+ Simulation (4):

By simulating results at pressure of 5 bar by Matlab with initial conditions and boundary conditions above, we have the partial pressure of O2 initially of 1 bar (corresponding to 20% of the mole of the initial 5 bar gas mixture) with t = 460 s:

Figure 4 shows that the partial pressure of the adsorbent (O2) decreases over time and according to height of the column corresponding to the gradual reduction of the adsorbed concentration (O2). This means that the concentration of N2 increases gradually at the output of the column.

**Figure 4.** The result of partial pressure (O2) following over time and height of column at 5 bar.

The following Figures 5 and 6 are the 2D sections of Figure 4 at the time t = 60 s and at the height of column h = 0.65 m.

**Figure 5.** The result of partial pressure (O2) following height of column at 5 bar.

**Figure 6.** The result of partial pressure (O2) following over time at 5 bar.

Figure 5 shows that the partial pressure 0.91 bar of the adsorbent is reduced to the lowest at 0.65 m height (the end of the column), and the corresponding pressure loss through the column is approximately 0.1 bar.

Figure 6 shows that the partial pressure starts to increase only after about 30 s. It means that at that time the column is saturated, the adsorption capacity decreases. Pressure at 460 s time decreases by approximately 0.1 bar.

Next, by simulation results at maximum pressure of 5.5 barby MATLAB with initial conditions and boundary conditions above, we have the partial pressure of O2 initially of 1.1 bar (corresponding to 20% of the mole of the initial 8 bar gas mixture) with t = 460 s.

The following Figures 8 and 9 are the 2D sections of Figure 7 at the time t = 60 s and at the height of column h = 0.65 m.

**Figure 7.** The result of partial pressure (O2) following over time and height of column at 5.5 bar.

Similar to the case of 5 bar, but the partial pressure decreases with time and the column height is faster, Figure 7 almost likes Figure 4.

Figure 8 shows that the partial pressure of the adsorbent (O2) decreases signifficantly at the output. This may be the optimal working point of the model (4). Drop pressure through column is 0.148 bar.

**Figure 8.** The result of partial pressure (O2) following height of column at 5.5 bar.

Figure 9 shows that partial pressure starts to increase after about 25 s. It means that when the column is saturated, the adsorption capacity decreases. The pressure at 460 s has increased by approximately 0 bar. That means the partial pressure (O2) at the output of the column is (O2) air feed. This confirms again that the pressure of 5.5 bar is the optimal value. Adsorption time is about 25 s.

**Figure 9.** The result of partial pressure (O2) following over time at 5.5 bar.

For simulation results (by Matlab) at maximum pressure of 8 bar with initial conditions and boundary conditions, the partial pressure of initial O2 gas is 1.6 bar (corresponding to 20% of the mole of the initial 8 bar gas mixture) at t = 460 s.

Similar to the case of 5 bar, but the partial pressure decreases with time and the column height is faster, Figure 10 indicates a larger slope.

**Figure 10.** The result of partial pressure (O2) following over time and height of column at 8 bar.

The following Figures 11 and 12 are the 2D sections of Figure 10 at the time t = 60 s and at the height of column h = 0.65 m.

**Figure 11.** The result of partial pressure (O2) following height of column at 8 bar.

**Figure 12.** The result of partial pressure (O2) following over time at 8 bar.

Figure 11 shows that the partial pressure 1.4 bar of the adsorbent is reduced to the lowest at 0.36 m of height (the middle of the column), and the corresponding pressure loss through the column isapproximately0.2bar.Attheendofthecolumn, thepartialpressure(O2)isincreasedbydesorption.

Figure 12 shows that partial pressure starts to increase after about 25 s. It also means that when the column is saturated, the adsorption capacity decreases. The pressure has increased by approximately 0.2 bar at the time t = 460 s. That means the partial pressure (O2) at the output of the column includes (O2) air feed and (O2) desorption.

Drop pressure adsorption and desorption processes are expressed as follow

$$\frac{\Delta P\_{hp}}{H} = \frac{150 \cdot \mu (1 - \varepsilon\_t)^2}{(d\_P \psi)^2 \varepsilon\_t^3} \nu\_{hp} + \frac{1.75 \cdot (1 - \varepsilon\_t) \rho\_\mathcal{\mathcal{S}}}{\varepsilon\_t^3 (d\_P \psi)} \nu\_{hp}^2 \tag{14}$$

Drop pressure through the particle layer is expressed as

$$
\Delta P\_{\rm CMS(tu)} = \lambda\_h \frac{2 \cdot H\_{\rm CMS}}{d\_o} \cdot \frac{\rho \cdot \nu\_{\rm tu}^2}{2} \tag{15}
$$

Total drop pressure through a bed is defined as

$$
\Delta P\_{T(hp)} = \lambda\_h \frac{2 \cdot H\_{\rm CMS}}{d\_o} \cdot \frac{\rho \cdot \nu\_{\rm fu}^2}{2} + \left[ \frac{150 \cdot \mu (1 - \varepsilon\_t)}{(d\_p \psi)^2 \varepsilon\_t^3} \nu\_{hp} + \frac{1.75 \cdot (1 - \varepsilon\_t) \rho\_\mathcal{g}}{\varepsilon\_t^3 (d\_p \psi)} \nu\_{hp}^2 \right] \cdot H \tag{16}
$$

The calculated results of drop pressure at 5 bar, 5.5 bar, and 8 bar are, respectively, 0.2 bar, 0.16 bar, and 0.14 bar. This calculation result has a slight di fference compared with the simulation. Both of these results are very good data to reference with the experimental results given below.

