**2. Method Development**

The reactor feed materials simulated in this work consists of a mixture of propylene with a purity of 94 mol % (containing equimolar impurities of propane and ethane), low-pressure steam (432 K, 5 bar) and compressed air (10 bar). The feed streams are fed into two multitubular fixed bed reactors in series, R-101 and R-102. The two-step oxidation process presented in this work contains a coordination of catalysts, with differing microstructures and operating conditions for each reactor. The partial oxidation of propylene, Equation (1), occurs exothermally within R-101. The tubes are packed with a bismuth molybdate catalyst. The reactor feed composition is comprised of a ratio of 5:30:65 of propylene, steam and air. Low-pressure steam is added to the reactor feed to act as thermal ballast [5]. R-102 operates within a lower temperature range and a vanadium molybdate catalyst. Molten salt was selected to be used as a coolant on the shell side to facilitate temperature control. The effluent from R-102 containing acrylic acid, unreacted propylene and associated byproducts, is then further processed and refined to the required grade of acrylic acid.

The multitubular fixed-bed reactor train was simulated on Aspen Plus® (AspenTech, Bedford, MA, USA) using the RPLUG (plug-flow reactor) model and the NRTL thermodynamic property method. The NRTL (non-random-two-liquid) thermodynamic property method was selected to simulate the physical properties of the reactant system, due to its ability to accurately predict highly nonideal chemical, polar or non-polar systems. The RPLUG model on Aspen Plus® (AspenTech, Bedford, MA, USA) employs ideal plug flow characteristics to the reacting systems. Therefore, radial velocity gradients were considered negligible. Interphase heat and mass transfer resistances and dispersion were also neglected. The RPLUG model required the following input parameters and reactor configuration choices for the rigorous design methodologies employed such as:


Reaction kinetics for the partial oxidation of propylene were extracted from Redlingshofer et al. [6], whilst Estenfelder and Lintz [7] reaction kinetics were used for the partial oxidation of acrolein to acrylic acid. The reaction kinetics used in this work were validated on Aspen Plus® (AspenTech, Bedford, MA, USA). A co-current flow configuration was selected. The overall heat transfer coefficient (per unit wall area) was interactively calculated using a macro-enabled excel spreadsheet which was coupled to the Aspen Plus® (AspenTech, Bedford, MA, USA) simulation platform for easy iteration during the development of the optimization methodology. Fouling factor resistances were extracted from literature. The overall heat transfer coefficient is given by Equation (7):

$$\frac{1}{\Delta I\_i} = \frac{1}{h\_i} + \frac{1}{h\_{id}} + \frac{d\_i \ln\left(\frac{d\_o}{d\_i}\right)}{2k\_w} + \frac{d\_i}{d\_o} \frac{1}{h\_{od}} + \frac{d\_i}{d\_o} \frac{1}{h\_{od}} + R \tag{7}$$

where *Ui* is the overall heat transfer coefficient based on the inside area of the tube, *hi* is the tube-side heat transfer coefficient, *hid* is the tube-side dirt coefficient (fouling factor), *do* is the tube outside diameter, *di* is the tube inside diameter, *kw* is the thermal conductivity of the tube wall material, *hod* is the shell-side dirt coefficient and *R* is a heat transfer resistance parameter. The tube-side and shell-side heat transfer coefficients are functions of the tube bundle geometry, and fluid hydrodynamics on the tube-side and shell-side, respectively.

The wall heat transfer coefficient on the tube side was determined from a packed bed correlation to take into account the presence of the catalyst and is illustrated by Equations (8) to (11) [8]. Kern's shell side heat transfer coefficient correlation was used to approximate the heat transfer coefficient on the shell side [9].

$$\frac{h\_{wd}d\_p}{k\_\%} = 0.16 \text{Re}^{\prime \, 0.93} \tag{8}$$

$$20 < \text{Re}' < 800 \tag{9}$$

$$0.03 \, < \, d\_p/d\_t < 0.2 \,\tag{10}$$

$$d\_p = \Theta V\_p / S\_p \tag{11}$$

In Equations (8) to (12), *hw* is the wall heat transfer coefficient, *dp* is the diameter of the catalyst particles, *kg* and *kf* are the thermal conductivities of the process gas and thermal fluid, respectively, *de* is the equivalent diameter of the of the flow area on the shell-side, Re and Pr are the fluid Reynolds and Prandtl numbers, and μ and μ*<sup>w</sup>* are the fluid viscosities in the bulk and at the wall, respectively.

The reactor train and heat exchange network optimizations considered the following variables, design constraints and possible optimizations:

**Variables**

