Maximum production rate

With few exceptions, reaction rates decline as reactant concentrations decline. This provides an easy method for determining the maximum production rate possible with a flow reactor. Maximum production occurs when the entire reactor is filled with the entering composition. Suppose A P. Then the maximum production rate of P is 

Maximum production is achieved by feeding the reactor at a high rate, Q oo. This high productivity is obtained at the price of very low conversion, dfout Omy a low outlet concentration of the product, Pout 0 and a large separation system. In contrast, maximum conversion, aout 0, is achieved when Q 0, Pout Om, and productivity is zero, Qpout 0. 

Equation 4.21 applies to almost any type of reactor and almost any type of single reaction. The exceptions with regard to type of reactor are generally pathological. There must be some portions of the reactor that are flow restricted so that these portions are unaffected by increases in Q and thus have some volume with concentrations 

For most reactions, the rate decreases as the reaction proceeds (important exceptions being a number of biological reactions which are autocatalytic). For a reaction with no volume change, the rate is represented by the slope of the curve of X (moles converted per unit volume) versus time (Fig. 1.10), which decreases steadily with increasing time. The maximum reaction rate occurs at zero time, and, if our sole concern were to obtain maximum output from the reactor and the shutdown time were zero, it appears that the best course would be to discharge the reactor after only a short reaction time tr, and refill with fresh reactants. It would then be necessary, of course, to separate a large amount of reactant from a small amount of product. However, if the shut-down time is appreciable and has a value ts then as we have seen in the example on ethyl acetate above, the average production rate per unit volume is  

The maximum production rate is therefore given by the maximum value of  

This maximum can be most conveniently found graphically (Fig. 1.10). The average production rate is given by the slope of the line ZA this is obviously a maximum when the line is tangent to the curve of x versus t, i.e. ZT as shown. The reaction time obtained tr max is not necessarily the optimum for the process as a whole, 

Maximum production rate in a batch reactor with a shut-down time ts 

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Because RPSA is appHed to gain maximum product rate from minimum adsorbent, single beds are the norm. In such cycles where the steps take only a few seconds, flows to and from the bed are discontinuous. Therefore, surge vessels are usuaHy used on feed and product streams to provide unintermpted flow. Some RPSA cycles incorporate delay steps unique to these processes. During these steps, the adsorbent bed is completely isolated and any pressure gradient is aHowed to dissipate (68). The UOP Polybed PSA system uses five to ten beds to maximize the recovery of the less selectively adsorbed component and to extend the process to larger capacities (69). 

Thus, for the rlh description of the reservoir, based on the material presented earlier, one can compute expected total oil production rate as well as the minimum and maximum production rates corresponding to a desired confidence level (1 -a). 

The right side of this expression is identical with the rate of production of species B and C. Hence the maximum production rate for a fixed reactor volume occurs when the reactor contents have a composition that maximizes the specific reaction rate. Now, in terms of the fraction conversion,... 

To find the reaction time corresponding to the maximum production rate the method outlined in Section 1.6.3 of Volume 3 is adopted as follows. From the relation ... 

The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 batches per week. The profit per batch would be 20, 6, and 8, respectively, on products 1, 2, and 3. 

Determine the maximum production rate and show that P°pt is indeed the maximum throughout. 

Figure 3.11 Nomogram for calculation of maximum production rate as a fimction of superficial velocity, bed height and air inlet temperature. From De Michelis and Calvelo (1985), by permission of the Institute of Food Technologists, USA.

For reactions in series we calculate the maximum production rate of R directly, as shown in Chapter 8. However, for reactions in parallel we find it useful to first evaluate the instantaneous fractional yield of R, or... 

From the performance equation we can show that everything—washout, optimum processing time, maximum production rate—all depend on and Ca0> combined as follows ... 

What feed rate of glucose solution (C o = 6 kg/m ) to a mixed flow reactor (V = 1 m ) would give the maximum consumption rate of glucose, and maximum production rate of E. coli cells ... 

Mixed Flow Fermentors for n = 1 649 the maximum production rate of cells and product is found to be... 

The maximum production rate, however, often results in nnacceptable recovery yields. Low recovery yield requires further processing by recycling the mixed fractions. The recovery yield at the maximum production rate strongly depends on the separation factor. In the cases of difficnlt separations, when the separation factor under linear conditions is aronnd or lower than a= 1.1, the recovery yield is not higher than 40%-60%. Even in the case of a=1.8, the recovery yield at the maximum production rate is only about 70%-80%. The situation is still less favorable in displacement chromatography, particularly if the component to be purified is more retained than the limiting impurity. In this case, from one side the impurity, whereas from the other side the displacer, contaminates the product. 

