Mean residence time determination

The RTD allows to calculate t, the residence time of the material in the device. If T is the mean residence time, determined by ... 

Global kinetics, however, allowed calculation of some parameters in normal volunteers, i.e., fractional catabolic rate, rate of synthesis, and mean residence time determined by the mathematical analysis of both plasma decay curves and urinary excretion rates. Such studies demonstrated different metaboUsms for Apo C-I, C-II, and C-III. They may supply essential information on the perturbations observed in pathology. 

The holdup of material in a continuous mill determines the mean residence time, and thus the extent of grinding. Gupta et al. [International J. Mineral Processing, 8, 345-358 (Oct. 1981)] analyzed published e)merimental data on a 40 X 40-cm grate discharge laboratoiy mill, ana determined that holdup was represented by = (4.020 — 0.176 WT)F , (0.040 0.01237 WT)S, - (4.970 0.395 Wl), where... 

The mean residence time T (defined as H JF) is the most important parameter, since it determines the time over which particles are exposed to grinding. Measurements on several industrial mills (Weller, Automation in Mining Mineral and Metal Processing, 3d IFAC Symposium, 303-309, 1980) (measured on the water, not the ore) showed that the maximum mill filhng was about 40 percent, and the maximum flow velocity through the mill is 40 m/h. 

The fractional conversion is determined from Equation 5-167 in terms of the mean residence time f = (V /u) to yield... 

A table was constructed to determine the mean residence time t, variance E(6), F(6), and 1(6) parameters from the effluent tracer versus time data. 

The CSD from the continuous MSMPR may thus be predicted by a combination of crystallization kinetics and crystallizer residence time (see Figure 3.5). This fact has been widely used in reverse as a means to determine crystallization kinetics - by analysis of the CSD from a well-mixed vessel of known mean residence time. Whether used for performance prediction or kinetics determination, these three quantities, (CSD, kinetics and residence time), are linked by the population balance. 

Example 3.5 A 1-in i.d coiled tube, 57 m long, is being used as a tubular reactor. The operating temperature is 973 K. The inlet pressure is 1.068 atm the outlet pressure is 1 atm. The outlet velocity has been measured to be 9.96 m/s. The fluid is mainly steam, but it contains small amounts of an organic compound that decomposes according to first-order kinetics with a half-life of 2.1s at 973 K. Determine the mean residence time and the fractional conversion of the organic. 

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 ... 

For the styrene polymerization in Example 5.7, determine those values of the mean residence time that give one, two, or three steady states. 

The density is constant and the mean residence time is 2h, as determined from the known volume of the reactor and the outlet flow rate. The temperature was the same for all runs. 

Example 12.8 The batch reactor in Example 12.7 has been converted to a CSTR. Determine its steady-state performance at a mean residence time of 4 h. Ignore product inhibition. 

Via a passive scalar method [6] where or, denotes the volume fraction of the i-th phase, while T, represents the diffusivity coefiBcient of the tracer in the i-th phase. The transient form of the scalar transport equation was utilized to track the pulse of tracer through the computational domain. The exit age distribution was evaluated from the normalized concentration curve obtained via measurements at the reactor outlet at 1 second intervals. This was subsequently used to determine the mean residence time, tm and Peclet number, Pe [7]. 

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... 

ILLUSTRATION 8.5 DETERMINATION OF MEAN RESIDENCE TIME IN A PLUG FLOW REACTOR UNDER ISOTHERMAL OPERATING CONDITIONS—VARIABLE DENSITY CASE... 

Levenspiel and Smith Chem. Eng. Sci., 6 (227), 1957] have reported the data below for a residence time experiment involving a length of 2.85 cm diameter pyrex tubing. A volume of KMn04 solution that would fill 2.54 cm of the tube was rapidly injected into a water stream with a linear velocity of 35.7 cm/sec. A photoelectric cell 2.74 m downstream from the injection point is used to monitor the local KMn04 concentration. Use slope, variance, and maximum concentration approaches to determine the dispersion parameter. What is the mean residence time of the fluid ... 

