System mean residence time

Now that the system mean residence time has been found to be 8.128 min, 6, defined by eqn. (2), and E(6), defined by eqn. (4), can be evaluated, thus enabling the system RTD to be presented in dimensionless form. These data are included in Table 2 appropriate calculations will confirm the unit area and unit mean properties of E(0). 

System mean residence time MRTs (units time). This is the average time the drug spends in the system before leaving the system for the last time. 

For the canonical input of drug, what information is needed For the bolus input, an estimate of the drug concentration at time zero, C(0), is needed in order to estimate Va- For a constant infusion of drug, an estimate of C(0) is needed to estimate Va, and an estimate of the plateau concentration, C, is needed to estimate clearance and the system mean residence time. 

A fines removal system is installed on the crystallizer designed in the first example. Assuming that the cut size for the fines removal system is 50 im and the ratio of mean residence times for product and fines, rp/rp( = 7), is 10, calculate the mean product residence time now required to produce the same dominant size of 600 pm at the same production rate and suspension density. 

Equation (1.40) is a special case of a far more general result. The mean residence time is the average amount of time that material spends in a flow system. For a system at steady state, it is equal to the mass inventory of fluid in the system divided by the mass flow rate through the system ... 

Also assume that the pilot- and full-scale vessels will operate at the same temperature. This means that A(o-out,bout, . )and/i/2 will be the same for the two vessels and that Equation (1.49) will have the same solution for provided that 7 is held constant during scaleup. Scaling with a constant value for the mean residence time is standard practice for reactors. If the scaleup succeeds in maintaining the CSTR-like environment, the large and small reactors will behave identically with respect to the reaction. Constant residence time means that the system inventory, pV, should also scale as S. The inventory scaleup factor is defined as... 

Solution The required flow rate is the mass inventory in the system divided by the mean residence time ... 

If the pilot reactor is turbulent and closely approximates piston flow, the larger unit will as well. In isothermal piston flow, reactor performance is determined by the feed composition, feed temperature, and the mean residence time in the reactor. Even when piston flow is a poor approximation, these parameters are rarely, if ever, varied in the scaleup of a tubular reactor. The scaleup factor for throughput is S. To keep t constant, the inventory of mass in the system must also scale as S. When the fluid is incompressible, the volume scales with S. The general case allows the number of tubes, the tube radius, and the tube length to be changed upon scaleup ... 

Note that VKQm -b ) is the per-pass residence time and is far different from the mean residence time for the system, t= VjQm- Equation (4.21) gives... 

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... 

This equation can be fit to experimental data in several ways. The model exhibits a sharp first appearance time, tf st = rpt, which corresponds to the fastest material moving through the system. The mean residence time is found using Equation (15.13), and Xp = tf,rsi/1 is found by observing the time when the experimental washout function first drops below 1.0. It can also be fit from the slope of a plot of In W versus t. This should give a straight line (for t > tfirst) with slope = 1/(F— tfirst)- Another approach is to calculate the dimen-... 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

An 02 flow must be maintained through the contaminated zone at a level sufficient for the aerobic biodegradation of contaminants. Note that during bioventing the main aim is the maximum utilization of 02 by the microbial cultures. For this reason, air flow rate is usually an order of magnitude lower than that applied in simple SVE systems. A simple empirical rule is that the mean residence time of air in the contaminated soil pore volume should be between 1 and 2 days. 

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

When the space time and the mean residence time differ, it is the space time that should be regarded as the independent process variable that is directly related to the constraints imposed on the system. We will see in Sections 8.2 and 8.3 that it is convenient to express the fundamental design relations for continuous flow reactors in terms of this parameter. We will also see that for these reactors the mean residence time cannot be considered as an independent variable, but that it is a parameter that can be determined only... 

Figure 11P.1 can be used to determine the dimensionless dispersion parmeter ( l/uL) for a system of interest. Use the transfer function method to evaluate the mean residence time and QjJuL) for a system subjected to the arbitrary input shown in the figure. Note that the output response has been shifted 62.5 sec to the left. Response values for the input and output streams were as follows. 

Develop the E(t) profile for a 10-m laminar-flow reactor which has a maximum flow velocity of 0.40 m min-1. Consider t = 0.5 to 80 min. Compare the resulting profile with that for a reactor system consisting of a CSTR followed by a PFR in series, where the CSTR has the same mean residence time as the LFR and the PFR has a residence time of 25 min. Include in the comparison a plot of the two profiles on the same graph. 

Consider the entry of a small amount of fluid as tracer into the PFR at time t = 0. No tracer leaves the PFR until t = VPF/q0 = fPF, the mean residence time in the PFR, and hence no tracer leaves the two-vessel system, at the exit from the CSTR, during the period 0 sk fpF. As a result,... 

Asif et al. (1991) studied distributor effects in liquid-fluidized beds of low-density particles by measuring RTDs of the system by pulse injection of methylene blue. If PF leads into and follows the fluidized bed with a total time delay of 10 s, use the following data to calculate the mean-residence time and variance of a fluid element, and find N for the US model. 

The system parameters are the feed concentration, cAo, the rate constant in the rate law, (—rA) = kAcA, the mean-residence time, t, and N. Equation 20.1-4 for this case is... 

Veng-Pedersen P, Gillespie W. The mean residence time of drugs in the systemic circulation. J Pharm Sci 1985 74 791-792. 

As a result of gas flow into a bubble, the mean residence time of the gas in such systems is reduced because the bubble rises more rapidly than the gas in the continuous phase. Thus, the injection of a single bubble into the bed will initially cause the bed to expand by an amount equal to the volume of the bubble. When this bubble breaks the surface of the bed, however, the bed volume decreases to a value less than its initial value, the gas content of the bed being reduced. If the value of uc is only slightly in excess of umf, the gas in a small injected bubble may become dispersed throughout the continuous phase so that no bubble appears at the surface of the bed. 

In the case of porous HDC, as Indicated, one needs to account for both HDC, pore partitioning, and hindered diffusion processes. A model should also have as asymptotes the mean residence time behavior given by Equations 1 to 3 for a nonporous system and Equation 4 for a purely flow-through porous system. 

Following IV administration, 66% of circulating radioactivity was attributed to unchanged drug and the remainder attributed to saquinavir metabolites, suggesting that saquinavir undergoes extensive first-pass metabolism. Systemic clearance of saquinavir was rapid, 1.14 L/h/kg after IV doses of 6, 36, and 72 mg. The mean residence time of saquinavir was 7 hours. 

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