Modeling of Adsorption in a Packed Bed Tower, the case study of Methane Removal and Parametric Calculation

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

J. Environ. Treat. Tech.

ISSN: 2309-1185

Journal weblink: http://www.jett.dormaj.com

Modeling of Adsorption in a Packed Bed Tower,

the Case Study of Methane Removal and

Parametric Calculation

Abdollah Norouzi

Department Of Chemical Engineering, Jami institute of Technology, Isfahan, Iran

Received: 25/05/2019

Accepted: 11/06/2019

Published: 01/12/2019

Abstract

In this work, the modeling of methane adsorption in a tower with fixed bed has been studied. In order to present a mathematical

model, the mass balance was written in the tower. The obtained equations with the assumption of no changes in the concentration,

temperature, and pressure in the radial direction as well as the axial dispersion of the flow pattern were solved by using numerical

methods. Among various numerical methods, an implicit finite difference method was used to solve the equations. Base on the

obtained model, the effect of temperature, inlet flow rate, bed length, and pressure on the adsorption tower was investigated. It was

observed that with the temperature decreases, the adsorption rate increases. At a specified time, the amount of adsorbate in the gas

phase at the outlet of the bed from 306 to 295 decreased by changing the temperature from T=298K to T=308K. also, the effect of

pressure, gas velocity, adsorbent size and bed length in separate diagrams was studied and it was determined that with increasing

pressure, decreasing gas velocity, increasing bed length and decreasing adsorbent size and adsorption rate increase.

Keywords: Adsorption, Modeling, Methane, Packed bed tower, fixed bed.

improves environmental performance [2]. Adsorption based

Introduction

processes include swing adsorption (PSA), technologies that

have the potential for recovery from methane from released.

Flow and methane enrichment to concentrations that can be

used in lean- gas turbines and fuel cells [3-7].

Research on the prevention of air pollution and the

environment has increased dramatically over the last few

decades, due to increasing social and economic concerns

about the environment. As

a result environmental

Several studies have been carried out on the separation

of various materials by adsorption in a fixed bed. In most of

these studies, laboratory work and simulations are carried

out simultaneously. For modeling a process, it is necessary

to simplify the equations and relations governing that

process. Given the fact that these equations and simplified

relationships can be used to predict the results of a process

and thereby improve its performance, the importance of

modeling becomes evident.

The adsorption of methane on zeolite 13x has been

studied by Alireza Eslami et al. In this study, the adsorption

process was investigated at 298, 308, 323 K and at 1 to 5

MPa pressures by Langmuir, Unilan, Sip and Toth isotherms

using a genetic algorithm. The results show that the isotherm

model of Toth adsorption at 308 K has a very good flexibility

to fit experimental data [8]. Delgado et al, also investigated

the adsorption of methane and nitrogen on a silica tablet in a

fixed bed. The model was used to simulate nitrogen and

methane adsorption curves and pressure cycling was

proposed to increase methane content from a mixture of

methane/nitrogen (85/15) [6].

organizations have imposed restrictive laws to reduce the

emission of pollutants into the atmosphere. Methane is a

gaseous pollutant that causes global warming. The main

sources of methane from oil and gas production facilities,

agricultural activities, such as animal husbandry and meat

production. The challenge of removing methane from

industrial waste gases is because waste streams are produced

at low pressures and have very low concentrations of

methane. For example, the release of methane from a coal

mine is typically less than 1.5% of methane [1]. The most

expensive and commonly used current technique is to

remove low concentration of methane from a low-pressure

gas flow, return thermal oxidation processes, and catalytic

thermal oxidation that converts methane into carbon dioxide

and water. Although some oxidation processes have the

potential to recover heat, generally these processes typically

incur additional costs for production. Therefore, there is a

clear incentive to create a methane recovery process that

returns methane to the mainstream gas or recycled methane

to generate power, which both reduces operational costs and

Corresponding author: Abdollah Norouzi, Department Of Chemical Engineering, Jami institute of Technology, Isfahan, Iran.

E-mail: keyvannoruzii@gmail.com.

