Mixing of gases. Molecular and molar (turbulent) diffusion
Molecular diffusion- the process of mutual penetration of molecules of one gas into another, leading to the formation of a perfect mixture, is observed in stationary gases and in laminar flows.
In molecular diffusion, the mixing of gases is determined by the thermal movement of molecules. Although the speed of movement of molecules W on average is very large, the free path length / is small. Therefore, molecular diffusion proceeds quite slowly. The amount of gas diffusing from one layer to another, according to Fick's law, is equal to
where is the molecular diffusion coefficient, m 2 /s; dC/dn -
concentration gradient of the diffusing gas, kg/m4.
As the temperature rises D and diffusion intensity increase. Size D can be determined using the Sutherland formula modified by N.D. Kosova:
where D)12 is the diffusion coefficient of one gas (1) into another (2) gas at pressure p Q and temperature 7o; Q and C2 are the Sutherland coefficients for the components of the mixture, K (for methane C = 198, air - 119, nitrogen - 107.0 2 - 138, C0 2 - 255); p 0, G 0 - the value of pressure and temperature, respectively, under normal physical conditions (po= 1.01 10 5 Pa; T 0= 273 K).
Often used to determine the molecular diffusion coefficient D a simple power formula is used
Where P- empirical coefficient
The dependences for the diffusion coefficients of a multicomponent mixture are more complex (see, p. 80).
In a turbulent flow, diffusion, as well as heat transfer and internal friction, is associated with turbulent transfer and mixing of finite macroscopic masses of gas - turbulent moles. The sizes of these moles and the paths of their movement before mixing are varied; there is a spectrum of values of these quantities. The movement of moths is pulsating in nature, the speeds of their movement are the speeds of pulsations across the flow. At low Re numbers, large-scale pulsations are observed; turbulent velocities change significantly only at large distances. Under pulsation scale(turbulence) understand the order of the length over which a significant change in speed occurs. The frequencies of large-scale pulsations are low.
As Re increases, along with large-scale ones, high-frequency small-scale pulsations also appear. The scale of large-scale pulsations is of the order of the determining dimensions of the system (. D, I channel or free jet, etc.). Large-scale pulsations determine the processes of turbulent mixing: internal friction, diffusion and heat transfer. Small-scale pulsations carry out viscous dissipation. Energy from large-scale moths is transferred to small-scale ones and dissipated by them. Mixing during turbulent diffusion is completed due to molecular diffusion.
Using dimensional considerations and analogy with molecular transfer processes, we introduce the concept turbulent transfer coefficient A T, which characterizes internal friction, diffusion and heat transfer in a turbulent flow:
Where G- scale of turbulence, length of turbulent movement
praying until mixed (analogue /); - root mean square
pulsating speed.
Coefficient A t is also the coefficient of turbulent diffusion D T turbulent thermal diffusivity a t and viscosity (v T). It does not depend on the properties of the gas and is determined by the characteristics of turbulence. 
Substituting (3.57) into (3.56), we obtain Prandtl’s formula
Relation (3.58) allows us to estimate the transfer coefficients in a turbulent flow. To calculate transfer (diffusion) processes, you can use relations (equations) related to molecular processes, replacing them D, a, V on D T, and t, vx. When the influence of turbulent and molecular transport is comparable, total coefficients are introduced.
Each gas in mixtures behaves as if it alone occupies the entire volume of the vessel: its molecules disperse evenly in space and create their own, so-called partial pressure pi on the walls of the vessel. If the mixture is in equilibrium, the temperature of all gases is the same and equal to the temperature of the mixture TCM. The mass of the mixture is equal to the sum of the masses of the components; The pressure of the mixture according to Dalton’s law of partial pressures (1801) is equal to the sum of the partial pressures:
where n is the number of components making up the mixture.
The English physicist and chemist John DALTON (1766–1844) formulated in 1803 the law of multiple ratios: if two simple or complex substances form more than one compound with each other, then the masses of one substance per the same mass of another substance are related as integers, usually small. For example, in five nitrogen oxides (N 2 O, NO, N 2 O 3, NO 2, N 2 O 5) the amount of oxygen to the same weight amount of nitrogen is 1: 2: 3: 4: 5. Dalton correctly explained this law by the atomic structure of matter and the ability of atoms of one substance to combine with varying numbers of atoms of another substance. At the same time, Dalton proposed using the concept of atomic weight in chemistry. Knowing the atomic weights of elements, it is possible to establish the measure of chemical transformations and chemical ratios of substances, as well as to draw up quantitative reaction equations. For the first time (1794), he conducted research and described a vision defect that he himself suffered from - color blindness, later named color blindness in his honor.
