CC BY
4DOI: 10.6060/ivkkt.20216412.6393 УДК: 544.723.23
МОДЕЛЬ КИНЕТИКИ АДСОРБЦИОННОЙ ОЧИСТКИ АТМОСФЕРНОГО ВОЗДУХА ГРАНУЛАМИ ЦЕОЛИТА NaX ПРИ НЕИЗОТЕРМИЧЕСКИХ УСЛОВИЯХ
О.Н. Филимонова, А.С. Викулин, М.В. Енютина, О.В. Хорват
Ольга Николаевна Филимонова *, Андрей Сергеевич Викулин, Марина Викторовна Енютина Научно-исследовательский центр, Военный учебно-научный центр Военно-воздушных сил «Военно-воздушная академия им. профессора Н.Е. Жуковского и Ю.А. Гагарина», ул. Старых Большевиков, 54А, Воронеж, Российская Федерация, 394064
E-mail: olga270757@rambler.ru*, mmiler5472@yandex.ru, maryena63@mail.ru Олеся Владимировна Хорват
Кафедра иностранных языков, Военный учебно-научный центр Военно-воздушных сил «Военно-воздушная академия им. профессора Н.Е. Жуковского и Ю.А. Гагарина», ул. Старых Большевиков, 54А, Воронеж, Российская Федерация, 394064 E-mail: olessja81@yandex.ru
На основе обобщенной теории Ленгмюра представлены эквивалентные многокомпонентные изотермы основных примесей атмосферного воздуха (водяной пар, диоксид углерода и ацетилен), с использованием экспериментальных данных их адсорбционной емкости в гранулах цеолита NaX и расчетом константы Генри по температуре кипения при атмосферном давлении, для термодинамических условий в блоке комплексной очистки воздухоразделительнойустановки ТКДС-100В. Внутригранулярный тепломассообмен рассмотрен в линейном приближении Глюкауфа с применением суперпозиционного принципа поведения примесей в условиях диффузионного механизма их поглощения (молекулярный, Кнудсеновский, Фольмеровский). Получена модель с сосредоточенными параметрами в виде задачи Коши, причем идентификация кинетических коэффициентов проведена из решения задачи диффузии в шаре при граничных условиях первого рода. Теплоты адсорбций примесей найдены по изостерическому состоянию из двумерного уравнения Ван-дер-Ваальса с использованием соотношения Вант-Гоффа. Нестационарная среднеобъ-емная температура гранулы вычислена из решения начально-краевой задачи для уравнения теплопроводности шара с граничным условием первого рода на его поверхности, в предположении теплового равновесия фаз, и объемным равномерным тепловым источником, обусловленным теплотой адсорбции. Установлено, что лимитирующим механизмом переноса примесей в гранулах адсорбента является диффузия в микропорах. В условиях пропорциональной зависимости параметра Ленгмюровской изотермы от температуры сделана оценка уменьшения адсорбционной емкости адсорбента с повышением температуры, что позволило с помощью вычислительного эксперимента проанализировать кинетику поглощения основных примесей атмосферного воздуха гранулами цеолита NaX.
Ключевые слова: модель, кинетика, адсорбция, очистка, воздух, цеолит, температура
Для цитирования:
Филимонова О.Н., Викулин А.С., Енютина М.В., Хорват О.В. Модель кинетики адсорбционной очистки атмосферного воздуха гранулами цеолита NaX при неизотермических условиях. Изв. вузов. Химия и хим. технология. 2021. Т. 64. Вып. 12. С. 17-23 For citation:
Filimonova O.N., Vikulin A.S., Enyutina M.V., Khorvat О.У. Model of kinetics of adsorption purification of atmospheric air by zeolite NaX granules under non-isothermal conditions. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2021. V. 64. N 12. P. 17-23
MODEL OF KINETICS OF ADSORPTION PURIFICATION OF ATMOSPHERIC AIR BY ZEOLITE NaX GRANULES UNDER NON-ISOTHERMAL CONDITIONS
O.N. Filimonova, A.S. Vikulin, M.V. Enyutina, O.V. Khorvat
Olga N. Filimonova *, Andrey S. Vikulin, Marina V. Enyutina
Scientific Research Center, Military Educational and Scientific Center of the Air Force «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy», Starykh Bolshevikov st., 54A, Voronezh, 394064, Russia E-mail: olga270757@rambler.ru *, mmiler5472@yandex.ru, maryena63@mail.ru
Olesya V. Khorvat
Department of Foreign Languages, Military Educational and Scientific Center of the Air Force «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy», Starykh Bolshevikov st., 54A, Voronezh, 394064, Russia E-mail: olessja81@yandex.ru
