# Benchmarking Thermodynamic Models for Optimization of PSA Oxygen Generators

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}in remote areas. Consequently, developing efficient air separation devices to produce medical oxygen onsite is greatly needed [1]. Moreover, oxygen is included on the World Health Organization (WHO) list of essential medicines [2]. Therefore, it must be made readily available in sufficient amounts and quality in the many developing countries with the most significant mortality of critically ill newborns, children, and adults [3,4].

_{2}[6]. Therefore, they can serve one of the three levels identified by WHO / UNICEF (see Figure 1). Therefore, this article aims to discuss optimizing oxygen production using PSA oxygen, recognizing the sustained increase in health infrastructure, which generates an increase in oxygen demand in many countries [7,8].

## 2. Oxygen Production

#### 2.1. Cryogenic Air Separation Unit (ASU)

- (1)
- The air is initially treated in a pre-operation to remove all gross impurities such as hydrocarbons, carbon dioxide, and others.
- (2)
- The treated air passes through a compressor to be placed under cooling conditions that condense and remove water vapors through a multi-stage process.
- (3)
- The air is then passed through a molecular sieve absorber that traps the remaining CO
_{2}, H_{2}O, and hydrocarbons. - (4)
- Finally, the (remaining) air enters the distillation columns that fraction (separate) it into its major components, notably nitrogen, oxygen, and argon.

_{2}purity. Argon is then vaporized, leaving behind liquid oxygen of 99.8% purity. The product can be stored as-is (or heated to ambient room temperature and stored in the gaseous form) [10,11].

#### 2.2. Oxygen Concentrators

_{2}delivery independent from the commercial gas producer’s supply [4,7]. Additionally, smaller oxygen concentrator units can be made and even used as portable devices (see Figure 3). Indeed, smaller devices are not the first choice of oxygen delivery system for severe patients, but would instead be a pertinent choice for oxygen therapy at home or in times of crisis, especially for long-term use.

#### 2.3. Pressure Swing Adsorption (PSA) Plant

^{3}/h) of oxygen, where 1 m

^{3}= 1000 L of medical oxygen [13].

_{2}concentration between 90% and 96% (with only N

_{2}and Ar and remaining). Most adsorption MOCs rely on a PSA process with a selective nitrogen adsorbent to meet this requirement. In addition, small adsorbing particles are used to reduce mass transfer resistance and improve adsorption kinetics. As a result, according to Chai et al. (2011), typical oxygen products obtained from MOC devices consist of 90 to 93% oxygen at a production rate of less than 10 L/min [8].

_{2}supply, the product (oxygen) can be collected in an overvoltage column and provided at a certain time, or multiple operations can be used. The configuration of the Skarstrom-type PSA cycle is generally used in MOCs, which consist of stages of production, depressurization, purge, and pressure (see annex A for more details) [14,15]. The quick cycle of the adsorption column maximizes the use of adsorbents and miniaturizes the size of the operation.

## 3. Observations Related to the Development and Optimization of PSA Units

#### Simulation Challenges

- (1)
- Increased adsorbent productivity;
- (2)
- Improved O
_{2}recovery; - (3)
- The development of smaller-size, lower-weight units.

## 4. Observations and Findings Related to Thermodynamic Analysis of PSA Processes

- (1)
- A simulation-based optimization framework;
- (2)
- A first-principles-based model;
- (3)
- A high-fidelity adsorption simulation model.

- (1)
- The generation of high-pressure products;
- (2)
- Depressurization;
- (3)
- A low-pressure purge;
- (4)
- Pressurization.

#### 4.1. Simulation-Based Framework

_{w}cross-section area of column wall, C molar concentration of mixture, C

_{i}molar concentrations of component i, c

_{pg}specific heat capacity of gas phase, c

_{pg}specific heat capacity of gas phase, c

_{ps}specific heat capacity of adsorbent, c

_{pw}specific heat capacity of column wall, h

_{in}heat transfer coefficient with inner wall of column, h

_{out}heat transfer coefficient with outer wall of column, Δh

_{i}heat of adsorption of component i, ΔH

_{i}heat of adsorption of component i, k

_{i}mass transfer coefficient of component i, M molar-averaged molecular weight of mixture, M

