CC BY
12
DOI: 10.17277/amt.2019.03.pp.056-065
A Numerical Study of Heat and Mass Exchange Processes in Swing Adsorption Device for Oxygen-Enriched Air
E.I. Akulinin*, O.O. Golubyatnikov, D.S. Dvoretsky, S.I. Dvoretsky
Tambov State Technical University, 106, Sovetskaya St., Tambov, 392000, Russia * Corresponding author. Tel.: +7 909 231 40 61. E-mail: [email protected]
Abstract
Using the developed mathematical model of the dynamics of cyclic adsorption processes for the separation of gas mixtures, numerical studies of heat and mass transfer processes in the PSA device for oxygen-enriched air have been carried out. Various programs have been studied to change the degree of opening of the inlet and outlet valves of the PSA device from the point of view of ensuring the maximum degree of oxygen concentration, a given value of the purity of the production gas and the permissible gas flow rate in the "front" layer of the adsorbent, at which the costly granular adsorbent is saved from destruction.
Keywords
Oxygen-enriched air; pressure swing adsorption; mathematical modeling; computational experiment; valve opening degree.
© E.I. Akulinin, O.O. Golubyatnikov, D.S. Dvoretsky, S.I. Dvoretsky, 2019
Introduction
One of the most effective and universal processes for purification and separation of gaseous media is cyclic adsorption processes carried out in pressure swing adsorption (PSA) devicess with a different number of adsorbers, receivers, valves and a complex process scheme. Various heat and mass transfer processes occur in adsorbers (more precisely, the adsorbent layer) (diffusion of the adsorbent in the gas mixture stream, mass transfer of the adsorbent and heat transfer between the gas phase and the adsorbent, adsorption of the adsorbent from the gas phase on the surface and in the micropores of the adsorbent granules with the release of heat and desorption adsorbate from micropores and from the surface of adsorbent granules into the gas phase with heat absorption) [1-8].
A distinctive feature of modern pressure swing adsorption processes and devices is the great complexity of the internal relationships of their parameters and characteristics, multi-stage processes (stages of adsorption and desorption of an adsorbent carried out under cyclically varying pressure; stages of drying and cooling of adsorbents, i.e. stages that mutually influence one another), the difference in
energy costs for carrying out the stages of the process. The successful implementation of pressure swing adsorption processes and devices in industry depends, in particular, on improving existing processes, engineering methods for calculating the equilibrium of adsorbent-adsorbate systems, kinetics in an individual adsorbent grain and the dynamics of the adsorbent macrolayer, design solutions and methods for optimizing cyclic adsorption processes. As a result, an important link in the development of cyclic adsorption processes at the design stage is the selection of optimal options for the design of processes, the modes of various stages of the pressure swing adsorption process for specific operating conditions when separating gas mixtures [9-12].
When designing / calculating PSA devices, they often use so-called undefined ("inaccurate") information on physicochemical parameters (for example, temperature, pressure, environmental composition, kinetic parameters of heat and mass transfer processes, etc.), which indirectly has a noticeable effect on the quality of functioning of cyclic adsorption processes.
Another problem of the effective functioning of the PSA devices is the high gas flow rate in the frontal
layer of the adsorbent, which leads to abrasion and destruction of the adsorbent granules [13-15]. It was shown in [16] that "careful" (stepwise opening of the intake valve) allows limiting the flow velocity in the frontal layer of the adsorbent, the maximum permissible value of which should not exceed ~ 0.2 m/s.
The aim of this research is a numerical study of heat and mass transfer processes in a PSA device for air-enriched oxygen and the influence of uncertain physicochemical parameters of cyclic adsorption processes on the efficiency of a PSA device, as well as a law (program) for changing the degree of inlet opening valves of the PSA device in time, providing the maximum degree of oxygen concentration, the specified purity of the production gas and the productivity of the installation, as well as the resource cutting of granular adsorbent.
The numerical study of heat and mass transfer processes and their influence on technological performance indicators of pressure swing adsorption processes
The technological process of oxygen concentration by adsorption separation of air is carried out in a two-adsorption PSA device with granular adsorbent -synthetic zeolite NaX [1-4, 17]. Input variables in PSA
devices include raw material load Gin - flow rate of the initial gas-air mixture (atmospheric air); vector of controls u = {P*n, tads, 0}; Pin - compressor outlet pressure; tads - adsorption stage duration (half cycle, tads = tdes); 0- backflow coefficient; uncertain
parameters: temperature Tgin; pressure p
out
and
component-wise composition yin of the initial air-gas mixture fed to adsorbers for separation. Design parameters include the inner diameter of the adsorber DA, absorber layer length L, adsorbent granule diameter dgr. The output variables are the degree of
oxygen extraction n, concentration y1out of production oxygen and related substances, performance Q of the PSA device.