Based on the generalized Langmuir theory, equivalent multicomponent isotherms of the main atmospheric air impurities (water vapor, carbon dioxide, and acetylene) are presented, using experimental data on their adsorption capacity in NaX zeolite granules and calculating the Henry constant from the boiling point at atmospheric pressure, for thermodynamic conditions in the block of complex cleaning of the TOPS-IOOV air separation unit. Intra-granular heat and mass transfer is considered in the linear Gluckauf approximation using the superposition principle of impurities behavior under the conditions of the diffusion mechanism of their absorption (molecular, Knud-senovsky, Folmerovsky). A model with lumped parameters is obtained in form of the Cauchy problem, and the identification of the kinetic coefficients is carried out from the solution of the diffusion problem in a ball under boundary conditions of the first kind. The impurities adsorption heats were found from the isosteric state from the two-dimensional equation van-der-Waals using the Van-Hoff ratio. The unsteady average volumetric granule temperature is calculated from the solution of the initial-boundary value problem for the equation of thermal conductivity of a sphere with a boundary condition of the first kind on its surface, under the assumption of thermal equilibrium of the phases, and a volumetric uniform heat source due to the adsorption heat. It was found that the limiting mechanism of impurity transfer in adsorbent granules is diffusion in micropores. Under the conditions of the proportional dependence of the Langmuir isotherm parameter on temperature, an estimate was made of the decrease in the adsorption capacity of the adsorbent with increasing temperature, which made it possible, using a computational experiment, to analyze the kinetics of absorption of the main atmospheric air impurities by granules of NaX zeolite.
Key words: model, kinetics, adsorption, purification, air, zeolite, temperature
INTRODUCTION
Granular synthetic zeolite NaX is the main component of a complex cleaning unit (CCU) of air separation units (ASU) for the oxygen and nitrogen separation from gaseous impurities (vaporous moisture (H2O), carbon dioxide (CO2), acetylene (C2H2)) of atmospheric air [1]. The exothermicity of the adsorption process reduces the adsorption capacity (static and dynamic) and reduces the efficiency of the adsorbers [2]; therefore, the heat and mass transfer processes accompanying adsorption are of a conjugate nature. In most cases, the presented nonisothermal models are limited to single-species adsorption [3], or the dependence of the governing parameters on temperature is neglected [4].
A common feature of solid-phase adsorbents, including zeolites, is their high specific absorption area due to the developed inner pore surface (for zeolites 200-600 m2/g [5], the average pore diameter is 2-10 A [6]), therefore, the adsorption process proceeds, according to the classical concepts [7], on the surface of the internal granules voids. This requires the transfer of molecules into the granules by the diffusion absorption mechanism with specific features depending on the pore size [8]. Diffusion in pores and molecular diffusion have the same driving force - the concentration gradient, however, their difference is that diffusion in pores occurs as a result of molecules collisions with walls, and molecular diffusion is initiated by collisions with other molecules in pores, and these two diffusions
types coincide when the pore diameter is large enough [9]. In the limiting case (the pore radius is less than the free path of molecules), pore diffusion becomes Knud-sen diffusion [10]:
Dk = 9700 • rp (t/^ )1/2, (1)
where rp is the average pore radius, cm; t is temperature, K; n is the molecular weight of the adsorbent, g/mol. To establish the relationship between diffusion in pores Dp and molecular diffusion, a semiempirical relation is used [8]
Dp = s pDM/lp, (2)
where Sp is the porosity of the adsorbent granules (0.05-0.5); lp is the pore tortuosity factor (for example, according to [11], it can reach values up to 100, but in most cases for zeolites it lies within 3.3-3.6); to calculate the molecular diffusion coefficient, the Chapman-Enskiy formula is applicable [12]
0.0018583 • t3/2 (1/^ A +1/^ B )1/2
Dm =-
pc22 Q(s /kt)
(3)
where цл, цв - molecular weights of gases A and B, g/mol; p- pressure, atm; 012 = (ол+ов)/2; ал, ав - diameters of molecules of gases A and B, A; Q(s/£i) is a di-mensionless function of temperature and intermolecular potential field for molecules A and B; s/k is the Len-nard-Johnson potential, K. If diffusion in pores and Knudsen diffusion occur simultaneously, then the joint diffusion coefficient is determined by the Bosanquit relation [12]
