Characterizing Gas Hydrate–Bearing Marine Sediments Using Elastic Properties—Part 1: Rock Physical Modeling and Inversion from Well Logs

Abstract

Gas hydrates are considered a potential energy source for the future. Rock physics modeling provides insights into the elastic response of sediments containing gas hydrates, which is essential for identifying gas hydrates using well-log data and seismic attributes. This paper establishes a rock physics model (RPM) by employing effective medium theories to quantify the elastic properties of sediments containing gas hydrates. Specifically, the proposed RPM introduces critical gas hydrate saturation for various modeling schemes. Such a key factor considers the impact of gas hydrates on sediment stiffnesses during the dynamic process of the gas hydrate accumulating as pore fillings and part of the solid components. Theoretical modeling illustrates that elastic characteristics of the sediments exhibit distinct variation trends determined by critical gas hydrate saturation. Numerical tests of the model based on the well-log data confirm that the proposed technique can be employed to rationally predict gas hydrate saturation using the elastic properties. The compressional wave velocity model is also developed to estimate the gas hydrate saturation, which gives reliable fit results to core measurement data. The proposed methods could improve our understanding of the elastic behaviors of gas hydrates, providing a practical approach to estimating their concentrations.

1. Introduction

Natural gas hydrates, which chiefly consist of water and methane, are believed to be a potential energy source that exhibits huge global reserves as hydrocarbon resources. The gas hydrates are extensively distributed in shallow marine sediments, permafrost areas, and polar regions, forming under conditions with the specific geological conditions of low temperature and high pressure [1,2,3,4].

Although exploration of gas hydrates has attracted considerable attention from the scientific and industrial communities worldwide for many years, accurate characterization of gas hydrate–bearing deposits based on geophysical methods remains a challenging problem. The main issues of challenges come from the limited understanding of the elastic properties of marine sediments, which affects the reliable interpretation of the elastic wave velocities from well-log and seismic data in estimating gas hydrate concentration and their mode of occurrence. The rock physics model (RPM) is commonly regarded as a powerful tool for describing physical relationships between elastic parameters and sedimentary properties. The RPM can be used to construct rock physics templates for quantitative seismic interpretation. At the same time, based on the modeling of wave velocities, the RPM can be appropriately extended to estimate gas hydrate concentrations using petrophysical parameters measured in boreholes, which is the primary objective of the current work.

So far, several models have been established to consider the relationships between gas hydrate concentration and seismic wave velocities for marine sediments. For instance, some early methodologies were developed based on various average equations to model elastic wave velocities for gas hydrate deposits, including the three-phase time average equation based on Wyllie’s equation [5,6,7,8]. Meanwhile, Lee et al. [9] proposed the three-phase Wood’s equation for gas hydrate deposits by extending Wood’s relation [10]. At the same time, based on Nobes et al. [11], Lee et al. [9] also suggested a combination of the three-phase time average equation and extended Wood’s equation by introducing adjustable parameters. Despite several successful applications in modeling the seismic wave velocities of marine sediments with gas hydrates, the main problem with the average models of various fashions is related to their empirical nature and thus cannot be readily generalized. Meanwhile, the determination of the adjustable parameters may be site specific. Most importantly, these average equations or their combinations offer little physical insight into the occurrence status of gas hydrates saturated in unconsolidated marine sediments.

On the other hand, Dvorkin et al. [12] established an effective medium model by extending the contact model via the bound theory for unconsolidated ocean bottom sediments [13,14]. Helgerud et al. [15] introduced a physics-based model by extending the work of Dvorkin et al. [12], which was extensively employed in subsequent explorations for characterizing gas hydrate sediments [16,17,18,19]. Additionally, other effective medium theories, such as the differential effective medium and self-consistent approximation models, were employed to evaluate the elastic properties of gas hydrate deposits and estimate gas hydrate saturation using well-log data [20,21]. In estimating the gas hydrate concentration with these models, the gas hydrate occurrence was commonly assumed to exhibit a particular distribution pattern. This assumption can be easily violated since the in situ gas hydrates may exhibit various distribution patterns.

Although it was noted that the presence of gas hydrates leads to an increase in seismic wave velocities according to the above explorations, the physical relationships between elastic parameters and gas hydrate concentrations and their modes of occurrence have not been adequately explored yet. Different modes of gas hydrate occurrence, such as pore fillings and part of solid components of dry sediment frame, may account for distinct elastic responses of gas hydrate-bearing sediments [22]. Therefore, to improve the estimation of gas hydrates using elastic properties, it is essential to establish a physics-based model that quantifies elastic responses of marine sediments associated with the various occurrence situations for gas hydrates.

