Application of Synthesized Hydrates in the National Economy

– The article analyses the thermodynamic conditions for long-term storage of hydrates and proposes a methodology for calculating the main thermodynamic parameters that ensure long-term stability of the structure of gas hydrates. A criterion for optimizing thermodynamic parameters and heat and mass transfer parameters for effective introduction of new technology


INTRODUCTION
Recently, research on the properties of gas hydrates has intensified and there are a number of reasons for this.Natural gas hydrates, consisting mainly of methane hydrate, are considered promising sources of hydrocarbon raw materials.Global estimates of hydrate-bound gas, which best reflect current knowledge of submarine gas hydrate, are in the range of (1-5)•10 15 m 3 (~500-2500 Gt of carbon-methane) [1]- [5].
However, the lack of sufficient information about the peculiarities of their formation and decomposition makes it difficult to actively implement gas hydrate technologies.Solving these problems will allow for optimizing the processes of extraction, synthesis, storage, transportation, and use of hydrates.Natural gas (methane) is stored in various ways, for example, in a liquefied form.In this state, gas can be transported from source to market, but is not convenient to store due to stringent temperature requirements and problems with continuous boiling of the gas.On the other hand, solid natural gas hydrates are stable at moderately high pressure (5 MPa) and 279 K.
According to many researchers, storing natural gas in clathrate hydrates offers the safest, cleanest, and most compact storage method, which is facilitated by the relative ease of extracting natural gas at minimal cost compared to known traditional storage methods [6], [7].
The works [8], [9] provide comprehensive information on the production, storage and transportation of gas hydrates (GH) and convincingly proves the feasibility of transporting and storing gases in a hydrated state.
The works [10]- [12] present technologies for the production of gas hydrate blocks and show the conditions for their long-term storage at atmospheric pressure and slightly negative temperatures.The ideas expressed in these articles could be developed in future gas hydrate storage or GH transport projects.According to the data presented, gas hydrate technologies for transporting or storing gas require an additional no more than 13 % of energy in the summer and about 2 % in the winter compared to traditional methods of gas transportation through gas pipelines.At the same time, gas liquefaction processes in LNG technologies require an additional 25 % of the energy contained in liquefied gas [13]- [15].Thus, the construction and use of light gas storage facilities (Fig. 1) in the form of gas hydrates is a relatively simple and obviously promising task.The dissociation of gas hydrates and the intensity of gas extraction depend on the conditions of thermodynamic equilibrium of GH in the storage volume and the characteristics of the GH dissociation process.

THE FEATURES OF GAS HYDRATE DISSOCIATION
Dissociation of GH begins when thermodynamic equilibrium is disturbed, for example, by increasing temperature.Therefore, determining the temperature on the surface of a gas hydrate is an important factor that needs clarification, which we carried out experimentally.
To measure the temperature, electronic sensors ds18b20 with a measurement accuracy of ±0.1 °C and a control thermometer with a division value of 0.1 °C were used.
The purpose of the research was to clarify the temperature distribution in the internal layers and surface of a large mass of propane hydrate.To achieve this, all temperature sensors were located inside the GH at different depths and on its surface.During the investigation, 'dry' GH with a gas capacity of 40 ml of gas/ml of water was used.The pilot plant diagram is shown in Fig. 2.
Analysis of the data obtained indicates that at low gas capacity of the hydrate (20 % gas hydrate), the temperature curve always starts at 0 °C and ends at the temperature of stable storage of the hydrate, see Fig. 3.As a result of increased air temperature, the hydrate layers that are in contact with the surface quickly dissociate.Gas is released through the cracks and cools the inner layers of the hydrate.At a certain depth, the temperature of the hydrate becomes close to equilibrium, while the pressure and the dissociation process slows down.Analysis of experimental data shows that the temperature distribution in the near-surface layer of propane hydrate is well approximated by the dependence.
-35 0.4 -0.47 where x is the distance from the surface, m.
In GH with a high gas capacity, the upper layer of dry, not covered with an ice crust, propane hydrate is in the positive temperature range of 0.5-0.8°C (Fig. 2).The hydrate immediately dissociates into water and gas without forming an ice crust.The deep layer is located under conditions close to thermodynamic stability at a temperature of −0.9 °C.There is a transition region about 50 mm thick, where a significant temperature gradient is observed (Fig. 4).The temperature distribution in the near-surface layer of propane hydrate is well approximated by the following dependence: -50 1.6 -0.9 x t e = . ( The approximation coefficient 50 in formula (2) reflects the rate of change of internal heat sources GH.This value is typical for a propane hydrate with a high gas capacity.
Thus, the experimental data to determine the temperature distribution at the depth of the dissociating GH can be approximated by equation: where te is the temperature of the thermodynamically stable hydrate layer, °C; tGHs is temperature on the hydrate surface, °C; k -approximation coefficient, m -1 .
The temperature of the deep layers of dissociating GH that are thermodynamically stable is determined by the composition of the hydrate and the intensity of heat input to the surface of the hydrate mass.The temperature on the surface of GH is determined by the thermal balance, which takes into account the heat input from the environment and the heat sink due to dissociation processes on the surface and deep layers of the hydrate.The approximation coefficient k indicates the intensity of the attenuation of heat sinks deep in the hydrate.Increasing the quality of the hydrate leads to an increase in this coefficient.

