Material balances for

The amounts of each phase and their compositions are calculated by resolving the equations of phase equilibrium and material balance for each component. For this, the partial fugacities of each constituent are determined ... 

Proportions correspond to the material balance for catalytic cracking in Figure 10.3 showing streams (l)(2)(3)(4) and (5). 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

Table 5. Typical Material Balance for Hydrogel Process, kg ...

Equation 235 is the basic expression of material balance for a closed system in which r chemical reactions occur. It asserts that ia such a system... 

In a typical balanced plant producing vinyl chloride from EDC, all the HCl produced in EDC pyrolysis is used as the feed for oxychlorination. On this basis, EDC production is about evenly spHt between direct chlorination and oxychlorination, and there is no net production or consumption of HCl. The three principal operating steps used in the balanced process for ethylene-based vinyl chloride production are shown in the block flow diagram in Eigure 1, and a schematic of the overall process for a conventional plant is shown in Eigure 2 (76). A typical material balance for this process is given in Table 2. 

Table 2. Typical Material Balance for Vinyl Chloride Production by the Air-Based Balanced Ethylene Process...

Formulate the constraining material-balance equations, based on conservation of the total number of atoms of each element in a system comprised of w elements. Let subscript k identify a particular atom, and define Ai as the total number of atomic masses of the /cth element in the feed. Further, let a be the number of atoms of the /cth element present in each molecule of chemical species i. The material balance for element k is then... 

Table 5-12 provides material balances for Cartesian, cylindrical, and spherical coordinates. The generic form applies over a unit cross-sectional area and constant volume ... 

Subscripts 1 and 2 refer to the bottom and top of the tower respectively, and the material balance for any one component may be written... 

Material balances, often an energy balance, and occasionally a momentum balance are needed to describe an adsorption process. These are written in various forms depending on the specific application and desire for simplicity or rigor. Reasonably general material balances for various processes are given below. An energy balance is developed for a fixea bed for gas-phase application and simphfied for liquid-phase application. Momentum balances for pressure drop in packed beds are given in Sec. 6. 

For the methods, we consider Eq. (16-52), the material balance for a fixed bed, written in the form... 

Equation (16-124) is a commonly used form of material balance for a fixed-bed adsorber. 

FIG. 16-26 Material balance for centering profile [from LeVan in Rodiigues et al. (eds). Adsorption Science and Technology, Kluwer Academic Puhlisheis, Doidrecht, The Netherlands, 1989 repiinted with pennission.]... 

As another example of the first interac tion, a potential parameter in the analysis of the CSTR is estimating the actual reactor volume. CSTR shown in Fig. 30-7. The steady-state material balance for this CSTR having a sin e reaction can be represented as ... 

The second section of the spreadsheet contains the overall flows, the calculated component flows, and the material balance closure of each. The weighted nonclosure can be calculated using the random error calculated above, and a constraint test can be done with each component constraint if desired. Whether the measurement test is done or not, the nonclosure of the material balance for each component gives an indication of the validity of the overall flows and the compositions. If particiilar components are found to have significant constraint error, discussions with laboratory personnel about sampling and analysis and with instrument personnel about flow-measurement errors can take place before any extensive computations begin. 

Comparison between plant and calculated material balance for tower... 

A similar material balance for the stripping stages which are labelled 1 to m + r yields... 

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x ... 

The material balance for steady-state operation of a perfectly mixed reactor is ... 

Step 6 Write the Component Material Balances. The Phase II auditing steps define the pollutants and wastes that are among the team s focus. Its objective has always been to identify specific wastes or pollutants that the enterprise can reduce these are the components the team needs to assess in the material balances. It is important to note that once the material balance for each unit operation has been completed for raw-material inputs and waste outputs, it is necessary to repeat the procedure for each contaminant of concern. 

Step 7 Write an Overall Material Balance. Remember that the P2 audit focuses on a unit process, but that there are individual unit operations that make up this process. The team will need to develop a series of material balances for each unit operation, and an overall material balance about the entire unit process, to bring closure to a solution of parameters of interest. The individual or component material balances developed may be summed to give a balance for the whole process, production area, or factory. 

The team is now at the point where it can prepare a material balance at a scale appropriate to the level of detail required in the assessment. For example, you may require a material balance for each unit operation, or one for a whole process may be sufficient. Decide on various levels of detail that may be needed. 

Now you can reconsider the material balance equations by adding those additional factors identified in the previous step. If necessary, estimates of unaccountable losses will have to be calculated. Note that, in the case of a relatively simple manufacturing plant, preparation of a preliminary material-balance system and its refinement (Steps 14 and 15) can usefully be combined. For more-complex P2 assessments, however, two separate steps are likely to be more appropriate. An important rule to remember is that the inputs should ideally equal the outputs - but in practice this will rarely be the case. Some judgment will be required to determine what level of accuracy is acceptable, and we should have an idea as to what the unlikely sources of errors are (e.g., evaporative losses from outside holding ponds may be a materials loss we cannot accurately account for). In the case of high concentrations of hazardous wastes, accurate measurements are needed to develop cost-effective waste-reduction options. It is possible that the material balance for a number of unit operations will need to be repeated. Again, continue to review, refine, and, where necessary, expand your database. The compilation of accurate and comprehensive data is essential for a successful P2 audit and subsequent waste-reduction action plan. Remember - you can t reduce what you don t know is therel... 

Phases I and II have eovered planning and undertaking a P2 audit, resulting in the preparation of a material balance for each unit operation. Phase III represents the interpretation of the material balance, to identify process areas or components of concern. 

Use the material balance for each unit operation to pinpoint the problem areas associated with a process. The material-balance exercise may have brought to light the origin of wastes with high treatment costs, or may indicate which wastes are causing process problems in which operations. The material balance should be used to set priorities for long-term waste reduction. 

The material balance for the single CFSTR in terms of for the first order irreversible reaction is... 

Consider the reversible first order reaction A R. It is possible to determine the minimum reactor volume at the optimum temperature Tgp( that is required to obtain a fractional conversion X, if the feed is pure A with a volumetric flowrate of u. A material balance for a CESTR is... 

As has been mentioned earlier, the CID generates a number Ni , of composition intervals. Within each interval, it is thermodynamically as well as technically feasible to transfer a certain mass of the key pollutant from a waste stream to a lean stream. Furthermore, it is feasible to pass mass from a waste stream in an interval to any lean stream in a lower interval. Hence, for the J th composition interval, one can write the following component material balance for the key pollutant ... 

Consider the mass exchanger shown in Fig. 5.6. The lean end of this exchanger is immediately above the pinch. A component material balance for the pollutant around the exchanger can be written as... 

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