Mathematical Modeling of Filtration Efficiency of Granular Bed
Filter Based on Semi-Coke as Filter Medium
Miao Wang
Xi′an Jiaotong University City College, Xi′an, China
Keywords: Granular Bed Filter, Semi-Coke, Filtration Efficiency, Mathematical Model, Characteristic Parameter.
Abstract: In order to more accurately describe the change of the filtration efficiency of the granular bed filter using
semi-coke as the filter medium during the whole filtering process, the effects of the apparent gas velocity,
filter material thickness and filter material particle size on the filtration efficiency of the granular bed filter
were investigated on a cold state experimental device, taking into account the changes in bed voidage, dust
deposition on the filter material surface, and secondary entrainment, The mathematical model of unsteady
filtration efficiency is derived theoretically, and the correction coefficient expression of the filtration
coefficient in the particle bed filtration model is introduced as F(σ)=(1+bσ)n1(1-aσ)n2, fitting the
experimental results under different operating conditions with Matlab programming software, and obtaining
the values of characteristic parameters a and b. Within the scope of the experiment, the calculated value of
the mathematical model is in good agreement with the experimental value.
1 INTRODUCTION
China's energy structure presents the resource
endowment characteristics of "lack of oil, less gas
and relatively rich coal" (Wang S M, 2021), and the
coal-based energy consumption structure is difficult
to change in a short time. In 2020, China's
dependence on crude oil and natural gas will be 73%
and 43%, and the security of energy supply has
become an important factor restricting China's
economic development (Ren L, 2019). Using coal
pyrolysis to produce coal-based liquid fuels such as
coal tar is an effective way to fill the gap in
petroleum consumption and promote the efficient,
clean and low-carbon utilization of coal (Li T, 2021).
The coal pyrolysis process will produce a large
amount of fine dust, resulting in poor oil quality and
difficulty in further deep processing (Du X, Yang S
Q). Moreover, dust deposition in tar will form tar
residue that is difficult to deal with, thus leading to
operation problems such as pipeline blockage and
corrosion (Zhang Y Q, 2017). Granular bed filter has
the advantages of high temperature resistance,
corrosion resistance, high filtration efficiency and
stable operating pressure, etc., and has great
potential in high temperature dust removal (Yan S -
Fan Y J).
In recent years, domestic and foreign scholars
have carried out experimental research and
mechanism exploration for granular bed filters. Chen
Junlin et al. (CHEN Junlin, 2018) used CFD and
DEM methods to fit the relationship between
filtration efficiency and experimental operating
parameters by using the empirical relationship of
dust removal mechanism, but the model did not
consider the influence of dust deposition and
secondary dust removal. Liu Shuxian et al.(Liu S X,
2016) experimentally studied the factors affecting
the filtration efficiency of granular bed filter and
established the unsteady mathematical model. Yan
Shen (Yan S., 2018) experimentally studied the
effect of dust feed concentration and apparent gas
velocity on filtration efficiency, and established a
macro filtration model of granular bed filter.
At present, most of the macroscopic models of
-granular bed filter filtration focus on the changes in
the early stage of filtration, and cannot describe the
filtration efficiency in the later stage of filtration,
and most of the filter media with a smooth surface
are used as the filtration medium. In order to reduce
the cleaning cost of the granular bed filter and more
accurately describe the change of filtration
efficiency in the whole filtration process, this study
took coal pyrolysis product semi-coke as the
filtration medium and adopted a fixed granular bed
to filter the powdered semi-coke in the gas. The
mathematical model of unsteady filtration was
established. Under different apparent gas velocity,
488
Wang, M.
Mathematical Modeling of Filtration Efficiency of Granular Bed Filter Based on Semi-Coke as Filter Medium.
DOI: 10.5220/0012286400003807
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2023), pages 488-492
ISBN: 978-989-758-677-4
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
filter material thickness and filter material particle
size, the variation rule of the model parameters of
filtration efficiency is analyzed.
2 THEORETICAL
CALCULATION OF
FILTRATION EFFICIENCY OF
PARTICULATE BED FILTER
The flow of dusty gas in the bed can be
approximately regarded as one-dimensional flow,
ignoring the axial and radial diffusion effects. The
continuity equation under the granular bed filtration
state is as follows:
0
s
c
u
yt
(1)
The research of granular bed filtration usually
starts from clean filter material, so the initial
conditions and boundary conditions of its governing
equation are:
0, 0 ( 0, 0)c y t
(2)
, ( 0, 0)
in i
c c y t
(3)
When the dusty airflow passes through the
granular bed filter, the dust concentration in the
granular bed filter along the airflow movement
direction obeys the exponential change law (Wang
M, 2019):
c
c
y
(4)
From formulas (1) and (4), it can be concluded
that:
s
uc
t
(5)
When Porous medium is used as the filter
material, the dust will deposit on the surface of the
filter material and in the bed gap during the filtering
process, which changes the porosity of the entire bed,
so the dust removal performance of the granular bed
is affected. With the filtering process, the filtration
coefficient λ It also changes accordingly, introducing
a correction factor F=(σ), Indicates the degree of
deviation of dust concentration in dusty gases during
the filtration process(Bruno M W, 2014):
0
= ( )F
(6)
When considering the changes in the bed porosity
and dust deposition on the filter surface, as well as
the secondary entrainment phenomenon, the
expression F(σ) is:
12
( ) (1 ) (1 )
nn
F b a
(7)
When
/0t
, that is, the accumulation of
dust in the granular bed tends to be stable and
reaches saturation σ
max
, where a=1/σ
max
. When b is
larger, F(σ) is larger, and the growth rate of σ with
time is faster, and the filtration efficiency is higher.
