(202s) Dynamic Modeling of Nonlinear Advection-Reaction Equation With Inconstant Molar Flow Rate
An advection-reaction equation is a 1-dimensional partial differential equation for describing a system where chemical reactions and bulk flow are involved. In an isothermal environment the model equation consists of the material balance, where the state variable is the molar concentration of chemical components inside the system. In this model, molar flow rate is generally regarded as a constant parameter when a dynamic simulation is executed. However, more realistic and coherent model predictions are possible if we allow the molar flow rate to change along temporal and spatial positions.
One example that may benefit from this modification is a gas-phase reactor system where change of molar concentration resulting from chemical reactions directly changes molar flow rate. If the model equation involves a single state variable and chemical reaction term is eliminated from the equation, it is reduced to an inviscid Burgers’ equation. Burgers’ equation describes the dynamic change of momentum in the system and involves the flow rate as a state variable. Since the system is expressed as a hyperbolic partial differential equation with more than one state variable, modeling and performing dynamic simulation are challenging tasks.
This study suggests a systematic approach for performing dynamic simulation of such a system with method of characteristics suitable for the nonlinear advection-reaction equation having more than one state variable, compared to existing approaches applied to the traditional Burgers’ equation with a single variable without reaction terms. An isothermal plug flow reactor, where a single chemical reaction involving two chemical components takes place, is illustrated for this study. The model equation is a 1-dimensional, 1st order hyperbolic partial differential equation with two state variables representing molar concentrations of chemical components. The molar flowrate is implicitly expressed as the total sum of molar concentrations.