8. Packed-Bed Methanation Reactor in CHEMCAD Linked to Mathematica.
Description
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].
Files
Steps to reproduce
We took the following steps to verify that the software connectivity, data maps, and calculations are working correctly. The work was verified by replicating published kinetics calculations[9,10]. We also had each contributor download the files and follow the procedure in the instructions file to make sure the guidance is correct. References [1] Vogt, Charlotte; Monai, M.; Kramer, G.J.; and Weckhuyzen, B.M. (2019), “The Renaissance of the Sabatier Reaction and its Applications on Earth and in Space,” Nature Catalysis, 2, 188-197. [2] Biaglow, Andrew; Cowart, Sam; Yuk, Simuck; James, Corey; Nagelli, Enoch (2024), “1. Simple Flash Unit in Mathematica Linked to CHEMCAD,” Mendeley Data, V1, doi: 10.17632/smzy2998df.1. [3] Biaglow, Andrew; Cowart, Sam; James, Corey; Nagelli, Enoch; Yuk, Simuck (2024), “2. Simple Membrane Unit in Mathematica Linked to CHEMCAD,” Mendeley Data, V1, doi: 10.17632/cdcgbsrrhc.1. [4] Biaglow, Andrew; Cowart, Sam; Yuk, Simuck; Nagelli, Enoch; James, Corey (2024), “3. Improved Membrane Unit in Mathematica Linked to CHEMCAD,” Mendeley Data, V1, doi: 10.17632/nz7p8bhhs3.1. [5] Biaglow, Andrew; Yuk, Simuck; James, Corey; Nagelli, Enoch; Cowart, Sam (2024), “4. Connecting CHEMCAD to the Wolfram Cloud for Flash Calculations,” Mendeley Data, V1, doi: 10.17632/3b8n72m28v.1. [6] Biaglow, Andrew; Yuk, Simuck; James, Corey; Nagelli, Enoch; Cowart, Sam (2024), “5. Connecting CHEMCAD to the Wolfram Cloud for Membrane Calculations,” Mendeley Data, V1, doi: 10.17632/6gw5m5d7pn.1. [7] Biaglow, Andrew (2024), “6. Connecting Aspen Plus to the Wolfram Cloud for Flash Calculations,” Mendeley Data, V1, doi: 10.17632/fhwzyk3n6g.1. [8] Biaglow, Andrew; James, Corey; Yuk, Simuck; Nagelli, Enoch; Cowart, Sam (2024), “7. Connecting CHEMCAD to a Machine Learning Model on the Wolfram Cloud”, Mendeley Data, V1, doi: 10.17632/ch7yy7xbgz.1 [9] Fogler, H.S (2006) Elements of Chemical Reaction Engineering, 4th Edition, Upper Saddle River, NJ: Prentice Hall, p. 180. [10] Xu, J. and Froment, G.F. (1989), “Methane Steam Reforming, Methanation, and Water-Gas Shift: I. Intrinsic Kinetics,” AIChE Journal, 35(1), 88-96. [11] Hou, K., and Hughes, R. (2001), “The Kinetics of Methane Steam Reforming Over a Ni/α-Al₂O Catalyst,” Chemical Engineering Journal, 82, 311-328.