When a is larger, F(σ) is smaller, the rate of decrease
with time is faster, and the filtration efficiency is
lower. Therefore, b represents the rising stage of
filtration efficiency before the granular bed reaches
saturation, that is, the accumulation process of dust;
a represents the decreasing stage of filtration
efficiency after the granular bed reaches saturation,
that is, the penetration process of dust.
It can be obtained by formula (4) ~ (7):
12
0
(1 ) (1 )
nn
s
u b a c
t
(8)
12
0
(1 ) (1 )
nn
c
b a c
y
(9)
Ives and Herzing et al. believe that there is the
following relationship between dust concentration in
the airflow and dust deposition density in the bed:
in i
c
c
(10)
The partial derivative of formula (10) is obtained
by substituting it into formula (9):
12
0
(1 ) (1 )
nn
ba
y
(11)
According to formula (8), the relationship
between the dust deposition rate on the bed surface
and time is as follows:
12
0
(1 ) (1 )
nn
i
s i i in
u b a c
t
(12)
Assuming that the filter material thickness is H
and the experimental boundary conditions are: dust
inlet concentration c(0)=c
in
, outlet concentration
c(H)=c
out
, it can be obtained:
0
0
d
d
out
in
cH
c
c
y
c
(13)
0
ln
out
in
c
c
H
(14)
When the operating conditions in the filtration
process are determined, the filtration efficiency of
the particle bed filter is:
=
in out
in
cc
c
(15)
In the formula: u
s
is the apparent gas velocity, m/s;
c is the dust concentration of dusty gas, kg/m
3
; σ is
the dust deposition rate, kg/m
3
; t is the filtering time,
s; λ is the filtration coefficient, 1/m; F(σ) is the
Mathematical Modeling of Filtration Efficiency of Granular Bed Filter Based on Semi-Coke as Filter Medium
489
correction factor; H is the filter material thickness, m;
η is the filtration efficiency of granular bed filter.
The bottom corner marks in and out are the dust
concentration at the inlet and outlet of the granular
bed filter respectively.
3 EXPERIMENTAL PART
The cold experimental device of granular bed filter
is shown in Figure 1, which mainly consists of a dust
feeding device, an air supply device, a granular bed
filter and a detection device. The dust is fed by a
screw feeder and mixed with air at the inlet of the
particle bed unit, and the dusty gas is separated by a
granular bed filter.
Figure 1: Experimental device for filtration characteristics
of granular bed filter.
4 RESULTS AND DISCUSSION
In the calculation formula of filtration efficiency, n
1
and n
2
are adjustment parameters and have no
specific physical significance. In order to study the
influence of a and b on the filtration efficiency, n
1
and n
2
are set. In this study, when n
1
=4 and n
2
=1.3,
the theoretical results have a good correlation with
the experimental results.
4.1 Effect of Apparent Gas Velocity on
Characteristic Constant of
Filtration Efficiency Equation
The filter material thickness is 150 mm, and the
filter material particle size is 0.83~ 1.25mm. Under
different apparent gas velocities, Matlab
programming software is used to fit the experimental
data. The fitting curve is shown in Figure 2, and the
characteristic constants of the equation are shown in
Table 1.
Simulated value: ─ 0.25m/s; ─ 0.35m/s; ─ 0.50m/s;
Experimental value: ● 0.25m/s; ■ 0.35m/s; ▲ 0.50m/s
Figure 2: Fitting curves of filtration efficiency at different
apparent gas velocities.
When the apparent gas velocity is 0.25 m/s, the
maximum filtration efficiency of the granular bed
filter for powdered semi-coke is 98.80%, and the
average filtration efficiency is 96.57%; when the
apparent gas velocity is 0.50 m/s, the maximum
filtration efficiency of the granular bed filter is
90.39%, and the average filtration efficiency is
82.92%.
Table 1: Characteristic constants of filtration efficiency
equation at different apparent gas velocities.
Apparent gas
velocity/(m·s-1)
λ0
a105/(m3·kg-1)
b105/(m3·kg-1)
R2
0.25
20.12
30.3
43
0.9935
0.35
17.91
42
39.80
0.9970
0.50
15.60
52
10
0.9973
As can be seen from Figure 2, in the rising stage
of filtration efficiency, the larger the apparent gas
velocity, the lower the filtration efficiency, that is,
the smaller the b value. With the increase of
apparent gas velocity, after the bed reaches
saturation, the faster the filtration efficiency
decreases, the lower the filtration efficiency, and the
larger the a value.
