Estimation of Gas Hydrate Saturation Regarding the Hydrate Morphology in Hydrate-Bearing Sands in the Qiongdongnan Basin, South China Sea

Abstract

The GMGS6 hydrate expedition discovered hydrates in the Quaternary channel sand by logging and coring for the first time in the Qiongdongnan Basin, with an average sand grain size of ~ 70 μm and sandy content over 80%. Hydrate saturation exceeds 80%, and the P-wave velocity exceeds 3500 m/s. The quantitative link between hydrate saturation and velocity is not clear due to the complex hydrate morphologies. In this study, we analyzed the possible hydrate morphologies regarding the variation in velocity, resistivity, and permeability versus hydrate saturation based on in situ permeability measurements, pressure core degassing testing, and well logs, which indicates that both cementing and frame-supporting behaviors occur within the pores. Using the cementing model alone underestimates saturation, while the frame-supporting model overestimates saturation. As a result, the cementation model and three-phase Biot equation are jointly used to quantitatively invert the hydrate saturation based on the least-squares principle. The inverted results agree with the saturation from pressure cores and resistivity, and indicate that the prevalence of cementing hydrates greatly increases the velocity and strength of the hydrate-bearing sands, which is consistent with laboratory observations of the “gas excess” scene from previous studies. With the continuous supply of gas-bearing fluids, more hydrates cement sediment particles and previously formed hydrates, occupying most of the pore space and consuming the free and bound water in the pore space. This study thus provides a new method for estimating the saturation in hydrate-bearing sands, which is also important for estimating the geomechanical behavior of hydrate-bearing sands.

Appendix A

The cementation models generally regard the sediment grain as an ideal aggregate of elastic spheres. In hydrate-bearing sediments, hydrate can be regarded as a very thin elastic medium when it is considered as a contact cement. Dvorkin and Nur (1996) proposed the classic cementation model (CCM) by defining the relationship between normal and tangential stiffness and the classic normalized contact cement radii with a statistical best-fit approach. The bulk and shear modulus of the “dry” matrix K_dry and µ_sat can be written as

$$\begin{gathered} k_{dry} = \frac{n(1 - \phi )}{6}\left(k_{h} + \frac{{4\mu_{h} }}{3}\right)S_{n} \hfill \\ \mu_{dry} = \frac{{3k_{dry} }}{5} + \frac{{3n(1 - \phi )\mu_{h} S_{t} }}{20} \hfill \\ \end{gathered}$$

(4)

$S_{n} ,S_{t}$ refer to the normal and tangential stiffness at the contact of the hydrate and sediment grain, which relate to the normalized contact cement radii $\alpha$. n refers to the number of contacts of each grain. Ideally, we set n = 6 because the sand grain is spherical.$K_{h} ,\mu_{h}$ refer to the bulk modulus and shear modulus of the hydrate (see Table 1).

As hydrate coats the sediment grain, the grain contact model (Walton, 1987; Winkler, 1983) can be used to calculate $S_{n} ,S_{t}$,

$$\begin{gathered} S_{n} = \frac{4GR}{{1 - \sigma }}\left[ {\frac{{2S_{h1} \phi }}{3n(1 - \phi )}} \right]^{0.5} \hfill \\ S_{t} = \frac{8RG}{{2 - \sigma }}\left[ {\frac{{2S_{h1} \phi }}{3n(1 - \phi )}} \right]^{0.5} \hfill \\ \end{gathered}$$

(5)

where $G,\sigma$ refer to the shear modulus and Poisson's ratio of the granular aggregate,$S_{h1}$ refers to the hydrate saturation in the cementing mode, $\phi$ is the density porosity, and$n$ represents the average coordination number of mineral grain. For different saturation and different hydrate cementation modes, the modulus of a dry rock matrix can be calculated by the above formulas.

Density can then be calculated as

$$\rho_{1} = \phi (S_{h1} \cdot \rho_{h} + (1 - S_{h1} ) \cdot \rho_{w} ) + (1 - \phi )\rho_{ma}$$

(6)

where $\rho_{h} ,\rho_{w}$ refer to the density of hydrate and pore water, respectively, and$\rho_{ma}$ refers to the density of the matrix, which is the weighted sum of different mineral components from logging capture spectrum.

Those cemented hydrates increase the dry modulus of the hydrate-bearing sediments, and the TPBE (Lee, 2007) was used to calculate the velocities after the hydrates take the frame-supporting mode on the basis of the cemented hydrates, assuming an idealized arrangement where gas hydrate, matrix, and pore fluid form three homogeneous and interlinked frameworks. Each of the frameworks contributes to P- and S-wave velocity of the sediments. The velocity can be calculated using Eqs. 4, 5, 6, 7, 8, and 9.

$$\left\{ {\begin{array}{*{20}c} {k = K_{dry} \left( {1 - \beta_{1} } \right) + \beta_{1}^{2} K_{av} } \\ {\mu = \mu_{dry} \left( {1 - \beta_{2} } \right)} \\ \end{array} } \right.$$

(7)

with

$$\begin{gathered} \begin{array}{*{20}c} {\frac{1}{{K_{av} }} = \frac{{\beta_{1} - \varphi }}{{K_{dry} }} + \frac{{\varphi_{w} }}{{k_{w} }} + \frac{{\varphi_{h} }}{{k_{h} }}} \\ {\beta_{1} = \frac{{\varphi_{as} \left( {1 + \omega } \right)}}{{1 + \omega \varphi_{as} }}} \\ {\beta_{2} = \frac{{\varphi \left( {1 + \gamma \omega } \right)}}{1 + \gamma \omega \varphi }} \\ {\gamma = \frac{1 + 2\omega }{{1 + \omega }}} \\ \end{array} \hfill \\ \phi_{as} = \phi_{w} + \varepsilon \phi_{h} \hfill \\ \end{gathered}$$

(8)

where $\omega$ is the consolidation parameter, which can be obtained by fitting the velocity and depth of the water-saturated sediments (Mindlin, 1949), k and $\mu$.

Since hydrates occupy the pores, the water porosity and hydrate porosity are written as

$$\varphi_{w} = \left( {1 - S_{h2} } \right)\left( {1 - S_{h1} } \right)\varphi$$

$$\varphi_{h} = S_{h2} \left( {1 - S_{h1} } \right)\varphi$$

(9)

where S_h2 refers to the hydrate saturation in frame-supporting mode. The bulk density of the sediments can be calculated by Eq. (10).

$$\rho_{2} = \rho_{ma} (1 - \phi ) + \rho_{w} \phi (1 - S_{h2} - S_{h1} ) + \rho_{h} (S_{h2} + S_{h1} )\phi$$

(10)

The density of the matrix $\rho_{ma}$ is calculated by the weighted sum of the mineral constituents in sediment grains. The volumetric fractions of these mineral compositions were obtained by element capture logging. The elastic modulus of sediment grains can be calculated using Hill's average (Hill, 1952). $\varepsilon$ denotes the empirical parameters to measure the support degree of hydrate to mineral matrix with a range of 0 ~ 1. In this paper, we set ε = 0.7 because the calculated velocities agree well with the measured velocities for those slowly increasing velocities with hydrate saturations (Fig. 7c).