Stirred-tank reactors graphical method

A simple graphical method may be used to perform many calculations involving continuous stirred tank reactors. From the design equation (130) for one tank... 

Flo. 1.19. Graphical construction for continuous stirred-tank reactors (a) General method... 

Bilous, 0., and Piret, E. L. 1955. Continuous stirred tank reactors A new graphical method for complex reactions and reflux designs. A.I.Ch.E. Journal 1, 480-487. 

Graphical methods can be used to obtain the conversion from a series of reactors and have the advantage of displaying the concentration in each reactor. Moreover, no additional complications are introduced when the rate equation is not first order. As an illustration of the procedure consider three stirred-tank reactors in series, each with a different volume, operating as shown in Fig. 4-13<7. The density is constant, so that at steady state the volumetric flow rate to each reactor is the same. The flow rate and reactant concentration of the feed Q and Cq) are known, as are the volumes of each reactor. We construct a graph of the rate of reaction r vs reactant composition. The curved line in Fig. 4- 3b shows how the rate varies with C according to the rate equation, which may be of any order. 

Acetic anhydride is hydrolyzed in three stirred-tank reactors operated in series. The feed flows to the first reactor (V = I liter) at a rate of 400 cm /min. The second and third reactors have volumes of 2 and 1.5 liters, respectively. The temperature is 25°C, and at this condition the first-order irreversible rate constant is 0.158 min . Use a graphical method to calculate the fraction hydrolyzed in the effluent from the third reactor. 

Consider the same reaction system, rate equation, feed rate, and composition as in Prob. 5-8. The reaction is to be carried out in two stirred-tank reactors, each with a volume of 750 liters. What should be the temperature (within the range 0 to 100°C) in each reactor in order to obtain the maximum conversion in the effluent from the second reactor The graphical method for multiple-stirred-tank reactors (described in Sec. 4-6) may be helpful. 

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