Skip to main content
SpringerLink
Log in

Optimal time-varying cell-voltage control of a parallel-plate reactor

  • Papers
  • Published:
Journal of Applied Electrochemistry Aims and scope Submit manuscript

Abstract

As a means to illustrate the calculation of an optimal cell-voltage control for a parallel-plate reactor, we determine the time-varying cell voltage that maximizes p-aminophenol produced from the electroreduction of nitrobenzene in a differential-conversion reactor operated in a batch mode; that is, the electrolyte is continuously recirculated from a batch holding tank through the reactor in which a low conversion per pass occurs. A rationale is given for restricting the search for the optimal control for this particular reaction network to a chattering-cell voltage that switches between a priori chosen minimum and maximum values. The optimal, time-varying duty cycle is computed using a gradient-search technique. The predicted concentrations are dependent upon the reaction time; for the conditions examined here, an improvement of twenty-five percent in the production and nine-hundred percent in the selectivity of p-aminophenol may be achieved by using the optimal, time-varying voltage in comparison to the best steady value. Since a chattering control is a mathematical construct, we illustrate that a rectangular, high-frequency waveform may be applied to yield results which are indistinguishable from those effected by a chattering cell voltage. The period of the waveform must be short enough so that surface concentrations are time invariant over it and yet, simultaneously, must be long enough so that double-layer charging does not account for a significant passage of coulombs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

cathode surface area per unit volume of electrolyte (cm−1)

C :

electrode capacitance (µF cm−2)

c i :

bulk concentration of species i (mol cm−3)

c i 0 :

initial concentration of species i (mol cm−3)

c is :

concentration of species i at electrode surface (mol cm−3)

E a :

anode potential (V)

E c :

cathode potential (V)

f :

F/RT (V−1)

F :

Faraday constant (96 487 C mol−1)

i :

current density (A cm−2)

I :

current (A)

I k :

kth value of a chattering current (A)

I eff :

current efficiency

i k :

kth value of a chattering i (A cm−2)

k 1 :

heterogeneous rate constant for the reaction NB → PHA (cm s−1)

k 2 :

heterogeneous rate constant for the reaction PHA → AN (cm s−1)

k 3 :

homogeneous rate constant for the reaction PHA → PAP (s−1)

k mi :

mass-transfer coefficient of species i (cm s−1)

R :

gas constant (8.314J mol−1 K−1)

R j :

kinetic resistance at electrode j (Ω cm2)

R Ω :

ohmic resistance (Ω cm2)

r i :

reaction rate for species i (mol cm−3 s−1 for homogeneous reaction, and mol cm−2 s−1 for heterogeneous reaction)

T :

temperature (K)

t :

time (s)

t f :

batch reaction time (s)

u i :

ith component of control vector u

u ci :

exp (−αiϕE c)

V :

cell voltage (V)

V :

V k

kth:

value of a chattering-cell voltage (V)

θ(t):

duty cycle for a chattering control

Ω:

duty cycle for a rectangular waveform

Δt :

period of the rectangular waveform (s)

α:

transfer coefficient (Equations 1–4)

0:

indicates exchange current

a:

anode

c:

cathode

References

  1. P. S. Fedkiw and W. D. Scott, J. Electrochem. Soc. 131 (1984) 1304.

    Google Scholar 

  2. T. R. Nolen and P. S. Fedkiw, J. Appl. Electrochem. 20 (1990) 370.

    Google Scholar 

  3. J. C. Smeltzer and P. S. Fedkiw, J. Electrochem. Soc. 139 (1992) 1358.

    Google Scholar 

  4. Idem, 139 (1992) 1366.

    Google Scholar 

  5. R. Bakshi and P. S. Fedkiw, J. Appl. Electrochem. 23 (1993) 715.

    Google Scholar 

  6. R. Bakshi, PhD. dissertation, North Carolina State University, Raleigh, NC (1992).

    Google Scholar 

  7. M. Fjeld, Chem. Eng. Sci. 29 (1974) 921.

    Google Scholar 

  8. R. V. Gamkrelidze, ‘Principles of Optimal Control Theory’, Plenum Press, New York (1978).

    Google Scholar 

  9. IMSL MATH/LIBRARY, ‘FORTRAN Subroutines for Mathematical Applications’, IMSL, Houston, TX (1982).

    Google Scholar 

  10. M. Minoux, ‘Mathematical Programming’, Wiley-Interscience, New York (1986).

    Google Scholar 

  11. J. C. Dunn, Control and Dynamic Systems 29(2) (1988) 135.

    Google Scholar 

  12. J. E. Bailey, Chem. Engr. Commun. 1 (1977) 111.

    Google Scholar 

  13. J. C. Puippe and N. Ibl, J. Appl. Electrochem. 10 (1980) 775.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, North Carolina State University, 27695-7905, Raleigh, NC, USA

    R. Bakshi & P. S. Fedkiw

Authors
  1. R. Bakshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Fedkiw
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bakshi, R., Fedkiw, P.S. Optimal time-varying cell-voltage control of a parallel-plate reactor. J Appl Electrochem 24, 1116–1123 (1994). https://doi.org/10.1007/BF00241309

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00241309

Keywords

Search

Navigation