For half of his life, Dalton had no idea that there was anything wrong with his vision. He studied optics and chemistry, but discovered his defect thanks to his passion for botany. The fact that he could not distinguish a blue flower from a pink one he initially attributed to confusion in the classification of flowers, and not to deficiencies in his own vision. Dalton noticed that a flower that looked sky blue in the light of the sun (or rather, the color he thought was sky blue) looked dark red in the light of a candle. He turned to those around him, but no one saw such a strange transformation, with the exception of his brother. So Dalton realized that there was something wrong with his vision and that this problem was inherited. In 1995, studies were carried out on John Dalton's preserved eye, which revealed that he suffered from a rare form of color blindness - deuteranopia. Deuteranopes have a lack of M-cone pigment, as a result of which the diseased are relatively insensitive to the average wavelengths of the green part of the spectrum, but at the same time perceive the short-wave part of the spectrum as blue and the long-wave part as yellow.
The properties of the mixture depend on its composition, which can be set in various ways. The simplest and most convenient is to specify the mass composition, i.e. For each gas, its mass fraction in the mixture is specified:
The mole fraction is the ratio of the number of kilomoles of a given gas to the number of kilomoles of the entire mixture:
where m i is the molecular weight of the i-th component.
Size
is called the apparent molecular weight of the mixture.
Often the composition of the mixture is specified by volume fractions
where V i is the partial volume of the i-th component, i.e. the volume that a given gas would occupy if its pressure were not p i , but p SM (at the same temperature T SM), .
For a real state, the relationship between the parameters is determined by the equation p i ×V CM =m i ×R i ×T CM, and for a conditional state - p CM ×V i = = m i ×R i ×T CM. From the equality of the right-hand sides of these equations it follows p i ×V CM =p CM ×V i , from which we find two important formulas:
It is important to know the relationships between the quantities g i, y i and r i. To find these relationships, we carry out the following simple transformations that do not require additional explanation:
Here 22.4 is the volume of 1 kmol of any gas under normal conditions, m 3 (according to Avogadro’s law, most gases have this volume, although there are small deviations).
Volume fraction
Since the right-hand sides of the last 2 formulas are the same, we can conclude that the mole fractions are equal to the volume fractions: y i = r i.
We get another relationship like this:
Replacing y i with r i, let’s write it differently:
r i ×m i =g i ×m SM.
Let us sum up the resulting formulas for all n components of the mixture. As a result we will have
because the .
Based on the property of additivity, the following formulas can be written to calculate the heat capacities of the mixture:
The value of the gas constant is found similarly:
or, as for any gas, through the universal gas constant according to the formula R CM = 8314/m CM.
Let's take a closer look at the two most typical mixing methods.
1. Mixing of gases by combining individual volumes. Let there be n different gases located in separate vessels with volumes V 1, V 2, .... The parameters of each gas are p 1, p 2, ... and T 1, T 2, ... To obtain a mixture, these volumes are combined or by removing partitions, or using short pipelines of a sufficiently large cross-section. As a result of the flow and diffusion of gases after a certain period of time, a homogeneous mixture is obtained, the mass and volume of which can be determined by simple summation:
where is the mass of the i-th component, R i is its gas constant.
When mixing, no external work is done and no external heat exchange occurs (dl = 0, dq = 0), which means the internal energy of each gas does not change (du = 0). Therefore, the internal energy of the mixture will be the sum of the internal energy of its components, i.e.
Here u CM = m CM × c V C M × (T C M – T 0) and u i = m i × c V i × (T i – T 0),
where c Vi is the average heat capacity of the i-th component in isobaric processes.
Let's substitute the given expressions into the original formula:
and carry out the following transformations: divide both sides by m SM (in this case, on the right side we get ), open the brackets and take out the constant value T 0 outside the sum sign:
If we take into account that , then after bringing similar terms the formula will take the form
We find the pressure of the mixture from the equation of state of an ideal gas:
Let us imagine that the formation of the mixture occurs in two stages. At the first stage, the partitions between the components become elastic and conduct heat well. Then, as a result of deformations and heat exchange occurring in a reversible manner, the temperatures and pressures of the components are equalized (they will become equal to p SM and T SM) and the volumes of gases change. The entropy of such a state will be
At the second stage, the partitions are removed. Then, as a result of diffusion, each gas will spread throughout the entire volume, and each component will have parameters T CM and p i = r i × p CM, where r i is the volume fraction of the component. In this case, the entropy of a mixture can be defined as the sum of the entropies of the components:
Comparison of these formulas allows us to find the increase in entropy due to irreversibility:
which makes it easy to find loss of performance
Dl = T 0 × Ds REV.
If, for example, it is necessary to divide the mixture into separate components, then at a minimum it will be necessary to expend the work Dl.
2. Mixing of gas streams is a method of continuously producing mixtures. Several gas streams are directed into one outlet channel. Let M i of gas flow through the i-th channel, kg/s, with parameters p i and T i . Then the volumetric flow rate of this flow will be
and the speed
When mixing flows, the velocities of gases are low and differ little from each other. Therefore, the difference in gas velocities can be neglected and it can be assumed that the pressures p i of the gases are practically the same and equal to p SM.
If the pressure is constant and there is no external heat exchange, the following enthalpy balance will occur:
Since for an ideal gas h = с р ×(Т – Т 0), the above formula can be written as follows:
Where ; c pi is the average isobaric heat capacity of the i-th component.
Carrying out transformations similar to the previous ones, we get
Now you can find the volumetric flow rate of the mixture and its speed in the output channel with cross section F OUT.
