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].萨巴捷反应（Sabatier reaction）因发电厂二氧化碳大规模回收利用的极具前景的理念再度引发关注[1]。该反应又称为CO₂甲烷化反应，可表示为二氧化碳与氢气发生甲烷化的过程： CO₂(g) + 4 H₂(g) ⇌ CH₄(g) + 2 H₂O(g) 该反应为放热且可逆的过程，可由负载型金属（如氧化镁负载镍）催化[10]。负载型金属催化剂可被配置为填充床反应器。该反应也可在流化床或生物反应器中进行，但本文未对此类反应器展开讨论。本研究针对壳管式构型下装填于管内的负载镍催化剂颗粒展开分析。 将反应器设计方程整合至流程模拟软件中可开展各类工业应用研究，但此类软件通常未内置填充床反应器模块，需由用户自行添加。CHEMCAD是一款常用的化工流程模拟软件，此前我们的研究已证明其可与Mathematica联用，以实时求解复杂数学问题[2-8]。我们先前的研究聚焦于代数方程组求解，即前述研究中的膜模型与闪蒸模型均基于代数方程组的求解。本研究将该方法拓展至数值求解的微分方程组场景。具体而言，本文演示了在耦合CHEMCAD的Mathematica环境中，同时求解两个微分方程dP/dW=F₁与dX/dW=F₂的过程，其中X为CO₂转化率，P为反应器内压力，W为催化剂质量[9]。本研究采用的动力学模型为包含固体催化剂表面同步吸附-脱附过程的气相模型，动力学速率定律与热化学性质均取自已有文献[10,11]。