_{j}molecular weight of component i, n

_{i}dynamic adsorption of component i, n

^{*}

_{I}equilibrium adsorption of component i, n

^{s}

_{i}saturation adsorption of component i, P pressure, q

_{i}dynamic adsorption mass of component i, R universal gas constant, R

_{in}inner radius of column, R

_{out}outer radius of column, t time, T temperature of adsorption bed, T

_{f}ambient temperature, T

_{w}wall temperature, x

_{i}mass fraction of component i y

_{i}, ε

_{b}bed porosity, ρ

_{g}mass concentration (density) of mixture gas, ρ

_{I}mass concentrations of component i, ρ

_{b}bed density of adsorbent, ρ

_{p}particle density of adsorbent, ρ

_{s}skeletal density of adsorbent, ρ

_{w}density of column wall, and Ψ shape factor of the adsorbent particles.

_{2}as possible) is preferable. This leads to a greater interstitial fluid velocity, reducing stay in the bed of the incoming ambient air. Moreover, increasing apparent adsorbent density leads to an increase in pressure drop, which could cause an unwanted fall in the product output power pressure. Thus, a higher apparent adsorbent density can lead to the under-use of the packed adsorbent and a reduction in the separation efficiency of the adsorbent. Consequently, it is necessary to balance this “compromise” to define the optimal density of the adsorbent.

#### 4.2. First Principles-Based Modeling

_{i,s}is the adsorption capacity for the site (solid phase), and P

_{i}is the partial pressure. In the above equation, b

_{i,s}is computed as follows:

_{o,i,s}, and U

_{i,s}are the isotherm fitting parameters.

- (1)
- Intake (air supply) consists of 21% O
_{2}and 79% N_{2}and is supposed to have an insignificant amount of water and argon. - (2)
- The purge and pressurization supply consists of an imposed composition of oxygen and nitrogen.
- (3)
- A minimum number of cycles (e.g., 50) are simulated to reach a cyclic but steady state, as the output properties are monitored to converge for these many cycles.
- (4)
- The purge and pressurization supply consists of an imposed composition of O
_{2}and N_{2}. - (5)
- The lowest achievable pressure is 1 bar.
- (6)
- PSA cycle steps are limited to a maximum number of four.
- (7)
- The bed is saturated with air at the first (initial) pressure and supply temperature stage of a PSA cycle.
- (8)
- The oxygen production stage of the cycle is defined as the first stage, in which air is introduced into the column.

#### 4.2.1. Ideal Gas Constitutive Equation

_{i}

_{,}and C

_{i}are the bulk gas-phase mole fraction and concentration of component i, and R is the universal gas constant.

#### 4.2.2. Mass Balances

_{g}is the superficial velocity (of the gas phase), ε

_{T}is the total bed void fraction, ρ

_{B}is the mass of the solid per unit volume of column (or the adsorbent bulk density), and q

_{i}is the particle-average specific concentration of species i in the adsorbed phase (i.e., per unit mass of solid).

#### 4.2.3. Mass Transfer Rate (w/r to LDF)

_{P}and ε

_{P}are the radius and porosity of the adsorbent particle (P), respectively.

_{K,i}is the local Henry’s coefficient found using the equilibrium isotherm as:

_{i}is the interstitial (or external) porosity.

_{P,mac}the macropore radius and M

_{W,i}the molecular weight of the constituent, we can evaluate the Knudsen diffusion coefficient (DK) using the following relationship:

_{g}is the dynamic gas viscosity and ρ

_{g}is the molar gas phase density, the film resistance coefficient k

_{f;I}is calculated from the Schmidt (Sc

_{i}), Reynolds (Re), and Sherwood (Sh

_{i}) numbers using the following set of equations:

#### 4.2.4. Linear Momentum Balance

#### 4.2.5. Equilibrium Isotherm

_{1,i}, and IP

_{2,i}are defined from the pure component i, and p represents the gas partial pressure.

#### 4.3. High-Fidelity Adsorption Simulation Model

#### 4.3.1. Conservation Equations

_{i}and C are the concentration of component i and total concentration in the gas phase, respectively; y

_{i}is component i gas phase mole fraction; ρ

_{b,ads}is the adsorbent bulk packing density; and ε

_{b}

_{,}and ε

_{t}are bed and total void fraction. Moreover, v is the interstitial velocity, q

_{i}is the component i solid phase concentration, DL is the axial dispersion coefficient, and z and t are the space and time dimensions, respectively.

