Decreasing

Such step-limiting is often helpful because the direction of correction provided by the Newton-Raphson procedure, that is, the relative magnitudes of the elements of the vector J G, is very frequently more reliable than the magnitude of the correction (Naphtali, 1964). In application, t is initially set to 1, and remains at this value as long as the Newton-Raphson correotions serve to decrease the norm (magnitude) of G, that is, for... 

BETA cols 11-20 oscillation control parameter default value is set equal to 0.25. To help prevent oscillations (thus slowing convergence) we not only require that the sum of squares, SSQ, decreases... 

This value determines the amount the step-size is reduced to satisfy the criteria of a SSQ which decreases from one iteration to the next. The amount of the decrease is equal to the previous value of the step-limiting parameter divided by RP. 

FIND NORM OF OBJECTIVE FUNCTION AND CHECK FOR DECREASE 260 FV ABS(F)... 

APPLY STEP-LIMITING PROCEDURE TO DECREASE OBJECTIVE FUNCTION 265 KD=l... 

Maximum selectivity requires a minimum ratio rjr in Eq. (2.17). A high conversion in the reactor tends to decrease Cfeed- Thus... 

If the secondary reaction is reversible and involves a decrease in the number of moles, such as... 

Decrease the concentration of inerts if the BYPRODUCT reaction involves an increase in the number of moles. 

If k-2 increases faster than kx, operate at low temperature (but beware of capital cost, since low temperature, although increasing selectivity, also increases reactor size). Here there is an economic tradeoff between decreasing byproduct formation and increasing capital cost. 

Increasing the pressure of irreversible vapor-phase reactions increases the rate of reaction and hence decreases reactor volume both by decreasing the residence time required for a given reactor conversion and increasing the vapor density. In general, pressure has little effect on the rate of liquid-phase reactions. 

The selection of reactor pressure for vapor-phase reversible reactions depends on whether there is a decrease or increase in the number of moles and whether there is a system of single or multiple reactions. 

An excess of ammonia in the reactor decreases the concentrations of monoetha-nolamine, diethanolamine, and ethylene oxide and decreases the rates of reaction for both secondary reactions. 

Thus an excess of ammonia in the reactor has a marginal eflFect on the primary reaction but significantly decreases the rate of the secondary reactions. Using excess ammonia also can be thought of as operating the reactor with a low conversion with respect to ammonia. 

An initial guess for the reactor conversion is very difficult to make. A high conversion increases the concentration of monoethanolamine and increases the rates of the secondary reactions. As we shall see later, a low conversion has the effect of decreasing the reactor capital cost but increasing the capital cost of many other items of equipment in the flowsheet. Thus an initial value of 50 percent conversion is probably as good as a guess as can be made at this stage. 

Multiple reactions. For multiple reactions in which the byproduct is formed in parallel, the selectivity may increase or decrease as conversion increases. If the byproduct reaction is a higher order than the primary reaction, selectivity increases for increasing reactor conversion. In this case, the same initial setting as single reactions should be used. If the byproduct reaction of the parallel system is a... 

For multiple reactions in which the byproduct is formed in series, the selectivity decreases as conversion increases. In this case, lower conversion than that for single reactions is expected to be appropriate. Again, the best guess at this stage is to set the conversion to 50 percent for irreversible reactions or to 50 percent of the equilibrium conversion for reversible reactions. 

Separation becomes more difficult (relative volatility decreases) i.e., more plates or reflux are required. 

Latent heat of vaporization decreases i.e., reboiler and condenser duties become lower. 

Another variable that needs to be set for distillation is refiux ratio. For a stand-alone distillation column, there is a capital-energy tradeoff, as illustrated in Fig. 3.7. As the refiux ratio is increased from its minimum, the capital cost decreases initially as the number of plates reduces from infinity, but the utility costs increase as more reboiling and condensation are required (see Fig. 3.7). If the capital... 

Decreases trays in the rectifying section but increases trays in the... 

Forward-feed operation is shown in Fig. 3.12a. The fresh feed is added to the first stage and fiows to the next stage in the same direction as the vapor flow. The boiling temperature decreases from stage to stage, and this arrangement is thus used when the... 

Temperature levels can be changed by manipulating the operating pressure. Figure 3.13a shows the effect of a decrease in pressure. 

The temperature difference between stages can be manipulated by changing the heat transfer area. Figure 3.136 shows the effect of a decrease in heat transfer area. 

Figure 4.9 shows a plot of Eq. (4.12). As the purge fraction a is increased, the flow rate of purge increases, but the concentration of methane in the purge and recycle decreases. This variation (along with reactor conversion) is an important degree of freedom in the optimization of reaction and separation systems, as we shall see later. 

The reader might wish to check that if the temperature of the phase split is increased or its pressure decreased, the separation between hydrogen, methane, and the other components becomes worse. 

---