Herein, an effective RPM is proposed to describe the elastic properties of gas hydrate deposits based on effective medium theories. To this end, the concept of critical gas hydrate saturation is introduced to consider the dynamic accumulation process of gas hydrates. After analyzing the impacts of gas hydrate saturation and porosity on the elastic properties of sediments, the proposed RPM model is calibrated using well-log data to interpret elevated wave velocities in marine sediments containing gas hydrates. Finally, the RPM is appropriately extended to rationally estimate the gas hydrate saturation in wellbores, and the predicted results are then validated using core measurement data.

2. Methods

2.1. Rock Physic Models for Marine Sediments Containing Gas Hydrates

Figure 1 presents the model of marine sediment containing gas hydrates with various modes of occurrence during the accumulation of gas hydrates. Gas hydrates were assumed to be generated and distributed in the pore space of highly porous ocean bottom sediments at the appropriate pressure and temperature conditions. In this case, the gas hydrates exhibit relatively low concentration and are part of pore fillings without altering the elastic properties of the dry sediment frame (status A). By approaching the gas hydrate saturation (S_gh) to a critical value (i.e., critical gas hydrate saturation, denoted by S_c), the extra gas hydrates initiate to form a part of the solid phase (status B). By continuously increasing S_gh, the gas hydrates existing as the solid components modify the elastic stiffnesses of the dry sediment frame (status C). In this case, the water saturation constantly lessens with the growth of the gas hydrate concentration. Status D corresponds to the case that solid gas hydrates occupy all initial pore spaces.

In the present paper, an appropriate RPM was established to model the elastic moduli of the marine sediments with varying gas hydrate concentrations and various modes of occurrence, as demonstrated in Figure 1. The key parameter introduced in rock physics modeling is the critical gas hydrate saturation (S_c) described above. Different modeling schemes should be adopted for the two major cases (i.e., S_gh is lower and higher than S_c) due to the existence of different modes of occurrence of gas hydrates (see Figure 1). In particular, for status C, gas hydrate particles in pores could contact with each other or touch their counterparts in the solid frame, forming the pore-filled gas hydrate fabric with non-zero bulk and shear moduli. Consequently, the gas hydrates and water mixture should be considered solid pore-fillings saturated in the dry sediment frame. These features should be appropriately taken into account in rock physics–based modeling.

Accordingly, Figure 2 presents a general workflow for rock physics modeling of elastic properties of marine sediments with various models of gas hydrate occurrences illustrated in Figure 1. The first step involves estimating elastic moduli of the solid matrix composed of minerals with the averaged Hashin–Shtrikman bounds (HSB) [14]. Depending on the mode of occurrence, as displayed in Figure 1, gas hydrates are treated as part of pore fillings for the case of S_gh lower than S_c; otherwise, gas hydrates exist as part of pore fillings and configure a component of the solid phase simultaneously.

Krief’s equations [23] were used to estimate the elastic moduli of the dry sediment frame:

$$K_{dry}=K_m{\left(1-\phi \right)}^{m\left(\phi \right)}$$

(1)

$${\mu }_{dry}={\mu }_m{\left(1-\phi \right)}^{m\left(\phi \right)}$$

(2)

where K_m and K_dry represent the bulk moduli of the solid matrix and dry frame, respectively. The factors μ_m and μ_dry denote the shear moduli of the solid matrix and dry frame, respectively. In addition, m(φ) = 3/(1 − φ), where porosity φ is defined as the volumetric fraction of pore-filled gas hydrates and water mixture. In the case of S_gh < S_c, porosity would be equal to φ₀, and for the case of S_gh ≥ S_c, porosity is given by φ = φ₀ [1 − (S_gh − S_c)]. In this relation, φ₀ is the initial porosity when gas hydrates only exit in pore spaces while not forming part of the solid components. Thus, φ₀ has a constant value for a dry frame with given mineralogical fractions. The parameter S_c denotes the critical gas hydrate saturation beyond which the extra amount of gas hydrate becomes a component of the dry frame. Note that S_gh represents the gas hydrate saturation, defined in terms of the ratio of the total volumetric fraction of gas hydrates as pore fillings and part of the solid phase to the initial φ₀. Therefore, φ lessens with increasing S_gh for S_gh ≥ S_c, with the lessening of φ corresponding to the increased volumetric fraction of gas hydrates as part of the dry frame.

