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Example CD12-3: Determining the Parameters That Give MSS²

All equation numbers refer to 2nd edition of Elements of CRE

		The oxidation of carbon monoxide is carried out in excess oxygen in a "fluidized" CSTR containing catalyst particles impregnated with platinum:
		The rate law for the disappearance of CO, (A), is	(CDE12-3.1)
		Combining a mole balance with the rate law gives	(CDE12-3.2)
		which is of the form
			(CDE12-3.3)
		At the bifurcation point,
			(CDE12-3.4)
		and Equation (CD12-12) requires
			(CDE12-3.5)
		Combining Equations (CDE12-3.4) and (CDE12-3.5) yields
			(CDE12-3.6)
		Solving Equation (CDE12-1.6) for CA gives us
			(CDE12-3.7)
		For, no real roots exist and there are no possible steady states. A rearrangement of Equation (CDE12-1.4) gives
			(CDE12-3.8)
		Note that the right-hand side of Equation (CDE12-3.8) goes through a maximum asis increased from 1. To find this maximum we set the derivative of the right-hand side of Equation (CDE12-3.8) with respect to CA equal to zero, and solve to find that the maximum occurs at
			(CDE12-3.9)
		Substituting Equation (CDE12-3.9) into the right-hand side of Equation (CDE12-3.8) gives the maximum as
			(CDE12-3.10)
		The maximum value of the right-hand side is 1/27; consequently, ifis smaller than 27. Equation CDE12-3.10 can never be satisfied and there will be no MSS. Figure CDE12-1.1 shows a mapping of those regions where no multiple steady states will exist.
		Figure CDE12-3.1 Mapping the regions of no multiple steady states.
		To learn the regions where MSS exist, we need to carry the analysis further. If we let, Equation (CDE12-3.6) can be written as
			(CDE12-3.11)
		and Equation (CDE12-3.5) as
			(CDE12-3.12)
		Equations (CDE12-3.11) and (CDE12-3.12) are used to form Table CDE12-3.1. Figure CDE12-3.2 shows a plot of as a function of. The shaded area shows the combinations of these variables that will produce multiple steady states.
		Figure CDE12-3.2 Region of possible multiple steady states.