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Научни трудове на Съюза на учените в България-Пловдив. Серия В. Техника и технологии, естествен ии хуманитарни науки, том XVI., Съюз на учените сесия "Международна конференция на младите учени" 13-15 юни 2013. Scientific research of the Union of Scientists in Bulgaria-Plovdiv, series C. Natural Sciences and Humanities, Vol. XVI, ISSN 1311-9192, Union of Scientists, International Conference of Young Scientists, 13 - 15 June 2013, Plovdiv.
SENSITIVITY ANALYSIS OF THE SIMULATION ALGORITHMS OF THREE-PHASE MASS TRANSITION PROCESSES
Atanas Terziyski1, Nikolay Kochev2, Vesselina Paskaleva3 i, 2, 3 University of Plovdiv, Department of Analytical Chemistry and
Computer Chemistry
e-mail1: atanas@uni-plovdiv.net e-mail2: nick@uni-plovdiv.net e-mail3:vessy@uni-plovdiv.net
Abstract
The mass transfer of atmospheric trace gases through the surface of ice particles is a complex process. We modeled the kinetics of three-phase mass processes in dynamic flow systems by fitting the coated wall flow tube reactor experiments with the developed by us simulation algorithms. We have implemented a kinetic model based on the Langmuir law for surface adsorption and desorption with bulk penetration defined by the second Fick's law. In this work we present sensitivity analysis of some kinetic parameters used in our model. This validation of the model is done in two schemes: firstly we present stepwise variations of single kinetic parameters and secondly simultaneous variation of two connected parameters while keeping the kinetic rate constant. The obtained results presented in this article show that the numerical models are reliable tool for studying the experimental data from coated wall flow tube reactors.
Introduction
A major part of the atmospheric research are the processes causing depleting of the ozone layer. They mostly involve free radical reactions, heterogeneous interactions and correlating studies. Coated wall flow tube reactors are suitable for laboratory research of gas phase and surface reactions. However, very often the measured output is a complex function of many parameters. In the past years we have developed a numerical model [1] which includes the reactor geometry and experimental setup properties as well as the physicochemical processes adsorption and desorption on ice, and surface to bulk processes solution and segregation together with the bulk diffusion. In this paper we study the sensitivity of the recently published model by stepwise variation of some kinetic parameters. Generally the simulated signal is a function of the input parameters G(t)=f(kad ,k,,c ,k ,k ,D)[l\. The basic means to estimate the physicochemical parameters is to find the
s des s,max sol seg A J A
best fit, G(t), for the experimental signal Gexp. We studied how the simulated signal curve, G(t), is influenced by various parameters and showed that the curve changes are sensitive enough to derive useful information from the obtained simulation results.
Simulation inputs
The model has been tested with the following initial set of parameters value: adsorption rate
coefficient describing the speed of adsorbing molecules on the surface kads = 1.04*10-14 cm3s-1, desorption rate coefficient, giving the molecule rate that leave the surface kdes = 0.06 s-1, maximum surface concentration c = 9.3*1014 cm-2, solution coefficient k , = 0.2 s-1, that accounts the
s,max 7 sol 7
number of thermalized on the surface molecules which enter the ice bulk, the segregation rate coefficient k = 6*10-21 cm3s-1, that accounts the segregating rate of molecules from the ice bulk to the surface. The diffusion bulk coefficient D has been chosen from literature data to be 8*10-11 cm2s-1, the ice bulk depth is 10-3 cm. The chosen initial values are in agreement with previously reported results [2,3,4]. The simulations were performed with segment length of 0.4 cm and the
ice bulk divided into 1000 layers.
Sensitivity analysis of gas to surface parameters
In this section we demonstrate the sensitivity of the model in respect to the Langmuir kinetic rate coefficients kads and kdes. Figure 1 represents the changes of kads by factors of 2 and 0.5 multiplied to the default value. The number of steady state (ss) molecules is proportional to the adsorption coefficient due to higher surface concentration. The desorption signal (ds) has a higher value but its kinetics is not significantly changed.
K_ada = 5.2 E-15 K_ad9 = 10.4E-15 K_ads = 20.8 E-15
Lab time [s]
Lab time [s]
Figure 1. Variations of the adsorption rate Figure 2. Variations of the desorption rate coefficient with factor of 2 and 0.5. coefficient with factor of 2 and 0.5.