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

Grand et al. examined the adsorption equilibrium of

propane and propylene on a honeycomb rock that was

blended with 4A zeolite crystals and inert materials in

conditions of 423 and 473 K and in the range of 0 to 100 KPa

Hence, in this section, adsorption fixed bed is modeled on

the mechanism of diffusion.

1.2 Modeling of adsorption in the fixed bed

[

9]. Ali Akbar Farzaneh et al. reviewed the simulation of

The purpose of this study is to find a suitable model for

adsorption of methane in the tower. In order to provide the

mathematical model of the adsorption tower, we must

establish a mass balance for the tower and write the

corresponding equations. The exact modeling is necessary

for the proper understanding of the physics of the system as

well as the phenomena in the process under study. To

accomplish this, we consider the differential height of the

filled column and write the mass equations for this

differential component. The proposed differential equations

should be solved to simulate a tower with a specific height

and profile.

In an adsorption fixed bed, the gas content of the

adsorbate material enters the bed on one side and leaves it

out. By passing on the adsorbent solid absorbed and thus the

concentration of the absorbing material in the exhaust gases

is reduced. With time and saturation of the primary portions

of the substrate, the concentration of the absorbing material

in the outlet increases and eventually reaches the

concentration of the input.In order to mathematical modeling

of the adsorption bed, appropriate element of the substrate

has been selected. The following figure 1 shows an element

of the fixed bed.

absorption towers. In order to solve the model, the dynamic

data provided by San and Monire was used and in the

equilibrium, the results were compared with the results

obtained from the leading approximation method in a non-

equilibrium mode with the results obtained from the QUDS

method obtained by San and Munire [10]. Khalid

Opportunity and colleagues explored the modeling of the

torpedo tower used in the sulfiran process. At first, the

required experimental data were collected in a laboratory

system under different conditions of H2S concentration and

gas flow. After performing the desired mass balance, the

developed equations were solved using numerical methods,

and the results of the modeling were compared with the

experimental results. Comparison of modeling and

experimental results indicated a sufficient accuracy of the

model to predict the behavior of the tower that was used in

the sulfiran process [11]. Studies by Shafiyan and his

colleagues on absorption modeling in a tower filled up [12-

2]. Due to the complexity of the models that have been

proposed for surface uptake so far, it seems necessary to

provide another model that is compatible with the previous

models. Therefore, by studying the different models

presented for such systems, considering the conditions of the

system under study, suitable model assumptions such as no

changes in concentration, temperature and pressure in the

radial direction, as well as the axial dispersion of the

constant temperature flow pattern have been selected. And

the simulation in the MATLAB program is based on it.

Finally, the effect of different parameters on the absorption

rate and the conformance of this model with the

experimental data presented earlier will be investigated.

Modeling

The mathematical models used to dynamically simulate

the behavior of an adsorption system based on equations.

The most important issue in simulating these processes is

that during the recovery stage, usually the adsorbent is not

completely recovered, and therefore the initial concentration

of the absorbed phase will not be zero. In practical systems,

there is usually a region at the entrance of the bed in both the

adsorption and disintegration stages, where the unpublished

material is present. This complexity causes problems in

mathematical simulation because the initial distribution of

absorbed concentration is not known in advance. In this case,

the concentrations remain constant at all points and all times

in the cycle and in all parts of the cycle. The number of

cycles required to achieve a uniform cyclic state depends on

the various parameters of the system, and it may take up to

Fig. 1: The element is considered in balance

2.2 Mass balance for each component

The assumptions used in the mass balance are as follows:

(a) The thermodynamic behavior of gas is an equation of

ideal gas. (b) Changes in Concentrations, temperatures, and

pressures in radial and angular directions are not neglected.

phase follows the LDF linear propulsion model. (d) The

axial dispersion is assumed to be the flow pattern. (e) It is

assumed that the plug flow is negligible with variations in

velocity along the bed. With these assumptions, the mass

balance equation for component I is written as follows:

Write equations 1:

30 cycles, such calculations are possible only by numerical

simulations, and analytical solutions cannot be used to

calculate precisely Specifications of operational systems

[23, 24]. The performance of a good absorbent is measured

휕푐푖

in real operating conditions. This can be done

experimentally in industrial or semi-industrial conditions,

but since this is very costly and time-consuming, using a

suitable model can be a good alternative to reducing costs.

