Component mass balances, for

Equation (20-70) is the unsteady-state component mass balance for fed-batch concentration at constant retentate volume. Integration yields the equations for concentration and yield in Table 20-19. 

For a batch system, with no inflow and no outflow, the total mass of the system remains constant. The solution to this problem, thus involves a liquid-phase, component mass balance for the soluble material, combined with an expression for the rate of mass transfer of the solid into the liquid. 

Component mass balances for the four liquid components in the still, are given by... 

In addition to the total mass balance, equations can be written to describe changes in each of the individual chemical species, or components, that are present. As with the total mass, the mass of a component can be altered by exchange with the surroundings. However, it can also be affected by chemical reactions occurring within the system, converting one component to another. The total mass of the system is not affected by such interconversions, since the mass of reactants consumed is exactly equal to the mass of products formed. In verbal form, the component mass balance for a particular component A in the system is... 

When fluid velocity is constant, a component mass balance for a chemical species A in plug flow can be written as... 

Fick s second law of diffusion can be derived from Fick s first law by using a mass balance approach. Consider the differential fluid element shown in Figure 4. This differential fluid element is simply a small cube of liquid or gas, with volume Ax Ay Az, and will be defined as the system for the mass balance. Assume now that component A enters the cube at position x by diffusion and exits the cube at x + Ax by the same mechanism. For the moment, assume that no diffusion occurs in the y or z directions and that the faces of the cube that are perpendicular to the y and z axes thus are impermeable to the diffusion of A. Under these conditions, the component mass balance for A in this system is... 

Equations (3) and (4) represent the component mass balances for continuous systems (packed columns). For discrete systems (tray columns), the differential terms transform to finite differences, and the balances are reduced to algebraic equations. 

Component mass balance for unit k 0 Total heat balance for unit k... 

The component mass balance for each of the two reactants is given below ... 

Flat plate geometry, corresponding to layer deposition of porous medium on monoliths, was selected as the basis for the analysis of diffusion effects. Other catalyst geometries would yield similar results and conclusions. A component mass balance for CO in the catalyst pore under isothermal conditions yields ... 

There is a mass flow of both liquid and solid into the tank the two are mixed well and then flow out of the tank to their application. The total and component mass balances for the system are ... 

Similar to the discussion in Chapter 2, a component mass balance for A gives... 

Remember, the negative sign indicates consumption while a positive sign indicates formation. We can now write the component mass balance for the bulk reactant as... 

Table 2.1 Model equations for the 1-D pseudo-homogeneous model Component mass balance for the gas phase ...

A single cylindrical pore of length L and radius of r (=d) located in a microscopic section of the catalyst particle is generally used for modeling the diffusion-reaction process (Figure 2.3). The steady-state component mass balance for a control volume extending over the cross section of the pore includes diffusion of reactant into and out of the control volume as well as reaction on the inner wall surface. The simple case taken as an example is that of an isothermal, irreversihle first-order reaction ... 

The mass balance subset of the model consists of the total mass balance and (K-1) component mass balances for every balance volume, where K is the number of components. The algebraic dependence between the masses is described by an appropriate closure constraint. 

We now proceed to present a proof of fhese statements. This is done by composing total and component mass balances for the mixtures and relating the resulting compositional changes to the line segments of Figure 6.11. Thus, for the total mass balance... 

A light component mass balance for the actual feed stream in the recycle separator leads to... 

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