Experimental Investigation into Three-Dimensional Spatial Distribution of the Fracture-Filling Hydrate by Electrical Property of Hydrate-Bearing Sediments

Abstract

As a future clean energy resource, the exploration and exploitation of natural gas hydrate are favorable for solving the energy crisis and improving environmental pollution. Detecting the spatial distribution of natural gas hydrate in the reservoir is of great importance in natural gas hydrate exploration and exploitation. Fracture-filling hydrate, one of the most common types of gas hydrate, usually appears as a massive or layered accumulation below the seafloor. This paper aims to detect the spatial distribution variation of fracture-filling hydrate in sediments using the electrical property in the laboratory. Massive hydrate and layered hydrate are formed in the electrical resistivity tomography device with a cylindrical array. Based on the electrical resistivity tomography data during the hydrate formation process, the three-dimensional resistivity images of the massive hydrate and layered hydrate are established by using finite element forward, Gauss–Newton inversion, and inverse distance weighted interpolation. Massive hydrate is easier to identify than layered hydrate because of the big difference between the massive hydrate area and surrounding sediments. The diffusion of salt ions in sediments makes the boundary of massive hydrate and layered hydrate change with hydrate formation. The average resistivity values of massive hydrate (50 $\mathsf{\Omega }\cdot \mathrm{m}$) and layered hydrate (1.4 $\mathsf{\Omega }\cdot \mathrm{m}$) differ by an order of magnitude due to the difference in the morphology of the fracture. Compared with the theoretical resistivity, it is found that the resistivity change of layered hydrate is in accordance with the change tendency of the theoretical value. The formation characteristic of massive hydrate is mainly affected by the pore water distribution and pore microstructure of hydrate. The hydrate formation does not necessarily cause the increase in resistivity, but the increase of resistivity must be due to the formation of hydrate. The decrease of resistivity in fine-grains is not obvious due to the cation adsorption of clay particles. These results provide a feasible approach to characterizing the resistivity and growth characteristics of fracture-filling hydrate reservoirs and provide support for the in-situ visual detection of fracture-filling hydrate.

1. Introduction

With an increase in the development of the economy and industry, the consumption of fossil fuels is increasing rapidly. The consumption of traditional fossil fuels also produces harmful gases, resulting in serious environmental problems [1,2,3]. Natural gas hydrates are ice-like crystalline compounds consisting of gases and water under relatively low-temperature and high-pressure conditions, which are widely discovered in marine and permafrost regions [4]. Natural gas hydrate is a kind of clean energy resource because burning natural gas hydrate only releases carbon dioxide and water. Meanwhile, natural gas hydrate is considered the future of energy due to its enormous resource potential [5]. Making full use of natural gas hydrates is significant to solving the energy crisis and improving environmental pollution.

Fracture-filling hydrate is an important type of natural gas hydrate in marine regions and in permafrost [6,7,8,9,10,11]. In-situ sample cores obtained from marine regions show that fracture-filling hydrates are deposited in different morphologies within the host sediments, such as massive, vein, nodular, and layered hydrate [12,13]. Without knowing the distribution of fracture-filling hydrate, it is difficult to provide evidence and support for fine characterization of the reservoir and the design of the production well, including saturation calculation [7,11], as well as the location and type of production well [14,15]. Therefore, investigating the spatial distribution of hydrates is critical for natural gas hydrate reservoir exploration and exploitation.

The gas hydrates have a significant effect on the physical properties of marine sediments [16]. The resistivity property is one of the most effective physical properties in hydrate identification [17,18] and saturation calculation [19,20]. Resistivity measurement has been widely used in gas hydrate reservoirs and physical experiments in the laboratory. The diverse morphologies of fracture-filling hydrate lead to the distinctly electrical anisotropy of the hydrate reservoir [21]. Hydrate developed in high angle fracture [22] and hydrate distributed in layered form [23] will lead to errors in saturation calculation by resistivity. However, the one-dimensional resistivity measurement fails to reflect the spatial distribution of fracture-filling hydrate. New resistivity measurement techniques are needed to investigate the distribution of fracture-filling hydrate.

