Residence time from pulse input

This program is designed to simulate the resulting residence time distributions based on a cascade of 1 to N tanks-in-series. Also, simulations with nth-order reaction can be run and the steady-state conversion obtained. A pulse input disturbance of tracer is programmed here, as in example CSTRPULSE, to obtain the residence time distribution E curve and from this the conversion for first order reaction. 

Water is drawn from a lake, flows through a pump and passes down a long pipe in turbulent flow. A slug of tracer (not an ideal pulse input) enters the intake line at the lake, and is recorded downstream at two locations in the pipe L meters apart. The mean residence time of fluid between recording points is 100 sec, and variance of the two recorded signals is... 

The extent of gas dispersion can usually be computed from experimentally measured gas residence time distribution. The dual probe detection method followed by least square regression of data in the time domain is effective in eliminating error introduced from the usual pulse technique which could not produce an ideal Delta function input (Wu, 1988). By this method, tracer is injected at a point in the fast bed, and tracer concentration is monitored downstream of the injection point by two sampling probes spaced a given distance apart, which are connected to two individual thermal conductivity cells. The response signal produced by the first probe is taken as the input to the second probe. The difference between the concentration-versus-time curves is used to describe gas mixing. 

Calculate the mean residence time and the variance for the reactor characterized in Example 13 -1 by the RTD obtained from a pulse input at 320 K. 

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). 

A similar analysis for a pulse input would give a response curve of Cpuise vs 0, but this can be obtained more easily by differentiating the J ) curve in Fig. 6-5. From Eq. (6-7), the derivative J B) is proportional to The derivative of the dashed line in Fig. 6-5 will be largest at 0 = 0 and will continually decrease toward zero as 0 increases. Such a distribution curve, given as the dashed line in Fig. 6-6, shows that the most probable [largest J ) d6 residence time is at 0 = 0 for a stirred-tank reactor. 

The additive property of variances also allows to treat any measured tracer pulse input and to extract from it the mean residence time and the variance of the measured outlet curve as indicated in Figure 3.13 and Equation 3.56. 

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