Reactor volume element

It should be emphasized that for ideal tubular reactors, it is the total volume per unit of feed that determines the conversion level achieved. The ratio of the length of the tube to its diameter is irrelevant, provided that plug flow is maintained and that one uses the same flow rates and pressure-temperature profiles expressed in terms of reactor volume elements. 

The differential energy balance equation for steady-flow reactors widi no mechanical work is obtained by differentiating Eq. 5.2.48 over a reactor volume element (IVr ... 

The batch reactor is assumed to be well stirred, so there are no concentration gradients anywhere in the reactor volume. In this case it is natural to consider the entire reactor contents to be the reactor volume element as in Figure 4.2, and V = Vr. Because the reactor is well stirred, the integrals in Equation 4.2 are simple to evaluate,... 

Because of the plug-flow assumption, it is natural to take a thin disk for the reactor volume element as shown in Figure 4.19. The concentration does not change over the volume element because there is complete mixing in the radial and angular directions and because the axial distance Az is small. The element has volume AV = A Az in which Ac is the tube cross-sectional area. Writing Equation 4.2 in this situation gives... 

Figure 7.25 Fixed-bed reactor volume element containing fluid and catalyst particles the equations show the coupling between the catalyst particle balances and the overall reactor balances.

Fixed-bed reactor volume element containing fluid and... 

Consider an arbitrary reactor volume element depicted in Figure 4.1, which has inlet and outlet streams with volumetric flowrates Qo and Qi, respectively. The molar concentrations of component j in the two streams are given by cjq and cji and the production rate of component j due to chemical reactions is Rj, The statement of conservation of mass for this system takes the form. 

Figure 4.19 Plug flow reactor volume element.

In both situations b and c the reactor volume elements can often be the same on different scales of operation. That makes scaling up of the volume elements quite straightforward. 

In this section, we will consider the tube reactor volume element. An inflow, (mol/s), enters this element, and an outflow, n,out> leaves it. The volume element is illustrated in Figure 3.9. 

Let us consider a cylindrical reactor volume element shown in Figure 5.29. The volume element, A V, is given by... 

After division by the reactor volume element, AVr, and allowing AVr 0, we obtain... 

FIGURE 9.22 (a) Reactor volume element and (b) the chemical system for skeletal isomerization. 

Let us look at a reactor volume element as illustrated in Figure 9.22. The mass balance of a component in the volume element is... 

The above enumerates the rate of mass (in units of moles) of A conserved within the fluid contained in the reactor volume element V at time t. One now proceeds to evaluate the six terms in Equation (8.1). 

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