Electrical resistivity tomography (ERT) is an imaging technique to establish the resistivity image by calculating the resistivity distribution within an object [24,25,26]. An electrode array is used to acquire the electrical signal around the object which is used to calculate the resistivity. As a non-destructive and non-invasive detection method, ERT has been applied to monitor the distribution of hydrate in the laboratory. Walsh preliminarily verified that ERT could identify the hydrate formation without sediments [27]. Priegnitz et al. carried out the hydrate formation and dissociation in sediments to reveal the spatial distribution of pore-filling hydrate and characterize core electrical properties [28,29]. Li et al. utilized ERT to monitor hydrate’s formation position and heterogeneity. They found that the formation position and heterogeneity of hydrate are controlled by the distribution of pore water and methane gas [30]. Liu et al. developed a cross-borehole electrical resistivity tomography array to monitor the dynamic evolution of hydrate-bearing sediments [31]. However, most of these researches are aimed at pore-filling hydrate, and the application of ERT in fracture-filling hydrate has been rarely reported.

The physical experiment is a key way to reveal the physical properties of hydrate-bearing sediments and hydrate’s spatial distribution [32]. In this paper, massive hydrate and layered hydrate are synthesized with sediments in the high-pressure simulation vessel, respectively. The ERT data of fracture-filling hydrate are acquired by a cylindrical array during the hydrate formation. The three-dimensional resistivity images of fracture-filling hydrate are established based on the ERT data. The change features of resistivity and the growth characteristics are discussed. The results of this paper facilitate the achievement of in-situ, three-dimensional visual detection of the fracture-filling hydrate.

2. Materials and Methods

2.1. Experimental Device

A cylindrical electrical resistivity tomography device was designed for the acquisition of ERT data during in-situ fracture-filling hydrate formation. The experimental device contains two main parts: a physical simulation module of hydrate in the dotted line of Figure 1 and an electrical parameter measurement system in the solid line of Figure 1. The physical simulation module of hydrate consists of a low-temperature, high-pressure vessel, a temperature controller, and an inner cylinder. The environment of low-temperature, high-pressure is simulated to form fracture-filling hydrate in the vessel. The inner cylinder with an inner diameter of 10.0 cm and a height of 150.0 mm is insulated, which is used to hold sediments. The electrical parameter measurement system consists of a cylindrical array and an electrical parameter collector. The cylindrical array is arranged at the inner cylinder to measure the voltage signal of six layers around sediments. Sixteen electrodes of one layer are evenly distributed at the same height of the inner cylinder. Two adjacent electrodes in one layer are chosen to supply current, and the remaining electrodes in the same layer are used as measuring electrodes. A total of 208 data points are collected after the 16 electrodes in one layer are used as supply electrodes. The interval between layers is 2.0 cm.

2.2. Experiments

The electrodes are in direct contact with sediments. To prevent hydrate from wrapping the electrodes during the formation of hydrate, pure hydrate in fracture (massive hydrate) and hydrate in sandy sediments bedded in fine-grained sediments (layered hydrate) are synthesized (Figure 2). Meanwhile, these two morphologies of fracture-filling hydrate are similar to natural conditions where natural gas hydrate reservoirs develop.

2.2.1. Procedures to Form Massive Hydrate

Massive hydrate is formed by using cylindrical ice powder. Ice powder formed from distilled water is made into a cylinder with a diameter of 4.0 cm and a height of approximately 13.0 cm (Figure 3a). The cylindrical ice powder is put into liquid nitrogen to keep the ice powder from melting. Then, it is buried in fine-grained sediments with particle sizes from 0.02 μm to 62.5 μm, which are cooled in advance to avoid melting ice powder. To simulate the marine environment, the salinity of pore fluid in fine-grained sediments is approximately 3.5 wt%, and the saturation is 100%. Methane gas (purity > 99.99%) is injected into the vessel to reach high pressure. The temperature in the vessel is reduced to −2 °C at first. Then, the temperature is raised slowly. The experiment lasted for 440 h to ensure that the ice powder was converted into massive hydrate (Figure 3b). The experiments of massive hydrate have been repeated three times.