_{i}is the component i gas phase mole fraction, P is the gas phase pressure, and T is the gas phase temperature.

_{p,ads}and c

_{p,a}which are the adsorbent and adsorbate heat capacity (in kJ/kmol), respectively; c

_{pg}is the ideal gas mixture heat capacity (in kJ/kmol); and K

_{z}, the axial heat conductivity:

_{,}h

_{in}is the column–wall heat transfer coefficient, and r

_{in}is the bed column radius.

_{p}is the particle radius and µ is the gas mixture viscosity.

_{i}to reduce the computational complexity of capturing the mass transfer of adsorbate from gas to the solid phase and vice versa,

_{i}is the LDF mass transfer coefficient.

#### 4.3.2. MOC Process Performance Metrics

_{2}at the product exhaust divided by the total amount of O

_{2}and N

_{2}as follows:

_{O}

_{2}and y

_{N}

_{2}are the gas phase compositions of oxygen and nitrogen; P, v, and T are the scaled pressure, interstitial velocity, and temperature, respectively; P

_{0}, v

_{0,}and T

_{0}are the respective scaling parameters; and t

_{f}is the production step duration of a cycle [37,38].

_{2}recovery (R

_{O2}) of a PSA cycle is derived as follows, wherein the denominator represents the amount of fresh oxygen fed during the production step:

_{p,O}

_{2}, y

_{pres,O}

_{2,}and y

_{f,O}

_{2}are the oxygen molar fractions of the purge, pressurization, and production feed streams and T

_{p}, T

_{f}

_{,}and T

_{pres}are the purge, production, and pressurization step feed temperatures. T

_{p}and t

_{f}are the duration for the purge and production steps, and Z = pres.inlet at the inlet column end during the pressurization step. In addition, v

_{p}, v

_{f}

_{,}P

_{p}, P

_{f}are the interstitial feed velocity and pressure for the purge and production streams.

_{O}

_{2}) as follows:

^{STP}= 273 K and P

^{STP}= 101,325 Pa are the standard temperature and pressure conditions, and t

_{cycle}is the duration of a PSA cycle in seconds.

_{2}product as follows:

_{b,ads}is the adsorbent bulk density, and r

_{in}and L are the column radius and length, respectively.

#### 4.4. Benchmarking Numerical Data and Modeling Output

_{2}/TPD with an oxygen recovery of 29.5%. Ref. [40] performed simulation and optimization studies for studying four-step PSA and PVSA cycles for oxygen production with three different candidate adsorbents. Out of Sylobead MS S624, Oxysiv5, and Oxysiv7, Oxysiv7 showed the best separation performance for both PSA and PVSA cycles with 94.5% oxygen purity, 21.3% recovery and a 3.7 L/min production rate. The authors extended their analysis to investigate a six-step PSA cycle for small-scale medical applications and obtained a 94.5% pure oxygen product with 34.1% recovery and a 4.3 L/min production rate. Ref [17] carried out simulation and experimental studies to investigate a two-bed four-step PSA process for air separation using 5A zeolite. The theoretical results confirm that an oxygen product with 93.4% purity can be obtained, notwithstanding a low oxygen recovery of 20.1% and a low production rate of 0.07 L/min. Ref [30] proposed a two-step pulsed PSA process to extend the potential miniaturization for medical applications. With alternating pressurization and depressurization steps, they were able to achieve an oxygen purity of 90% at a production rate of 5 L/min using 5A and Ag⋅Li⋅X zeolite adsorbents. The authors of [34] elaborated a four-step rapid PSA process that produces a 90% oxygen product at 1–3 L/min with an oxygen recovery of 15–30% and BSF of 45–70. Ref. [29] developed a four-bed rotary value rapid PSA process to enhance air separation performance. The results indicate that a 92% O

_{2}purity at 1 L/min production can be achieved with an oxygen recovery of 30% and a BSF of 78. Finally, [8] developed a rapid PSA process using Li⋅X zeolite with a total cycle time in the range of 3–5 s. They were able to obtain 90% pure oxygen product with 25–35% recovery with a BSF of 11.3–26.7 kg ads. O

_{2}/TPD. Overall, all three models show good correspondence with experimental data with ±5 to 10% accuracy.

