Mass balance calculations

If the concentrations and particle size distributions of the solids within the network itself do not have to be known then the system can be considered as a single separator and its efficiency can be calculated from that of the individual stages within it. The system efficiency thus obtained can then be used in simple one-pass predictions of particle losses to overflow and other overall separation performances of the train. This allows direct comparisons of alternative systems, as shown in the worked example in section 16.4.1. 

If the grade efficiency curves are known for all stages in a system, an equation for the grade efficiency of the whole system may be derived from mass balance around the arrangement. Reference 1 gave, for the first time. 

Example of derivation of overall efficiency from that of the individual separators 

All of the mass flow rates annotated as M in the above three equations can now be eliminated, to give a relationship between the total efficiencies  

Now what holds for total efficiencies must also hold for grade efficiencies, hence 

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C - Estimate is based on mass balance calculations, such as calculation of the amount of the toxic chemical in streams entering and leaving process equipment. 

If a mass balance calculation yields the flow rate of a waste-stream, but the quantity of reported chemical in the waste-... 

If the concentration of the chemical in the wastestream was measured by monitoring equipment and the flow rate of the wastestream was determined by mass balance, then the primary basis of estimate is "monitoring" (M). Even though a mass balance calculation also contributed to the estimate, "Monitoring should be indicated because monitoring data was used to estimate the concentration of the waste stream. 

The facility wastewater monitoring program does not determine the concentration of lead and lead compounds in the scrubber discharge water, and releases to the surface impoundment (releases to land) must be calculated using mate-riai balance information. These releases to land are determined from the amount of lead removed by the scrubber (using the efficiency data provided by the scrubber manufacturer). The volume of the scrubber blowdown Is found to be 1,500 pounds per year. Enter the estimate of the amount of lead and lead compounds released to surface Impoundments in the space provided in Part III, Section 5.5.3 of the form. Because releases of lead to the surface Impoundment are greater than 999 pounds per year, you must enter the actual calculated amount in column A.2 of Section 5.5.1. The basis for the estimate of releases to the surface impoundment, entered in column B of Section 5, is mass balance calculations (code C). 

Table 10-13 Mass balance calculation for removal of river-derived constituents from the ocean (all units in lO mmol)...

The failure to identify the necessary authigenic silicate phases in sufficient quantities in marine sediments has led oceanographers to consider different approaches. The current models for seawater composition emphasize the dominant role played by the balance between the various inputs and outputs from the ocean. Mass balance calculations have become more important than solubility relationships in explaining oceanic chemistry. The difference between the equilibrium and mass balance points of view is not just a matter of mathematical and chemical formalism. In the equilibrium case, one would expect a very constant composition of the ocean and its sediments over geological time. In the other case, historical variations in the rates of input and removal should be reflected by changes in ocean composition and may be preserved in the sedimentary record. Models that emphasize the role of kinetic and material balance considerations are called kinetic models of seawater. This reasoning was pulled together by Broecker (1971) in a paper called "A kinetic model for the chemical composition of sea water."... 

Craig, S., Holmen, K. and Bjorkstrom, A. (1997). Net terrestrial carbon exchange from mass balance calculations an uncertainty estimate, Tellus, Ser. B, 49, 136-148. 

In the Delaware and Chesapeake estuaries (USA), uranium shows distinctly nonconservative behavior at salinities <5 (Sarin and Church 1994 Church et al. 1996). This was suggested to be due to sedimentary redox processes in the extensive salt marshes in the Delaware and Chesapeake bays. From mass balance calculations it was concluded that almost two-thirds of the uranium in the tidal waters were retained in the sediments. It was also suggested that, extrapolated globally, uranium removal in salt marshes and marine wetlands, including mangroves, are important sinks for U that may responsible for up to 50% of the total marine removal (Church et al. 1996). Removal of U is also observed within the Baltic Sea, related to the association of U with colloids (see Section 2.5). 

In mass balance calculations the presence of recycle streams makes the calculations more difficult. 

A very approximate mass balance calculation for the whole range of employed SO2 concentrations based on known amount of SO2... 

First, we read in the dataset of complexation reactions and specify that the initial mass balance calculations should include the sorbed as well as aqueous species. We disable the ferric-ferrous redox couple (since we are not interested in ferrous iron), and specify that the system contains 1 g of sorbing mineral. 

Mass balance calculations were performed on till samples using Sn concentrations. Tin concentrations in till are sensitive to grain size partitioning and differing analytical methods, thus results from these calculations are qualitative. In the till, concentration gains relative to Sn in Zn, Au, Cd, Hg and Co were obvious after performing the calculations all of... 

Fig. 1. Distribution of Hg (and Cd) in till at the MFN deposit. DDH MF00-31 and DDH MF00-29 are marked with an X subcropping mineralization is marked by a dashed line. Arrows indicate ice flow directions, the youngest flow was northeastward, elements by electrochemical mechanisms and hydromorphic dispersal. These conclusions are supported by qualitative mass balance calculations and variable geochemical distribution patterns in till, in the context of local and regional ice flow.

Table 1 presents the results of fractionations of the DOM. The result of mass balance calculation of the DOC system shows that more than 55 % of the total DOC was retained by XAD-8 resin column, involving the portions of Ho A and HbN/B, and DOC concentrations of the portion eluted by blackwashing (HoA) accounted for 47.4 % of total DOC, as compared with 26.25 % hydrophilic acids (HiA) of the total DOC. More than 11% of the total DOC passed through two resin columns, indicating that small molecular weight polar components were not absorbed onto by XAD-8 and XAD-4. The fractionation did cause potential loss of organic matter by permanent adsorption onto resin s polymers, which were 8.34 % for the XAD-8 resin and 6.41 % for the XAD-4 resin, respectively. 

The results of the calculations using Equations (51) through (54) are given in Table III, which includes the pH values of the original equilibrations. In addition, mass balance calculations were carried out to see whether the solid particles had accumulated fluoride in their surface layer from the aqueous solutions. The mass balance showed that an accumulation of fluoride had occurred in the equilibration of all solid solutions. This discounts an interpretation of the solubility data as carried out by Moreno et al. (58). 

Empirical [65-79] Equilibration technique The most direct approach is to equilibrate the organic pollutant in the octanol/water system and measure its concentration in both phases Concentrations derived from mass balance calculation, though less time-consuming, can introduce considerably more uncertainty... 

On occasion, the concentration is measured in only one phase, with concentration in the other being derived from a mass balance calculation Other experimental considerations in obtaining accurate values by this approach have been discussed by several workers... 

The model depicted in Figure 9 can be tested by a simple mass balance calculation (Barling et al. 2001,... 

Table 21.11 Mass Balance Calculation for the Removal of River-Derived Constituents from the Ocean. ... 

A mass balance calculation was used to better understand the extent to which the IPGE are controlled by chromite. First, we... 

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