MATHEMATICAL MODEL OF QUASI-STATIONARY DISSOCIATION OF GAS HYDRATES
Several processes simultaneously occur in a dissociating hydrate: the process of decomposition with the absorption of heat and the release of gas; the process of heat transfer to the deep layers by thermal conduction; phase transitions on the surface; and heat removal when heating the gas moving inside the crevice structure from the depths of the hydrate to its surface.To reproduce thermophysical processes as accurately as possible in mathematical Environmental and Climate Technologies ____________________________________________________________________________ 2024 / 28 153 modelling, we will focus on experimental data on the temperature distribution inside the dissociating gas hydrate.
Let there be a large enough mass of gas hydrate such that the temperature field in it can be considered one-dimensional [10].Heat is supplied to the surface of the hydrate by heat exchange.For this case, the mathematical model of the thermal regime of hydrate dissociation will be based on the one-dimensional nonlinear equation of Fourier thermal conductivity with specific volumetric heat sources (sinks) [16], which has the form  Depending on the heat exchange conditions on the hydrate surface, three main models of dissociation of the GH massif can be distinguished.Let us present them in order of intensification of heat supply to the surface: a model of self-preservation, melting of the ice crust, and intense dissociation of hydrate.In the self-preservation model, the heat supply to the GH surface is relatively small.The surface temperature of the gas hydrate is one or two degrees below 0 °C, so the ice crust does not melt.
The process of GH dissociation can be considered to be quite long, and the temperature distribution in the hydrate mass can be considered to be stationary, then Eq. ( 4) simplifies According to experimental data, the temperature regime inside the hydrate mass is described by Eq. ( 3).For stationary conditions, using equation ( 6), it is possible to determine the power of volumetric heat sinks as a function of the coordinate, W/m 3 , After substituting the second derivative from equation (3) into formula (7), we obtain the equation for the distribution of volumetric heat sinks in the hydrate, W/m 3 , Under conditions of slow dissociation (in particular, during self-preservation), the geometric shape of the hydrate remains virtually unchanged for a long time.Consequently, in equation ( 6) we can assume that because of the small amount of gas released during dissociation, the heat consumption for its heating will be considered insignificant compared to the heat drain for the dissociation of the hydrate.In this case, equation ( 6) can be written in a simplified form Using Eq. ( 9), the temperature of the hydrate surface can be determined.First derivative of equation ( 3) with respect to Substituting the obtained dependence (10) at x = 0 into Eq.( 9) allows one to calculate the temperature on the hydrate surface under self-preservation conditions a s GHs GHs s .
Ice crust melting model.If the intensity of the heat supply increases, this leads to an increase in the temperature on the hydrate surface to 0 °C.The ice crust is melting.The process proceeds slowly, and the hydrate bordering the surface ice crust has time to almost completely dissociate.This model is also typical for low-concentration hydrate.Gas consumption is insignificant and they do not contribute significantly to the thermal balance of the surface of the array.The boundary condition has the form Taking into account the fact that the temperature on the surface of the hydrate mass is tGHs, the temperature regime inside the hydrate mass is determined as follows Distribution of volumetric heat sources in the depth of the massif, W/m 3 , From the boundary condition (12) we determine the rate of melting of the ice crust, m/s, s a e ice ice d α λ dτ ρ The intense dissociation mode is characteristic of concentrated gas hydrates under conditions of active surface heating.An increase in the intensity of the heat flux on the GH surface leads to the dissociation of the hydrate directly located on the surface, and not just the deep layers, as was the case with the self-preservation of GH.The surface temperature exceeds 0 °C and an ice crust does not form on the surface of the GH massif.
Under conditions of active heating of the hydrate surface, the gas yield increases and must be taken into account under the boundary conditions To assess the influence of the cGρGgG component, it is necessary to determine the gas flow rate during the dissociation of hydrates.The gas flow consists of two parts: dissociation of deep layers and hydrate formed on the surface of the massif.The dissociation of deep layers of gas hydrate is not fundamentally different from the conditions considered for selfpreservation.Its intensity is relatively low and gas consumption, which is formed during slow dissociation inside the GH, can be neglected.However, gas flow rates resulting from the dissociation of the GH surface layer can be significantly higher and must be taken into account under boundary.Specific volumetric gas flow rate on the hydrate surface, m 3 /(m 2 s) where KGH is the volumetric gas content of the hydrate, m 3 /m 3 .
Because GH has a porous structure with a large heat exchange surface area, the temperature of the gas released from the surface of the dissociating hydrate can be taken equal to the surface temperature of the hydrate   .Then, taking into account (17) of equation ( 16), we can determine the dissociation rate on the surface of the GH Comparing the values in the denominator of formula (18) with each other, you can see that the component