## 5. Discussions

#### 5.1. Modeling Considerations

_{2,}notably for patients with serious lung diseases, COVID-19 or COPD. In particular, we can model or optimize flexible adsorption PSA-based apparatuses able to produce O

_{2}with variable flow rates and purity requirements over time. In addition, the flexible design is inherently advantageous because the same device can be adapted to meet changing oxygen needs.

#### 5.1.1. Maximum Flow Output

_{2}needs evaluation to characterize the upper limit flow a MOC should deliver. Small MOCs are often available as 3 to 10 LPM units. As an example, while children take at most 2 LPM, a 5 LPM device could simultaneously support two pediatric patients (even if one is with hypoxic acute respiratory illness). On top of that, this 5 LPM unit could help adults. Based on current WHO guidelines [3]: “An oxygen concentrator unit that delivers between 1 and 10 LPM would be the most versatile for surgical care applications.”.

#### 5.1.2. Oxygen Concentration Output at Higher Altitudes

_{2}become 19.4% at 2000 m or even 18.6% at 3000 m). Although partial (O

_{2}) pressure in the atmosphere is smaller at high altitudes, patients in the installations of these higher altitudes may require higher volumetric flowrates for adequate medical oxygen quality than patients at sea level, this being especially true for longer duration therapy. Beyond 2000 m (above sea level), the performance requirements of devices at high temperatures and humidity should not be as strict as those provided in early studies since the conditions rarely reach up to extremes (i.e., 313 K and 95% RH simultaneously) at these altitudes because temperature and humidity tend to decrease at higher altitudes [5]. Since two parameters play opposite directions, modeling might be the only way to define a design’s final outcome or optimum.

#### 5.1.3. Humidification

_{2}is utilized at minimal flow rates (i.e., less than 2 L per minute), nonetheless, it may be necessary for higher O

_{2}flowrate needs. In this case, a special bottle (for example, for humidification) might be connected between the MOC and the patient (i.e., in the breathing circuit). Humidifiers typically have threads for direct attachment to concentrators with threaded outputs or require a humidifier adapter for concentrators with oxygen-barbed connectors.

#### 5.1.4. Recommendations

- First, we suggest considering a simulation-based optimization framework (see Section 4.1) or high-fidelity modeling (see Section 4.3) to cope with the optimization-related challenges with varying specifications and operations and to achieve this with higher accuracy. These two would allow for the best synthesis (design + operation) of adsorption-based MOC systems but also require more computation time and resources.
- Second, the simpler first-principles-based model (see Section 4.2), with simplifications and assumptions, makes it faster to generate a large volume of scenarios and, in that way, could represent a better approach for a feasibility study dealing with many options and designs. So, it would be the first choice for a quick turnaround process evaluation, establishing a diversity of scenarios, or unfolding feasibility studies.

#### 5.2. Cost Effectiveness

_{2}.

_{2}therapy, notably where oxygen cylinders and piped systems are unsuitable or inaccessible (Duke et al. 2010, WHO 2020) [2,7]. This relies on high-quality MOCs that can provide multiple patients with a viable but flexible and reliable source of O

_{2}. While oxygen concentrators draw from the ambient air to deliver constant, clean, and highly-concentrated O

_{2}, MOCs may operate for multiple years (e.g., up to five years) with minimal energy supply, maintenance, and upkeep needs. Therefore, it is important to have them properly designed, if not optimized, to support a mix of potential situations.

_{AMB}is the ambient temperature, and Sgen is the entropy generated (in [kJ/K⋅kmol]). The destroyed exergy might then be divided into exergy lost to irreversibility and waste. Figure 6 illustrates, with a “Grassman” diagram, the flow of exergy in the system for operation at 390 kPa operating conditions (numbers in % of Input exergy or Exfeed).

#### 5.3. New Avenues

_{2}flow and purity can be accommodated with the use of flexible MOCs. Even though a PSA unit is 0intended for assumed flow and purity levels, the controller can make appropriate operating modifications to achieve a patient’s oxygen specification requirements. The exergy analysis performed and reported in Section 5.2 outlines the potential for improvements in the process in reducing the exergy destroyed at the compressor level, in the PSA process and in waste stream management (see Figure 6).

_{2}demand distribution requires developing a high-fidelity microcontroller with a fast feedback time, a topic for another discussion. To make it effective and accurate, the way forward would be an efficient translation into machine learning models or even deep learning networks that might be better suited to simulate the complex PSA process. Artificial intelligence might be needed to aim beyond the prediction of such a dynamic process outcome to implement real-time adjustments of these outcomes.