The effective medium model proposed by Dovrkin et al. [12] was implemented to predict the non-zero bulk and shear moduli of the gas hydrate fabric filled in pores. For the pore-filled mixture composed of gas hydrates and water, the corresponding bulk modulus K_hf and shear modulus μ_hf of the gas hydrate fabric in the mixture can be computed in the following form:

$$K_{hf}=\{\begin{array}{ll}{\left[\frac{{\phi }_w/{\phi }_c}{K_{HM}+4{\mu }_{HM}/3}+\frac{1-{\phi }_w/{\phi }_c}{K_m+4{\mu }_{HM}/3}\right]}^{-1}-\frac{4}{3}{\mu }_{HM},& {\phi }_w<{\phi }_c\\ {\left[\frac{\left(1-{\phi }_w\right)/\left(1-{\phi }_c\right)}{K_{HM}+4{\mu }_{HM}/3}+\frac{\left({\phi }_w-{\phi }_c\right)/\left(1-{\phi }_c\right)}{4{\mu }_{HM}/3}\right]}^{-1}-\frac{4}{3}{\mu }_{HM},& {\phi }_w\ge {\phi }_c\end{array}$$

(3)

$${\mu }_{hf}=\{\begin{array}{ll}{\left[\frac{{\phi }_w/{\phi }_c}{{\mu }_{HM}+Z}+\frac{1-{\phi }_w/{\phi }_c}{{\mu }_m+Z}\right]}^{-1}-Z,& {\phi }_w<{\phi }_c\\ {\left[\frac{\left(1-{\phi }_w\right)/\left(1-{\phi }_c\right)}{{\mu }_{HM}+Z}+\frac{\left({\phi }_w-w{\phi }_c\right)/\left(1-{\phi }_c\right)}{Z}\right]}^{-1}-Z,& {\phi }_w\ge {\phi }_c\end{array}$$

(4)

$$Z=\frac{{\mu }_{HM}}{6}\left(\frac{9K_{HM}+8{\mu }_{HM}}{K_{HM}+2{\mu }_{HM}}\right)$$

(5)

where φ_w represents the volumetric fraction of water in the pore-filled mixture of gas hydrates and water. Additionally, φ_w is equal to 1 − S_gh in the case of S_gh < S_c, while it can be expressed as φ_w = (1 − S_gh)/[1 − (S_gh − S_c)] for the case of S_gh ≥ S_c. The factor φ_c stands for the critical porosity in the Hertz–Mindlin contact theory [13]. K_HM and μ_HM are the bulk and shear moduli at φ_c and can be stated by:

$$K_{HM}={\left[\frac{n^2{\left(1-{\phi }_c\right)}^2{\mu }_m^2}{18{\pi }^2{\left(1-\nu \right)}^2}P\right]}^{\frac{1}{3}}$$

(6)

$${\mu }_{HM}=\frac{5-4\nu }{5\left(2-\nu \right)}{\left[\frac{3n^2{\left(1-{\phi }_c\right)}^2{\mu }_m^2}{2{\pi }^2{\left(1-\nu \right)}^2}P\right]}^{\frac{1}{3}}$$

(7)

where μ_m and ν represent the shear modulus and Poisson’s ratio of the solid gas hydrate matrix, respectively, and n denotes the average number of grains in contact at critical porosity. Furthermore, the effective pressure is provided by P = (ρ_b − ρ_w)/gh, where ρ_b indicates sediment bulk density, ρ_w stands for water density, g is the acceleration of gravity, and h denotes the depth below the sea floor.

Subsequently, the bulk modulus K_mix and shear modulus μ_mix of the pore-filled gas hydrates and water mixture were obtained from Gassmann’s equations [24] as follows:

$$K_{mix}=K_{hf}+\frac{K_f{(K_{hf}-K_{gh})}^2}{K_{gh}{}^2{\phi }_w-K_{hf}{K}_f+K_{gh}{K}_f-K_{gh}{K}_f{\phi }_w}$$

(8)

$${\mu }_{mix}={\mu }_{hf}$$

(9)

where K_gh and K_f represent the bulk moduli of gas hydrates and water.

