Residence time curves, concentration

A similar treatment of the propylene pyrolysis data at 750°C is shown in Figure 18. In this case, the calculated rates obtained by extrapolating Equation 2 to higher temperatures are much smaller than those determined by graphical differentiation of yield-to-residence time curves. The rate of formation of cyclics is linear with butadiene concentration. This... 

To find out the effective number of compartments that corresponds to the horizontal equipment of Fig. 7.38, tracer experiments were conducted. After a prescribed time at steady operating conditions a granular tracer substance was added to the solid feed stream. Samples were taken at the discharge of the plant at defined time intervals and analyzed by means of pH measurement after dissolution in de-mineralized water. The pH value of the solution corresponds to the concentration of tracer, and can be used to calculate residence time curves. Measurements were carried out for the two already mentioned total gas flow rates of 500 and 700 m h under otherwise the same conditions (mass flow rate of solids 20 kg h , bed mass 25 kg, tracer mass 5 kg, test duration 140-150 min). 

The evaluation of the experiments in both reactors was based on the mechanism of the oxidation. The concentration profiles measured in the integral reactor, as well as the finite slope in the origin of the concentration-residence time curves from the loop reactor, reveal that, the xylene is converted by simultaneous reactions to the products phthalicanhydride, phthalide, toluylaldehyde, CO and CO2. The distinct maximum of the phthalide- and tolualdehyde -concentration curve indicates that these are intermediate products which are converted mainly to phthalicanhydride in a consecutive step. From the decrease of the PSA-concentration at high residence times it may be concluded that, this species oxidize to CO, CO2, as well as water and to a lower extend, to MSA. For the evaluation of the ex-... 

In Fig. 28, the abscissa kt is the product of the reaction rate constant and the reactor residence time, which is proportional to the reciprocal of the space velocity. The parameter k co is the product of the CO inhibition parameter and inlet concentration. Since k is approximately 5 at 600°F these three curves represent c = 1, 2, and 4%. The conversion for a first-order kinetics is independent of the inlet concentration, but the conversion for the kinetics of Eq. (48) is highly dependent on inlet concentration. As the space velocity increases, kt decreases in a reciprocal manner and the conversion for a first-order reaction gradually declines. For the kinetics of Eq. (48), the conversion is 100% at low space velocities, and does not vary as the space velocity is increased until a threshold is reached with precipitous conversion decline. The conversion for the same kinetics in a stirred tank reactor is shown in Fig. 29. For the kinetics of Eq. (48), multiple solutions may be encountered when the inlet concentration is sufficiently high. Given two reactors of the same volume, and given the same kinetics and inlet concentrations, the conversions are compared in Fig. 30. The piston flow reactor has an advantage over the stirred tank... 

Typical results for these three collision mechanisms are shown in Figure 3 where the relative intensities of the primary, secondary, and tertiary ions are plotted against N, the concentration of molecules in the source. In deriving these curves, the parameters used were kp = 2.0 X 10 9 cc./molecule-sec. k8 = 1.0 X 10 9 cc./molecule-sec. tp = 8.5 X 10 7 sec., (the residence time of the ion (jn/e — 33) in a field of strength 9.1 volts/cm. in the Leeds mass spectrometer). In applying this analysis to a system in which the tertiary ion reacts to form quaternary and higher order ions, ITtotal represents the sum of tertiaries, quaternaries, etc. 

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]. 

This model accurately predicted the time curves for blood concentration and urinary excretion of metabolites by male volunteers exposed to 100 ppm trichloroethylene (Sato et al. 1991). It was found that, while the amount of metabolite excretion increases with body weight, the concentration does not, because of a corresponding increase in urinary volume. Also, women and obese people, compared with slim men, have lower concentrations but longer residence times of blood trichloroethylene because of their higher fat content (Sato et al. 1991). As a consequence, the model predicted that 16 hours after exposure to trichloroethylene, one could expect a woman s blood level to be 30% higher and an obese man s level to be twofold higher than that of a slim man (Sato 1993). 

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

OS 87] [R 35] [P 67] Generally, on-line analysis allows one to determine product concentrations, giving proper conversion [72, 74], A limit is given by intermediates which also absorb in the same spectral range, also shifting the maximum of the absorption curve. It was assumed that the product pinacol does not contribute to the absorption, only the reactant and the intermediates. In addition, a delay arises between the end of irradiation and on-line analysis as the reaction mixture has to pass a conduit between the two locations. Hence the reaction proceeds further and this is dependent on the flow rate and residence time. 

The variance of the residence times VRT is derived from the area under the second moment of the plasma concentration curve AUSC ... 

In a real stirred tank with bypassing or short-cut flow (Fig. 3.22), highly concentrated tracer comes out early, and the residence time distribution depends on the fraction a of the flow in the bypass (Fig. 3.23). The tailing of the response curve is caused by the perfect mixing in the main part of the tank. 

In addition to the aforementioned slope and variance methods for estimating the dispersion parameter, it is possible to use transfer functions in the analysis of residence time distribution curves. This approach reduces the error in the variance approach that arises from the tails of the concentration versus time curves. These tails contribute significantly to the variance and can be responsible for significant errors in the determination of Q)L. 

