Residence time analysis

Albarede F (1993) Residence time analysis of geochemical fluctuations in volcanic series. Geochim Cosmochim Acta 57 615-621... 

Single-variable residence time analysis would be at steady-state but not 87Sr, which translates into... 

The axial dispersion coefficient Dax was estimated from conventional residence time analysis for nonreacting conditions [14, 47]. The lines shown in Fig. 12.8 demonstrate that essential features of the reactor behavior are well represented. This also indicates a certain reliability of the derived kinetic equation Eq. (30). 

Figure 18.4A shows the output from a tanks-in-series model for a unit impulse or bolus input into the Ml compartment. Each compartment was assumed to have T= 1. The mean residence time, t, in an (V-compartment tanks-in-series model is simply the sum of the residence times in each compartment and f = At. The change in the variance of the signal upon passage through the compartments is given by Arl In residence time analysis, it is conventional to normalize the time values through a simple division by the mean residence time value. The mean and variance of the normalized residence times of a tanks-in-series model are ju = 1 and Acr = l/N,... 

Ritchie, B. W. and A. H. Tobgy. Residence Time Analysis in Systems Having Many Connections with their Environment. Ind. Eng. Chem. Fundamentals 17 (1978) 287. 

Chemical Reaction Measurements. Experimental studies of incineration kinetics have been described (37—39), where the waste species is generally introduced as a gas in a large excess of oxidant so that the oxidant concentration is constant, and the heat of reaction is negligible compared to the heat flux required to maintain the reacting mixture at temperature. The reaction is conducted in an externally heated reactor so that the temperature can be controlled to a known value and both oxidant concentration and temperature can be easily varied. The experimental reactor is generally a long tube of small diameter so that the residence time is well defined and axial dispersion may be neglected as a source of variation. Off-gas analysis is used to track both the disappearance of the feed material and the appearance and disappearance of any products of incomplete combustion. 

The Z-concept permits scale-up between sinulat centrifuges solely on the basis of sedimentation performance. Other criteria and limitations, however, should also be investigated. Scale-up analysis for a specified sohds concentration, for instance, requires knowledge of sohds residence time, permissible accumulation of sohds in the bowl, G level, sohds conveyabihty, flowabihty, compressibihty, limitations of torque, and sohds loading. Extrapolation of data from one size centrifuge to another calls for the apphcation of specific scale-up mechanisms for the particular type of centrifuge and performance requirement. 

Composition The law of mass aclion is expressed as a rate in terms of chemical compositions of the participants, so ultimately the variation of composition with time must be found. The composition is determined in terms of a property that is measured by some instrument and cahbrated in terms of composition. Among the measures that have been used are titration, pressure, refractive index, density, chromatography, spectrometry, polarimetry, conduclimetry, absorbance, and magnetic resonance. In some cases the composition may vary linearly with the observed property, but in every case a calibration is needed. Before kinetic analysis is undertaken, the data are converted to composition as a function of time (C, t), or to composition and temperature as functions of time (C, T, t). In a steady CSTR the rate is observed as a function of residence time. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

Equations (2-3.7) forQjand Eqs. (2-3.1), (2-3.2), and (2-3.8) forr are used extensively in static hazard analysis. Examples include selection and use of instrumentation (3-5.3) and residence time provisions for charged liquids (5-2.4). 

As we have said, the key to the analysis of asystemlike this one is tohave a function that approximates to the actual residence time distribution. The tracer experiment is used to find that distribution function,butwewillworkfroman assumed function to the tracer concentration-timecurvetoseewhattheexperimentaloutcomemightlooklike. 

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. 

A pilot-scale continuous MSMPR crystallizer of 10 litre capacity is used to crystallize potash alum from aqueous solution, supersaturation. This is being achieved using a 15-min residence time, a 100-ml slurry sample was taken and the crystals contained in this sample subjected to a size analysis. The results of this analysis are given below... 

The quality of the packed bed may also be determined by frontal analysis where the sample is applied until it reaches a plateau to give the residence time function and then the solution is momentarily switched to wash to give the washout function. The latter is used to calculate the plate height of the column... 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

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. 

Monomer concentration dynamics are presented in Figure 5. Additional observations for Run 5 are accurately correlated during the reactor startup and at final steady state. The observation at one residence time, Run 4, may be in error. The total cummu-lative, molar concentrations of macromolecules as a function of time are presented in Figure 6. The errors associated with this dependent variable are also evident during the steady state analysis of initiation... 

Assuming an input flux equal to oceanic evaporation, this would give a turnover time of about 750 years. The turnover time analysis is not strictly correct since freshwater resides in a number of interconnected reservoirs however. 

Suppose now that a pilot-plant or full-scale reactor has been built and operated. How can its performance be used to confirm the kinetic and transport models and to improve future designs Reactor analysis begins with an operating reactor and seeks to understand several interrelated aspects of actual performance kinetics, flow patterns, mixing, mass transfer, and heat transfer. This chapter is concerned with the analysis of flow and mixing processes and their interactions with kinetics. It uses residence time theory as the major tool for the analysis. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

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