To identify the characteristics of the conditions of moist air, let us mentally carry out the following experiment. Let's place a small amount of water in a closed volume with dry air. As a result of its evaporation, a mixture is formed, which is called moist air. If you add a small amount of water, the concentration and partial pressure of the vapor will increase after evaporation. However, this will only be observed until dynamic equilibrium between vapor and liquid occurs, i.e. until the steam in the mixture becomes saturated with a pressure of pH.
With sufficient accuracy for practice, both components of moist air are taken to be an ideal gas. As for any gas mixture, in this case the pressure of the mixture is determined by the sum of the partial pressures: p SM = p SV + p P.
Usually you have to deal with atmospheric moist air, then p CM is equal to barometric pressure B, i.e. r SV + + r P = V.
The mass of steam contained in 1 m 3 of moist air is called absolute humidity. Absolute humidity is equal to the density of vapor in moist air. Maximum absolute humidity of saturated humid air r" = 1/v".
Relative humidity is the ratio of absolute humidity to the maximum possible under the same conditions: j = r P /r".
Applying the ideal gas equation of state for the vapor component, we can write
The resulting relationship is often taken as the definition of j. Usually the value j is expressed not in shares, but as a percentage. The relative humidity of saturated air is 100%. The value j is measured using psychrometers or hygrometers.
The simplest psychrometer consists of two alcohol thermometers, one is a regular dry thermometer, and the second has a humidification device. The temperature sensor of a wet bulb thermometer is wrapped in cotton cloth, which is placed in a container of water. The rate of moisture evaporation increases as the relative air humidity decreases. Evaporation of moisture causes cooling of the object from which the moisture evaporates. As the temperature sensor of the wet thermometer cools, the rate of moisture evaporation decreases until, at a certain temperature, dynamic equilibrium is reached - the amount of evaporated moisture is equal to the amount of condensed moisture. Thus, the wet bulb temperature will give information about the relative humidity of the air. Thermometers have precise graduations with division values of 0.2–0.1 degrees. A psychometric table may be included in the design of the device for ease of use.
The mass of moist air located in a certain volume V , determined by the sum of the masses of dry air and steam
m BB = m C B + m P.
After dividing this formula by the value V we get
r BB = r C B + r P.
Using the equation of state for dry air and the above relationships, we find
Let us substitute the found values into the formula for the density of moist air and after simple transformations we obtain:
Note now that R B< R П, значит (1/R B – 1/R П) >0. The quantity B/(R B ×T) is equal to the density of dry air at barometric pressure. Then the conclusion follows from the last formula: the density of moist air is less than the density of dry air at the same (usually barometric) pressure. True, the difference in densities is small, so in technical calculations they usually take r BB = r C B, although, if necessary, more accurate calculations can be performed using the last expression.
In practical calculations, the humid air parameter called moisture content d is widely used. By definition, moisture content is the amount of moisture or steam, kg (g), per kilogram of dry air:
For volume V the quantities m P = V × r P, m SV = V × r SV. Then
The ratio R SV /R P = 0.622, so we finally have
An important parameter of moist air is its enthalpy, which is the sum of the enthalpy of dry air and the enthalpy of steam contained in the mixture:
H = H CB + H P = c R CB × t + d × (h" + r + c R P × (t – t N)).
Analytical connections between t, j, d and H are quite complex and often non-algebraic. Therefore, solving many problems is difficult and requires iterative methods. To simplify and facilitate calculations, use a special H–d diagram constructed for pressure B = 745 mm Hg. Art. based on the saturation tables and the above formulas. This diagram is plotted in an oblique coordinate grid:
The diagram shows a grid of lines j = const, a grid of isotherms t = const and lines Н = const, directed at an angle of 45° to the vertical. The presence of these grids makes it possible to use any two given parameters from the list of t, j, d and H to find a point on the diagram, and therefore the other two unknown parameters.
In many technical devices, for example, steam jet apparatus, mixing steam heaters, etc., adiabatic (without external heat exchange) mixing of water vapor flows is carried out, as a result of which the steam parameters of the initial flows undergo changes.
So, let there be two (for simplicity of reasoning) steam flows with mass flow rates M 1 and M 2 and steam parameters p 1, v 1, t 1, h 1, s 1 and p 2, v 2, t 2, h 2, s 2 are mixed in the chamber and leave it with the parameters p CM, v CM, t CM, h CM, s CM. It is necessary to determine the parameters of the mixture.
It is clear that the mass flow rate of the output flow will be M SM = = M 1 + M 2, and the mass fractions g 1 and g 2 are a pair of corresponding flows
The problem posed is quite simple to solve using the h–s diagram of water and steam. Using the given parameters p 1, t 1 and p 2, t 2, we find points 1 and 2 on the diagram. If the mixing process occurs in a reversible way, then the specific entropy of the mixture s CM, as an additive value, will be determined by the sum s CM = g 1 ×s 1 + g 2 ×s 2, reflecting the reversibility condition:
We will find the parameters of the resulting mixture by connecting points 1 and 2 and determining the position of point 3 in relation to the segments l 13 and l 32, the length of which is determined by the relation
Let us prove that such a proportion satisfies both the reversibility condition and the heat balance equation h SM = g 1 ×h 1 + g 2 ×h 2 .
