Snyder and co-workers (1988) emphasized the importance of column equilibrium since it is an indication of the repeatability of the experiments. A repeat experiment under the same conditions is required to achieve equilibrium. Failure to equilibrate the column and to reproduce the chromatograms, results in the hindrance of the HPLC method development (Snyder et al., 1988). As such, column equilibrium was maintained for the current work. A minimum passage of 10 column volumes of a new mobile phase was applied, like what was suggested by Snyder and co-workers (1988).
The remaining steps which were suggested by Snyder and co-workers (1988) (quantitation and method validation; problem identification; and method robustness) were not considered for HPLC methods developed for this work. This is because the methods were not developed for publication, rather, they were developed to quantify the percentage degradation of the pharmaceuticals due to the respective pharmaceutical degradation methods.
Annexure F: Optimized system energy requirement
The energy required to operate the optimized hydrodynamic cavitation (HC) system was calculated to find whether the use of the optimized HC system to degrade pharmaceuticals is economical. The principle of energy conservation for the optimized HC energy requirements.
We know from Himmelblau and Riggs (2012) that the equation given for the energy balance equation is as follows:
π₯πΈ
π₯π‘ = πΉπππΈππ β πΉππ’π‘πΈππ’π‘ + π β π
π₯πΈ
π₯π‘ = Cumulative system energy
πΉπππΈππ = Transfer of energy into the system πΉππ’π‘πΈππ’π‘ = Transfer of energy out of the system π = Generated system energy
π = Consumed system energy
Furthermore, the total energy of the system was given as a sum of three different forms of energy which are: kinetic energy (Ek), potential energy (Ep) and internal energy (U), see Equation 5. The kinetic energy results from the movement of the sample solution from one point of the system to another, while Ep is due to the relative position of a sample solution within a gravitational field. On the other hand, U represents all the other energy types found within a system including vibrational energy in chemical bonds (Geankoplis, 1994). As such, the total energy of a system is explained by Geankoplis (1994) in the following way:
πΈ = πΈπΎ + πΈπ + π
Where:
πΈπΎ = π£2
2, where π£ is the velocity of the sample solution
πΈπ = π§π, where π§ is the relative position of the sample solution and π is the acceleration of gravity
π = π = π» β ππ, where π» is the enthalpy, π is the pressure and π is the volume
Furthermore, Geankoplis (1994) gave the overall energy balance equation for a steady state system as follows:
π»2β π»1+ 1
2 β (π£22 β π£12) + π(π§2 β π§1) = π β ππ Where:
π = System heat ππ = System work
Energy calculation
The energy balance for the optimized hydrodynamic cavitation (HC) system considered the pump position as the reference point i.e., position 1. The HC system shown in Figure F1 was used for the energy balance calculations. To simplify the energy balance calculation, two tanks are shown in the diagram, however, only one tank is used in the actual HC system since the sample solution is recycled throughout the cavitational process.
Figure F1: Hydrodynamic cavitation system energy diagram.
The following assumptions were made for the energy balance calculations:
1. Point 1 is the reference elevation, therefore π§1 = 0
2. The tank is open to the atmosphere, therefore π1 = atmospheric pressure
3. There was no phase change or chemical reactions that occurred during the cavitation process
4. The velocity at point 1 is negligible, therefore π£1 = 0
5. The sample solution is incompressible; therefore, the density of the fluid remains constant
6. Although a urea-water solution was used, the urine density of 1025 kg/m3 was used (Pradella et al., 1988)
7. Steady flow in the pipes
8. Surface friction occurred in the pipes
9. Friction loses resulting from contraction, fittings, valves, venturi, and the orifice plate were negligible
10. The viscosity of urine was used even though a urea-water solution was used 11. Stainless steel was used for the pipe material
The input parameters for the energy balance calculations are given in Table F1.
Table F1: Energy balance input parameters.
