Simple mass balance

Taking the basis as a unit mass of solid, the unit can be analysed by simple mass balance on the suspension as follows ... 

All the internal flowrates are related to the inlet/outlet flowrates by simple mass balances ... 

Low-temperature, photoaggregation techniques employing ultraviolet-visible absorption spectroscopy have also been used to evaluate extinction coefficients relative to silver atoms for diatomic and triatomic silver in Ar and Kr matrices at 10-12 K 149). Such data are of fundamental importance in quantitative studies of the chemistry and photochemistry of metal-atom clusters and in the analysis of metal-atom recombination-kinetics. In essence, simple, mass-balance considerations in a photoaggregation experiment lead to the following expression, which relates the decrease in an atomic absorption to increases in diatomic and triatomic absorptions in terms of the appropriate extinction coefficients. 

However, conducting a complete LCA is very time consuming. Fortunately, simple mass balancing may already indicate most relevant requirements for action. This was illustrated by one case study concerning a pharmaceutical intermediate (Scheme 5.1). Compared to LCA, the system boundaries of mass balancing are relatively narrow. For instance, the case study focuses on the chemical reaction and does not take into account the production of substrates. In this respect, a look at two reduction reactions of the synthetic routes via B and via C is worthwhile (Scheme 5.1). 

In Chapter 9, it was shown how the Underwood Equations can be used to calculate the minimum reflux ratio. A simple mass balance around the top of the column for constant molar overflow, as shown in Figure 11.3, at minimum reflux gives ... 

A second major estimating technique is the materials balance approach—the original focus of this paper. A chemical engineering standard, the materials balance can reduce to the simple mass balance, as when the measured mass of a chemical in products leaving the plant is subtracted from the raw material entering the plant to yield the loss. This loss is then partitioned among releases to various media or other sinks. If... 

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Different levels of description of the rate expressions, rw and tp can be selected when using a simple mass balance as expressed in Equation (5.10). Matos and de Sousa (1996) propose a temperature-dependent, however, DO nondependent value for rw ... 

Adsorption phenomena frequently are studied by measuring solely the change in concentration of a species i in the aqueous solution phase. Simple mass-balance considerations (1) show that Equation 1 can be rewritten in a form compatible with this methodology ... 

If the user writes a simple mass balance for the solubility equilibrium or ionic equilibrium such as - the reaction of b moles of B with c moles of C has come to equilibrium with the product of d moles of D and e moles of E, then the mass balance is given by... 

If the products n, of this reaction are known, Eq. (1.11) can be solved for the flame temperature. For a reacting lean system whose product temperature is less than 1250 K, the products are the normal stable species C02, H20, N2, and 02, whose molar quantities can be determined from simple mass balances. However, most combustion systems reach temperatures appreciably greater than 1250K, and dissociation of the stable species occurs. Since the dissociation reactions are quite endothermic, a small percentage of dissociation can lower the flame temperature substantially. The stable products from a C—H—O reaction system can dissociate by any of the following reactions ... 

We now turn to the Fe isotope fractionations that are predicted by a model where oxidation of Fe(II)aq to Feflll) occurs, followed by precipitation of Feflll) to ferrihydrite (FH) (Eqn. 5). In a closed system, the 8 Te values of the three components are constrained by simple mass balance as ... 

Once temporal changes in the relative proportions of the species FcjO, Fe(III)-Lpe(, ), Fe(II)-Lpe(ii), and Fe(II)s j are computed, the 5 Te values for the various components may be defined by a simple mass-balance equation ... 

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

The situation is somewhat different with porous membranes, where the permselectivities for all components do not equal zero but exhibit certain values determined in most cases by the Knudsen law of molecular masses. In general, when porous membranes are used as separators in a membrane reactor next to the catalyst or the reaction zone (Figure 7.2a), it has been shown experimentally (Yamada et al. 1988) and theoretically (Mohan and Govind 1986, 1988a, b, Itoh et al. 1984, 1985) that there is a maximum equilibrium shift that can be achieved. On the basis of simple mass balances one can calculate that this maximum depends on, besides the reaction mechanism, the membrane permselectivities (the difference in molecular weights of the components to be separated) and it corresponds to an optimum permeation to reaction-rate ratio for the faster permeating component (which is a reaction product). 

Each component is calculated in turn. It is assumed that the relative split of the component on a stage is correct as reported from the iteration just calculated. A simple mass balance then gives new estimates for the amount of the component in the phases without any calculation of a flash. If the component is in exact balance at all points, no change will be made in its flow amount at any point by this procedure. However, if there is an unbalance at any point, this unbalance will be lessened and propagated outward. 

The composition profile is approximated by a step profile, with a uniform composition xf in the surface layer (0bulk phase x, at z>L. It is assumed that the total amount of liquid can be divided into two parts with the first constituting the homogeneous bulk phase (mole numbers in it n° = til -I- 2) and the remainder standing under the influence of the forces emanating from the solid surface causing adsorption (mole numbers, referred to unit mass of adsorbent, = n, -i- 2 the superscript a referring to adsorption) [17]. Simple mass balance considerations lead to the following expressions [12] ... 

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... 

In a search for sources of alkaline materials in rural air and rain, we have sampled and performed multi-element analyses on ambient particulate matter and potential source materials. Ambient aerosols were sampled daily using single Nuclepore filters or Florida State University "streakers." Samples of soil and unpaved road materials were also collected and analyzed. The samples were analyzed by various multi-element methods, including ion-and proton-induced X-ray emission and X-ray fluorescence, as well as by atomic absorption spectrophotometry. Visual observations, as well as airborne elemental concentration distributions with wind direction and elemental abundances in aerosols and source materials, suggested that soil and road dust both contribute to airborne Ca. Factor analysis was able to identify only a "crustal" source, but a simple mass balance suggested that roads are the major source of Ca in rural central Illinois in summer. 

Other Applications of the Multiple-Core Approach. The bulk of this chapter has dealt with the specific application of multiple-core methodology to questions of atmospheric Hg deposition. Whole-basin Hg accumulation rates for seven lakes, calculated from multiple sediment cores, were used in a simple mass-balance model to estimate atmospheric fluxes and Hg transport from catchment soils. This approach can be used to answer other limnological questions, and the model is not restricted to Hg or atmospheric deposition. 

If whole-basin accumulation rates for a substance are produced for multiple lakes in a geographic region, it is possible to use a simple mass-balance model to estimate both the atmospheric deposition rate and transport from the terrestrial catchment. The model was applied to both modern and preindustrial Hg accumulation in seven undisturbed lakes in the upper midwest... 

Implementation of conditions (1) to (3) is done following a similar procedure as that of a two-phase system (Rachford and Rice, 1952). For a system with C components and n possible phases, satisfying a simple mass balance for each component in each phase results in the following objective function ... 

Due to the highly nonideal behavior of the hydrate phases, Equation 5.46 is not used to update the hydrate composition. However, the compositions of all nonhydrate phases are determined via Equation 5.46. All composition corrections of a given phase are scaled such that no composition in that phase is changed by more than 50% of its original value. The expression for the composition of species in the hydrate follows from a simple mass balance ... 

Finally we note that the relation (6.129) can also be obtained by a simple mass balance. 

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