2.2.2. Procedures to Form Layered Hydrate

Hydrate formation in fine-grained sediments is very time-consuming when the pore fluid saturation is 100%. Hence, coarse-grained quartz sands with particle sizes of >500 μm are chosen as the sandy sediments bedded in fine-grained sediments to make the hydrate form in quartz sands as soon as possible. The particle sizes of fine-grained sediments are from 0.02 μm to 62.5 μm. Pores of quartz sands are filled with 3.5 wt% NaCl to simulate pore fluid in subsea. The salinity of pore fluid in fine-grained sediments is also approximately 3.5 wt%. The pore fluid saturation in the quartz sands and fine-grained sediments is 100%. Methane gas (purity > 99.99%) is injected into the vessel to reach high pressure. The temperature is stable at 0°, which will not freeze the pore fluid. The experiment lasted for 320 h until the pressure in the vessel almost maintained stability. The experiments of layered hydrate have been repeated two times because the formation of hydrate is time-consuming.

2.3. Acquirement of Hydrate Saturation

According to the material conservation principle, the number of moles of methane gas is constant before and after hydrate formation. The hydrate saturation can be calculated by the number of moles of consumed methane gas [33]. The expression is given in Equation (1).

$$S_h=\frac{\mathrm{\Delta }P·V·M}{Z·R·T·V_{\phi }·\rho }$$

(1)

where $S_h$ is the hydrate saturation, fraction; $\mathrm{\Delta }P$ is the pressure difference before and after hydrate formation, Pa; $V$ is the volume of gas phase in the vessel, m³; $M$ is the molecular weight of hydrate (assuming hydrate coefficient equals to 5.75), 119.5 g/mol; Z is compressibility factor; R is the universal gas constant, J/(mol·K); T is the instantaneous temperature of methane gas; $V_{\phi }$ is the total volume of the pore space in sediments; $\rho$ is the density of methane hydrate, 0.91 g/cm³. Please note that the ice powder is regarded as a pore when we calculate the hydrate saturation. As a result, ice powder that is not transformed into hydrate is treated as fluid in pores.

3. Three-Dimensional Resistivity Imaging of Fracture-Filling Hydrate

The two-dimensional resistivity image of fracture-filling hydrate is established by using finite element forward and Gauss–Newton inversion based on ERT data. Finite element forward is suitable for the complex geoelectric model of hydrate-bearing sediments. We adopt the regularization matrix and parameter in Gauss–Newton inversion to acquire a stable solution and improve the convergence rate. Then, the three-dimensional resistivity image of fracture-filling hydrate is established using inverse distance weighted interpolation.

3.1. Finite Element Forward

According to Ohm’s law and the charge–balance equation, the potential distribution function and conductivity distribution function satisfy the Laplace equation in field. The expression is given in Equation (2).

$$\nabla ·\left[\sigma \left(x,y\right)·\nabla \varphi \left(x,y\right)\right]=-I\delta (x-x_A)\delta (y-y_A)\left(x,y\right)\in \mathsf{\Omega }$$

(2)

where $\varphi \left(x,y\right)=\varphi$ is potential distribution function; $\sigma \left(x,y\right)=\sigma$ is conductivity distribution function; $I$ is current intensity; $\delta$ is Dirichlet function; $\mathsf{\Omega }$ is steady current field; $\left(x_A,y_A\right)$ is the location of the current source.

The Neumann boundary condition is used because the boundary of the current field is insulated. Then, we can get Equation (3).

$$\frac{\partial u}{\partial n}{|}_{\partial \mathsf{\Omega }}=\phi$$

(3)

where $u$ is the potential function in the boundary; $n$ is the unit normal vector. $\partial \mathsf{\Omega }$ is the boundary of the current field. $\phi$ is the function value of the boundary.

Therefore, the boundary value problem can be converted to a variational problem by combining Equations (2) and (3). The expression is written as Equation (4)

$$F\left(\varphi \right)={{\displaystyle \int }}_{\mathrm{s}}^{ }\frac{1}{2}\epsilon \left[{\left(\frac{\partial \varphi }{\partial x}\right)}^2+{\left(\frac{\partial \varphi }{\partial y}\right)}^2\right]dxdy\to min$$

(4)

To solve the variational problem, the finite element method divides the study area into triangular elements. Meanwhile, it is assumed that the conductivity of triangular elements is constant. The surface integral in Equation (3) can be expressed as the sum of the surface integral of triangular elements. Equation (4) can be written into Equation (5).

$$F\left(\varphi \right)={\displaystyle \sum }_{e=1}^n{{\displaystyle \int }}_{s_e}^{ }\frac{1}{2}\epsilon \left[{\left(\frac{\partial \varphi }{\partial x}\right)}^2+{\left(\frac{\partial \varphi }{\partial y}\right)}^2\right]dxdy$$

(5)

where $n$ is the number of the triangular elements.