Parameter description Value Unit
Density (π) 1025 Kg/m3
Discharge pressure (P2) 400 000 Pa
Height (Z2) 0.63 m
Inner diameter (D) 0.025 m
Total length (L) 2.2 m
Suction pressure (P1) 101325 Pa
Viscosity (ΞΌ) 0.000716 Pa.s
Volumetric flow rate (αΉΌ) 0.000120 m3 s-1
Pump head calculation
Geankoplis (1994) defined the pumping head of a fluid as the distance the fluid can be lifted using the pump. This is defined by Equation 7 as follows:
π»π· = (π2 β π1) + π£22 β π£12
2πΌπ + π2 β π1 ππ + π»πΏ
Where:
π2 β π1 = elevation change (m)
π£22β π£12 = velocity change (m/s), the velocity before (π£1) and after (π£2) the fluid enters the pump
πΌ = kinetic energy correction factor π = acceleration of gravity (m s-2)
π»πΏ = head loss
π = density (kg m-3) π2 β π1 = pressure change (Pa)
Once the pumping head was calculated, the power of the fluid would be determined after which the energy required to operate the hydrodynamic cavitation (HC) system at the optimized conditions would be quantified. However, to a calculate the pumping head, the area of the pipe, the velocity of the fluid, the Reynold number, friction factor and the head loss were calculated first.
Pipe area
π΄ = ππ2
4 = π(0.025)2
4 = 4.91 Γ 10β4 π2 Fluid velocity
π£ = αΉΌ
π΄= 0.000120
4.91 Γ 10β4= 0.24 π π β1 Reynold number
π π = ππ£π·
π = 1025 Γ 0.24 Γ 0.025
0.000716 = 8589.39
Since the Reynold number exceeds 4100, the flow within the optimized HC system is turbulent (Geankoplis, 1994).
Friction factor
The absolute roughness (π) of stainless steel is 3 x 10-5 m, and the relative roughness is given by π = π
π· (Geankoplis, 1994).
π = π
π· = 3 Γ 10β5
0.025 = 1.2 Γ 10β3
Using the Moody chart (given in Figure F2), the Darcy friction factor for the optimized HC system was 0.038.
Figure F2: Moody Diagram (Beck and Collins, 2008).
Head loss
π»πΏ = π Γ πΏ
π· Γπ£2
2π
(Geankoplis, 1994)
π»πΏ = 0.038 Γ 2.2
0.025 Γ 0.242
2 Γ 9.81= 0.00982 π
Pumping head
Since we know that the fluid is under turbulent flow, the kinetic energy coefficient (πΌ) is given as 1, therefore:
π»π· = (π2 β π1) + π£22β π£12
2πΌπ + π2 β π1
ππ + π»πΏ π»π· = (0.63 β 0) + 0.242β 02
2 Γ 1 Γ 9.81 + 400 000 β 101325
1025 Γ 9.81 + 0.00982 = 30.42 π
Fluid power
ππππΈπ πΉππ’ππ = αΉΌ Γ π Γ π»π· Γ π
ππππΈπ πΉππ’ππ = 0.000120 Γ 1025 Γ 30.42 Γ 9.81 = 36.71 π
System energy required
The power required to operate the optimized HC system for an average pharmaceutical degradation of 74.5% is 36.71 W. The corresponding energy required to treat the waste solution using the optimized HC system is:
36.71 π Γ 1 ππ
1000 ππ Γ 30 Γ 1 β
60 πππ Γ 1
10 πΏ Γ 1000 πΏ
π3 = 1.84 πβπ πβ3
Therefore, the optimized HC system would require 1.84 kW m-3. The energy required is realistic for industry application considering that Yen (2016) used 1.73 kW/hr for the decolourize textile water using the UV/H2O2 process. The energy from the treatment process by Yen (2016) is comparable to the energy which required to operate the HC system at the operating conditions which were optimized for the current work (Yen, 2016).