Assessment of Hydrogen Sulfide Emission during Asteroid Impact in the Black Sea.

Degterev Andrey Kharitonovich Professor; Department of Radioecology and Environmental Safety; Sevastopol State University 7 Kurchatov St., Sevastopol, 299015, Russia degseb@yandex.ru Other publications by this author

Kucherik Galina Valentinovna ORCID: 0000-0001-8155-917X PhD in Technical Science Head of the Department of Radioecology and Environmental Safety; Institute of Nuclear Energy and Industry; Sevastopol State University 7 Kurchatov St., Sevastopol, 299015, Russia GVKucherik@sevsu.ru

Introduction

In recent years, there has been a noticeable increase in interest in predicting the collision of the Earth with asteroids and comets. This is partly due to the recent fall of the Chelyabinsk meteorite in February 2013. Despite the fact that it was, judging by the power of the explosion, the most dangerous collision after the fall of the Tunguska meteorite (or comet) in 1908, the meteorite was seen only 10 seconds before its explosion in the atmosphere. Its size reached 20 m before entering the stratosphere, but it was almost impossible to notice it from the Ground – it flew from the direction of the sun at 9 a.m.

The explosion of the meteorite occurred at an altitude of 23 km, which was due to a small angle of slip (less than 20 °) when it entered the atmosphere. At the same time, the power of the explosion was ten times stronger than when the atomic bomb exploded over Hiroshima. Casualties were avoided only because of the high altitude, in Hiroshima the city was completely destroyed in an explosion at an altitude of 600 m. That is, in the event of an explosion of the Chelyabinsk meteorite closer to the Earth's surface, the consequences would be catastrophic. In this regard, in recent years, it has been concluded that the fall of meteorites measuring 10 m or more poses a real threat.

Before that, the main focus was on observing large asteroids of the order of 1-10 km in size, which can lead to a global or regional catastrophe and are available for observation. Guaranteed tracking of such bodies ensures sufficient accuracy in calculating their orbits, and hence predicting collisions. Moreover, the significant mass of such bodies makes it possible not to take into account the change in orbit due to an increase in their thermal radiation when heated by sunlight (the Yarkovsky effect). In the case of small meteorites like the Chelyabinsk meteorite, the corresponding changes in the orbit are much stronger, which makes it difficult to assess the danger of a collision in the near future. Long-term observations of large asteroids suggest that the probability of a collision with at least one of them in the coming decades does not exceed 0.1%. For small asteroids, it is much larger, for example, the probability of an Earth collision with an asteroid larger than 30 m is 20 times greater than with an asteroid larger than 100 m ^[8].

Thus, the relevance of studying collisions with small celestial bodies is related, on the one hand, to their poor knowledge and difficulties in observing these objects, and, on the other, to the much higher probability of collisions with them.

Recently, there has been increased attention to the consequences of meteorites or comets falling into the ocean ^[3]. This is quite natural, since two thirds of the planet's surface is on the ocean, which means that the probability of a celestial body falling into the ocean is twice as high as falling on land. In this regard, it is of interest to study the consequences of an asteroid impact into the Black Sea using mathematical modeling, estimated calculations and literary analysis to describe the process of degassing of hydrogen sulfide dissolved in seawater.

Scientific novelty

The scientific novelty lies in the authors' attempt to quantify the concentration of hydrogen sulfide in the atmospheric pressure layer in the area of the asteroid impact based on the calculations performed. In other works on this topic, this effect was estimated either only by the release of steam from the water cavity, or it was not considered at all, and the emphasis was on studying the danger of tsunami waves.

We also estimated the effect of the rise of deep waters due to the intense vertical mixing of waters during the impact of the asteroid on the bottom. The estimates obtained show that the associated degassing of deep waters is much more dangerous than the formation of a cloud from the released steam. This is partly due to the fact that ^[9] used an approach related to modeling the consequences of a nuclear explosion followed by the formation of a radioactive cloud.

In this case, this model does not describe the effect discussed here and gives an overestimate of the concentration of hydrogen sulfide in the cloud. Suffice it to say that hitting the bottom is not considered in it at all (it simply does not exist in a nuclear explosion).

