## Fz Bxb Dxd32

At a given feed flow rate and feed composition, there are two equations [Eqs. (3.1) and (3.2)] and four unknowns: B, D, xB> and xD. There fore, only two variables can be specified for the separation. Further, at least one of the two specified variables must be a composition. Usually, either two purities or a purity and a product rate are specified.

Product rate specification. The product rate specification can be expressed simply as a flow rate. Alternatively, it can be expressed as a "recovery." Some examples of the use of recovery specification are

1. "60 percent (say) of the feed is to be recovered as the distillate." This is equivalent to setting the distillate rate to 0.6F.

2. "95 percent (say) of the light key component in the feed is to be recovered in the distillate." This is equivalent to setting the distillate rate to (0.95^2^ + impurities + light nonkeys).

3. A double-recovery specification is equivalent to specifying one product rate and one product purity. For instance, "95 percent of the light key in the feed is to be recovered in the distillate, and 90 percent of the heavy key in the feed is to be recovered in the bottom." This sets both the distillate rate to (zlnk + 0 952LK + 0.10?HK)i,( and the heavy key concentration of the distillate at

0-10*hk 0.95zLK + O.IOzhk + Zlnk Example 3.3 in Sec. 3.2.3 uses a double-recovery specification.

Composition specification. If one recovery or one product flow is specified, the concentration of one component either in the distillate or in the bottom (but not both) can be specified. If neither a recovery nor a product rate is specified, the concentration of one component in the distillate and one component in the bottom can be specified.

The above applies to both binary and multicomponent distillation. In multicomponent distillation, once the above are specified, other components will distribute according to the equilibrium relationship. Frequently, a product spec sets the maximum concentration of impurities that can be tolerated in the product. Product specs are "less than" specifications. The one impurity which is dependent on the column separation and is most difficult to achieve sets the composition specification in the column. This is illustrated in Table 3.1 for a propylene-propane separation (C3 splitter). Since the light nonkeys (hydrogen, methane, ethylene, ethane, and oxygen) end up in the distillate, their concentration in the distillate is independent of the column. Of the others, the most difficult purity to achieve sets the composition specification. Similarly, the heavy nonkeys (MAPD, C4 and

 Component Top product— polymer grade propylene Bottom product—propane Hydrogen < 10 ppmv < 100 ppmv Methane < 4000 ppmv < 0.5% Ethylene < 50 ppmv < 1% Ethane < 4000 ppmv < 1% Propylene >99.5 mole < 5% mole Propane < 5000 ppmv > 90% mole MAPD (methyl acetylene/ propadiene) < 5 ppmv < 5% mole Butadiene < 1 ppmv <1% mole Butenes < 50 ppmv < 1% mole Butanes < 4000 ppmv < 10% mole

heavier, and sulfur) end up in the bottom product; their concentration in the bottom product is independent of the column. Of the others, the most difficult purity to achieve sets the composition specification.

Sometimes, column design has a bearing on which spec is most difficult to achieve. For instance, in some C3 splitters, the feed point location has a greater effect on MAPD than on the propane concentration in the top product. With a low feed point, the propane spec may be the most difficult to achieve; with a high feed point, the MAPD spec may be more difficult to achieve. The nonkey content of the feed also has an effect. For instance, if the methane plus ethane in the product is 500 ppmv, then up to 4500 ppm propane can be tolerated. This may be easier to achieve than the MAPD spec. On the other hand, if methane plus ethane is 3000 ppm, then no more than 2000 ppm of propane can be tolerated. This may be more difficult to achieve than the MAPD spec.

Physical property specification. A product composition can often be specified in terms of a physical property that is a direct function of composition. For instance, the vapor pressure of a bottom product is often a good measure of the concentration of lights in the bottoms, and may be specified instead. Other physical properties include the Reid vapor pressure (RVP), viscosity, refractive index, freezing point, mo lecular weight, and others. A physical property specification is often preferred either when it is easy to monitor (e.g., refractive index), or when it provides a good functional spec of product purity.

Heat duty (or internal flow) specification. A composition or product rate specification may be substituted by a heat duty or internal flow (e.g., reflux) specification. This is done either to improve convergence in a computer simulation (especially if compositions are in the part per million levels), or in a revamp when the column or its exchangers are at a capacity limit. The mass, component, and energy balance equations translate this specification into a composition or product rate specification. Sections 4.2.3 and 4.3.1 have some further discussion.

Side product. For each side product, one additional specification is required. This specification is either a product rate (e.g., the side product rate) or a product composition.

Heat addition or removal. For each point of heat addition or removal, an additional specification is required. This specification is usually a heat duty or an internal product flow.

3.1.2 Optimizing product recovery (material balance optimization)

The previous section assumed that product composition (or product flow) requirements are fixed. In this very common situation, the optimum design minimizes the costs of achieving these requirements. Often, product specs are not fixed, but depend on economics. Even when a product must obey a "less than" purity spec, better purity may fetch a better price. The better price may justify additional investment in equipment and/or a higher operating cost. Here, a design must optimize product purity value versus distillation cost. This optimization is also important in an operating column and is commonly performed by on-line computer control. It is outlined below, and discussed in detail elsewhere (1,2).

Material balance optimization. Figure 3.1a shows the concentration of the light key at the distillate and bottoms at a fixed separation S, where

The x axis of Fig. 3.1a is D/F, or the distillate recovery. When D/F approaches zero, almost all the material entering the column leaves in the bottoms. The bottom composition approaches the feed composition,

(a)

Figure 3.1 Concentration of the light key component at the distillate and bottom products, (a) At a single separation, S (or at a single reflux ratio); (i>) effect of S (or of reflux ratio). (Reprinted by permission. Copyright © Instrument Society of America, 1978, from P. R. Latour, Instrumentation Technology, July 1978).