(

uAε

)І

-( c

uA휀 )Іz+Δz+( -Dax,i Aε

)І

- (-Dax,i _휕_푧

푏

휕푧

휕푞푖

⁾^A^Δ^z휕푡

∂ci

Aε

)Іz+Δz=ε

AΔz

+ ( 1-ε

(Eq. 1)

∂z

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

where εb is substrate porosity, ρp is density of particles

important issue in using this model is to calculate the mass

transfer coefficient (K_LDF). The mass transfer coefficient

of the film around the adsorbent is obtained according to the

following equation 3 [23]:

(

kg/m ), C

is concentration of i in the fluid phase (mol/m ),

qi is concentration of i in phosgate (mol/kg), A is cross

section of tower (m ), u is fluid velocity (m/s) and Dax, i is

dispersion coefficient (m /s). By dividing the sides by the

ꢋ

ꢊ ]

size of the element (AΔz) we have (equation 2):

0.6

ꢈ_푀

ꢇ푢푅_푝

휇

휈

퐾_퐿_퐷_퐹

+ [ꢇ + 1.1ꢉ

ꢊ

ꢉ

(퐸ꢄ. ꢌ)

ꢇ푅푝

ꢈ푀

ꢀ

ꢁ_ꢂ(1 − ε_푏) ꢀꢄ_ꢂ

ꢀ(푢ꢁ_ꢂ)

ꢀꢅ

ꢀ ꢁ

ꢂ

ρ_푝

= −

+ Dax, ꢆ

ꢀꢅ²

(Eq. ꢇ)

ꢀ

ꢃ

휀_푏

ꢀꢃ

2.6 Boundary and initial conditions and model

calculations

2.3 Pressure drop

The input boundary condition of the adsorption step is,

in fact, the input feed condition. Given that the differential

equations are two-dimensional relative to the place variable,

there is a need for another boundary condition. This

condition is provided by assuming zero flux in the output.

For an initial condition, it requires a basic assumption. This

assumption is assumed to be taken into account when the qi

adsorption value is considered to be zero, and the initial

concentration of the gas in the bed is also considered to be

free from the adsorbate material (the concentration of the

adsorbate components is equal to Zero; t = ꢍ: ∁_ꢎ_ꢏ∁_ꢎ|adsorbent

free.

Due to the diameter/longitudinal ratio of the substrate

studied in this modeling, the pressure variations in the bed

are neglected and constant total pressure is considered.

.4 Equilibrium relationship between two phase

concentrations

Due to the type of adsorbent used, which is zeolite and

adsorption in zeolites, which is usually single-layered, the

Langmuir model is a suitable model for use in simulating

this process.

.5 Mass transfer coefficient between phases

The mass transfer velocity between the solid phase and

In Table 1, the boundary and initial conditions are

required. The boundary and initial conditions of the general

mass balance are also similar to the partial balance.

the gas can be expressed by the approximate linear driving

force model. According to the available literature, this model

is suitable for long-term adsorption cycles. The most

Table 1. Boundary and initial conditions

ꢐ = ꢍ

∁_ꢎ= ∁_ꢎ_,_f

ꢑꢒ_ꢎ

Boundary conditions

ꢍ

ꢐ = L

t = ꢍ

Adsorption step

ꢑꢐ

∁_ꢎ= ꢍ

Initial condition

.6.1The numerical form of the equations

Solving the equations of the model involves

(∆ꢐ)²

ꢑ X

ꢑꢐ²

− ꢇX + X

mꢔꢋ

mꢓꢋ

≈

(퐸ꢄ. ꢕ)

simultaneous solving NC of the differential equation with

partial derivatives of mass balance, NC is the ordinary

differential equation of mass transfer between the gas phase

and the fluid phase. It is very difficult and even impossible

to solve these equations by an analytical method. For this

reason, numerical methods are used to solve these equations.

Of the various numerical methods, the explicit finite

difference method, given the long time of the cycle stages,

and the limitation in this method for the length of the time

interval, do not seem to be a suitable method for the solution.