Models of an asteroid falling into the ocean

Mathematical modeling of the process of an asteroid falling into the ocean shows that in this case, as in a fall to land, a water crater forms first. If the size of the asteroid exceeds 500 m, it reaches the ocean floor and a crater forms there too ^[3]. However, there are only two dozen such craters on the ocean floor, while there are hundreds of meteorite craters on land. The fact is that on a geological timescale, the oceanic crust is relatively young, about 10-100 million years old. So it is difficult to study the consequences of an asteroid falling into the ocean using preserved ancient craters, as it is done on land. Of course, there are also technical problems associated with the need to use special deep-sea vehicles. Therefore, the application of physical and mathematical models is of particular importance here.

Mathematical models of this kind are based on solving the classical Euler and Navier-Stokes equations, taking into account changes in the position of the free water surface ^{[11, 12]}. For example, models that were previously used to simulate underwater and surface nuclear explosions are used. Modeling of the evolution of a temporary water crater has shown that the main danger in this case is represented by surface tsunami waves hundreds and thousands of meters high, which propagate at high speed and are capable of destroying coastal territories ^[4]. However, for this to happen, the size of a water crater must be 3-4 times the depth of the ocean in a given location. The fact is that the length of the waves formed is half the size of a water crater, and a tsunami is basically long waves. That is, with an average ocean depth of 4 km, the water crater should be at least 12 km in diameter, which corresponds to the impact of an asteroid 1 km in size. The wave height also reaches large values of the order of ocean depth only when the size of the asteroid is of the order of depth, that is, over 1 km.

When relatively small asteroids up to 200 m in size fall, when the sea depth is correspondingly much greater than the wavelength, there will actually be no tsunami. Calculations and laboratory experiments show that the real danger of a tsunami occurs when the size of the asteroid is more than 10% of the depth of the sea. In the case of the Black Sea, the depth of which reaches 2,200 m in the deep part, the fall of asteroids measuring 100-150 m, respectively, does not cause the formation of a megatsunami. It's just that there will be so-called waves in deep water, which are relatively small and do not spread so fast. In this regard, a number of papers even suggest correcting the trajectories of such asteroids towards the middle of the ocean in order to avoid a catastrophe on land ^[12].

In inland seas and even large lakes, there is even less tsunami in the event of an asteroid impact. Thus, during the eight-magnitude Crimean earthquake of 1927 with the epicenter in the Black Sea, the height of the tsunami waves did not exceed 0.5 m even in the Crimea. This is partly why, until recently, with rare exceptions ^{[9, 10]}, the consequences of an asteroid impact into the Black Sea were practically not considered.

Nevertheless, the relevance of studying the fall of an asteroid into the Black Sea is quite high due to a number of features of the Black Sea, such as the presence of large amounts of hydrogen sulfide and methane in it. Moreover, methane is present both in well-known natural gas deposits on the shelf in the Northwestern part of the sea, and in the form of large reserves of methane gas hydrates at depths over 600 m ^{[1, 6]}. In this regard, it is of interest to consider the fall of an asteroid into the Black Sea, taking into account the influence of vertical mixing, heating and evaporation of water on the degassing of its waters.

Hydrodynamic effects

If you scroll through the process of an asteroid falling to Earth in the opposite direction, it will turn out as if it starts to other celestial bodies. From this it can be concluded that the speed of approach to the surface of the water is not less than the second cosmic velocity, that is, not less than 11 km/s. The loss of kinetic energy of an asteroid to overcome the atmosphere for sufficiently large asteroids with a not very shallow fall trajectory is estimated at 1% ^[12]. At a maximum depth of 2.2 km in the Black Sea, the asteroid's movement from the surface to the bottom will take a fraction of a second ^[11].

The main difference between an asteroid hitting water and hitting a solid surface is the fact that it does not immediately explode or melt, but goes under water. Calculations and laboratory experiments show that the asteroid enters the water at high speed, forming a cavity in the water elongated along its trajectory, filled with steam. The depth of this water crater is 12 times the size of an asteroid ^[7], that is, an asteroid with a diameter of 100 m is capable of creating a cavity with a length of 1200 m. As the steam pressure decreases and under the influence of the lateral pressure of the water, it first collapses in the upper part of the trajectory, forming a large underwater bubble in the lower part. After that, the underwater bubble collapses with the jet ejecting upwards and forming a turbulent wake with developed cavitation. The asteroid itself continues to move in the water until it collides with the bottom, gradually slowing down to a maximum speed of about several km/s.

