Batch Reactors (BRs)

When is a batch reactor used?

A batch reactor is used for small-scale operation, for testing new processes that have not been fully developed, for the manufacture of expensive products, and for processes that are difficult to convert to continuous operations. The reactor can be charged (i.e., filled) through the holes at the top (see Figure l-5(a)). The batch reactor has the advantage of high conversions that can be obtained by leaving the reactant in the reactor for long periods of time, but it also has the disadvantages of high labor costs per batch, the variability of products from batch to batch, and the difficulty of large-scale production (see Industrial Reactor Photos in Professional Reference Shelf [PRS] on the CRE Web sites, www.umich.edu/~elements/5e/index.html). Also see http://encyclopedia.che.engin.umich.edu/Pages/Reactors/menu.html.

Also see http://encyclopedia.che.engin.umich.edu/Pages/Reactors/Batch/Batch.html.

A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out: F_j0 = F_j = 0. The resulting general mole balance on species j is

If the reaction mixture is perfectly mixed (Figure l-5(b)) so that there is no variation in the rate of reaction throughout the reactor volume, we can take r_j out of the integral, integrate, and write the mole balance in the form

Perfect mixing

Let’s consider the isomerization of species A in a batch reactor

As the reaction proceeds, the number of moles of A decreases and the number of moles of B increases, as shown in Figure 1-6.

We might ask what time, t₁, is necessary to reduce the initial number of moles from N_A0 to a final desired number N_A1. Applying Equation (1-5) to the isomerization

rearranging,

and integrating with limits that at t = 0, then N_A = N_A0, and at t = t₁, then N_A = N_A1, we obtain

This equation is the integral form of the mole balance on a batch reactor. It gives the time, t₁, necessary to reduce the number of moles from N_A0 to N_A1 and also to form N_B1 moles of B.

1.4 Continuous-Flow Reactors

Continuous-flow reactors are almost always operated at steady state. We will consider three types: the continuous-stirred tank reactor (CSTR), the plug-flow reactor (PFR), and the packed-bed reactor (PBR). Detailed physical descriptions of these reactors can be found in both the Professional Reference Shelf (PRS) for Chapter 1 and in the Visual Encyclopedia of Equipment, http://encyclopedia.che.engin.umich.edu/Pages/Reactors/CSTR/CSTR.html, and on the CRE Web site.

1.4.1 Continuous-Stirred Tank Reactor (CSTR)

A type of reactor commonly used in industrial processing is the stirred tank operated continuously (Figure 1-7). It is referred to as the continuous-stirred tank reactor (CSTR) or vat, or backmix reactor, and is primarily used for liquid-phase reactions. It is normally operated at steady state and is assumed to be perfectly mixed; consequently there is no time dependence or position dependence of the temperature, concentration, or reaction rate inside the CSTR. That is, every variable is the same at every point inside the reactor. Because the temperature and concentration are identical everywhere within the reaction vessel, they are the same at the exit point as they are elsewhere in the tank. Thus, the temperature and concentration in the exit stream are modeled as being the same as those inside the reactor. In systems where mixing is highly nonideal, the well-mixed model is inadequate, and we must resort to other modeling techniques, such as residence time distributions, to obtain meaningful results. This topic of nonideal mixing is discussed on the Web site in PDF Chapters 16, 17, and 18 on nonideal reactors.

Also see http://encyclopedia.che.engin.umich.edu/Pages/Reactors/CSTR/CSTR.html.

What is a CSTR used for?

When the general mole balance equation

is applied to a CSTR operated at steady state (i.e., conditions do not change with time),

in which there are no spatial variations in the rate of reaction (i.e., perfect mixing),

The ideal CSTR is assumed to be perfectly mixed.

it takes the familiar form known as the design equation for a CSTR

The CSTR design equation gives the reactor volume V necessary to reduce the entering molar flow rate of species j from F_j0 to the exit molar flow rate F_j, when species j is disappearing at a rate −r_j. We note that the CSTR is modeled such that the conditions in the exit stream (e.g., concentration and temperature) are identical to those in the tank. The molar flow rate F_j is just the product of the concentration of species j and the volumetric flow rate υ

Similarly, for the entrance molar flow rate we have F_j0 = C_j0 · υ₀. Consequently, we can substitute for F_j0 and F_j into Equation (1-7) to write a balance on species A as

The ideal CSTR mole balance equation is an algebraic equation, not a differential equation.