Simulation of the Process of Injection of Liquid Sulfur Dioxide into a Porous Reservoir Initially Saturated with Methane and Ice

Abstract

The paper presents the results of modeling the problem of injecting liquid sulfur dioxide into a porous reservoir initially saturated with methane and ice. The model presented in the paper assumes the formation of three different regions, namely the near one, saturated with liquid SO₂ and its hydrate; the far one, containing methane and ice; and the intermediate one, saturated with methane and water. The effects of various parameters of the porous medium and injected SO₂ on the nature of the course of the hydrate formation process have been studied. It is shown that with a decrease in reservoir permeability or injection pressure, the length of the intermediate region decreases, which, in the limiting case, means the formation of SO₂ hydrate in the mode without the formation of an extended region saturated with methane and water. It is shown that such a regime is also typical for the case of high initial injection pressures, as well as low values of the initial reservoir temperature and injection temperature.

1. Introduction

Gas hydrates or clathrates are crystalline compounds formed under certain thermobaric conditions and containing gas and water in their composition. Under certain thermobaric conditions, gas hydrates are formed mainly from gas and water (or ice) [1,2]. Since the 1960s, the emphasis in the study of gas hydrates began to shift toward the extraction of gas from their composition. At that time, the Messoyakh gas hydrate field, deposits in the Mackenzie Delta, and natural accumulations of hydrates at the bottom of the seas and oceans were discovered. At present, the volume of gas in the composition of gas hydrates is estimated at about 10¹⁶ m³ [3]. Therefore, the development of gas from such fields is quite relevant. In particular, the following methods of gas production from the gas hydrate composition have been proposed [4,5]: thermal, depressurization, and injection of inhibitors. These methods of extracting gas from the composition of the gas hydrate are called traditional methods. Theoretical studies published over the past 15 years and devoted to the study of traditional methods of extracting hydrocarbons from gas hydrates are presented, in particular in [6,7,8,9,10,11,12]. Thus, in [6,7], the process of dissociation of gas hydrate in a closed reservoir caused by depressurization of a well is numerically investigated on the basis of the constructed mathematical model in flat one-dimensional and axisymmetric formulations. In particular, this paper presents estimates of pressure and temperature fields implemented in the hydrate and gas regions, as well as temporary changes in the output of natural gas caused by the decomposition of hydrate. The results of analytical solutions to the problems of decomposition of gas hydrates in a porous medium are presented in [8,9,10] and summarized in the monograph [10]. In these works, the peculiarities of the processes of dissociation of gas hydrates into gas and water, depending on the parameters of the system, are investigated. The obtained results were also generalized to the region of negative temperatures when hydrate decomposition occurs with the formation of ice. The study of hydrate decomposition, when this process takes place not on the frontal surface but in some sufficiently extended area, is considered in [12]. It should be noted that, in the presented works, mathematical models are based on methods and equations of mechanics of multiphase media (the system of basic equations necessarily includes the continuity equation, Darcy’s law, and the energy equation). The most complete mathematical models of the formation and decomposition of gas hydrates, close to the real conditions of the development of gas hydrate deposits, are presented in [13,14,15,16,17].

It should be noted that traditional methods of gas production from the gas hydrate composition are, for the most part, inefficient and costly. First, they require a significant amount of energy to be supplied to the system, which leads to high extraction costs. Second, they destabilize hydrate formations because both pressure release and heat input cause the hydrate to melt. This can lead to destabilization or sudden collapse of hydrated deposits and other nearby subterranean formations. Therefore, the task of finding new methods of influencing gas hydrate formations that minimize the energy costs for extracting gas from them is urgent. One such method is the injection of industrial and greenhouse gases (e.g., sulfur dioxide, carbon dioxide) into gas hydrate deposits. In particular, in [18,19], the very possibility of the reaction of the substitution of methane molecules by carbon dioxide molecules in methane gas hydrate was convincingly proved. It was also found in [18] that the reaction of replacing methane with carbon dioxide proceeds with the release of heat. It was established in [20,21] that if the system temperature is below the equilibrium temperature (at a given pressure) of the decomposition of methane gas hydrate into methane and water, then the reaction of replacing methane with carbon dioxide does not lead to the release of free water. In this case, carbon dioxide hydrate is formed instead of methane hydrate without the formation of an intermediate liquid phase. The studies presented in [22,23,24] proved that the injection of carbon dioxide into underground porous reservoirs is a fairly effective way to capture it. It was also found in [25,26] that one of the promising methods for utilizing sulfur dioxide is its injection in the liquid phase into depleted natural gas fields. This method, firstly, provides a fairly reliable preservation of SO₂ in the solid phase at relatively low economic costs and, secondly, ensures the release of natural gas (methane) from such reservoirs.