A mathematical model of the dynamics of the cyclic adsorption process for air-enriched oxygen is given in [18, 19]. It includes the following equations:
1) component-wise material balance of components (O2, N2) in the gas phase flow, taking into account longitudinal mixing in the adsorbent layer (nonlinear partial differential equation of parabolic type);
2) kinetics of adsorption - desorption (nonlinear differential equation in ordinary derivatives);
3) heat distribution in the gas and solid phases, taking into account the convective component and thermal conductivity (nonlinear partial differential equations of parabolic type);
4) changes in the flow rate of the gas-air mixture and the pressure of the gas mixture (Ergun's differential equation in ordinary derivatives) along the height of the adsorbent.
To solve the equations of the mathematical model with the corresponding initial and boundary conditions, we used the direct method in the Matlab software environment [20].
A mathematical model of the dynamics of the cyclic process of adsorption concentration was used for the numerical study of heat and mass transfer processes and the influence of uncertain parameters on the output coordinates and technological performance indicators of the two-adsorption PSA device.
The source data for the computational experiments are presented in Table 1.
Fig. 1 shows the correlation graphs of oxygen
concentration j1out in the production flow and duration
tads = tc / 2 of adsorption-desorption half cycle for
different values of pressure Pin at the compressor
outlet and pressure Paidns at the adsorption stage and
temperature T™ of the environmental concentration of
production oxygen and the PSA device performance. From the analysis of the graphs it follows that with
an increase in pressure Pin at the compressor outlet and, accordingly, the pressure at the adsorption stage,
oxygen concentration >1out in the production flow and the PSA device performance increase. With an increase
of Pin from 2-105 to 6-105 Pa, the gas-air flow rate in the adsorber increases, as a result of which the time of occurrence of an oxygen-enriched air flow at the outlet
of the adsorber decreases (if Tgin = 303 K, Pin =
= 2-105 Pa, for tads = 3.5 s, Fig. 1a, curve 3; if
Pin = 6-105 Pa, for tads = 0,5 s, Fig. 1e, curve 3).
Especially noticeable is an increase in the concentration and performance of the PSA device at
elevated ambient temperature Tgin = 303 K
(Fig. 1a, b, e, f curve 3), when the equilibrium nitrogen concentration and the amount of adsorbed nitrogen at the adsorption stage decrease.
Table 1
Source data for computational experiments
Source data Nominal (working) values
The composition of the gas mixture i 1 _ o2; 2 - N2; 3 - Ar
Zeolite adsorbent NaX
Adsorption limit W0, sm3/g 0.17
Parameter B of the Dubinin equation, x10-6 1/K2 6 55
Design parameters
The number of adsorbents in the PSA device 2
Adsorbent inner diameter DA, m 0.04
Adsorbent layer length L, m 0.2
Adsorbent granule diameter dgr, mm 16
Receiver volume VR, l 2
Variables Range of variation Nominal values
Load
Flow capacity of input and output valves KV, l/min - 15
Compressor capacity GC, l/min 1-50 10
Controls
Adsorption stage duration tads (Adsorption-desorption half cycle), s
0.5-20 5
Compressor outlet pressure Pm x 10-5, Pa 2-6 4
Backflow coefficient 6, RU 1.0-2.4 1.7
Valve opening degree , RU 0-1 1
Uncertain parameters
Component concentration in the initial mixture yin = yenv 19.8-21.3; 78.2; 0.5-2.0 20.8; 78.2; 1.0
Initial mixture temperature Tg11 = Tenv, K 243-303 293
Outlet device pressure P1out = Benv, x 10-5, Pa 0.25-1.0 1
With an increase of Pin from 2-105 to 6-105 Pa there is an increase in maximum concentration yout of production oxygen from ot 61 to 87 % vol. (Fig. 1a, e, curves 3). An increase in yout along with a decrease in
9 and an increase in Pin provides an increase in the performance Q of the PSA device in oxygen enriched air (curves 3, Fig. 1b, d, f). For example, at ambient
temperature Tgin = 243 K, tads = 10 s, the device performance with increasing pressure Pin increases from 0.21 (curve 1, Fig. 1b) to 2.9 l/min (curve 1, Fig. 1f). The effect of desorption pressure (at the discharge
outlet of the PSA device P1out on the concentration and degree of oxygen extraction in the PSA device is shown in Fig. 2. With a decrease of P1out from 1-105 to
0.25-10 Pa the fraction of the flow taken for regeneration of the adsorbent decreases (characterized by a backflow coefficient 9), which is ensured by
increasing the pressure ratio kp (if Pin = 2-105 and P1out= 1105 Pa, kp = 2, and if P1out = 0.25-105 Pa, kp = 8). As a result, the performance of the device increases (for example, if tads = 10 s, Pin = 2-105 Pa,
Q increases from 0.25 to 5.2 l/min; and if Pin = 4-105 Pa, Q increases from 1.9 to 5.8 l/min). The degree of oxygen extraction n increases from 7 % (Fig. 2b, curve 3)
to 61 % if tads = 10 s, Pin = 2-105 Pa (Fig. 2b, curve 1),
and if Pin = 4-105 Pa it increases from 51 % (Fig. 2d, curve 3) to 73 % (Fig. 2d, curve 1). Thus, an increase in
n is ensured by a simultaneous increase in Pin and
decrease in P1out (i.e. increase in kp).
