# Simulation and Experimental Study of a Single Fixed-Bed Model of Nitrogen Gas Generator Working by Pressure Swing Adsorption

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}gas generator using pressure swing adsorption (PSA) was simulated and investigated to present the material equilibrium equation describing the change in concentration of substance adsorbed in the gas phase and solid phase over time upon changing the height of the bed. The thermal equilibrium equation described the change in temperature over time upon changing the height of the bed, as well as the capacity of heat adsorption, desorption, and transfer through the column wall. The Langmuir adsorption isotherm equation was predicted, whereas the momentum equation described the changing pressure and drop pressure according to the height of the bed and its head and boundary conditions. These equations could be solved using analytical, finite element, and numerical methods or commercial software such as Pascal, Fortran, Matlab, or Visual Basic when determining parameters such as porosity (ε), axial diffusion coefficient (DL), and velocity (u) in the column. However, verifying these models is very difficult because parameters such as concentration and temperature vary smoothly according to the height of the column, and their determination needs a high-precision measuring device. This article was not intended to solve these problems.

_{2}PSA systems, generating good results when compared to experimental and simulated models. The effects of flow, loading rate, cycle time, and column length on purity and product recall were investigated. The results showed that the N

_{2}purity decreased as the period of the cycle and the feed flow increased. However, upon increasing the feeding rate and bed length, the purity of the product also increased. All of the above conclusions were inversely proportional to the amount of recovery. It was observed that, during a defined cycle time, the effects of feed and discharge flow on purity and recovery were larger than the other parameters. The effects of drop pressure and non-isothermal conditions did not show a significant change.

_{2}. However, they did not study the effects of process parameters such as pressure, flow, and concentration of the bed or the influence of pressure, flow, drop pressure, pressurization time, adsorption time, and amount of O

_{2}gas absorbed at different pressures to find the optimal working regime of the bed. While the findings of other studies [1,2,3,4,5,6,7,8,9,10,11,12,13,14] proposed different mathematical models to simulate and examine the work cycle of the equipment, the use of a single bed as the basis for research cycles and equipment was not mentioned [15,16,17,18,19].

_{2}. Therefore, the Institute of Technology, General Department of Defense Industry, Vietnam researched, designed, and manufactured an N

_{2}gas generator from open air using a CMS-240 carbon molecular sieve, implementing a pressure swing adsorption cycle to investigate, simulate, and optimize the industrial scale-up.

_{2}gas adsorbed and the optimal working mode of the bed. This study is important to determine the mutual influence of technological parameters and to optimize the best working mode. Hence, the ultimate goal is to optimize the N

_{2}gas generator, allowing an industrial scale-up of the used equipment. The results of this study were used to verify other published theoretical and simulation studies using this equipment. Simulation and experimental studies of a single fixed-bed model to produce N

_{2}gas using a CMS-240 adsorption material and the PSA cycle were carried out. In particular, the authors built and simulated pressure as a function of the height of the column over time to find the optimal working mode of the bed in case of instability.

## 2. The Model and Theoretical Basis

#### 2.1. The Model

_{2}gas generator working according to PSA pressure change cycle [15,16,17,18]. Material CMS-240 means that it can produce 240 m

^{3}/h.1ton CMS (N

_{2}99.5%) at standard conditions. The capacity of the column is 14 L/minute N

_{2}99.5% at standard conditions.

- -
- F1-primary filter; C1—piston compressor; T01—compressed air tank; D1—column of silica gel to remove water steam; F2—secondary filter;
- -
- B1-adsorption column (D × H = 102 × 950 mm) contains 3.5 kg CMS-240; T02-N
_{2}gas product tank; - -
- FM01—mass flow sensor to measure gas feed; FM02—mass flow sensor to measure N
_{2}gas product with the purpose of measuring the change of flow over time and determine the amount of adsorption is an important parameter showing the adsorption capacity of the material. - -
- CT02—nitrogen gas concentration sensor to measure nitrogen gas concentration output with the purpose of measuring the change in gas concentration N
_{2}at the output of the column over time and pressurization time, adsorption time, discharge pressure time, and desorption time. - -
- TT01, TT02—temperature sensors to measure the input/output temperature of a single fixed bed model to determine the temperature difference through the column.
- -
- PT-01/06: six pressure sensors installed according to the bed height (10 cm/1 sensor), and the purpose is to measure the pressure change according to the height of the bed and over time. These sensors are deeply inserted into the center of the bed to measure the different pressure between absorbent layers (fitting at the edge of the column will be no difference in pressure).
- -
- The V1 and V7 control valves (on/off; normal close), according to the settings and measurement parameters, are transmitted to S7-1200 PLC computer and recorded on the computer with control monitoring by SCADA interface programmed by WinCC V14.