Process Reliability Simulation VIP The process reliability simulation VIP is the use of reliability, availability, and maintainability (RAM) computer simulation modeling of the process and the mechanical reliability of the facility. A principal goal is to optimize the engineering design in terms of life cycle cost, thereby maximizing the project s potential profitability. The objective is to determine the optimum relationships between maximum production rates and design and operational factors. Process reliability simulation is also applied for safety purposes, since it considers the consequences of specific equipment failures and failure modes. 

Extrusion parameters, such as basket temperature, extrusion rate, and die design, can be adjusted to suit a particular formulation and granule size. This is an empirical process based on experience. Extrusion characteristics represent an intimate interplay between press parameters and dough properties, the latter predominating. What is wanted is maximum production rate of a smooth, dense, homogeneous strand of these qualities, smoothness is perhaps most sensitive to extrusion conditions. 

Now suppose a saturated solution at temperature T is fed to a crystallizer operating at temperature Since it is saturated, the feed has a mole fraction of R equal to x . The maximum production rate of crystals occurs when the solution leaving the crystallizer is saturated, meaning that the crystal production rate, mprod, depends on the value of Ty... 

Figure 11-20 shows production rate, cell concentration, and substrate concentration as functions of dilution rate. From Equation 11-74, the maximum production rate can be determined. 

Total Main-cut Products = 156.5 mol Total Campaign Time = 16.95 hr Maximum Production Rate = 9.23 mol/hr... 

As observed with this HEWL-Cibacron Blue F3GA immobilized Frac-tosil 1000 system, and numerous other cases of polypeptide or protein interaction with HPLC sorbents, the maximum production rate tends to increase with the increase of the terminating effluent concentration. At fluid velocities lower than the optimum velocities, the effect of the terminating effluent concentration, however, becomes less important. The use of a flow rate at the maximum capacity of the pump (or to the pressure limit of the system as is sometimes practiced) will usually lead to an impaired production rate with HP-BAC, HP-BMC, and HP-HIC sorbents.307,422,423 This conclusion has been also supported by other experimental data on large-scale chromatographic purification of proteins with HP-IEX sorbents.368,406,421,424... 

FIGURE 39 Operating regions based on the product yield and processing rate for a human serum albumin (HAS)-DEAE Trisacryl M ion-exchange chromatographic system. The open circles are the maximum production rates (0.87 and 1.46 mg/mL- min) for the 100 and 99% product yield curves derived from the tanks-in-series sectional model approach. Data from Mao, Q. M. and Hearn, M. T. W 1996. Biotechnol. Bioeng., 52, 202. Reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc. 

Except for theophyllin, the solubilities are similar at a dissolution temperature (Td) and a dissolution pressure (Pd) of 65°C and 250bar, respectively, the mole fractions are of 2.5e-4 for anthracene, 5e-4 for caffeine and 6.5e-4 for salicylic acid. Theophyllin is an order of magnitude lower, with a value of 0.2e-4. The mole fractions allow one to estimate the maximum production rate for the experimental set up. Assuming a recovery of produced particles of 100%, and no dilution required for processing, the production rates are 1.0, 1.2, 0.5 and 0.04 g/h for caffeine, salicylic acid, anthracene and theophyllin, respectively (conditions Pd = 220bar, Td=65°C, capillary =1.5cm x 75pm flow rate of liquid C02=11.2ml/min)... 

Operating time, rate of production, and sales demand are closely interrelated. The ideal plant should operate under a time schedule which gives the maximum production rate while maintaining economic operating methods. In this way, the total cost per unit of production is kept near a minimum because the fixed costs are utilized to the fullest extent. This ideal method of operation is based on the assumption that the sales demand is sufficient to absorb all the material produced. If the production capacity of the process is greater than the sales demand, the operation can be carried on at reduced capacity or periodically at full capacity. 

At some concentration of NO the system reaches a maximum production rate for ozone at dP(03)/d(N0 c) = 0 and even though P(03) is still significantly larger than 2.(03) the net production rate begins to fall off with increasing NO - Until this maximum is reached the system is said to be NO c limited with respect to the production of ozone. The turn-over, i.e. dP(03)/d(NO t) = 0 is caused by the increased competition for NO by the reaction... 

Fig. 4. Sustained oscillations that occur during the oxidation of CO over Pt(lOO) at 500 K, Poj = 5 X 10 Pa, Pco = 5 X lo Pa. The dashed vertical lines that coincide with the sudden decrease in the c(2 X 2) signal occur at the maximum work function (oxygen coverage), which also corresponds to the maximum production rate of CO2. The next vertical line corresponds to the maximum in the hex signal, and the simultaneous minima for the oxygen surface coverage and the CO2 production rate (after 82).

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