# Review of the Pressure Swing Adsorption Process for the Production of Biofuels and Medical Oxygen: Separation and Purification Technology

Authors: Jesse Y. Rumbo Morales; Gerardo Ortiz-Torres; Rodolfo Omar Domínguez García; Carlos Alberto Torres Cantero; Manuela Calixto Rodriguez; Estela Sarmiento-Bustos; Edén Oceguera-Contreras; Alberto Arturo Flores Hernández; Julio César Rodríguez Cerda; Yehoshua Aguilar Molina; Mario Martínez García
Journal: Adsorption Science & Technology
 (2022)

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## Abstract

The production of biofuels has had a great impact on climate change and the reduction of the use of fossil fuels. There are different technologies used for the separation and production of biofuels, which allow having compounds such as ethanol, methane, oxygen, and hydrogen, one of these promising technologies is the Pressure Swing Adsorption process (PSA). The objectives of this article focus on the production and purification of compounds that achieve purities of 99.5% bioethanol, 94.85% biohydrogen, 95.00% medical oxygen, and 99.99% biomethane through the PSA process; also, a significant review is contemplated to identify the different natural and synthetic adsorbents that have greater adsorption capacity, the different configurations in which a PSA operates are studied and identified, and the different mathematical models that describe the dynamic behavior of all the variables are established that interact in this PSA process, parametric studies are carried out in order to identify the variables that have the greatest effect on the purity obtained. The results obtained in this review allow facilitating the calculation of parameters, the optimization of the process, the automatic control to manipulate certain variables and to achieve the rejection of disturbances to have a recovery and production of biofuels with a high degree of purity.


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## Body

## 1. Introduction

Currently, PSA processes are displacing other distillation technologies that aim to separate chemical compounds from a mixture at the nanomolecular level, these present a significant contribution in obtaining compounds such as oxygen (O2), nitrogen (N2), hydrogen (H2), carbon dioxide (CO2), ethanol (C2 H5 OH), and methane (CH4). The PSA process contemplates at least 2 columns refilled with adsorbents (natural or synthetic), to be able to carry out the adsorption stage (production) and the regeneration stage (release of the active sites of the adsorbent) synchronously. These 2 stages are carried out through steps, which can be adsorption, depressurization, purge, equalization, and repressurization. The PSA process has a cyclical nature, therefore the pressure, temperature, and molar composition profiles will have an oscillatory dynamic generated by the pressure changes inside the columns. Pressure changes can go from a high pressure (200 kPa 4000 kPa) and down to a vacuum pressure between the ranges of 100 kPa and 10 kPa. The approach of these pressure ranges is derived from experimental tests that show that at high pressure, a greater number of molecules or atoms are adsorbed, being retained on the surfaces of the adsorbents (selectivity over the adsorbed molecules or atoms), and at low pressure that can easily break the weak bond that has formed between the adsorbent and the adsorbed molecules or atoms, resulting in a release of the active sites of the adsorbent. These adsorbents can be zeolites, silica gel, activated carbon, clays, porous glass, montmorillonite, halloysite, silicon dioxide, mesoporous silica, etc. These materials contain nanomolecular pores ranging from 1 to 24 Armstrong (Å); the more contact surface they have, the greater adsorption capacity they will present. Metal-Organic Frameworks (MOFs) have emerged as novel fabulous materials for applications in numerous fields, doing to their exceptional physicochemical characteristics such as high surface area, large porosity with tunable pore properties, presence of abundant active sites, and ease of functionalization [1, 2].For the PSA process to work synchronously and autonomously, it is necessary to contemplate valves (on-off and proportional) that connect all the columns to achieve the operational cyclical functioning of the process, obtaining separations of chemical compounds with a high degree of purity. Likewise, it is necessary to implement pressure, temperature, flow, and purity sensors along with the columns to acquire as much information or data as possible about these important variables that influence the PSA process.PSA processes have been involved in several alternatives; one of them is the production of biofuel from renewable raw materials and biomass. Another use of this process is the purification of oxygen, separating it from the gases that pollute the environment (CO and CO2), which are generated by automobiles and industries. For these reasons, the PSA process is considered a solution to climate change. Currently, with what is being experienced on COVID-19, the design and development of oxygen purifiers-generators are necessary due to the demand that is currently being met and the use of this PSA process is necessary to be used as a separator and gas purifier, and to produce 99% oxygen or according to the user’s need.One of the works found related to the PSA process is the one presented in [3], which reviewed the principles of the PSA process for the capture of carbon dioxide. Wiheeb et al. presented previous works on modeling and comparisons with experimental development of the PSA process. Mention is made of the importance of the steps that contemplate the adsorption and regeneration stages, as well as maintaining stable high temperatures since it favors the regeneration of the adsorbent.Later in [4], advanced technologies related to hot gas carbon capture and hydrogen production from carbon-based fuels using the PSA process are reviewed. Zhu et al. presented important advances in the development of adsorption kinetic models, the study of adsorption mechanisms, synthesis of efficient CO2 adsorbents, design, and optimization of adsorption/desorption reactor processes, and integration of purification systems, as well as main challenges and perspectives for the fundamental and pilot study. The development of the system at scale is discussed. Recent advances in the development of high temperature CO/CO2 purification technologies for hydrogen-rich gas were summarized.Likewise in [5], Abd et al. described the fundamentals of the PSA process by investigating the main innovative process engineering approaches that improved the performance of the PSA process. Previous research on PSA, simulation, and experimental development for biogas upgrading (biomethane purification) exists and highlights significant findings. In addition, their work analyzes the impact of some parameters on the performance of the PSA process, such as bed porosity, adsorption pressure and time, PSA unit size, and purge/feed ratio.In [6], Luberti et al. performed a systematic review of the Polybed H2 PSA process, which includes more than six beds and a complex cycle configuration, showing that it can maximize H2 recovery and yield, exceeding 90%. A bespoke Polybed PSA process designed for the simultaneous production of high purity hydrogen and carbon dioxide (CO2) was also reviewed in light of recent international directives aimed at reducing CO2 emissions and producing blue hydrogen.Likewise in [7], the progress made in the implementation of mathematical models, simulation, and optimization methods for the improvement of biogas with emphasis on processes based on adsorption are presented. In their work, Hosseini et al. described strategies and methodologies for the development of mathematical models and process simulations based on transport mechanisms, considering the PSA, VPSA (Vacuum Pressure Swing Adsorption), TSA (Temperature Swing Adsorption) process, and fixed adsorption beds for trace removal. Based on studies to date, these processes have offered methane purity and recovery within an adjustable range of 50 to 99% and 75 to 99.4%, respectively.Later in [8], Zhang et al. carried out a review of the literature on the analytical part of the PSA process, focused on the numerical development to carry out the modeling, optimization, and control of the PSA process. It was determined that the combination of deep learning technology with optimization algorithms based on artificial intelligence and advanced control strategies is of great importance.This work has several contributions, one of them focuses on providing relevant data on adsorbents for the separation and purification of bioethanol, biohydrogen, medical oxygen, and biomethane; another of the contributions is to present the current reports of parameters to configure and model a PSA process, depending on the compound to be purified. Another important contribution is the parametric study that demonstrates the possible input variables that can affect the purity obtained as a final product, which can also be defined as manipulated variables that can control the desired purity in the face of disturbances, with the aim of being able to keep the purity stable and meet international standards for the use as fuel or medical oxygen. The parametric study will allow defining optimal parameters that favor the start-up of the PSA process to have greater production and recovery. Likewise, obtaining input and output data is very useful for designing neural network structures with the aim of predicting the dynamic behavior of the PSA process.Table1 shows the nomenclature that will be used for this work, which has a great contribution to PSA processes for the production of biofuels and medical oxygen.Table 1
Nomenclature.
Parameter
Description
Units
a
Specific particle surface
m2m-3
aHi
Specific heat exchanger surface
m2m-3
ap
Specific particle surface per unit volume bed
m2m-3
A
Area
AA
Placeholder variable used for Dubinin-Astakhov isotherm evaluation
b
Kinetic Langmuir factor
bar-1
cbi
Bulk gas phase concentration
kmolm-3
ci
Molar concentration of component i
kmolm-3
cmsi
Macropore gas phase concentration
kmolm-3
csol
Concentration of solid phase reactant
kmolkg-1
cpai
Specific heat capacity of adsorbed phase
MJkmol-1K-1
cpcat
Specific heat capacity of catalyst
MJkg-1K-1
cpg
Specific gas phase heat capacity at constant pressure
MJkmol-1K-1
cps
Specific heat capacity of adsorbent
MJkg-1K-1
cpW
Specific heat capacity of column wall
MJkg-1K-1
cvg
Specific gas phase heat capacity at constant volume
MJkmol-1K-1
DB
Bed diameter
m
Defc
Effective micropore diffusion coefficient
m2s-1
Defp
Effective macropore diffusion coefficient
m2s-1
Dek
Effective adsorbed phase diffusivity of componenti
m2s-1
Dki
Knudsen diffusion coefficient of componenti
m2s-1
Dmi
Mean molecular diffusion coefficient of componenti
MJkmol-1
Eact
Activation energy for Arrhenius relationship
MJkmol-1
Eii
Radial dispersion coefficient of componenti
m2s-1
Ezi
Axial dispersion coefficient of componenti
m2s-1
Hamb
Wall-ambient heat transfer coefficient
MWm2K-1
HB
Height of adsorbent layer
m
Hi
Rate of change of heat of adsorbed phase
MJm-3s-1
HR
Combined heats of homogenous and heterogeneous reactions
MJm-3s-1
HRcat
Heat of catalytic reaction
MJkmol-1
HRgas
Gas phase heat of reaction
MJkmol-1
HTi
Heat of adsorption contribution to solid phase energy balance
MJm-3s-1
HW
Gas-wall heat transfer coefficient
MJm-3s-1
ΔHi
Heat of adsorption of componenti
MJkmol-1
HTC
Gas-solid heat transfer coefficient
MJm-3s-1
IP
Isotherm parameter, units depend on isotherm
j
Colburn j-factor for heat or mass transfer
Jads,i
Mass transfer rate of componenti owing to adsorption
kmolm-3s-1
Jcat,reac,i
Mass transfer rate of componenti owing to heterogeneous catalytic reactions
kmolm-3s-1
Jgas, reac ,i
Mass transfer rate of componenti owing to homogenous, gas phase reactions
kmolm-3s-1
Ji
Mass transfer rate of componenti to/from adsorbent
kmolm-3s-1
k0,i
Pre-exponential factor for Arrhenius relationship
ms-1
k0P,i
Pre-exponential factor for pressure dependent Arrhenius relationship
ms-1
kfi
Film mass transfer coefficient of componenti
ms-1
kfi
Gas phase thermal conductivity
MWm-1K-1
kgr
Effective radial gas phase thermal conductivity
MWm-1K-1
ki
Effective, lumped mass transfer coefficient of componenti
s-1
ks
Solid thermal conductivity
MWm-1K-1
kgs
Effective axial gas phase thermal conductivity
MWm-1K-1
ksr
Effective radial solid phase thermal conductivity
MWm-1K-1
ksg
Effective axial solid phase thermal conductivity
MWm-1K-1
kW
Thermal conductivity of column wall
MWm-1K-1
Kmac
Macropore mass transfer coefficient
s-1
Kmic
Micropore mass transfer coefficient
s-1
Kp
Darcy’s constant
barsm-2
Kpi
Macropore diffusion coefficient
m2s-1
L
Length of horizontal bed
m
M
Molecular weight
kgkmol-1
MTCg
Gas film mass transfer coefficient
s-1
MTCs
Solid film mass transfer coefficient
s-1
P
Pressure
bar
Psat
Saturation pressure
bar
QHi
Heat transfer rate to internal heat exchanger
MJm-2s-1
r
Radial coordinate (in packed bed or particle)
m
rc
Microparticle (crystal) radius
m
rp
Particle radius
m
R
Universal gas constant
barm-3kmol-1K-1
Rcat
Catalytic reaction rate
kmolkg-1s-1
Rgas
Gas phase reaction rate
kmolm-3s-1
Rsol
Solid phase reaction rate
kmolkg-1s-1
t
Time
s
tcycle
Adsorption cycle time
s
T
Temperature
K
T0
Initial temperature
K
Tamb
Ambient temperature
K
Tc
Critical temperature
K
Ts
Solid phase temperature
K
Tg
Gas phase temperature
K
THi
Heat exchange medium temperature
K
TW
Wall temperature
K
Tort
Adsorbent tortuosity
vg
Gas phase superficial velocity
ms-1
Wi
Loading
kmolkg-1
Wi0
Pure component loading of componenti
kmolkg-1
yi
Mole fraction of componenti in the gas phase
kmolkg-1
z
Axial coordinate
m
Greek symbols
ϵ
i
Bed (interparticle) voidage
m3 m-3
ϵ
p
Intraparticle voidage
m3 m-3
μ
Dynamic viscosity
N s m-2
Ω
Parameter in Glueckauf expression
ψ
Particle shape factor
ρ
b
Bed packing density
kg m-3
ρ
g
Gas phase molar density
kmol km-3
ρ
p
Particle density
kmol km-3
ρ
s
Adsorbent bulk density
kg m-3
Subscripts
b
Bulk or packed bed
F
Feed stream
g, s
Gas and solid phase
i
Component water (w) or ethanol (e)
p
ParticleThis work is presented as follows. In Section2, the complete model of a PSA process is shown, which includes equations of pressure, temperature, flow, and mole fraction in function of time and space (axial and radial part). In Sections 3–6, the results of the works found on the purification and production of bioethanol, biohydrogen, medical oxygen, and biomethane are shown, and the different works that use the PSA process are visualized in comparative tables taking into account the sizing, the number of columns, the type of adsorbent, the pressure and temperature ranges, the feed composition, and the number of PDEs that are considered to obtain approximate solutions to the PSA process. Likewise, simulations and a demonstrative table (parametric study) are presented that allow defining the possible input variables that can affect the purity of bioethanol, biohydrogen, medical oxygen, and biomethane obtained as a final product.


## 2. Schematic and Modeling of the PSA Process

Gas-phase adsorption is currently being used to purify and separate chemical compounds, natural gas, and petrochemicals since they present better-operating conditions and reduce energy and equipment costs.The adsorbent must have selectivity over the molecule or atom to be retained on its surface, allowing the separation and purification of the other compounds that passes through it. Adsorbents must withstand high temperatures and work under different pressure conditions (high and low).For PSA processes, there may be variations in your mathematical model, this will depend on the need for the data that is required to be obtained, that is, the following assumptions can be considered:(1)
They can work in isothermal or nonisothermal conditions(2)
Heat exchange with environment(3)
Gas-solid heat transfer(4)
Enthalpy of mixing is negligible(5)
Include wall energy data(6)
Heat of adsorption(7)
Thermal conductivity of gas and thermal conductivity of solid(8)
Compression(9)
The system is fully mixed in the radial direction(10)
Plug flow with axial dispersion occurs(11)
The gas phase is ideal or nonideal(12)
The driving force is based on a gas or solid film, and is either linear or quadratic(13)
Gas phase pressure is either constant or the pressure varies according to a laminar or turbulent flow momentum balance(14)
Mass transfer coefficients are either constant or vary with local conditions(15)
Mass transfer is described using a lumped overall resistance, or by a model that accounts separately for micro- and macropore effects(16)
Adsorption isotherms are either applicable for single or multicomponent adsorptionThe cyclical nature of the PSA process and its operating conditions determine the type of model to use. For example, a separation process for producing pure oxygen from air requires a different model to that for a purification process for the production and separation of dehydrated ethanol. PSA process models use a set of partial differential equations to represent moment balance, energy balance, and material balances across the column.From all this analysis, a general mathematical model of the PSA process is established, this involves most of the equations necessary to determine the important dynamics that characterize the PSA process, this detailed general model is shown in the following:


### 2.1. Mass Balance

(1)
−
ϵ
i
E
zi
∂
2
c
i
∂
z
2
−
ϵ
i
E
ri
1
r
∂
∂
r
r
∂
c
i
∂
r
+
∂
c
i
v
g
∂
z
+
ϵ
i
∂
c
i
∂
t
+
J
i
=
0
.Flow over the solid surface(2)J=−ρ∂Wi∂t.The convection∂CiVg/∂z with estimated dispersion −ϵiEzi∂2ci/∂z2 option assumes that the dispersion coefficient varies along the length of the bed.


### 2.2. Solid Phase Energy Balance

(3)
−
k
sa
∂
2
T
s
∂
2
z
2
−
k
sr
1
r
∂
∂
r
1
r
∂
T
s
∂
r
+
C
ps
ρ
s
+
ρ
s
∂
T
s
∂
t
∑
i
=
1
n
C
pai
W
i
∂
T
s
∂
t
+
ρ
s
∑
i
n
Δ
H
i
∂
W
i
∂
t
−
MT
C
ap
T
g
−
T
s
=
0
.The energy balance (solid phase) represents the heat of adsorptionρs∑inΔHi∂Wi/∂t, accumulation of heat Cpsρs+ρs∂Ts/∂t, and gas-solid heat transfer MTCapTg−Ts.


### 2.3. Wall Energy Balance

(4)
−
k
w
∂
2
T
w
∂
z
2
+
ρ
w
c
p
w
∂
T
w
∂
t
−
H
w
4
D
B
D
B
+
w
r
2
−
D
B
2
T
g
−
T
w
+
H
amb
4
D
B
+
w
r
2
D
B
+
w
r
2
−
D
B
2
T
w
−
T
amb
=
0
.


### 2.4. Momentum Balance

(5)
−
∂
P
∂
z
=
−
150
x
1
0
−
3
1
−
ϵ
i
2
2
r
p
Ψ
2
ϵ
i
2
μ
v
g
+
1.75
×
1
0
−
5
M
ρ
g
1
−
ϵ
i
2
r
p
Ψ
ϵ
i
3
v
g
2
.We use the Ergun equation, which combines the description of pressure drops by the Karman-Kozeny equation−∂P/∂z=−150x10−31−ϵi2/2rpΨ2ϵi2μvg for laminar flow and the Burke-Plummer equation 1.75x10−5Mρg1−ϵi/2rpΨϵi3vg2 for turbulent flow.


### 2.5. Kinetic Models

(i)
Lumped resistance(6)∂Wi∂t=MTCsiWi∗−Wi
(ii)
Micro- and macropore effects(7)1−εpρs∂Wi∂t=1−εpρsKmicWi∗−Wi,(8)1−εiεp∂cmsi∂t+1−εpρs∂Wi∂t=1−εpρsKmacWi∗−Wi.
(iii)
Particle material balance(9)∂Wi∂t−Dei2r∂Wi∂r+∂Wi2∂r2=0.(a)
Mass transfer coefficients: Arrhenius(10)MTCsi=k0iexp−EactiRT.(b)
Mass Transfer Coefficients: Lumped Resistance, Micro-, and Macropore(11)MTCsi=ΩDeirp2.Ω is the parameter in the Glueckauf expression
(12)MTCmic=15Dmicrm2,(13)MTCmac=15Dmacrp2.(c)
Mass Transfer Coefficients: Pressure Dependent Arrhenius(14)MTCsi=k0piPexp−EactiRT.


### 2.6. Lumped Resistance

#### 2.6.1. Thermodynamic Equilibrium: Langmuir as a Function of Pressure and Concentration

(15)
W
i
∗
=
I
p
1
P
i
1
+
I
p
2
P
i
,
(16)
W
i
∗
=
I
p
1
c
i
1
+
I
p
2
c
i
.To solve these PDEs, it is necessary to contemplate initial and boundary conditions, which will allow connecting the adsorption, depressurization, purge, equalization, and repressurization steps, that is, the results obtained in the adsorption step will become the initial and boundary conditions of the depressurization step and this methodology will be repeated for the successive steps. For the last step (repressurization) the results obtained will become the initial and boundary conditions of the first step (adsorption) to contemplate a 1 cycle of production and regeneration of the bed. This continues cyclically until the Cyclic Steady State (CSS) is reached, which is when the pressure, temperature, and mole fraction profiles have oscillatory cyclic dynamics, resulting in stable behavior at a setpoint.It is important to mention that the initial and boundary conditions will depend on the number of variables involved in the PDEs.There are several numerical methods (orthogonal placement, finite element, finite difference, etc.) to discretize the PDEs, which will allow the bed to be sectioned or partitioned into meshes, nodes, points, or areas; this will depend on the numerical method used. Likewise, it is necessary to define the number to be sectioned or partitioned, since the approximation obtained on the real results presented by a PSA plant will depend on that. The software used to simulate these PSA cases is Aspen Adsorption [9].Figure1 shows the general scheme of a PSA process contemplating pressure, temperature, flow, purity sensors, valves, metallic structure, and the PSA cycle.Figure 1
Schematic diagram of the PSA process.