From the similarity of triangles 1a3 and 3b2, a simple relation follows
where do we get it from?
h 3 ×g 1 – h 1 ×g 1 = h 2 ×g 2 – h 3 ×g 2.
h 3 ×(g 1 + g 2) = h 1 ×g 1 + h 2 ×g 2.
Ho g 1 + g 2 = 1, which means
h 3 = h SM = h 1 ×g 1 + h 2 ×g 2.
Similarly, by analyzing the relationships between the segments l 1 a and l 3 b, one can verify that the reversibility condition is also satisfied.
In reality, the mixing process is an irreversible process and, in accordance with the second law of thermodynamics, the entropy of the mixture is greater than the entropy of both flows before mixing:
s CM = g 1 ×s 1 + g 2 ×s 2 + Ds UNINV.
Typically, the steam pressures at the inlets and outlets of the mixing chamber are very close, and they can be considered the same, i.e. points 1, 2 and 3 H lie on the same isobar:
If, during such mixing, heat is supplied or removed, then the enthalpy and entropy of the mixture will additionally change. Since heat exchange here occurs at p=const, the enthalpy value will change by the amount of heat involved in the heat exchange, Dh = q:
The presented method makes it possible to determine the parameters of the mixture state even when mixing several steam streams. In this case, the state of the steam is first determined when mixing two streams, then similarly when mixing the resulting mixture with a third stream, etc.
The mass fractions of each component of any mixture are determined by the values of the mass flow rates M 1 and M 2 of the first and second flows. Moisture content d and enthalpy h are additive parameters, so we can write
d CM = g 1 ×d 1 + g 2 ×d 2 and h CM = g 1 ×h 1 + g 2 ×h 2 = g 1 ×h 1 + (1 – g 1)×h 2 ,
since g 1 + g 2 = 1.
The values of d 1, d 2, h 1, h 2 can be determined from the h–d diagram based on the given temperatures t 1 and t 2 and relative humidity j 1 and j 2:
On the diagram, in addition to points 1, 2 and 3, which display the parameters of each of the flows and the resulting mixture, points 4, 5 and 6 are plotted, which are necessary for further reasoning.
The parameters of the mixture can be determined without resorting to calculations. To do this, you need to draw a straight line through points 1 and 2 and find the position of point 3, using the previously obtained relation
Let's carry out the simplest transformations by substituting the value of h CM:
It remains to prove that with such a division of segment 1–2, the value of d CM will also be determined correctly. To do this, we write down the ratios of the sides of the selected triangles to their heights, taking into account that these heights are determined by the differences in moisture content d:
From here we will find
g 2 ×d 2 – g 2 ×d SM = g 1 ×d SM – g 1 ×d 1.
d SM ×(g 1 + g 2) = g 1 ×d 1 + g 2 ×d 2; d SM = g 1 ×d 1 + g 2 ×d 2.
The last formula fully corresponds to the property of additivity.
Chapter 9. General information about mixing gases.
Goals and objectives of the chapter:
Learn about fire safety rules when working with oxygen
Learn about the rules for handling and working with oxygen
Learn about the application of the "40% rule"
Learn about different systems for mixing gases.
New terms in this chapter.
Flammable (fire hazardous) triangle
Oxygen-compatible grease
Adiabatic heating (Diesel process)
Oxygen cleaning
40% rule
Mixing partial pressures
Constant flow mixing
Absorption with periodic cleaning of the absorbent
Membrane separation.
As a diver using enriched mixtures in your dives, you must be able to obtain these mixtures. You do not need to know how to prepare nitrox yourself, however, you should have an understanding of how it is prepared and the cleaning requirements of your equipment that nitrox imposes. Some of the commonly used methods for producing fortified mixtures are reviewed in this chapter, and their advantages and disadvantages are discussed. The mixture you breathe must have the appropriate oxygen content.
1. Handling and working with oxygen.
Oxygen is an amazing gas. He can be both a friend and an enemy. When mixing gases for scuba use, the operator must obtain the appropriate oxygen content in the high-pressure mixture. This can be done by mixing pure oxygen with nitrogen or air, or by removing some of the nitrogen from the air. The main problem with mixing high-pressure oxygen is the fire hazard. Anything that is not completely oxidized - and that means practically everything - will burn in high-pressure oxygen if an ignition source is present. There is some risk when handling mixtures, but handling pure compressed oxygen poses a much greater risk. A diver using enriched mixtures does not need to be proficient in handling pure oxygen, but should have some understanding of the associated risks as oxygen is used as the diver's activities become more complex and extensive.
