Reaction operating curve

The solution of the design equation, Z(t) versus t, provides the dimensionless reaction operating curve of the reactor. It describes the progress of the chemical reaction with time. Furthermore, once Z(t) is known, we can apply stoichiometric relation (Eq. 6.1.7) to obtain the composition of each species at time t. Also, if one prefers to express the design equation in terms of the actual operating time t, rather than the dimensionless time t, using Eq. 6.1.3, the design equation becomes... 

Figure 6.4 Reaction operating curves for nth-order reaction of the form A products.

Figure 6.4 shows the reaction operating curve for different values of a. Note that each reaction order is represented by a eurve that is independent of the specific value of the rate eonstant and the initial reactant concentration. We determine the reaction time needed to achieve a certain extent by reading from the chart the value of T for the respective order and then calculating the actual operating time t, using Eq. 6.2.11. Once Z(t) is known, we can use Eq. 2.7.4 to determine the content of reactant A in the reactor at any time t ... 

Equation (d) is the expression of the reaction operating curve. Using Eq. 2.7.4, the species curves are... 

To obtain the reaction operating curve, Z(t) versus t, (f) is solved, subject to the initial condition that Z(0) = 0. In this case an analytical solution is obtained by separating the variables and integrating ... 

Figure E6.3.1 shows the reaction operating curve for different values of K /Cq. b. Once the reaction operating curve is known, the species composition is readily determine using Eq. 2.7.4,...

Figure 6.5 Reaction operating curves a reaction of the form A + B —> products.

We solve (h) numerically, subject to the initial condition that at t = 0, Z = 0, and plot flie reaction operating curve, shown in Figure E6.4.1. 

Solve the design equations (Z s as functions of t) and obtain the reaction operating curves. 

Figure 6.8 shows the reaction operating curve for different values of 2/ 1 Note that the design equation for batch reactors with single reversible reactions has two parameters ( 1 and 2). whereas the design equation for reactors with an irreversible reaction has only one parameter. Also note that for an irreversible reaction, 2 = 0, and, from Eq. 6.3.3, Zi q = aCO). 

Figure 6.8 Reaction operating curves for single reversible reaction.

We substitute these values into (j), (k), and (1), and solve them numerically subject to the initial conditions that at t = 0, Zi = = Z3 = 0. Figure E6.11.1 shows the solutions of the design equations—the reaction operating curves. Next, we use (m) through (r) to determine the species curves, shown in Figure E6.11.2. 

Figure E6.12.1 Reaction operating curves—isothermal operation.

Figure E6.13.4 Reaction operating curves—adiabatic operation.

Derived the dimensionless design equation for isothermal operation with single reactions and obtained the reaction operating curve. 

Figure E7.11.1 Reaction operating curves— isothermal operation.

Figure E7.12.4 Reaction operating curves—actual operation.

The reaction operating curves and species operating curves... 

As discussed in Chapter 4, to describe the operation of a CSTR with multiple reactions, we have to write Eq. 8.1.1 for each independent chemical reaction. The solution of the design equations (the relationships between Z Js and t) provide the reaction operating curves and describe the reactor operation. To solve the design equations, we have to express the rates of the chemical reactions that take place in the reactor in terms of Z s and t. Below, we derive the auxiliary relations used in the design equations. 

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