But in the implicit finite difference method, this limitation

does not exist and can be used to solve equations. Based on

this method, the numerical form of the terms of the

differential equations is as follows:

.7 The numerical form of the equations in the interior of

the substrate

By establishing the partial mass survival law for the

detachable component, the following equation is obtained to

express the variation in the concentration of the desired

component in relative to time and place (equation 4).

ꢑꢒ_ꢎ(1 − ε_b) ꢑq_ꢎ

ρ_p

ꢑ(uꢒ_ꢎ)

ꢑꢐ

ꢑ ꢒ

ꢎ

= −

+ D_ꢖ_ꢗ_ꢎ,

ꢑꢐ²

(퐸ꢄ. 7)

ꢑt

^εb

ꢑt

By applying these alternatives we have the following in mass

balance equation 5:

jꢓꢋ

⁻^Cm

jꢓꢋ

⁻^qm

jꢓꢋ

1 − ε

− C

ꢑX

ꢑt

− X_m

mꢓꢋ

+ ꢉ

ꢊ ꢘ

ꢙ + ρ

≈

(퐸ꢄ. 4)

(퐸ꢄ. 5)

∆

∆t

∆ꢐ

∆t

− ꢇC + C

mꢔꢋ

mꢓꢋ

^Dꢖꢗ

(퐸ꢄ. 8)

ꢑX

ꢑꢐ

− X

∆ꢐ

mꢓꢋ

(

_∆_ꢐ₎2

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

The above equation is solved by the method x = g (x).

So we have (equation 6):

the tower. (3) Investigating the impact of the tower's

operational parameters.

∆

∆ꢐ

∆t

∆ꢐ

∆t

+ u )C

∆ꢐ

jꢓꢋ

^ε푏 ⁻¹

2.8.2 Input and output of the program

. Fixed parameters, including tower and adsorbent

specification

2. Operating parameters such as tower's function time

3. Input feed conditions (temperature, pressure, flow

intensity and composition percent)

(

₂)C

+ (D

+ C_m− ( )

mꢔꢋ

mꢓꢋ

ε푏

∆

∆t

∆ꢐ

ε − 1 q

푏

ꢇD

+ u + 1 − ꢚ

ꢛ

∆

ꢐ

ε푏

(

퐸ꢄ. 9)

2.7.1 The process of solving equations in the isothermal

4. Adsorption equilibrium data

state

In isothermal conditions, the temperature is assumed to

5. The concentration of adsorbate component in the gas

phase at the outlet of the substrate

be constant at different stages, and various parameters are

determined at this constant temperature. Therefore, only the

mass balance equations and mass transfer velocity equations

will remain. In this case, there is a partial mass balance

equation and a mass transfer velocity equation for adsorbate

mass and a general mass balance. If we consider the number

of divisions over the length of NL, the equations must be

solved simultaneously, taking into account the boundary

condition NL-1. In the isothermal mode, the form of all

relationships related to temperature and energy balance is

eliminated, so the convergence time is reduced.

6. The concentration of adsorbate component in the solid

phase at the outlet of the substrate

7. partial pressure of adsorbate in the gas phase at the outlet

of the substrate

2.8.3 Problem-solving

Since the equation is based on time and space, it should

start from zero time and solve for the whole region, and after

solving it at time zero, it was time one and so on for the

whole time. That's mean, at time n, the data is obtained for

all points and by that the data is calculated at time n + 1.

Therefore, there is a 'for' external loop that actually changes

from one step to the next. Inside the 'for' outer loop which

time is there, there is a 'for' inner loop for, which indicates

location changes from the beginning to the end of the

substrate. The inner loop is about the 'while' loop that is

solved within this equation loop at a constant time and place.

In fact, in the two previous 'for' loops, one time and another

determined the location, and in the last loop (while) at this

time and place, the amount of adsorbate concentration in the

solid phase (q) and the adsorbate concentration in the gas

phase (c) comes.

.8 Describe the computer program

To solve the equations and calculate the values of

different variables, the computer program is written in the

Matlab 7software environment.