#### 2.2. The Theoretical Basis

- +
- Survey 1 column with different pressures to achieve the highest concentration of N
_{2}gas with hypothetical pressure, adsorption and desorption time to determine the real-time parameters and best working conditions of the column. - +
- Determining the optimal working mode of the column.

_{2}) changes over time and according to the height of the column is expressed as:

_{L}) and speed apparent (u) by analysis, calculation, and experiment. But testing by experiment is difficult because it is hard to install a device that measures the exact concentration according to the height of the column.

_{i}= y

_{i}P/RT), Equation (1) is transformed into following forms:

_{w}= π(R

^{2}

_{B}

_{,o}− R

^{2}

_{B}

_{,i}).

_{2}being adsorbed. So, the error between theory data and experiment data can reach 20%.

^{d}is the partial pressure of the adsorbed material in the adsorption column at z = L;

^{c}is the duration of the adsorption cycle.

^{d}is the partial pressure of the adsorbed material in the adsorption column at x = L;

^{c}is the duration of the adsorption cycle.

## 3. Calculation and Simulation Results

^{3}, particle density ${\rho}_{p}=0.78$ g/cm

^{3}and solid density ${\rho}_{s}=2.174$ g/cm

^{3}by means of volume, mass weighing, and pycnometer.

_{2}initially of 1 bar (corresponding to 20% of the mole of the initial 5 bar gas mixture) with t = 460 s:

_{2}) decreases over time and according to height of the column corresponding to the gradual reduction of the adsorbed concentration (O

_{2}). This means that the concentration of N

_{2}increases gradually at the output of the column.

_{2}initially of 1.1 bar (corresponding to 20% of the mole of the initial 8 bar gas mixture) with t = 460 s.

_{2}) decreases signifficantly at the output. This may be the optimal working point of the model (4). Drop pressure through column is 0.148 bar.

_{2}) at the output of the column is (O

_{2}) air feed. This confirms again that the pressure of 5.5 bar is the optimal value. Adsorption time is about 25 s.

_{2}gas is 1.6 bar (corresponding to 20% of the mole of the initial 8 bar gas mixture) at t = 460 s.

_{2}) is increased by desorption.

_{2}) at the output of the column includes (O

_{2}) air feed and (O

_{2}) desorption.

## 4. Experiment Results and Discussions

_{2}we can observe the rule when surveying the column at 1 bar pressure. The data resolution is drawn on the graph with higher quality.

- +
- Temperature: the temperature is considered constant
- +
- Pressure: The pressure changes over time and according to the height of the column. The experimental results of the pressure changes over time and the pressure distribution of the column height (with 6 sensors CB-1.1 to CB-1.6) are clearly seen in Figure 13 when surveying one column according to setup mode in Table 3 at 1 bar pressure. At the higher pressures, the lower resolution makes it more difficult to see.

_{2}gas and O

_{2}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.

_{2}at the output of the column: Experimental results of concentration N

_{2}and O

_{2}obtained by CT-02 sensor are observed in Figure 15 at 1 bar pressure. The highest concentration of N2 reached 82.6%.

_{2}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 N

_{2}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 N

_{2}concentration decreases.

_{2}.

_{2}gas at the output of the column from 1 bar to 8 bar pressure.

_{2}gas at output also increased to 5 bar, after decreasing due to the saturation.

_{2}by determining the difference between input and output flow with sensors FM1 and FM2 from 1 bar to 8 bar pressure.

_{2}gas absorbed also increased to 5 bar, remaining so as pressure increases further due to the saturation.

_{2}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 O

_{2}/1 kg CMS-240.The maximum adsorption time of O

_{2}gas is 35 s. The maximum pressurization is 15 s.

