Mass balance overall

Distillation columns are controlled by hand or automatically. The parameters that must be controlled are (/) the overall mass balance, (2) the overall enthalpy balance, and (J) the column operating pressure. Modem control systems are designed to control both the static and dynamic column and system variables. For an in-depth discussion, see References 101—104. 

Material Balances Whenever mass-transfer applications involve equipment of specific dimensions, flux equations alone are inadequate to assess results. A material balance or continuity equation must also be used. When the geometiy is simple, macroscopic balances suffice. The following equation is an overall mass balance for such a unit having bulk-flow ports and ports or interfaces through which diffusive flux can occur ... 

The mass-balance restrictions are the C balances written for the C components present in the system. (Since we will only deal with non-reactive mixtures, each chemical compound present is a phase-rule component.) An alternative is to write (C — 1) component balances and one overall mass balance. 

The population balance accounts for the number of particles at each size in a continuous distribution and may be thought of as an extension of the more familiar overall mass balance to that of accounting for individual particles. 

The first, and simplest, step in predicting crystallizer performance is the calculation of crystal yield. This can easily be estimated from knowledge of solution concentration and equilibrium conditions permitting calculation of the overall mass balance... 

Mass balance. An overall mass balance is stated as... 

Here, m(tp) is the mass of the system contents at final time t and m(t ) is the mass at initial time t . As before, both component and overall mass balances may be written in integral form. 

It must be kept in mind that the reaction term will not occur in the overall mass balance equations of reactive systems because S(R- = 0, i.e., there is no net mass gain or loss as a result of chemical reactions. 

Identification of the input and output streams used in the overall mass balance equation. 

Input and Output Streams in the Overall Mass Balance... 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

Most of this chapter assumes that the mass flow rate down the tube is constant i.e., the tube wall is impermeable. The reactor cross-sectional area Ac is allowed to vary as a function of axial position, Ac = Adz). Figure 3.1 shows the system and indicates the nomenclature. An overall mass balance gives... 

Closure normally begins by satisfying the overall mass balance i.e., by equating the input and outlet mass flow rates for a steady-state system. For the present case, the outlet flow was measured. The inlet flow was unmeasured so it must be assumed to be equal to the outlet flow. We suppose that A and B are the only reactive components. Then, for a constant-density system, it must be that... 

An overall mass balance is written for the system as a whole. Interphase mass transfer does not appear in the system mass balance since gains in one phase exactly equal losses in the other. The net result is conceptually identical to Equation (1.3), but there are now two inlets and two outlets and the total inventory is summed over both phases. The result is... 

In the case of NO reduction by propene, the only detectable reaction products were CO2, N2, N2O and H2O. The overall mass balance was found to close within 5% as observed by a combination of GC and mass spectroscopic analyses. Figure 3 shows the effect of varying the catalyst potential on the rate of production of CO2, N2, N2O and on the selectivity towards nitrogen formation, Sn2- As can be seen from this figure, both the CO2 and N2... 

Substituting the overall mass balance, Equation 9.7, gives ... 

For a saturated liquid feed q = 1, and for a saturated vapor feed <7=0. The flowrate of feed entering the column as liquid is q-F. The flowrate of feed entering the column as vapor is (1 - q)-F. Figure 9.8 shows the feed stage. An overall mass balance on the feed stage for the vapor gives ... 

An overall mass balance for the liquid on the feed stage gives ... 

If it is also assumed initially that S = E, an overall mass balance can be applied for acetic acid (see Figure 10.5) ... 

Assume initially, F = R and S = E and perform an overall mass balance on acetic acid from Equation 10.16 ... 

Consider a second example involving the separation of a mixture of ethanol and water that forms an azeotrope at around a mole fraction of ethanol of 0.88. It is proposed to use ethylene glycol as entrainer. An overall mass balance for the separation is shown in Figure 12.22a. As with the... 

There must be an overall mass balance in which the mass of the component to be separated that enters with... 

Table 18.2 lists 30 of the molecules used in this study that are known to be substrates for active transport or active efflux. The mechanistic ACAT model was modified to accommodate saturable uptake and saturable efflux using standard Michaelis-Menten equations. It was assumed that enzymes responsible for active uptake of drug molecules from the lumen and active efflux from the enterocytes to the lumen were homogeneously dispersed within each luminal compartment and each corresponding enterocyte compartment, respectively. Equation (5) is the overall mass balance for drug in the enterocyte compartment lining the intestinal wall. 

If one considers the overall CTL process, considering the input to and outputs from the process, the overall mass balance for the system can be written as follows ... 

Thus, by considering the overall mass balance, i.e., looking at the inputs and outputs of the process, one can gain many insights into a process and also identify opportunities for C02 emissions reduction and enhancing feedstock utilization. 

Taking 100 kmol of feed, as a basis, an overall mass balance and a balance for the n-heptane give ... 

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