Tracers mass balance

So far, all of the material presented has been discussed in the absence of any numerical examples. At this point, we introduce such an example the initial calculations will be used subsequently as a basis for further examples and, in this way, it will be possible to see how raw tracer data can be processed. Eventually, predictions will be made of what conversion can be expected when a reaction with known kinetics takes place in the system from which the tracer information was gathered. In the examples which involve tracer data, it should be emphasised that only in the most carefully engineered equipment could data of the accuracy quoted be obtained. In real situations, tracer mass balances may close inadequately and predictions of reactor performance must be treated with appropriate caution. 

P14-1b Make up and solve an original problem. The guidelines are given in Problem P4-1. However, make up a problem in reverse by first choosing a model system such as a CSTR in parallel with a CSTR and PFR [with the PFR modeled as four small CSTRs in series Figure P14-l(a)] or a CSTR with recycle and bypass [Figure P14-l(b)]. Write tracer mass balances and use an ODE solver to predict the effluent concentrations. In fact, you could build up an arsenal cf tracer curves for different model systems to compare against real reactor RTD data. In this way you could deduce which model best describes the real reactor. 

Thus, the RTD E 6) can be determined from the measured outlet concentrations in arbitrary units and without knowing the exact amount of tracer injected. In practice, it is recommended to also use the tracer mass balance (12.6.2.B-a) to check the quality of the experiment. Alternatively, from a known amount M of tracer injected and the integral of the outlet tracer concentration curve, the flow rate F can be found via (12.6.2.B-b) (often used in physiology). 

Equation (11) is model independent and provides the means for determining the unknown volume of the system. The question arises in practice whether t can be evaluated accurately from eq. (11). Small errors in the tracer mass balance, eq. (7), can lead to large errors in t and even larger errors in the estimation of the variance of the E curve (43). Due to the relationship of E(t) and F(t) the mean residence time can also be obtained directly from a step-up or a step-down test ... 

If the source fingerprints, for each of n sources are known and the number of sources is less than or equal to the number of measured species (n < m), an estimate for the solution to the system of equations (3) can be obtained. If m > n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for L. This is the basis of the chemical mass balance (CMB) method (20,21). If each source emits a particular species unique to it, then a very simple tracer technique can be used (5). Examples of commonly used tracers are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. The condition that each source have a unique tracer species is not often met in practice. 

The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the air-tracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test section has a zero concentration, the air volume flow rate can be calculated based on the mass balance of the tracer... 

Total mass balance 15, 29, 131 Total reflux 588, 615 Tracer 162... 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

Expired air. For 14C-labeled chemicals, the tracer carbon may be incorporated in vivo into carbon dioxide, a possible metabolic product. Therefore, when the position of the radiolabel indicates the potential for biological instability, a pilot study to collect expired air and monitor its radioactivity content should be conducted prior to initiating a full-scale study. Expired air studies should also be performed in situations where the radiolabel has been postulated to be stable but analyses of urine and feces from the toxicokinetic study fail to yield complete recovery (mass balance) of the dose. 

Writing an unsteady state mass balance on the tracer... 

The first check is to see whether the information presented is self-consistent and that all the dye injected has flowed out of the system. Problems in carrying out this check may be expected because, from the tabulated data, it is evident that the tracer response has a long tail which is still present to a small extent after 20 min, after which time no more data are available. From mass balance considerations... 

Using benzene as a tracer, it is possible to estimate the volume of the injection loop under the assumption that all the material injected leaves the columns in the interval (to - tf). The mass of material injected can be calculated by integrating the contents of the detector cell. A simple mass balance gives... 

Masclet and co-workers (1986) have also developed a relative PAH decay index. They used it, for example, to identify various major sources of urban pollution and developed a model for PAH concentrations at receptor sites. An interesting and relevant area that is beyond the scope of this chapter is the use of PAHs as organic tracers and incorporating their relative decay rates (reactivities) into such receptor-source, chemical mass balance models. Use of relative rates can significantly improve such model performances (e.g., see Daisey et al., 1986 Masclet et al., 1986 Pistikopoulos et al., 1990a, 1990b Lee et al., 1993 Li and Kamens,... 