V-,out\% vol
10
15
c)
10
15
e)
'ads - '
'ads - '
0.6 0.4 0.2
0, 1 mill
3
2
|—-
O, I linn
10
b)
10
f)
15
^ads 5 c
^—
H---
^ads 3 ®
15
^ads 3 S
Fig. 1. The dependence of the concentration of production oxygen y™1 (a,c, e) and device performance Q (b, d, f)
on duration iads of "adsorption-desorption" half cycle for the compressor inlet pressure ffn = 2-105 Pa (a, b), 4-105 Pa (c, d), 6-105 Pa (e, f) and the temperature of the initial gas-air mixture:
1 - Tgn = 243 K; 2 - Tgn = 293 K; 3 - Tgn = 303 K
It can also be noted that with a decrease in P1out from 1-105 to 0.25-105 Pa, oxygen concentration at the device outlet y'°ut varies slightly: by ~ 5 % vol. for Pin = 2-105 Pa (Fig. 2a, curves 1, 3) and by ~ 3 % vol. -
if Pin = 4-105 Pa (Fig. 2c, curves 1, 3).
In the study of the influence of the composition of the initial gas-air mixture (oxygen concentration at the
device inlet y1n) on the concentration and degree of oxygen extraction at the PSA device outlet (Fig. 3) the following regularities were found. With an increase in
Pin from 2-105 to 6-105 Pa an increase in the gas-air
flow rate in the adsorber is observed, respectively, as in the case described in Fig. 1, the time of air enrichment with oxygen is reduced to the maximum achievable concentration. A comparative analysis of the curves in Fig. 3 showed that the change in the concentration of oxygen in the input stream from 19.8 up to 20.3 % vol. causes a change in the maximum oxygen concentration
at the PSA outlet: if Pin = 2-105 Pa, it varies from 76.2 to 78.6 % vol. (Fig. 3a, c, curves 1), as well as the degree of its extraction from 8.2 to 10.1 % (Fig. 3b, d,
curves 1); if Pin = 4-105 Pa, it varies from 83.6 to 85.4 % vol. (Fig. 3a, c, curves 3), as well as the degree of its extraction from 62 to 64.2 % (Fig. 3b, d, curves 3).
v-|out,% vol.
a)
10 c)
15
Fig. 2. Dependence of concentration y™* (a, c) and degree of extraction n (b, d) of production oxygen on the duration of half cycle iads if pressure at the compressor outlet Pin = 2-105 Pa (a, b); 4-105 Pa (c, d) and pressure at the device outlet: 1 - P°ut = 0.25-105 Pa; 2 - P°ut = 0.5-105 Pa; 3 - P°ut = 1105 Pa
80 60 40 20 0
60 40 20 0
10 b)
n, % 3
T 2 1
f y 1---
y
T 1
■ ►----
15
fads ?
n, %__ 1-- t—5-a
■--Il
1 2
>--- --t-<►
1
o
15
5 10
c) d)
Fig. 3. Dependence of concentration j0" (a, c) and degree of extraction of production oxygen n (b, d) on duration iads of "adsorption-desorption" half-cycle if oxygen concentration in the initial gas-air mixture y[n = 19.8 % vol. (a, b);
y{n = 20.3 % vol. (c, d) and pressure at the compressor outlet:
1 - Pin = 2-105 Pa; 2 - Pin = 4-105 Pa; 3 - Pin = 6-105 Pa
An increase in Pin from 2-105 to 6-105 Pa provides an increase in maximum oxygen concentration
y1out by ~ 7 % vol. (Fig. 3a, c, curves 1, 3), and the degree of extraction - by more than 6 times (Fig. 3b, d, curves 1, 3).
