ХИМИЧЕСКАЯ ФИЗИКА, 2014, том 33, № 1, с. 58-68
ХИМИЧЕСКАЯ ФИЗИКА ЭКОЛОГИЧЕСКИХ ПРОЦЕССОВ
УДК 533.7
PREDICTION OF TRANSPORT PROPERTIES OF CO2-N2 BINARY MIXTURES VIA THE INVERSION OF REDUCED-VISCOSITY COLLISION INTEGRALS
© 2014 T. Hosseinnejad1*, H. Behnejad2
department of Chemistry, Faculty of Science, Alzahra University, Vanak, Tehran, Iran 2Department of Physical Chemistry, Faculty of Chemistry, University college of Science, University of Tehran, Tehran, Iran *E-mail: tayebeh.hosseinnejad@gmail.com Received 21.11.2012
In the present study, the main purpose is to extract information about the effective intermolecular potential energy function for binary mixture of nitrogen and carbon dioxide by the usage of a direct inversion of the experimentally reduced viscosity and second virial coefficient data and then to reproduce the dilute gas transport properties from the inverted potential energy. The Lennard-Jones (12, 6) potential energy function has been employed as the initial potential model required by the inversion method. The MSV potential obtained in this way is in reasonable agreement with the independently known CO2—N2 potential energy function. Using the inverted pair potential energies, the Chapman-Enskog scheme is employed to calculate transport properties of CO2—N2 in a wide composition and temperature range. The close agreement between the predicted values and the literature results of transport properties demonstrate the predictive power of the inversion scheme.
Keywords: transport properties, corresponding states, intermolecular potential for CO2—N2, direct inversion procedure, collision integrals.
DOI: 10.7868/S0207401X13120030
1. INTRODUCTION
It is clear that the transport properties of fluids are of great significance in many areas of technology.The design of chemical reactors, refrigeration and air conditioning equipment, process of heat exchange and lubrication requires the knowledge of the transport properties.
Increasingly, there is a demand for improved safety of technological processes. For example, the description of the process of pollutant dispersion contains diffusive and convective components into which the transport coefficients of the gas or liquid medium enter.
From the scientific viewpoint, accurate knowledge of transport properties of gases is essential for determination of intermolecular potential energy functions and for development of accurate theories of transport properties in the dense state. They are especially of interest because they provide a framework for an understanding of intermolecular forces. Accurate determination of the potential interaction has proven to be a challenging and interesting area of vigorous activity from both the experimental and the theoretical point ofview, including the analysis of molecular beam scattering data [1, 2], multiproperty fits [3] and ab initio calculation methods [4, 5].
A more desirable method of inferring molecular interactions directly from the experimental viscosity measurements in the form of the extended law of corresponding states, without explicit assumption of a mathematical model for intermolecular potential energy function, V(r), is inversion procedure [6, 7]. This iterative method permits us to calculate symmetrical effective interaction potential energy and then reproduce the other fluid transport properties. The reason for choosing the viscosity is that this property can usually be measured more easily and accurately than, say, the mutual diffusion coefficient of gases can. Meanwhile dilute gas transport properties have proven to be quite useful for testing and refining intermolecular potentials. For noble gases it is even possible to obtain an accurate representation of the pair-interaction potential directly from the inversion of transport properties, especially viscosity and diffusion data of gases [8, 9]. For polyatomic gases, however, the Chapman-Enskog theory of transport properties is fundamentally different from the monatomic molecules due to inelastic collisions which make a change in the rotation and vibration energies [10]. Consequently, the kinetic theory of polyatomic molecules is extremely difficult and only a few attempts perform to calculate the transport properties from this theory. To the first approximation
for polyatomic gases, we assume that direct inversion of the data for any of these properties gives an effective isotropic pair-interaction potential energy function. The other approximation has been proposed by Mason and Monchick, who assumed that the Chapman-Enskog theory of non-spherical molecules retains its original form, but the collision integrals must be averaged over all possible orientations occurring in collisions.
The precisely accurate correlations for low density thermodynamic and transport properties of noble gases have been formulated as the extended principle of corresponding states [11]. Also, the work concerning to the low density thermodynamic and transport properties of some polyatomic gases and their binary gas mixtures strongly indicates a similar principle could be applied to them [12, 13].