Since the concentration profile given by Equation (2) is nearly symmetrical, it can be assumed that t occurs at the midpoint of the curve, therefore, this value is equivalent to the mean residence time, . For columns consisting of a large number of theoretical stages, the quantity (N-1)/N approaches unity and Equation (3) becomes... 

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. 

Material balances relating concentration and temperature of adiabatic reaction in a CSTR are obtained for several different rate equations or conditions. The curves are drawn with feed concentration Caf = 1 and residence time t = 1 in the equation,... 

This relationship is drawn in Figure 7.5 for various runoff 87Sr/86Sr ratios at t = 0, 15, and 30 Ma BP. Quite surprisingly, the Sr residence time of 4Ma requires that seawater Sr concentration should change at a rate in excess of 20 percent per million year, which is extremely unrealistic. Curves were also drawn for tSr = 20 Ma, which... 

To be able to interpret these results and to correct for the lower calcium concentrations at high sulfate and phosphate concentrations, the partition coefficients D have been determined. These values follow from the slopes of the curves in figure 7. For 5.5 and 6.0 M HjPO a D of about 1.5 10" is obtained. A similar D-value for both acid concentrations should indeed be obtained, when the activity coefficients of the ions in solution is not strongly affected by the acid concentration. The D-value for 6.5 M H PO lies somewhat higher. This could e.g. be caused by a higher activity coefficient of cadmium compared to calcium at this acid concentration. The thermodynamic D-value cannot be determined by increasing the residence time, because a residence time of 2400 seconds already caused anhydrite formation. 

In these equations kei is the elimination rate constant and AUMC is the area under the first moment curve. A treatment of the statistical moment analysis is of course beyond the scope of this chapter and those concepts may not be very intuitive, but AUMC could be thought of, in a simplified way, as a measure of the concentration-time average of the time-concentration profile and AUC as a measure of the concentration average of the profile. Their ratio would yield MRT, a measure of the time average of the profile termed in fact mean residence time. Or, in other words, the time-concentration profile can be considered a statistical distribution curve and the AUC and MRT represent the zero and first moment with the latter being calculated from the ratio of AUMC and AUC. 

The first term is the ratio of maximum loading of solid for a specific inlet concentration to that concentration, whereas the second term is the space velocity (the reciprocal of the residence time), and the third term is the slope of the breakthrough curve. Thus, the constant pattern condition is achieved for... 

Initially, all the hydrocarbon is adsorbed on the core and none is observed at the outlet. Once the core is saturated, hydrocarbon breakthrough is observed. Example breakthrough curves for two temperatures are shown in Fig. 27. The amount of hydrocarbon adsorbed is given by the area above the breakthrough curve (after correction for the residence time of the reactor). By conducting experiments with different hydrocarbon concentrations and at different temperatures, the temperature and concentration dependency of the amount stored can be determined and hence isotherms generated. 

The reaction rate curve R is zero at complete conversion and also has low (but non-zero) values close to 1 — a = 0, with a maximum close to two-thirds conversion (actually at 1 — a = — / 0). Importantly, R does not depend on the residence time rres, although it does vary if / 0 is changed. The flow line L is zero when 1 — a = 0 since the inflow and outflow have the same composition (no conversion of A to B). The gradient of the flow line (Fig. 6.7(b)) is given by 1 /Tres, so it is steep for short residence times (fast flow rates) and relatively flat for long rres. (Note how tres actually compares fres and lch, so short residence times are those that are much less than the chemical timescale etc.) The flow line is, however, unaffected by the inflow concentration of the autocatalyst f 0. 

The full expressions for R and L have been given in eqns (6.52) and (6.53). The only difference between these forms and those of the previous subsection is that the reaction rate curve R now involves the inflow concentration of the autocatalyst. The flow line L, its dependence on the residence time, and its minimum gradient are all independent of po. 

Residence time distribution (RTD). The curve of concentration of tracer, C(t). as a function of time, recorded at the exit, in effect displays the distribution of residence times or holding times of the vessel. 

Here it was assumed that n=3. From bqs. 14 and IS, we calculate that o2(r0)=0.333. and K/vl. 0 115. Be tween the two predictions is a composite curve. This is an interpolation predicting what the retention time distribution should be for the constant-level skim tank based on the two models. According to this curve, the peak concentration is predicted to occur at t-O. Stp, and the time span at one half the peak concentration is t. The peak concentration should be about 0.9 (/ ). The variance. aJ, of this vessel, should he 0.333 the mean residence time is 0.78fp. The actual retention time distribution for this vessel is plotted in Fig. 6. It can he seen that the peak concentration actually occurs at /=O.35r0. From Eq. 8. T=54.9 minutes (1.0lro) for this distribution and we can calculate that 02( d)sO.3O3. Thus, in this vessel the actual constants are rt 3.29 and A/vT.=0.106, using Eqs. 14 and IS. 

The residence time distribution is measured by monitoring the outlet concentration of an inert tracer that can be analyzed for accuracy. The shape of response curve is compared with that of a thoroughly (ideally) mixed tank. 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

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