Numerical modeling of the replacement of methane by carbon dioxide in methane gas hydrate is the subject of, in particular, works [27,28,29]. Basically, they study only the kinetics of the process. At the same time, the formulation of problems in them corresponds to the case when carbon dioxide instantly fills all points of the reservoir saturated with methane and water, i.e., does not take into account the processes of heat and mass transfer in the reservoir itself (at the macro level). Thus, at present, there is a sufficient number of theoretical and experimental works, which present the results on the injection of carbon dioxide into systems containing methane gas hydrate or free methane. The above experimental works also do not give a complete description of the processes occurring in this case. This is due, firstly, to the fact that this process is studied in a free volume and not in a pore space. Secondly, in experimental studies, studies were carried out, as a rule, in samples of small size and under conditions of thermal and pressure control. Therefore, in these studies, the substitution process is primarily limited by the kinetics of the process. This circumstance is already unacceptable for cases when the replacement process is considered for sufficiently large porous reservoirs. In this case, the heat and mass transfer will play the main role.

This paper presents a mathematical model and the results of numerical simulation of the process of injection of liquid sulfur dioxide into a natural porous reservoir containing methane and ice. The influence of the main parameters of the system on the features of the binding of SO₂ into a solid hydrate form is studied. It is shown that at high intensities of sulfur dioxide supply to the phase transition front, hydrate formation occurs from SO₂ and water and at low values—without the formation of a region saturated with methane and water. Also presented is a critical diagram separating these two modes.

The experimental phase diagram (Figure 1) shows the thermobaric conditions for the existence of sulfur dioxide gas hydrate [30]. In the above diagram, curve 1 corresponds to a three-phase equilibrium between gaseous sulfur dioxide, its gas hydrate, and water (ice); curve 2 corresponds to a two-phase equilibrium between gaseous and liquid sulfur dioxide; and curve 3 corresponds to an equilibrium between liquid sulfur dioxide, its gas hydrate, and water. SO₂ gas hydrate exists above curve 1 and to the left of curve 3, i.e., at sufficiently high pressures and low temperatures. At the upper quadrupole point Q₂ (T_Q = 285.1 K and p_Q = 0.233 MPa), gaseous and liquid sulfur dioxide, as well as its gas hydrate and water, are in equilibrium.

Let a porous horizontal layer of length L in the initial state be saturated with ice with initial saturation S_w0 and methane. We will assume that the initial values of temperature T₀ and pressure p₀ of the formation correspond to the thermodynamic conditions for the existence of sulfur dioxide (in the liquid state) and its gas hydrate (i.e., above curve 2 in Figure 1). Let liquid sulfur dioxide be injected through the left boundary of the formation (x = 0), the pressure p_e and temperature T_e of which correspond to the conditions for the existence of sulfur dioxide gas hydrate. We will assume that, in this case, three regions are formed in the reservoir: near, far, and intermediate. In the near zone, liquid sulfur dioxide and its gas hydrate will be present in the formation pores. The intermediate zone will be saturated with water and methane, while the far zone will be saturated with ice and methane. In this case, two boundaries of phase transitions will appear in the reservoir, separating these areas and moving deep into the reservoir. Therefore, at the near boundary of the phase transition x = x_(n), SO₂ gas hydrate is formed from water and sulfur dioxide, and at the far surface of the phase transition x = x_(d), ice is melting.

2. Basic Equations

To describe the processes of heat and mass transfer, accompanied by the formation of sulfur dioxide hydrate and melting of ice, we will use a single-temperature model of the system under consideration with a constant value of porosity. In this case, the skeleton of a porous medium, gas hydrate, and water are incompressible and motionless; methane will be considered a calorically perfect gas, and liquid sulfur dioxide will be considered an elastic liquid. In addition, SO₂ hydrate is a two-component system with a mass fraction of the hydrate-forming gas equal to G. The system of basic equations, which is the laws of conservation of mass and energy, Darcy’s law, and the equation of state under the above assumptions in each of the regions, has the form [31,32]

