On mass balance

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. 

Velbel, M. A. (1985). Hydrogeochemical constraints on mass balances in forested watersheds of the southern Appalachians. In "The Chemistry of Weathering" (J. I. Drever, ed.), pp. 231-247. G. Reidel, Dordrecht, Holland. 

Cost evaluation based on mass balancing results in clearly lower cost indices for the biocatalytic process as compared to the chemical catal)d ic process (Figure 5.6). For three of the substances of the chemical procedure (Jacobsen catalyst (catalyst), 4-phenylpyridine... 

This section describes the continuous flux melting model used in Bourdon et al. (2003) and has many similarities with the model of Thomas et al. (2002). A significant difference is that the model described here keeps track of the composition of the slab as it dehydrates. This model is based on mass balance equations for both the mantle wedge and the slab. We assume secular equilibrium in the U-series decay chain initially ... 

The most effective spectrophotometric procedures for pKa determination are based on the processing of whole absorption curves over a broad range of wavelengths, with data collected over a suitable range of pH. Most of the approaches are based on mass balance equations incorporating absorbance data (of solutions adjusted to various pH values) as dependent variables and equilibrium constants as parameters, refined by nonlinear least-squares refinement, using Gauss-Newton, Marquardt, or Simplex procedures [120-126,226],... 

Similar logic gives the mass balance equations for the species components. The mass of the i th component is distributed among the single basis species A, and the secondary species in the system. By Equation 3.22, there are v, j moles of component i in each mole of secondary species Aj. There is one mole of Na+ component, for example, per mole of the basis species Na+, one per mole of the ion pair NaCl, two per mole of the aqueous complex Na2SC>4, and so on. Mass balance for species component i, then, is expressed... 

Lee and Bethke (1996) presented an alternative technique, also based on mass balance equations, in which the reaction modeler can segregate minerals from isotopic exchange. By segregating the minerals, the model traces the effects of the isotope fractionation that would result from dissolution and precipitation reactions alone. Not unexpectedly, segregated models differ broadly in their results from reaction models that assume isotopic equilibrium. 

Figure 6. Summary of existing Mo isotope data from natural samples. Isotopic composition of ocean source is based on mass balance (see text). Data are presented as 5 Mo and S Mo relative to the Rochester JMC standard (5 Mo 2/3 x 5 Mo). References ( ) McManus et al. 2002 (t) Siebert et al. 2003 ( ) Barling et ah 2001 ( ) Arnold et al. 2004. Molybdenite values of Wieser and DeLaeter (2003) are omitted because of standard normalization problems (see text). Data obtained by different research groups using different standards are cross-calibrated by comparing seawater 5 values.

Subsequently, analytical expressions for the time dependence concentration of all components in the system were obtained based on mass balance principles and also considering the reactor type, the flow rates of the feed streams, and the concentrations of substrates. Using these models we found that the basic system considered is able to perform several informationprocessing functions, such as division, rectification, and switching. 

The analytical models developed in this part of the study describe the performance of the basic system and allow one to predict the output signal produced by the system when its operational parameters are known. Unlike previous work [76-86], these models explicitly take into account the operational mode of the system (i.e., the reactor type in which the reactions involved take place). This approach was taken in order not only to use these analytical models for numerical simulations, but also to allow us to interpret the experimental results obtained using real systems (Section 4.3) and to assess the validity of the analytical models employed. The models developed are based on mass balances of the components involved and on the characteristics related to the particular reactor used. Unless otherwise indicated, the simulations described below were carried out using these types of input signals with variations of the parameters defined above. 

The dual prices of slacks on mass balance and product requirement rows can be interpreted more specifically. Consider a mass balance constraint ... 

Impacts on mass balance but should not affect concentration ratio if system is at equilibrium. 

Based on mass balance, Cf+ Cf =pXfCo + qXfCq = constant, pXfCo + qX Co = constant. That is. and Cf + Cf =... 

An empirical distribution ratio model was first elaborated to describe the extraction of Am(III) and Ln(III) in kerosene by purified HBTMPDTP, based on mass balances and mass-action laws of HBTMPDTP dimerization in kerosene, dissociation... 

Harland et al.12 developed a model for drug release based on mass balances of the drug and the solvent at the swelling front and the erosion front. The release profile was found to be a combination of Fickian and zero order, as shown by Eq. (5.16) ... 

The strategy for determining the differential equations for biochemical reactants, pH, and binding ions is to express the equations for reactants based on the stoichiometry of the reference reactions and to determine the kinetics of pH and binding ions based on mass balance. 

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