{ }
G G G a Gs ρ -c g t t is at least two orders of magnitude less than rρGH.Therefore, with sufficient accuracy for practical calculations, formula (18) can be written in the form: Formula ( 19) makes it possible to determine the temperature on the surface of the dissociating GH only if the linear rate of dissociation of GH is known.To calculate it, we will use the distribution of volumetric heat sources in the hydrate mass.Since the process of GH dissociation begins deep in the massif, we will take into account the exponential nature of the distribution of heat sources and integrate them along the coordinate axis.When the From where it is possible to determine the temperature on the surface of the hydrate mass under conditions of intensive heating of its surface e s e GHs s 2 2 Compared to formula (11) (for slow dissociation), we see that in the case of intensive heat supply, the heat flow in the hydrate is evenly distributed equally into two parts: dissociation and transfer to the depths of GH by thermal conductivity.
The obtained dependencies allow one to analyse the experimental results.During the experiments, the outside air temperature was ta = +11 °C.For heat flow from top to bottom in still air, the heat transfer coefficient at the surface is αs = 4 W/(m 2 °С).Thermal conductivity of propane hydrate λ = 0.5 W/(m °С), coefficient k = 50 m −1 , measured temperatures of the surface of the hydrate tGHs = 0.7 °C and temperature of the deep layers of the hydrate te = −0.9°C.Substituting the experimental data into formula (11), we can obtain the temperature value on the dissociating surface of the hydrate, °C, k = 0.74.
The calculated temperature almost coincides with the one experimentally measured.Since the temperature on the surface of the hydrate is above 0°C, the hydrate dissociates into gas and water and the self-preservation effect is not observed.After substituting the initial data into Eq.( 9), we obtain the value of the volumetric heat sinks, W/m 3 , -50 -2000 x q e = .This equation shows that heat sinks with a power of 2000 W/m 3 act on the surface of the dissociating propane hydrate.In deep layers, their power drops quickly and at a depth of 50 mm, it is only 164 W/m 3 .
Analysing the above equations, it is not difficult to notice the key role of the dimensionless complex (criterion), which describes the similarity of temperature fields at the surface and in the depths of the dissociating gas hydrate This criterion can be called the criterion of dissociation (KD).In its essence, it resembles the Biot criterion; however, unlike the latter, it can be used to describe the similarity of nonlinear temperature fields in solids under conditions of stationary convective heat exchange with the environment.
Thus, we have obtained dependencies for determining the temperature on the surface and depth of a gas-hydrate massif, the distribution of heat sources and the rate of dissociation under various conditions of heating the surface of this massif.