## 2.1. Mass Balance

(1)
−
ϵ
i
E
zi
∂
2
c
i
∂
z
2
−
ϵ
i
E
ri
1
r
∂
∂
r
r
∂
c
i
∂
r
+
∂
c
i
v
g
∂
z
+
ϵ
i
∂
c
i
∂
t
+
J
i
=
0
.Flow over the solid surface(2)J=−ρ∂Wi∂t.The convection∂CiVg/∂z with estimated dispersion −ϵiEzi∂2ci/∂z2 option assumes that the dispersion coefficient varies along the length of the bed.


## 2.2. Solid Phase Energy Balance

(3)
−
k
sa
∂
2
T
s
∂
2
z
2
−
k
sr
1
r
∂
∂
r
1
r
∂
T
s
∂
r
+
C
ps
ρ
s
+
ρ
s
∂
T
s
∂
t
∑
i
=
1
n
C
pai
W
i
∂
T
s
∂
t
+
ρ
s
∑
i
n
Δ
H
i
∂
W
i
∂
t
−
MT
C
ap
T
g
−
T
s
=
0
.The energy balance (solid phase) represents the heat of adsorptionρs∑inΔHi∂Wi/∂t, accumulation of heat Cpsρs+ρs∂Ts/∂t, and gas-solid heat transfer MTCapTg−Ts.


## 2.3. Wall Energy Balance

(4)
−
k
w
∂
2
T
w
∂
z
2
+
ρ
w
c
p
w
∂
T
w
∂
t
−
H
w
4
D
B
D
B
+
w
r
2
−
D
B
2
T
g
−
T
w
+
H
amb
4
D
B
+
w
r
2
D
B
+
w
r
2
−
D
B
2
T
w
−
T
amb
=
0
.


## 2.4. Momentum Balance

(5)
−
∂
P
∂
z
=
−
150
x
1
0
−
3
1
−
ϵ
i
2
2
r
p
Ψ
2
ϵ
i
2
μ
v
g
+
1.75
×
1
0
−
5
M
ρ
g
1
−
ϵ
i
2
r
p
Ψ
ϵ
i
3
v
g
2
.We use the Ergun equation, which combines the description of pressure drops by the Karman-Kozeny equation−∂P/∂z=−150x10−31−ϵi2/2rpΨ2ϵi2μvg for laminar flow and the Burke-Plummer equation 1.75x10−5Mρg1−ϵi/2rpΨϵi3vg2 for turbulent flow.


## 2.5. Kinetic Models

(i)
Lumped resistance(6)∂Wi∂t=MTCsiWi∗−Wi
(ii)
Micro- and macropore effects(7)1−εpρs∂Wi∂t=1−εpρsKmicWi∗−Wi,(8)1−εiεp∂cmsi∂t+1−εpρs∂Wi∂t=1−εpρsKmacWi∗−Wi.
(iii)
Particle material balance(9)∂Wi∂t−Dei2r∂Wi∂r+∂Wi2∂r2=0.(a)
Mass transfer coefficients: Arrhenius(10)MTCsi=k0iexp−EactiRT.(b)
Mass Transfer Coefficients: Lumped Resistance, Micro-, and Macropore(11)MTCsi=ΩDeirp2.Ω is the parameter in the Glueckauf expression
(12)MTCmic=15Dmicrm2,(13)MTCmac=15Dmacrp2.(c)
Mass Transfer Coefficients: Pressure Dependent Arrhenius(14)MTCsi=k0piPexp−EactiRT.


## 2.6. Lumped Resistance

### 2.6.1. Thermodynamic Equilibrium: Langmuir as a Function of Pressure and Concentration

(15)
W
i
∗
=
I
p
1
P
i
1
+
I
p
2
P
i
,
(16)
W
i
∗
=
I
p
1
c
i
1
+
I
p
2
c
i
.To solve these PDEs, it is necessary to contemplate initial and boundary conditions, which will allow connecting the adsorption, depressurization, purge, equalization, and repressurization steps, that is, the results obtained in the adsorption step will become the initial and boundary conditions of the depressurization step and this methodology will be repeated for the successive steps. For the last step (repressurization) the results obtained will become the initial and boundary conditions of the first step (adsorption) to contemplate a 1 cycle of production and regeneration of the bed. This continues cyclically until the Cyclic Steady State (CSS) is reached, which is when the pressure, temperature, and mole fraction profiles have oscillatory cyclic dynamics, resulting in stable behavior at a setpoint.It is important to mention that the initial and boundary conditions will depend on the number of variables involved in the PDEs.There are several numerical methods (orthogonal placement, finite element, finite difference, etc.) to discretize the PDEs, which will allow the bed to be sectioned or partitioned into meshes, nodes, points, or areas; this will depend on the numerical method used. Likewise, it is necessary to define the number to be sectioned or partitioned, since the approximation obtained on the real results presented by a PSA plant will depend on that. The software used to simulate these PSA cases is Aspen Adsorption [9].Figure1 shows the general scheme of a PSA process contemplating pressure, temperature, flow, purity sensors, valves, metallic structure, and the PSA cycle.Figure 1
Schematic diagram of the PSA process.


## 2.6.1. Thermodynamic Equilibrium: Langmuir as a Function of Pressure and Concentration

(15)
W
i
∗
=
I
p
1
P
i
1
+
I
p
2
P
i
,
(16)
W
i
∗
=
I
p
1
c
i
1
+
I
p
2
c
i
.To solve these PDEs, it is necessary to contemplate initial and boundary conditions, which will allow connecting the adsorption, depressurization, purge, equalization, and repressurization steps, that is, the results obtained in the adsorption step will become the initial and boundary conditions of the depressurization step and this methodology will be repeated for the successive steps. For the last step (repressurization) the results obtained will become the initial and boundary conditions of the first step (adsorption) to contemplate a 1 cycle of production and regeneration of the bed. This continues cyclically until the Cyclic Steady State (CSS) is reached, which is when the pressure, temperature, and mole fraction profiles have oscillatory cyclic dynamics, resulting in stable behavior at a setpoint.It is important to mention that the initial and boundary conditions will depend on the number of variables involved in the PDEs.There are several numerical methods (orthogonal placement, finite element, finite difference, etc.) to discretize the PDEs, which will allow the bed to be sectioned or partitioned into meshes, nodes, points, or areas; this will depend on the numerical method used. Likewise, it is necessary to define the number to be sectioned or partitioned, since the approximation obtained on the real results presented by a PSA plant will depend on that. The software used to simulate these PSA cases is Aspen Adsorption [9].Figure1 shows the general scheme of a PSA process contemplating pressure, temperature, flow, purity sensors, valves, metallic structure, and the PSA cycle.Figure 1
Schematic diagram of the PSA process.


## 3. Bioethanol Purification by PSA

Bioethanol comes from renewable biological raw material; it is not corrosive or toxic. This product can be used in the pharmaceutical industry, alcoholic beverages, cooking, perfumery, cosmetics, solvents, and mainly as an oxygenating additive (they increase the octane number) or be used as a fuel and reduce the risk of climate change, which is caused by fuels developed from fossils. However, for bioethanol to be used as fuel, it is necessary that its water content be very low and obtains a purity of 99% by weight of ethanol, to avoid the formation of two liquid phases in the mixture and be able to meet standards set by international norms.One of the important aspects of the study of the PSA process is the selection of the adsorbent or molecular sieves that will allow the separation and purification of an ethanol-water mixture.


### 3.1. Adsorption and Separation for the Ethanol-Water Mixture with Different Adsorbents

The study of the adsorption phenomenon with molecular sieves makes it possible to determine models capable of predicting the thermodynamic equilibrium of different adsorbents used for the ethanol-water mixture. The thermodynamic equilibrium of each adsorbent is represented by an adsorption isotherm at a constant temperature, which determines the maximum adsorption capacity. The adsorption isotherm is obtained from experimental data. These represent the amount of material (water in this case) adsorbed on the surface of the adsorbent, as a function of the composition of the material (water) present in the gas phase, the latter is expressed as a molar fraction or partial pressure. There are 5 types of adsorption isotherms as shown in Figure2, they can be monomolecular isotherms (monolayers) or polymolecular isotherms (multilayers). The most common isotherms are types I, II, and III. To describe the adsorption isotherms that are obtained experimentally and can be represented in different mathematical models, each model contemplates a series of considerations.Figure 2
Adsorption isotherms.For the ethanol-water mixture a type I adsorption isotherm is obtained, which is represented by the Langmuir model. This model proposes a constant temperature, localized adsorption only active sites, a homogeneous surface, and the adsorption occurs in a monolayer, assuming that each adsorption site can adhere to only one adsorbate molecule, the adsorption energy is the same for all adsorption sites and there is no interaction between the adsorbed molecules [10–13]. The thermodynamic equilibrium provides a measure of adsorption efficiency during the removal of specific impurities (water molecules), as well as the maximum adsorption capacity. On the other hand, the kinetic equilibrium data are represented using breakdown curves, in these, the composition of the adsorbed phase is related to the adsorption time to reach the maximum capacity. The increase in temperature favors the adsorbent to retain the molecules or atoms and reach its maximum saturation point in less time, but it does not favor thermodynamic equilibrium since the maximum adsorption capacitance is reduced. The rate of adsorption is proportional to the rate of diffusion in the pores.Among the adsorbents that have been used to separate the ethanol-water mixture, natural zeolites are good candidates and have an advantage over some types of membranes or natural adsorbents because they remain stable in harsh chemical environments and high temperatures [14–18]. Dehydration of ethanol through adsorption with natural zeolites is acceptable and effective in adsorbing large amount of water, but the use of synthetic zeolites has recently been suggested as a promising alternative. One of the most accepted and studied with good results is the synthetic zeolite 3A. The review of several studies allowed us to make a concentrate on works, in which different adsorbents are applied, useful to separate the ethanol-water mixture. The information is contained in Table 2, which describes the characteristics of thermodynamic equilibrium and the time it reaches its maximum saturation point at different time, these determine the maximum capacity and time with which they adsorb. The results were obtained as a function of temperature since the adsorption capacity depends significantly on this variable. Table 2 shows the different adsorbents used for the separation of the ethanol-water mixture, as well as the constants Q and K, referred to as the maximum adsorption capacity and the Langmuir constant.Table 2
Comparison of the thermodynamic values of various adsorbents as a function of temperature.
Reference
Adsorbents
TemperatureK
Maximum adsorption capacityQ gwatergads‐1
Langmuir constant
Adsorption time
[19]
Cornmeal
333.15
0.029
—
—
364.15
0.025
—
300 min
[20]
ZSG-1
303.15
0.1046
—
—
ZSG-1
352.15
0.1241
—
—
ZSG-1
357.15
0.1499
—
—
ZSG-1
362.15
0.1511
—
—
ZSG-1
370.15
0.1529
—
80 min
[21]
Silicalite
298
0.116
—
9 min
[10]
Clinoptilolite
373
0.198
—
—
[11]
Zeolite 3A
348
0.18
25
—
3A
373
0.171
8
—
3A
398
0.162
2.9
—
3A
423
0.135
1.19
—
3A
448
0.108
0.54
—
[12]
LTA-K
298
0.130
0.735
—
LTA-Na
298
0.150
0.563
—
LTA-ca
298
0.094
0.589
—
FAU-Na
298
0.166
0.611
—
MOR-Na
298
0.045
0.403
—
[14]
Zeolite 3A
323.15
0.1915
0.00791
200 min
3A
343.158
0.180
0.00655
180 min
Heulandite-Sonora
323.15
0.1
0.00925
185 min
Heulandite-Sonora
343.158
0.097
0.00345
150 min
Clinoptilolite-Potosí
323.15
0.097
0.00491
180 min
Clinoptilolite-Potosí
343.158
0.094
0.00253
145 min
[13]
Clinoptilolite
293.15
0.161
—
24 h
[22]
Clinoptilolite
283
0.13428
0.0179
—
Clinoptilolite
298
0.12618
0.0156
—
Clinoptilolite
313
0.12402
0.0125
24 h
Clinoptilolite
328
0.11916
0.0113
—
Clinoptilolite
343
0.11304
0.0106
—
[23]
Sylobead 3A
373.15
0.198
—
—
[24]
Zeolite 3A
393.15
0.085
0.1006
135 min
3A
413.15
0.065
0.0828
75 min
[25]
Zeolita NaA
378
0.155
—
[15]
Philipsita
326.3
0.0432
0.76
57 min
Philipsita 0.5 M
326.3
0.0800
0.81
34 min
Philipsita 0.75 M
326.3
0.0770
0.83
35 min
Philipsita 1 M
326.3
0.1054
1.2
55 min
Philipsita 2 M (natural)
326.3
0.1016
0.93
41 min
[16]
ACF
298.15
0.1571
0.58
600 s
ACF
308.15
0.1567
0.30
—
ACF
318.15
0.1576
0.15
1800 s
ACF-850
298.15
0.2266
0.22
680 s
ACF-850
308.15
0.2244
0.12
—
ACF-850
318.15
0.2264
0.06
700 s
ACF-750
298.15
0.1488
0.59
200 s
ACF-750
308.15
0.1477
0.29
—
ACF-750
318.15
0.1456
0.16
450 s
[17]
ZIF-8
298.15
0.45661
5.30
5 min
ZIF-67
298.15
0.4633
5.35
5 min
[26]
Zeolita 4A
336.15
0.1030
—
57 min
3A
298.15
0.249
0.317
40 min
3A
313.15
0.238
0.153
30 min
3A
323.15
0.220
0.090
22 min
3A Sintética)
333.15
0.200
0.052
20 min
[18]
Clinoptilolite (1-2 mm)
298.15
0.405
2019.56
540 s
Clinoptilolite (3 mm)
298.15
0.31
1386.20
720 s
Clinoptilolite (5 mm)
298.15
0.29
3521.28
180 s
LV-NENG
298.15
0.275
1353.44
720 s
Sorbead
298.15
0.26
1053.11
540 sTable2 shows that natural zeolites have disadvantages over synthetic zeolites, specifically compared to 3A zeolites and ZIF, since the latter adsorb a greater amount of water. However, clinoptilolite presents large contributions with a maximum adsorption capacity, between 0.27 and 0.3 gwatergads−1.


### 3.2. Mathematical Models, Characteristics, and Configuration of the PSA Process for the Production of Bioethanol

There are some studies on PSA processes with columns packed with zeolite, specifically designed to dehydrate ethanol [27–29], in which advantages and disadvantages of different operational methods are compared such as the use of two beds, three beds, and multibeds (see Table 3).Table 3
Works reported on the different configurations of PSA processes for purification of bioethanol.
Reference
Experimental /simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Ethanol feed (% wt)
[32]
Simulated
2 beds
200 to 13
5.3
90
4 steps
[33]
Experimental
2 beds
(200-240) to 20
7
95
4 steps
[34]
Experimental
2 beds
379.79 to 13.8
5.4
92
5 steps
[35]
Experimental
2 beds
120 to 20
3.8
93.2
4 steps
[36]
Experimental
3 beds
(120, 130) to 20
6.6
87
4 steps
[37]
Experimental
2 beds
303 to 30
45
88.57
4 steps
[14]
Simulated
2 beds
204.5 to 13.4
2.91
90
4 steps
[30]
Simulated
2 beds
340 to 30
—
86
2 stepsIt is important to take into account the additional energy required to circulate the mixture, as well as the electricity required to operate the adsorption and desorption beds and the air and vacuum compressor [30, 31]. Table 3 shows the cycle times considered in different articles, regeneration takes between 3 and 45 min.In the study of Jeong et al. [36], the two-bed process and the multibed process produced 99.5% anhydrous ethanol by weight, with a feed of 87.0% by weight ethanol. However, the multibed process presented lower energy consumption (higher energy efficiency). On the other hand, the two-bed process has the advantage of producing anhydrous ethanol from the input ethanol concentration as low as 81.3% in weight. And lastly, the three-bed process required the longest regeneration time (twice the amount of time) for zeolite, but a very stable process with higher performance was achieved due to less time lost in the change of cycle, so it was concluded that this is the most suitable for a large-scale commercial application. The process flow diagram is shown in Figure 3.Figure 3
Schematic diagram of the PSA process using different types of connection configurations: (a) two beds, (b) multiple tubes, (c) two-pass beds, and (d) three beds.
(a)
(b)
(c)
(d)The PSA process is more used than the TSA due to its efficiency and low energy cost, for this reason, there is interest in presenting proposals to improve the operation of PSA processes for different applications [38]. To this end, different analyzes have been carried out based on the mathematical models reported in Table 4.Table 4
Distributed parameter models of the PSA processes for bioethanol production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[34]
6 PDE
Consider adsorption isotherms
Consider pressure gradient
[37]
5 PDE
Consider adsorption isotherms
Consider pressure gradient
[29]
6 PDE
Consider adsorption isotherms
No pressure gradient
[23]
3 PDE
Does not present adsorption isotherms
Consider pressure gradient
[39]
6 PDE
Consider adsorption isotherms
Consider pressure gradient
[40]
3 PDE
Does not present adsorption isotherms
Consider pressure gradientTable4 shows a concentration of studies in which different mathematical models for PSA processes are proposed. In this table, the number of PDEs is indicated, if it presents a model for the adsorption isotherms and if they consider pressure variations. The mathematical model of the PSA process or the numerical simulation of the same makes it possible to determine the diameter, the height of the bed, and the amount of zeolite required. On the other hand, they allow establishing nominal operating conditions. The PDEs that represent the behavior of the process, normally consider variations in the axial direction of temperature, pressure, composition, and speed, and neglect variations in other directions. Temporal variations are also considered.In general, the models of a cyclic PSA process can be curves of the hyperbolic or parabolic type, depending on the assumptions of the modeling. The numerical methods to discretize these PDEs are finite differences, finite elements, and orthogonal placement on finite elements. An example of mathematical modeling of a PSA process is reported by Simo et al. [34] and is shown in Table 5.Table 5
Governing equations and simplifications for production and purification of bioethanol.
Mass balance for adsorbing component
∂
Y
i
∂
t
=
D
ax
∂
2
Y
i
∂
z
2
−
u
∂
Y
i
ϵ
∂
z
−
1
−
ϵ
ϵ
ρ
s
RT
∂
q
i
P
∂
t
1
−
Y
i
Overall mass balance
1
∂
P
P
∂
t
−
1
∂
T
T
∂
t
=
−
1
∂
u
ϵ
∂
z
−
1
u
∂
P
ϵ
P
∂
t
+
1
u
∂
T
ϵ
T
∂
t
−
1
−
ϵ
ϵ
ρ
s
RT
P
∑
i
n
∂
q
i
∂
t
LDF rate
∂
q
i
∂
t
=
k
LDF
q
i
∗
−
q
i
Energy balance
ρ
g
c
pg
+
1
−
ϵ
ϵ
ρ
s
c
ps
∂
T
∂
t
=
K
ef
∂
2
T
∂
z
2
−
u
ϵ
C
pg
ρ
g
∂
T
∂
z
+
Q
1
−
ϵ
ϵ
ρ
s
∂
q
i
∂
t
Pressure drop
−
∂
P
∂
z
=
150
×
1
0
−
5
μ
g
1
−
ϵ
i
2
2
r
p
ψ
2
ϵ
i
3
v
g
+
1.75
×
1
0
−
5
M
w
ρ
g
1
−
ϵ
i
2
r
p
ψ
ϵ
i
3
v
g
2
Equilibrium
q
i
∗
=
q
i
s
K
T
P
i
1
+
K
T
P
i
in
K
K
0
=
Q
R
1
T
−
1
T
0
Cycle steps
I. Adsorption
(i)t=0
y
=
W
=
0
,
T
=
T
F
,
P
=
P
F
,
y
=
Y
IV
W
=
W
IV
T
=
T
IV
,
P
=
P
IV
(ii)z=0
y
=
y
F
,
T
=
T
F
,
P
=
P
F
,
F
=
F
F
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
II. Depressurization
(i)t=0
y
=
y
I
,
W
=
W
I
,
T
=
T
I
,
P
=
P
I
(ii)z=0
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
,
F
=
F
valve
III. Purge
(i)t=0
y
=
y
II
,
W
=
W
II
,
T
=
T
II
,
P
=
P
II
(ii)z=0
Y
=
Y
P
,
T
=
T
P
,
F
=
F
P
(iii)z=L
P
=
P
P
,
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
IV. Repressurization
(i)t=0
y
=
y
III
,
W
=
W
III
,
T
=
T
III
,
P
=
P
III
(ii)z=0
y
=
y
P
,
T
=
T
P
,
F = F(valve)
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0To solve this type of PDE, initial and boundary conditions are needed in each step of the PSA process, as an example, the conditions established for the model of Simo et al. [34] are shown in Table 5, where the Roman numerals indicate the sequence in how they should be applied successively for each step of the process:


### 3.3. Parametric Study of the PSA Process for the Production of Bioethanol

To observe the dynamics of the purity achieved from the start and reach the CSS, the case of Simo et al. [34] is proposed. The parameters of this PSA process for the production and purification of bioethanol are shown in the following Table 6.Table 6
Start-up parameters of the PSA process for the purification and production of bioethanol.
FEED
Flow
512
kmolh-1
Ethanol
0.818
kmolkmol-1
Water
0.182
kmolkmol-1
Temperature
440
K
Production pressure
379
kPa
Purge pressure
13.5
kPa
SIZING
Bed height
7.3
m
Bed diameter
2.4
m
Zeolite type 3A particle radius
0.0015875
m
Bulk solid density
729.62
kg m-3Figure4 shows how the purity of ethanol increases and the purity of water decreases, this is due to the conditions established in Table 6 and the selective characteristics of the adsorbent to retain the greatest number of water molecules. The ethanol profile rises as the cycles pass until reaching the CSS and obtaining a purity of 99% by wt of ethanol. CSS is reached after 350 cycles (67 h).Figure 4
Purification and production of bioethanol from the start-up.Subsequently, Figure5 shows the possible input variables that can have a greater and lesser effect on the purity of bioethanol. These tests were done in the CSS.Figure 5
Sensitivity analysis applied to the PSA process for the production of bioethanol [41].
(a)
Temperature: 440 K to 418 K; Flow: 512 kmolh-1; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(b)
Temperature: 440 K to 462 K; Flow: 512 kmolh-1; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(c)
Flow: 512 kmolh-1 to 486 kmolh-1; Temperature: 440 K; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(d)
Flow: 512 kmolh-1 to 537 kmolh-1; Temperature: 440 K; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(e)
Pressure: 379 kPa to 360 kPa; Flow: 512 kmolh-1; Temperature: 440 K; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(f)
Pressure: 379 kPa to 398 kPa; Flow: 512 kmolh-1; Temperature: 440 K; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(g)
Molar fraction: 0.182 (water) and 0.818 (ethanol) to 0.2229 (water) and 0.7771 (ethanol), Pressure: 379 kPa; Flow: 512 kmolh-1; Temperature: 440 K
(h)
Molar fraction: 0.182 (water) and 0.818 (ethanol) to 0.1411 (water) and 0.8589 (ethanol), Pressure: 379 kPa; Flow: 512 kmolh-1; Temperature: 440 KThe results obtained with this analysis show that the temperature, flow, and composition of the feed have a greater effect on the purity of ethanol. On the other hand, the pressure variable has no effect on purity. An important difference between the variables that had the greatest effect on ethanol purity was the convergence time. Due to this criterion, it can be seen that the feed composition has the shortest time compared to the other two variables. For this reason, it is of great importance to have the composition of the feed controlled at the time of entering it at the entrance of the real PSA process, since this can cause decreases in purity, acting as a disturbance (see Table7).Table 7
Data obtained in the CSS from the parametric study.
Run
Temperature (K)
Flow kmolh-1
Pressure kPa
Composition water-ethanol
Purity % wt of ethanol
Number of cycles
1
440
512
379
0.182-0.818
99.5
350
2
418
512
379
0.182-0.818
99.23
363
3
462
512
379
0.182-0.818
99.63
579
4
440
486
379
0.182-0.818
99.75
579
5
440
537
379
0.182-0.818
99.33
370
6
440
512
360
0.182-0.818
99.60
362
7
440
512
398
0.182-0.818
99.54
440
8
440
512
379
0.2229-0.7771
98.95
327
9
440
512
379
0.1411-0.8589
99.71
464


## 3.1. Adsorption and Separation for the Ethanol-Water Mixture with Different Adsorbents

The study of the adsorption phenomenon with molecular sieves makes it possible to determine models capable of predicting the thermodynamic equilibrium of different adsorbents used for the ethanol-water mixture. The thermodynamic equilibrium of each adsorbent is represented by an adsorption isotherm at a constant temperature, which determines the maximum adsorption capacity. The adsorption isotherm is obtained from experimental data. These represent the amount of material (water in this case) adsorbed on the surface of the adsorbent, as a function of the composition of the material (water) present in the gas phase, the latter is expressed as a molar fraction or partial pressure. There are 5 types of adsorption isotherms as shown in Figure2, they can be monomolecular isotherms (monolayers) or polymolecular isotherms (multilayers). The most common isotherms are types I, II, and III. To describe the adsorption isotherms that are obtained experimentally and can be represented in different mathematical models, each model contemplates a series of considerations.Figure 2
Adsorption isotherms.For the ethanol-water mixture a type I adsorption isotherm is obtained, which is represented by the Langmuir model. This model proposes a constant temperature, localized adsorption only active sites, a homogeneous surface, and the adsorption occurs in a monolayer, assuming that each adsorption site can adhere to only one adsorbate molecule, the adsorption energy is the same for all adsorption sites and there is no interaction between the adsorbed molecules [10–13]. The thermodynamic equilibrium provides a measure of adsorption efficiency during the removal of specific impurities (water molecules), as well as the maximum adsorption capacity. On the other hand, the kinetic equilibrium data are represented using breakdown curves, in these, the composition of the adsorbed phase is related to the adsorption time to reach the maximum capacity. The increase in temperature favors the adsorbent to retain the molecules or atoms and reach its maximum saturation point in less time, but it does not favor thermodynamic equilibrium since the maximum adsorption capacitance is reduced. The rate of adsorption is proportional to the rate of diffusion in the pores.Among the adsorbents that have been used to separate the ethanol-water mixture, natural zeolites are good candidates and have an advantage over some types of membranes or natural adsorbents because they remain stable in harsh chemical environments and high temperatures [14–18]. Dehydration of ethanol through adsorption with natural zeolites is acceptable and effective in adsorbing large amount of water, but the use of synthetic zeolites has recently been suggested as a promising alternative. One of the most accepted and studied with good results is the synthetic zeolite 3A. The review of several studies allowed us to make a concentrate on works, in which different adsorbents are applied, useful to separate the ethanol-water mixture. The information is contained in Table 2, which describes the characteristics of thermodynamic equilibrium and the time it reaches its maximum saturation point at different time, these determine the maximum capacity and time with which they adsorb. The results were obtained as a function of temperature since the adsorption capacity depends significantly on this variable. Table 2 shows the different adsorbents used for the separation of the ethanol-water mixture, as well as the constants Q and K, referred to as the maximum adsorption capacity and the Langmuir constant.Table 2
Comparison of the thermodynamic values of various adsorbents as a function of temperature.
Reference
Adsorbents
TemperatureK
Maximum adsorption capacityQ gwatergads‐1
Langmuir constant
Adsorption time
[19]
Cornmeal
333.15
0.029
—
—
364.15
0.025
—
300 min
[20]
ZSG-1
303.15
0.1046
—
—
ZSG-1
352.15
0.1241
—
—
ZSG-1
357.15
0.1499
—
—
ZSG-1
362.15
0.1511
—
—
ZSG-1
370.15
0.1529
—
80 min
[21]
Silicalite
298
0.116
—
9 min
[10]
Clinoptilolite
373
0.198
—
—
[11]
Zeolite 3A
348
0.18
25
—
3A
373
0.171
8
—
3A
398
0.162
2.9
—
3A
423
0.135
1.19
—
3A
448
0.108
0.54
—
[12]
LTA-K
298
0.130
0.735
—
LTA-Na
298
0.150
0.563
—
LTA-ca
298
0.094
0.589
—
FAU-Na
298
0.166
0.611
—
MOR-Na
298
0.045
0.403
—
[14]
Zeolite 3A
323.15
0.1915
0.00791
200 min
3A
343.158
0.180
0.00655
180 min
Heulandite-Sonora
323.15
0.1
0.00925
185 min
Heulandite-Sonora
343.158
0.097
0.00345
150 min
Clinoptilolite-Potosí
323.15
0.097
0.00491
180 min
Clinoptilolite-Potosí
343.158
0.094
0.00253
145 min
[13]
Clinoptilolite
293.15
0.161
—
24 h
[22]
Clinoptilolite
283
0.13428
0.0179
—
Clinoptilolite
298
0.12618
0.0156
—
Clinoptilolite
313
0.12402
0.0125
24 h
Clinoptilolite
328
0.11916
0.0113
—
Clinoptilolite
343
0.11304
0.0106
—
[23]
Sylobead 3A
373.15
0.198
—
—
[24]
Zeolite 3A
393.15
0.085
0.1006
135 min
3A
413.15
0.065
0.0828
75 min
[25]
Zeolita NaA
378
0.155
—
[15]
Philipsita
326.3
0.0432
0.76
57 min
Philipsita 0.5 M
326.3
0.0800
0.81
34 min
Philipsita 0.75 M
326.3
0.0770
0.83
35 min
Philipsita 1 M
326.3
0.1054
1.2
55 min
Philipsita 2 M (natural)
326.3
0.1016
0.93
41 min
[16]
ACF
298.15
0.1571
0.58
600 s
ACF
308.15
0.1567
0.30
—
ACF
318.15
0.1576
0.15
1800 s
ACF-850
298.15
0.2266
0.22
680 s
ACF-850
308.15
0.2244
0.12
—
ACF-850
318.15
0.2264
0.06
700 s
ACF-750
298.15
0.1488
0.59
200 s
ACF-750
308.15
0.1477
0.29
—
ACF-750
318.15
0.1456
0.16
450 s
[17]
ZIF-8
298.15
0.45661
5.30
5 min
ZIF-67
298.15
0.4633
5.35
5 min
[26]
Zeolita 4A
336.15
0.1030
—
57 min
3A
298.15
0.249
0.317
40 min
3A
313.15
0.238
0.153
30 min
3A
323.15
0.220
0.090
22 min
3A Sintética)
333.15
0.200
0.052
20 min
[18]
Clinoptilolite (1-2 mm)
298.15
0.405
2019.56
540 s
Clinoptilolite (3 mm)
298.15
0.31
1386.20
720 s
Clinoptilolite (5 mm)
298.15
0.29
3521.28
180 s
LV-NENG
298.15
0.275
1353.44
720 s
Sorbead
298.15
0.26
1053.11
540 sTable2 shows that natural zeolites have disadvantages over synthetic zeolites, specifically compared to 3A zeolites and ZIF, since the latter adsorb a greater amount of water. However, clinoptilolite presents large contributions with a maximum adsorption capacity, between 0.27 and 0.3 gwatergads−1.


## 3.2. Mathematical Models, Characteristics, and Configuration of the PSA Process for the Production of Bioethanol

There are some studies on PSA processes with columns packed with zeolite, specifically designed to dehydrate ethanol [27–29], in which advantages and disadvantages of different operational methods are compared such as the use of two beds, three beds, and multibeds (see Table 3).Table 3
Works reported on the different configurations of PSA processes for purification of bioethanol.
Reference
Experimental /simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Ethanol feed (% wt)
[32]
Simulated
2 beds
200 to 13
5.3
90
4 steps
[33]
Experimental
2 beds
(200-240) to 20
7
95
4 steps
[34]
Experimental
2 beds
379.79 to 13.8
5.4
92
5 steps
[35]
Experimental
2 beds
120 to 20
3.8
93.2
4 steps
[36]
Experimental
3 beds
(120, 130) to 20
6.6
87
4 steps
[37]
Experimental
2 beds
303 to 30
45
88.57
4 steps
[14]
Simulated
2 beds
204.5 to 13.4
2.91
90
4 steps
[30]
Simulated
2 beds
340 to 30
—
86
2 stepsIt is important to take into account the additional energy required to circulate the mixture, as well as the electricity required to operate the adsorption and desorption beds and the air and vacuum compressor [30, 31]. Table 3 shows the cycle times considered in different articles, regeneration takes between 3 and 45 min.In the study of Jeong et al. [36], the two-bed process and the multibed process produced 99.5% anhydrous ethanol by weight, with a feed of 87.0% by weight ethanol. However, the multibed process presented lower energy consumption (higher energy efficiency). On the other hand, the two-bed process has the advantage of producing anhydrous ethanol from the input ethanol concentration as low as 81.3% in weight. And lastly, the three-bed process required the longest regeneration time (twice the amount of time) for zeolite, but a very stable process with higher performance was achieved due to less time lost in the change of cycle, so it was concluded that this is the most suitable for a large-scale commercial application. The process flow diagram is shown in Figure 3.Figure 3
Schematic diagram of the PSA process using different types of connection configurations: (a) two beds, (b) multiple tubes, (c) two-pass beds, and (d) three beds.
(a)
(b)
(c)
(d)The PSA process is more used than the TSA due to its efficiency and low energy cost, for this reason, there is interest in presenting proposals to improve the operation of PSA processes for different applications [38]. To this end, different analyzes have been carried out based on the mathematical models reported in Table 4.Table 4
Distributed parameter models of the PSA processes for bioethanol production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[34]
6 PDE
Consider adsorption isotherms
Consider pressure gradient
[37]
5 PDE
Consider adsorption isotherms
Consider pressure gradient
[29]
6 PDE
Consider adsorption isotherms
No pressure gradient
[23]
3 PDE
Does not present adsorption isotherms
Consider pressure gradient
[39]
6 PDE
Consider adsorption isotherms
Consider pressure gradient
[40]
3 PDE
Does not present adsorption isotherms
Consider pressure gradientTable4 shows a concentration of studies in which different mathematical models for PSA processes are proposed. In this table, the number of PDEs is indicated, if it presents a model for the adsorption isotherms and if they consider pressure variations. The mathematical model of the PSA process or the numerical simulation of the same makes it possible to determine the diameter, the height of the bed, and the amount of zeolite required. On the other hand, they allow establishing nominal operating conditions. The PDEs that represent the behavior of the process, normally consider variations in the axial direction of temperature, pressure, composition, and speed, and neglect variations in other directions. Temporal variations are also considered.In general, the models of a cyclic PSA process can be curves of the hyperbolic or parabolic type, depending on the assumptions of the modeling. The numerical methods to discretize these PDEs are finite differences, finite elements, and orthogonal placement on finite elements. An example of mathematical modeling of a PSA process is reported by Simo et al. [34] and is shown in Table 5.Table 5
Governing equations and simplifications for production and purification of bioethanol.
Mass balance for adsorbing component
∂
Y
i
∂
t
=
D
ax
∂
2
Y
i
∂
z
2
−
u
∂
Y
i
ϵ
∂
z
−
1
−
ϵ
ϵ
ρ
s
RT
∂
q
i
P
∂
t
1
−
Y
i
Overall mass balance
1
∂
P
P
∂
t
−
1
∂
T
T
∂
t
=
−
1
∂
u
ϵ
∂
z
−
1
u
∂
P
ϵ
P
∂
t
+
1
u
∂
T
ϵ
T
∂
t
−
1
−
ϵ
ϵ
ρ
s
RT
P
∑
i
n
∂
q
i
∂
t
LDF rate
∂
q
i
∂
t
=
k
LDF
q
i
∗
−
q
i
Energy balance
ρ
g
c
pg
+
1
−
ϵ
ϵ
ρ
s
c
ps
∂
T
∂
t
=
K
ef
∂
2
T
∂
z
2
−
u
ϵ
C
pg
ρ
g
∂
T
∂
z
+
Q
1
−
ϵ
ϵ
ρ
s
∂
q
i
∂
t
Pressure drop
−
∂
P
∂
z
=
150
×
1
0
−
5
μ
g
1
−
ϵ
i
2
2
r
p
ψ
2
ϵ
i
3
v
g
+
1.75
×
1
0
−
5
M
w
ρ
g
1
−
ϵ
i
2
r
p
ψ
ϵ
i
3
v
g
2
Equilibrium
q
i
∗
=
q
i
s
K
T
P
i
1
+
K
T
P
i
in
K
K
0
=
Q
R
1
T
−
1
T
0
Cycle steps
I. Adsorption
(i)t=0
y
=
W
=
0
,
T
=
T
F
,
P
=
P
F
,
y
=
Y
IV
W
=
W
IV
T
=
T
IV
,
P
=
P
IV
(ii)z=0
y
=
y
F
,
T
=
T
F
,
P
=
P
F
,
F
=
F
F
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
II. Depressurization
(i)t=0
y
=
y
I
,
W
=
W
I
,
T
=
T
I
,
P
=
P
I
(ii)z=0
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
,
F
=
F
valve
III. Purge
(i)t=0
y
=
y
II
,
W
=
W
II
,
T
=
T
II
,
P
=
P
II
(ii)z=0
Y
=
Y
P
,
T
=
T
P
,
F
=
F
P
(iii)z=L
P
=
P
P
,
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0
IV. Repressurization
(i)t=0
y
=
y
III
,
W
=
W
III
,
T
=
T
III
,
P
=
P
III
(ii)z=0
y
=
y
P
,
T
=
T
P
,
F = F(valve)
(iii)z=L
∂
y
∂
z
=
0
,
∂
T
∂
z
=
0To solve this type of PDE, initial and boundary conditions are needed in each step of the PSA process, as an example, the conditions established for the model of Simo et al. [34] are shown in Table 5, where the Roman numerals indicate the sequence in how they should be applied successively for each step of the process:


## 3.3. Parametric Study of the PSA Process for the Production of Bioethanol

To observe the dynamics of the purity achieved from the start and reach the CSS, the case of Simo et al. [34] is proposed. The parameters of this PSA process for the production and purification of bioethanol are shown in the following Table 6.Table 6
Start-up parameters of the PSA process for the purification and production of bioethanol.
FEED
Flow
512
kmolh-1
Ethanol
0.818
kmolkmol-1
Water
0.182
kmolkmol-1
Temperature
440
K
Production pressure
379
kPa
Purge pressure
13.5
kPa
SIZING
Bed height
7.3
m
Bed diameter
2.4
m
Zeolite type 3A particle radius
0.0015875
m
Bulk solid density
729.62
kg m-3Figure4 shows how the purity of ethanol increases and the purity of water decreases, this is due to the conditions established in Table 6 and the selective characteristics of the adsorbent to retain the greatest number of water molecules. The ethanol profile rises as the cycles pass until reaching the CSS and obtaining a purity of 99% by wt of ethanol. CSS is reached after 350 cycles (67 h).Figure 4
Purification and production of bioethanol from the start-up.Subsequently, Figure5 shows the possible input variables that can have a greater and lesser effect on the purity of bioethanol. These tests were done in the CSS.Figure 5
Sensitivity analysis applied to the PSA process for the production of bioethanol [41].
(a)
Temperature: 440 K to 418 K; Flow: 512 kmolh-1; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(b)
Temperature: 440 K to 462 K; Flow: 512 kmolh-1; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(c)
Flow: 512 kmolh-1 to 486 kmolh-1; Temperature: 440 K; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(d)
Flow: 512 kmolh-1 to 537 kmolh-1; Temperature: 440 K; Pressure: 379 kPa; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(e)
Pressure: 379 kPa to 360 kPa; Flow: 512 kmolh-1; Temperature: 440 K; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(f)
Pressure: 379 kPa to 398 kPa; Flow: 512 kmolh-1; Temperature: 440 K; Molar fraction: 0.182 (water) and 0.818 (ethanol)
(g)
Molar fraction: 0.182 (water) and 0.818 (ethanol) to 0.2229 (water) and 0.7771 (ethanol), Pressure: 379 kPa; Flow: 512 kmolh-1; Temperature: 440 K
(h)
Molar fraction: 0.182 (water) and 0.818 (ethanol) to 0.1411 (water) and 0.8589 (ethanol), Pressure: 379 kPa; Flow: 512 kmolh-1; Temperature: 440 KThe results obtained with this analysis show that the temperature, flow, and composition of the feed have a greater effect on the purity of ethanol. On the other hand, the pressure variable has no effect on purity. An important difference between the variables that had the greatest effect on ethanol purity was the convergence time. Due to this criterion, it can be seen that the feed composition has the shortest time compared to the other two variables. For this reason, it is of great importance to have the composition of the feed controlled at the time of entering it at the entrance of the real PSA process, since this can cause decreases in purity, acting as a disturbance (see Table7).Table 7
Data obtained in the CSS from the parametric study.
Run
Temperature (K)
Flow kmolh-1
Pressure kPa
Composition water-ethanol
Purity % wt of ethanol
Number of cycles
1
440
512
379
0.182-0.818
99.5
350
2
418
512
379
0.182-0.818
99.23
363
3
462
512
379
0.182-0.818
99.63
579
4
440
486
379
0.182-0.818
99.75
579
5
440
537
379
0.182-0.818
99.33
370
6
440
512
360
0.182-0.818
99.60
362
7
440
512
398
0.182-0.818
99.54
440
8
440
512
379
0.2229-0.7771
98.95
327
9
440
512
379
0.1411-0.8589
99.71
464