Then, the linear algebraic equations of the function value on the nodes of triangular elements are obtained under the constraint of extremum as in Equation (6).

$$KU=P$$

(6)

where $K$ is the stiffness matrix; $U$ is the column vector composed of the potential of nodes. $P$ is the load vector, which is determined by the position and the value of the current source. The distribution of potential in the study area is acquired by solving Equation (6).

3.2. Gauss-Newton Inversion

The minimum objective function consists of model constraint and data constraint in Gauss–Newton inversion. The expression is given in Equation (7).

$$\mathrm{\Phi }\left(\rho \right)=\min {\left|\left|V-U\left(\rho \right)\right|\right|}^2+\alpha {\left|\left|L\rho \right|\right|}^2$$

(7)

where $\rho$ is resistivity; $U\left(\rho \right)$ is a function between voltage and resistivity; $L$ is regularization matrix, and $\alpha$ is the regularization parameter. V is the ERT data.

Equation (7) can be solved by using Newton iteration, which is expressed as in Equations (8) and (9).

$${\rho }_{i+1}={\rho }_i+\mathsf{\Delta }{\rho }_i$$

(8)

$$\mathsf{\Delta }{\rho }_i=-H^{-1}\nabla \mathrm{\Phi }={\left(J^{T}J+\alpha L^{T}L\right)}^{-1} \left[J^T\left(V-U\left({\rho }_i\right)\right)-\alpha L^{T}L{\rho }_i\right]$$

(9)

where $H$ is Gauss–Newton approximation $\mathsf{\Phi }\left({\rho }_i\right)$’s Hessian matrix. $\nabla \mathsf{\Phi }$ is $\mathsf{\Phi }\left({\rho }_i\right)$’s gradient. $J$ is the Jacobian matrix. The distribution of resistivity in the study area is acquired by solving Equation (7).

3.3. Inverse Distance Weighted Interpolation

According to the inverse distance weighted interpolation, the characteristic of the interpolation point is more similar to the characteristic of a closer sample point than to the sample points farther away [34]. It can be described as in Equation (10).

$$\left\{\begin{array}{c}f\left(x,y,z\right)={\displaystyle \sum _{i=1}^n}{\lambda }_{i}f\left(x_i,y_i,z_i\right)\\ {\lambda }_i=\frac{d_i^{-p}}{{{\displaystyle \sum }}_{i=1}^n{d}_i^{-p}}\\ {\displaystyle \sum _{i=1}^n}{\lambda }_i=1\end{array}\right.$$

(10)

where $f\left(x,y,z\right)$ is the resistivity of interpolation point; $n$ is the number of samples; ${\lambda }_i$ is the weight of samples; $f\left(x_i,y_i,z_i\right)$ is the resistivity of point $i$. $d$ is the distance between interpolation point and the sample. $p$ is an exponent, which is 2, generally.

4. Results and Discussion

4.1. Visualization of Three-Dimensional Spatial Distribution

4.1.1. Massive Hydrate

Figure 4 shows the three-dimensional resistivity image of the massive hydrate, clearly identifying the massive hydrate in fine-grained sediments. In the initial state, the resistivity of ice powder is about 8 $\mathsf{\Omega }\cdot \mathrm{m}$, and the resistivity of fine-grained sediments is about 1 $\mathsf{\Omega }\cdot \mathrm{m}$. After 40 h, the resistivity of ice powder is greater than 100 $\mathsf{\Omega }\cdot \mathrm{m}$, and the resistivity of sediments is about 13 $\mathsf{\Omega }\cdot \mathrm{m}$. It is obvious that the resistivity of fracture-filling hydrate sediments increases rapidly with the formation of hydrate. This phenomenon agrees well with the others’ results [35,36].

