Download Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.) PDF

By James Wei (Ed.)

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48) is {e[4*(w);vi[~(v’;v)sq(v’)} I = 0. (57) This has to hold for arbitrary 6q(u). Hence, I erq*(w);m(v,u) 1 = 0. (58) The argument (and the assumptions) following Eq. , if attention is restricted to systems for which only strong equilibria are possible), the equilibrium condition is eyU) = o (59) and that, since the kernel of B(v,u) contains only the zero function, the functional R[;]can be inverted at q*(u). This leads to the following generalization of Eq. (51): = 0. (60) It is important to realize that any distribution of chemical potentials satisfying Eq.

In Eq. (126) the first term within the square brackets represents the rate of formation of species x from higher molecular weight ones; the second term represents its rate of cracking to lower molecular weight products. With E = 0 and F[ ] identical to unity (first-order intrinsic kinetics), Eq. (126) reduces to the form given by A r i s and Gavalas (1966) in the part dealing with thermal cracking of their pioneering work on the continuous description of mixtures. OCONE AND G. ASTARITA so that Eq.

OCONE AND G . ASTARITA tivity problem has a different solution in the mixture and in the single reactant cases). The parallel case has been discussed by Astarita and Ocone (1991). Let u(x) be proportional to the kinetic constant of the A + C step, with 0 5 u(x) 5 x. One obtains CB(&t) = u(x)r#J(a,x)(l - e-xf)/x. (114) The case where ~ ( x is) a constant is trivial, but all other cases are not. For instance, suppose that u = x2eCX,and let ( a + l)/a = m. One obtains c B ( t )= m“+’ - (m/(l + t/m))“+’.

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