Figure 2 respectively expresses the influence of kdes by stepwise variation by factor of 2 and 0.5. We do observe different desorption kinetics, however the adsorption and steady state part of the curves are also changed. The two figures clearly express that the simulated signal is very sensitive. The ratio between kads and kdes is the Langmuir constant, which is proportional to the number of adsorbed molecules on the surface.
Sensitivity analysis of surface to bulk transfer parameters
In this section we vary analogously the solution and segregation coefficients. Figure 3 illustrates the changes in the result signal as function of the solution rate coefficient, ksoP is changed by factors of 2 and 0.5 while figure 4 presents the stepwise change of the segregation coefficient, kseg, and the corresponding resulting curves.
"1.2 3
■a i
Lab time [s] L.D0m8151
Figure 3. Variations of the solution rate coefficient Figure 4 Variations of the segregation rate with factor of 2 and 0.5. coefficient with factor of 2 and 0.5.
It can be clearly seen that the two figures are not distinguishable within the experimental error. The ratio of the two kool and k (KS=kso/kseg) has significantly higher influence, rather than their specific values as shown later in the report.
Sensitivity analysis of the bulk properties
In this section we study how the bulk definitions influence the obtained simulation signals.
Lab time [s] Lab time [s]
Figure 5. Variations of the diffusion coefficient Figure 6. Variations of the bulk depth with factor with factor of 2 and 0.5. of 2 and 0.5.
The diffusion coefficient, D, influences the steady state level of the signal (see Figure 5, between 200 and 400). Depending on the specific D value, the role of the ice thickness on the steady state level is important. Figure 6 shows that at chosen relatively low diffusion coefficient of 8*10" cm2s-1, ice depth does not play any role. However this tendency would be different for significantly higher values of D.
Sensitivity analysis of various kinetic parameters with fixed thermodynamical values
Figure 7 illustrates the combined effect obtained from changing both adsorption and desorption coefficients while keeping their ratio constant (KL=const). Figure 8 shows the results from a variation of both solution and segregation coefficients with constant ratio K==const. Both figures we reveal clearly that the gas-to-surface kinetics have much higher influence on the signal than the bulk processes. 228
Lab time [s] Lab time [s]
Figure 7. Variations of the adsorption and Figure 8. Variations of the solution and segregation diffusion coefficients with fixed Langmuir coefficients with fixed ratio of the two. constant.
Conclusions
The studied algorithms for simulation of three-phase mass transfer (adsorption-desorpion, solution-segregation, diffusion) are quite sensitive in respect to the studied input parameters: k ,,k, ,c ,k ,k ,D. The behavior of the simulated resulting curves obeys the logic of the
ads des s,max sol seg 0 jo
observed physicochemical processes. The developed numerical algorithms can be efficiently used to derive useful information from the experiments with coated wall flow tube reactors.
Acknowledgments
This work is supported by the Bulgarian National Fund for Scientific Research NFNI (project
MU02/12).
References:
1. N. Kochev, A. Terziyskil and M. Milev, Numerical Modeling of Three-Phase Mass Transition with an Application in Atmospheric Chemistry, Applied Mathematics, Vol.4 No.8A, 2013 (accepted for publication)
2. Behr, P., A. Terziyski, R. Zellner, Z., Acetone Adsorption on Ice Surfaces in the Temperature Range T = 190-220 K: Evidence for Aging Effects Due to Crystallographic Changes of the Adsorption Sites, J. Phys. Chem. A, 110 (26), 8098-8107 (2006)
3. Behr, P., U. Scharfenort, A. Terziyski, R. Zellner, Thermodynamics of the interaction of acetone and acetic acid with ice surfaces at temperatures between 190 and 223 K, Torus Press (2004)
4. A. Terziyski, P. Scheiff, N. Kochev, R. Nehme, P. Behr, and R. Zellner, A Dynamical Model for Surface Adsorption / Bulk Penetration of Acetic Acid on / into Ice Surfaces in Coated Wall Flow Reactors, 22nd International Symposium on Gas Kinetics, Boulder, Colorado, USA, June (2012)
