and the support from Khalifa University of Science and Technology through the grant No. RC2-2018-024.

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Authors and Affiliations

  1. Mechanical Engineering Department, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE

    Ahmed M. Alatyar & Abdallah S. Berrouk

  2. Center for Catalysis and Separation (CeCas), Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE

    Abdallah S. Berrouk

  3. Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Tanta, P.O. Box 31521, Egypt

    Ahmed M. Alatyar

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  1. Ahmed M. Alatyar
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  2. Abdallah S. Berrouk
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Correspondence to Abdallah S. Berrouk.

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Alatyar, A.M., Berrouk, A.S. Machine learning-aided modeling of dry pressure drop in rotating packed bed reactors. Acta Mech 234, 1275–1291 (2023). https://doi.org/10.1007/s00707-022-03428-8

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