## 4. Biohydrogen Purification by PSA

Biohydrogen is a biologically produced gas; it is obtained from algae, bacteria, and archaea. Biohydrogen is a biofuel with great potential that can be obtained through specific cultivation or from organic waste [42, 43]. Biohydrogen can serve as the energy source for gas turbines and fuel cells, or as the raw material for chemical industries [44]. The development of a biohydrogen station system is important to the commercialization of fuel cells and fuel cell-powered vehicles. One of the key challenges for biohydrogen production is the design of an efficient purification process. In conventional hydrogen production plants, the shifted gas should first be precooled to meet the temperature requirement of CO2 absorption units, and then be reheated after the CO2 removal [4]. Additional purification units are needed to remove the residual trace CO because of the thermodynamically [45]. Alternatively, the elevated-temperature pressure swing adsorption process based on WGS catalysts and CO2 and methane adsorbents are able to achieve triple functions: CO catalytic conversion, methane and CO2 adsorption, and hydrogen purification in a single unit [46].The main methods for hydrogen production can be categorized as follows:(i)
Fossil fuels as a source of hydrogen production(ii)
Water as a source of hydrogen production(iii)
Utilization of solar energy(iv)
Biological methods of hydrogen production(v)
Fermentative hydrogen production from organic compounds(vi)
Hydrogen production from biomassOur lab is focused on hydrogen production by mean dark fermentation using different consortia and agroindustrial waste as substrate. Hydrogen production by fermentative processing has been given little attention, while hydrogen production by photosynthetic microorganisms has been studied extensively. The evolution of hydrogen by fermentation has, however, several advantages for industrial production [47–49].Fermentative bacteria have a very high evolution rate of hydrogen. They can produce hydrogen constantly, day and night, from organic substrates. They can have a growth rate adequate for the supply of microorganisms to the production systems.Therefore, fermentative evolution is more advantageous than photochemical evolution for the mass production of hydrogen by microorganisms. Fermentative hydrogen production can be maximized through the effective coupling of the following factors:(i)
An accessible and rich source of electron and biochemical electron pump(ii)
An active hydrogenase


### 4.1. Adsorption and Separation for the CO, CO2, Nitrogen, Methane, Water, H2S, and Hydrogen Mixture with Different Adsorbents

In the case of the separation and purification of hydrogen, it is necessary to consider adsorbents (activated carbon, zeolite, silica gel, activated alumina) that have selectivity over the components: CO, CO2, methane, etc. This makes it possible to use multigas isotherms (without interaction parameters) for multicomponent adsorption modeling [50].The PSA process for the purification and production of hydrogen is necessary the use of different types of adsorbents with a high degree of selectivity, for this, silica gel can remove moisture and higher hydrocarbons, and the use of activated carbon retains CH4, CO2, and H2S [51]. Finally, it is known that zeolite 5A is one of the adsorbents that have a high selectivity over N2 and CO. There are several different materials and adsorbents on the market, making it difficult to compare data from the literature.For this, the different adsorbents that can be used to purify hydrogen have been investigated in detail; the results found are shown in Table8.Table 8
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
TemperatureK
Maximum adsorption capacityQ ggads−1
Langmuir constant (bar-1)
Pressure Atm
[52]
Carbon molecular sieve
293
0.1170 (CO)
0.130
16
Carbon molecular sieve
293
0.0736 (CH4)
0.232
16
[43]
Activated carbon
289.1
0.368 (CO)
9.867
×
10
6
—
Activated carbon
289.1
0.350 (CH4)
1.916
×
10
7
—
Activated carbon
289.1
0.411 (CO2)
3.526
×
10
7
—
Zeolite 5A
289.1
0.129 (CO)
2.828
×
10
7
—
Zeolite 5A
289.1
0.086 (CH4)
2.410
×
10
7
—
Zeolite 5A
289.1
0.150 (CO2)
3.229
×
10
8
—
[53]
CMS-T3A
293
0.044 (N2)
0.105
16
CMS-T3A
293
0.060 (O2)
0.088
15
CMS-T3A
293
0.140 (Ar)
0.093
16
CMS-T3A
293
0.073 (CO)
0.179
14.85
CMS-T3A
293
0.161 (CO2)
0.983
15.5
CMS-T3A
293
0.050 (CH4)
0.351
15
CMS-T3A
293
0.378 (SO2)
2.253
4.5
CMS-T3A
303
0.040 (N2)
0.102
15
CMS-T3A
303
0.056 (O2)
0.076
14.6
CMS-T3A
303
0.128 (Ar)
0.082
15
CMS-T3A
303
0.073 (CO)
0.150
14.2
CMS-T3A
303
0.158 (CO2)
0.764
15.6
CMS-T3A
303
0.045 (CH4)
0.329
15
CMS-T3A
303
0.365 (SO2)
2.170
4.8
CMS-T3A
313
0.035 (N2)
0.097
14.5
CMS-T3A
313
0.055 (O2)
0.065
16
CMS-T3A
313
0.118 (Ar)
0.079
14.4
CMS-T3A
313
0.071 (CO)
0.137
15.8
CMS-T3A
313
0.154 (CO2)
0.583
15
CMS-T3A
313
0.043 (CH4)
0.269
15
CMS-T3A
313
0.349 (SO2)
2.163
4.7
[50]
PCB-activated carbon
295
0.088 (CH4)
0.0155
68.04
PCB-activated carbon
295
0.148 (CO)
0.0056
51.03
PCB-activated carbon
295
0.392 (CO2)
0.0227
37.42
PCB-activated carbon
295
0.335 (H2S)
0.0479
13.60
[54]
Activated carbon
293.15
0.102 (CO)
9.075
×
10
6
20
Activated carbon
293.15
0.080 (CH4)
1.812
×
10
7
18
Activated carbon
293.15
0.308 (CO2)
3.356
×
10
7
10
Activated carbon
293.15
0.014 (N2)
1.657
×
10
7
15
Zeolite 5A
293.15
0.049 (CO)
2.727
×
10
7
17
Zeolite 5A
293.15
0.030 (CH4)
2.386
×
10
7
18
Zeolite 5A
293.15
0.202 (CO2)
3.197
×
10
4
17
Zeolite 5A
293.15
0.238 (N2)
1.055
×
10
7
20
[55]
AC5-KS
303
0.147 (CO)
1.428
×
10
9
—
AC5-KS
303
0.582 (CO2)
3.937
×
10
9
—
AC5-KS
303
0.0116 (N2)
9.797
×
10
8
—
AC5-KS
303
0.0973 (CH4)
2.986
×
10
9
—
[56]
CuBTC (KRICT)
303
0.022 (N2)
0.0386
7
CuBTC (KRICT)
303
0.019 (CO)
0.2443
1
CuBTC (KRICT)
308
0.444 (CO2)
0.2963
7
CuBTC (KRICT)
308
0.056 (CH4)
0.0861
7
CuBTC (KRICT)
343
0.014 (N2)
0.0216
7
CuBTC (KRICT)
343
0.008 (CO)
0.0901
1
CuBTC (KRICT)
343
0.290 (CO2)
0.1185
7
CuBTC (KRICT)
343
0.036 (CH4)
0.0657
7
CuBTC (KRICT)
373
0.009 (N2)
0.0152
7
CuBTC (KRICT)
373
0.042 (CO)
0.0491
1
CuBTC (KRICT)
373
0.187 (CO2)
0.0619
7
CuBTC (KRICT)
373
0.024 (CH4)
0.0410
7
[57]
Cu-BTC
303
0.125 (CO)
2.4433
—
Cu-BTC
303
0.660 (CO2)
0.3437
—
Cu-BTC
303
0.104 (N2)
0.0386
—
Cu-BTC
303
0.116 (CH4)
0.1416
—
[58]
Zeolite 5A
303
0.064 (CO)
0.2363
10
Zeolite 5A
303
0.034 (CH4)
0.2003
10
[59]
TDA AMS-19
453.15
0.268 (CO2)
4.634
×
10
−
8
41
TDA AMS-19
513.15
0.198 (CO2)
4.349
×
10
−
8
18
TDA AMS-19
573.15
0.158 (CO2)
4.135
×
10
−
8
18
[60]
BPL 4X10 activated carbon
293.15
0.311 (CO2)
0.4
12
[61]
MG50
623.15
0.085 (CO2)
64.8
—
[62]
MG50
523.15
0.043 (CO2)
7.8
×
10
−
5
1
MG50
623.15
0.034 (CO2)
7.3
×
10
−
5
1
MG50
723.15
0.032 (CO2)
5.0
×
10
−
5
1
[63]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673.15
0.019 (CO2)
37.4
1
[64]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.027 (CO2)
16.9
0.45
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.022 (CO2)
17.0
0.58
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.028 (CO2)
23.6
0.19
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
753
0.025 (CO2)
19.3
0.19
[65]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673.15
0.011 (CO2)
37.4
3
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
793.15
0.011 (CO2)
21.2
3
[18]
K-MG30
723.15
0.028 (CO2)
—
10.85
K-MG30
673.15
0.022 (CO2)
—
10.85
K-MG30
623.15
0.015 (CO2)
—
10.85
K-MG30
573.15
0.009 (CO2)
—
10.85
[2]
CuBTC-OMC (MOF-composite)
298.15
0.191 (CO2)
—
1
CuBTC/GO (MOF-composite)
295
0.135 (CO2)
—
1.1
CuBTC@MWCNT (MOF-composite)
298.15
0.149 (CO2)
—
1
Cu3(BTC)2 (MOF-composite)
298.15
0.595 (CO2)
—
18
CG-9 (CuBTC-GO-9) (MOF-composite)
273
0.363 (CO2)
—
1Table8 shows different types of adsorbents, however, the most outstanding are CMS-T3A, PCB-activated carbon, and activated carbon. These adsorbents show selectivity over a variety of compounds (N2, O2, Ar, CO, CO2, CH4, and H2S) and have higher adsorption compared to other natural and synthetic adsorbents. One difference between these three defined adsorbents is the adsorption capacity from temperature change.


### 4.2. Mathematical Models, Characteristics, and Configuration of the PSA Process for the Production of Biohydrogen

To ensure a continuous separation process, multiple columns are required (see Table9). H2 purification is done with the PSA process, using an adsorption pressure of 500 to 4000 kPa and for the purge step, only 100 kPa is used. A temperature of 295 K is contemplated in the production and regeneration stages. For the production and purification of biohydrogen, a minimum of 4 columns is used (see Figure 6).Table 9
Works reported on the different configurations of PSA processes for purification of biohydrogen.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Hydrogen feed (% molar fraction)
[55]
Simulated
2 beds
500 to 50
5
79
10 steps
[67]
Simulated
10 beds
(1300-1200) to 20
—
62.57
5 steps
[56]
Experimental
2 beds
350 to 100
7.5
67, 68, 78, and 81
4 steps
[57]
Experimental
2 beds
350 to 100
5.8
67, 68, and 78
4 steps
[58]
Simulated
6 beds
1100 to 100
6.6
70
9 and 12 steps
[68]
Experimental
4 beds
(1400-1600) to (131-50)
—
55
8 steps
[59]
Simulated
4, 6, 8, and 10 beds
(3450-1730) to 100
4.6
15
4, 6, 8, and 10 steps
[60]
Simulated
4 beds
1600 to 100
—
25, 50, and 75
7 steps
[69]
Experimental
2 beds
(1000-4000) to 100
0.8
50
5 steps
[70]
Experimental
8 beds
3500 to 100
4
88.75
12 steps
[71]
Experimental
2 and 4 beds
(3000-3500) to 110
5 and 6.3
88
6 and 10 stepsFigure 6
Schematic diagram of the PSA process using 4-beds, 9-steps.Different types of structures and configurations have been studied with respect to the PSA process, one of them presented a study of the performance of the PSA process using multiple beds to produce high purity biohydrogen from synthesis gas H2: 72.2%, CH4: 4.17%, CO: 2.03%, CO2: 21.6%). In the study of Yang et al. [66], it was an experimental and theoretical work, as a result, they obtained purity of 99.999% of biohydrogen and recovery of 66% of the synthesis gas, with an oscillating pressure of 100 to 800 kPa and ambient temperature.Table9 shows the different configurations presented by the PSA processes for the production of biohydrogen.It can be seen in Table9 that more beds are used compared to bioethanol production, likewise, the number of steps is greater and the pressure values are high with oscillations between 1000 and 10000 kPa. To do the purge, it is only necessary to handle an atmospheric pressure and it is not necessary to use a vacuum pressure.In the study of Liemberger et al. and Yang et al. [50, 66], they showed that the recovery of hydrogen increases when the linear speed and the adsorption time increase, however, the purity of the hydrogen decreases. On the other hand, the 4-bed 9-step PSA process could be optimally operated at a linear speed of 3 cms-1, adsorption time of 50 s, and a pressure of 200 kPa in the purge step (see Figure 7).Figure 7
Purification and production of biohydrogen from the start-up.Table10 shows the modeling characteristics that describe the PSA process for biohydrogen production and shows that the number of PDEs can vary, depending on the considerations to obtain a less complex model. In some works, the results and profiles of pressure and temperature are considered, and in others only one of these variables that are a function of time and space.Table 10
Distributed parameter models of the PSA processes for biohydrogen production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[71]
6 PDEs
Consider adsorption isotherms
Consider pressure gradient
[68]
4 PDEs
Consider adsorption isotherms
No pressure gradient
[58]
3 PDEs
Does not present adsorption isotherms
No pressure gradient
[57]
4 PDEs
Does not present adsorption isotherms
Consider pressure gradient
[56]
5 PDEs
Consider adsorption isotherms
Consider pressure gradient
[55]
6 PDEs
Does not present adsorption isotherms
Consider pressure gradientThe base mathematical model that was taken from the works of Lee et al. and Xiao et al. [42, 43] (see Table 11). A semicomplete model is proposed since it does not contemplate the part of the equations of the wall and a general balance. It uses four steps to complete one cycle of the PSA process.Table 11
Governing equations and simplifications for production and purification of biohydrogen.
Mass balance equation
−
D
L
∂
2
c
i
∂
z
2
+
∂
U
z
c
i
∂
z
+
∂
c
i
∂
t
+
1
−
ϵ
b
ϵ
b
ρ
p
∂
n
i
∂
t
=
0
Energy balance equation
K
L
∂
2
T
∂
z
2
+
ϵ
b
c
C
pg
+
1
−
ϵ
b
ρ
p
C
ps
∂
T
∂
t
−
ϵ
b
c
C
pg
U
z
∂
T
∂
z
=
1
−
ϵ
b
ρ
p
∑
j
=
1
N
Δ
H
j
∂
n
j
∂
t
+
2
h
in
R
in
T
w
−
T
Ergun equation for momentum balance
−
∂
P
∂
z
=
150
μ
V
z
1
−
ϵ
b
2
4
R
p
2
ϵ
b
3
+
1.75
ρ
g
1
−
ϵ
b
2
R
p
ϵ
b
3
v
g
2
Adsorption isotherms and kinetics
n
i
∗
=
n
i
s
b
i
P
i
/
1
+
∑
j
=
1
N
b
j
P
j
∂
n
i
/
∂
t
=
k
i
n
i
∗
−
n
i
,
i
=
1
,
⋯
,
N
Boundary and initial conditions
I. Adsorption
(i)t=0
c
H
2
z
,
0
=
c
0
,
c
CO
z
,
0
=
0
,
c
CH
4
z
,
0
=
0
,
c
CO
2
z
,
0
=
0
T
z
,
0
=
T
0
,
T
w
z
,
0
=
T
0
,
p
z
,
0
=
p
0
,
η
i
z
,
0
=
η
i
∗
(ii)z=0
−
D
L
∂
c
i
/
∂
z
=
u
c
i
0
−
,
t
−
c
i
0
+
,
t
,
p
=
p
0
,
U
z
=
U
zo
−
K
L
∂
T
/
∂
t
=
ε
b
c
C
pg
U
z
T
0
−
,
t
−
T
0
+
,
t
(iii)z=L
−
D
L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
−
K
L
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
II. Depressurization
(i)t=0
c
H
2
z
,
0
=
c
0
I
,
c
CO
z
,
0
=
c
CO
I
,
c
CH
4
z
,
0
=
c
CH
4
I
,
c
CO
2
z
,
0
=
c
CO
2
I
T
z
,
0
=
T
I
,
T
w
z
,
0
=
T
I
,
p
z
,
0
=
p
I
,
η
i
z
,
0
=
η
i
I
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
,
F
=
F
valve
III. Purge
(i)t=0
c
H
2
z
,
0
=
c
0
II
,
c
CO
z
,
0
=
c
CO
II
,
c
CH
4
z
,
0
=
c
CH
4
II
,
c
CO
2
z
,
0
=
c
CO
2
II
T
z
,
0
=
T
II
,
T
w
z
,
0
=
T
II
,
p
z
,
0
=
p
II
,
η
i
z
,
0
=
η
i
II
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
F
=
F
valve
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
IV. Pressurization
(i)t=0
c
H
2
z
,
0
=
c
0
III
,
c
CO
z
,
0
=
c
CO
III
,
c
CH
4
z
,
0
=
c
CH
4
III
,
c
CO
2
z
,
0
=
c
CO
2
III
T
z
,
0
=
T
III
,
T
w
z
,
0
=
T
III
,
p
z
,
0
=
p
III
,
η
i
z
,
0
=
η
i
III
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
F
=
F
valve
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0The initial and boundary conditions are contemplated in Table11, the mathematical model finds solutions of Y, c, T, and P as a function of time and space.