$$\begin{array}{c}\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left({\rho }_i\varphi S_i\right)+\frac{\mathsf{\partial }}{\mathsf{\partial }x}\left({\rho }_i\varphi S_i{\upsilon }_i\right)=0,\\ \frac{\mathsf{\partial }}{\mathsf{\partial }t}\left(\rho C\cdot T\right)+{\rho }_i{C}_i\varphi S_i{\upsilon }_i\frac{\mathsf{\partial }T}{\mathsf{\partial }x}=\frac{\mathsf{\partial }}{\mathsf{\partial }x}\left(\lambda \frac{\mathsf{\partial }T}{\mathsf{\partial }x}\right),\\ \varphi S_i{\upsilon }_i=-\frac{k_i}{{\mu }_i}\frac{\mathsf{\partial }p}{\mathsf{\partial }x},\\ {\rho }_s={\rho }_{0s}\cdot \exp \left(\beta (p-p_0)\right), {\rho }_g=p/R_{g}T.\end{array}$$

(1)

Here, the subscripts i = s, m refer to the parameters of liquid sulfur dioxide and methane, respectively; φ is the porosity; ρ_i, υ_i, k_i, C_i, and μ_i are, respectively, the true density, velocity, permeability, specific heat, and dynamic viscosity of the i-phase; p is the pressure; T is the temperature; S_i is the saturation of pores with the i-phase; R_g is the gas constant of methane; β is the volumetric compression ratio of liquid SO₂; ρ_0s is the true density of liquid sulfur dioxide corresponding to pressure p₀; and ρC and λ are the specific volumetric heat capacity and thermal conductivity of the system, respectively. Since the main contribution to the values of ρC and λ is made by the corresponding parameters of the skeleton of the porous medium, we will assume them to be constant values.

The dependence of the phase permeability coefficient k_(i) on saturation S_(i) is set based on the Kozeny formula [33]:

$$k_i=k_0{S}_i^3,$$

where k₀ is the absolute permeability of the reservoir.

The conditions for the balance of mass and heat at the near boundary of the phase transition x = x_(n), which separates the near and intermediate regions and at which SO₂ hydrate is formed from water and sulfur dioxide, can be represented as

$$\begin{array}{c}-\frac{k_s}{{\mu }_s}\frac{\mathsf{\partial }{p}_{\left(1\right)}}{\mathsf{\partial }x}=\varphi \left(S_s+\frac{{\rho }_{h}G}{{\rho }_s}{S}_h\right){\dot{x}}_{\left(n\right)},-\frac{k_{m\left(2\right)}}{{\mu }_m}\frac{\mathsf{\partial }{p}_{\left(2\right)}}{\mathsf{\partial }x}=\varphi S_{m\left(2\right)}{\dot{x}}_{\left(n\right)},\\ \varphi S_h{\rho }_h(1-G){\dot{x}}_{\left(n\right)}=\varphi S_l{\rho }_l{\dot{x}}_{\left(n\right)}, \lambda \frac{\mathsf{\partial }{T}_{(1)}}{\mathsf{\partial }x}-\lambda \frac{\mathsf{\partial }{T}_{(2)}}{\mathsf{\partial }x}=\varphi {\rho }_h{L}_h{S}_h{\dot{x}}_{\left(n\right)}.\end{array}$$

(2)

Here, ρ_h and ρ_l are the densities of hydrate and water, respectively; S_h and S_l are the hydrate saturation and water saturation, respectively; L_h is the specific heat of SO₂ hydrate formation; and ${\dot{x}}_{\left(n\right)}$ is the velocity of the phase transition boundary. Here and below, the subscripts 1, 2, and 3 refer to the parameters of the near, intermediate, and far regions, respectively.

Similarly, the conditions at the far boundary of the phase transition x = x_(d), where ice melts, can be represented as

$$\begin{array}{c}-\frac{k_{m\left(2\right)}}{{\mu }_m}\frac{\mathsf{\partial }{p}_{\left(2\right)}}{\mathsf{\partial }x}=-\frac{k_{m\left(3\right)}}{{\mu }_m}\frac{\mathsf{\partial }{p}_{\left(3\right)}}{\mathsf{\partial }x}, \varphi S_l{\rho }_l{\dot{x}}_{\left(d\right)}=\varphi S_{w0}{\rho }_{w0}{\dot{x}}_{\left(d\right)},\\ \lambda \frac{\mathsf{\partial }{T}_{(3)}}{\mathsf{\partial }x}-\lambda \frac{\mathsf{\partial }{T}_{(2)}}{\mathsf{\partial }x}=\varphi {\rho }_{w0}{S}_{w0}{L}_w{\dot{x}}_{\left(d\right)}.\end{array}$$

(3)

Here, ρ_w0 and L_w are the density and specific heat of ice melting, respectively; and ${\dot{x}}_{\left(d\right)}$ is the velocity of the far boundary of the phase transition.