The main scope of this study, is to calculate ther-mophysical properties such as viscosity, diffusion and thermal diffusion of CO2—N2 by the aid of inversion process. In this respect, we describe inversion procedure for generating the inner branch of the effective potential energy of CO2—N2 from the corresponding states correlation of viscosity and the outer branch of the potential energy, corresponding to the second vir-ial coefficient data. The crucial benefit of the collision integrals obtained from the inversion of experimental viscosity is that they are expected to be more accurate than those obtained from other transport properties directly because measurement of viscosity is more practical and accurate than measurement of other transport properties, say diffusion and thermal conductivity.
We assume that the molecules have a fixed relative orientation during a collision. The physical basis for this assumption is that most of the interaction in a collision occurs in the vicinity of the distance of closest approach, during which the relative orientation does not change much, so that one relative orientation dominates each collision. The obtained results are then fitted to MSV potential model and compared with the previously determined potential [14].
We have then applied expressions obtained from the Chapman-Enskog theory [10, 15] together with our calculated collision integrals obtained from the inverted potential energy to reproduce viscosity, diffusion at P = 1.01325 bar, thermal conductivity and thermal diffusion factor of the binary mixture of CO2— N2 in a wide temperature and composition range. The validation of our recommended data for transport properties based on inversion method has been represented by comparison with the available experimental data which demonstatred that the average absolue deviation is within experimental error.
2. THE KINETIC THEORY OF DILUTE GASES
According to the kinetic theory and non equilibrium statistical mechanical theories of dilute gases, transport properties have been used to predict the forces between pairs of molecules. Thus, the knowledge of these fundamental intermolecular forces can inversely lead to gaseous transport coefficients. The Chapman-Enskog solution of Boltzmann transport equation [15] leads to the expressions for transport
properties based on a series of collision integrals that depends on the intermolecular potential energy V (r ), which is defined as
Q(l,s)(T) = [(1 + S)! (kT)S+2 J x x JQ(l)ES+1 exp(-E/kT) dE,
(1)
Q(l )(E ) = 2n
1 -
1 + (-1)' 2(l +1)
-1 w
J(1 - cos')bdb, (2)
x (b, E ) = n-
1 - ç ■
r
2V (r ) "
mw
-1/2 ]
(3)
in these expressions, m is the molecular mass, x is the
scattering angle, Q\E) is the transport collision integral, b is the impact parameter, E is the relative kinetic energy of colliding molecules, w is the relative velocity of colliding molecules, rm is the closest approach of two molecules and kT is the molecular thermal energy. Superscripts "l" and "s" appearing in the collision integral, fi, denote weighting factors that account for the mechanism of transport by molecular collision.
In order to determine the transport properties of polyatomic molecules numerically, we apply an approximation has been proposed by Monchick and Mason, who assumes that the Chapman-Enskog theory of nonspherical molecules retains its original form, but the collision integrals must be averaged over all possible relative orientations occurring in collisions. Thus Mason-Monchick orientation averaged collision integral [16], which is used in our calculation, is given by
1 1 2n
(/,s)*^ = 1 JJ Jq(/,s)*d9d(cos01 )d(cose2), (4)
-1 -1 0
^Q where
q(M*(T*) = Q(l,s)(T*)/
na
(5)
here the collision diameter a is defined as the separation distance when the intermolecular potential is equal to zero and T* = kT/s, where s is the potential well depth.
0
Following the kinetic theory of dilute gases, the mutual diffusion and viscosity coefficient of single substances in term of collision integrals are defined as
D12 =
^12 =
^k 3T3 (m1 + m2 ) 2nm1m2
5 [ 2nm1m2kT 16 ^ m1 + m2
a2 p( Q^*
(2,2)*
(6)
(7)
where m1 and m2 are the molar mass of two components, fD and f is the second-order Kihara correction factor for the calculation of transport properties which normally differs from unity by only 1%;
fD = 1 + (1/8) (6C* - 5)2/(2A* + 5), fn = 1 + (3/196)(8E* - 7)2.
(8) (9)
The ratios of collision integrals , B*, C*, E*, and necessary for calculating transport properties, are defined by the following formulas:
Q
(2,2)*
Q
(1,1)*\ '
A* =
h Qa2)*\ - Mq(13)*
(10a)
B* =
Q
(1,1)*
C* =
E* =
F * =
Q
(1,2)*
Q
(1,1)*
Q
(2,3)*
Q
(2,2)*
Q
(3,3)*
Q
(1,1)*
et al. [12] and Bzowski et al. [13] named as "The Extended Law of Corresponding States". So the extended corresponding state
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