## 6. Conclusions

- (1)
- Enhancing adsorbent productivity;
- (2)
- Increasing O
_{2}recovery; - (3)
- Improving unit compactness and weight.

_{2}/O

_{2}), efficient cyclic procedures, and PSA-based devices. Furthermore, optimization is even more important since these technologies have already undertaken substantial reductions in CAPEX and OPEX (i.e., capital and operating expenditures). This makes them more and more viable (per production unit) compared with cryogenic ASUs. However, further modeling and optimization are required to implement adaptable systems in specific and varying contexts, such as remote locations, energy-limited regions, and low-resource areas.

## Supplementary Materials

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**WHO-UNICEF technical specifications and guidance for oxygen therapy devices. Geneva: WHO and UNICEF, 2019 (WHO medical device technical series) [2] (CC BY-NC-SA 3.0 IGO).

**Figure 2.**Dr. Carl von Linde pioneered a cryogenic oxygen plant process in 1902. Its oxygen product purity ranges from 97.5 to 99.5% (Source: SPI).

**Figure 3.**Portable medical oxygen PSA concentrators (

**left**) and PSA oxygen concentrator plant medical oxygen generator (

**right**) (Source: SPI).

**Figure 5.**The mathematical models of the column (including mass, energy, momentum, adsorption equilibrium, and LDF equations) are set up to define the dynamic behaviors of air on the molecular sieve. The physical parameters of the adsorption bed and the initial conditions and the boundary conditions of the adsorption column need to be determined for each simulation.

**Figure 6.**Exergy Grassman diagram for a MOC operating at 390 kPa (Exergy values in % of input exergy = Exfeed).

WHO ESFT Total Oxygen Requirements Formula | ||
---|---|---|

${O}_{2TOT}=\left[0.75\left(Bed{s}_{TOT}-\left(Bed{s}_{ICU}+Bed{s}_{OT}\right)\right)+7\left(Bed{s}_{OT}\right)+30\left(Bed{s}_{ICU}\right)\right]\raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{min}$}\right.$ | ||

Example/scenario | 50-bed hospital | 200-bed hospital |

With 20% ICU beds, five operation theatres, | With 25% ICU beds, ten operation theatres, | |

Oxygen requirement calculations | =[{50 − (10 + 5)} × 0.75] + (5 × 7) + (10 × 30) | =[{200 − (50 + 10)} × 0.75] + (10 × 7) + (50 × 30) |

$\mathrm{Total}\mathrm{oxygen}\mathrm{demand};{O}_{2TOT}$ | =361.25 L/min | =1710 L/min |

List of Initial Conditions of the Adsorption Bed | |
---|---|

${y}_{i}\left(z\right)=0$, ${y}_{inert}\left(z\right)=1,$ ${q}_{i}\left(z\right)=0,{q}_{inert}\left(z\right)={q}_{eq,inert}\left(z\right),$ | |

${C}_{i}\left(z\right)=\frac{P{y}_{i}}{{R}_{g}T}$, $P\left(z\right)={P}_{feed},$ ${T}_{g}\left(z\right)={T}_{s}\left(z\right)={T}_{w}\left(z\right)={T}_{feed}$ | |

Boundary Conditions for PSA bed simulation | |

PR (inlet, z = L) | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=0}=0$ | |

${\left.{u}_{o}\right|}_{z=0}=0$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=0}=0$ | |

${\left.{u}_{o,inlet}{C}_{inlet,i}\right|}_{z=L}={u}_{o}C{C}_{p}{T}_{g}-{k}_{g}\frac{\partial {T}_{g}}{\partial z}$ | |

${\left.P\right|}_{z=L}={P}_{outlet}$ | |

${\left.{u}_{o,inlet}{C}_{inlet}{C}_{p}{T}_{inert}\right|}_{z=L}={u}_{o}{C}_{i}-{\epsilon}_{b}{D}_{ax}\frac{\partial {y}_{i}}{\partial z}$ | |

AD1, AD2 (inlet, z = 0) | |

${\left.{u}_{o,inlet}{C}_{inlet,i}\right|}_{z=0}={u}_{o}{C}_{i}-{\epsilon}_{b}{D}_{ax}\frac{\partial {y}_{i}}{\partial z}$ | |

