Mass balance methods

The measurement of carotenoid absorption is fraught with difficulties and riddled with assumptions, and it is therefore a complex matter. Methods may rely on plasma concentration changes provoked by acute or chronic doses, oral-faecal mass balance method variants and compartmental modelling. 

Methods used in studies of NH3 loss at AGRI, Hurley, involve the micrometeorological mass balance method for studies in grazed swards and a system of wind tunnels for small field plots to which specific treatments have been applied (e.g., slurry or urine). In the mass balance method, NH3 loss is calculated from measurements of (i) wind speed to a height of 3 m (ii) wind direction and (iii) the NH3 concentration profile in air windward and leeward of a treated area. The method has been successfully applied in studies in which the distance between the windward and leeward sampling... 

Rate of ammonia lose (mass balance method), rngNm h-1... 

Fig. I. Relationship between concurrent measurements of the rate of ammonia loss made using the wind tunnel and micrometeorological mass balance methods during an experiment in which the mean air speed through the tunnels was adjusted to maintain a value within 20% of the mean ambient wind speed. Rates of loss measured using the wind tunnels are the means of four replicates, the bars around each point indicating the 95% confidence limits (reproduced from ref. 12).

RYDEN, J.C. and McNEILL, J.E. (1984). Application of the micro-meorological mass balance method to the determination of ammonia loss from a grazed sward. Journal of the Science of Food and Agriculture 35, 1297-1310. 

Rogers used two methods to determine the burning rate. They will be referred to here as (1) weighing method (2) mass-balance method. Rogers used the latter method to verify the former method. 

The mass-balance method is very similar to the one developed by this author. Rogers presented a physical model and a mathematical model of the method. Here is a short summary. 

Figure 2 Rogers system definition of the mass-balance method [2]...

The main assumptions of the method are not explicitly declared. For example, Rogers does not discuss the problems with respect to the conflict between the transient behaviour of a batch process and the implicit steady-state assumption of the mass balance. However, the mathematical model behind the mass-balance method is quite clear. The work does not include any uncertainty propagation analysis of the mass-balance method. 

According to this author s opinion, only Rogers and Axell have presented their applied measurement methods in a reproducable manner to the reader. However, Rogers mass-balance method is not analysed with respect to uncertainty and it is only verified in two single tests. 

Toriyama S, Shimada H, Arakawa H, et al. 1991. An estimate of source contrihution of atmospheric aerosols in Toyama Prefecture by chemical mass balance method. Nippon Kagaku Kaishi N5 454-464. 

This approach has clearly allowed the resolution of the sources with results that appear to be very competitive to the chemical mass balance method. However, it was not necessary to make initial assumptions regarding the number of particle sources or their elemental composition. Additional studies need to be made to test the accuracy and precision with which such resolutions can be made. 

The chemical mass balance method starts with a single column vector from the ambient data matrix, C]. This vector represents the chemical concentrations for the kth filter, which is combined with the best available estimates of the source compositions from the fractional composition matrix, Fij> to form a series of linear equations in which the Mj are the only unknowns. This set of equations is then solved by the least squares method to obtain the best fit of the ambient chemical data on a single filter. 

A substantial amount of confusion (9,10.13,14) has recently developed as to an approach s dependence on conservation of mass. As Cooper and Watson ( ) have noted, the F j factors refer to the source chemistry as it arrives at the receptor. It is assumed with the conservation of mass that the Fj j as might be measured at a receptor, is the same as have been measured at the source. As noted above, this may not be valid depending on the source and the method used for source sampling. The chemical mass balance method incorporates the F j directly in its calculations and as a result is often perceived as having a greater dependence on this assumption than methods such as factor analysis which do not use Fy values in their calculations. Factor analysis methods, however, identify abstract factors, which explain variability. It is impossible to attribute a common... 

A source apportionment study using the receptor model should include interpretation of the chemical data set by both multivariate and chemical mass balance methods The most critical steps in a receptor model study are the initial review of potential source characteristics and the development of an appropriate study plan. 

Core, J.E. Hanrahan, P.L. Cooper, J.A. "Air Particulate Control Strategy Development A New Approach Using Chemical Mass Balance Methods." This symposium. 

The source contributions of aerosol formed from gaseous emissions, such as sulfate, nitrate and certain organic species, cannot be quantified by chemical mass balance methods, Watson (9>) proposes a unique source type which will put an upper limit on the contributions of secondary aerosol sources, but it cannot attribute those contributions to specific emitters. 

Next, the applications have to be validated and placed into standardized forms. Validation should consist of two steps. First, simulated data sets of aerosol properties should be generated from pre-selected source contributions as did Watson in his simulation studies of the chemical mass balance method. These data should be perturbed with the types of uncertainties expected under field conditions. The types of sources and their contributions predicted by the receptor model application should be compared with the known source model values and the extent of perturbation tolerable should be assessed. 

A New Approach Using Chemical Mass Balance Methods... 

Sources of Portland s total suspended particulate mass (Figure 1) were successfully identified by Chemical Mass Balance methods ( ). The key results of the study were as follows ... 

Application of Chemical Mass Balance Methods to the Identification of Major Aerosol Sources in the Medford Airshed", Interim Report to the State of Oregon Department of Environmental Quality, November 1979. 

Cooper, J. A. and J. G. Watson. Portland Aerosol Characterization Study (PACS). Application of Chemical Mass Balance Methods to the Identification of Major Aerosol Sources in the Portland Airshod. Final report Summary. Prepared for the Portland Air Quality Maintenance Area Advisory Committee and the Oregon Department of Environmental Quality. April 23, 1979. 

There are a number of different types of source apportionment models, including the chemical mass balance method, factor analysis, multiple linear regression analysis, and Lagrangian modeling. The chemical... 

Steady-State Mass Balance Method In theory, the Ki a in an apparatus that is operating continuously under steady-state conditions could be evaluated from the flow rates and the concentrations of the gas and liquid streams entering and leaving, and the known rate of mass transfer (e.g., the oxygen consumption rate of microbes in the case of a fermentor). However, such a method is not practical, except when the apparatus is fairly large and highly accurate instruments such as flow meters and oxygen sensors (or gas analyzers) are available. 

Unsteady-State Mass Balance Method One widely used technique for determining Kj a in bubbling gas-liquid contactors is the physical absorption of oxygen or COj into water or aqueous solutions, or the desorption of such a gas from a solution into a sparging inert gas such as air or nitrogen. The time-dependent concentration of dissolved gas is followed by using a sensor (e.g., for O2 or CO2) with a sufficiently fast response to changes in concentration. 

Stable-Isotope Mass-Balance Method. The equations presented in this section apply to groundwater-lake systems that are at hydrological and isotopic steady states. Equations that describe isotopic mass balances for non-steady-state systems and forms that pertain to the estimation of evaporation from lakes have been presented by other authors (13, 14). 

Reliable estimates of relative humidity are critical for use of the isotope mass-balance method however, humidity data are difficult to interpret and commonly not available for a specific study area. The index-lake method provides a means for checking the accuracy of these data and the validity of their use in isotope hydrology. The equation that describes the steady-state isotopic composition of a lake (35) is... 

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... 

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