Dpk = D,1 + Dk\ (4)
Folmer diffusion characterizes the mass transfer of already adsorbed molecules over the inner pore surface [13]
lg Ds = 1.8 - 0.20AQ/(mRt),
(5)
Sc(r, t) Sq(r, т) + P p
p St
_L
r2 Sr
Dpkr
St
2 Sc(r,
P p
Dsr ■
Sq(r, t)
(6)
where t is time, s; rg - radius of the granule, m; r - current radius (0 < r < rg), m; c(r,x), q(r,x) - are the local
concentrations of the adsorbate in the pore medium and the adsorbed phase within the granule, kg/m3, wt. shares; pp is the density of the granule, kg/m3. The dependence of the diffusion coefficients (1)-(5) on temperature requires knowledge of the temperature fields inside the granules associated with the adsorption heat and the conditions at its outer boundary [15] using an equation of the thermal conductivity type, as well as the relationship between c(r,x)) and q(r,x), assuming that they are in equilibrium [16]
q=f W (7)
In addition to this, an appropriate set of initial and boundary conditions is required. If we take into account the adsorbate multicomponent, then it turns out that the problem can be solved only numerically, while there is no certainty about the existence and uniqueness of the result obtained [17]. The implementation of such an approach in a parametric search for the determination of effective modes of adsorbers operation is apparently justified, but when evaluating pre-design solutions for a reasonable choice of separation equipment, when it is necessary to carry out optimization procedures, a more flexible toolkit is needed in the form of models with lumped parameters, which integrally takes into account the adsorption process reference features. This study is devoted to the development of such a model.
MULTICOMPONENT IMPURITY ISOTHERMES
Let gaseous impurities in atmospheric air have the following subscript numbering: H2O - 1; CO2 - 2; C2H2 - 3. According to the generalized Langmuir theory [18], the equivalent expression for the 7-th (i = 1,3) adsorption component has the form
where AQ is the heat of adsorption, J/mol; R - universal gas constant, J/(mol K); m - surface index.
Due to the fact that the driving force of various diffusion mechanisms directly depends on the adsorbate concentration outside the granules, the heat and mass transfer inside them determines the adsorption processkinetics, it is necessary to consider together with the entire adsorbent layer [14]. In this case, the mixed kinetics of pore and surface mass transfer under the assumption of the diffusion mechanisms and monodisperse granules sphericity summation is described by the equation [8]
aiPi
1+
j=1
(8)
where p7 is the partial pressure of the 7-th component of the impurity, Pa; 07, b7 - are parameters determined from adsorption isotherms in a monovariant presence in atmospheric air, Pa-1, that is
0 aiPi q = 1+bp
(9)
The adsorption capacity of impurities in granules of zeolite NaX according to [19] is given in Table 1. For zeolites in [20] it was found that the Henry constant of the 7-th adsorbate K7 [mol/(g Pa)] can be determined by the empirical relation
lnK « 0.0623- tbj -18.12, (10)
where tb is the boiling point at atmospheric pressure
a
)
2
r
of the 7-th adsorbate, K (50 < tb < 350). It follows
ui
from the structure of the Langmuir equation that
ai = Mm, = Ki • (11)
Calculations of the values of a7 and b7 (see Table 1) are given for thermodynamic conditions at the entrance to the CCU ASU TOPS-IOOV [21] (po = 20 MPa, to = 288 K, density of granules pp = 1100 kg/m3 and their diameter dg = 4 mm), while the partial pressures of water vapor, carbon dioxide and acetylene are respectively equal [22]: pi* = 25.8 kPa; p2* = 0.608 kPa; p3* = 0.002 kPa.
Table 1
Isotherms parameters calculation
Parameter Adsorbate
H2O CO2 C2H2
qmi ' kg/m3 120.0 20.0 60.0
%, к 373.0 194.5 190.0
Цi, kg/mol I8.OIIO-3 44.010-3 26.04 10-3
üi, kg/(m3 Pa) 3308.0 0.069 0.054
bi, Pa-1 27.57 3.4510-3 9.05 10-4
From a comparative analysis of isotherms (Fig. 1) it follows that at the beginning the granules are saturated with water vapor, and then with carbon dioxide and acetylene (the same qualitative conclusion was made based on the results of pilot experiments in [19]).