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. 

Adsorption Isotherms. The adsorption isotherms were determined using the serum-replacement adsorption or desorption methods (7). For the adsorption method, the latex samples (50 or 100 cm 2% solids) containing varying amounts of PVA were equilibrated for 36 hours at 25°C, placed in the serum replacement cell equipped with a Nuclepore membrane of the appropriate pore size, and pressurized to separate a small sample of the serum from the latex. For the desorption method, the latex samples (250 cm 2.5% solids) were equilibrated for 36 hours at 25°C and subjected to serum replacement with DDI water at a constant 9-10 cm /hour. The exit stream was monitored using a differential refractometer. The mean residence time of the feed stream was ca. 25 hours. It was assumed that equilibrium between the adsorbed and solute PVA was maintained throughout the serum replacement. For both methods, the PVA concentration was determined using a An-C calibration curve. 

This involves obtaining the mean-residence time, 0, and the variance, (t, of the distribution represented by equation 19.4-14. Since, in general, these are related to the first and second moments, respectively, of the distribution, it is convenient to connect the determination of moments in the time domain to that in the Laplace domain. By definition of a Laplace transform,... 

If the results cited above are put another way, from the point of view of determining fB for a given f (or reactor size), a mean residence time of 1.7 min gives fB = 0.80 for ash-layer control, as noted, but only 0.37 for reaction control, and only 0.23 for gas-film control. 

Experimentally, VDSS is determined by calculating the area under the first moment of the plasma versus time curve (AUMC), which when combined with AUC will yield the mean residence time. 

Chanter DO. The determination of mean residence time using statistical moments is it correct J Pharmacokinet Biopharm 1985 13 93-100. 

Primary outputs are produced essentially by sedimentation and (to a much lower extent) by emissions in the atmosphere. The steady state models proposed for seawater are essentially of two types box models and tube models. In box models, oceans are visualized as neighboring interconnected boxes. Mass transfer between these boxes depends on the mean residence time in each box. The difference between mean residence times in two neighboring boxes determines the rate of flux of matter from one to the other. The box model is particularly efficient when the time of residence is derived through the chronological properties of first-order decay reactions in radiogenic isotopes. For instance, figure 8.39 shows the box model of Broecker et al. (1961), based on The ratio, normal-... 

Numerous meteorites have been collected in Western Australia and terrestrial ages have been determined for 50 of them. Ages range from very young to around 40 000 years. There is a rough exponential decline in the number of meteorites as a function of age. The distribution of ages gives a mean residence time of 10 000 years at this location. 

Our aim is to determine the concentration of A in the reactor as a function of time and in terms of the experimental conditions (inflow concentrations, pumping rates, etc.). We need to obtain the equation which governs the rate at which the concentration of A is changing within the reactor. This mass-balance equation will have contributions from the reaction kinetics (the rate equation) and from the inflow and outflow terms. In the simplest case the reactor is fed by a stream of liquid with a volume flow rate of q dm3 s 1 in which the concentration of A is a0. If the volume of the reactor is V dm3, then the average time spent by a molecule in the reactor is V/q s. This is called the mean residence time, tres. The inverse of fres has units of s-1 we will call this the flow rate kf, and see that it plays the role of a pseudo-first-order rate constant. We denote the concentration of A in the reactor itself by a. 

Consider the shallow well-mixed pond (average depth = 2 m, T = 25°C pH = 8.5 a(A) see Table 15.6 mean residence time of the water 35d) introduced in Illustrative Example 16.2. In this pond, a midday, near-surface steady-state concentration of 02 ([ 02] (noon)) of 8 x 10 14 M has been determined using FFA as probe molecule (see Eq. 16-12). Recall that maximum 02 production occurs at... 

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