2.8.1 Program capabilities

The provided program has the following capabilities: (1)

Calculate and plot the concentration profile of various

components along the tower. (2) Calculate the time variation

of the concentration of different components at each point of

Table 2: Incoming applications

Parameter

temperature

symbol

unit

Pressure

number of intervals

number of spatial distance

Length of bed

length ratio to the number of spatial distances

time of passage of gas from the whole bed

Adsorbate mole fraction at the moment of entering the bed

speed

Adsorbent density

substrate porosity

m/s

kg/m3

ρ_p

ε_푏

Maximum adsorption capacity in dual-Langmuir isotherm

Coagulation coefficient of adsorption in the Langmuir isotherm

linear force propulsion coefficient

axial dispersion coefficient

mol/kg

1/Pa

1/s

LDF

performance in the towers. First of all, you need to ensure

the performance of the model. To evaluate the proposed

model, experimental data of Habib Mohammadinezhad have

been used [25]. In this study, the adsorption curve for carbon

dioxide adsorption by zeolite 5A at temperature and pressure

Results and discussion

Based on the model derived from this study, the effective

parameters on adsorption will be analyzed individually in

order to provide optimum conditions for adsorption

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

of the experiment has been investigated. Comparison of the

results of the model and experimental data is shown in Fig.

the superconducting forces (superficial potential) will be

deflected against the temperature (kinetic) forces, although

the pressure is too high. As the temperature rises, the

adsorption rates are rapidly degraded, so it is best to perform

adsorption at lower temperatures if possible [26].

1. The results of this comparison show that the proposed

model can predict the experimental data. As shown in Fig. 1,

the model developed by the laboratory data for carbon

dioxide adsorption is well-suited to zeolite. Therefore, this

model can be used to predict the effect of operating

conditions on adsorption and to achieve optimal conditions

to improve the performance of an adsorption tower.

Table 3: Construction characteristics of the filled tower

L =0.254 m

D=0.0472 m

Length of the tower

Tower diameter

=0.464

Substrate porosity

Table 4: Adsorption Operating Conditions

T=298 K

Temperature

P= 108109 pa

U=0.523362 m/s

LDF=0.00101 s

Pressure

Speed

Linear force

-1

مدل

شگاهیꢀآزما

ꢁدꢂ

Experimental data

Model

ax=0.0003

휌_푃= 2220 kg/m

Axial dispersion coefficient

The apparent density

Input mole fraction of

adsorbate

in=0.0073

Table 5: Convergence of the two-site Langmuir isotherm

= 2.2 3446*10^-⁵pa^-¹

s1= 1.599 mol/kg

= 0.048905 s2=0.049 mol/kg

pa^-¹

100

t(min)

150

200

Fig. 2: Comparison of experimental and model adsorption data

As shown in Fig. 4.1, at 65min the adsorbate amount in

the outlet gas phase from the bed at T = 298, T = 308, and T

= 318, respectively, is 306.0, 295.0, and 285.0. Since the

adsorption step is relatively long and it is considered to avoid

temperature changes due to heat exchange with a feed

temperature near the ambient temperature.

.1 Performance conditions for adsorption

Adsorption of carbon dioxide on zeolite 5A in laboratory

conditions. Specifications and test conditions are presented

in Tables 3 and 4 [25]. The least squares error method has

been used in order to obtain the dual-Langmuir isotherm

quantities. Equilibrium quantities of this isotherm are

presented in Table 5.

3.2.2 Effect of feed flow intensity

The flow Intensity in this process is affected by gas

velocity in the equations. Increasing gas velocity increases

the speed of movement of the activated region, and as the

region approaches the outlet, the concentration of the

adsorbate material in the product increases. In the lower flow

rate due to more contact time, the pollutant has more chance

of bonding with the adsorbent particles. Therefore, the

adsorption efficiency increases. The amount of air inflow

strongly affects adsorption capacity. As the flow rate

increases, the adsorption and trapping of methane molecules

decrease. The reason for this is that methane remains in the

adsorption bed, and some of it leaves the bed before reaching

the balance point. Similar results are presented by other

researchers [27-31]. As shown in Fig. 4, the adsorbate

concentration in the outlet gas phase reaches a value of 0.15,

with a velocity of = 0.4, u = 0.52and u = 0.6respectively of

30, 23 and 20 minutes is required.