SELF-PRESERVATION OF GAS HYDRATES
In view of the importance of the self-preservation effect for gas hydrate technologies, it is necessary to characterize the thermophysical features of this process in more detail.In the above formulas, the coefficient k reflects the intensity of the changes in internal heat sinks in the hydrate.It is possible to determine at what k the self-preservation effect will be observed, m -1 , Substituting the value for propane hydrate at tGH = 0 °C, room temperature +18 °C, on the open surface in the room the heat transfer coefficient on the vertical surface αs = 8.7 W/(m 2 °C), we obtain, k = 125 m −1 .Thus, theoretically, the self-preservation effect for propane hydrate can be expected at values of 125.However, the experimentally determined value of k does not exceed 50.
Using formula (25), the value of k for methane hydrate can be calculated.According to the data presented in [11], [17]- [19], the temperature on the surface of the ice crust is −2 °C, and the equilibrium temperature inside the methane hydrate mass at atmospheric pressure is -33 °C.Let us substitute the value for methane hydrate, m −1 , k = 11.2.
Therefore, for methane hydrate, self-preservation will already be observed at values of k >11.2.At the same time, the intensity of internal heat flows near the surface GH, W/m 3 , q = −1944.
In a similar way, it is possible to determine the coefficient k and the power of volumetric heat flows for other hydrate-forming gases.The calculation results for various gases are summarized in Table 1.
Analysing the obtained results, it can be observed that the intensity of heat flows in GH is much lower (approximately 10 times) than is required to obtain the effect of self-preservation.Therefore, self-preservation of hydrate "at room temperature" is not observed.
From formula (25), it is possible to obtain a dependence to determine the temperature of the outside air below which the effect of self-preservation can exist, °С, Thus, for propane GH, self-preservation can be expected when the ambient temperature drops below ta = 7.1 °C.Thus, formula (26) is of great practical importance, since it allows one to calculate the conditions under which long-term storage of hydrates in a nonequilibrium state can be achieved.
Several scientific works by different authors [17]- [19] note the key role of the ice crust on the surface of the hydrate in obtaining the self-preservation effect.To analyse the influence of this factor, we will determine the influence of the thermal resistance of the ice crust formed on the GH surface.If the effect of self-preservation is observed (as for methane hydrate), then in a stationary mode the layer of ice on the surface can be represented as additional resistance to heat transfer.Taking into account the thickness of the ice crust, the total resistance to heat transfer, (m 2 °C)/W, ice s According to the data presented in [11], the thickness of the surface of the ice crust on the GH is on average only 0.3 mm.
To determine the gas flow rate inside a gas hydrate massif, it is necessary to consider in more detail the processes of dissociation of its deep layers.The heat balance of an elementary section of a gas hydrate is described by the difference in heat flows supplied by thermal conduction and removed as a result of the dissociation of the hydrate and cooling by gas coming from deeper layers of the hydrate.For an arbitrary cross section, the change in these specific heat flows can be described by the equation W/(m 2 m), where qtc is the heat flow transmitted by thermal conductivity, W/m 2 ; qd is the specific heat flux that causes the dissociation of GH, W/m 2 ; qgh -heat flow for gas heating, W/m 2 .Knowing the change in heat flow, it is possible to calculate the change in gas flow rate formed during the dissociation process in each section of the hydrate mass, m 3 /(m 2 s m), where K is the volumetric gas content of the hydrate, m 3 /m 3 ; r -specific heat of dissociation, J/kg; ρGH -hydrate density, kg/m 3 .Substituting the heat flux change from equation (28) into equation ( 29), we obtain, m 3 /(m 2 s m), Eq. ( 30) allows us to determine the specific gas release in each section of the hydrate mass.To do this, we will reveal the meaning of the configurations of individual heat flows.In particular, the change in heat flow resulting from the thermal conductivity of the hydrate By double differentiation of Eq. ( 3) we obtain the following The heat flow from gas hydrate to gas, the flow rate of which in section x is an integral value, can be found using the formula After substituting the values of the heat flows into equation (30), we obtain the following Under conditions of low gas flow rates, its temperature practically does not differ from the surrounding hydrate mass, so we can assume that Taking into account expression (35), the gas distribution in the dissociating GH can be determined by the formula Eq. ( 36) can be conveniently solved using digital methods.
To test the mathematical model, the decomposition of the hydrate of propane gas was calculated using the initial data of experimental studies: hydrate surface temperature tGH = 0.7 °С, temperature of the thermodynamically stable state of the hydrate te = −0.9°С; its thermal conductivity λ = 0.5 W/(m C); density ρGH = 899 kg/m 3 ; heat of dissociation r = 6 640 000 J/kg; mass heat capacity of propane (gas phase) cGH = 1863 J/(kg °C); propane density ρp = 2.0 kg/m 3 .
Therefore, after substituting the initial data into equation (36), we obtain the value of the specific volumetric gas flow rates in an arbitrary section of the hydrate mass, Fig. 5.The dependence of the gas flow on the hydrate temperature (Fig. 6) is described by a linear equation, m 3 /(m 2 s), G 7 0.9 3•10 Analysis of the components of Eq. (32) shows that in the case of slow hydrate dissociation, is four orders of magnitude less than ( ) λk , so it can be neglected in calculations.In this case, with sufficient accuracy for practical application, Eq. (36) can be written as (37)  Therefore, the analysis of the components of Eq. (36) shows that the value of G G G ρ c g is approximately four orders of magnitude less than αs.Therefore, when calculating the self-preservation of GH, the use of a boundary condition is completely justified.For the case of active heat supply and rapid heating of GH, it is advisable to apply the limit condition (6).
Under the conditions of self-preservation, the volume of the hydrate mass changes insignificantly; however, due to gradual dissociation, its gas content decreases.This leads to a change in the thermophysical properties of the hydrate; in particular, there is a decrease in the intensity of volumetric heat sinks.As a result, the temperature regime of the gas-hydrate mass will change.
To determine changes in the characteristics of a hydrate depending on its concentration, we denote the mass concentration of the hydrate as the fraction of pure hydrate in the mixture of hydrate and ice where mh is the mass of pure hydrate, m 3 ; M -the mass of total mass of the gas hydrate, m 3 .It is obvious that, other things being equal, the power of specific volumetric heat sources will be proportional to the mass of the dissociating hydrate Substituting the known values of volumetric heat flows, we obtain an expression to determine the volumetric heat sinks under conditions of gradual dissociation of the hydrate where kGH is the coefficient for concentrated gas hydrate, m -1 .
As experimental studies indicate, the coefficient k decreases with decreasing gas content GH.A change in the thermal conductivity of the deep layers of hydrate is not typical for a natural massif of concentrated hydrate, since during the decomposition of the hydrate, recrystallization with the formation of ice occurs only on its surface.As for the deep layers, the hydrate decomposes while maintaining the structure of the frame.As a result, the thermal conductivity of the hydrate can be considered constant over a wide range of its concentration.This remark does not apply to artificial gas hydrate, which may contain ice in its initial composition.If the thermal conductivity of the gas hydrate does not change, then for a hydrate of arbitrary concentration Taking into account formula (41), the equation of specific volumetric heat flows takes the form The dependence obtained (42) allows us to determine the distribution of heat sinks deep in the gas hydrate under conditions of slow dissociation.For example, to calculate the specific volumetric heat sinks at different values of GH concentration, we will use experimental data: Сh = 1.0; αs = 4 W/(m °C); k = 50 m −1 ; tGHs = +11 °C; tGH = 0.7 °C; te = −0.9°C; λ = 0.5 W/(m °C).The results of calculating the volumetric heat sinks in propane hydrate are shown in Fig. 7. Analysis of the results obtained indicates the existence of a zone with intense thermal processes, about 6 cm deep.In the deeper layers of gas hydrate, the intensity of the heat sinks is approximately the same.Thus, the results of the studies show that the main reason for the effect of hydrate self-preservation is a decrease in the temperature of its deep layers as a result of partial dissociation.The formation of an ice crust on the surface of dissociating GH is the result, not the cause, of the self-preservation effect.Therefore, when the thermal processes occurring during the dissociation of a hydrate mass are mathematically modelled, it is necessary to take into account that heat sinks are functions of temperature and pressure at this point in the hydrate mass.It has been established that the influence of the size of the hydrate mass on the self-preservation effect is the temperature distribution within the hydrate mass.In a large massif, a lower temperature is achieved in the deep layers of the hydrate, facilitating its better storage.