A study of the effect of changes in time of the degree of valve opening on the performance of a pressure swing adsorption device for air-enriched oxygen
When implementing the step-by-step law of valve opening in order to limit the gas-air flow rate in the frontal layer of the adsorbent, it is necessary to
determine the program for changing the degree of their opening in time, ensuring the achievement of maximum values of concentration, degree of extraction, and PSA device performance. The source data for the computational experiments are presented in Table. 2.
The program of change in time of the degree of opening of the inlet valves can be implemented in accordance with the uniform, convex and concave laws of change. The pressure dynamics in the adsorber, corresponding to the law of the change in time of the degree of valve opening is shown in Fig. 4.
Table 2
The Source data for a computational experiment to study the influence of the law (program) of the degree of opening of the inlet valves in time on the performance of the PSA device
Source data
Nominal values
Gas mixture composition i 1 - O2; 2 - N2, 3 - Ar
Zeolite adsorbent NaX
3 Adsorption limit W0, sm /g 0.17
Parameter B for Dubinin equation, x10 6, 1/K2 6.55
Design parameters
The number of adsorbers in the PSA device 2
Adsorber internal diameter DA, m 0.05
Adsorbent layer length HL, m 0.5
Adsorbent granule diameter dgr, mm 2
Reciver volume VR, l 5
Variables Range of variation Nominal values
Load
Capacity of inlet and oulet discharge valves GV, l/min 2-72 18
Controls
Time tc of adsorption-desorption cycle, s 1-360 30
Pressure at the adsorption stage P^ x 10 - 5, Pa 2-6 3
Pressure ad the desorption stage P^ x 10-5, Pa 0.25-1 1
Backflow coefficient 6, RU 0-2 1.6
Degree of valve opening , RU:
convex law 0.05; 0.1; 0.2; 0.5; 1.0
uniform law 0.2; 0.4; 0.6; 0.8; 1.0
concave law 0.55; 0.8; 0.9; 0.95; 1.0
Valve full opening time, s 12
Uncertain parameters
Component concentration in the initial mixture yenv,i , % vol. 19 .8-21.3; 78.2; 0.5-2.0 20.8; 78.2; 1.0
Initial mixture temperature Tlnv, °C -40 - +40 20
a)
0.18 0.15 0.12 0.09 0.06 0.03 0
Fig. 4.
g, k
\v V
V/ V X / V
—-^J iy —--
—
12
t, s
c)
20 16 12 o Gin, 1 min
\
V x / \
v
2 / C/
4
0
12
t s
d)
Dynamics of changes in the degree of opening valves of (a), pressure (b), velocity (c) and inlet flow rate (d) in an adsorber in one cycle (0-15 s - adsorption; 16-30 s - desorption) for different laws of change:
1 - uniform; 2 - convex; 3 - concave
When implementing the concave law of valve opening (Fig. 4b, curve 3) an increased rate of pressure build-up in the adsorbent layer is observed, which is explained by a higher opening velocity of the inlet valves (Fig. 4a, curve 3), and, accordingly, higher velocity (Fig. 4c, curve 3) and gas flow rate (Fig. 4d, curve 3) at the outlet to the adsorber if t = 0 - 6 s.
An analysis of the dependence of the concentration and degree of production oxygen extraction on the cycle time in the PSA device for various laws of changing the degree of valve opening allows us to conclude that the use of the concave law ensures the achievement of the maximum oxygen concentration
j1out= 92 % vol. at the outlet of the PSA device is much faster than the use of uniform law (14 s against 16 s, Fig. 5a, curvese 3,1) and convex law (14 s against 28 s, Fig. 5a, curvese 3, 2). The degree of extraction using the concave law (Fig. 5b, curve 3) is significantly higher compared to using the uniform law (Fig. 5b, curve 1) and convex law (Fig. 5b, curve 2). In particular, this regularity manifests itself for duration tc = 5-30 s of "adsorption-desorption cycle". For comparison, for duration tc = 20 s of "adsorption-
desorption cycle" we have: 1 - n = 14 %; 2 - n = 4 %; 3 - n = 27 % (Fig. 5b).
