Stage operations material balances

In case A the solvents are immiscible, so the rate of feed solvent alone in the feed stream F is the same as the rate of feed solvent alone in the raffinate stream R. In like manner, the rate of extraction solvent alone is the same in the stream entering S as in the extract stream leaving E (Fig. 15-12). The ratio of extraction-solvent to feed-solvent flow rates is therefore S /F = E /R. A material balance can be written around the feed end of the extrac tor down to any stage n (see Fig. 15-12) and then rearranged to a McCabe-Thiele type of operating line with a slope of F /S [Eq. (15-11)]. 

Similarly, the same operating line can be derived from a material balance around the raffinate end of the extractor up to stage n [Eq. (15-12)]. 

The operating company must underwrite the emissions associated with the plant through environmental impact reporting. Such accounting has become an important part of the design. Rather than pass over the need for a closed heat and material balance at the study stage of a project, it is better to get this job done as early as possible. Persistence is sometimes required. 

With the exception of this method, all the methods described solve the stage equations for the steady-state design conditions. In an operating column other conditions will exist at start-up, and the column will approach the design steady-state conditions after a period of time. The stage material balance equations can be written in a finite difference form, and procedures for the solution of these equations will model the unsteady-state behaviour of the column. 

Two other problems that fit this category are calculating the number of stages in a multicomponent distillation problem, and obtaining the material balance when complicated recycle operations occur. 

The intersection of extended lines FEX and RNS locates the operating point P The material balance from stage 1 through k is... 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

Single-Stage Adsorption Contact filtration can be carried out as a single-stage operation (Figure 10.8) either in a batch or a continuous mode. If we assume that the amount of liquid retained with the solid is negligible, the material balance for a solute gives... 

Equation (24) is an equation of a straight line when plotted on x —y coordinates, with a slope of LfM/GfM and an intercept of y[ — LrMxr0/G u. This line is often referred to as the operating line and is the locus of all the points that obey the stage material balance given by Eq. (20). 

To obtain the number of ideal stages in the contactor, one starts by plotting the point y +1 (which is the feed composition of the gas) on the operating line this defines x N. This corresponds to solving the material balance given by Eq. (24) to determine x N. Next, one draws a vertical line from the point (x N, y +1) to the equilibrium curve this defines y N. This corresponds to solving the equilibrium relationship to determine yfN. From the point... 

Example 2.4 A material balance for the column is shown in Table 2.7. Tbe column operates at a pressure of 315 peia. The feed is 66 percent vapor at the column inlet- Tlie relative volatilities of the components at 206°F (feed plate temperature) are shown in Table 2.3. The column is equipped with a partial condenser, and the reflux ratio is 1.5. It is required to determine the number of theoretical stages. 

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