The pressure and temperatures at the boundaries of phase transitions will be considered continuous quantities. In addition, since ice melts at the far boundary of phase transitions x = x_(d), we assume that its temperature is T_(d) = 273 K.

Since the initial ice saturation was assumed to be equal to S_w0, then from the equations of systems (2) and (3) for the values of S_l and S_h, one can obtain

$$S_l=\frac{{\rho }_{w0}{S}_{w0}}{{\rho }_l}, S_h=\frac{{\rho }_l{S}_l}{{\rho }_h\left(1-G\right)}=\frac{{\rho }_{w0}{S}_{w0}}{{\rho }_h(1-G)}.$$

The initial conditions, as well as the conditions at the outer boundaries of the reservoir, can be represented as

$$\begin{array}{c}t=0: p=p_0, T=T_0 (0 \le x \le L);\\ x=0: p=p_e, T=T_e (t > 0);\\ x=L: \frac{\mathsf{\partial }p}{\mathsf{\partial }x}=0, \frac{\mathsf{\partial }T}{\mathsf{\partial }x}=0 (t > 0).\end{array}$$

(4)

From system (1), the piezoconductivity equation for the near region (i = 1) can be represented as

$$\frac{\mathsf{\partial }{p}_{\left(1\right)}}{\mathsf{\partial }t}=\frac{k_s}{\varphi \left(1-S_h\right){\rho }_s\beta {\mu }_s}\frac{\mathsf{\partial }}{\mathsf{\partial }x}\left({\rho }_s\frac{\mathsf{\partial }{p}_{\left(1\right)}}{\mathsf{\partial }x}\right).$$

(5)

Similar equations for the intermediate and far regions (i = 2, 3) have the form

$$\frac{\mathsf{\partial }{p}_{\left(i\right)}}{\mathsf{\partial }t}=\frac{k_m}{\varphi S_m{\mu }_m}\frac{\mathsf{\partial }}{\mathsf{\partial }x}\left(p_{\left(i\right)}\frac{\mathsf{\partial }{p}_{\left(i\right)}}{\mathsf{\partial }x}\right).$$

(6)

The equation of heat influx after transformations can also be represented as

$$\frac{\mathsf{\partial }{T}_{\left(i\right)}}{\mathsf{\partial }t}=\frac{\mathsf{\partial }}{\mathsf{\partial }x}\left({\kappa }^{\left(T\right)}\frac{\mathsf{\partial }{T}_{\left(i\right)}}{\mathsf{\partial }x}\right)+{{\rm X}}_{\left(i\right)}\frac{\mathsf{\partial }{p}_{\left(i\right)}}{\mathsf{\partial }x}\frac{\mathsf{\partial }{T}_{\left(i\right)}}{\mathsf{\partial }x} (i=1, 2, 3),$$

(7)

where ${\kappa }^{\left(T\right)}=\lambda /\rho C$ is the formation thermal diffusivity; ${{\rm X}}_{\left(1\right)}=\frac{{\kappa }^{\left(T\right)}{\rho }_s{C}_s}{\lambda }\frac{k_s}{{\mu }_s}$; and ${{\rm X}}_{\left(i\right)}=\frac{{\kappa }^{\left(T\right)}{\rho }_m{C}_m}{\lambda }\frac{k_{m\left(i\right)}}{{\mu }_m}$ (i = 2, 3).

To solve a closed system of Equations (5)–(7) with initial boundary conditions (4) and conditions (2)–(3) at the boundaries of the phase transition, the method of catching fronts in the nodes of a spatial grid is used [34]. In this case, a uniform spatial grid is constructed with a step h (h = L/N, N—the number of split points). It is assumed that for the unknown time step τ determined in the course of the solution from the finite-difference representation (2), the near front of the phase transition moves along the coordinate by the value h. The far boundary of the phase transition, at which ice melts, also correlates with the node of the spatial grid, for which the temperature is close to the melting temperature of ice. For each time layer, the constructed difference scheme is a system of non-linear algebraic equations. This system is solved using the Thomas algorithm and the method of simple iterations [35]. The iterative process at each time layer continued until the specified accuracy was achieved for all considered quantities: pressure, temperature, and coordinates of the fronts.

