Tubular models

The Fractional Tubularity Model. Piston flow has cr = 0. A CSTR has cr = 1. 

Real reactors can have 0 < cr < 1, and a model that reflects this possibility consists of a stirred tank in series with a piston flow reactor as indicated in Figure 15.1(a). Other than the mean residence time itself, the model contains only one adjustable parameter. This parameter is called the fractional tubularity, Xp, and is the fraction of the system volume that is occupied by the piston flow element. Figure 15.1(b) shows the washout function for the fractional tubularity model. Its equation is... 

FIGURE 15.1 The fractional tubularity model (a) physical representation (b) washout function. 

The fractional tubularity model has been used to fit residence time data in flui-dized-bed reactors. It is also appropriate for modeling real stirred tank reactors that have small amounts of dead time, as would perhaps be caused by the inlet and outlet piping. It is not well suited to modeling systems that are nearly in piston flow since such systems rarely have sharp first appearance times. 

The reactor is a gas-fluidized bed for which the fractional tubularity model is usually appropriate. 

Suppose k = 2s and =0.8m /mol. Determine bounds on the yield for a reactor having t = 3 s and an inlet feed concentration of 2mol/m. Suppose the reactor in Problem 15.14 obeys the fractional tubularity model with Xp = 0.5. Use this information to calculate narrower bounds on the 5deld. 

Two types of injection devices are available. Long tubular models are used to place chemicals into the base of trees and the ax-like Hypo-hatchet for injection higher on the stem. Both tools are effective (Holt 1975). 

Suppose the reactor in Problem 15.14 obeys the fractional tubularity model with xp = 0.5. Use this information to calculate narrower bounds on the yield. 

The porous structure of MCM-41 materials was characterized by their BET surface area, mesopore volume and diameter (Tab.1 and 2). The mesopore volume Vme was obtained as the adsorption (converted to liquid volume) corresponding to the filling of the MCM-41 porous system proper. The external surface area of crystals was estimated from the desorption branch of the hysteresis loop as the surface area of pores larger than the MCM-41 pores proper. The size (diameter) of mesopores was calculated using a tubular model as 4V S where S stands for the BET surface area minus the external surface area. 

The Fractional Tubularity Model. Piston flow has cr = 0. A CSTR has = 1. Real reactors can have 0 < < 1, and a model that reflects this possibility... 

TCE concentration, tubular model, t = 13 h TCE concentration, spherical model, t = 13 h... 

The concentration distribution for the spherical and tubular model are shown in Figure 15.9. The evolution of the total saturation Sn,tot nd the total mass flux /tot of the TCE is shown in Figure 15.10. The total saturation or the total mass flux is given by the integration of Sn or / over the domain S2, respectively. 

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