FEATURES OF HYDRATE STORAGE IN HYDRATE STORAGE FACILITIES
To store hydrates, hydrate storage facilities can be used, in which GH is stored at atmospheric pressure under self-preservation conditions.The main enclosure structure of such storage facilities is a sealed tent, which must have certain thermal insulation properties.To determine the design and technical and economic characteristics of such storage facilities, thermal calculations.
When hydrate in the temperature regime, the minimum required resistance to heat transfer of the enclosing structures of a hydrate storage facility can be determined by the formula ac GHs hc GH e -, ( -) where tac is the external design air temperature, °C; tGHs -temperature on the surface of the gas hydrate block under self-preservation conditions, °C.
The maximum temperature of the outdoor air during the gas hydrate storage period of gas hydrates should be taken as the external design temperature (tac).For example, for the use of gas hydrate blocks for heating, this temperature will be the temperature at the beginning of the heating period (+8 °C).The temperature on the surface of the gas hydrate block under self-preservation conditions can be taken around −1-−2 °C (Table 1).The thermal insulation properties of the hydrate storage tent are provided not only by the gas layer, but also by the heat transfer resistance of all structural elements of the tent.
An example of calculating the storage of methane hydrate during the transitional and cold periods of the year.The outside air temperature is +8 °C, the temperature on the surface of the hydrate block is −2 °C, the temperature at the depths of the hydrate is −33 °C.The thermal conductivity of methane hydrate is 0.5 W/(m 2 °C), k = 11.2 m −1 .The heat transfer coefficient on the outer surface of the tent structure is 23 W/(m 2 °C).
The minimum required resistance to heat transfer to comply with the self-preservation mode, 0.498 (m 2 °C)/W.Thus, the heat transfer resistance of the tent film exceeds the minimum necessary condition for the existence of the self-preservation mode.In cold weather, one layer of film coated with aluminium spray is enough to thermally insulate the storage facility.
Warm period.The average temperature in July is 20.6 °C.The highest daily amplitude of fluctuations in the outside air temperature is 17.8 °C.Estimated outside air temperature, tac = 29.5 °C.
Calculated value of the resistance to heat transfer of the tent structure 0.38 (m 2 °С)/W.Therefore, the calculation results show the possibility of using GH storage facilities for different climatic conditions.Using the proposed calculation methodology and applying the reduced-cost method, it is possible to determine the optimal thickness of the thermal insulation of the hydrate storage tent.

