Zero conversion diagrams

Fig. 7.2. Thermal or flow diagram for the first-order non-isothermal reaction (FON1) in a non-adiabatic CSTR the rate curve R and the flow line L both depend on the dimensionless residence time, but their intersections still correspond to stationary-state solutions—and tangen-cies to points of ignition or extinction. Note that R has a non-zero value at zero conversion. Exact numerical values correspond to 0ai = 10, t, = tn = A ...

Primary products of a complex reaction can be inferred from zero conversion extrapolation of selectivity diagrams, as first described by Schneider and Frolich (16). According to this method, the molar selectivity of each product (mol product formed per 100 mol of reactant decomposed) is plotted against the percent conversion. The validity of this method has been seriously questioned (17). In principle, this method suffers from the fact that at the very low conversions required for reliable extrapolation to zero conversion, data on yields of individual products are subject to substantial analytical uncertainty. Consequently, the calculated conversion is subject to the summation of all of the errors in the yields of all of the products, and the calculated selectivities are increasingly unreliable as the conversion decreases. However, because of the vastly improved accuracy available through the use of modern analytical techniques, the criticism of the use of this method is far less valid, and significant insight into initial product distribution can be derived. 

From the sensitivity diagrams it would appear that the influence of parameter Vq is small at the beginning, peaks over the range approximately between 8 and 12 days, and slowly fades, being still evident at 20 days conversely, the MCCC study would indicate its maximal effect at the very beginning of the experiment, with a subsequent fast monotonic decrease to essentially zero within 5 days. 

The simultaneous solution of eqns. (72) and (79) when h is not zero is generally achieved by a numerical method which considers small increments in reactor volume and then iterates the calculation of the resulting temperature and fractional conversion in a manner similar to that described for Sect. 2.5.3 for a batch reactor. Cooper and Jeffreys [3] give an illustrative example, together with a computer flow diagram, for calculating the reactor volume. 

Returning to the simple cubic autocatalysis model above, we shall be more interested later in the relationship between the rate and the extent of conversion. This is shown for various values of b0 in Fig. 1.7. If b0 = 0 (Fig. 1.7(a)), the rate curve is both a minimum and zero at no conversion (i.e. there is a double root at the origin) and has a further zero at complete conversion (a = 0, a0 — a = a0). The rate has a maximum value of (4/27)/ccao occurring two-thirds of the way across the diagram (a = a0). There is also a point of inflection at 50 per cent conversion, a0 — a — a0. 

Figure 8.8(a) shows a typical example of the phase plane for a system with three stationary solutions, chosen such that there are two stable states and the middle saddle point. The trajectories drawn on to the diagram indicate the direction in which the concentrations will vary from a given starting point. In some cases this movement is towards the state of no conversion (ass = 1, j8ss = 0), in others towards the stable non-zero solution. Only two trajectories approach the saddle point these divide the plane into two and separate those initial conditions which move to one stable state from those which move to the other. These two special trajectories are known as the separatrices of the saddle point. 

Here, the enthalpy of the products of mass flowrate G and specific heat c is measured relative to T0, the inlet temperature of the reactants. The term for rate of heat generation on the left-hand side of this equation varies with the temperature of operation T, as shown in diagram (a) of Fig. 1.20 as T increases, lA increases rapidly at first but then tends to an upper limit as the reactant concentration in the tank approaches zero, corresponding to almost complete conversion. On the other hand, the rate of heat removal by both product outflow and heat transfer is virtually linear, as shown in diagram (b). To satisfy the heat balance equation above, the point representing the actual operating temperature must lie on both the rate of heat production curve and the rate of heat removal line, i.e. at the point of intersection as shown in (c). 

A simplified procedure may also be used as a rule of thumb. Its principle is as follows If the detection limit of an instrument working in the dynamic mode under defined conditions is known, then at the beginning of the peak, the conversion is close to zero and the heat release rate is equal to the detection limit, that is, the temperature at which the thermal signal differs from the signal noise. Thus, the detection limit can serve as a reference point in the Arrhenius diagram. By assuming activation energy and zero-order kinetics, the heat release rate may be calculated for other temperatures. 

The values of are obtained from the reactor mass balances, as will be shown in Chapter 14 on the design of gas-liquid reactors. Figure 6.3.f-3 shows the effect of the group Djki) klbg on the R yield as a function of the conversion of B in a semibatch reactor. When this group is zero (i.e., kt > k) the purely chemical yield is obtained. Hashimoto et al. also presented their results in a diagram like that of Fig. 6.3.f-2. Since they accounted for reaction in the bulk, they could... 

The degree of titration can assume values between zero and infinity. It is unity (1.00) at the equivalence point, that is, for an almost 100 % conversion of the titrated species, and exactly an addition of 100 % of the titrator with respect to the titrated species. To easily understand titration diagrams, it makes sense to plot them in the range of t = 0 to t = 2. The condition r = 2 means a 100 % overtitration, which means that 200 % of the titrator has been added with respect to the amount of species to be titrated. One should understand here that the titratirHi reaction takes place only up to t = 1, and after t = 1 the amount of reacting species tends to zero (although it is not zero because the equilibrium is still shifted). For small equilibrium constants of the titration reaction, the amount of species that are converted after t = 1 may of course be more significant. Such titration reactions are certainly less useful for analytical purposes. 

If we substitute (9.3.23) into (9.3.13), we find that critical points occur at extrema on isothermal Px and Py plots. Likewise if we substitute (9.3.23) into (9.3.16), we find that critical points occur at extrema on isobaric Tx and Ty plots. However, the converses of these statements are not true extrema on such plots are not necessarily critical points we have already seen that they could be azeotropes. Further, those extrema mean that the numerator and denominator in the triple product rule (9.3.18) are both zero however, that ratio need not be zero, so on PT diagrams, critical points rarely occur at extrema of constant-composition lines. 

If component A is the impurity, A > 1 indicates that the impurity will be enriched in the precipitate. Conversely, if A < 1 it will be depleted. A schematic diagram of the effect of precipitation rate on A is shown in Figure 8.6 (Walton, 1967). In enrichment systems, A —> Ae = Z)e as the precipitation rate tends to zero. For fast rates of precipitation A —> 1. For depletion systems, an analogous situation exists with A Ad = i)d for very slow precipitation and A 1 for rapid precipitation. 

In all cases the lowest value of O never occurs either at absolutely zero or at absolutely complete conversion. The term irreversible as applied to a reaction is merely descriptive and implies that a reaction proceeds to such a degree that the residual amounts of unchanged reactants are almost immeasurably small. In such a case the minimum value of O could not be represent at all conveniently on a diagram. 

---