### 4.3. Parametric Study of the PSA Process for the Production of Biohydrogen

The base model of the works of Lee et al. and Xiao et al. [42, 43] was used. The parameters of this PSA process for the production and purification of biohydrogen are shown in Table 12.Table 12
Start-up parameters of the PSA process for the purification and production of biohydrogen.
FEED
Flow
0.162
kmolkmol-1
CO
0.02
kmolkmol-1
CO2
0.26
kmolkmol-1
Hydrogen
0.69
kmolkmol-1
Methane
0.03
kmolkmol-1
Temperature
298.15
K
Production pressure
980
kPa
Purge pressure
100
kPa
SIZING
Bed height
1
m
Bed diameter
0.037
m
Zeolite type 5A particle radius
0.0015
m
Bulk solid density
850.0
kg m-3The results found from the start-up to reaching the CSS are shown in Figures6 and 8.Figure 8
Sensitivity analysis applied to the PSA process for the production of biohydrogen [72].
(a)
Temperature: 298.15 K to 283.24 K; Flow: 0.162 kmolh-1; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(b)
Temperature: 298.15 K to 313.05 K; Flow: 0.162 kmolh-1; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(c)
Flow: 0.162 kmolh-1 to 0.153 kmolh-1; Temperature: 298.15 K; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(d)
Flow: 0.162 kmolh-1 to 0.170 kmolh-1; Temperature: 298.15 K; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(e)
Pressure: 980 kPa to 931 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(f)
Pressure: 980 kPa to 1029 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(g)
Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2 and 0.03 CH4 to 0.6555 (H2), 0.2945 (CO2), 0.03 (CH4), and 0.02 CO; Pressure: 980 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K
(h)
Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4 to 0.7245 (H2), 0.2255 (CO2), 0.03 (CH4), and 0.02 CO; Pressure: 980 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 KFigure6 shows how the purity of hydrogen increases and the purities of CO, CO2, and methane decreases; this is due to the selectivity of the adsorbent and the nominal star-up conditions shown in Table 12. The hydrogen profile goes up as the cycles pass until reaching the CSS and obtaining a purity of 95%. CSS is reached after 30 cycles (1.2 h).Figure8 shows the results obtained from variations of 0.5% on the input variables. In most cases (pressure, flow, and composition), the effects on hydrogen purity were negligible. However, the effect of the temperature variable presented important changes, defined as the main variable that can be used to control the purity of hydrogen. It is important to mention that this variable is limited in its small values since it cannot generate values less than 5° since this would generate energy costs due to the demand to use temperatures less than 0°.Table13 shows the detailed data of the results presented in Figure 8. It shows the cycle times, the purities, and the changes generated by each input variable.Table 13
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature (K)
Flow kmolh−1
Pressure kPa
Composition CO-CO2-hydrogen-methane
Purity % molar fraction of hydrogen
Number of cycles
1
298.15
0.162
980
0.02-0.26-0.69-0.03
94.85
30
2
283.24
0.162
980
0.02-0.26-0.69-0.03
98.01
2
3
313.05
0.162
980
0.02-0.26-0.69-0.03
90.02
2
4
298.15
0.153
980
0.02-0.26-0.69-0.03
94.95
1
5
298.15
0.170
980
0.02-0.26-0.69-0.03
94.75
1
6
298.15
0.162
931
0.02-0.26-0.69-0.03
95.00
1
7
298.15
0.162
1029
0.02-0.26-0.69-0.03
94.65
1
8
298.15
0.162
980
0.02-0.2945-0.6555-0.03
94.00
2
9
298.15
0.162
980
0.02-0.2255-0.7245-0.03
95.50
2


## 4.1. Adsorption and Separation for the CO, CO2, Nitrogen, Methane, Water, H2S, and Hydrogen Mixture with Different Adsorbents

In the case of the separation and purification of hydrogen, it is necessary to consider adsorbents (activated carbon, zeolite, silica gel, activated alumina) that have selectivity over the components: CO, CO2, methane, etc. This makes it possible to use multigas isotherms (without interaction parameters) for multicomponent adsorption modeling [50].The PSA process for the purification and production of hydrogen is necessary the use of different types of adsorbents with a high degree of selectivity, for this, silica gel can remove moisture and higher hydrocarbons, and the use of activated carbon retains CH4, CO2, and H2S [51]. Finally, it is known that zeolite 5A is one of the adsorbents that have a high selectivity over N2 and CO. There are several different materials and adsorbents on the market, making it difficult to compare data from the literature.For this, the different adsorbents that can be used to purify hydrogen have been investigated in detail; the results found are shown in Table8.Table 8
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
TemperatureK
Maximum adsorption capacityQ ggads−1
Langmuir constant (bar-1)
Pressure Atm
[52]
Carbon molecular sieve
293
0.1170 (CO)
0.130
16
Carbon molecular sieve
293
0.0736 (CH4)
0.232
16
[43]
Activated carbon
289.1
0.368 (CO)
9.867
×
10
6
—
Activated carbon
289.1
0.350 (CH4)
1.916
×
10
7
—
Activated carbon
289.1
0.411 (CO2)
3.526
×
10
7
—
Zeolite 5A
289.1
0.129 (CO)
2.828
×
10
7
—
Zeolite 5A
289.1
0.086 (CH4)
2.410
×
10
7
—
Zeolite 5A
289.1
0.150 (CO2)
3.229
×
10
8
—
[53]
CMS-T3A
293
0.044 (N2)
0.105
16
CMS-T3A
293
0.060 (O2)
0.088
15
CMS-T3A
293
0.140 (Ar)
0.093
16
CMS-T3A
293
0.073 (CO)
0.179
14.85
CMS-T3A
293
0.161 (CO2)
0.983
15.5
CMS-T3A
293
0.050 (CH4)
0.351
15
CMS-T3A
293
0.378 (SO2)
2.253
4.5
CMS-T3A
303
0.040 (N2)
0.102
15
CMS-T3A
303
0.056 (O2)
0.076
14.6
CMS-T3A
303
0.128 (Ar)
0.082
15
CMS-T3A
303
0.073 (CO)
0.150
14.2
CMS-T3A
303
0.158 (CO2)
0.764
15.6
CMS-T3A
303
0.045 (CH4)
0.329
15
CMS-T3A
303
0.365 (SO2)
2.170
4.8
CMS-T3A
313
0.035 (N2)
0.097
14.5
CMS-T3A
313
0.055 (O2)
0.065
16
CMS-T3A
313
0.118 (Ar)
0.079
14.4
CMS-T3A
313
0.071 (CO)
0.137
15.8
CMS-T3A
313
0.154 (CO2)
0.583
15
CMS-T3A
313
0.043 (CH4)
0.269
15
CMS-T3A
313
0.349 (SO2)
2.163
4.7
[50]
PCB-activated carbon
295
0.088 (CH4)
0.0155
68.04
PCB-activated carbon
295
0.148 (CO)
0.0056
51.03
PCB-activated carbon
295
0.392 (CO2)
0.0227
37.42
PCB-activated carbon
295
0.335 (H2S)
0.0479
13.60
[54]
Activated carbon
293.15
0.102 (CO)
9.075
×
10
6
20
Activated carbon
293.15
0.080 (CH4)
1.812
×
10
7
18
Activated carbon
293.15
0.308 (CO2)
3.356
×
10
7
10
Activated carbon
293.15
0.014 (N2)
1.657
×
10
7
15
Zeolite 5A
293.15
0.049 (CO)
2.727
×
10
7
17
Zeolite 5A
293.15
0.030 (CH4)
2.386
×
10
7
18
Zeolite 5A
293.15
0.202 (CO2)
3.197
×
10
4
17
Zeolite 5A
293.15
0.238 (N2)
1.055
×
10
7
20
[55]
AC5-KS
303
0.147 (CO)
1.428
×
10
9
—
AC5-KS
303
0.582 (CO2)
3.937
×
10
9
—
AC5-KS
303
0.0116 (N2)
9.797
×
10
8
—
AC5-KS
303
0.0973 (CH4)
2.986
×
10
9
—
[56]
CuBTC (KRICT)
303
0.022 (N2)
0.0386
7
CuBTC (KRICT)
303
0.019 (CO)
0.2443
1
CuBTC (KRICT)
308
0.444 (CO2)
0.2963
7
CuBTC (KRICT)
308
0.056 (CH4)
0.0861
7
CuBTC (KRICT)
343
0.014 (N2)
0.0216
7
CuBTC (KRICT)
343
0.008 (CO)
0.0901
1
CuBTC (KRICT)
343
0.290 (CO2)
0.1185
7
CuBTC (KRICT)
343
0.036 (CH4)
0.0657
7
CuBTC (KRICT)
373
0.009 (N2)
0.0152
7
CuBTC (KRICT)
373
0.042 (CO)
0.0491
1
CuBTC (KRICT)
373
0.187 (CO2)
0.0619
7
CuBTC (KRICT)
373
0.024 (CH4)
0.0410
7
[57]
Cu-BTC
303
0.125 (CO)
2.4433
—
Cu-BTC
303
0.660 (CO2)
0.3437
—
Cu-BTC
303
0.104 (N2)
0.0386
—
Cu-BTC
303
0.116 (CH4)
0.1416
—
[58]
Zeolite 5A
303
0.064 (CO)
0.2363
10
Zeolite 5A
303
0.034 (CH4)
0.2003
10
[59]
TDA AMS-19
453.15
0.268 (CO2)
4.634
×
10
−
8
41
TDA AMS-19
513.15
0.198 (CO2)
4.349
×
10
−
8
18
TDA AMS-19
573.15
0.158 (CO2)
4.135
×
10
−
8
18
[60]
BPL 4X10 activated carbon
293.15
0.311 (CO2)
0.4
12
[61]
MG50
623.15
0.085 (CO2)
64.8
—
[62]
MG50
523.15
0.043 (CO2)
7.8
×
10
−
5
1
MG50
623.15
0.034 (CO2)
7.3
×
10
−
5
1
MG50
723.15
0.032 (CO2)
5.0
×
10
−
5
1
[63]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673.15
0.019 (CO2)
37.4
1
[64]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.027 (CO2)
16.9
0.45
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.022 (CO2)
17.0
0.58
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673
0.028 (CO2)
23.6
0.19
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
753
0.025 (CO2)
19.3
0.19
[65]
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
673.15
0.011 (CO2)
37.4
3
K
2
C
O
3
/
Mg
3
AI
−
C
O
3
793.15
0.011 (CO2)
21.2
3
[18]
K-MG30
723.15
0.028 (CO2)
—
10.85
K-MG30
673.15
0.022 (CO2)
—
10.85
K-MG30
623.15
0.015 (CO2)
—
10.85
K-MG30
573.15
0.009 (CO2)
—
10.85
[2]
CuBTC-OMC (MOF-composite)
298.15
0.191 (CO2)
—
1
CuBTC/GO (MOF-composite)
295
0.135 (CO2)
—
1.1
CuBTC@MWCNT (MOF-composite)
298.15
0.149 (CO2)
—
1
Cu3(BTC)2 (MOF-composite)
298.15
0.595 (CO2)
—
18
CG-9 (CuBTC-GO-9) (MOF-composite)
273
0.363 (CO2)
—
1Table8 shows different types of adsorbents, however, the most outstanding are CMS-T3A, PCB-activated carbon, and activated carbon. These adsorbents show selectivity over a variety of compounds (N2, O2, Ar, CO, CO2, CH4, and H2S) and have higher adsorption compared to other natural and synthetic adsorbents. One difference between these three defined adsorbents is the adsorption capacity from temperature change.


## 4.2. Mathematical Models, Characteristics, and Configuration of the PSA Process for the Production of Biohydrogen

To ensure a continuous separation process, multiple columns are required (see Table9). H2 purification is done with the PSA process, using an adsorption pressure of 500 to 4000 kPa and for the purge step, only 100 kPa is used. A temperature of 295 K is contemplated in the production and regeneration stages. For the production and purification of biohydrogen, a minimum of 4 columns is used (see Figure 6).Table 9
Works reported on the different configurations of PSA processes for purification of biohydrogen.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Hydrogen feed (% molar fraction)
[55]
Simulated
2 beds
500 to 50
5
79
10 steps
[67]
Simulated
10 beds
(1300-1200) to 20
—
62.57
5 steps
[56]
Experimental
2 beds
350 to 100
7.5
67, 68, 78, and 81
4 steps
[57]
Experimental
2 beds
350 to 100
5.8
67, 68, and 78
4 steps
[58]
Simulated
6 beds
1100 to 100
6.6
70
9 and 12 steps
[68]
Experimental
4 beds
(1400-1600) to (131-50)
—
55
8 steps
[59]
Simulated
4, 6, 8, and 10 beds
(3450-1730) to 100
4.6
15
4, 6, 8, and 10 steps
[60]
Simulated
4 beds
1600 to 100
—
25, 50, and 75
7 steps
[69]
Experimental
2 beds
(1000-4000) to 100
0.8
50
5 steps
[70]
Experimental
8 beds
3500 to 100
4
88.75
12 steps
[71]
Experimental
2 and 4 beds
(3000-3500) to 110
5 and 6.3
88
6 and 10 stepsFigure 6
Schematic diagram of the PSA process using 4-beds, 9-steps.Different types of structures and configurations have been studied with respect to the PSA process, one of them presented a study of the performance of the PSA process using multiple beds to produce high purity biohydrogen from synthesis gas H2: 72.2%, CH4: 4.17%, CO: 2.03%, CO2: 21.6%). In the study of Yang et al. [66], it was an experimental and theoretical work, as a result, they obtained purity of 99.999% of biohydrogen and recovery of 66% of the synthesis gas, with an oscillating pressure of 100 to 800 kPa and ambient temperature.Table9 shows the different configurations presented by the PSA processes for the production of biohydrogen.It can be seen in Table9 that more beds are used compared to bioethanol production, likewise, the number of steps is greater and the pressure values are high with oscillations between 1000 and 10000 kPa. To do the purge, it is only necessary to handle an atmospheric pressure and it is not necessary to use a vacuum pressure.In the study of Liemberger et al. and Yang et al. [50, 66], they showed that the recovery of hydrogen increases when the linear speed and the adsorption time increase, however, the purity of the hydrogen decreases. On the other hand, the 4-bed 9-step PSA process could be optimally operated at a linear speed of 3 cms-1, adsorption time of 50 s, and a pressure of 200 kPa in the purge step (see Figure 7).Figure 7
Purification and production of biohydrogen from the start-up.Table10 shows the modeling characteristics that describe the PSA process for biohydrogen production and shows that the number of PDEs can vary, depending on the considerations to obtain a less complex model. In some works, the results and profiles of pressure and temperature are considered, and in others only one of these variables that are a function of time and space.Table 10
Distributed parameter models of the PSA processes for biohydrogen production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[71]
6 PDEs
Consider adsorption isotherms
Consider pressure gradient
[68]
4 PDEs
Consider adsorption isotherms
No pressure gradient
[58]
3 PDEs
Does not present adsorption isotherms
No pressure gradient
[57]
4 PDEs
Does not present adsorption isotherms
Consider pressure gradient
[56]
5 PDEs
Consider adsorption isotherms
Consider pressure gradient
[55]
6 PDEs
Does not present adsorption isotherms
Consider pressure gradientThe base mathematical model that was taken from the works of Lee et al. and Xiao et al. [42, 43] (see Table 11). A semicomplete model is proposed since it does not contemplate the part of the equations of the wall and a general balance. It uses four steps to complete one cycle of the PSA process.Table 11
Governing equations and simplifications for production and purification of biohydrogen.
Mass balance equation
−
D
L
∂
2
c
i
∂
z
2
+
∂
U
z
c
i
∂
z
+
∂
c
i
∂
t
+
1
−
ϵ
b
ϵ
b
ρ
p
∂
n
i
∂
t
=
0
Energy balance equation
K
L
∂
2
T
∂
z
2
+
ϵ
b
c
C
pg
+
1
−
ϵ
b
ρ
p
C
ps
∂
T
∂
t
−
ϵ
b
c
C
pg
U
z
∂
T
∂
z
=
1
−
ϵ
b
ρ
p
∑
j
=
1
N
Δ
H
j
∂
n
j
∂
t
+
2
h
in
R
in
T
w
−
T
Ergun equation for momentum balance
−
∂
P
∂
z
=
150
μ
V
z
1
−
ϵ
b
2
4
R
p
2
ϵ
b
3
+
1.75
ρ
g
1
−
ϵ
b
2
R
p
ϵ
b
3
v
g
2
Adsorption isotherms and kinetics
n
i
∗
=
n
i
s
b
i
P
i
/
1
+
∑
j
=
1
N
b
j
P
j
∂
n
i
/
∂
t
=
k
i
n
i
∗
−
n
i
,
i
=
1
,
⋯
,
N
Boundary and initial conditions
I. Adsorption
(i)t=0
c
H
2
z
,
0
=
c
0
,
c
CO
z
,
0
=
0
,
c
CH
4
z
,
0
=
0
,
c
CO
2
z
,
0
=
0
T
z
,
0
=
T
0
,
T
w
z
,
0
=
T
0
,
p
z
,
0
=
p
0
,
η
i
z
,
0
=
η
i
∗
(ii)z=0
−
D
L
∂
c
i
/
∂
z
=
u
c
i
0
−
,
t
−
c
i
0
+
,
t
,
p
=
p
0
,
U
z
=
U
zo
−
K
L
∂
T
/
∂
t
=
ε
b
c
C
pg
U
z
T
0
−
,
t
−
T
0
+
,
t
(iii)z=L
−
D
L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
−
K
L
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
II. Depressurization
(i)t=0
c
H
2
z
,
0
=
c
0
I
,
c
CO
z
,
0
=
c
CO
I
,
c
CH
4
z
,
0
=
c
CH
4
I
,
c
CO
2
z
,
0
=
c
CO
2
I
T
z
,
0
=
T
I
,
T
w
z
,
0
=
T
I
,
p
z
,
0
=
p
I
,
η
i
z
,
0
=
η
i
I
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
,
F
=
F
valve
III. Purge
(i)t=0
c
H
2
z
,
0
=
c
0
II
,
c
CO
z
,
0
=
c
CO
II
,
c
CH
4
z
,
0
=
c
CH
4
II
,
c
CO
2
z
,
0
=
c
CO
2
II
T
z
,
0
=
T
II
,
T
w
z
,
0
=
T
II
,
p
z
,
0
=
p
II
,
η
i
z
,
0
=
η
i
II
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
F
=
F
valve
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0
IV. Pressurization
(i)t=0
c
H
2
z
,
0
=
c
0
III
,
c
CO
z
,
0
=
c
CO
III
,
c
CH
4
z
,
0
=
c
CH
4
III
,
c
CO
2
z
,
0
=
c
CO
2
III
T
z
,
0
=
T
III
,
T
w
z
,
0
=
T
III
,
p
z
,
0
=
p
III
,
η
i
z
,
0
=
η
i
III
∗
(ii)z=0
∂
c
i
/
∂
z
=
0
,
∂
p
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
F
=
F
valve
(iii)z=L
∂
c
i
/
∂
z
=
0
,
∂
U
z
/
∂
z
=
0
,
∂
T
/
∂
t
=
0
,
∂
p
/
∂
z
=
0The initial and boundary conditions are contemplated in Table11, the mathematical model finds solutions of Y, c, T, and P as a function of time and space.