2. Flammable (fire hazardous) triangle.
To prevent a fire, you need to know what components cause and support a fire. These components are shown in the figure
in the form of a so-called “flammable or fire-hazardous triangle”. Fire is a rapid chemical reaction between fuel and oxygen (oxidizer) that can only occur if there is an ignition source (heat). Oxidation can occur without combustion, as, for example, during the rusting process. Fire occurs when there is a source of ignition (heat). After ignition, a chemical combustion reaction releases energy (heat), which supports further combustion. If we remove one of the components (fuel, oxygen, ignition source), fire cannot occur. If, therefore, all three components are not present at the same time, fire will be prevented. If a flame already exists, removing one of the components will cause the flame to go out. These are the basics of fire fighting theory. Another important point is that fire must spread in order to maintain its existence. Sometimes the desire to spread fire is even added as another component of the “triangle” described above.
3.Oxygen.
In the situations discussed below, oxygen is present in concentrations greater than its concentration in air. This means that the oxidizer in the “flammable triangle” is always present by default and cannot be removed from this “fire formula”. Everyone knows that atmospheric oxygen can actively participate in combustion reactions under appropriate circumstances, so it should not be surprising that higher concentrations can only increase the risk. Further, it is necessary to remember that an increased oxygen content in the air means a reduced inert gas content. For this and some other reasons, the combustion intensity does not depend linearly on the percentage of oxygen. It depends on both the percentage (share) of oxygen in the mixture and its partial pressure and increases significantly as these parameters increase.
4.Fuel.
In this paragraph we will talk about the fuel available in the gas system that provides the use of gas for breathing. At high oxygen pressures, if a fire occurs, the system itself can become the fuel for a chemical reaction, but something more flammable is needed to start a fire. This could be some separate part of the system, a solvent, a lubricant, or soft components of the system (rubber, plastic).
Some fuels found in gas systems may be virtually non-flammable under normal conditions and highly flammable in an oxygen-enriched environment. These types of fuel include silicone grease, silicone rubber, neoprene, compressor lubricants, plastic and metal shavings and burrs, organic substances and materials, dust of various types, even grease on hoops. Perhaps the most dangerous fuels are various lubricants. There is a common misconception that silicone (probably due to the exotic name) is safe when used with oxygen. Actually this is not true. There are special oxygen-compatible lubricants, such as Christo-lube, Krytox, Halocarbon. It is precisely these self-lubricants that should be used in an oxygen-enriched environment.
5. Ignition.
Some ignition sources are obvious, however, most of them are outside the gas system and are not considered by us. The two main sources of ignition within a system are friction and compression of the gas as it passes through the system. The term "friction" is used here in a general sense: in the sense of the presence of any particles in the gas flow or in the sense of the movement of the gas flow itself and its collision with the corners of gas pipelines or other obstacles. Another phenomenon - the same one that causes the cylinder to heat up - can also cause a fire (if enough heat is released). This is the same effect that causes fuel to ignite in the cylinders of a diesel engine without a spark plug. This effect is called "adiabatic heating (Diesel process)".
The sudden opening and closing of a cylinder valve during gas compression can cause an increase in temperature to the ignition point, and if there are contaminants in the gas flow, the ignition itself. Therefore, compressors do not use quick changeover valves (“ball valves”).
6.Use of oxygen systems.
The important message of this chapter is that the risk of handling oxygen can be minimized by following certain rules in the design and handling of systems. In particular, it is important to avoid sharp corners and quick change valves and to use appropriate materials. The metals used to make air systems are also suitable for making oxygen systems. As for “soft components”, such as gaskets, flexible joints, diaphragms, they must be replaced with oxygen-compatible ones. In some cases the main criterion is less flammability in oxygen, but in most cases it is increased resistance to oxygen under high pressure. Special kits are available that allow you to convert air equipment into equipment for using nitrox.
These include proper cleaning and maintenance of equipment, use of appropriate lubricants, handling gases in a manner that does not cause ignition, and opening valves slowly and smoothly.
7.Cleaning equipment for use with oxygen. Some considerations regarding equipment cleaning.
The concept of “oxygen cleaning” causes some confusion among amateur divers. The reason is that it is not entirely clear whether equipment needs to be cleaned for use with mixtures containing 21% to 40% oxygen. This problem has deeper roots: there are no developed and standardized industrial procedures for handling mixtures containing some intermediate amount of oxygen in the range from 21% (air) to 100% (pure oxygen). Standards exist only for the handling of pure oxygen; Thus, any mixture containing more than 21% oxygen is equivalent to pure oxygen by current standards. Therefore, in order to perform all operations in accordance with industry standards, any enriched mixture must be treated as pure oxygen.
The Compressed Gas Association CGA, the National Fire Protection Association NFPA, NASA and several other organizations recommend treating gases with intermediate concentrations as pure oxygen. This does not mean that they have performed any studies in this concentration range. This only means that there are no industrially developed and accepted standards, and these organizations prefer to take a conservative position. On the other hand, the US Navy has developed procedures stating that mixtures with an oxygen concentration of up to 40% can be treated as air for handling purposes. No test results have been published that would suggest that this conclusion is true, however, this approach has been practiced for many years and there have been no reports of accidents related to this issue. NOAA has adopted this concentration limit when working with fortified mixtures; NAUI, in general, too, however, with some restrictions.
Clean compressed air.