#### **4. Experiment Results and Discussions**

To verify the calculation and simulation results above, we conduct the experiment set up according to Figure 2 (the data Table 3 below). The investigation of a single fixed bed from 1 bar to 8 bar is carried out and we assume an adsorption time of 60 s and a desorption time of 400 s to observe the real adsorption and desorption process on real-time graphs and determine the adsorption and desorption time.


**Table 3.** Set up parameters for the experimental process from 1 bar to 8 bar.

According to the principle of technological parameters in the operation such as temperature, pressure, flow, and gas concentration N2 we can observe the rule when surveying the column at 1 bar pressure. The data resolution is drawn on the graph with higher quality.


**Figure 13.** Pressure over time and heigh of a single fixed bed (see Figure 2).

From Figure 13, we see the rule of pressure change in a column over time an adsorption cycle set. One column adsorption cycle includes pressurization time, adsorption time, pressure release time and desorption time. Observing the above graphs shows the form of the pressure line: straight-line pressurization phase with slope coefficient >0 pressure increased rapidly over time, the adsorption phase of the convex curve type slightly increased to constant, straight-line pressure release phase with slope coefficient <0 pressure rapid decrease over time, the desorption phase form concave curve pressure decreases slowly under low pressure and desorption along time. From this figure, we can determine the drop pressure through the column. Figure 13 shows the two-dimensional (2D) section of the change and distribution of the total pressure over time and the height of the column; it is similar to the three-dimensional (3D) simulation of partial pressure presented in Figures 4, 7 and 10, which are processed by MATLAB according to Equation (4).

+ Mass flow input/output: Experimental results of input/output flow stream are obtained by 02 sensors FM1, FM2 (slm) referring to standard conditions. The experimental results at 1 bar pressure are observed in Figure 14 (the blue line is the flow from FM1, the red line is the flow from FM2). The difference between the two lines can determine the adsorption and desorption processes of the column

**Figure 14.** Mass flow input/output of a single fixed bed (see Figure 2).

Figure 15, we can see the changing law N2 gas and O2 gas concentration at the output of the column over time, here we can determine the pressurization time, adsorption time, pressure release time, desorption time, and the change in concentration according to pressure until saturation. From this image, we can determine the amount of adsorption.

+ Concentration of gas N2 at the output of the column: Experimental results of concentration N2 and O2 obtained by CT-02 sensor are observed in Figure 15 at 1 bar pressure. The highest concentration of N2 reached 82.6%.

**Figure 15.** Concentration of gas N2 at the output of a single fixed bed (see Figure 2).

Figure 15 shows clearly that the concentration of N2 gas changes over time at the output of the column. The time of hypertension is the time when the concentration does not change, the adsorption time is the time of increasing concentration of N2 gas, the pressure drop time is constant high concentration-time (this is the time to take reasonable products), and the time of sorption release is the time that N2 concentration decreases.

Combining Figures 13–15, we can completely determine the parameters of time, amount of adsorbed and pressure loss through the column. The following Table 4 presents experimental results of column survey from 1 bar to 8 bar. However, the 5 bar column has shown saturation.


**Table 4.** Experimental results from 1 to 5 bar.

Table 4 is clearly shown in Figures 17–20 below, showing the relationship and interplay between the technological parameters and workability of the column. Survey data to 8 bar demonstrate saturation of the column.

Figures 16–20 are experimental results of one column from 1 bar to 8 bar pressure. We can observe that, at 5 bar pressure, the column reaches saturation state.

Figure 16 presents the flow measurement of input/output streams of the column from 1 bar to 8 bar pressure, and the black line is the amount of adsorbed O2.

**Figure 16.** The amount of adsorbed material depends on the adsorption pressure.

Figure 16 shows that when the pressure increases, the inlet/outlet airflow also increases, the amount of adsorbent increases to a certain limit at 5 bar pressure.

Figure 17 shows the experimental results of the boosting time and adsorption time from Figures 13–15 (1 bar to 8bar pressure) according to real changes (when setting the running time is 460 s).

**Figure 17.** Adsorption time depends on adsorption pressure.

Figure 17 shows that when the pressure increases, pressurization time and adsorption time also increased to the limit at 5 bar pressure.

Figure 18 presents the experimental data of the drop pressure changing over time and according to the height of the column, which is shown in Figure 13. This result is determined by the maximum difference between the sensors CB-1.1 and CB-1.6.

**Figure 18.** Drop pressure depends on incoming air flow input.

Figure 18 shows that when the mass flow increases, drop pressure also increased.

Figure 19 presents the highest concentration of N2 gas at the output of the column from 1 bar to 8 bar pressure.

**Figure 19.** The dependence of N2 concentration on adsorption pressure.

**Figure 20.** The amount of O2 gas absorbed depends on the pressure.

Figure 19 shows that when the pressure increases, concentration N2 gas at output also increased to 5 bar, after decreasing due to the saturation.

Figure 20 is the experimental data of absorbed O2 by determining the difference between input and output flow with sensors FM1 and FM2 from 1 bar to 8 bar pressure.

Figure 20 shows that, when the pressure increases, the amount of O2 gas absorbed also increased to 5 bar, remaining so as pressure increases further due to the saturation.

From Figures 16–20, we see the optimal working point of the column at a pressure of 5 bar, the concentration N2 gas product of the column reaches the highest of 93.4%. The maximum amount of adsorbent 18.26 L/minute is equivalent to 0.0044 kg O2/1 kg CMS-240.The maximum adsorption time of O2 gas is 35 s. The maximum pressurization is 15 s.

Finally, the compare simulation and experimental results are listed in Table 5.


