A System with Multiple Chemical Reactions

If there are multiple ongoing chemical reactions in the system, an independent extent of reaction, (j = I,.,S),should be defined for each and every reaction. Equations 3.53 and 3.54 are then consequently replaced by analogous definitions for continuous and discontinuous reactors  

Thus we have here i reacting components and S chemical reactions in the system. Analogously, the specihc extent of reaction can be defined for a system with multiple chemical reactions  

After adding the molar amounts and flows of all components. Equations 3.71 and 3.72 transform to 

The definition of molar fraction gives us, starting from Equations 3.71 and 3.72, as well as from Equations 3.73 and 3.74, an expression for the molar fraction x/  

Equation 3.75 can be written in a compact form with arrays as 

---

For a system with multiple chemical reactions, the expression for the total concentration (Equation 3.87) is naturally still valid. By inserting expressions of the molar fractions. Equations 3.76 and 3.85, into the definition of the concentration. Equations 3.44 and 3.45, the following expressions are obtained for the concentrations ... 

For a system with multiple chemical reactions, we obtain analogously... 

If a reduction in the number of molar balances is desired for the calculations, the stoichiometric relationships developed in the previous section must be utilized. We can thus reduce the number of necessary balance equations from N to S one should keep in mind that the number of chemical reactions is usually much lower than the number of components in a system. The molar flows, /, can be replaced by expressions containing reaction extent, specific reaction extent, and reaction extent with concentration dimension or conversion (, I, I", or tia) in a system containing a single chemical reaction. For systems with multiple chemical reactions, h is replaced by an expression containing or i). ... 

Expression 5.163 is valid for systems with a single chemical reaction, but it is conveniently generalized for systems with multiple chemical reactions ... 

As a common analysis tool, residue curve mapping (RCM) is well established. Fien and Liu [4] published a comprehensive review of the synthesis and shortcut design of non-reactive separation processes based on RCMs. Barbosa and Doherty [5] developed RCMs for RD processes with single chemical equilibrium reaction. Ung and Doherty [6] extended this method to systems with multiple equUibrium reactions. 

If the system comprises multiple chemical reactions, the quantity %" should be replaced with a vector, defined as... 

Nassar et al. [10] employed a stochastic approach, namely a Markov process with transient and absorbing states, to model in a unified fashion both complex linear first-order chemical reactions, involving molecules of multiple types, and mixing, accompanied by flow in an nonsteady- or steady-state continuous-flow reactor. Chou et al. [11] extended this system with nonlinear chemical reactions by means of Markov chains. An assumption is made that transitiions occur instantaneously at each instant of the discretized time. 

Determine the equilibrium composition for a system with a single chemical reaction and with multiple chemical reactions given the reaction stoichiometry, temperature, and pressure. 

To understand the reculiarities of multiple layer formation, it suffices to consider the A-B binary system with three chemical compounds ApBq, ArBs and AiBn on the equilibrium phase diagram (Fig. 3.1). The scheme of analysis of the process of their occurrence at the A-B interface is analogous to that of two compound layers (see Chapter 2). First of all, the equations of partial chemical reactions taking place at phase interfaces must be written. These are as follows. 

The role of mixing has been studied in systems with more complex reaction schemes or considering more complex fluid-dynamical properties, and in the context of chemical engineering or microfluidic applications (for reviews on microfluidics see e.g. Squires (2005) or Ottino and Wiggins (2004)). Muzzio and Liu (1996) studied bi-molecular and so-called competitive-consecutive reactions with multiple timescales in chaotic flows. Reduced models that predict the global behavior of the competitive-consecutive reaction scheme were introduced by Cox (2004) and by Vikhansky and Cox (2006), and a method for statistical description of reactive flows based on a con-... 

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

Second, we discuss front propagation in systems with multiple stationary states, again far from equilibrium. Consider a chemical system with two stable stationary states at given external constraints. Contact of two such systems, one in each of the two stable stationary states, leads to a front propagation of transition from the less to the more stable stationary state. We report on studies of this process by means of numerical solutions of reaction diffusion equations, experiments and a thermodynamic analysis of stability and relative stability based on the concept of excess work. 

---