8. Packed-Bed Methanation Reactor in CHEMCAD Linked to Mathematica.

The Sabatier reaction is receiving renewed attention because of the promising concept of large-scale recycling of carbon dioxide in power plants.[1] The reaction, also known as CO₂ methanation, can be written for the methanation of CO₂ with hydrogen, as:

CO₂(g) + 4 H₂(g) ⇌ CH₄(g) + 2 H₂O(g)

The reaction is exothermic and reversible, and is catalyzed by supported metals such as nickel on magnesia.[10] The supported metal catalysts can be configured into a packed bed. The reaction can also be accomplished in fluidized-bed or biological reactors, but those are not considered here. In this study, we consider supported-nickel catalyst pellets poured into pipes in a shell-and-tube configuration.

Various commercial applications can be studied by incorporation of the reactor design equations into process simulator software, but this software does not generally contain built-in packed bed reactors. This type of reactor needs to be added by the user. CHEMCAD is one commonly used chemical process simulator and we have shown previously that it can be used in tandem with Mathematica for real-time solutions of advanced mathematical problems.[2-8] Our previous work showed application to algebraic solutions. That is, the membrane and flash models in those studies involved solutions of systems of algebraic equations. This study extends the method to systems of differential equations solved numerically. Specifically, this paper demonstrates the simultaneous solution of the two equations dP/dW=F₁ and dX/dW=F₂, where X is conversion of CO₂, P is pressure in the reactor, and W is catalyst mass[9], in Mathematica coupled to CHEMCAD. Kinetic models used are gas-phase with simultaneous adsorption-desorption on the solid catalyst, with kinetic rate laws and thermochemical properties taken from the literature [10,11].