# Scale-up and Economic Assessment of Biofunctional Particles Synthesis for Bilirubin Removal
## 3 Results and Discussion
### Economic Assessment
#### 3.2.3 Investment Calculation  
The investment includes all the factors related to the plant building and operation: capital, costs, and sales. The capital investment is formed by the money required for the equipment acquisition and plan construction, known as \"fixed capital investment\"; and that required for the plant operation, named \"working capital\". The fixed capital is defined as that required for the purchase of manufacturing resources and to maintain the production. Fixed capital includes equipment, installation costs, or licenses [34]. Fixed capital can be determined by the percentages method, in which the investment is estimated as a function of the equipment's cost [35]. Thus, the cost of the equipment must be estimated. * Industrial reactor (R-01) design  
As previously mentioned, the scale-up of the reactor requires the geometrical similarity, and this similarity is related to shape factors (Table 3). Besides, to design the industrial reactor, the relation between scales (Kv) should be determined. Since the number of particles  
Figure 6: Process Flow Diagram for the industrial synthesis of St-MMA-GMA-PEGMA particles with HAS. is related to the organic phase, the relation between scales is determined as the coefficient between the organic phase required in industrial and laboratory scales (Equation (9)) [36]:  
\[\mathrm{K_{v}}=\frac{\mathrm{industrial\ organic\ phase\ (g)}}{\mathrm{pilot\ plant\ organic\ phase\ (g)}}=\frac{4,570,719\ g}{1752\ g}=2609 \tag{9}\]  
Once determined Kv, the volume of the industrial reactor can be determined according to Equation (10). \[\mathrm{K_{v}}=\frac{\mathrm{V_{INDUSTRIAL}}}{\mathrm{V_{PILOT\ plant}}} \rightarrow\mathrm{V_{INDUSTRIAL}}=\mathrm{K_{v}}\cdot\mathrm{V_{PILOT\ plant}} \tag{10}\]  
The volume of the industrial reactor is 26,090 L. The geometrical relation between the volume of both reactor is determined by cube of the dimensionless constant (k), that for the studied case has a value of 13.8. The relation between diameters is also proportional to the constant k. Thus, the diameter at industrial scale must have a value of 2898 mm. The dimensions of the industrial reactor and stirrer according to the shape factors (see Table 3) are summarized in Table 7.  
Next, the power consumption (P) of the stirrer at the pilot plant was determined. This power consumption is a function of the stirrer diameter (D), the gravitational acceleration (g), the fluid density (\(\rho\)), the fluid viscosity (\(\upmu\)), and the stirrer speed (N). These variables can be grouped in dimensionless modules [16]:  
\[\frac{\mathrm{P}}{\mathrm{D^{5}}\cdot\mathrm{N^{3}}\cdot\rho}=\mathrm{K^{ \prime}}\cdot\left(\frac{\mathrm{D^{2}}\cdot\mathrm{N}\cdot\rho}{\upmu}\right)^ {\mathrm{b}}\cdot\left(\frac{\mathrm{D}\cdot\mathrm{N^{2}}}{\mathrm{g}}\right)^ {\mathrm{c}} \tag{11}\]  
\[\mathrm{P_{0}}=\mathrm{K^{\prime}}\cdot\mathrm{Re^{b}}\cdot\mathrm{Fr}^{ \mathrm{c}} \tag{12}\]  
where P\({}_{0}\) is the power number; Re is the Reynolds number, and Fr is the Froude number. From this analysis, power number represents the friction factor, Reynolds number can be understood as the relation between the inertia forces and the viscous ones, while the Froude number represents a relation between inertial and gravitational forces [37]. For the studied process at pilot plant scale, the Reynolds number at had a value of 18,561. As it is higher than 300, Froude number has effect. In addition, the installation of baffles should be considered for this calculation. Considering the impeller type (six pallets Rushton type agitator), the Reynolds number, and the curves of the power number versus the Reynolds number from [PERSON] (2001) [38], the power number can be determined. A value of P\({}_{0}\) of 1.46 was obtained and, with it, the power requirement for the stirring of the pilot plant reactor is calculated with a value of 0.1 W.  
In order to ensure an accurate scale-up process, the power required for the stirring was determined by a criterion of constant power per unit of volume.