4.1.2. Layered Hydrate

Figure 5 shows the three-dimensional resistivity image of the layered hydrate, clearly identifying the layered hydrate in sediments. In the initial state, the high resistivity of quartz sands distributed in the layer is identified. In the middle state, the resistivity increases because of hydrate formation. However, the resistivity in some places decreases in the terminal state. The effect of “salt-removing” during the hydrate formation increases the salinity of pore water [37]. As a result, the resistivity of layered hydrate in some places decreases, which is also observed in previous results [30]. At the low hydrate stages, the resistivity of pore-filling hydrate sediments increases slowly with the formation of hydrate [35]. The hydrate formed in sandy sediments can be considered as pore-filling hydrate. Therefore, the resistivity changes a little in this area, increasing from 1 $\mathsf{\Omega }\cdot \mathrm{m}$ to 2.6 $\mathsf{\Omega }\cdot \mathrm{m}$.

From the images of massive hydrate and layered hydrate at different times (Figure 4 and Figure 5), the greater the resistivity difference between the hydrate area and surrounding sediments, the more distinct the boundary. When the resistivity of fine-grained sediments remains unchanged, the boundary of layered hydrate in the quadrilateral area of Figure 5 becomes increasingly obvious with the hydrate formation in quartz sands. The boundaries of massive hydrate and the boundary of layered hydrate change over time. The position of hydrate formation is decided by the spatial distribution difference of salt ions concentration [30]. Therefore, the diffusion of salt ions in sediments causes boundary changes.

4.1.3. Resistivity Comparison between Massive Hydrate and Layered Hydrate

Three experiments’ results concerning massive hydrate in this paper show that the average resistivity of massive hydrate-bearing sediments increases rapidly with the hydrate formation. When the hydrate saturation is approximately 14%, the resistivity of massive hydrate is up to 50 $\mathsf{\Omega }\cdot \mathrm{m}$. However, the average resistivity of layered hydrate only changes from 1 $\mathsf{\Omega }\cdot \mathrm{m}$ to 1.4 $\mathsf{\Omega }\cdot \mathrm{m}$ even with the hydrate saturation of 15%. We compared the average resistivity of three groups of massive hydrate and two groups of layered hydrate. We found that the average resistivity values of massive hydrate and layered hydrate differ by an order of magnitude (Figure 6). In addition to the characteristics of pore water and the hydrate morphology, the orientation of the resistivity measurement is a significant factor in controlling the measured resistivity [23]. When the current flows perpendicular to the hydrate layers, the resistivity is an abnormally high value. According to the model of massive hydrate and layered hydrate in Figure 2, the ice powder area can be treated as a vertical hydrate layer. The current flows into the sediments in a horizontal direction, leading to high resistivity. Therefore, compared to the layered hydrate, the higher resistivity of massive hydrate is observed.

4.2. Comparisons with the Theoretical Resistivity of Fracture-Filling Hydrate

We can compare our experimental results with the theoretical resistivity of gas hydrate-filled fractures if we consider the whole ice powder area a vertical fracture. It is found that when the hydrate saturation is less than 12%, the change features of resistivity of sediments in this paper are closer to the theoretical value in which the fracture porosity is 5%. Then, the resistivity of sediments increases to the theoretical value with a fracture porosity of 3.5% (Figure 6). Theoretically, when the fracture is vertical, the resistivity of sediments decreases with the increase of fracture porosity [7,35]. In our experiments, the fracture porosity is approximately 12.8%, which is far greater than 3.5% or 5%. In addition to the influence of intrinsic sediment properties and pore water salinity, the ice powder is regarded as a pore when calculating the fracture porosity. The space originally belonging to pore water is occupied by ice powder. This may be the reason why the resistivity of massive hydrate is higher than the theoretical resistivity.

The resistivity of massive hydrate increases rapidly with the hydrate saturation. However, the theoretical resistivity increases slowly, especially at the high hydrate saturation. After the cylindrical ice powder is buried in sediments, pore water in sediments will enter the space among ice powder. So, the formation of massive hydrate can be divided into two parts. One is that pore water among ice powder reacts with methane to form hydrate. The other is that ice powder reacts with methane to form hydrate. In the ice powder, when the hydrate saturation reaches a certain value, part of the pore water in ice powder is transformed into hydrate. Due to the very small pore of ice powder, the conductive path in the ice powder will be seriously blocked, resulting in a great increase in its resistivity.