${\left.{u}_{o,inlet}{C}_{inlet}\right|}_{z=0}={u}_{o}C-{\epsilon}_{b}{D}_{ax}\frac{\partial {y}_{i}}{\partial z}$ | |

${\left.{u}_{o,inlet}{C}_{inlet}{C}_{p}{T}_{inert}\right|}_{z=0}={u}_{o}C{C}_{p}{T}_{g}-{k}_{g}\frac{\partial {T}_{g}}{\partial z}$ | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=L}=0$ | |

${\left.P\right|}_{z=L}={P}_{outlet}$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=L}=0$ | |

ED1, ED2, ED3, CoD (outlet, z = L) | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=0}=0$ | |

${\left.{u}_{o}\right|}_{z=0}=0$ | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=L}=0$ | |

${\left.P\right|}_{z=L}={P}_{outlet}$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=0}=0$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=L}=0$ | |

BD (outlet, z = 0) | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=0}=0$ | |

${\left.{u}_{o}\right|}_{z=L}=0$ | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=L}=0$ | |

${\left.P\right|}_{z=0}={P}_{outlet}$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=0}=0$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=L}=0$ | |

ER1, ER2, ER3, PUR (inlet, z = L) | |

${\left.{u}_{o,inlet}{C}_{inlet,i}\right|}_{z=L}={u}_{o}{C}_{i}-{\epsilon}_{b}{D}_{ax}\frac{\partial {y}_{i}}{\partial z}$ | |

${\left.{u}_{o,inlet}{C}_{inlet}\right|}_{z=L}={u}_{o}C$ | |

${\left.{u}_{o,inlet}{C}_{inlet}{C}_{p}{T}_{inert}\right|}_{z=0}={u}_{o}C{C}_{p}{T}_{g}-{k}_{g}\frac{\partial {T}_{g}}{\partial z}$ | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=0}=0$ | |

${\left.{u}_{o}\right|}_{z=0}=0$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=0}=0$ | |

PUR (inlet, z = L) | |

${\left.{u}_{o,inlet}{C}_{inlet,i}\right|}_{z=L}={u}_{o}{C}_{i}-{\epsilon}_{b}{D}_{ax}\frac{\partial {y}_{i}}{\partial z}$ | |

${\left.{u}_{o,inlet}{C}_{inlet}\right|}_{z=L}={u}_{o}C$ | |

${\left.{u}_{o,inlet}{C}_{inlet}{C}_{p}{T}_{inert}\right|}_{z=0}={u}_{o}C{C}_{p}{T}_{g}-{k}_{g}\frac{\partial {T}_{g}}{\partial z}$ | |

${\left.\frac{\partial {C}_{i}}{\partial z}\right|}_{z=0}=0$ | |

${\left.P\right|}_{z=L}={P}_{outlet}$ | |

${\left.\frac{\partial {T}_{g}}{\partial z}\right|}_{z=0}=0$ |

**Table 3.**Experimental data used to benchmark the 3 models under specific operating condition compared in terms of BSF, purity, and recovery.

Model | Pa | Pd | Cycle | Cycle | Purity | Recovery | Flowrate | BSF | Ref. |
---|---|---|---|---|---|---|---|---|---|

(kPa) | (kPa) | Type | Duration (s) | (%) | (%) | (LPM) | (kg ads/TPD) | ||

(1) S-BOF | 240 | 60 | 5-step | 7 | 90 | 29.5 | 0.75 | 82.8 | [12] |

(1) S-BOF | 355 | 101 | 2-step | 1.32 | 90 | 10–55 | 5 | – | [30] |

(1) S-BOF | 300 | 100 | 4-step | 18 | 94.5 | 21.3 | 3.7 | – | [40] |

(1) S-BOF | 300 | 100 | 6-step | 16 | 94.5 | 34.1 | 4.3 | – | [40] |

(2) F-P-BM | 150 | 101 | 4-step | 100 | 93.4 | 20.1 | 0.07 | – | [17] |

(2) F-P-BM | 400 | 100 | 4-step | 3 to 9 | 90 | 15–30 | 1–3 | 45–70 | [34] |

(2) F-P-BM | 253 | 101 | 6-step | 5 | 92 | 30 | 1 | 78 | [29] |

(3) H-FASM | 195 | 43 | 6-step | 3.8 to 6.8 | 92–93 | 41–45 | – | 23.1–36.7 | [15] |