Figure 3.1 Concentration of the light key component at the distillate and bottom products, (a) At a single separation, S (or at a single reflux ratio); (i>) effect of S (or of reflux ratio). (Reprinted by permission. Copyright © Instrument Society of America, 1978, from P. R. Latour, Instrumentation Technology, July 1978).

while the distillate contains the highest possible fraction of light key. The converse applies when DIF approaches unity.

Fixing S is equivalent to setting a composition specification. At a fixed S, each D/F in Fig. 3.1a specifies a recovety and a composition. These specifications are sufficient for setting all product flows and purities (Sec. 3.1.1). Since D/F fixes distillate and bottoms flows and purities, each D/F also fixes the total product value. The total (distillate plus bottom product) values can therefore be calculated and plotted against DIF at fixed S (Fig. 3.2).

FJgur« 3.2 Material balance optimization at a fixed separation S (or reflux ratio). (Reprinted by permission. Copyright © Instrument Society of America, 1978, from P. R. Latour, Instrumentation Technology, July 1978).

The optimum in Fig. 3.2, termed the optimum recovery value, gives the highest total aggregate value of the top and bottom products. At lower recovery CD/F), more bottoms are produced, but at a lower purity (and, therefore, at a lesser value). At higher recovery, more distillate is produced, but at a lower purity (and therefore at a lesser value).

Not shown on Fig. 3.2 are constraints. Each product usually has a maximum impurity level, beyond which it cannot be sold or utilized. Each constraint can be marked on the diagram either as a vertical line at the D/F value corresponding to this maximum impurity level, or as a drop of product value to zero (or even negative) at that point. A constraint precludes operation at the optimum recovery value when the optimum coincides with one of the products being "off-spec." The best product value is then realized where the vertical constraint line meets the aggregate value curve.

In the above discussion, the optimization was described as a function of the recovery D/F. This was done for convenience only. The same optimization can also be described in terms of any other variable. Figure 3.3 shows a similar optimization (2), where product losses are described as an annual cost on they axis, and the bottoms concentration is the x axis. As in Fig. 3.2, the curve in Figure 3.3 is for a fixed separation S.

The optimization described so far is referred to as material balance optimization, or D versus B optimization. At a fixed separation, the capital and utility costs of the column are relatively insensitive to the

Figure 3.3 Material balance optimization at a fixed separation S. Numbers marked on curve show the percent recovery of light component in the distillate stream. (Reprinted with permission from W. R. Fisher, M. F. Doherty, and J. H. Douglas, lnd. Eng. and Chem. Proc. Des. and Bevel., Vol, 24, p. 955, Copyright © (1985), American Chemical Society.)

Figure 3.3 Material balance optimization at a fixed separation S. Numbers marked on curve show the percent recovery of light component in the distillate stream. (Reprinted with permission from W. R. Fisher, M. F. Doherty, and J. H. Douglas, lnd. Eng. and Chem. Proc. Des. and Bevel., Vol, 24, p. 955, Copyright © (1985), American Chemical Society.)

location of the optimum. This is because the costs are primarily dependent on the separation S, which is assumed to be fixed.

In an operating column, a symptom of nonoptimum material balance is one product far purer than needed, and the other experiencing excessive impurity levels. The culprit is usually a deficiency in the control system or a constraint in the column.

3.1.3 Optimizing separation (energy balance optimization)

Figure 3.16 shows the effect of changing separation on Fig. 3.1a. For a fixed recovery (DIF), the greater the separation, the better the purity of both products.

Unlike the material balance optimization, which has a relatively small impact on the column capital and utility costs, the energy balance optimization is the prime factor setting these costs. Reflux and stage requirements strongly depend on the separation S. The greater S, the higher the reflux and stage requirements, and the greater the capital and utility costs. For an existing column, the capital costs are fixed, but the utility costs increase with S.

Diagrams similar to Fig. 3.2 can be drawn for several different values of S. Constraints should be marked on each. Each diagram determines the best product value within the constraints. The best product values are plotted against S, normally showing a monotonous increase with S. On the same plot, a cost curve is required. A rough column design, therefore, needs to be performed separately for several values of S. Each design should be performed at the best achievable recovery for the given S (i.e., from Fig. 3.2, taking constraints into account). The capital cost needs to be expressed as dollars per day; this can be obtained by dividing the total capital cost by the life (or equivalent life based on discounted cash flow) of the column. The capital cost for a given value of S is then added to the corresponding operating cost, and the total is plotted as a point against S. The costs should include the column auxiliaries (e.g., reboiler reflux pumps) and allow for effects on other equipment (e.g., cooling tower, vent header). The total costs would normally monotonously increase with S.

The difference between the product value and the total costs can now be determined for each value of S. This difference is the profit from the separation as a function of S. The profit curve will normally show a maximum (unless restricted by constraints). The highest profit will set the optimum value of S. Going back to the Fig. 3.2 diagram for the optimum value of S, the optimum D/F value can be determined. This procedure sets the optimum product purity and recovery values.

Figure 3.4 illustrates this type of analysis for an existing column. Since the number of stages is fixed, S becomes a function of the reflux

Figure 3.4 Reflux rate optimization for an existing column. (Reprinted by permission. Copyright © Instrument Society of America, 1978, from P. R, Latour, Instrumentation Technology, July 1978.)