Material balances general procedure

This procedure for deriving the set of material balance equations is quite general. For a process with n units there will be a set of n equations for each component. 

The split-fraction coefficients can be estimated by considering the function of the process unit, and by making use of any constraints on the stream flows and compositions that arise from considerations of product quality, safety, phase equilibria, other thermodynamic relationships and general process and mechanical design considerations. The procedure is similar to the techniques used for the manual calculation of material balances discussed in Section 4.3. 

In the beginning there is a general loop to decide if more lot sizing procedures should be applied to the existing quant network to meet the constraint of the minimum batch sizes of products. Then the quant network is examined, free usable stocks and free quantities of quants are made available. The material balances of any quant are calculated and decisions are taken whether quants require further explosions of their BOM. Structures for a fast cycle checking, sorting of existing quants and quant links and forecast intervals are built up. A recalculation of the due dates for all quants - also the ones of orders - can be done if specified by the user. 

With the above In mind, a° can be determined by colloid titrations, as described In sec. I.5.6e. To review the experimental ins and outs, consider (insoluble) oxides, subjected to potentiometric acid-base colloid titration. Basically the procedure Is that o° (at say pH , and c ) Is related to a° at pH" and the same Salt adding acid or base. The titration Is carried out in an electrochemical cell In such a way that not only pH" is obtainable, but also the part of the acid (base) that is not adsorbed and hence remains In solution. Material balance then relates the total amount (of acid minus base) adsorbed, a°A (where A is the interfacial area) at pH" to that at pH. By repeating this procedure a complete relative isotherm a°A as a function of pH Is obtainable. We call such a curve "relative" because it Is generally not known what <7° was In the starting position. 

Using the data provided, f = 7.9 X 10 s or 2.2 h to reach 95 percent conversion of the benzoquinone. This example illustrates the general procedure used for solving isothermal problems. First, write down the reaction rate expression. Second, formulate the material balance. Third, substitute the reaction rate expression into the material balance and solve. 

The calculation of an adiabatic flame temperature follows the general procedure outlined in Section 9.5b. Unknown stream flow rates are lirst determined by material balances. Reference conditions are chosen, specific enthalpies of feed components are calculated, and specific enthalpies of product components are expressed in terms of the product temperature, Finally, AH(Tiii) for the process is evaluated and substituted into the energy balance equation (Aw = 0), which is solved for... 

Here is the general procedure for writing and solving a transient material balance equation ... 

NOfl, material balances were measured for several experiments and the results are contained in Table III. The high solution level for run No. 12-17-71 is probably a result of dissolved carbonate ion which interferes with the spectrophotometric procedure. This species is produced by the CO2 in the flue gas. In general the balances are acceptable. 

The reaction characteristic of the present system are best performed in a semicontinuous reactor in which the solid is stationary, as described in the previous section. This easily permits the two steps. In general, however, continuous reactors in which both the gas and solid phases move continuously are more important. We therefore briefly consider in this section the mathematical basis for the design of such a reactor. The chief reactor and operating parameters are gas and solids feed rates, product size distribution, bed size, and so on, and procedures for determining them are described. With a size distribution o(R), an elutriation stream and an arbitrary rate law for the changing particle size, a material balance on solids of size between R and R + dR yields... 

We begin the development of graphical design procedures by deriving generalized material balance equations for countercurrent cascades. These are first applied to simple, single-section distillation, extraction, absorption, and... 

F. Generalize. This type of procedure can be applied to many multiconponent distillation problems. It is more common to specify fractional recoveries rather than concentrations because it is more convenient. Note that it is inportant to not make specifications that violate material balances and distillation fundamentals (e.g., 99.4% recovery of C4 in the distillate and 90% mole fraction of C5 in the bottoms). 

As we progress through the chapter we will be discovering and structuring a general procedure to facilitate the formulation and solution of real material balance problems. 

This easy example helps in understanding some basic concepts of material balance and demonstrates a procedure to be considered when solving complex material balance problems. In the following sections, we will further analyze the specifics of material balance and then design and develop a general procedure for solving material balance problems, whether basic or complex. 

First, for now, these nine points are simply a list of recommendations, but we will analyze these recommendations later when we focus on developing an integral and general procedure for approaching, formulating, and solving material balance problems. Second, we will exemplify the relevance of these tips on warm-up examples and when solving problems in Sect. 7.9 (solved... 

Designing and Structuring a General Procedure to Formulate and Solve Material Balance Problems... 

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