**Design Constraints**/**Possible Optimizations**


Similar optimization methodologies were developed for reactors R-101 and R-102, with differences occurring due to the varying extents of the respective exothermic reactions. The Wegstein method is usually the most reliable method for tear stream convergence, such as with the RPLUG model in Aspen Plus® (AspenTech, Bedford, MA, USA). Interactions between variables are ignored therefore the Wegstein method results in oscillating solutions whenever variables are strongly coupled. Owing to the heavily coupled nature between the parameters, the sensitivity of each variable to the next was difficult to determine even when using combinations of optimizations, sensitivities and design spec/vary models in Aspen Plus® (AspenTech, Bedford, MA, USA). Consequently, algorithms were derived iteratively using the RPLUG model on Aspen Plus® (AspenTech, Bedford, MA, USA) in addition to manual (offline) iterations to ensure that the most optimum design choices for the reactors were made. The optimization methodology used aimed at minimizing the total capital expenditure and operating costs, i.e., minimizing reactor sizing and heat input, for the required design constraints.

The optimization procedure, illustrated by Figure 2, entailed iteratively adjusting the tube length to determine the most efficient length for the reactor. The reactor tube length affects the tube and shell side pressure drops since pressure drop correlations are directly proportional to tube length. In addition, the tube length determines the overall dimensions of the reactor since the tube length is inversely proportional to the number of tubes. The tube length was therefore iteratively varied whilst Aspen Plus® (AspenTech, Bedford, MA, USA) models were used to determine the minimum number of tubes required for the respective tube length, the thermal fluid inlet temperature and thermal fluid flow rate required. The minimum number of tubes was governed by the propylene and acrolein conversions specified, which was ultimately dependent on the reaction kinetics and heat transfer within the reactor. Both the reaction kinetics and heat transfer were constrained by the allowable temperature ranges per reactor. The allowable temperature ranges per reactor were controlled by varying the thermal fluid inlet temperature and flow rate. Preliminary base case reactor optimizations illustrated large tube side pressure drops that were not conforming to the allowable 10% design constraint for economical and practical industrial reactors. Hollow cylinder catalyst particles were selected for the simulation

to improve the tube side pressure drop to within the design constraint. Following the optimization of the tube side pressure drop, preliminary analysis was conducted on the shell-side pressure drop. The shell-side pressure drop was increased to promote more efficient heat transfer on the shell side. The same methodology was applied to reactor R-102.

**Figure 2.** R-10X (X = 1 or 2) optimization algorithm.

The following subsections aim to discuss the differences in the optimization methodologies for R-101 and R-102.

Redlingshofer et al. [6] presented reaction kinetics that were valid in the temperature range from 633–703 K for the partial oxidation of propylene. Typically, a preheater would be used to ensure that the reactor feed temperature is within the required range for the reaction kinetics. The duty of heat exchange equipment required to increase the R-101 feed from a mixture temperature of 363 K to 633 K was calculated on Aspen Plus® (AspenTech, Bedford, MA, USA) as 6.19 MW. In typical Lurgi GmbH and Nippon Kayaku processes of acrylic acid, recovered heat from the exothermic reactions is used to generate steam. Instead of generating steam, in this work, an inert preheating zone was used in R-101, as illustrated by Figure 3, to use the heat absorbed by the molten salt circulating in R-101. This concept was derived from the production of phthalic anhydride.

Estenfelder and Lintz [7] presented reaction kinetics that were valid in the temperature range from 533–573 K for the partial oxidation of acrolein. When employing the method developed to optimize R-102 as per the design constraints, the reactor temperature could not be maintained within the required temperature range due to the formation of a hotspot near the entrance of the reactor. Dilution of catalysts with inert material is a widely practiced means of mitigating hotspots in wall-cooled reactors, therefore alternate mass % inert material were used to mitigate the hotspot, which is illustrated in Figure 3. As an initial estimate, 25 mass % inert material was simulated in R-102 to determine the extent to which the reactor temperature would be controlled within the reactor. Increasing the mass % of inert material however does increase the reactor dimensions as well as capital and operating costs.

An alternate method to remove the hotspot is therefore proposed in this work. With reference to the process of ethylene dehydrogenation, an air injection was used to lower the temperature of R-101 effluent and introduce sufficient inert (nitrogen) into the process fluid to successfully remove the hotspot [10].

**Figure 3.** Studied process and catalyst packing configurations of multitubular fixed bed reactors R-101 and R-102.
