*3.7. Assumptions and Simulation*

Rigorous design of multitubular reactors can be effectively carried out in the Aspen Plus® (AspenTech, Bedford, MA, USA) simulation platform, provided that mass transfer resistances are either designed-out or accounted for in the reaction rate [17]. Design heuristics, in Table 3, from the indicated literature sources were used to develop the optimized reactor configuration in this work. Heat and mass transfer approximations and calculations were critically evaluated in the reactor.

**Table 3.** General multitubular rector design heuristics.


The RPLUG model on Aspen Plus® (AspenTech, Bedford, MA, USA) assumes ideal plug flow. Axial and radial dispersion was neglected since the tube length to particle diameter was large. Since both heat and mass transfer coefficients increase with increasing mass velocities, in most industrial reactors with large throughputs at high pressures, it is practical to avoid significant interphase gradients.

Convergence on the optimization model could not be achieved by varying all critical parameters together due to their heavily coupled nature therefore, the iterative methods in the algorithms illustrated by Figure 2 was used to best approximate a convergence sequence.

Sensitivities were conducted on the thermal fluid flow rate and inlet temperature using a base case reactor to determine which variable controlled the maximum and minimum temperatures within the reactor. For R-101, the heat transfer fluid flow rate affected the minimum temperature the most whilst the maximum temperature was affected by the heat transfer fluid inlet temperature the most, as illustrated by Table 4. The same methodology was applied to reactor R-102.


**Table 4.** R-101 sensitivity results to determine relationship between parameters.

<sup>1</sup> Required temperature range for R-101 was 633 to 703 K.

The overall heat transfer coefficient in exothermic reactions can independently determine the size of a reactor unit and is therefore of pivotal importance. All heat transfer resistances were taken into consideration when determining the overall heat transfer coefficient and then iterated in the optimization methodologies used.

The feasibility of the packed bed design is substantially dependent on the catalyst structure and packing matrix employed. The catalyst is also required to be resistant to crushing and abrasion. Spherical catalyst particles are commonly used for propylene partial oxidation in industry. However, owing to the large tube-side pressure drop, which exponentially surpassed the general design heuristic of 10%, the catalyst geometry was revisited and hollow cylinder catalyst pellets were selected [19]. The use of hollow cylinder catalyst pellets enhances conversion levels in reactors due to the better utilization of the catalytic material, with the most notable feature being the absence of the pellet core, which lowers internal transport resistances and the reactor pressure drop [20]. Greater catalyst surface areas result in smaller reactor volumes, which is arguably the ultimate design feasibility decision. Therefore, hollow cylinder catalysts were selected and ensured that the tube side pressure drop was within 10% [21]. Following the control of the tube side pressure drop, analysis was conducted on the shell-side pressure drop. Low shell-side pressure drops are indicative of low turbulence in the shell. Heat transfer coefficients are directly proportional to Reynolds number, which is an indication of the degree of turbulence. A high heat transfer coefficient would require a smaller heat transfer surface area, thereby reducing the size of the reactor, by increasing the overall heat transfer coefficient. As a result, higher turbulence on the shell side was required. The shell-side pressure drop was therefore increased by varying the reactor tube length until the tube-side pressure drop constraint was met. These results are illustrated in Table 5 for R-101. A similar optimization procedure was conducted for R-102.

Heat integration was employed within R-101 to negate the additional capital and operating costs associated with a waste heat exchanger network. Reactor R-101 is essentially modeled and simulated as two series reactors with an inert preheating zone and a reacting zone, as illustrated by Figure 3. The preheating zone was used as part of energy optimization since the temperature of molten salt needed to heat the feed to 633 K was close to the exiting molten salt temperature. The resultant temperature and composition profiles in R-101 are illustrated by Figure 4.


**Table 5.** R-101 optimization results.

**Figure 4.** R-101 temperature and molar composition profiles: (**a**) process fluid and molten salt temperature profiles in R-101 for inert preheating and reacting zones; (**b**) molar composition profile in R-101 of major components.

The optimization algorithms for R-101 and R-102 are similar, with differences occurring due to the varying extents of the respective exothermic reactions. Temperature ranges and hotspot formation were more difficult to control in R-102 as compared to R-101 hence rigorous design changes to R-102 were made. As an initial estimate, 25 mass % inert material was assumed to be used in R-102 to determine the extent to which the reactor temperature would be controlled. In addition, the hotspot was required to be mitigated since the reaction is prone to rapid runaway with minor coolant variations. Figure 5 illustrates the results of sensitivities conducted on varying quantities of inert material (0 to 45 mass %) in an attempt to control the reaction temperature range as well as prevent the formation of the hotspot. The temperature profile along the reactor is typical of that for a highly exothermic and rapid reaction. When the temperature of the reaction mixture reaches a satisfactory value with fresh catalyst, the reaction takes off and a hotspot begins to develop. The reaction temperature rapidly exceeds the salt temperature. The reaction rate increases exponentially and the heat removal rate increases only linearly as the reaction mixture temperature exceeds the temperature of the molten salt. The temperature begins to decline as the reaction rate declines with increasing conversion.

**Figure 5.** R-102 temperature profiles for varying inert compositions (— Process fluid temperature; — Molten salt temperature): (**a**) R-102 temperature profile for 0 mass % inert material; (**b**) R-102 temperature profile for 25 mass % inert material; (**c**) R-102 temperature profile for 35 mass % inert material; (**d**) R-102 temperature profile for 45 mass % inert material.

By incorporating inert material into the catalyst bed, the reaction and heat generation rate per unit volume is decreased, and it was postulated that this may be able to eliminate the hotspot. The actual shape and limits of the temperature profiles are dependent on the feed temperatures for the process fluid and thermal fluid, the driving force for heat transfer and the net generation of heat within the reaction zone [22]. As can be seen in Figure 5, all inert packing configurations exhibited hotspot behavior, thus the incorporation of inert material into the bed, even up to 45%, did not have the necessary effect on the temperature moderation and hence selectivity. In the case of 35% inert, the system exhibited a high final temperature, with a flatter and more sustained overtemperature in the response. Since the simulations were carried out with constraints on the overall conversion, the reduced rate at the start of the bed required a higher temperature towards the end of the bed to meet the necessary conversion value. Such behavior was not observed for the 45% inert system. Here the driving force for heat transfer was low and once the reaction was initiated, a rapid increase in temperature and conversion was observed, as in the case of 0% and 25% inert material.

As illustrated, since the reaction could still not be optimally controlled, literature was consulted to determine other methods of optimal temperature control in similar exothermic, runaway reactions. A multitubular reactor process for the oxidative dehydrogenation of ethylene was studied due to the similarities between the processes [10]. The reactor had a runaway temperature problem which was overcome by the use of distributed air injection schemes. The injection of cold feed is often used for the control of the reaction exotherm [23]. The ratio of oxygen to nitrogen in air essentially controls the reaction rate due to the inert nitrogen, hence allowing a wider range of operation. A similar methodology was applied to R-102. A cold injection of air was used to collectively cool R-101 effluent to the required temperature of 533 K whilst ensuring that the feed stream contained sufficient inert gases to control the reaction rate in R-102 and hence remove the formation of the hotspot. These results are illustrated by Figure 6.

**Figure 6.** R-102 temperature and molar composition profiles: (**a**) process fluid and molten salt temperature profile in R-102; (**b**) molar composition profile in R-102 of major components.