Another confusion arises in relation to the concept of “air purity”. The different "grades" of breathing gas purity used by various associations and organizations (CGA, US Navy) are confusing when it comes to the purity of the enriched mixture. Standards allow for the presence of some oil (hydrocarbon) vapor in compressed air (usually 5 mg/cu.m.). This amount is safe from a breathing point of view, but can be dangerous from a fire point of view when working with compressed oxygen.
Thus, there are no generally accepted and agreed upon gradations of air purity that determine its suitability for mixing with pure oxygen. Industry standard setters have agreed that hydrocarbon levels are on the order of 0.1 mg/m3. m can be considered acceptable for air, which "must further be mixed with oxygen." In the last few years, filter systems (pictured) have become available to produce compressed air that meets these requirements. Compressors that prevent air from contacting the lubricant, of course, cope with this task better, but they are significantly more expensive. A formalized approach to oxygen cleaning.
The phrase “oxygen cleaning” also sounds scary for the reason that its industrial implementation requires compliance with fairly strict procedures. These periodic procedures are published by the CGA and other organizations. They are designed to maintain safety when working with compressed oxygen.
NAUI states that any equipment intended for use with pure oxygen or with mixtures containing more than 40% oxygen at pressures greater than 200 psi (approximately 13 atm) must be oxygen-compatible and purified for use with oxygen. The cylinder, the first stage of the regulator and all hoses must be cleaned. Some pieces of equipment can be converted to handle such mixtures by using components from special kits.
8. Informal approach to oxygen cleaning: “40% rule”
Despite the lack of formal testing, the so-called “40% rule” has been used quite successfully in the diving industry, and its application has not revealed any problems. Numerous fires in diving gas mixing systems have occurred but were caused by higher oxygen concentrations.
NAUI accepts this rule but requires that equipment be oxygen-cleaned and that oxygen-compatible lubricants be used. This approach is less strict than the formal one, however, when done correctly it is very effective. Cleaning must be performed by qualified technicians.
The equipment must be cleaned of all visible dirt and grease, then brushed or ultrasonically cleaned using a strong detergent in hot water. Liquid cleaning products like Joy are good for home use. Cleanliness should be no less than that expected of plates and silverware. After drying, the soft components must be replaced with oxygen-compatible ones, after which the equipment is lubricated with an oxygen-compatible lubricant.
After cleaning, the equipment should only be used for enriched mixtures and should not be used with compressed air, otherwise it will have to be cleaned again.
9. Preparation of enriched mixtures.
The traditional scheme for constructing a gas mixing system is based on adding oxygen to the air in one way or another. Two new methods have recently been developed and become available that enrich the air in a different way - by removing nitrogen. This section will cover 3 oxygen addition methods: weight mixing, partial pressure mixing, constant flow mixing; and 2 methods with nitrogen removal: absorption with periodic cleaning of the absorbent, membrane separation (Ballantyne and Delp, 1996).
The type of gas mixing system used is important to the end user in that it determines the cylinder filling procedures and the range of possible oxygen concentrations in the resulting mixture.
Mixing gases by weight.
The simplest and most reliable method of obtaining mixtures that are accurate in composition is to purchase ready-made mixtures. Industrial gas producers typically mix pure oxygen and pure nitrogen rather than pure oxygen and air.
Gases mix by weight. This makes it possible to ignore many anomalies in the behavior of gases caused by their differences from ideal ones and provides a very accurate gas composition of mixtures. Mixing can be done in cylinders, cylinder banks or tanks. It is necessary to have accurate scales, which are quite expensive, since they must be able to measure small changes with large weights. This method of mixing gases is the most accurate, and the resulting mixtures are carefully analyzed to ensure that the actual composition matches the declared one. When preparing such mixtures, the industrial company is forced to use pure oxygen, but the retailer of the mixtures can avoid this. This method is quite expensive, and its cost is increased by the fact that the containers for storing the mixtures belong to the supplier of the mixtures, and therefore are rented by the seller of the mixtures.
Mixing of partial pressures.
As the name of the method itself says, it is based on the ratio of partial pressures. The technician fills the tank with the specified amount of oxygen (measured by the pressure value), then tops it up with ultra-pure air to the desired final pressure. First of all, oxygen is pumped in when the cylinder is still empty, which reduces the fire hazard of the procedure, since there is no need to manipulate oxygen at the full pressure of the filled cylinder. Since pure oxygen is used, the entire system, including the cylinder being filled, must be oxygen compatible and cleaned. Since pressure depends on temperature, and the cylinder heats up when filling, it is necessary to either allow the cylinder to cool or take into account the influence of temperature when measuring pressure. Since the final adjustment of the composition is often made after the cylinder has completely cooled, the entire process of preparing the mixture takes quite a lot of time. This process can also be used to refill a container of a mixture of known composition to obtain a mixture of the same or a different specific composition.
A compressor for mixing using this method is not required if the air is supplied at a pressure sufficient to fill scuba tanks without additional compression. To achieve maximum utilization of the bank of refill cylinders, they use the so-called “cascade technology”, which consists in using the refill cylinder with the lowest pressure first, followed by the cylinder with the highest pressure, and so on. Sometimes the method itself is called the “cascade mixing method.”