Fig. 1. Isotherms of impurities: 1 - H2O; 2 - CO2; 3 - C2H2 (the
dotted line is the partial pressure of impurities) Рис. 1. Изотермы примесей: 1 - H2O; 2 - CO2; 3 - C2H2 (пунктирная линия - парциальные давления примесей)
INTRAGRANULAR MASS EXCHANGE
Regardless of which diffusion mechanism dominates during the transport of adsorbates into a granule, quantitative analysis requires the joint solution of equations (6) and (7) for each adsorbate with additional conditions. This problem is simplified using
the postulate of Gluckauf [23] that the rate of absorption of adsorbates by a granule is linearly proportional to the driving force of the process, which is defined as the difference between the concentration on the surface of the granule q and the superposition of the average
volumetric concentrations of adsorbed phases q; (t)
\dqi (T)-=kPi L - a;«! i=û
dx dq(r)
dx ^ dx
1=1
with initial conditions
q (0) = = const (13)
and limitation on adsorption capacity
q(x0) = q° = const, (14)
where q is the current concentration of the 7-th adsorbate in the adsorbent, kg/m3; q - total concentration
of adsorbates in the adsorbent granule, kg/m3; k - ki-
pi
netic coefficients, s-1, which are related to the geometrical dimensions of the granule, its physical characteristics and the diffusion mechanism; T0 - time to reach 99% of the adsorption capacity of the granule, s. The
identification k was carried out for the quasi-iso-
pi
steric adsorption mode (practically unchanged temperature and pressure). If, as in [8], we assume that in (6)
(s p / p p )dci (r, x)/ dx <<dqi (r, x)/ dx and fin (7) is
differentiable with respect to C7 (the Langmuir relation assumes this for c;- e [0,»), which is explicitly related to p7 through the equation of state for an ideal gas), that is dqt = f (c )dc, then from (6) it follows
d4i (7)
(12)
'i(r'T) - 11\D ¿Z2L - ..2 dr\De'r -
dx r2 dr \ ' dr where the effective diffusion coefficient is
D
Dei -
Pki
- + Dsj - const
(15)
(16)
f(ci )P p
Equation (15) is supplemented with the initial condition
q, (r,0) = 0, (17)
the condition for the concentration constancy of the 7-th adsorption phase at the outer boundary of the granule
q,i (rg, t) = am (18)
and the axisymmetry condition
dq, (0, T) dr
■ 0.
(19)
Solution of the initial-boundary value problem (15), (17) - (19) [24]
q,i(r, T) - qm +
2rgq
g4mt
(-1Г
2 ^ 2 n-1 n
4- z
( \ nnr
exp
( De п2к2т ^
(20)
3
2
r
r
g
g
к
у
It follows from (20) that
œ I
q (t) = 4mt + ^-2exP
( nen2K2^
n=1n
dT
(T) -qmiDei œ — =-Y^ ^exp
( Den2K2T ^
e
r g n=1
Substituting (21) and (22) into system (12),
and bearing in mind that for D n2n2x/r2 >> 1
ei s
œ 2
Z-rexp
n=1n
we get
( De n2n2T^ ei
g
Zexp
n=1
( De n2n2TÏ
e
g
^ 1,
= n2D / r2
p, = Щ1-
q,
-q,
-exp
q,
2acr qi
qm, -q, bc R,tqmi
27 R
8 ^i
I b = cri
Ltcribcri ' Cri' p™
Aß, = ß^ - Rit = 2^
dt(r, t)_ kp d
CpP p =T2 dr
>dt(r, t)'
dr
Aß P p s pTo
Table 2
(21) (22)
The adsorbates adsorption heat
Parameter Adsorbate
H2O CO2 C2H2
r, , J/(kgK) 461 189 320
t , K 647.3 304.1 309.0
pcn, pa 214.0105 71.5105 60.9105
acri 1755.4 194.95 677.1
bcr 1.743 10-3 1.005 10-3 2.029 10-3
Aß, J/mol 36272 17072 17368
Aß, J/kg 2.014106 0.388 106 0.667 106
"Pi n Det"g■ (23)
IMPURITIES ADSORPTION HEAT
The isosteric adsorption heat of the 7-th adsorbate was determined from the theoretical adsorption isotherm based on the two-dimensional Van-der-Waals equation [25]
f o A
t(r,0) = t(rg,t) = to, dt(0,t)/dr = 0. (28)
Solution of the initial-boundary value problem (27) and (28) [26]
T (R,0) = W
1 2 œ (iV*
-(1 - R2) + — X^^ sin(nnR)exp(-n2n20)
n=1
(24)
where ^7 is the gas constant of the 7-th adsorbate,
J/(kg K); t - average volumetric granule temperature,
K; £ - thermodynamic constant, Pakg/J; n , h are
cri cri
critical parameters equal to
R tcr
where t (R, 0) = t(r, t) - to; 0 = iaq / rg2; aq = Äp /(ppCp ); R = r/rg; W = Aß*pprg /(t0spkp). Average pellet temperature
1 1 œ
T (0) = -W
(-l)n
- + — X^^ cos(nn)exp(-n2n20)
15 n n=1 n
COMPUTATIONAL EXPERIMENT
(29)
(25)
where t , p are the critical temperature and pres-
cri r cri
