INDEX mass balance

The vessels were indexed by the subscript "j" (j = 0 refers to the reactor and j from 1 to 4 to the UF cells) and oligomers were lumped in two categories "P" (Permeated) and "R" (Rejected). Let label "in" species entering a cell and "out" those leaving it. Instantaneous mass-balance in the stream leaving a cell and feeding the following one is ... 

Yield and other mass-related metrics such as atom economy, reaction mass efficiency and mass intensity have been examined by Constable et al with regard to their significance concerning greenness and costs. The importance of using a (product) concentration term, which can be mass intensity or mass index, is additionally emphasized by Laird et al This is in compliance with Winterton, who in his twelve more green chemistry principles demands the establishment of full mass balances. 

The biocatalytic reduction step B in synthetic route B demands more raw materials (mass index S , see equation (5.1)) and generates more waste (environmental factor , see equation (5.2)) as compared to reduction step C (Figure 5.1). Solvents used to perform the extraction of the product from the aqueous phase in reduction step B are denoted as auxiliaries in Figure 5.1. These solvents and the aqueous phase dominate the mass balances as well as the environmental scores in Figure 5.2 (M4, M8). 

Inputs and outputs assessed in mass balancing are shown in Figure 5.3. The software EATOS was used to calculate all mass balances of processes. Outputs of EATOS are the mass index (equation (5.1), mass of raw material per mass of product output), and the environmental factor (equation (5.2), mass of waste output per mass of product output). EATOS also allows the calculation of cost indices (e.g., reference [15]) (equation (5.3), cost of raw material per mass of product output). 

A major difference in the evaluation of the two approaches concerns catalyst synthesis. Whereas catalyst production is integrated in the biocatalytic procedure (Scheme 5.4) and thus also contained in the cost index and the environmental factor, it is not considered in the chemical catalytic approach. A more realistic approach is to include the synthesis of the Jacobsen catalyst (Scheme 5.5) in the mass balance. In Figure 5.8, resources used for catalyst production are separately indicated ( Further Syntheses ). For the biocatalytic procedure, water dominates the environmental factor. The environmental factor increases for the chemical procedure, whereas the cost index, when representing only the raw material costs, declines if the (salen)Mn-catalyst is assumed to be synthesized and not bought. 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Masclet and co-workers (1986) have also developed a relative PAH decay index. They used it, for example, to identify various major sources of urban pollution and developed a model for PAH concentrations at receptor sites. An interesting and relevant area that is beyond the scope of this chapter is the use of PAHs as organic tracers and incorporating their relative decay rates (reactivities) into such receptor-source, chemical mass balance models. Use of relative rates can significantly improve such model performances (e.g., see Daisey et al., 1986 Masclet et al., 1986 Pistikopoulos et al., 1990a, 1990b Lee et al., 1993 Li and Kamens,... 

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... 

The mixture of PAHs present in a particular sample in many cases mirrors the sources that produce them. Several methods can be used to qualitatively identify the probable sources of PAHs. Commonly used methods include the abundance ratios of individual compounds, the fossil fuel pollution index (FFPI), and diagnostic ratios indicative of sources (petrogenic vs. pyrogenic). Quantitative apportionment of sources needs sophisticated statistical approaches such as the chemical mass balance models (Li et al., 2003). 

If one wants to take into account all three mass-transfer resistances, the mass-balance equation [Equation 14.16] should be given for every layer. From that one can obtain the solution for every layer (i = m for membrane layer, i = g for gel layer, the concentration-polarization layer has no index according to Figure 14.4) ... 

Further, mixing/turbulent diffusivity derived by considering that the mixing process in a liquid is caused by the random movement of inner substances based on the turbulent flow can also be used as an index for the evaluation of the local mixing rate. The mass balance in the flow field is written as... 

After writing mass balances, energy balances, and equilibrium relations, we need system property data to complete the formulation of the problem. Here, we divide the system property data into thermodynamic, transport, transfer, reaction properties, and economic data. Examples of thermodynamic properties are heat capacity, vapor pressure, and latent heat of vaporization. Transport properties include viscosity, thermal conductivity, and difiusivity. Corresponding to transport properties are the transfer coefficients, which are friction factor and heat and mass transfer coefficients. Chemical reaction properties are the reaction rate constant and activation energy. Finally, economic data are equipment costs, utility costs, inflation index, and other data, which were discussed in Chapter 2. 

Now suppose the system in fact exists as N separate phases, with K = 1,2,.. ., N the phase index let be the number of moles of phase K per mole of the system. The a f s must satisfy the mass balance condition... 

To derive a function for the buffer index of a weak monoprotic acid, HA, we begin as before with equilibrium, mass-balance, and charge-balance equations, and first derive an equation for the titration curve. We are given the following expressions ... 

Sip = 0 when the pth precipitate is in equilibrium with the aqueous phase if the saturation index is negative, the system is undersaturated with respect to that species, and if the index is positive, the solution is supersaturated. TTie Newton-Raphson method uses the logarithmic expressions for the saturation indexes in a similar manner to the mass balance residue expressions. 

Mass balances of alternative routes in chemical processing can be compared using measures such as the E factor and mass index 5 The E factor (ratio of waste Peg] to product unit [kg]) is an output orientated indicator, whereas the mass index (ratio of all raw materials [kg] to the product [kg])is an input oriented indieator. These measures and the cost index Cl (currency unit per kg product) clarify the benefits and drawbacks of changes in synthesis design, i.e. the strong and weak points, which must be addressed [6]. 

The operation mode of fixed bed adsorbers can be isothermal (very small adsorptive concentration in the fluid and low heats of adsorption), nonisothermal, and adiabatic. The heat loss of large industrial adsorbers is often so small in comparison to the heat production by adsorption that the bed is nearly operated adiabatically. In such a case not only the mass balances but also the ener balances have to be taken into accoimt to get information on the operating mode and the fields of concentration and temperature in a fixed bed. These balances for the adsorbent (Index S = solid) and the fluid (Index G) are... 

The mass balance is for a formation of component A and j is the reaction index. 

The index j in relation (5.65) is converted to the index fc by a purely formal process. The reason follows from the following modification. We now substitute from relation (5.66) into the mass balance equations (5.59). We obtain a set of equations... 

Here, we follow a later, simpler formulation that illustrates the power of optimal control for finite-time thermodynamic processes [11]. We take as the control variable the set of temperatures at a given number of equally spaced heat-exchange points along the length of the distillation column. The (assumed) binary mixtme comes in as a feed at rate F and is separated into the less volatile bottom at rate B and the distillate, at rate D, that collects at the top of the colmrm. Let x be the mole fraction of the more volatile component in the liquid and y, the corresponding mole fi action in the vapom, and their subscripts, the indications of the respective points of reference. Thus the total flow rates, for steady flow, must satisfy F = D + B, and xpF = x D + xbB. We index the trays from 0 at the top to N at the bottom. Mass balance requires that the rate V +i of vapour coming up from tray n + 1, less the rate of liquid dropping from tray n, L , must equal D for trays above the feed point at which F enters, and must equal —B below the feed point. Likewise the mole fractions must satisfy the condition that Vn+iVn+i —XnLn = xpD above the feed and —xpB below the feed. The heat required at each nth tray is... 

In Equation 5.231, the indexes b, c, and e refer to the bubble, cloud, and emulsion phases, respectively. The mass balance for component i is valid in the bubble phase... 

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