## 5. Conclusions

_{2}from air working in environmental, isothermal, working regime stability (pressure change over time) can separate N

_{2}gas to reach a maximum concentration of 93%. Total pressure changes over time and decreases with column height. The optimal working mode at a pressure of 5 bar with adsorption time parameters is determined in Figure 20. Experimental results also show the mutual influence of technological parameters and the adsorption capacity of materials and columns.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Symbol | Unit | Meaning |

D_{L} | [cm^{2}·s^{−1}] | Vertical dispersion coefficient (adsorption column) |

k_{i} | [1·s^{−1}] | Mass transfer factor of the component i |

K_{i} | [-] | Equilibrium constant of the component i |

Z | [m] | Distance along the column (from the beginning of the column to the end of the column) |

ΔP | [bar] | Drop pressure of the column |

q_{i} | [g·g^{−1}] | The amount of gas absorbed in the adsorbent of the component i |

q^{*}_{i} | [g·g^{−1}] | The amount of gas adsorbed in the material adsorbing when equilibrium of the component i |

r_{p} | [µm] | Particle radius |

${\epsilon}_{t}$ | $\left[\frac{{m}^{3}void}{{m}^{3}}\right]$ | Total porosity (porosity inside and between particles) |

P | [mmHg, KG/cm^{2}] | Pressure |

V | [m^{3}] | Volume |

T | [K] | Absolute temperature |

C_{i} | [mole/cm^{3}] | The concentration of component i in the gas mixture |

t | [s] | Time |

U | [m/s] | velocity inside the column |

ρ_{p} | [g/cm^{3}] | Particle density of adsorbent |

K_{L} | [J/cm·s·K] | Thermal conductivity coefficient along the axis |

T_{w} | [K] | The temperature of the column wall |

T_{atm} | [K] | Temperature of the surrounding environment |

ρ_{g} | [g/cm^{3}] | Density of gas |

ρ_{b} | [g/cm^{3}] | Bulk density of adsorbent |

ρ_{w} | [g/cm^{3}] | The density of material column wall |

C_{pg} | [J/g·K] | Specific heat capacity of gas |

C_{ps} | [J/g·K] | Specific heat capacity of adsorbent |

C_{pw} | [J/g·K] | Specific heat capacity of material column wall |

−ΔH | [J/mol] | Heat effect of adsorption process |

h_{i} | [J/cm^{2}·K·s] | Internal heating factor |

h_{o} | [J/cm^{2}·K·s] | External heating factor |

R_{Bi} | [cm] | Inner radius of the column |

R_{Bo} | [cm] | Outside radius of the column |

A_{w} | [cm^{2}] | Cross-sectional area of the wall |

B | [kPa^{−1}] | Langmuir equation parameters expanded |

q_{m} | [mol/kg] | The equilibrium parameter for the extended Langmuir equation |

