Total Mass Balances

As an example, the experimental data using stirred semi-batch laboratory-scale reactor [7] was obtained from the catalytic degradation of various plastics over spent FCC 

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FIGURE 1.1 Control volume for total mass balance. 

We also need a total mass balance. The general form is... 

Overall and Phase Balances for Mass. The examples so far in Chapter 11 were designed to be simple yet show some essential features of gas-Uquid reactors. Only component balances for the phases, Equations (11.11) and (11.12), have been used. They are reasonably rigorous, but they do not provide guidance regarding how the various operating parameters can be determined. This is done in Section 11.1.2. Also, total mass balances must supplement the... 

A dynamic model should be consistent with the steady-state model. Thus, Eqs (1) and (4) should be extended to dynamic form. For the better convergence and computational efficiency, some assumption can be introduced the total amounts of mass and enthalpy at each plate are maintained constant. Then, the internal flow can be determined by total mass balance and total energy balance and the number of differential equations is reduced. Therefore, the dynamic model can be established by replacing component material balance in Eq. (1) with the following equation. 

INITIAL specifies the start of the INITIAL region specify the initial concentrations DYNAMIC specifies the start of the DYNAMIC region represent the model equations is a check on the total mass balance... 

In this section the application of the total mass balance principles is presented. Consider some arbitrary balance region, as shown in Fig. 1.14 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 

The steady-state condition of constant volume in the tank (dV/dt = 0) occurs when the volumetric flow in, Fq, is exactly balanced by the volumetric flow out, Fi. Total mass balances therefore are mostly important for those modelling situations in which volumes are subject to change, as given in simulation examples CONFLO, TANKBLD, TANKDIS and TANKHYD. 

In this case, the problem involves a combination of the total mass balance with a hydraulic relationship, representing the rate of drainage. 

For zero flow of liquid into the tank and assuming constant density conditions, the total mass balance equation, becomes... 

This situation is one involving both a total and a component mass balance, combined with a kinetic equation for the rate of decomposition of the waste component. Neglecting density effects, the total mass balance equation is... 

Liquid flows continuously into an initially empty tank, containing a full-depth heating coil. As the tank fills, an increasing proportion of the coil is covered by liquid. Once the tank is full, the liquid starts to overflow, but heating is maintained. A total mass balance is required to model the changing liquid volume and this is combined with a dynamic heat balance equation. 

It becomes necessary to incorporate a total mass balance equation into the reactor model, whenever the total quantity of material in the reactor varies, as in the cases of semi-continuous or semi-batch operation or where volume changes occur, owing to density changes in flow systems. Otherwise the total mass balance equation can generally be neglected. 

The dynamic total mass balance equation is represented by... 

The information flow diagram, for a non-isothermal, continuous-flow reactor, in Fig. 1.19, shown previously in Sec. 1.2.5, illustrates the close interlinking and highly interactive nature of the total mass balance, component mass balance, energy balance, rate equation, Arrhenius equation and flow effects F. This close interrelationship often brings about highly complex dynamic behaviour in chemical reactors. 

It is assumed that all the tank-type reactors, covered in this and the immediately following sections, are at all times perfectly mixed, such that concentration and temperature conditions are uniform throughout the tanks contents. Fig. 3.10 shows a batch reactor with a cooling jacket. Since there are no flows into the reactor or from the reactor, the total mass balance tells us that the total mass remains constant. 

A total mass balance is necessary, owing to the feed input to the reactor, where... 

Neglecting the effects of any density changes, the total mass balance then provides the relationship for the change of total volume in the mixer with respect to time. 

These equations complete a preliminary model for the mixer. Note that it is also possible, in principle, to incorporate changing density effects into the total mass balance equation, provided additional data, relating liquid density to concentration are available. 

Extending the method to a multicomponent mixture, the total mass balance remains the same, but separate component balance equations must now be written for each individual component i, i.e.. 

The balances for the reactor liquid are as follows Total mass balance, assuming constant density... 

For the semi-batch operation the total mass balance is... 

Simulate the effect of a process operator adding an additional charge of solvent part way through the extraction. Note that you now need to allow for both total mass balance and component mass balance changes. Use the interactive facility of ISIM, to effect the changes. 

Steady-state total mass balances can also be written for Sections 1, 2 and 3, based on the flow rates in each section and the permeation rates between sections. They are as follows... 

Throughout the column the total mass balance gives... 

Total mass balance 15, 29, 131 Total reflux 588, 615 Tracer 162... 

When the system has been defined, an equation can be written to state the law of conservation of mass. Such a total mass balance equation can be given in verbal form as... 

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