## 4.3. Parametric Study of the PSA Process for the Production of Biohydrogen

The base model of the works of Lee et al. and Xiao et al. [42, 43] was used. The parameters of this PSA process for the production and purification of biohydrogen are shown in Table 12.Table 12
Start-up parameters of the PSA process for the purification and production of biohydrogen.
FEED
Flow
0.162
kmolkmol-1
CO
0.02
kmolkmol-1
CO2
0.26
kmolkmol-1
Hydrogen
0.69
kmolkmol-1
Methane
0.03
kmolkmol-1
Temperature
298.15
K
Production pressure
980
kPa
Purge pressure
100
kPa
SIZING
Bed height
1
m
Bed diameter
0.037
m
Zeolite type 5A particle radius
0.0015
m
Bulk solid density
850.0
kg m-3The results found from the start-up to reaching the CSS are shown in Figures6 and 8.Figure 8
Sensitivity analysis applied to the PSA process for the production of biohydrogen [72].
(a)
Temperature: 298.15 K to 283.24 K; Flow: 0.162 kmolh-1; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(b)
Temperature: 298.15 K to 313.05 K; Flow: 0.162 kmolh-1; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(c)
Flow: 0.162 kmolh-1 to 0.153 kmolh-1; Temperature: 298.15 K; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(d)
Flow: 0.162 kmolh-1 to 0.170 kmolh-1; Temperature: 298.15 K; Pressure: 980 kPa; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(e)
Pressure: 980 kPa to 931 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(f)
Pressure: 980 kPa to 1029 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K; Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4
(g)
Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2 and 0.03 CH4 to 0.6555 (H2), 0.2945 (CO2), 0.03 (CH4), and 0.02 CO; Pressure: 980 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 K
(h)
Molar fraction: 0.02 (CO), 0.26 (CO2), 0.69 H2, and 0.03 CH4 to 0.7245 (H2), 0.2255 (CO2), 0.03 (CH4), and 0.02 CO; Pressure: 980 kPa; Flow: 0.162 kmolh-1; Temperature: 298.15 KFigure6 shows how the purity of hydrogen increases and the purities of CO, CO2, and methane decreases; this is due to the selectivity of the adsorbent and the nominal star-up conditions shown in Table 12. The hydrogen profile goes up as the cycles pass until reaching the CSS and obtaining a purity of 95%. CSS is reached after 30 cycles (1.2 h).Figure8 shows the results obtained from variations of 0.5% on the input variables. In most cases (pressure, flow, and composition), the effects on hydrogen purity were negligible. However, the effect of the temperature variable presented important changes, defined as the main variable that can be used to control the purity of hydrogen. It is important to mention that this variable is limited in its small values since it cannot generate values less than 5° since this would generate energy costs due to the demand to use temperatures less than 0°.Table13 shows the detailed data of the results presented in Figure 8. It shows the cycle times, the purities, and the changes generated by each input variable.Table 13
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature (K)
Flow kmolh−1
Pressure kPa
Composition CO-CO2-hydrogen-methane
Purity % molar fraction of hydrogen
Number of cycles
1
298.15
0.162
980
0.02-0.26-0.69-0.03
94.85
30
2
283.24
0.162
980
0.02-0.26-0.69-0.03
98.01
2
3
313.05
0.162
980
0.02-0.26-0.69-0.03
90.02
2
4
298.15
0.153
980
0.02-0.26-0.69-0.03
94.95
1
5
298.15
0.170
980
0.02-0.26-0.69-0.03
94.75
1
6
298.15
0.162
931
0.02-0.26-0.69-0.03
95.00
1
7
298.15
0.162
1029
0.02-0.26-0.69-0.03
94.65
1
8
298.15
0.162
980
0.02-0.2945-0.6555-0.03
94.00
2
9
298.15
0.162
980
0.02-0.2255-0.7245-0.03
95.50
2


## 5. Medical Oxygen Purification by PSA

Medical oxygen is a mixture of gases that typically has an oxygen percentage equal to or greater than 93%, and is widely prescribed for mechanically ventilated patients in intensive care units [73]. The rest of the compounds of the mixture includes nitrogen and argon, and contain 0.03% CO2 or 0.001% CO [74]. To achieve that percentage of oxygen, PSA processes are necessary. In them, air from the environment is subjected to filtration and compression stages before passing through a bed of zeolites. The adsorption of the molecules will depend on the pressure and temperature; these zeolites have greater selectivity over nitrogen molecules than oxygen, thus resulting in the air with a higher proportion of oxygen.The last year has seen an increase in the demand for medical oxygen due to the pandemic generated by COVID-19. That is why it has ventured into the development of portable technologies that generate oxygen, having a resource that provides oxygen supply for anoxic environments, due to its profitability, operating flexibility, and oxygen purification. It may be used in chemical processing, fishing farms, medical applications, combustion enhancement, oxyfuel cutting operations in metal fabrication, bleaching in the paper industry, wastewater treatment, fuel cells, etc. [75, 76]. One of the technological alternatives to purify and produce medical oxygen is the adsorption process with molecular sieves using the pressure swing adsorption method. The PSA can be operated with a pressure range from 1 to 1000 kPa and room temperature for small-scale oxygen production with high purity between 90%, 95%, and 99%. In general, the separation of the air is carried out at relatively high pressure and the nitrogen molecules are retained on the natural or synthetic zeolites [77, 78].


### 5.1. Adsorption and Separation for the O2, N2, and Ar with Different Adsorbents

In the case of the nitrogen and oxygen separation isotherms, it was determined by the energetic homogeneity of the surface of the adsorbents. The isotherms for this type of separation are concave towards the axis of relative pressure or concentrations (see Figure2), so it is assumed that they correspond to the type I isotherms, which are for adsorption of gases in microporous solids.For this separation of compounds, there are different types of adsorbents; these can be Ca-X, CMS, LiX, 5A or 13X, NaX, or LiLSX. However, the concentration of the product is limited to 95% oxygen, because of the presence of argon in air, since these adsorbents present similar adsorption capacities for oxygen and argon.For this reason, there are several adsorbents that can be used to adsorb and separate oxygen from argon. Some natural and synthetic zeolites are also identified in the following Table14.Table 14
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
Temperature K
Maximum adsorption capacity Qggads−1
Langmuir constant (bar-1)
Pressure Atm
[79]
5A
273
0.063 (N2)
0.073
1.97-5.9
5A
293
0.049 (N2)
0.073
1.97-5.9
5A
313
0.040 (N2)
1.214
1.97-5.9
5A
333
0.035 (N2)
1.214
1.97-5.9
[80]
CMS
283
0.07 (N2)
20.5
7.8
CMS
298
0.0588 (N2)
15.6
7.8
CMS
308
0.0532 (N2)
10.7
7.8
[81]
CMS
297
0.8430 (N2)
4.663
×
10
4
4-6
CMS
297
0.4430 (Ar)
714.904
4-6
CMS
296
0.85 (N2)
4.741
×
10
4
4-6
CMS
296
0.5107 (N2)
717.548
4-6
[82]
5A
298.15
0.1484 (N2)
—
1.48-4.35
CMS
298.15
0.07392 (N2)
—
2.0-6.7
[77]
Li-LSX
288
0.0392 (N2)
0.8574
1
Li-LSX
298
0.0308 (N2)
0.8574
1
Li-LSX
308
0.0252 (N2)
0.8574
1
Na-LSX
288
0.014 (N2)
0.1037
1
Na-LSX
298
0.0112 (N2)
0.1037
1
Na-LSX
308
0.0084 (N2)
0.1037
1
K-LSX
288
0.0077 (N2)
0.00479
1
K-LSX
298
0.0056 (N2)
0.00479
1
K-LSX
308
0.00378 (v)
0.00479
1
[83]
5A
298.15
0.146 (N2)
2813.7
1
Li-ag-X
298.15
0.089 (N2)
28613.0
[84]
NaX
296.15
0.083 (N2)
8.319
×
10
−
5
1-1.4
[85]
Oxysiv 5
293.15
0.0865 (N2)
0.1006
3-4
Oxysiv 5
293.15
0.123 (Ar)
0.03365
3-4
AgLiLSX
293.15
0.0738 (N2)
0.2581
3-4
AgLiLSX
293.15
0.2900 (Ar)
0.0230
3-4
[86]
Mordenite
303.15
0.0532 (N2)
—
3
A
303.15
0.0252 (N2)
—
2.5
X
303.15
0.0259 (N2)
—
3.5
[87]
LiLSX
289.15
0.0602 (N2)
2.418
×
10
−
6
1
[78]
LiLSX (Zeochem)
273.1
0.07 (N2)
2.587
×
10
−
5
1
LiLSX (Zeochem)
303.1
0.0476 (N2)
2.585
×
10
−
5
1
LiLSX (Zeochem)
338.1
0.035 (N2)
2.577
×
10
−
5
1
LiLSX (Arkema)
273.1
0.063 (N2)
3.446
×
10
−
5
1
LiLSX (Arkema)
303.1
0.0434 (N2)
3.406
×
10
−
5
1
LiLSX (Arkema)
338.1
0.0308 (N2)
3.366
×
10
−
5
1
[88]
LSCF1991
773.15
0.0168 (N2)
0.0693
1
LSCF1991
873.15
0.014 (N2)
0.0854
1
LSCF1991
973.15
0.0112 (N2)
0.1001
1
LSCF1991
1073.15
0.0105 (N2)
0.1082
1
[89]
LiX
288.15
0.042 (N2)
9.50
×
10
−
6
3.5
LiX
303.15
0.035 (N2)
9.39
×
10
−
6
3.5Table14 shows varieties of adsorbents with different adsorption capacities on the selective compounds. It will be observed that at lower temperatures, adsorbents tend to adsorb more molecules or atoms. It can be seen that zeolite type 5A and CMS have higher adsorption capacity compared to the other adsorbents. Likewise, it observes that the ranges in which the PSA process works for the production of medical oxygen range from 1 to 4 bar, which are lower compared to the other PSA processes for the production of bioethanol and biohydrogen.The basic PSA process may be using only one bed, however up to two or three beds may be implemented. These adsorbent-packed columns can release heat energy in the adsorption step and adsorb it in the regeneration step. In this case, the PSA process for the production of medical oxygen does not contemplate very high pressures since it uses the heat produced to improve the regeneration capacity.For the production of medical oxygen using the PSA process, there is a great variety of structures and configurations, but there is one in particular for the separation of oxygen, which is the Rapid Pressure Swing Adsorption (RPSA), this type of configuration has been shown in several works. Related to the production of medical oxygen and above 99% in purity, the times contemplated by this configuration are very short with very small columns. Table15 shows the different works that exist.Table 15
Works reported on the different configurations of PSA processes for purification of medical oxygen.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Oxygen feed (% molar fraction)
[83]
Experimental
1 bed4 steps
400 to 100
0.016
21
[90]
Simulated
2 beds5 steps
100 to 90
—
21
[91]
Simulated
4 beds7 steps
300 to 50
1.3
22
[79]
Experimental
2 beds6 steps
150 to 50
—
50
[75]
Simulated
6 beds9 steps
1000 to 100
—
21
[92]
Experimental
2 beds6 steps
355 to 101
0.33
90
[93]
Simulated
2 beds5 steps
150 to 100
0.1 to 2.1
—
[94]
Simulated
2 beds4 steps
250 to 75
0.666
20.8
[95]
Experimental
2 beds3 steps
250 to 100
0.166
21
[96]
Simulated
1 beds4 steps
—
0.083
20 to 50
[97]
Experimental
4 and 6 beds5 steps
250 to 101
0.5, 0.8, and 1
—The scheme of the PSA process for the production of medical oxygen is shown in Figure9. Two stainless steel columns with a length of 1 m are presented. Temperature sensors (RTD and PT 100) are provided along the column, providing data from the feed end to the top. Two pressure transducers placed on the flanges, the feed flow to the columns is controlled with a tank and regulating valve, concentration variations in the stages are analyzed with oxygen sensors.Figure 9
Schematic diagram of the PSA process using 2-beds, 6-steps.A wide variety of works that have developed numerical calculations with different simplifications or considerations applied to PSA processes for medical oxygen production.Numerical methods techniques have been used to obtain an approximate solution of the PDEs that represent the complex model of the PSA process. Table16 shows the different works that implement certain conditions to simplify the PSA mathematical model.Table 16
Distributed parameter models of the PSA processes for medical oxygen production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[98]
4 PDEs
Does not present adsorption isotherms
Consider pressure gradient
[87]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[94]
5 PDEs
Consider adsorption isotherms
Consider pressure gradient
[77]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[88]
4 PDEs
Consider adsorption isotherms
Consider pressure gradientThe PSA process model used in this section is shown in Table17. An energy balance equation is included, establishing that the temperatures in the solid and gas are constant and equal. The pressure drop is represented using the Ergun equation; Langmuir model was used to describe the adsorption isotherm. Mass transfer is represented using a linear driving force model based on solid charge. These equations represented by PDEs contemplate their initial and boundary conditions to obtain a solution in each step of the PSA process for medical oxygen production.Table 17
Governing equations and simplifications for production and purification of medical oxygen.
Overall mass balances
−
D
l
∂
C
i
/
∂
z
2
+
∂
u
c
i
/
∂
z
+
∂
c
i
/
∂
t
+
ρ
p
1
−
ε
/
ε
∂
¯
q
i
/
∂
t
=
0
Energy balance equation
−
K
L
∂
2
T
∂
z
2
+
ε
ρ
g
C
pg
∂
u
T
∂
z
+
ε
t
ρ
g
C
pg
+
ρ
B
C
ps
∂
T
∂
t
−
ρ
B
∑
i
=
1
n
−
¯
Δ
H
∂
¯
q
i
∂
t
+
2
h
i
R
B
i
T
−
T
W
=
0
Pressure drop
−
dP
dz
=
a
μ
u
+
b
ρ
u
u
,,
a
=
150
4
R
p
2
1
−
ε
2
ε
2
,
,
b
=
1.75
1
−
ε
2
2
R
p
ε
Multicomponent adsorption equilibrium
q
i
=
q
mi
B
i
P
i
ni
1
+
∑
j
=
1
n
B
j
P
j
nj
LDF model
∂
¯
q
i
/
∂
t
=
w
i
q
i
∗
−
q
¯
i
,,
w
i
=
K
D
ei
/
R
p
2
Boundary and initial conditions
I. Pressurization
(i)t=0
c
i
Z
,
0
=
0
,
q
¯
i
Z
,
0
=
0
,
T
i
=
Z
,
0
=
T
0
,
P
i
Z
,
0
=
P
p
(ii)z=0
−
∂
c
i
∂
Z
=
P
e
m
U
C
i
z
=
0
−
C
i
z
=
0
+
1
,
q
¯
i
0
,
t
=
0
,
T
i
=
0
,
1
=
T
0
,
P
i
0
,
t
=
P
p
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
II. Adsorption
(i)t=0
c
i
Z
,
0
=
c
i
I
,
q
¯
i
Z
,
0
=
q
i
I
,
T
i
=
Z
,
0
=
T
i
I
,
P
i
Z
,
0
=
P
i
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
III. First blowdown
(i)t=0
c
i
Z
,
0
=
c
i
I
I
,
q
¯
i
Z
,
0
=
q
i
I
I
,
T
i
=
Z
,
0
=
T
i
I
I
,
P
i
Z
,
0
=
P
i
I
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
IV. Second blowdown
(i)t=0
c
i
Z
,
0
=
c
i
I
I
I
,
q
¯
i
Z
,
0
=
q
i
I
I
I
,
T
i
=
Z
,
0
=
T
i
I
I
I
,
P
i
Z
,
0
=
P
i
I
I
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
V. Purge
(i)t=0
c
i
Z
,
0
=
c
i
I
V
,
q
¯
i
Z
,
0
=
q
i
I
V
,
T
i
=
Z
,
0
=
T
i
I
V
,
P
i
Z
,
0
=
P
i
I
V
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
/
∂
Z
=
0
,
∂
T
i
/
∂
Z
=
0
,
∂
P
i
/
∂
Z
=
0The works of Todd et al. and Webley and He [84, 99] were contemplated to structure the PSA model for medical oxygen production, this is shown in Table 17.


### 5.2. Parametric Study of the PSA Process for the Production of Medical Oxygen

Table18 shows the parameters with which the process begins until reaching the CSS and obtaining a purity of medical oxygen of 95.00%.Table 18
Start-up parameters of the PSA process for the purification and production of medical oxygen.
FEED
Flow
0.894
kmolh-1
Nitrogen
0.78
kmolkmol-1
Oxygen
0.22
kmolkmol-1
Temperature
296.15
K
Production pressure
150
kPa
Purge pressure
20
kPa
SIZING
Bed height
1.8
m
Bed diameter
0.11
m
NaX zeolite
Particle radius
0.000985
m
Bulk solid density
911.72
Kg m−3The results found from the start-up to reaching the CSS are shown in Figures10 and 11.Figure 10
Purification and production of medical oxygen from the start-up.Figure 11
Sensitivity analysis applied to the PSA process for the production of medical oxygen.
(a)
Temperature: 296.15 K to 281.34 K; Flow: 0.89436528 kmolh-1; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(b)
Temperature: 296.15 K to 310.95 K; Flow: 0.89436528 kmolh-1; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(c)
Flow: 0.89436528 kmolh-1 to 0.849647016 kmolh-1 Temperature: 296.15 K; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(d)
Flow: 0.89436528 kmolh-1 to 0.939083544 kmolh-1 Temperature: 296.15 K; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(e)
Pressure: 150 kPa to 142.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K; Molar fraction: 0.78 (N2) and 0.22 (O2)
(f)
Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K; Molar fraction: 0.78 (N2) and 0.22 (O2)
(g)
Molar fraction: 0.78 (N2) and 0.22 (O2). to 0.741 (N2) and 0.259 (O2); Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K
(h)
Molar fraction: 0.78 (N2) and 0.22 (O2). to 0.819 (N2) and 0.181 (O2); Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 KFigure10 shows the oxygen and nitrogen profiles. Between cycles 3 and 4, the molar fraction of oxygen experiences a drop, this is due to the fact that both beds start with atmospheric pressure, and this continues until the beds stabilize with the appropriate pressure of 150 kPa. Subsequently, the mole fraction of oxygen begins to rise, and that of nitrogen falls. These continue until reaching the CSS, which is fulfilled at 23 cycles, obtaining a medical oxygen purity of 95.00%.Table19 and Figure 11 show the changes made to the input variables and the results obtained on oxygen purity. The variation that was made while in the CSS was 0.5%.Table 19
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature (K)
Flow kmolh-1
Pressure kPa
Composition nitrogen-oxygen
Purity % molar fraction of oxygen
Number of cycles
1
296.15
0.89436528
150
0.78-0.22
95.00
40
2
281.34
0.89436528
150
0.78-0.22
94.90
16
3
310.95
0.89436528
150
0.78-0.22
94.90
16
4
296.15
0.849647016
150
0.78-0.22
95.20
14
5
296.15
0.939083544
150
0.78-0.22
94.80
15
6
296.15
0.89436528
142.5
0.78-0.22
95.30
12
7
296.15
0.89436528
157.5
0.78-0.22
94.60
11
8
296.15
0.89436528
150
0.741-0.259
95.40
9
9
296.15
0.89436528
150
0.819-0.181
94.00
10The results shown in Figure11 demonstrate that all input variables have an effect on oxygen purity. However, the most outstanding variables are feed pressure and composition. A differentiator between these two variables is the purity is obtained. It is observed that by varying the feed composition, higher oxygen purity can be achieved with a shorter cycle time compared to that shown by the pressure variable. It is of great importance to be able to manipulate this variable since it can cause the purity to drop during the production and purification of medical oxygen.Table19 shows the detailed data of the results presented in Figure 8. It shows the cycle times, the purities, and the changes generated by each input variable.