CONCLUSIONS
1. Experimental studies of the thermal regime of the gas hydrate massif were carried out.
The exponential nature of the temperature distribution in the depth of the dissociating gas hydrate has been established.The results of experimental studies of the temperature regime of dissociating propane hydrate are presented.2. A mathematical model of thermal processes of a gas-hydrate block under conditions of self-preservation, melting of the ice crust and intense dissociation has been developed.Comparison with experimental data showed good convergence.A mathematical model has been developed to calculate the decomposition of gas hydrates under non-equilibrium conditions.A dissociation criterion (KD) is proposed to describe the similarity of nonlinear temperature fields in a solid under the conditions of stationary convective heat exchange with the environment.3. The self-preservation processes of gas hydrates have been studied.It has been determined that the reason for self-preservation is a decrease in the temperature of the internal layers of the gas hydrate block due to its partial dissociation.Dependencies have been established that determine the conditions for the occurrence of the phenomenon of self-preservation.Dependencies have been identified to determine the gas flow rate formed in the depths of the dissociating hydrate block.The influence of the concentration of GG on its temperature during storage has been established.4. The practical significance of the research results is to determine the quantitative relationship between the rate of hydrate dissociation, the climatic data, and the thermal protective properties of the coating.The prospects for further scientific developments in this direction are the optimization of design solutions for the enclosing structures of hydrate storage facilities.

Fig 1 .
Fig 1. Scheme for the synthesis and storage of gad hydrate [10].

Fig. 4 .
Fig. 4. Temperature distribution near the surface of a hydrate with a 100 % gas content:

Fig. 5 .
Fig. 5. Gas flow in the dissociating hydrate (gGH) and temperature regime in the GH (tGH) depending on the depth of the hydrate layer (X), m.

Fig. 6 .
Fig. 6.Dependence of propane flow on GH temperature in the corresponding layers.
Dividing the thermal power supplied to compensate for cold sources by the total amount of thermal energy to melt this block rρGH, we obtain the linear dissociation rate of the block GH, m/sec,

TABLE 1 .
CHARACTERISTICS OF GH UNDER SELF-PRESERVATION CONDITIONS