Mass balance for

Three additional equations are needed. The first of these equations is a mass balance for NH3. 

Using these assumptions allows us to simplify several equations. The mass balance for N1T3 is now... 

The mass balance for A is best represented as a straight line in hypothetical coordinates and X ... 

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 ... 

To illustrate the development of a physical model, a simplified treatment of the reactor, shown in Fig. 8-2 is used. It is assumed that the reac tor is operating isothermaUy and that the inlet and exit volumetric flows and densities are the same. There are two components, A and B, in the reactor, and a single first order reaction of A B takes place. The inlet concentration of A, which we shall call Cj, varies with time. A dynamic mass balance for the concentration of A (c ) can be written as follows ... 

Mass balances for common, unsynchronized batch culture give ... 

Mass balances for one vessel in a series of continuous fermenters... 

The removal of impurity in one pass can be calculated by making a mass balance for the advancing liquid phase. If the original impurity content of the bar is Co, and Cl is the impurity content of the liquid, then for an advatrce <5jc of the liquid, the amount dissolved into the advancing liquid minus dre amount deposited behind dre liquid is equal to the increase in the impurity content of the liquid... 

To estimate the current yield of magnesium alloys, the weight loss is determined indirectly over the volumetric measurement of the evolved hydrogen in the apparatus in Fig. 6-9 in Section 6.2.4. The mass balance for oxygen-free media follows from Eqs. (6-1) and (6-5a,b) or (6-14) ... 

The chemistry in this case is the irreversible conversion of A to B, which follows simple, linear kinetics. When we write the time-dependent mass balances for this system we have ... 

The following differential equation (or something similar), derived from a mass balance for the room, is solved to find the correlation between flow rates, source rate, contaminant concentrations, cleaning efficiency, and time. 

On the other hand, in the steady state the mass balance for the gas in a tube with a constant cross-sectional area is simply... 

Mass balances for a species j in the three zones give... 

At steady state, the mass balance for S, = q results in the following equation ... 

The production rate of acetic acid was 2kg-h 1, where the maximum acetic acid concentration was 12%. Air was pumped into the fermenter with a molar flow rate of 200 moMi-. The chemical reaction is presented in (E. 1.1) and flow diagram in Figure 9.5. Determine the minimum amount of ethanol intake and identify the required mass balance for the given flow sheet. The ethanol biochemical oxidation reaction using A. aceti is ... 

The mass balance for each combustible species j in cell i is... 

One thus obtains the following differential steady-state mass balance for the surface concentration, Ci, of the promoting species ... 

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. 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Thus, the initial value of the initiator concentrations, [Il]° and [I2]°, are calculated with Equation 15, for given values of the initial loading, feed rates, temperature, and time for the main semi-batch step, and [M]° is fixed according to experimental data from the base case semi-batch step. The nonlinear differential equation for [M] in terms of [II] and [I2] is given by Equation 16. Equation 10, with a redefinition of terms, is the differential equation mass balance for [II] and [12]. In the finishing step, only one of the initiators would be added for residual monomer reduction. Thus, Qm = 0,... 

A mass balance for an arbitrary liquid-phase component in the stirred tank reactor is thus written as follows dci... 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

The catalyst prepared above was characterized by X-ray diffraction, X-ray photoelectron and Mdssbauer spectroscopic studies. The catalytic activities were evaluated under atmospheric pressure using a conventional gas-flow system with a fixed-bed quartz reactor. The details of the reaction procedure were described elsewhere [13]. The reaction products were analyzed by an on-line gas chromatography. The mass balances for oxygen and carbon beb een the reactants and the products were checked and both were better than 95%. 

Figure 1.7 Conversion, selectivity and mass balance for a reaction to produce methyl chloride from methanol.

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. 

The mass balance for a continuous-flow, stirred-tank reactor with first-order reaction is... 

By simplifying the general component balance of Sec. 1.2.4, the mass balance for a batch reactor becomes... 

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