.2 The effect of changing the input feed conditions of the

unit

Feed conditions are one of the main determinants of any

chemical process. Therefore, the effect of these conditions

on process performance improvement is very effective. In

general, adsorption processes have a good flexibility versus

changing various feed conditions. In this section, the effect

of temperature, flow, and methane concentration of the input

has been investigated by using this simulation.

3.2.1 Effect of feed temperature

Since the study is carried out at the same temperature,

the temperature of the feed determines the temperature of the

adsorption step. In order to investigate the effects of

temperature on adsorption, the simulation was carried out at

several temperatures and it was found that with increasing

temperature, the amount of adsorption decreased. Because

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

.35

.25

.15

1200

000

800

600

400

200

.05

t (min)

T=298 K

T=308 K

T=318 K

T=298 K

T=308 K

T=318 K

Fig. 3: Effect of feed temperature on output concentration

200

.35

.25

.15

1000

.05

t (min)

u=0.6 (m/s)

t (min)

u=0.523362 (m/s)

u=0.4 (m/s)

u=0.6 (m/s)

u=0.523362 (m/s)

u=0.4 (m/s)

Fig. 4: Effect of speed on output concentration

.2.3 The effect of pressure

In order to investigate the effect of pressure on the

3.2.4 Effect of bed length

By increasing the height of the adsorption bed in the

column, the contact time of the pollutant is increased with

the absorbent and the slope of the deflection curve decreases,

which indicates a massive mass transfer region at higher

altitudes. These results indicate that adsorbent optimum

efficiency is achieved with higher heights. As shown in Fig.

6 the adsorbate concentration in the outlet solid phase from

the bed reaches a value of 200, with a bed length of L =

0.254, L = 0.3and L = 0.35, respectively of 13, 20 and 25

minutes are needed.

performance of the absorption tower, the crevice curve has

been plotted for several different pressures. According to the

diagram, with increasing the pressure in the bed, the slope of

the curve increases and the time of saturation of the bed

specified length decreases. The reason for this is that with

increasing pressure the length of the mass transfer region

increases. With increasing pressure, adsorbents absorb more

pollutant gas. As shown in Fig. 5, at a specified time of 50

minutes, the adsorbate amount in the outlet gas phase from

the bed was P = 15.68, P = 18and P = 20= 0.28, 0.33, and

0.37.

3.2.5 Effect of adsorbent particle size

The amount of adsorbent in the absorption column

determines the number of available and active adsorption

sites. According to Equation 3, the mass transfer coefficient

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

with the absorbent diameter has a reverse relation and, with

increasing mass transfer coefficient, the absorbent diameter

decreases. As shown in Fig. 7, the time to reach the breaking

point in the diagram increases with decreasing mass transfer

coefficient. By increasing the number of adsorbent particles,

the time remaining in the column and the time to reach the

breaking point increases, and the saturation of the substrate

occurs later, which leads to an increase in adsorption

capacity. This is due to an increase in the absorbent special

level and absorption sites.

0.5

0.4

0.3

0.2

0.1

1400

200

000

t (min)

P=20 psi

t (min)

p=20 psi

P=15.68 psi

P=18 psi

p=15.68 psi

p=18 psi

Fig. 5: Effect of pressure on the output concentration

.35

.25

.15

1200

000

800

600

400

200

.05

t(min)

L=0.3 m

t (min)

L=0.3 m

L=0.254 m

L=0.35 m

L=0.254 m

L=0.35 m

Fig. 6: Effect of bed length on output concentration

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 324-333

.35

.25

.15

1200

000

.05

t(min)

k=0.0015 (1/S)

t(min)

k=0.00101 (1/S)

k=0.002 (1/S)

k=0.00101 (1/S)

k=0.002 (1/S)

k=0.0015 (1/S)

Fig 7: Effect of bed length on output concentration

3X, National Conference on Modern Technology in

Conclusion

The results of this study indicate that bed length, tower

Chemical Engineering, 2014

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investigated.

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