^{1}

^{2}

^{1}

^{3}

One of the main problems in the flow-through gas purification technologies is related with continuous control of the outlet gas purity. The information concerning purity of the produced gas is on high demand, e.g., for processing systems integrated with gas purifiers. The positive solution of this problem has become possible only now due to the appearance of reactive getters (reactants) that serve as highly efficient sinks for gas impurities and our sorption model of the processes, which take place in gas purifiers with these reactants. According to the given model the appearance of a single valued functional connection between the purity of the gas product and the duration of the treatment of the gas flow by the sorbing powder is typical for any system Me -Y, where Me is a powder reactant and Y is an impurity gas. This strict correlation provides the mathematical justification to a simple method of determining the concentration of the impurity in the gas flow at the exit from the gas purifier. This method comes down to measuring of the quantity of the purified gas by a gas flow meter, the readings of which are graduated in the units of gas concentration.

In the production of high purity gases an important place belongs to gas purifiers, which in the essence are flow-through tubes by themselves with a sink for capturing impurities from the treated gas. The molecular sieves or getter materials are commonly used for this purpose in powder form or in the form of sintered porous bodies [

Therefore, the progress in this field can be feasible only with drastic impro- vements in the capturing capacity of getters and simplification of the methods for continuous control of impurities in the outlet gas.

The main step in the indicated direction is the development of getters with sorption capacity much larger compared to similar materials on the basis of transition metals [

The aim of the present paper is to describe the impurity gas capturing with a powder reactant in the flow-through gas purifier. The theory of the process is further used for searching the methods allowing replacing of costly direct measurements with inexpensive indirect ones.

The dynamic sorption of gases by adsorbents is well studied [

While the surface of adsorbents rapidly passivates in gas medium and gas sorption by absorbents is limited at room temperature by diffusion and low values of the ultimate solubility of gases in solids, reactants continuously capture gases till the material is entirely exhausted in the chemical reaction. At the limit sorption capacity of reactants is determined by the ratio Me:Y = 1:1, i.e. for capturing of one gas atom one metal atom is “spent”, which is unique for such application field as gas purification.

The difference between adsorbents and reactants is also significant in respect to the sorption kinetics. At initial stages, when active surface sites are abundant, adsorbents and reactants are similar in their activity. However, the saturation of the surface with impurity adatoms results in practical termination of the sorption process while in the case of reactants it is accompanied only with a change in the intake mechanism. The quantity m of the captured impurity Y at constant concentration in the gas phase may change with time either as

or

Now we can start solving the problem of gas purification in a flow-through tube with the powder reactant Me. Let’s consider an elementary layer dx containing n particles of the reactant limited by coordinates x_{1} and _{0}, and the porosity coefficient of the powder mass is ε. Then the layer volume

Hence, we find that

The gas enters the layer with the impurity concentration _{,} where

The material balance for the sink of impurities is

where

Me. The right hand part

Let us assume that we deal with a linear sorption law and a chemical reaction of first order. Then the increment of the amount of gas Y that sank in the layer

where _{0} to 0 in the intake process.

The value

where _{Me} and M_{Y} designate molar mass of Me and Y, respectively. Substituting the found value

Here,

Equation (4) is to be supplemented with the obvious boundary conditions

Let us introduce dimensionless parameters:

In this case the mathematical model is transformed to the form:

where

is a functional of the dimensionless concentration

The solution of the problem (7)-(10) was found with the help of an iterative method (see Appendix II). The problem has two controlling parameters: A and B, where A determines the rate of the impurity intake from the gas and B determines the lifespan of the powder reactant. At the stage of the analysis an issue of the time scale of the discussed process arises. As it follows from the model (7)-(10) the solution at the first iteration (formula II.1, Appendix II) describes the steady-state impurity concentration distribution in the conditions of “inexhaustible sink” when function

The calculated time dependent changes for the gas concentration are pre- sented in

Particularly illustrative is the curve

The plots in

In fact, it can be seen that curve u_{3} is clearly closer to curve u_{2} than the latter is to curve u_{1}. Let us also have in mind that qualitative behavior of curves repeats for all the iterations. That is, there are all the reasons to believe that the presented here approximation is correct and can be used for searching for correlations between the purity of the end gas product and one or another measurable parameter of the sorption process.

The question about the dependence of concentration Y in the flow of gas in the outlet from the gas purifier on time is the question about the behavior of function_{0} = 0.05 mol/m^{3}, ε = 0.33, r_{0} = 10^{−4} m, L = 0.1 m, k_{0} = 0.14 mol/m^{2}・s and v = 0.02 m/s.