4.2 Effect of Filter Material Thickness
on Characteristic Constant of
Filtration Efficiency Equation
The apparent gas velocity is 0.35 m/s, and the filter
material particle size is 0.83~ 1.25mm. Under
different filter material thickness, the fitting curve of
filtration efficiency is shown in Figure 3, and the
characteristic constants of the equation are shown in
Table 2.
ANIT 2023 - The International Seminar on Artificial Intelligence, Networking and Information Technology
490
Simulated value: ─ 100mm; ─ 130mm; ─ 150mm;
Experimental value: ● 100mm; ■ 130mm; ▲ 150mm
Figure 3: Fitting curve of filtration efficiency under
different filter material thickness.
When the filter material thickness is 100 mm, the
maximum filtration efficiency of the granular bed
filter for powdered semi-coke is 95.29%, and the
average filtration efficiency is 88.38%. When the
filter material thickness is 150 mm, the maximum
filtration efficiency of the granular bed filter is
97.71%, and the average filtration efficiency reaches
the maximum, which is 95.48%.
Table 2: Characteristic constants of filtration efficiency
equation under different filter material thickness.
Filter
thickness/(mm)
λ
0
a10
5
/(m
3
·kg
-1
)
b10
5
/(m
3
·kg
-1
)
R
2
100
30.5
51.50
6
0.9971
130
19
45.20
27.90
0.9973
150
17.91
42
39.80
0.9970
Before reaching bed saturation, the larger the
filter material thickness, the higher the efficiency
and the larger the b value; After the bed reaches
saturation, with the extension of filtration time, the
dust in the filter material will flow to the bottom of
the bed under the scouring effect of the air flow, the
greater the filter material thickness, the greater the
probability of the dust washed by the air flow is
intercepted by the bottom of the bed, so it is
intercepted in the bed, therefore, the greater the filter
material thickness, the smaller the a value.
4.3 Effect of Filter Particle Size on
Characteristic Constant of
Filtration Efficiency Equation
The apparent gas velocity is 0.25 m/s and the filter
material thickness is 150 mm. Under different filter
particle sizes, the fitting curve of filtration efficiency
is shown in Figure 4, and the characteristic constants
of the equation are shown in Table 3.
Simulated value: ─ 0.38~0.83 mm; ─ 0.83~1.25 mm; ─
1.25~2.50 mm;
Experimental value: ● 0.38~0.83 mm; ■ 0.83~1.25 mm;
▲ 0.83~1.25 mm
Figure 4: Fitting curve of filtration efficiency under
different filter size.
When the filter material particle size decreases
from 1.25~ 2.50mm to 0.38~ 0.83mm, the maximum
filtration efficiency of the granular bed filter
increases from 95.26% to 99.08%, and the average
filtration efficiency increases from 85.70% to
97.16%.
Table 3: Characteristic constants of filtration efficiency
equation under different filter material particle size.
Filter
size/(mm)
λ
0
a10
5
/(m
3
·kg
-1
)
b10
5
/(m
3
·kg
-1
)
R
2
0.38~0.83
21.10
35
40.46
0.9354
0.83~1.25
17.91
42
39.80
0.9970
1.25~2.50
14.50
47
33
0.9996
In the initial stage of filtration, the larger the filter
material particle size, the lower the efficiency and
the smaller the b value; The larger the filter material
particle size, when the bed reaches saturation, the
less the amount of dust accumulated in the bed, the
larger the voidage, with the extension of the
filtration time, the more easily the dust that has been
captured to penetrate the bed with the air flow, the
lower the filtration efficiency, so the larger the filter
material particle size, the greater the a value.
5 CONCLUSION
Considering the changes in the porosity of the
surface and bed of the porous media filter material,
the filtration coefficient is introduced into the
particle bed filtration model, and the model
calculation is in good agreement with the
experimental value. The model can provide a
reference for the calculation of the filtration
efficiency of the particle bed using porous media as
filter material.
Mathematical Modeling of Filtration Efficiency of Granular Bed Filter Based on Semi-Coke as Filter Medium
491
In the experimental range, reducing the apparent
gas velocity and filter particle size and increasing
the filter material thickness can increase the
characteristic parameter b in the rising section of
filtration efficiency, and reduce the characteristic
parameter a in the falling section of filtration
efficiency, so as to improve the filtration efficiency
during the entire filtration time.
From the perspective of filtration efficiency of
granular bed filter, the operating conditions can be
selected as the apparent gas velocity of 0.25 m/s, the
filter material thickness is 150 mm, and the filter
material particle size is 0.38~0.83 mm. Under the
experimental conditions, the filtration efficiency of
the granular bed filter is 99.20%.
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