The deceleration process is associated with the action of a resistance force, the expression for which follows from the Bernoulli equation:

F _sopr = ξ٠S٠ρ _in v ^2/2, ( 1 )

where rv = 1000 kg/m3 is the density of water, v is the velocity of the asteroid in the water, and S is its cross–sectional area. The resistance coefficient ξ included here depends on the Reynolds number Re for not very large values. For a ball falling in water with a diameter of d, this number is expressed in terms of the coefficient of kinematic viscosity of water v _k = 10-6 ^m2 / s by the formula:

Re = vd/v _k . ( 2 )

This shows that at a speed of about 10 km/s, Re is very high even for meter-high asteroids, and therefore, when an asteroid moves in water, there is a so-called drag crisis ^[5]. In this self-similar mode, we can assume that ξ is of the order of 0.1. Substituting this value and S = nd ^2/4 in (1), we obtain:

Fsopr = 0.025 nd2p ⁱⁿ v2. ( 3 )

Accordingly, the acceleration modulus a = F _copr/m, where m is the mass of the asteroid, which is expressed for the ball in terms of its density pa _and diameter as pa(4/3)π(d/2)³ = (1/6)πρ _a d ³. From here:

a = 0.025 nd2p ⁱⁿ v2/(1/6)πρ _а d ³ 3 3 = = = = = 3 = 0.15(ρ _в//ρ)))v²/d . ( 4 )

For example, for a stony asteroid with pb/pa = 0.3, diameter d = 200 m and ^v = 20 km/s, we get a = 105 m/^s2. Thus, to a first approximation, in t = 0.1 s, the asteroid's velocity will decrease by a·t = 10 km/s, that is, by half. As a result, it will reach the bottom in less than 0.15 seconds without slowing down to its maximum speed.

The processes occurring during the movement of an asteroid under water strongly depend on its density (iron or stone) and on the angle of sliding relative to the surface of the water. The maximum effect is obtained when falling vertically. All other things being equal, the deceleration of an iron asteroid, as can be seen from (4), occurs 3 times slower than a stone asteroid. So, when an iron asteroid measuring 150 m falls at a speed of 20 km/s, it will pass through a layer of water 600 m thick almost without slowing down and almost the same crater will form at the bottom as if it had fallen on land. However, a large amount of water will evaporate ^[11].

Release of water vapor with hydrogen sulfide

In any case, when an incandescent asteroid falls into the water, a large amount of water vapor is formed, which is released into the atmosphere. In addition, a powerful fountain of water is ejected to a great height when a water crater collapses. According to estimates ^[11], when an asteroid measuring 250 m falls, up to 250 Mt of water vapor is released, which corresponds to the evaporation of 0.25 km3 ^of water.

For the release of hydrogen sulfide dissolved in water with steam, the water crater must reach the hydrogen sulfide zone, that is, its depth must exceed 200 m. Taking into account the significant increase in the concentration of hydrogen sulfide in the Black Sea with depth ^[1], the greatest release of hydrogen sulfide will be during evaporation of seawater at depths above 600 m. In this regard, the minimum size of an asteroid capable of causing a noticeable release of hydrogen sulfide along with steam is 50 m when falling vertically.

However, more often asteroids fall along a gentle trajectory, with a slip angle of up to 60 degrees. For example, the Chelyabinsk meteorite fell at an angle of 20 degrees, and the Tunguska meteorite, according to eyewitnesses, also flew at a low angle. When falling at an angle of 30 °, to reach a depth of 600 m, the length of the cavity formed in the water will require 1200 m. Accordingly, then the minimum size of the asteroid increases to 100 m. The concentration of hydrogen sulfide in water deeper than 750 m already increases slightly with depth, reaching a concentration of 10 mg/l, taking into account hydrosulfide ions.

A simple estimate shows that the kinetic energy of a 200 m stone asteroid with a density of ³ t/m3 entering the water at a speed of 20 km/s is 2.4 ·^10-18 Joules. According to numerical experiments, such events are characterized by the efficiency of energy transfer to surface waves and turbulence at the level of 15% ^[11], so 85% goes to heating and evaporation of water.

The critical temperature of the water is 374oC, the temperature of the deep waters of the Black Sea is 8oC, and its specific heat capacity is C = 4.2·^10.3 J/kg٠ deg. Accordingly, C · 366 J is consumed for heating 1 kg of water. With a specific heat of vaporization of L = 2.5 · ¹⁰⁶ J / kg, this is 38% of the total energy consumption for heating and evaporation of water. Thus, water evaporation consumes about half of the asteroid's energy (0.85٠0.62 = 0.53), that is, 1.27· 10 ¹⁸ J. Dividing this value by L, we get 0.5٠10 ⁹ tons of water, that is 0.5 km3. The corresponding total release of hydrogen sulfide at its average concentration in water of 5 mg/l is 2500 tons.