Compressors are also often used with this method. They must not use oil lubricants or must provide ultra-high purity air suitable for mixing with oxygen. Another way to pump air into a cylinder is to use a pneumatic pump that compresses air in a set of cylinders of different diameters, the pistons of which are connected to the same camshaft. Ogna of the most popular models is Haskel.
Partial pressure mixing is very popular among diving centers, which prepare many different mixtures in small volumes for various purposes of recreational and technical diving, including mixtures with an oxygen content of more than 40%. In this case, a significant portion of the cost of the system is a high-precision pressure gauge. In this case, the use of a pneumatic pump is very effective. This method is used in remote diving sites. Because oxygen is added at low pressure, some technicians do not clean the oxygen cylinders. This practice should be avoided: the cylinder should always be cleaned for use with oxygen.
10.Constant flow mixing.
This method (also called the atmospheric loading method) was first developed by NOAA (1979, 1991) and is the most user-friendly method (Figure 9-7). In this method, oxygen at low pressure is added to the inlet air stream entering the compressor with a high degree of oil vapor removal. The effluent stream is continuously analyzed for composition and the result of this analysis is used to adjust the oxygen admixture into the inlet stream accordingly. The output flow can bypass the bank of filling cylinders while the mixture composition is adjusted. Once the mixture is pumped into the refill cylinders, it can then be transferred to the scuba cylinders by bypass or using an air pump. A constant flow plant may also use an absorption subsystem as the oxygen source, with periodic purification of the PSA absorbent.
There is another class of constant flow units that provide air to the commercial diver through an air supply hose. Such installations have means of monitoring the constancy of the mixture composition - various flow meters and regulators. Their output pressure is typically less than 200 psi (13 atm).
11. Absorption with periodic cleaning of the absorbent (PSA).
This method is based on the use of a material called a "molecular sieve" - a synthetic porous clay-like material whose pores provide a very large surface area. This surface adsorbs gases (“adsorb” means “absorb on a surface”). Nitrogen is adsorbed faster than oxygen, so the air passing through the adsorbent becomes richer in oxygen (more precisely, poorer in nitrogen). Two absorbent plates are used, between which the air flow is switched. When the flow is directed at one plate, it adsorbs nitrogen, while the second plate at this time is cleared of previously adsorbed nitrogen. Then the plates switch roles.
By changing the pressure and frequency of cleaning the plates, it is possible to obtain different values of oxygen content in the output mixture. The maximum achievable oxygen content is 95%, the rest is argon. Argon behaves in relation to this type of adsorbent almost like oxygen (i.e. it is not adsorbed), therefore it will be contained in the output mixture in almost the same proportion to oxygen as in the input air. This argon has no effect on the diver.
Installations of this type do not require oxygen under high pressure, but they are complex and quite expensive in terms of acquisition and maintenance; the output flow must be pumped into cylinders using an oxygen-compatible purified compressor or air pump (pictured).
12. Membrane separation.
This method is based on the use of a membrane, which, when clean air passes through it, allows oxygen molecules to pass through better than nitrogen molecules. The output mixture is thus enriched with oxygen, and the oxygen concentration is determined by the input flow. The maximum achievable oxygen content in commercially available systems is about 40%. The same technology, by the way, is used to separate helium in some other processes.
Similar to PSA units, there is no need to use high pressure oxygen. The effluent must be pumped into cylinders using an oxygen-compatible purified compressor or air pump. Membrane systems are quite reliable and do not require special maintenance, provided that the purity of the inlet flow is sufficient.
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Let in separate thermostated vessels under the same pressure p there are gases A And IN, taken in quantities and moles. When these vessels are connected, spontaneous mixing of gases will occur until a homogeneous composition of the gas mixture is established throughout the entire volume of the system. We will assume that the source gases and their mixtures obey the equations of state of ideal gases. Then, while maintaining a constant total gas pressure p the partial pressures of gases in the resulting mixture will be equal
When ideal gases are mixed, there are no thermal effects, so there is no heat exchange between the gases and the thermostat, and the change in the entropy of the system will be completely determined by the irreversibility of the processes within the system.
To find the desired change in entropy, it is necessary to contrast the described spontaneous process with a mental equilibrium transition between the same initial and final states of the system.
For equilibrium mixing of gases, we will use a special hypothetical device, by analogy with a thermostat, called a chemostat . This device consists of a thermostatically controlled cylinder equipped with a friction-free moving piston; at the base of the cylinder there is a membrane that is selectively permeable only to a given individual chemical; the latter separates the individual substance loaded into the chemostat from the mixture of substances being studied located in another vessel. Unlike a thermostat, designed to maintain a given temperature of a body immersed in it, or to heat or cool the latter in an equilibrium mode, with the help of a chemostat they ensure the maintenance of a certain value of the chemical potential of a given individual substance in the mixture of substances under study, as well as the equilibrium supply and removal of the substance from mixtures. Chemical Potential i - the chemical component in the chemostat is uniquely determined by temperature T and the pressure created on the piston. By changing the pressure on the piston, it is possible to change the direction of transition of a given component through the selective membrane: if is the chemical potential of the component in the mixture under study, then when the substance will be added to the mixture, when – it will be removed from the mixture, and when chemical equilibrium is maintained between the chemostat and the mixture. A quasi-equilibrium change in the composition of the mixture corresponds to the diffusion transfer of a substance through the membrane under the influence of a very small difference in the chemical potential values on both sides of the membrane.