## 5.1. Adsorption and Separation for the O2, N2, and Ar with Different Adsorbents

In the case of the nitrogen and oxygen separation isotherms, it was determined by the energetic homogeneity of the surface of the adsorbents. The isotherms for this type of separation are concave towards the axis of relative pressure or concentrations (see Figure2), so it is assumed that they correspond to the type I isotherms, which are for adsorption of gases in microporous solids.For this separation of compounds, there are different types of adsorbents; these can be Ca-X, CMS, LiX, 5A or 13X, NaX, or LiLSX. However, the concentration of the product is limited to 95% oxygen, because of the presence of argon in air, since these adsorbents present similar adsorption capacities for oxygen and argon.For this reason, there are several adsorbents that can be used to adsorb and separate oxygen from argon. Some natural and synthetic zeolites are also identified in the following Table14.Table 14
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
Temperature K
Maximum adsorption capacity Qggads−1
Langmuir constant (bar-1)
Pressure Atm
[79]
5A
273
0.063 (N2)
0.073
1.97-5.9
5A
293
0.049 (N2)
0.073
1.97-5.9
5A
313
0.040 (N2)
1.214
1.97-5.9
5A
333
0.035 (N2)
1.214
1.97-5.9
[80]
CMS
283
0.07 (N2)
20.5
7.8
CMS
298
0.0588 (N2)
15.6
7.8
CMS
308
0.0532 (N2)
10.7
7.8
[81]
CMS
297
0.8430 (N2)
4.663
×
10
4
4-6
CMS
297
0.4430 (Ar)
714.904
4-6
CMS
296
0.85 (N2)
4.741
×
10
4
4-6
CMS
296
0.5107 (N2)
717.548
4-6
[82]
5A
298.15
0.1484 (N2)
—
1.48-4.35
CMS
298.15
0.07392 (N2)
—
2.0-6.7
[77]
Li-LSX
288
0.0392 (N2)
0.8574
1
Li-LSX
298
0.0308 (N2)
0.8574
1
Li-LSX
308
0.0252 (N2)
0.8574
1
Na-LSX
288
0.014 (N2)
0.1037
1
Na-LSX
298
0.0112 (N2)
0.1037
1
Na-LSX
308
0.0084 (N2)
0.1037
1
K-LSX
288
0.0077 (N2)
0.00479
1
K-LSX
298
0.0056 (N2)
0.00479
1
K-LSX
308
0.00378 (v)
0.00479
1
[83]
5A
298.15
0.146 (N2)
2813.7
1
Li-ag-X
298.15
0.089 (N2)
28613.0
[84]
NaX
296.15
0.083 (N2)
8.319
×
10
−
5
1-1.4
[85]
Oxysiv 5
293.15
0.0865 (N2)
0.1006
3-4
Oxysiv 5
293.15
0.123 (Ar)
0.03365
3-4
AgLiLSX
293.15
0.0738 (N2)
0.2581
3-4
AgLiLSX
293.15
0.2900 (Ar)
0.0230
3-4
[86]
Mordenite
303.15
0.0532 (N2)
—
3
A
303.15
0.0252 (N2)
—
2.5
X
303.15
0.0259 (N2)
—
3.5
[87]
LiLSX
289.15
0.0602 (N2)
2.418
×
10
−
6
1
[78]
LiLSX (Zeochem)
273.1
0.07 (N2)
2.587
×
10
−
5
1
LiLSX (Zeochem)
303.1
0.0476 (N2)
2.585
×
10
−
5
1
LiLSX (Zeochem)
338.1
0.035 (N2)
2.577
×
10
−
5
1
LiLSX (Arkema)
273.1
0.063 (N2)
3.446
×
10
−
5
1
LiLSX (Arkema)
303.1
0.0434 (N2)
3.406
×
10
−
5
1
LiLSX (Arkema)
338.1
0.0308 (N2)
3.366
×
10
−
5
1
[88]
LSCF1991
773.15
0.0168 (N2)
0.0693
1
LSCF1991
873.15
0.014 (N2)
0.0854
1
LSCF1991
973.15
0.0112 (N2)
0.1001
1
LSCF1991
1073.15
0.0105 (N2)
0.1082
1
[89]
LiX
288.15
0.042 (N2)
9.50
×
10
−
6
3.5
LiX
303.15
0.035 (N2)
9.39
×
10
−
6
3.5Table14 shows varieties of adsorbents with different adsorption capacities on the selective compounds. It will be observed that at lower temperatures, adsorbents tend to adsorb more molecules or atoms. It can be seen that zeolite type 5A and CMS have higher adsorption capacity compared to the other adsorbents. Likewise, it observes that the ranges in which the PSA process works for the production of medical oxygen range from 1 to 4 bar, which are lower compared to the other PSA processes for the production of bioethanol and biohydrogen.The basic PSA process may be using only one bed, however up to two or three beds may be implemented. These adsorbent-packed columns can release heat energy in the adsorption step and adsorb it in the regeneration step. In this case, the PSA process for the production of medical oxygen does not contemplate very high pressures since it uses the heat produced to improve the regeneration capacity.For the production of medical oxygen using the PSA process, there is a great variety of structures and configurations, but there is one in particular for the separation of oxygen, which is the Rapid Pressure Swing Adsorption (RPSA), this type of configuration has been shown in several works. Related to the production of medical oxygen and above 99% in purity, the times contemplated by this configuration are very short with very small columns. Table15 shows the different works that exist.Table 15
Works reported on the different configurations of PSA processes for purification of medical oxygen.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Oxygen feed (% molar fraction)
[83]
Experimental
1 bed4 steps
400 to 100
0.016
21
[90]
Simulated
2 beds5 steps
100 to 90
—
21
[91]
Simulated
4 beds7 steps
300 to 50
1.3
22
[79]
Experimental
2 beds6 steps
150 to 50
—
50
[75]
Simulated
6 beds9 steps
1000 to 100
—
21
[92]
Experimental
2 beds6 steps
355 to 101
0.33
90
[93]
Simulated
2 beds5 steps
150 to 100
0.1 to 2.1
—
[94]
Simulated
2 beds4 steps
250 to 75
0.666
20.8
[95]
Experimental
2 beds3 steps
250 to 100
0.166
21
[96]
Simulated
1 beds4 steps
—
0.083
20 to 50
[97]
Experimental
4 and 6 beds5 steps
250 to 101
0.5, 0.8, and 1
—The scheme of the PSA process for the production of medical oxygen is shown in Figure9. Two stainless steel columns with a length of 1 m are presented. Temperature sensors (RTD and PT 100) are provided along the column, providing data from the feed end to the top. Two pressure transducers placed on the flanges, the feed flow to the columns is controlled with a tank and regulating valve, concentration variations in the stages are analyzed with oxygen sensors.Figure 9
Schematic diagram of the PSA process using 2-beds, 6-steps.A wide variety of works that have developed numerical calculations with different simplifications or considerations applied to PSA processes for medical oxygen production.Numerical methods techniques have been used to obtain an approximate solution of the PDEs that represent the complex model of the PSA process. Table16 shows the different works that implement certain conditions to simplify the PSA mathematical model.Table 16
Distributed parameter models of the PSA processes for medical oxygen production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[98]
4 PDEs
Does not present adsorption isotherms
Consider pressure gradient
[87]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[94]
5 PDEs
Consider adsorption isotherms
Consider pressure gradient
[77]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[88]
4 PDEs
Consider adsorption isotherms
Consider pressure gradientThe PSA process model used in this section is shown in Table17. An energy balance equation is included, establishing that the temperatures in the solid and gas are constant and equal. The pressure drop is represented using the Ergun equation; Langmuir model was used to describe the adsorption isotherm. Mass transfer is represented using a linear driving force model based on solid charge. These equations represented by PDEs contemplate their initial and boundary conditions to obtain a solution in each step of the PSA process for medical oxygen production.Table 17
Governing equations and simplifications for production and purification of medical oxygen.
Overall mass balances
−
D
l
∂
C
i
/
∂
z
2
+
∂
u
c
i
/
∂
z
+
∂
c
i
/
∂
t
+
ρ
p
1
−
ε
/
ε
∂
¯
q
i
/
∂
t
=
0
Energy balance equation
−
K
L
∂
2
T
∂
z
2
+
ε
ρ
g
C
pg
∂
u
T
∂
z
+
ε
t
ρ
g
C
pg
+
ρ
B
C
ps
∂
T
∂
t
−
ρ
B
∑
i
=
1
n
−
¯
Δ
H
∂
¯
q
i
∂
t
+
2
h
i
R
B
i
T
−
T
W
=
0
Pressure drop
−
dP
dz
=
a
μ
u
+
b
ρ
u
u
,,
a
=
150
4
R
p
2
1
−
ε
2
ε
2
,
,
b
=
1.75
1
−
ε
2
2
R
p
ε
Multicomponent adsorption equilibrium
q
i
=
q
mi
B
i
P
i
ni
1
+
∑
j
=
1
n
B
j
P
j
nj
LDF model
∂
¯
q
i
/
∂
t
=
w
i
q
i
∗
−
q
¯
i
,,
w
i
=
K
D
ei
/
R
p
2
Boundary and initial conditions
I. Pressurization
(i)t=0
c
i
Z
,
0
=
0
,
q
¯
i
Z
,
0
=
0
,
T
i
=
Z
,
0
=
T
0
,
P
i
Z
,
0
=
P
p
(ii)z=0
−
∂
c
i
∂
Z
=
P
e
m
U
C
i
z
=
0
−
C
i
z
=
0
+
1
,
q
¯
i
0
,
t
=
0
,
T
i
=
0
,
1
=
T
0
,
P
i
0
,
t
=
P
p
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
II. Adsorption
(i)t=0
c
i
Z
,
0
=
c
i
I
,
q
¯
i
Z
,
0
=
q
i
I
,
T
i
=
Z
,
0
=
T
i
I
,
P
i
Z
,
0
=
P
i
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
III. First blowdown
(i)t=0
c
i
Z
,
0
=
c
i
I
I
,
q
¯
i
Z
,
0
=
q
i
I
I
,
T
i
=
Z
,
0
=
T
i
I
I
,
P
i
Z
,
0
=
P
i
I
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
IV. Second blowdown
(i)t=0
c
i
Z
,
0
=
c
i
I
I
I
,
q
¯
i
Z
,
0
=
q
i
I
I
I
,
T
i
=
Z
,
0
=
T
i
I
I
I
,
P
i
Z
,
0
=
P
i
I
I
I
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
V. Purge
(i)t=0
c
i
Z
,
0
=
c
i
I
V
,
q
¯
i
Z
,
0
=
q
i
I
V
,
T
i
=
Z
,
0
=
T
i
I
V
,
P
i
Z
,
0
=
P
i
I
V
(ii)z=0
∂
c
i
∂
Z
=
0
,
∂
T
i
∂
Z
=
0
,
∂
P
i
∂
Z
=
0
,
F
=
F
v
a
l
v
e
(iii)z=L
∂
c
i
/
∂
Z
=
0
,
∂
T
i
/
∂
Z
=
0
,
∂
P
i
/
∂
Z
=
0The works of Todd et al. and Webley and He [84, 99] were contemplated to structure the PSA model for medical oxygen production, this is shown in Table 17.


## 5.2. Parametric Study of the PSA Process for the Production of Medical Oxygen

Table18 shows the parameters with which the process begins until reaching the CSS and obtaining a purity of medical oxygen of 95.00%.Table 18
Start-up parameters of the PSA process for the purification and production of medical oxygen.
FEED
Flow
0.894
kmolh-1
Nitrogen
0.78
kmolkmol-1
Oxygen
0.22
kmolkmol-1
Temperature
296.15
K
Production pressure
150
kPa
Purge pressure
20
kPa
SIZING
Bed height
1.8
m
Bed diameter
0.11
m
NaX zeolite
Particle radius
0.000985
m
Bulk solid density
911.72
Kg m−3The results found from the start-up to reaching the CSS are shown in Figures10 and 11.Figure 10
Purification and production of medical oxygen from the start-up.Figure 11
Sensitivity analysis applied to the PSA process for the production of medical oxygen.
(a)
Temperature: 296.15 K to 281.34 K; Flow: 0.89436528 kmolh-1; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(b)
Temperature: 296.15 K to 310.95 K; Flow: 0.89436528 kmolh-1; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(c)
Flow: 0.89436528 kmolh-1 to 0.849647016 kmolh-1 Temperature: 296.15 K; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(d)
Flow: 0.89436528 kmolh-1 to 0.939083544 kmolh-1 Temperature: 296.15 K; Pressure: 150 kPa; Molar fraction: 0.78 (N2) and 0.22 (O2)
(e)
Pressure: 150 kPa to 142.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K; Molar fraction: 0.78 (N2) and 0.22 (O2)
(f)
Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K; Molar fraction: 0.78 (N2) and 0.22 (O2)
(g)
Molar fraction: 0.78 (N2) and 0.22 (O2). to 0.741 (N2) and 0.259 (O2); Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 K
(h)
Molar fraction: 0.78 (N2) and 0.22 (O2). to 0.819 (N2) and 0.181 (O2); Pressure: 150 kPa to 157.5 kPa; Flow: 0.89436528 kmolh-1; Temperature: 296.15 KFigure10 shows the oxygen and nitrogen profiles. Between cycles 3 and 4, the molar fraction of oxygen experiences a drop, this is due to the fact that both beds start with atmospheric pressure, and this continues until the beds stabilize with the appropriate pressure of 150 kPa. Subsequently, the mole fraction of oxygen begins to rise, and that of nitrogen falls. These continue until reaching the CSS, which is fulfilled at 23 cycles, obtaining a medical oxygen purity of 95.00%.Table19 and Figure 11 show the changes made to the input variables and the results obtained on oxygen purity. The variation that was made while in the CSS was 0.5%.Table 19
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature (K)
Flow kmolh-1
Pressure kPa
Composition nitrogen-oxygen
Purity % molar fraction of oxygen
Number of cycles
1
296.15
0.89436528
150
0.78-0.22
95.00
40
2
281.34
0.89436528
150
0.78-0.22
94.90
16
3
310.95
0.89436528
150
0.78-0.22
94.90
16
4
296.15
0.849647016
150
0.78-0.22
95.20
14
5
296.15
0.939083544
150
0.78-0.22
94.80
15
6
296.15
0.89436528
142.5
0.78-0.22
95.30
12
7
296.15
0.89436528
157.5
0.78-0.22
94.60
11
8
296.15
0.89436528
150
0.741-0.259
95.40
9
9
296.15
0.89436528
150
0.819-0.181
94.00
10The results shown in Figure11 demonstrate that all input variables have an effect on oxygen purity. However, the most outstanding variables are feed pressure and composition. A differentiator between these two variables is the purity is obtained. It is observed that by varying the feed composition, higher oxygen purity can be achieved with a shorter cycle time compared to that shown by the pressure variable. It is of great importance to be able to manipulate this variable since it can cause the purity to drop during the production and purification of medical oxygen.Table19 shows the detailed data of the results presented in Figure 8. It shows the cycle times, the purities, and the changes generated by each input variable.


## 6. Biomethane Purification by PSA

Biomethane is a gas generated from renewable resources, produced from organic matter (biomass, agricultural, industrial, urban waste, etc.). This has characteristics similar to natural gas and has great advantages over fossil fuels, which allow the reduction and dependency on external energy. This biogas can be applied in the market for the industry, domestic sector, and electricity generation. However, for this biogas to be used, it is necessary to separate it from the compound CO2 and contaminants such as H2S, which may be present in the gas with concentrations of CO2 35-50%, CH4 50-65%, H2S up to 4000 ppm, and siloxanes of 0-20 mgm3. There are several technologies to produce biomethane, some of them are chemical absorption, water washing, membranes, pressure swing adsorption, and cryogenic. However, PSA has better advantages compared to the technologies mentioned, which are lower energy demand, higher biomethane recovery, separation of other possible compounds present in the biogas (N2 and O2), and it does not need H2O.


### 6.1. Adsorption and Separation for the CH4, CO2 with Different Adsorbents

Isotherms for different single components of CO2, CH4, or CO were fitted using the BET, Langmuir, Freundlich, single or double-site isotherm. The isotherms are type I, II, and III. (see Figure 2).There are different adsorbents to separate biogas and purify biomethane, these can be activated carbon, zeolite type 13X, clinoptilolite, etc. Table20 simplifies the important points of each adsorbent, showing the adsorption parameters and capacities.Table 20
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
Temperature K
Maximum adsorption capacityQggads−1
Langmuir constant (bar−1)
Pressure Atm
[100]
Silicalite
313.15
0.125 (CO2)
1.089
5
[5]
NaA zeolite
277
0.228(CO2)
—
10
ZSM/C
293
0.139(CO2)
—
4
T-type nanoparticles zeolite
288
0.21296(CO2)
—
1
13X zeolite
323
0.229(CO2)
—
1
SX-[bmim] [TF2N]
298
0.2234(CO2)
—
20
BphC18PMOP 1200
298
0.04092(CO2)
—
1
APTES@SHEPF
298
0.10516(CO2)
—
1
APTMS@PhC12PMO
298
0.03168(CO2)
—
1
[101]
Silica gel
298.15
0.264(CO2)
8.609
×
10
−
6
1
[102]
CMS-3 K
323
0.1188(CO2)
12.74
×
10
−
6
6.5
CMS-3 K
308
0.1012(CO2)
12.74
×
10
−
6
6.5
CMS-3 K
298
0.088(CO2)
12.74
×
10
−
6
6.5
[103]
COSMO zeolite 13X
298
0.1936(CO2)
0.149
3
COSMO zeolite 13X
333
0.1364(CO2)
0.149
3
UOP zeolite 13X
298
0.2288(CO2)
0.149
3
UOP zeolite 13X
333
0.1584(CO2)
0.149
3
EIKME zeolite 13X
298
0.22(CO2)
0.149
3
EIKME zeolite 13X
333
0.132(CO2)
0.149
3
COSMO zeolite 5A
298
0.154(CO2)
0.149
3
COSMO zeolite 5A
333
0.1496(CO2)
0.149
3
Activated carbon
298
0.1276(CO2)
0.149
3
Activated carbon
333
0.0748(CO2)
0.149
3
[104]
Potassium clinoptilolite N
573
0.00638(CO2)
—
10
Potassium clinoptilolite N
573
0.00286(CO2)
—
11
Potassium clinoptilolite N
573
0.00308(CO2)
—
16
Potassium clinoptilolite N
548
0.00616(CO2)
—
10
Potassium clinoptilolite N
548
0.00264(CO2)
—
10
Potassium clinoptilolite Z1
548
0.0044(CO2)
—
10
Potassium clinoptilolite Z1
523
0(CO2)
—
—
Potassium clinoptilolite Z1
523
0.002684(CO2)
—
12.5
Potassium clinoptilolite Z1
523
0.00484(CO2)
—
20
Potassium clinoptilolite Z1
498
0(CO2)
—
10
Potassium clinoptilolite Z2
498
0.003476(CO2)
—
10
Potassium clinoptilolite Z2
498
0.0044(CO2)
—
10
Potassium clinoptilolite Z2
473
0(CO2)
—
10
Potassium clinoptilolite Z2
473
0.00277(CO2)
—
10
Potassium clinoptilolite Z2
473
0.0044(CO2)
—
10
[105]
MOF-508b
296.15
0.083(N2)
0.12
5
CMS-3 K
296.15
0.080(N2)
1.13
5
[106]
Zeolite 13X
313
0.176 (CO2)
2.93
×
10
−
10
1.5
Zeolite 13X
323
0.0924(CO2)
2.93
×
10
−
10
1.5In Table20, it can be seen that the adsorbents that have the highest adsorption capacity are zeolite type 13X, activated carbons and carbon molecular sieves, these zeolites are synthetic, however, clinoptilolite (natural zeolite) has good adsorption capacity despite being tested with high temperatures.The design and configuration of the PSA for biomethane production depends largely on the properties of the adsorbent: adsorption load and diffusion, pressure, stable temperature, etc.In Table21, it can be seen that there are experimental and simulated works related to the production and purification of biomethane, some of them work with more than two columns; however, the classic configuration is two columns. The pressure values in which the process oscillates are above 300 kPa up to 1000 kPa. Therefore, for the production of biomethane, it is necessary to contemplate pressures above 300 kPa. Regeneration times are longer compared to PSA for the production of medical oxygen and bioethanol.Table 21
Works reported on the different configurations of PSA processes for purification of biomethane.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Steam feed composition (% molar fraction of CH4)
[105]
Experimental
2 bed
600-800 to 30-15
3.33-11.66
50-75
6 steps
[102]
Simulated
2 beds
650
4.16667
55
6 steps
[103]
Simulated
1-2 beds
347-350
2.3-2.55 min
64
3-6 steps
[101]
Experimental
2 beds
400
1.81667
55
4 steps
[100]
Simulated
3 beds
100
—
60
10 stepsFigure12 shows the flow diagram of the PSA process for the production of biomethane. The feed flow is compressed to a specific pressure, then it is injected into the packed columns with selective adsorbents on the CO2 compound. As a final product, a highly pure CH4 is obtained. Part of the flow is recirculated through the vacuum pump to purge the column being regenerated. This process continues cyclically until a biomethane purity above 99% is obtained.Figure 12
Schematic diagram of the PSA process using 2-beds, 6-steps.There are few works related to the production of biomethane, however, those found in the literature show a great contribution. Most of them are very complete works in describing their equations and propose models that consider both adsorption isotherms and pressure gradients. Table22 shows some of them.Table 22
Distributed parameter models of the PSA processes for biomethane production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[101]
4 PDEs
Consider adsorption isotherms
Consider pressure gradient
[102]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[107]
4 PDEs
Consider adsorption isotherms
Consider pressure gradient
[103]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[100]
4 PDEs
Consider adsorption isotherms
Consider pressure gradientTable23 shows a general model of the PSA process for biomethane production. The model was obtained from works the works of Abd et al., Ali et al., and Wu et al. [5, 101, 105]. The PSA cycle applied in this work consists of two integrated beds with four consecutive steps. The scheme of the cycle and its sequence are shown in Table 23. The Roman numerals represent the sequence of the steps, which are: (I) adsorption step; (II) blowdown step; (III) purge step; and (IV) repressurization step.Table 23
Governing equations and simplifications for production and purification of biomethane.
The componenti mass balance
−
ε
D
a
x
∂
y
i
∂
z
2
+
∂
v
g
c
i
∂
z
+
ε
b
+
1
−
ε
b
ε
p
∂
c
i
∂
t
+
ρ
p
1
−
ε
b
∂
q
i
∂
t
=
0
The energy balance
ε
b
+
1
−
ε
b
ε
p
∑
i
=
1
N
c
i
C
cpg
,
i
M
i
−
R
+
1
−
ε
b
ρ
s
C
ps
+
1
−
ε
b
ρ
s
∑
i
=
1
N
q
i
c
pg
,
i
M
i
−
R
∂
T
∂
t
+
v
g
ρ
g
∑
i
=
1
N
C
pg
,
i
M
i
∂
T
∂
Z
+
ρ
s
1
−
ε
b
∑
i
=
1
N
∂
q
i
∂
t
Δ
H
+
2
h
T
−
T
W
R
b
−
ε
b
+
ε
p
1
−
ε
b
∂
P
∂
t
−
k
g
∂
2
T
∂
Z
2
=
0
The momentum balance
−
∂
P
∂
Z
=
150
μ
1
−
ε
p
2
2
R
p
2
ε
b
3
V
g
+
1.75
1
−
ε
b
ρ
g
2
R
p
ε
b
3
V
g
V
g
Extended Langmuir equation
q
i
∗
=
q
m
,
i
b
i
P
i
1
+
∑
i
=
1
n
b
i
P
i
,
b
i
=
b
0
ex
p
−
Δ
H
i
/
R
1
/
T
−
1
/
313
−
15
LDF model
∂
q
i
∂
t
=
15
D
c
,
i
R
p
2
q
i
∗
−
q
i
,
D
c
,
i
=
ε
p
D
k
,
i
D
m
τ
D
k
,
i
+
D
m
Boundary and initial conditions
I. Adsorption step
(i)t=0
Y
i
=
inlet
.
Y
i
,
T
=
inlet
.
T
,
P
=
inlet
.
P
(ii)z=0
V
g
>
0
,
Y
i
=
inlet
.
Y
i
,
T
=
inlet
.
T
,
P
=
inlet
.
P
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
II. Blowdown step
(i)t=0
Y
i
=
Y
i
I
,
T
=
T
I
,
P
=
P
I
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
III. Purge step
(i)t=0
Y
i
=
Y
i
II
,
T
=
T
II
,
P
=
P
II
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
IV. Repressurization step
(i)t=0
Y
i
=
Y
i
III
,
T
=
T
III
,
P
=
P
III
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0