Two dynamic alternatives to the static approach have been used in HO calibration and measurement. In the CSTR (continuously stirred tank reactor) approach, air containing the tracer or tracers flows into the reactor to balance the bulk flow out to the HO measuring devices, and the contents are stirred by a fan or other means. The HO chemical tracer is measured in the inlet flow to obtain [T]() and in the outlet flow to obtain [T], Mass balance requires... 

An interesting implication of the Toth-Freeze-Witherspoon model is the deep penetration of surface water into the basin over geologic time. This has been used to derive a geochemical mass balance model for the mixing of surface water and diagenetically modified sea water in the Western Canada sedimentary basin using deuterium as a tracer (204). 

Groundwater-inflow rates as calculated by the solute and isotope mass-balance methods for several northern Wisconsin lakes are listed in Table I. Dissolved calcium was used as the solute tracer because it is the constituent whose concentration differs the most between groundwater and precipitation, the two input components to be separated by the method. In addition, calcium is nearly conservative in the soft-water, moderately acidic to cir-cum-neutral lakes in northern Wisconsin. Results from the two methods agree relatively well, except for Crystal Lake, where groundwater-flow reversals are frequent. 

The isotope mass-balance method is not as useful for estimating groundwater-flow rates for groundwater-poor lakes as it is for lakes that receive substantial quantities of groundwater. Solute tracers, such as dissolved calcium, may be useful in assessing... 

The inherent chemical complexity of DOM presents many challenges to understanding the role of DOM in C and N cycling and other processes in aquatic ecosystems. The measurement of trace organic moieties in major fractions of DOM, such as fulvic acids, can provide valuable data for understanding sources and biogeochemical pathways. In field studies, multiple lines of evidence can be critical for definitive interpretation of results. The tracer approaches outlined in this chapter should be used in conjunction with mass balance and flux measurements, for example. 

The theory and verification of the mixing-cell mass balance equation has been reported previously (2). For a cell with initial concentration of tracer, C, flushed with tracer-free... 

In this study we have employed the simultaneous collection of atmospheric particles and gases followed by multielement analysis as an approach for the determination of source-receptor relationships. A number of particulate tracer elements have previously been linked to sources (e.g., V to identify oil-fired power plant emissions, Na for marine aerosols, and Pb for motor vehicle contribution). Receptor methods commonly used to assess the interregional impact of such emissions include chemical mass balances (CMBs) and factor analysis (FA), the latter often including wind trajectories. With CMBs, source-strengths are determined (1) from the relative concentrations of marker elements measured at emission sources. When enough sample analyses are available, correlation calculations from FA and knowledge of source-emission compositions may identify groups of species from a common source type and identify potential marker elements. The source composition patterns are not necessary as the elemental concentrations in each sample are normalized to the mean value of the element. Recently a hybrid receptor model was proposed by Lewis and Stevens (2) in which the dispersion, deposition, and conversion characteristics of sulfur species in power-plant emissions... 

This model combines the results of an effort to measure ventilation flows within residences via a perfluorocarbon tracer method (Versar, Inc., 1989) with a two-zone mass balance model to allow estimation of potential dose rates to users and non-users. 

The basic equations are derived from a mass balance of a tracer component as follows ... 

Now imagine a perfectly mixed CSTR operating with a tracer material with inlet concentration Cj and effluent concentration Com- The mass balance for this system is... 

Because dissolved N2 is assumed to be inert in seawater (at least under the most common condition, see discussion below), it can serve as a tracer of physical processes (Emerson et al., 1995) Measurements of dissolved N2 in combination with Ar and O2 measurements were successfully used in mass balance models of the upper ocean in order to quantify the net biological O2 production and the associated carbon production (Emerson et al., 1991, 1995, 1997). 

Mass balance and isotopic tracer approaches have been used to quantify N fluxes associated with marsh plant growth and death. One study in a very productive, medium form of S. alterniflora from a Georgia salt marsh shows that total uptake of N by roots of S. alterniflora was 34.8 g N m year. Of this 43% was lost by death or leaching from aboveground plant parts, while the rest was lost by death of roots and rhizomes. Total transfer of N from below-to aboveground tissues was 33 g N m ... 

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