At atmospheric pressure and above sea level, 22.4 liters of steam will contain 1 mol, which corresponds to 18 g. This amounts to 18 ml of liquid water, so the hydrogen sulfide content in a mole of steam is 0.18٠5 mg, that is 0.9 mg. In terms of 1 ^m3, then we get its atmospheric concentration of 0.038 g/^m3. Upon subsequent mixing with air, this value can be used as an estimate from above, taking into account the gradual condensation of water in the atmosphere. Note that the water content of ordinary clouds is about 1 g/^m3.

In terms of relative units, taking into account the molar mass of hydrogen sulfide of 34 g/mol, the values obtained above 38 mg/^m3 are 25٠10^-6 = 25 million ^-1 = 25 ppm. The value obtained is close to the minimally dangerous concentration of hydrogen sulfide in the cloud formed during the asteroid impact of 20 ppm ^[9], whereas it is deadly to humans The concentration is estimated as 500 ppm. But according to our data, when an asteroid up to 250 m in size falls at the same speed, it is not reached in a cloud above the sea. Even an order of magnitude lower concentration of 50 ppm is not reached, at which the evacuation of the population begins.

Hydrogen sulfide emission due to gas exchange

The fall of the asteroid to the bottom will cause a shock wave and thermal convection along with developed turbulence, which will result in vertical mixing of waters. This will result in the release of deep hydrogen sulfide waters mixed with the overlying layers to the surface. At a gas exchange rate of V _L = 10-5 m/s and a hydrogen sulfide concentration in water of 5 g/ ^m3, the hydrogen sulfide flux density into the atmosphere in the first hours will be V _L ·5 g/s·^m2 = 0.2 g/^m2·hour, and hydrogen sulfide is heavier than air and will accumulate near the surface of the water. We considered this effect in ^[2], where it was shown that due to gas exchange through the water surface, in accordance with Henry's law, a saturating concentration of hydrogen sulfide of 1 g/^m3 can be achieved in the near-surface air layer in the area of the asteroid impact. This is a deadly concentration, although an order of magnitude less explosive. However, it is not associated with clouds and decreases rapidly due to vertical and horizontal mixing of air.

In this sense, this danger is quite comparable to the methane emissions observed during the Crimean earthquake of 1927 in the form of flares burning over the sea at a height of 30 m. Gorenje At that time, this was due to the formation of a fault at a shallow depth in the area of modern gas production platforms west of the Crimea. However, an asteroid can cause the melting of methane gas hydrate deposits in many other areas of the sea (Fig. 1) with an increase in water temperature of only a few degrees. In this case, methane gas is also released in a jet, followed by the formation and explosion of a gas-air mixture. And this temperature increase is inevitable when hitting the bottom. Moreover, for example, in the area of the Sorokin trough near the southern coast of Crimea, this blow can also provoke a strong earthquake. It was there that the epicenter of the earthquake in 1927 was located, and then many others, less powerful. The fact is that the deposits of gas hydrates on the seabed are associated with tectonic structures.

Fig. 1. Location of methane gas hydrate deposits and mud volcanoes at the bottom of the Black Sea ^[6]: 1 – mud volcanoes, 2 – gas hydrates, 3 – boundaries of tectonic structures, 4 – ring structure, 5 – Odessa-Sinop fault zone, III – Sorokin trough.

Conclusion

The analysis shows that when an asteroid measuring 200 m falls into the Black Sea, hydrogen sulfide will be released in an amount of 2500 tons due to evaporation of seawater. However, the hydrogen sulfide content in this vapor, and then in the resulting cloud, is half the dangerous values at which evacuation of the population is necessary.

A much greater danger is associated with the impact of an asteroid on the bottom and the subsequent release of deep waters to the surface. In this case, the concentration of hydrogen sulfide in the air up to 1 g/^m3 may be observed for a short time in the area of the fall. At the same time, the concentration of hydrogen sulfide in surface waters can reach 5 mg/l, which will cause mass death of marine fauna in the area.

The fall of even small bodies measuring 30-100 m in some areas of the Black Sea can lead to local methane emissions due to melting of gas hydrate ice on the bottom. In contrast to hydrogen sulfide emissions, an explosive concentration of the gas-air mixture can be achieved.