The chemical potential of an ideal gas, regardless of whether this gas is in an individual state or in a mixture with other ideal gases, is expressed by the simple relation where p i is either the pressure of the pure gas or its partial pressure in the mixture. Therefore, when an ideal gas is transferred through a semipermeable membrane, the equilibrium between the mixture and the chemostat is characterized by the equality of the pressure in the chemostat and the partial pressure of the gas in the mixture.
Rice. 2.3. Equilibrium mixing of two gases using chemostats: a– initial state of the system; b– state of the system after isothermal expansion of gases; V– final state after mixing gases through membranes; 1 – individual gas chemostats A and B ; 2 – semi-permeable membranes; 3 – a vessel for equilibrium mixing of gases.
Equilibrium mixing of ideal gases A And B will be carried out in a thermostated system consisting of two chemostats of individual components A And B, connected to a third vessel - a collection of the resulting mixture, equipped, like chemostats, with a movable piston (Fig. 2.3).
Let at the initial moment the chemostats contain, respectively, moles of the component A and moles of component B under the same pressure p
; the piston in the mixture collector is in the zero position (the volume of gas under the piston is zero). The mixing process is carried out in two stages. At the first stage, we perform a reversible isothermal expansion of gases A And B; while the pressure A reduce from p
to the set pressure and pressure B accordingly from p
before . The volumes occupied by gases in the first and second chemostats will change, respectively, from to and from to . The work done by the expanding gas in the first chemostat is equal to 
; in the second 
. Thus, at the first stage, total work is performed in our hypothetical device. Since during isothermal expansion of an ideal gas its internal energy does not change, this work is carried out due to the equivalent supply of heat from the thermostat. Hence the reversible change in entropy in the system will be equal to
At the second stage of the process (mixing itself), we transfer gases from the chemostats through selective membranes into the mixture reservoir by synchronized movement of three pistons. At the same time, a constant pressure is maintained on each of the pistons, respectively, both in the chemostats and in the collector, which ensures an equilibrium transition of gases through the membranes (more precisely, a pressure is created in the collector that is slightly less p , maintaining a non-zero driving force for diffusion through membranes). The reversibility of the mixing process in this case is ensured by the possibility of synchronously changing the direction of movement of all three pistons, which would lead to the reverse division of the mixture into individual components. After the operation is completed, the mixture will obviously occupy a volume of .
Since in the case of ideal gases mixing is not accompanied by any thermal effect, there is no heat exchange between our device and the thermostat at the second stage of the operation. Consequently, there is no change in the entropy of the system at this stage.
It is useful to verify by direct calculation that the work done by the gases in the second stage is zero. Indeed, work is consumed to move the pistons in chemostats, while at the same time the same amount of work is performed in the gas collector. From here.
So, the total increase in entropy during mixing of gases is determined by expression (2.9), . If, in the equilibrium version of mixing, this increase is associated with the return supply of heat and the production of an equivalent amount of work 
, then with direct (irreversible) mixing of gases, the same increase in entropy occurs due to its generation inside the system; the system does not perform any work.
After substitution (2.8), expression (2.9) can be rewritten as
. (2.10)
This relationship is given a mandatory place in thermodynamics courses due to its apparent paradox. It is noteworthy that for changes in entropy (when mixing ideal gases!) it does not matter what is mixed with what, as well as at what pressure and temperature. Essentially, here is an informal derivation (2.10).
Let us supplement the conclusion (2.10) with its useful consequences. Introducing mole fractions of components 
and , we obtain an expression for the change in entropy per 1 mole of the resulting mixture:
. (2.11)
The maximum of this function occurs at an equimolar mixture of gases, 0.5.
From the point of view of the theory of separation of mixtures of substances, it is of interest to trace the change in entropy production when adding a sufficiently large number of moles of a component B to one mole of component A. Setting and in (2.10), we obtain
When deriving (2.12), the mathematical representation of the logarithmic function was used
.
Formula (2.12) shows that successive dilution of the mixture is accompanied by an infinite increase in entropy per mole of impurity component.
Formula (2.10) gives the integral value of the entropy increment when mixing finite amounts of gas. In order to arrive at a compact differential expression similar to formula (2.7) for heat transfer, we modify the component mixing model (see Fig. 2.4). We will assume that mixing occurs through a membrane permeable to both components, or through a sufficiently narrow valve separating the vessels filled with mixtures A And B of different composition. The system is thermostatically controlled, and constant pressure is maintained in both vessels using pistons p . With a limited mixing speed, the composition of the mixture in each of the vessels can be considered homogeneous over the volume of the vessel. Thus, this system is similar to a heat exchange system with a weakly conductive partition.