Laminar Reactor without Radial Diffusion

Since the volume element diminishes, the left-hand side of the derivative of caw is 

The above equation is valid for both gas- and liquid-phase reactions. In the case of gas-phase reactions, the flow velocity varies even in the length coordinate of the reactor, since the total molar amount changes as the reaction proceeds, causing pressure changes in the reactor tube. In the case of liquid-phase reactions, the velocity can often be considered as approximately constant, simplifying Equation 4.132 to 

After insertion of Equation 4.130 for the flow velocity, we obtain 

On the other hand, let us take into account that dZ/w = dt, that is, equal to the residence time element. The balance Equation 4.133 can therefore be written in a new form. 

Recalling an earlier derivation for volume flow, V = %R wo/2, inserting it into Equation 4.136, and performing a few rearrangements, we obtain 

---

The RTD in laminar flow reactor without radial diffusion is shown in Figure 3.8. The first volume elements reach the reactor outlet after 7/2 (0 = 0.5) and approaches zero slowly. 

Figure 3.8 Residence time distribution in a laminar flow reactor (without radial diffusion).

Figure 8.1 gives conversion curves for an isothermal, first-order reaction in various types of reactor. The curves for a PFR and CSTR are from Equations 1.38 and 1.49. The curve for laminar flow without diffusion is obtained from Equation 8.14 and the software of Example 8.2. Without diffusion, the laminar flow reactor performs better than a CSTR but worse that a PFR. Add radial diffusion and the performance improves. This is illustrated by the curve in Figure 8.1 that is between those for laminar flow without di ffusion and piston flow. The intermediate curve is one member of a family of such curves that depends on theparameter f// . IfL // is small, <... 

X 10 according to Equation 8.3, then radial diffusion is unimportant and reactor performance is similar to that for laminar flow without diffusion. If is large,... 

In a continuous tank-type reactor, the flow should not follow preferential paths. In the continuous tubular reactor, the flow can be in extreme cases laminar (not desired) or turbulent (desired), but without dead volume. The type of flow may cause radial and longitudinal diffusion effects causing radial or axial temperature and concentration gradients and consequently affecting the chemical reaction. 

---