The plot for _{c} then the projection of the intersection point of the red line with curve _{с} of the given gas purification tube. That is, the problem of tracking the quality of gases treated by gas purifiers is in principle solvable and the solution follows directly from the described sorption model.

As regards the degree of purification of the gas flow, its maximal value according to Appendix II is limited by

the first portions of purified by the reactant gas will have the purity of about 99.9999995%.

For better understanding let us go back to

In the given figure a chain of situated along axis _{2} (

Function

under the condition that the characteristics of the system Me-Y as well as the technical data of the equipment and the process parameters retain their values with time, curve

The total amount of gas that passed through the tube at time τ is _{B} is the Boltzmann constant and T is absolute temperature. The amount of the captured impurity Y at time τ is_{A} is the Avogadro constant. Then the impurity concentration in the outlet gas is

where

Then the share of the reactant spent at time τ and coordinate

while the total share of the reactant that has entered into reaction with impurity Y at time τ (see

The graphical form of this function (D(τ) henceforth) is given in

On the other hand, the same share D(τ) can be expressed as

Substituting (12) in (11) we finally arrive to dependence of the purity of outlet gas on τ

where _{B} is the universal gas constant.

Formulas (12) and (13) are the contribution of the sorption theory of reactants, which we are developing, in the technology of gas purification. Formula (12) allows estimating in the efficiency of purification according to the cost/quality criterion. For this it is enough to assume in (12)

and to repeat these estimations, if required, for other purity levels u_{c} of the end product.

In its turn formula (13) can be considered as a theoretical grounding of the

method of determination of the purity of the outlet gas according to purification time. At engineering level this method is realized by using a timer with a display graduated according to the results of the analysis of the gas samples taken in specified time intervals at the outlet of the flow tube. This supposes organization of a preliminary testing procedure with the involvement of precision analytical equipment according to the data of which experimental curve

In industrial conditions it is more convenient to use not

If in expression for N we pass over from τ to real time

In this case in much the same way as an experimental curve

The reliability of such an indicator will be very high if in its graduating the results of several tests performed with the help of Atmospheric Pressure Chemical Ionization Mass Spectrometer (APCI-MS) are used. The existing gas analyzers for gas stream monitoring are capable of detecting only a very limited set of gas species. For this reason the indicator, which we are describing here, should be tuned for determining the concentration of the main, i.e. the target gas and in this case the APCI-MS is indispensable.

So, the analysis of the sorption phenomena in powder reactants shows the possibility of solving the problem of economical security of the process systems, which use in their technologies gases fed from gas purifiers. The authors realize the importance of this problem for gas industry and are planning to describe in their next publication how the idea of the indicator of purity of the gas product is modifies depending on the conditions of the sorption process. What is understood here is the substitution in gas purifiers the reactants following the linear sorption law with the reactants following parabolic law as well as the transfer from the sorption processes in motionless powders to the processes with the participation of tribological effects.

1) A mathematical model is developed for the process impurity gas capturing by powder reactants in flow tubes targeted for finishing gas purification.

2) The solutions of the model show the existence of the single valued functional connection

3) The mentioned function provides the theoretical basis for the attempts of creating indirect methods of measuring purity of the gas product.

4) Any attempt of this kind by necessity includes certain practical actions aimed at building experimental curves

5) The simplest variant of this kind of an indicator is a gas flow meter calibrated for the units of gas concentration.

On the whole, it can be expected that the appearance of gas purifiers with metallic reactants and purity indicators of the outlet gas will considerably improve the efficiency of gas purification and the level of economical security for the customers of high purity gases.

A. O. Ivanov gratefully acknowledges research funding from the Ministry of Education and Science of the Russian Federation [Contract no. 02.A03.21.0006, Project no. 3.1438.2017/4.6].

Chuntonov, K., Ivanov, A.O., Verbitsky, B. and Kozhevnikov, V.L. (2017) Gas Purification and Quality Control of the End Gas Product. Journal of Materials Science and Chemical Engineering, 5, 44-58. https://doi.org/10.4236/msce.2017.58005

The current radius _{ }is formed (

The consumption of the metal Me in an act like this one is measured by a layer of thickness

If the reactant has a shape of a ball particle of radius r (

Basing on the above said and taking into account the data of

where _{Ме} and M_{Y} are molar masses of Me and Y respectively. From here we find

taking into consideration that

One more remark. The thickness of the layer

process is accompanied with volume contraction of the product. The given fact together with the equality

Equation (7) with boundary conditions (8) and (9) can be solved with the help of an iterative procedure, which in the essence is building up disturbances accord- ing to the small value of parameter B.

The first iteration gives

with the solution

The second iteration

results in the solution

Here

The third iteration is so bulky that it is presented only in a graphical form.

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