The influence of the backflow coefficient 9 on the concentration and degree of extraction of production oxygen for different laws of change in time of the degree of opening of the valves is less significant than, for example, the effect of the duration of the "adsorption-desorption" cycle (Fig. 5c, d). If 9 = 0.5, the difference between the values of the degrees of extraction when using concave and convex laws is 11 %, and for 9 = 1.5 this difference increases to ~ 18 % (Fig. 5d, curves 3, 2).
The analysis of dependence j1out and n on temperature 77gin and impurity concentration y™ in the
initial gas-air mixture indicates that the oxygen concentration at the outlet of the PSA device is practically independent of the type of law of the change in time of the degree of opening of the inlet valves (Fig. 6a, c), and the difference between the values of the degrees of extraction (Fig. 6b, d) is proportional to the performance of the installation under various laws
and is practically independent of Tgin and y3in .
a)
100 Vlou\ % vol 80
0.5
1.5
c)
d)
Fig. 5. Dependence of concentration y°ut (a, c) and degree of extraction of production oxygen n (b, d)
on duration tc (a, b) of "adsorption-desorption" cycle and backflow coefficient 0 (c, d) for different laws
of change in time of the opening degree of valves:
1 - uniform; 2 - convex; 3 - concave 40
93 91 89 87
i'1i:iUt, % vol.
2
3
0.5
1.5 v3in,%vol.
35 30 25 20 15 10
35 30 25 20 15 10
n, %
3
1
2
233
253
273 b)
293 TJ\ K
3 ■ " " —
--j—
2
0.5
1
1.5 V3m, % vol.
c)
d)
Fig. 6. Dependence of concentration y™1 (a, c) and degree of extraction n (b, d) of production oxygen on temperature 7gin (a, b) initial air-gas mixture and concentration j3'n (c, d) of impurities in the initial gas-air mixture
with various laws of change in time of the degree of opening of the valves:
1 - uniform; 2 - convex; 3 - concave
а)
80
60
40
20
80
60
40
20
0
n, %
3
------
0.25
b)
П , % "
^ 3
2
0.5
/V", x105 Pa
c) d)
Fig. 7. Dependence of concentration yout (a, c) and degree of extraction n (b, d) of production oxygen on pressures
i/dS (a, b), (c, d) at the stages of adsorption and desorption, respectively, with different laws of change in time of the degree of opening of the valves: 1 - uniform; 2 - convex; 3 - concave
From the analysis of the dependencies jiout and n
on pressure at the adsorption stag id it follows that the oxygen concentration at the outlet of the PSA device during the transition from concave to convex law changes less than 1% vol. (Fig. 7a). With an
increase in ids) there is also an increase in n (Fig. 7 b)
y1out, as the equilibrium nitrogen concentration in the adsorbent increases (Fig. 7a) and, so does the efficiency of gas separation [1-3]. The latter is largely due to the increased productivity of the PSA device
(an increase in id contributes to a decrease in the return flow coefficient 9 and, respectively, to an increase in the production flow extraction).
The analysis of dependencies jiout and n on
pressure values at the desorption stage shows that the dependence of the oxygen concentration at the outlet of the PSA device on the type of valve opening
law appears only if is less than 0.5 * 105 Pa (Fig. 7c). The difference between the values of the
degrees of extraction (рис. 7d) is proportional to the performance of the device under different laws of change in time of the degree of opening of the valves.
The similar character of the influence on y^ and П have changes in P.Jds and рЩ , which is explained
by a change in the coefficient of pressure ratio kp in almost the same range: or example, with an increase in pressure at the adsorption stage kp changes from 3 to 6, and with a decrease in pressure at the desorption stage, it changes from 1 to 4.
Conclusions
The studies of heat and mass transfer processes in pressure swing adsorption processes for oxygen-enriched air established a rational law of time variation in the degree of opening of the inlet and outlet valves of PSA devices (as well as its effect on the performance of PSA devices), which, along with resource-saving expensive adsorbent, provides the highest degree of extraction of oxygen from atmospheric air. The results
can be used to optimize and optimize the design of cyclic adsorption processes and resource-saving PSA devices for the separation and purification of gas mixtures
The research was funded by the Russian Ministry of Education and Science for Project No. 10.3533.2017
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