Multi mass balance

Wania F, Persson J, Di Guardo A, McLachlan MS (2000) CoZMo-POP. A fugacity-based multi-comparlmental mass balance model of the fate of persistent organic pollutants in the coastal zone. WECC report 1/2000. Toronto (April)... 

Let us now consider an interface between two isotropic multi-component phases. The number of moles of a component i in the two phases adjacent to the interface are given as n and nSince the mass balance of the overall system must be obeyed, it is necessary to assume that the dividing surface contains a certain... 

By Morel s method, mass balance breaks down in two steps. First, in much the same way as we constructed a mineralogical matrix for a multi-mineral rock, we can build a component matrix for the solution we are dealing with, including all the possible species. Second, the solution recipe is written down. We may think of producing a solution by dissolving a given quantity (the recipe ) of NaCl and K2S04,... 

We consider a molten multi-mineral assemblage, referred to as the source, which is presumed to give rise to an erupting magma. X is the mass-fraction of each phase j relative to the molten source (and not to the residue). Subscript j= 1 refers to the melt, j = 2,..., n to the n — 1 residual mineral phases. The sum of the Xj over all the n phases is unity. If Cliq is the concentration of the ith among m elements in the liquid, the concentration of element i in phase j will be K/C,iq . Let C0 be the concentration of i in the source prior to melting. Hence, mass balance requires... 

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. 

There are several characteristics common to the describing equations of all types of multicomponent, vapor-liquid separation processes, both single- and multi-stage, that make it possible to exploit the inside-out concept in similar ways to solve them efficiently and reliably. The equations have as common members component and total mass balance, enthalpy balance, constitutive and phase equilibrium equations. In addition, all such processes require K-value or fugacity coefficient and vapor and liquid enthalpy models. In all cases the describing equations have similar forms, and depend on the primitive variables (temperature, pressure, phase rate and composition) in essentially the same ways. Before presenting the inside-out concept, it will be useful to identify two classes of conventional methods and discuss their main characteristics. 

One of the difficulties about discussing tropospheric chemistry in general terms is that by the very nature of the troposphere being the lowest layer of the atmosphere it has complex multi-phase interactions with the earth s surface, which can vary considerably between expanses of ocean to deserts (see Figure 7). The fate of any chemical species (C,) in the atmosphere can be represented as a continuity or mass balance equation such as... 

This multi-chamber mass-balance model has been developed by using air infiltration rates and corresponding interzonal air flows for a nser-selected residence or a user-defined residence. The model provides a spreadsheet environment to the user in which time service data for emission rates in one or more zones, the zone of exposure and concentration values of the contaminant outdoors can be entered. 

Where t is time, z are the axial position in the column, qt is the concentration of solute i in the stationary phase in equilibrium with Cu the mobile phase concentration of solute /, u is the mobile phase velocity, Da is the apparent dispersion coefficient, and F is the phase ratio (Vs/Vm). The equation describes that the difference between the amounts of component / that enters a slice of the column and the amount of the same component that leaves it is equal to the amount accumulated in the slice. The fist two terms on the left-hand side of Eq. 10 are the accumulation terms in the mobile and stationary phase, respectively [109], The third term is the convective term and the term on the right-hand side of Eq. 10 is the diffusion term. For a multi component system there are as many mass balance equation, as there are active components in the system [13],... 

For a multi-zone SMB, each zone of the TMB system can be described by the same differential mass balance and kinetic equations. However, these equations are coupled by the boundary conditions which incorporate the injection and withdrawal of fluid streams at the appropriate points. Analytical solution carmot be obtained, only numerical solution is available. 

For an individual species c in a multi-component mixture the species mass balance principle postulates that the time rate of change of the mass of a system of species c is equal to the rate at which the mass of c is produced by homogeneous chemical reactions. 

The calculation of multi-stage separation processes involves the solution of phase equilibrium relationships, mass balances, and energy balances. Energy balances require the computation of enthalpies of streams entering and leaving an equilibrium stage. The enthalpy is a function of state, defined in Section 1.1.2 as H = U -i- PV. It is a function of the stream composition, its temperature, and its pressure. 

Boston, J. F. and S. L. Sullivan, Jr., An improved algorithm for solving mass balance in multi-... 

The choice of model should be based on biological, physiological, and pharmacokinetic plausibility. For example, compartmental models may be used because of their basis in theory and plausibility. It is easy to conceptualize that a drug that distributes more slowly into poorly perfused tissues than rapidly perfused tissues will show multi-phasic concentration-time profiles. Alternatively, the Emax equation, one of the most commonly used equations in pharmacodynamic modeling, can be developed based on mass balance principles and receptor binding kinetics. 

The lET approach can also be applied to multiple closely spaced hand samples if it is assumed that they were equilibrated with each other at the peak temperature (Farquhar et al. 1993, 1996). If each sample has different modal proportions, then the lET for any given mineral will be different in each lithology due to mass-balance effects. If the lET s for a single mineral are plotted together, they will intersect at the closure temperature for the multi-rock system, Tc(sys). Tc(sys) can be higher than Tc for any individual mineral. If more than two rocks are plotted, the redundant information serves as a check for... 

The objective of this investigation was, therefore, (i) to assimilate flie rqipropriate plant data from various sources, (ii) to determine and estimate their accuracy, (iii) to calculate closed mass balances for defined intervals of time, and (iv) to develop quantitative model to predict the production of ZIC and its composition based on the feed materials and their analysis. In the course of the investigation, the mass balance model was developed first (Model 1) with the aid of data reconciliation. Then, the prediction model (Model 2) was calculated based on the results of Model 1 incorporating a multi-parametrical regression analysis, hi this paper, the capabilities of the combination of these two modem computer-aided tools will be demonstrated as applied to the Ruhr-Zink flowsheet. With these methods, a plant simulator can be updated in a relatively short time that incorporates the latest changes in the flowsheet. 

For a multi-injection MSR with a total of N injection points (Figure 5.26), the mass balance can be derived in a similar approach as for a plug flow reactor with only one inlet (Equation 5.27) [35]. 

In conclusion the discretization method of computing mass balances in separator networks can cope with the large number of streams and data handled even in the most complicated separator system such as multi-stage countercurrent washing and can do so in reasonable time. 

The above equatirms (mass actirm law, extended Deye-Hiickel equatirm, electroneutrahty relatitMi, mass balance equations) can be solved by several procedures such as graphic method, and Newton-Raphson method (Stumm and Morgan 1970). Examples of interpretatiOTi of natural water chemistry in multi-component—... 

When considering a mass balance as a component of a multi-component system, the overall mass balance can be shown as in Eq. 4.4 ... 

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