Chemical reaction with coupled heat and mass flows

3 CHEMICAL REACTION WITH COUPLED HEAT AND MASS FLOWS 

Nonisothermal reaction-diffusion systems represent open, nonequilibrium systems with thermodynamic forces of temperature gradient, chemical potential gradient, and affinity. The dissipation function or the rate of entropy production can be used to identify the conjugate forces and flows to establish linear phenomenological equations. For a multicomponent fluid system under mechanical equilibrium with n species and A r number of chemical reactions, the dissipation function 1 is 

Excluding the coupling of chemical reactions with the heat and mass flows, and using the relationship AfiA = (dprA/dCA)ACA, Eq. (9.54) reduces to 

Using Fourier s law 3q = keVT in Eq. (9.57), the primary coefficient Lqq is related to the effective thermal conductivity ke by 

Coupled systems of chemical reactions and transport processes 

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Chemical reaction with coupled heat and mass flows... 

These equations display the spatial order with the thermodynamically coupled heat and mass flows. Here, the coupling between chemical reactions and transport processes of heat and mass is excluded. The analysis of reaction-diffusion systems would be more complete if we consider heat effects and coupling among fluxes of mass and heat. The nonequi-librium thermodynamics approach is useful for incorporating the coupling phenomena into reaction-diffusion systems. 

The above phenomenological equations represent coupled heat and mass flows with chemical reaction in an anisotropic medium. The phenomenological equations above in vector form are... 

By substituting Eqs. (9.116) and (9.118) into Eqs. (9.80) and (9.82), we find the thermodynamically and mathematically coupled chemical reaction velocity with heat and mass flows... 

Previously, we considered the case where heat and mass flows are coupled in a reaction diffusion system with heat effects, in which the cross coefficients Zrq. Zqr. and LlS, LSl have vanished (Demirel, 2006). Here, we consider the other three cases. The first involves the stationary state balance equations. In the second case, there is no coupling between the heat flow and chemical reaction with vanishing coefficients Zrq and Zqr. Finally, in the third, there is no coupling between the mass flow and chemical reaction because of vanishing cross-coefficients of ZrS and LSl. The thermodynamically coupled modeling equations for these cases are derived and discussed briefly in the following examples. 

Example 9.8 Stationary coupling of chemical reactions with heat and mass flows Stationary forms of Eqs. (9.150) and (9.151) are... 

At this time, only a small number of nanoscale processes are characterized with transport phenomena equations. Therefore, if, for example, a chemical reaction takes place in a nanoscale process, we cannot couple the elementary chemical reaction act with the classical transport phenomena equations. However, researchers have found the keys to attaching the molecular process modelling to the chemical engineering requirements. For example in the liquid-vapor equilibrium, the solid surface adsorption and the properties of very fine porous ceramics computed earlier using molecular modelling have been successfully integrated in modelling based on transport phenomena [4.14]. In the same class of limits we can include the validity limits of the transfer phenomena equations which are based on parameters of the thermodynamic state. It is known [3.15] that the flow equations and, consequently, the heat and mass transport equations, are valid only for the... 

Other models directly couple chemical reaction with mass transport and fluid flow. The UNSATCHEM model (Suarez and Simunek, 1996) describes the chemical evolution of solutes in soils and includes kinetic expressions for a limited number of silicate phases. The model mathematically combines one- and two-dimensional chemical transport with saturated and unsaturated pore-water flow based on optimization of water retention, pressure head, and saturated conductivity. Heat transport is also considered in the model. The IDREAT and GIMRT codes (Steefel and Lasaga, 1994) and Geochemist s Workbench (Bethke, 2001) also contain coupled chemical reaction and fluid transport with input parameters including diffusion, advection, and dispersivity. These models also consider the coupled effects of chemical reaction and changes in porosity and permeability due to mass transport. 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

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