P_{i} | [kPa] | Pressure of the component i |

K | - | The coefficient of Langmuir equation extends |

## References

- Kulkarami, S.J. Pressure Swing Adsorption: A Summary on Investigation in Recent Past. Int. J. Res. Rev.
**2016**, 3, 46–49. [Google Scholar] - Ashkan, M.; Masoud, M. Simulation of a Single Bed Pressure Swing Adsorption for Producing Nitrogen. In Proceedings of the International Conference on Chemical, Biological and Environmental Sciences, Bangkok, Thailand, 23–24 December 2011. [Google Scholar]
- Smith, A.R.; Klosek, K. A review of air separation technologies and their integration with energy conversion processes. Fuel Process. Technol.
**2011**, 70, 115–134. [Google Scholar] [CrossRef] - Carlos Grande, A. Advance in Pressure Swing Adsorption for Gas Separation. ISRN Chem. Eng.
**2012**, 2012, 982934. [Google Scholar] - Snehal Patel, V.; Patel, J.M. Separation of High Purity Nitrogen from Air by Pressure Swing Adsorption on Carbon Molecular Sieve. Int. J. Eng. Res. Technol.
**2014**, 3, 450–454. [Google Scholar] - Delavar, M.; Nabian, N. An investigation on the Oxygen and Nitrogen separation from air using carbonaceous adsorbents. J. Eng. Sci. Technol.
**2015**, 10, 1394–1403. [Google Scholar] - Roy Chowdhury, D.; Sarkar, S.C. Application of Pressure Swing Adsorption Cycle in the quest of production of Oxygen and Nitrogen. Int. J. Eng. Sci. Innov. Technol.
**2016**, 5, 64–69. [Google Scholar] - Shafeeyan, M.S.; Daud, W.M.A.W.; Shamiri, A. A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption. Chem. Eng. Res. Des.
**2014**, 92, 961–988. [Google Scholar] [CrossRef] - Zhe, X.U. Mathematically modeling fixed-bed adsorption in aqueous systems. Appl. Phys. Eng.
**2013**, 3, 155–176. [Google Scholar] - Ehsan, J.S.; Masoud, M. Pilot-Scale Experiments for Nitrogen Separation from Air by Pressure Swing Adsorption. S. Afr. J. Chem. Eng.
**2014**, 19, 42–56. [Google Scholar] - Shokrooi, E.J.; Motlaghian, S.M.A.M. A robust and user friendly sofware (TB-PSA-SS) for numberical simulation of two-bed pressure swing adsorption processes. Pet. Coal
**2015**, 57, 13–18. [Google Scholar] - Furtat, I.B. Mathematical model of the process of adsorption. Models and modeling. ASTU Bull.
**2008**, 42, 24–30. [Google Scholar] - Akulinin, E.I.; Butler, D.S.; Dvoretsky, S.I.; Simanenkov, A.A. Mathematical Modeling of the Process of Oxygen Enrichment with Air in the Installation of Short-Cycle Adsorption. TSTU Bull.
**2009**, 2, 341–355. [Google Scholar] - Akulinin, E.I.; Dvoretsky, D.S.; Dvoretsky, S.I. Investigation of Heat and Mass Transfer Processes for Enriching Air with Oxygen with Hydrogen through Short-Cycle Adsorption Method. TSTU Bull.
**2016**, 22, 411–419. [Google Scholar] - Kevin Wood, R.; Liu, Y.A.; Yu, Y. Design, Simulation and Optimization of Adsorption and Chromatographic Separation: A Hand-on Approach, 1st ed.; Wiley-VCH Verlag GmbH and Co. KGaA: Hoboken, NJ, USA, 2018. [Google Scholar]
- Suzuki, M. Adsorption Engineering; University of Tokyo: Tokyo, Japan, 1990. [Google Scholar]
- Ruthven, D.M. Principles of Adsorption and Adsorption Process; Wiley-VCH Publishers: New York, NY, USA, 1984. [Google Scholar]
- Douglas Ruthven, M.; Shamsuzzanman, F.; Kent Knaebel, S. Pressure Swing Adsorption; Wiley-VCH Publishers: New York, NY, USA, 1994. [Google Scholar]
- Seader, J.D.; Ernest Heney, J.; Keith Roper, D. Separation Process Principles Chemical and Biochemical Operations; John Wiley and Sons, Inc.: Hoboken, NJ, USA, 2011. [Google Scholar]

**Figure 7.**The result of partial pressure (O

_{2}) following over time and height of column at 5.5 bar.

**Figure 10.**The result of partial pressure (O

_{2}) following over time and height of column at 8 bar.

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

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

1 | Porosity outside or between particles | ε_{i} | m^{3}/m^{3} | ${\epsilon}_{i}=\frac{{V}_{X}}{{V}_{T}}=1-\frac{{\rho}_{b}}{{\rho}_{p}}$ | 0.1326 |

2 | Porosity in the grain | ε_{p} | m^{3}/m^{3} | ${\epsilon}_{p}=\frac{{V}_{p}}{{V}_{T}-{V}_{X}}=1-\frac{{\rho}_{b}}{{\rho}_{s}}$ | 0.556 |

3 | Total porosity | ε_{t} | m^{3}/m^{3} | ${\epsilon}_{t}=\frac{{V}_{p}+{V}_{X}}{{V}_{T}}$${\epsilon}_{t}={\epsilon}_{i}+{\epsilon}_{p}(1-{\epsilon}_{i})$ | 0.615 |

Order | Pressure | P | bar | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | Gas velocity in the column | u_{c} | m/s | 0.058 | 0.038 | 0.029 | 0.023 | 0.019 | 0.016 | 0.014 | 0.013 |

2 | Temperature | T | K | 298 | 298 | 298 | 298 | 298 | 298 | 298 | 298 |

3 | Pore radius | R_{p} | 10^{−8} cm | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

4 | Molecular weight | M(O_{2}) | kg/kmol | 32 | 32 | 32 | 32 | 32 | 32 | 32 | 32 |

5 | Flow diffusion coefficient | D_{k} | 10^{−6} cm^{2}/s | 592 | 592 | 592 | 592 | 592 | 592 | 592 | 592 |

6 | Molecular diffusion coefficient | D_{AB} | 10^{−6} cm^{2}/s | 8.6 | 5.8 | 4.3 | 3.5 | 2.9 | 2.5 | 2.2 | 1.92 |