### 6.2. Parametric Study of the PSA Process for the Production of Biomethane

The parameters of this PSA process for the production and purification of biomethane are shown in the following Table24.Table 24
Start-up parameters of the PSA process for the purification and production of biomethane.
FEED
Flow
0.0719
kmolh-1
Methane
0.65
kmolkmol-1
CO2
0.35
kmolkmol-1
Temperature
298.15
T
Production pressure
1000
kPa
Purge pressure
100
kPa
SIZING
Bed height
1
m
Bed diameter
0.06
m
Zeolite 13X
Particle radius
0.00157
m
Bulk solid density
1160.0
Kg m−3Figure13 shows the methane and CO2 profiles. The molar fraction of the methane rises in the first 3 cycles, this continues until reaching the CSS, which achieves a biomethane purity above 99%. On the other hand, the purity of CO2 is declining.Figure 13
Purification and production of biomethane from the start-up.Figure14 shows the results of the sensitivity analysis and it is observed that all the variables have the same effect taking into account a variation of±0.05%. The effects shown on biomethane purity are small, but the flow variable can be taken into account as a possible variable to manipulate since it shows more outstanding profiles compared to the other variables. In order to better visualize this performance, it would be convenient to increase the variation value, in order to observe greater effects on biomethane purity.Figure 14
Sensitivity analysis applied to the PSA process for the production of biomethane.
(a)
Temperature: 303.15 K to 287.99 K; Flow: 0.0719 kmolh-1; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(b)
Temperature: 303.15 K to 318.30 K; Flow: 0.0719 kmolh-1; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(c)
Flow: 0.0719 kmolh-1 to 0.0683 kmolh-1; Temperature: 303.15 K; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(d)
Flow: 0.0719 kmolh-1 to 0.0755 kmolh-1; Temperature: 303.15 K; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(e)
Pressure: 400 kPa to 380 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(f)
Pressure: 400 kPa to 420 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(g)
Molar fraction: 0.65 (CO2) and 0.35 (CO2) to 0.6175 (CH4) and 0.3825 (CO2); Pressure: 400 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K
(h)
Molar fraction: 0.65 (CH4) and 0.35 (CO2) to 0.6825 (CH4) and 0.175 (CO2); Pressure: 400 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 KTable25 shows the detailed data of the results presented in Figure 14. It shows the cycle times, the purities, and the changes generated by each input variable.Table 25
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature(K)
Flow kmolh-1
Pressure kPa
Composition CH4-CO2
Purity % molar fraction of CH4
Number of cycles
1
303.15
0.0719
400
0.65-0.35
99.99
10
2
287.99
0.0719
400
0.65-0.35
99.9965
18
3
318.30
0.0719
400
0.65-0.35
99.997
13
4
303.15
0.0683
400
0.65-0.35
99.998
26
5
303.15
0.0755
400
0.65-0.35
99.996
18
6
303.15
0.0719
380
0.65-0.35
99.997
10
7
303.15
0.0719
420
0.65-0.35
99.9960
11
8
303.15
0.0719
400
0.6175-0.3825
99.9965
20
9
303.15
0.0719
400
0.6825-0.3175
99.9975
21


## 6.1. Adsorption and Separation for the CH4, CO2 with Different Adsorbents

Isotherms for different single components of CO2, CH4, or CO were fitted using the BET, Langmuir, Freundlich, single or double-site isotherm. The isotherms are type I, II, and III. (see Figure 2).There are different adsorbents to separate biogas and purify biomethane, these can be activated carbon, zeolite type 13X, clinoptilolite, etc. Table20 simplifies the important points of each adsorbent, showing the adsorption parameters and capacities.Table 20
Comparison of the thermodynamic values of various adsorbents as a function of different temperatures and pressures.
Reference
Adsorbents
Temperature K
Maximum adsorption capacityQggads−1
Langmuir constant (bar−1)
Pressure Atm
[100]
Silicalite
313.15
0.125 (CO2)
1.089
5
[5]
NaA zeolite
277
0.228(CO2)
—
10
ZSM/C
293
0.139(CO2)
—
4
T-type nanoparticles zeolite
288
0.21296(CO2)
—
1
13X zeolite
323
0.229(CO2)
—
1
SX-[bmim] [TF2N]
298
0.2234(CO2)
—
20
BphC18PMOP 1200
298
0.04092(CO2)
—
1
APTES@SHEPF
298
0.10516(CO2)
—
1
APTMS@PhC12PMO
298
0.03168(CO2)
—
1
[101]
Silica gel
298.15
0.264(CO2)
8.609
×
10
−
6
1
[102]
CMS-3 K
323
0.1188(CO2)
12.74
×
10
−
6
6.5
CMS-3 K
308
0.1012(CO2)
12.74
×
10
−
6
6.5
CMS-3 K
298
0.088(CO2)
12.74
×
10
−
6
6.5
[103]
COSMO zeolite 13X
298
0.1936(CO2)
0.149
3
COSMO zeolite 13X
333
0.1364(CO2)
0.149
3
UOP zeolite 13X
298
0.2288(CO2)
0.149
3
UOP zeolite 13X
333
0.1584(CO2)
0.149
3
EIKME zeolite 13X
298
0.22(CO2)
0.149
3
EIKME zeolite 13X
333
0.132(CO2)
0.149
3
COSMO zeolite 5A
298
0.154(CO2)
0.149
3
COSMO zeolite 5A
333
0.1496(CO2)
0.149
3
Activated carbon
298
0.1276(CO2)
0.149
3
Activated carbon
333
0.0748(CO2)
0.149
3
[104]
Potassium clinoptilolite N
573
0.00638(CO2)
—
10
Potassium clinoptilolite N
573
0.00286(CO2)
—
11
Potassium clinoptilolite N
573
0.00308(CO2)
—
16
Potassium clinoptilolite N
548
0.00616(CO2)
—
10
Potassium clinoptilolite N
548
0.00264(CO2)
—
10
Potassium clinoptilolite Z1
548
0.0044(CO2)
—
10
Potassium clinoptilolite Z1
523
0(CO2)
—
—
Potassium clinoptilolite Z1
523
0.002684(CO2)
—
12.5
Potassium clinoptilolite Z1
523
0.00484(CO2)
—
20
Potassium clinoptilolite Z1
498
0(CO2)
—
10
Potassium clinoptilolite Z2
498
0.003476(CO2)
—
10
Potassium clinoptilolite Z2
498
0.0044(CO2)
—
10
Potassium clinoptilolite Z2
473
0(CO2)
—
10
Potassium clinoptilolite Z2
473
0.00277(CO2)
—
10
Potassium clinoptilolite Z2
473
0.0044(CO2)
—
10
[105]
MOF-508b
296.15
0.083(N2)
0.12
5
CMS-3 K
296.15
0.080(N2)
1.13
5
[106]
Zeolite 13X
313
0.176 (CO2)
2.93
×
10
−
10
1.5
Zeolite 13X
323
0.0924(CO2)
2.93
×
10
−
10
1.5In Table20, it can be seen that the adsorbents that have the highest adsorption capacity are zeolite type 13X, activated carbons and carbon molecular sieves, these zeolites are synthetic, however, clinoptilolite (natural zeolite) has good adsorption capacity despite being tested with high temperatures.The design and configuration of the PSA for biomethane production depends largely on the properties of the adsorbent: adsorption load and diffusion, pressure, stable temperature, etc.In Table21, it can be seen that there are experimental and simulated works related to the production and purification of biomethane, some of them work with more than two columns; however, the classic configuration is two columns. The pressure values in which the process oscillates are above 300 kPa up to 1000 kPa. Therefore, for the production of biomethane, it is necessary to contemplate pressures above 300 kPa. Regeneration times are longer compared to PSA for the production of medical oxygen and bioethanol.Table 21
Works reported on the different configurations of PSA processes for purification of biomethane.
Reference
Experimental/simulated
PSA cycles
Pressure swing (kPa)
Bed regeneration time (min)
Steam feed composition (% molar fraction of CH4)
[105]
Experimental
2 bed
600-800 to 30-15
3.33-11.66
50-75
6 steps
[102]
Simulated
2 beds
650
4.16667
55
6 steps
[103]
Simulated
1-2 beds
347-350
2.3-2.55 min
64
3-6 steps
[101]
Experimental
2 beds
400
1.81667
55
4 steps
[100]
Simulated
3 beds
100
—
60
10 stepsFigure12 shows the flow diagram of the PSA process for the production of biomethane. The feed flow is compressed to a specific pressure, then it is injected into the packed columns with selective adsorbents on the CO2 compound. As a final product, a highly pure CH4 is obtained. Part of the flow is recirculated through the vacuum pump to purge the column being regenerated. This process continues cyclically until a biomethane purity above 99% is obtained.Figure 12
Schematic diagram of the PSA process using 2-beds, 6-steps.There are few works related to the production of biomethane, however, those found in the literature show a great contribution. Most of them are very complete works in describing their equations and propose models that consider both adsorption isotherms and pressure gradients. Table22 shows some of them.Table 22
Distributed parameter models of the PSA processes for biomethane production.
Reference
Equations governing the PSA process (nonlinear model)
Temperature effects
Pressure effects
[101]
4 PDEs
Consider adsorption isotherms
Consider pressure gradient
[102]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[107]
4 PDEs
Consider adsorption isotherms
Consider pressure gradient
[103]
3 PDEs
Consider adsorption isotherms
No pressure gradient
[100]
4 PDEs
Consider adsorption isotherms
Consider pressure gradientTable23 shows a general model of the PSA process for biomethane production. The model was obtained from works the works of Abd et al., Ali et al., and Wu et al. [5, 101, 105]. The PSA cycle applied in this work consists of two integrated beds with four consecutive steps. The scheme of the cycle and its sequence are shown in Table 23. The Roman numerals represent the sequence of the steps, which are: (I) adsorption step; (II) blowdown step; (III) purge step; and (IV) repressurization step.Table 23
Governing equations and simplifications for production and purification of biomethane.
The componenti mass balance
−
ε
D
a
x
∂
y
i
∂
z
2
+
∂
v
g
c
i
∂
z
+
ε
b
+
1
−
ε
b
ε
p
∂
c
i
∂
t
+
ρ
p
1
−
ε
b
∂
q
i
∂
t
=
0
The energy balance
ε
b
+
1
−
ε
b
ε
p
∑
i
=
1
N
c
i
C
cpg
,
i
M
i
−
R
+
1
−
ε
b
ρ
s
C
ps
+
1
−
ε
b
ρ
s
∑
i
=
1
N
q
i
c
pg
,
i
M
i
−
R
∂
T
∂
t
+
v
g
ρ
g
∑
i
=
1
N
C
pg
,
i
M
i
∂
T
∂
Z
+
ρ
s
1
−
ε
b
∑
i
=
1
N
∂
q
i
∂
t
Δ
H
+
2
h
T
−
T
W
R
b
−
ε
b
+
ε
p
1
−
ε
b
∂
P
∂
t
−
k
g
∂
2
T
∂
Z
2
=
0
The momentum balance
−
∂
P
∂
Z
=
150
μ
1
−
ε
p
2
2
R
p
2
ε
b
3
V
g
+
1.75
1
−
ε
b
ρ
g
2
R
p
ε
b
3
V
g
V
g
Extended Langmuir equation
q
i
∗
=
q
m
,
i
b
i
P
i
1
+
∑
i
=
1
n
b
i
P
i
,
b
i
=
b
0
ex
p
−
Δ
H
i
/
R
1
/
T
−
1
/
313
−
15
LDF model
∂
q
i
∂
t
=
15
D
c
,
i
R
p
2
q
i
∗
−
q
i
,
D
c
,
i
=
ε
p
D
k
,
i
D
m
τ
D
k
,
i
+
D
m
Boundary and initial conditions
I. Adsorption step
(i)t=0
Y
i
=
inlet
.
Y
i
,
T
=
inlet
.
T
,
P
=
inlet
.
P
(ii)z=0
V
g
>
0
,
Y
i
=
inlet
.
Y
i
,
T
=
inlet
.
T
,
P
=
inlet
.
P
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
II. Blowdown step
(i)t=0
Y
i
=
Y
i
I
,
T
=
T
I
,
P
=
P
I
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
III. Purge step
(i)t=0
Y
i
=
Y
i
II
,
T
=
T
II
,
P
=
P
II
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
IV. Repressurization step
(i)t=0
Y
i
=
Y
i
III
,
T
=
T
III
,
P
=
P
III
(ii)z=0
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0
(iii)z=L
∂
Y
∂
z
=
0
,
∂
T
∂
z
=
0
,
∂
P
∂
z
=
0


## 6.2. Parametric Study of the PSA Process for the Production of Biomethane

The parameters of this PSA process for the production and purification of biomethane are shown in the following Table24.Table 24
Start-up parameters of the PSA process for the purification and production of biomethane.
FEED
Flow
0.0719
kmolh-1
Methane
0.65
kmolkmol-1
CO2
0.35
kmolkmol-1
Temperature
298.15
T
Production pressure
1000
kPa
Purge pressure
100
kPa
SIZING
Bed height
1
m
Bed diameter
0.06
m
Zeolite 13X
Particle radius
0.00157
m
Bulk solid density
1160.0
Kg m−3Figure13 shows the methane and CO2 profiles. The molar fraction of the methane rises in the first 3 cycles, this continues until reaching the CSS, which achieves a biomethane purity above 99%. On the other hand, the purity of CO2 is declining.Figure 13
Purification and production of biomethane from the start-up.Figure14 shows the results of the sensitivity analysis and it is observed that all the variables have the same effect taking into account a variation of±0.05%. The effects shown on biomethane purity are small, but the flow variable can be taken into account as a possible variable to manipulate since it shows more outstanding profiles compared to the other variables. In order to better visualize this performance, it would be convenient to increase the variation value, in order to observe greater effects on biomethane purity.Figure 14
Sensitivity analysis applied to the PSA process for the production of biomethane.
(a)
Temperature: 303.15 K to 287.99 K; Flow: 0.0719 kmolh-1; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(b)
Temperature: 303.15 K to 318.30 K; Flow: 0.0719 kmolh-1; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(c)
Flow: 0.0719 kmolh-1 to 0.0683 kmolh-1; Temperature: 303.15 K; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(d)
Flow: 0.0719 kmolh-1 to 0.0755 kmolh-1; Temperature: 303.15 K; Pressure: 400 kPa; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(e)
Pressure: 400 kPa to 380 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(f)
Pressure: 400 kPa to 420 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K; Molar fraction: 0.65 (CH4) and 0.35 (CO2)
(g)
Molar fraction: 0.65 (CO2) and 0.35 (CO2) to 0.6175 (CH4) and 0.3825 (CO2); Pressure: 400 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 K
(h)
Molar fraction: 0.65 (CH4) and 0.35 (CO2) to 0.6825 (CH4) and 0.175 (CO2); Pressure: 400 kPa; Flow: 0.0719 kmolh-1; Temperature: 303.15 KTable25 shows the detailed data of the results presented in Figure 14. It shows the cycle times, the purities, and the changes generated by each input variable.Table 25
Analysis of the possible input variables that have the greatest effect on the purity obtained.
Run
Temperature(K)
Flow kmolh-1
Pressure kPa
Composition CH4-CO2
Purity % molar fraction of CH4
Number of cycles
1
303.15
0.0719
400
0.65-0.35
99.99
10
2
287.99
0.0719
400
0.65-0.35
99.9965
18
3
318.30
0.0719
400
0.65-0.35
99.997
13
4
303.15
0.0683
400
0.65-0.35
99.998
26
5
303.15
0.0755
400
0.65-0.35
99.996
18
6
303.15
0.0719
380
0.65-0.35
99.997
10
7
303.15
0.0719
420
0.65-0.35
99.9960
11
8
303.15
0.0719
400
0.6175-0.3825
99.9965
20
9
303.15
0.0719
400
0.6825-0.3175
99.9975
21


## 7. Conclusions

The phenomenon of adsorption with molecular sieves has a great contribution to separating atoms or molecules from a gas or mixture, but it has a greater impact and scope using the PSA method. In this contributing review, the importance of the PSA process to purify and produce bioethanol, biohydrogen, medical oxygen, and biomethane is demonstrated.The tendency to use this process is referred to the scope it has to produce purities above 99%, this scope of purification that this PSA process has is of great importance since they meet international purity standards to be used as fuels.In this review, the different adsorbents that can be used for the separation and purification of the compounds of ethanol, hydrogen, oxygen, and methane were summarized. The effects of temperature and pressure have a great effect on the adsorption capacity. Synthetic adsorbents show that they have a better adsorption capacity, but natural adsorbents can be a widely used alternative to adsorb different compounds of natural gas or mixture since they have pores of different sizes and this is a great advantage over synthetic adsorbents.The different configurations and models of the PSA process were shown and analyzed, showing that it is of great importance to contemplate the greatest number of PDEs in order to have general balance data, mass balance moment balance, energy balance, wall balance, thermodynamic balance, and kinetic, this in relation to having an approximation of results to real plants.A parametric study was carried out, which allowed observing the purity achieved and the cycle times that are reached by varying certain input parameters. These results show that not all variables have the same effect and that they may be insignificant in the effect that is generated on the purity obtained.Likewise, it can be concluded that the parametric study that was carried out for each case of separation and production of compounds was a great contribution to defining one or two variables that can control the purity obtained as a final product. These variables can also be seen as disturbances since they are at the input of the PSA process and can affect it if not controlled in a secondary way.As future works, controllers can be designed on these plants to maintain the desired purity stable and meet international standards to be used as fuel. Processes can be optimized based on the results obtained and have greater recovery and production of bioethanol, biohydrogen, medical oxygen, and biomethane.



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*Source: 3030519-2022-10-29.xml*