3. Analysis of the Results

In Figure 2, for time t = 10 day, the reservoir temperature and pressure distributions are presented. The injection pressure of liquid sulfur dioxide corresponds to the value p_e = 3.2 MPa (fragment Figure 2a) and p_e = 3.1 MPa (fragment Figure 2b). The values of other parameters used in the model are presented in

Table 1. Basic parameters for the model.

Variables	Symbol	Value	Unit
Porosity	φ	0.2	–
Initial ice saturation	Sw0	0.2	–
Permeability	k0	10−15	m2
Reservoir length	L	50	m
Dynamic viscosity of sulfur dioxide	μs	3.68 × 10−4	Pa∙s
Dynamic viscosity of methane	µm	10−5	Pa∙s
Mass concentration of sulfur dioxide in gas hydrate	G	0.327	–
Gas constant of methane	Rg	520	J/(K∙kg)
Thermal conductivity coefficient of the formation	λ	2	W/(m∙K)
Specific volumetric heat capacity	ρC	2 × 106	J/(K·m3)
Volume compression factor of sulfur dioxide	β	1.35 × 10−9	Pa−1
Density of sulfur dioxide hydrate	ρh	1390	kg/m3
Density of water	ρl	1000	kg/m3
Density of ice	ρw0	900	kg/m3
Density of sulfur dioxide	ρ0s	1434	kg/m3
Heat capacity of sulfur dioxide	Cs	1350	J/(K∙kg)
Heat capacity of methane	Cm	1560	J/(K∙kg)
Specific heat of melting of ice	Lw	3.3 × 105	J/kg
Specific heat of formation of sulfur dioxide hydrate	Lh	2.5 × 105	J/kg
Initial pressure	p0	3	MPa
Initial temperature	T0	272	K
Injection temperature	Te	268	K

. As follows from Figure 2, when SO₂ is injected at a pressure of p_e = 3.2 MPa, the temperature of the system rises above the melting temperature of ice. This means that in addition to the formation of sulfur dioxide hydrate and displacement of methane, the process of ice melting and, as a result, the formation of an area containing methane and water take place in the reservoir. In this case, the region 0 ≤ x < x_(n) contains liquid SO₂ and its hydrate in pores; the region x_(n) < x <x_(d) is methane and water, and the region x > x_(d) contains methane and ice. At lower injection pressures (p_e = 3.1 MPa), as follows from fragment b, the temperature of the system is below the melting point of ice; in this case, the formation of a region containing methane and water does not occur. Thus, at high liquid sulfur dioxide injection pressures, the formation of SO₂ hydrate occurs with the formation of three different areas from water and liquid sulfur dioxide, according to the problem statement. In the case of low injection pressures, the formation of SO₂ hydrate occurs from SO₂ and ice without the formation of a region saturated with methane and water.

In Figure 3, for the moment of time t = 10 days, the dependences of the temperature T_(n) on the near surface of the phase transition, as well as the coordinates of the near and far boundaries of the phase transition, on the injection pressure p_e are presented. As follows from the figure, with a decrease in the injection pressure, both the temperature at the near boundary of the phase transition and the length of the region containing methane and water decrease. This is due to the fact that with a decrease in the value of p_e, the intensity of SO₂ hydrate formation decreases, which is proportional, according to Darcy’s law, to the pressure drop in the system. As a result, there is also a decrease in the magnitude of the thermal effect caused by the reaction of hydrate formation. Thus, in the case of low values of p_e (less than 3.2 MPa), the intensity of hydrate formation is low, and the temperature does not rise above the melting temperature of ice. In this case, the formation of sulfur dioxide occurs from ice and SO₂ without the formation of a region saturated with methane and water.

Figure 4 shows the dependences of the temperature T_(n) on the near surface of the phase transition, as well as the coordinates of the near and far boundaries of the phase transition, on the initial pressure of the system p₀. As follows from the figure, with an increase in the initial pressure of the system, both the temperature at the near boundary of the phase transition and the length of the region containing methane and water decrease. This is explained by the fact that with increasing p₀, the pressure drop in the system and, as a consequence of the Darcy law, the intensity of the phase transition decrease. Thus, the formation of sulfur dioxide hydrate from SO₂ and water, according to the formulation of the problem, is possible only in the case of low values of the initial pressure. An increase in p₀ values leads to a decrease in the length of the region containing methane and water, and, as a consequence, the possible formation of SO₂ hydrate without its formation from sulfur dioxide and ice.

