Residence time from step input

A typical reactor operates at 600—900°C with no catalyst and a residence time of 10—12 s. It produces a 92—93% yield of carbon tetrachloride and tetrachloroethylene, based on the chlorine input. The principal steps in the process include (/) chlorination of the hydrocarbon (2) quenching of reactor effluents 3) separation of hydrogen chloride and chlorine (4) recycling of chlorine to the reactor and (i) distillation to separate reaction products from the hydrogen chloride by-product. Advantages of this process include the use of cheap raw materials, flexibiUty of the ratios of carbon tetrachloride and tetrachloroethylene produced, and utilization of waste chlorinated residues that are used as a feedstock to the reactor. The hydrogen chloride by-product can be recycled to an oxychlorination unit (30) or sold as anhydrous or aqueous hydrogen chloride. 

The chief quantities based on tracer tests are summarized in Table 23-4. Effluent concentrations resulting from impulse and step inputs are designated Cg and C , respectively. The initial mean concentration resulting from an impulse of magnitude m into a vessel of volume is C = mfVr- The mean residence time is the ratio of the vessel volume to the volumetric flow rate, t = V fV or t = jo tCg dt/jo Cg dt. The reduced time is t = t/t. 

In the case of tracer from a vessel that contained an initial average concentration C°, the area under a plot of E(t) = Cgff[ygj,/C° between the ordinates at tj and tj is the fraction of the molecules that have residence times in this range. In the case of step constant input of concentration Cf to a vessel with zero initial concentration, the ratio F(t) = Cgff ygj,/Cf at tj is the fraction of molecules with residence time less than tj. 

The characteristics of uniform velocity profile and no axial mixing in a plug-flow reactor require that the residence time be a constant, 9 = VjQ. The curve for response to a step-function input is as shown in Fig. 6-5. From Eq. (6-3), the response curve is equal to J 9). Then J 9) = 0 for 6 < VjQ and J 9) = 1 for 0 > VjQ. The input and response curve for a pulse input would correspond to narrow peaks at 0 = 0 and 0 = VjQ, as shown in Fig. 6-6 (solid lines). The response curve, according to Eq. (6-7), is proportional to J 9). 

The Level III model includes all the important fate and transport processes in a real environment and is one step more complex than Level n. As in the Level II model, the chemical is discharged at a constant rate into the environment to reach a steady state (at which input equals output). Unlike Level II, equilibrium between different media is not assumed and rates of chemical transfer by intermedia transport processes are defined. The individual discharges to all environmental media must be specified because fhe disfribufion of the chemical between media now depends on how the chemical enters the system. Depending on the properties of a chemical, the mode of entry can also significantly alter chemical persistence or residence time in the environment to viues that are quite different from Level II results. A series of 12 transport velocities control chemical transfer between the four primary environmental media (air, water, soil, and sediment). Equilibrium is assumed, however, within each medium. For example, suspended matter and fish are assumed to be at the same fugacity as water. 

F(t) is a probability distribution which can be obtained directly from measurements of the system s response in the outflow to a step-up tracer input in the inflow. Consider that at time t = 0 we start introducing a red dye at the entrance of the vessel into a steady flow rate Q of white carrier fluid. The concentration of the red dye in the inlet flow is C. At the outlet we monitor the concentration of the red dye, C(t . If our system is closed, i.e. if every molecule of dye can have only one entry and exit from the system (which is equivalent to asserting that input and output occur by convection only), then QC(t)/QCQ is the residence time distribution of the dye. This is evident since all molecules of the dye appearing at the exit at time t must have entered into the system between time 0 and time t and hence have residence times less than t. Only if our red dye is a perfect tracer, i.e.. if it behaves identically to the white carrier fluid, then we have also obtained the residence time distribution for the carrier fluid and F(t) = C(t)/C. To prove that the tracer behaves ideally and that the F curve is obtained, the experiment should be repeated at different levels of C. The ratio C(t)/C at a given time should be invariant to C, i.e. the tracer response and tracer input must be linearly related. If this is not the case, then C(t)/CQ is only the step response for the tracer, which includes some nonlinear effects of tracer interactions in the system, and which does not represent the true residence time distribution for the system. 

---