Total Material Balances

A total material balance assay is a Fischer assay in which the retort gases are collected. A complete material balance closure and yields in excess of those expected from Fischer assay results are achieved. More complete descriptions of both the Fischer assay and the Tosco material balance assay methods have been reported (9). 

Next, Eq. (13-68) is summed over the C components and over stages 1 throiign j and combined with Eqs. (13-7o (13-71), and X Z-ij — 1.0 = 0 to give a total material balance over stages 1 through J ... 

Compute a corresponding new set of Vj tear variables from the following total material balance, which is obtained by combining Eq. (13-74) with an overall material balance around the column ... 

To isolate a system for study, the system is separated from the surroundings by a boundary or envelope that may either be real (e.g., a reactor vessel) or imaginary. Mass crossing the boundaiy and entering the system is part of the mass-in term. The equation may be used for any compound whose quantity does not change by chemical reaction or for any chemical element, regardless of whether it has participated in a chemical reaction. Furthermore, it may be written for one piece of equipment, several pieces of equipment, or around an entire process (i.e., a total material balance). 

In this chapter we will apply the conservation of mass principle to a number of different kinds of systems. While the systems are different, by the process of analysis they will each be reduced to their most common features and we will find that they are more the same than they are different. When we have completed this chapter, you will understand the concept of a control volume and the conservation of mass, and you will be able to write and solve total material balances for single-component systems. 

Therefore, the sum of the component balances is the total material balance while the net rate of change of any component s mass within the control volume is the sum of the rate of mass input of that component minus the rate of mass output these can occur by any process, including chemical reaction. This last part of the dictum is important because, as we will see in Chapter 6, chemical reactions within a control volume do not create or destroy mass, they merely redistribute it among the components. In a real sense, chemical reactions can be viewed from this vantage as merely relabeling of the mass. 

As indicated previously, Eq. (4.5.1) may be applied to die total mass of each stream (referred to as an overall or total material balance) or to die individual eomponents of the streams (referred to as a componential or component material balance). Often the primary task in preparing [Pg.120]

This combined equation represents a differential total material balance of a component, whether present as HA or the reaction product A-, within the reacting phase. The reader is referred to Olander s original paper for a more complete rationale for generating these differential component material balances for systems of reacting species near equilibrium. By using Olander s technique, the system of four differential equations with reaction terms can be simplified significantly to two differential equations with no reaction terms. 

It was decided to increase the pressure in subsequent experiments to push the anion-free water out. Experiments 5 and 6 were performed at 400 psi at a NaCl concentration around 0.01 M. Experiments 5-10 were performed in the compaction cell as described in the experimental section. This apparatus was rated for 10,000 psi. The pressure regulation at 400 psi region was about 100 psi. Some evaporation occurred that made the total fluid collection less than expected from total material balance. NaCl concentration of the collected fluid could not be measured accurately. However, the amount of fluid collected and the amount of water retained in the sediments in Experiments 5 and 6 clearly indicated some anion-free water was mobilized. 

If the initial condition of the reactor contents is known and if the feedstream conditions are specified, it is possible to solve equation 8.6.1 to determine the effluent composition as a function of time. The solution may require the use of material balance relations for other species or a total material balance. This is particularly true of variable volume situations where the following overall material balance equation is often useful. 

In this section, the application of the total material balance principle is presented. Consider some arbitrary balance region, as shown in Fig. 1.11 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, F0, is exactly balanced by the volumetric flow out, Fi. Total material balances therefore are mostly important for those modelling situations in which volumes are subject to change, as in simulation examples CONFLO, TANKBLD, TANKDIS and TANKHYD. 

In this case, the problem involves a combination of the total material 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 material balance equation becomes... 

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

The situation is the same as in Fig. 1.18 but without material leaving the reactor. 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 material 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 material 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 material balance equation can generally be neglected. 

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

The information flow diagram for a non-isothermal, continuous-flow reactor (in Fig. 1.18, shown previously in Section 1.2.5) illustrates the close interlinking and highly interactive nature of the total material balance, component material 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. Figure 3.8 shows a batch reactor with a cooling jacket. Since there are no flows into the reactor or from the reactor, the total material balance tells us that the total mass, within the reactor, remains constant. 

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

Neglecting the effects of any density changes, the total material 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 material balance equation, provided additional data, relating liquid density to concentration, are available. 

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

The total material balance under constant density conditions is... 

A total material balance on a binary droplet yields d (4rta ... 

A total material balance around one column of the two-column process at cyclic steady state is... 

Table I contains the elemental analysis of the T102 bottoms, the material brought overhead with toluene, the residue remaining after the toluene destraction, and the starting coal used at Wilsonville during Run 242. The toluene overhead represented 66.8 percent of the material charged to the FDU, and the residue accounted for 27.9 percent. Other material collected from the FDU includes 4.2 percent in the spent solvent and 2.7 percent recovered during cleaning of the FDV and separator with tetrahydrofuran. The total material balance is 101.6 percent. This number also includes any residual toluene or tetrahydrofuran in the various samples. The overhead collected from the five destractions was ground and combined before use in the reflux mode experiments.

This equation is the total material balance for the stage. Another balance can be written by equating input to output for component i giving the component i balance ... 

Obviously, if all the component balances for a system were added up, the sum would be equal to the total material balance. 

Solution. A total material balance over the whole column, where F, D and B are the feed, top product and bottom product flow rates, respectively, yields ... 

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