Figure 5 shows the dependences of the temperature T_(n) on the near surface of the phase transition, as well as the coordinates of the near and far boundaries of the phase transition, on the absolute permeability k₀ of the reservoir. It follows from the figure that at high values of the absolute permeability of the reservoir (greater than 10⁻¹⁵ m²), the formation of sulfur dioxide hydrate from SO₂ and water occurs. In this case, there are three areas in the reservoir according to the formulation of the problem under consideration. With a decrease in the value of k₀, the temperature at the phase transition boundary decreases. This is due to a decrease in the intensity of the phase transition, which is limited by the flow of SO₂ to it and, according to Darcy’s law, is proportional to the reservoir permeability. In this case, at low values of k₀, the temperature T_(n) can become lower than the melting temperature of ice. In this case, the formation of SO₂ hydrate occurs with the formation of two regions of SO₂ and ice, without the formation of a region containing methane and water.

It should be noted that the results obtained in this work are qualitatively correlated with the theoretical calculations obtained, for example, in [30,31]. Thus, according to [31], injection of liquid carbon dioxide into a gas hydrate formation also leads to an increase in the temperature of the system; at high injection intensities, a mode with decomposition of gas hydrates is possible, and at low—without its dissociation.

Figure 6 shows the dependences of the temperature T_(n) on the near surface of the phase transition, as well as the coordinates of the near and far boundaries of the phase transition, on the initial reservoir temperature T₀ (fragment Figure 6a) and the injection temperature T_e (fragment Figure 6b) of liquid sulfur dioxide. As follows from the figure, the temperature at the near boundary of the phase transition increases with an increase in both the initial reservoir temperature and the temperature of the injected sulfur dioxide. In this case, the coordinate of the phase transition front at which SO₂ hydrate is formed (curve 1) does not depend on the values of T₀ and T_e, i.e., determined by the mass transfer of sulfur dioxide. In this case, the coordinate of the boundary on which ice melts (curve 2) increases with both T₀ and T_e, i.e., determined by heat transfer deep into the reservoir. Thus, as follows from the figure, the formation of sulfur dioxide from SO₂ and water occurs at high values of the initial formation temperature and the injection temperature of liquid sulfur dioxide.

In Figure 7, for the moment of time t = 10 days, the dependence of the critical injection temperature T_*, below which the formation of SO₂ hydrate occurs without the formation of a region saturated with methane and water, on the injection pressure of sulfur dioxide is presented. As follows from the figure, with an increase in the value of p_e, the value of the critical temperature decreases. This is due to the fact that, in this case, the intensity of the phase transition increases; therefore, the formation of sulfur dioxide hydrate from ice and SO₂ occurs at lower temperatures. In addition, as follows from the figure, the critical temperature also depends on the formation permeability. As the reservoir permeability increases, the critical injection temperature also decreases. This is explained by the fact that an increase in the value of k₀ also leads to an increase in the intensity of the phase transition.

4. Conclusions

The article presents a mathematical model of the process of pumping liquid sulfur dioxide into a porous reservoir initially saturated with methane and ice. The influence of the initial system, as well as the parameters of the injected sulfur dioxide on the formation of SO₂ hydrate in the formation, has been studied. It was found that at high values of the injection pressure (greater than 3.2 MPa) and the permeability of the porous reservoir (greater than 10⁻¹⁵ m²), SO₂ hydrate is formed with the formation of a region containing methane and water. It is shown that the coordinate of the phase transition front at which SO₂ hydrate is formed is determined by the mass transfer of sulfur dioxide, and the coordinate of the boundary at which the ice-melting process occurs is determined by heat transfer. It was also found that with an increase in the initial pressure of the system, the formation of sulfur dioxide hydrate occurs without the formation of a region saturated with methane and water. It is shown that the formation of sulfur dioxide from SO₂ and water occurs at high values of the initial formation temperature and injection temperature of liquid sulfur dioxide. The dependence of the critical injection temperature, below which the formation of SO₂ hydrate occurs without the formation of a region saturated with methane and water, on the injection pressure of sulfur dioxide is presented. It is shown that with increasing injection pressure, the value of the critical temperature decreases. The results obtained can also be used as recommendations for the possible disposal of sulfur dioxide in natural porous reservoirs containing methane and ice. Since ice is a component that cements the formation, it is relevant to choose such pumping modes of liquid sulfur dioxide, in which there is no ice-melting process. Thus, the injection of sulfur dioxide into natural formations containing methane and ice must be carried out in low-permeable reservoirs at relatively low (relative to the initial) injection pressures.