(3) H-FASM | 304 to | 101 | 4-step | 3 to 5 | 90 | 25–35 | 5 | 11.3–22.7 | [8] |

405 | |||||||||

(1) S-BOF: Simulation-based optimization framework, | |||||||||

(2) F-P-BM: First-principle-based modeling | |||||||||

(3) H-FASM: High-fidelity adsorption simulation Model. Fitting Parameters: Operating pressure: adsorption P _{a} and desorption P_{d} (kPa)Cycle duration of the PSA process t _{cycle}_{:} (s)Oxygen purity (%) Oxygen recovery (%) Production flowrate (LPM) BSF: Amount of adsorbent required in kg to generate 1 ton per day of net O _{2} product (kg ads/TPD) |

**Table 4.**Variation in the operating pressure, compressor work, and energy consumption with feed purity for MOCs at an operating temperature of 333 K.

Mole Fraction of Oxygen in Feed | Pressure | Compressor Work (Wc) | Energy Consumption per O_{2} Nm^{3} | |
---|---|---|---|---|

kPa | (kJ/mol) | (kWh) | (kJ) | |

0.21 | 390 | 41,120 | 0.509 | 1832 |

0.40 | 290 | 23,620 | 0.293 | 1055 |

0.50 | 250 | 18,430 | 0.228 | 821 |

0.60 | 220 | 14,600 | 0.181 | 652 |

0.70 | 190 | 11,640 | 0.144 | 518 |

**Table 5.**Impact of operating conditions on power consumption and lost work (exergy destruction) for MOCs.

Input Temperature (K) | N_{2} Equilibrium Constant | O_{2} Equilibrium Constant | Operating Pressure | Compressor Work (Wc) | Lost Work (Destroyed Ex) in PSA | MOC Typical Power Consumption | ||
---|---|---|---|---|---|---|---|---|

5 LPM | 10 LPM | 20 LPM | ||||||

(kPa) | (kJ/kmol) | (kJ/kmol) | (W) | (W) | (W) | |||

303 | 9.94 | 5.40 | 390 | 41,120 | 13,430 | 153 | 305 | 611 |

318 | 8.24 | 4.50 | 380 | 40,080 | 12,940 | 149 | 298 | 595 |

333 | 7.55 | 3.72 | 420 | 44,490 | 14,980 | 165 | 330 | 661 |

293 | 5.98 | 2.56 | 460 | 48,880 | 16,960 | 182 | 363 | 726 |

Variable | Notes | Example Value |
---|---|---|

(A) MOC consumption [power in W] | Usually, 100 W and 600 W for small units, contingent on the operating conditions and sizes | 600 W (Corresponding to a 20 LPM unit approximately—see exergy analysis) |

(B) The approximate duration of a typical power outage to support [average in hours per day] | Varies from facility to facility | 3 h |

(C) Additional compensation for losses [% relating to a reasonable reserve according to the context] | Consider that electric energy storage (such as Li batteries) will lose capacity and necessitate replacement over time | 10% |

(D) Battery depth-of-discharge | 10–70% depending on the battery type | 40% |

Sample calculations | ||

(E) Total concentrator backup energy requirement per day | A × B × (1 + C) | 600 W × 3 h × (1 + 0.10) = 1980 Wh = 1.98 kWh |

Total backup (electrical battery) energy storage requirements | E × (1/D) | 1980 Wh × (1/0.4) = 3960 Wh = 4.95 kWh |

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## Share and Cite

**MDPI and ACS Style**

Carty, M.L.; Bilodeau, S.
Benchmarking Thermodynamic Models for Optimization of PSA Oxygen Generators. *J* **2023**, *6*, 318-341.
https://doi.org/10.3390/j6020023

**AMA Style**

Carty ML, Bilodeau S.
Benchmarking Thermodynamic Models for Optimization of PSA Oxygen Generators. *J*. 2023; 6(2):318-341.
https://doi.org/10.3390/j6020023

**Chicago/Turabian Style**

Carty, Michael L., and Stephane Bilodeau.
2023. "Benchmarking Thermodynamic Models for Optimization of PSA Oxygen Generators" *J* 6, no. 2: 318-341.
https://doi.org/10.3390/j6020023