7 | Axial diffusion coefficient | D_{L} | 10^{−6} cm^{2}/s | 8.5 | 5.7 | 4.29 | 3.44 | 2.87 | 2.46 | 2.16 | 1.92 |

8 | Equilibrium constant O_{2} | K | - | 9.25 | 9.25 | 9.25 | 9.25 | 9.25 | 9.25 | 9.25 | 9.25 |

Time, Pressure Set Up | T = 460 s; P = 1 to 8 Bar | |
---|---|---|

Valve status | T_{1} = 60 s | T_{2} = 400 s |

V_{1} | ON | OFF |

V_{7} | ON | ON |

Parameter/Experiment | 1 | 2 | 3 | 4 | 5 |

Pressure, bar | 1 | 2 | 3 | 4 | 5 |

Number of unstable cycles, n | 4 | 3 | 3 | 3 | 2 |

Weight of CMS in single bed, kg | 3.5 | 3.5 | 3.5 | 3.5 | 3.5 |

Pressurization time, s | 5 | 9 | 9 | 10 | 15 |

Adsorption time, s | 27 | 29 | 31 | 33 | 35 |

Drop pressure, bar | 0.12 | 0.14 | 0.16 | 0.17 | 0.18 |

Mass Flow Input FM1, sml | 39.65 | 60.97 | 84.56 | 112.16 | 125.20 |

Recovery ratio, R | 0.62 | 0.86 | 0.80 | 0.77 | 0.82 |

Mass Flow Output FM2, sml | 24.58 | 52.43 | 67.65 | 86.36 | 102.66 |

The best concentration N_{2}, % (Take the product at atmospheric pressure) | 82.60 | 87.90 | 88.90 | 93.40 | 93.40 |

O_{2} gas flow is calculated adsorption, sml | 3.65 | 5.85 | 9.40 | 16.73 | 18.26 |

Specific gravity of O_{2} at standard conditions, kg/m^{3} | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 |

The amount of O_{2} gas absorbed per 1 kg CMS-240, kg | 0.0007 | 0.0012 | 0.0020 | 0.0038 | 0.0044 |

Order. | Research Parameters | Simulation | Experimental | Conclusion |
---|---|---|---|---|

1 | Rules of pressure change, bar | Partial pressure (O_{2}) changes over time and according to the height of the column. | The change in total pressure over time and the height of the column. | The same rule, but the experiment measured the rule of total pressure and gas concentration N_{2} and O_{2} at the output of the column. The concentration of O_{2} gas decreases in accordance with the height of the column, which can confirm the reliability of the model being established. |

2 | The optimal working pressure of the column, bar | 5.5 bar | 5 bar | The optimum pressure is nearly the same, because this error is chosen because the speed in the model is constant, in fact it is changed by 20% because O^{2} is adsorbed. In addition, there are errors due to the calculation of porosity and diffusion coefficient. So, this error is acceptable. |

3 | Drop pressure, bar | 0.148 bar | 0.18 bar | The drop pressure measured is greater because in the simulation only the material layer is calculated without taking into account the upper and lower filter materials and sieves. |

4 | Adsorption time, s | 25 s | 35 s | Experimental adsorption time is greater due to the late flow of air through the empty front and rear cylinders to stabilize the pressure and evenly distribute the gas. |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chinh, P.V.; Hieu, N.T.; Tien, V.D.; Nguyen, T.-Y.; Nguyen, H.N.; Anh, N.T.; Thom, D.V.
Simulation and Experimental Study of a Single Fixed-Bed Model of Nitrogen Gas Generator Working by Pressure Swing Adsorption. *Processes* **2019**, *7*, 654.
https://doi.org/10.3390/pr7100654

**AMA Style**

Chinh PV, Hieu NT, Tien VD, Nguyen T-Y, Nguyen HN, Anh NT, Thom DV.
Simulation and Experimental Study of a Single Fixed-Bed Model of Nitrogen Gas Generator Working by Pressure Swing Adsorption. *Processes*. 2019; 7(10):654.
https://doi.org/10.3390/pr7100654

**Chicago/Turabian Style**

Chinh, Pham Van, Nguyen Tuan Hieu, Vu Dinh Tien, Tan-Y Nguyen, Hoang Nam Nguyen, Ngo Thi Anh, and Do Van Thom.
2019. "Simulation and Experimental Study of a Single Fixed-Bed Model of Nitrogen Gas Generator Working by Pressure Swing Adsorption" *Processes* 7, no. 10: 654.
https://doi.org/10.3390/pr7100654