Pyrolytic Dehydrogenation of Benzene to Diphenyl and Triphenyl

Let us now consider the pyrolytic dehydrogenation of benzene to diphenyl and triphenyl (Seinfeld and Gavalas, 1970 Hougen and Watson, 1948)  

As both state variables are measured, the output vector is the same with the state vector, i.e., yi=x, and y2=x2. The feed to the reactor was pure benzene. The equilibrium constants K and K2 were determined from the run at the lowest space velocity to be 0.242 and 0.428, respectively. 

Using our standard notation, the above problem is written as follows  

The sensitivity matrix, G(t), is a (2x2)-dimemional matrix with elements  

Taking into account Equation 6.53, the above equations can also be written as follows  

---

In this section we shall only present the derivative approach for the solution of the pyrolytic dehydrogenation of benzene to diphenyl and triphenyl regression problem. This problem, which was already presented in Chapter 6, is also used here to illustrate the use of shortcut methods. As discussed earlier, both state variables are measured and the two unknown parameters appear linearly in the governing ODEs which are also given below for ease of the reader. 

---