sure of the 7-th adsorbate, respectively K and Pa. According to the van-Hoff equation [12]
-2 -
Qst =Rit dlnpi /dt,
whence the value of the heat of adsorption follows (Table 2) at qj / qm ^ 1
Evaluation of kinetic coefficients k assumes
pi
knowledge of the limiting diffusion mechanism in the granule and the corresponding value of the diffusion coefficient, and a comparative analysis using relation (16) (Table 3) shows that De « D k
Table 3
Diffusion coefficients and kinetic parameters for t0 = 288 K and p0 = 20 MPa Таблица 3. Коэффициенты диффузии и кинетиче-
(26)
The local temperature of the adsorbate granule porous matrix, under the assumption of phases thermal equilibrium, is determined from the thermal conductivity of a sphere with a uniform volumetric heat source due to the heat of adsorption
Parameter Adsorbate
H2O CO2 C2H2
Dpkt , m2/s 9.653 10-8 5.760 10-8 7.01010-8
kp, , s-1 0.238 0.142 0.173
(27)
where Xp, Cp - thermal conductivity and heat capacity of the adsorbent matrix, respectively, W/(m K) and J/(kg K); AQ* - specific heat of adsorption per granule, J/kg,
The time to of filling the adsorbate granules with adsorbates was calculated as follows. It follows from (12) and (13) that
(qm - q0) exp(- t) (30)
Substitution of (30) into the second equation of system (12) and subsequent integration from 0 to to,
2
r
g
v
/
2
r
g
ч
/
œ
2
2
ч
/
ч
/
q
m
a„„ =
cr
r
taking into account (14), allows obtaining an expression for the total concentration of adsorbates in a granule
q(To) = = £ f - ¡0] exp(- kptt) (31)
o t=Л
\n view of the fact that q(x0) = 0.99qw ,
from (31), T0 = 4.4 s was calculated. Since cp = 870 J/(kgK), Ap = 0.14 W/(mK) [14], therefore 60 = Ta/rg2 = 0.16 and, according to (29), the increase in the temperature of the adsorbent granule due to adsorption absorption will be ~ 4 K. If in (11) we restrict ourselves to the linear approximation of the parameter of the Langmuir isotherm on the temperature bi ~ t, then qm = a,- K /1 the coefficients a for the thermody-
namic conditions at the entrance to the adsorber are calculated (Table 4).
Table 4
The adsorption capacity of zeolite for impurities at t = 292 K
Таблица 4. Адсорбционная емкость цеолита по примесям при t = 292 К
Parameter Adsorbate
H2O CO2 C2H2
ai 10.447 83.48 103 32.0104
qm 118.35 19.72 59.38
Integration results (12) with initial conditions
(13), when q0 - 0
q,(T) = qjl-exp(-kpi)] (32)
q(T) = X qjl - exp (- kpT)] (33)
i=1
Calculations using relations (32) and (33) in the presence of a restrictive condition on the adsorption capacity (14) show (Fig. 2) that the influence of the ad-
sorption heat during the purification of atmospheric air cannot be neglected, since this can lead to the appearance of a "breakthrough" concentration impurities before the development of the CCU. For example, in this case, with a six-hour adsorption cycle, a decrease in the adsorption capacity by «1% due to an increase in the temperature of the adsorbent granule by 4 K reduces the operating time by 0.5 h.
Fig. 2. Kinetics of intragranular adsorption of impurities at 288 K (solid curves) and 292 K (dotted curves): 1, 1' - the total concentration of impurities; 2, 2' - water vapor; 3, 3' - acetylene; 4, 4' - carbon dioxide
Рис. 2. Кинетика внутригранулярной адсорбции примесей при 288 К (сплошные кривые) и 292 К (пунктирные кривые): 1, 1' - суммарная концентрация примесей; 2, 2' - водяной пар;
3, 3' - ацетилен; 4, 4' - диоксид углерода
CONCLUSION
The presented tools for assessing the adsorption heat effect on the intragranular kinetics of adsorption absorption of the main gaseous impurities from the atmospheric air by the NaX zeolite makes it possible to evaluate the purification efficiency.
The authors declare the absence a conflict of interest warranting disclosure in this article.
Авторы заявляют об отсутствии конфликта интересов, требующего раскрытия в данной статье.
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Поступила в редакцию (Received) 03.03.2021 Принята к опубликованию (Accepted) 21.10.2021