For the layered hydrate, we can regard the sandy sediments bedded in the fine-grained sediments as a horizontal fracture. Consequently, the resistivity increases slowly with the increase of hydrate saturation, which is in accordance with the change tendency of the theoretical value (Figure 6). However, the resistivity decreases when hydrate saturation is greater than 14%. It can be concluded that the influence of “salt-removing” plays a major role in the resistivity decrease. The resistivity of the two types of fractured hydrates is very different, even if the hydrate saturation is similar. Therefore, investigating the spatial distribution of the fracture-filling hydrate is of significance in characterizing the electrical property of sediments with fracture-filling hydrate.

4.3. Growth Characteristics of Massive and Layered Hydrate Reflected by the Resistivity Images

From the two-dimensional resistivity image of the massive hydrate, the exterior of cylindrical ice powder is converted into hydrate firstly (Figure 7). Pore water in sediments enters the space among ice powder, resulting in a liquid layer on the surface of ice powder particles. The liquid layer promotes the formation of hydrate [38,39]. Therefore, we observe that the exterior of cylindrical ice powder is converted into hydrate firstly. After 180 h, the resistivity of ice powder in the ellipse area increases rapidly. In addition, the hydrate formed by ice powder has a rough pore microstructure, which leads to capillary force. Water molecules can diffuse due to the capillary force, which promotes hydrate formation [40]. This may be why the resistivity of ice powder in the ellipse area increases rapidly after 185 h.

The resistivity change with the hydrate formation is controlled by the effect of “salt removal”, hydrate formation, and the consumption of free gas [37,41,42]. The conversion of free methane gas to hydrates may not cause resistivity change [40]. Therefore, where the resistivity remains unchanged in Figure 8, it may be that free methane gas is converted into hydrate or hydrate is not formed. Nevertheless, the increase in resistivity must be caused by hydrate formation.

The resistivity of fine-grained sediments also increases, which means the hydrate is formed in fine-grained sediments. However, the decrease of resistivity in fine-grained sediments with the formation of hydrate is not obvious compared to the quartz sands (Figure 8). Clay particles adsorb the cation in pore water [43]. The salt ions generated by “salt-removing” are adsorbed by clay particles, limiting the diffusion of salt ions in pore water. Therefore, there is no obvious decrease in resistivity in fine-grained sediments.

5. Conclusions

The investigation of hydrate spatial distribution is essential for the exploration and exploitation of natural gas hydrate reservoirs. Simulation experiments of massive hydrate and layered hydrate were carried out to investigate the three-dimensional spatial distribution of the fracture-filling hydrate with ERT. The main conclusions are as follows:

(1)

Massive hydrate and layered hydrate are formed in the cylindrical electrical resistivity tomography device to acquire the ERT data. Based on ERT data, the three-dimensional resistivity image of fracture-filling hydrate is established by using finite element forward, Gauss–Newton inversion, and inverse distance weighted interpolation. Compared to layered hydrate, massive hydrate is easier to identify in the resistivity image. However, the boundaries of massive hydrate and layered hydrate change over time because of the diffusion of salt ions in sediments.

(2)

The resistivity of massive hydrate (50 $\mathsf{\Omega }\cdot \mathrm{m}$) is about an order of magnitude higher than that of layered hydrate (1.4 $\mathsf{\Omega }\cdot \mathrm{m}$), even if the saturation of massive hydrate is similar to that of layered hydrate. The big difference is caused by the morphology of the fracture. The resistivity of massive hydrate is higher than the theoretical resistivity because the ice powder is treated as pore water. The resistivity of layered hydrate is in good agreement with the theoretical value.

(3)

Under the influence of pore water distribution and hydrate’s pore microstructure, cylindrical ice powder is gradually transformed into hydrate from exterior to interior. Where the resistivity remains unchanged, it does not mean that hydrate does not form, but the increase of resistivity must be caused by the hydrate formation. The phenomenon of resistivity decrease in fine-grained sediments is not obvious due to the cation adsorption of clay particles.