Temperature profile, minimization

There may also be an optimum temperature profile. If the temperature-dependences of the specific reaction rates ki and kj are the same (if their activation energies are equal), the reaction should be run at the highest possible temperature to minimize the batch time. This maximum temperature would be a limit imposed by some constraint maximum working temperature or pressure of the equipment, further undesirable degradation or polymierization of products or reactants at very high temperatures, etc. 

If the same amount of source energy were delivered by, say, an electric current over a time larger than the time of development of a minimal flame, the temperature at the core would drop below the flame temperature, the heat liberation in the reaction zone would not attain a balance with the outflow of heat into the preheat zone, and the flame would become extinct. On the other hand, if the current flow were continued for a longer period, the temperature profile ultimately would become sufficiently broad, and the temperature in the core sufficiently high, so that heat liberation within the reaction zone overbalances the outflow of heat and ignition occurs... 

Figure 26 shows the predicted axial gas temperature profiles during reactor start-up for standard type I conditions with varying numbers of axial collocation points. Eight or more axial collocation points provide similar results, and even simulations with six collocation points show minimal inaccuracy. However, reducing the number of collocation points below this leads to major discrepancies in the axial profiles. 

Figure 28 shows comparisons of the transient gas and solid axial temperature profiles for a step-input change with the full model and the reduced models. The figure shows negligible differences between the profiles at times as short as 10 sec. Concentration results (not shown) show even smaller discrepancies between the profiles. Additional simulations are not shown since all showed minimal differences between the solutions using the different linear models. Thus for the methanation system, Marshall s model reduction provides an accurate 2Nth-order reduced state-space representation of the original 5/Vth-order linear model. 

In general, an objective function in the optimization problem can be chosen, depending on the nature of the problem. Here, two practical optimization problems related to batch operation maximization of product concentration in a fixed batch time and minimization of batch operation time given amount of desired product, are considered to determine an optimal reactor temperature profile. The first problem formulation is applied to a situation where we need to increase the amount of desired product while batch operation time is fixed. This is due to the limitation of complete production line in a sequential processing. However, in some circumstances, we need to reduce the duration of batch run to allow the operation of more runs per day. This requirement leads to the minimum time optimization problem. These problems can be described in details as follows. 

Is the temperature profile in batch or semi-batch the optimum Can the temperature peak be minimized ... 

In this paper, a tube of size 1/4" in diameter was considered with styrene monomer preheated to 135 C. The radial variations in temperature are minimal and good control over the concentration profile was possible. Some typical variations in conversion with radial position are shown in Figure 10. The zone temperatures for this example represent a sub-optimal case. However, it is readily seen that as we approach the optimal solution, the first zone temperature converges to an upper limit, while the second zone temperature goes to absolute zero. Figure 11 shows this trend. We also note that as the optimal temperatures are approached, there is a steady drop in the... 

Description A single jacketed fixed-bed reactor removes the heat of the reaction by producing high-pressure steam. The process is carried out with a large ethylene excess. The flexibility of catalyst staging, reactor temperature profiles, and feed flowrates with EVC s single reactor system, produces maximum throughput with minimal byproducts. After condensation and separation of the reaction products (EDC and water), excess ethylene is compressed and recirculated. 

There are several ways to minimize batch time. One can either raise the reaction temperature or simply add more initiator to the system. However, both methods will reduce the molecular weight. High levels of expensive initiators result in lower molecular weight and leave a larger amount of undecomposed initiator, which is costly to remove and also an environmental hazard. Using more initiators also increases the product cost. Hence it is preferable to run the reaction initiated by the right type of initiator or even multiple initiators at a temperature or a customized temperature profile to produce the desired polymer at low cost. 

Butala et al. [43] applied optimization techniques to styrene polymerization initiated by BPO (dibenzoyl peroxide, 1 h half-life time, 91°C) and TBPB (tert-butyl perbenzoate, 1 h half-life time, 124°C). As mentioned before, the batch time can be minimized by using nonisothermal temperature profiles. Three independent runs with different optimization policies were performed. The detailed control policies are listed in Table 5.1. 

All experiments were carried out in a simple flow system. A schematic diagram of the apparatus is shown in Figure 1. The quartz reactor (10 mm i.d.) was heated in a three-zone electric furnace which gave a flat ( 2°C) temperature profile over about 45 cm. Reactor temperatures were measured by a thermocouple which could be moved in a sheath attached to the outside of the reactor. Initially, the sheath was placed inside the reactor, but the inside temperatures agreed so closely with the reactor wall temperatures that the inner thermocouple was removed to minimize catalytic effects. 

Figure 4.14 shows a comparison of the temperature profile obtained from the solution of the above system along with the energy balance equation (4.4), with that from the original 47-step scheme. The period from the minimum scheme is less than half that for the full scheme and the maximum temperature rise is much less. Therefore, this scheme could not be used as an accurate representation of experimental results but is of interest because it provides the minimal oscillating mechanism that we are able to generate for the present conditions. 

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