Computers and Chemical Engineering 25 (2001) 1241 – 1250 Modeling steady-state heterogeneous gas – solid reactors using feedforward neural networks Daniel R. Parisi *, Miguel A. Laborde Departamento de Ingenierı ´a Quı ´mica, Facultad de Ingenierı ´a, Uniersidad de Buenos Aires, Pabello ´n de Industrias, Ciudad Uniersitaria (1428), Buenos Aires, Argentina Received 28 February 2000; received in revised form 26 February 2001; accepted 26 February 2001 Abstract A new method for solving gas – solid heterogeneous reactors is proposed. Mass balance inside the pellet (numerical integration of a differential equations system) is replaced by an analytical function, which functionality corresponds to an adequate trained three-layer feedforward neural network. The global reaction rate evaluated by using this function includes the complex phenomena of simultaneous diffusion and chemical reaction into the solid. The methodology was successfully applied to the steam reforming of methane. Both methods are compared. Results of the reactor simulation are very similar in both cases but the one that used neural networks is about 20 times faster. The method proposed could also be applied to any type of two-phase heterogeneous reactors. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Heterogeneous gas – solid reactor simulations; Neural networks; Hybrid modeling Nomenclature reactor transversal area (cm 2 ) A mean specific heat (cal/g/K) C p reactor diameter (cm) d effective diffusion coefficient of gases into the porous solid D e E activation energy (cal/mol) general vector function f  molar flow (mol/s) F mass flux (g/cm 2 /s) G g neuron activation function kinetics coefficient k equilibrium constant K k 0 pre-exponential factor (mol/cm 3 /s/atm 2 ) L reactor length number of reactive species M number of linearly independent reactions N O  neural network output vector P partial pressure inside the pellet (atm) partial pressure at external surface of the catalyst and at reactor gas bulk (atm) P s P g total pressure in the bulk gas flow (atm) www.elsevier.com/locate/compchemeng * Corresponding author. Tel.: +54-11-45763240; fax: +54-11-45763241. E-mail addresses: parisi@di.fcen.uba.ar (D.R. Parisi), miguel@di.fcen.uba.ar (M.A. Laborde). 0098-1354/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII:S0098-1354(01)00688-3