Finally, the elastic moduli K_sat and μ_sat of the sediments with gas hydrates were modeled with the generalized solid substitution theory [25]:

$$K_{sat}=K_{dry}+\frac{K_{mix}{(K_{dry}-K_0)}^2}{K_0{}^2\phi -K_{dry}{K}_{mix}+K_0{K}_{mix}-K_0{K}_{mix}\phi }$$

(10)

$${\mu }_{sat}={\mu }_{dry}+\frac{{\mu }_{mix}{({\mu }_{dry}-{\mu }_0)}^2}{{\mu }_0{}^2\phi -{\mu }_{dry}{\mu }_{mix}+{\mu }_0{\mu }_{mix}-{\mu }_0{\mu }_{mix}\phi }$$

(11)

where K₀ and μ₀ are the bulk and shear moduli of the solid phase, which solely compose minerals in the case of S_gh < S_c, and consists of minerals and gas hydrates simultaneously for the case of S_gh ≥ S_c.

2.2. Model-Based Methodology for the Estimation of the Gas Hydrate Concentration from Well-Log Data

Using well-log data, we proposed a quantitative method to estimate gas hydrate saturation (S_gh) and concentration (C_gh) according to the flowchart given in Figure 3. The core of the method is the RPM for the gas hydrate sediments established in Figure 2. At each depth sampling interval in a wellbore, the values of P-wave velocity (V_P-calculated) were computed with the RPM from volumetric fractions of minerals and porosity for the preset searching range of S_gh and assumed critical gas hydrate saturation (S_c). Subsequently, the objective function compares V_P-calculated with the measured P-wave log data (V_P-measured) to find a specific S_gh value that leads to the best matches between V_P-calculated and V_P-measured. The estimated S_gh and fitted P-wave velocity (V_P-fitted) represent the outputs at this depth, and C_gh can be estimated by C_gh = S_gh × φ. By repeating this procedure for each depth, the plots of S_gh and C_gh can be produced for the depth interval of interest.

3. Results

3.1. Modeling Analyses of Wave Velocities of Marine Sediments Associated with Gas Hydrates

Based on the constructed RPM presented in Figure 2, we analyzed the speed of passage of the wave through marine sediments associated with gas hydrate saturations. Figure 4 and Figure 5 illustrate the variations of P- and S-wave velocities (i.e., V_P and V_S) in terms of S_gh for three values of S_c (i.e., 0.1, 0.3, and 0.5). The S_c value is referred to the critical status where the gas hydrates become part of the dry sediment frame.

According to the plotted results in Figure 4, an increase in S_gh remarkably elevates the V_P of sediments, with V_P increasing more rapidly in the case of S_gh ≥ S_c for the selected values of rock porosity (φ). As presented in Figure 1, this can be interpreted that gas hydrates begin to become part of the solid component of sediments for the saturation higher than S_c. In this case, the presence of the gas hydrates enhances the rigidity of the dry sediment frame; thus, it alters the elastic moduli of sediments more significantly than in the case where only the gas hydrates exist in the pores. For a given porosity, Figure 5 reveals that the plots of vs. exhibit variation trends similar to the plots of V_P for various values of S_gh and S_c. However, as demonstrated in Figure 5, the sediments were also modeled to have non-zero V_S, even for relatively high porosity (φ) and lower gas hydrate saturation (S_gh). Specifically, the sediments exhibit non-zero vs. that at a porosity higher than the critical value (~0.4). The obtained results are consistent with the investigations of Dvorkin et al. [12] and Helgerud et al. [15] for shallow marine sediments.

Because the gas hydrate concentration is simultaneously controlled by gas hydrate saturation (S_gh) and rock porosity (φ), we modeled V_P and vs. for continuously varying S_gh and φ, as shown in Figure 6. For this purpose, the value of S_c was set equal to 0.3. For given ranges of S_gh and φ of the marine sediments containing gas hydrates, Figure 6 provides some insights for a better understanding of anomaly responses of the sediments in terms of elastic properties. In particular, for φ lower than ~0.35, V_P and vs. present fewer variations in terms of S_gh. This fact reveals that sufficient anomaly responses of elastic properties for detecting gas hydrates should be expected for the sediments with relatively higher φ.

3.2. Log Data of Marine Sediments in the Shenhu Area in the Northern Part of the South China Sea

We applied the proposed methods to the well-log data from the Shenhu area in the northern part of the South China Sea. Located in the Baiyun Sag of the Pearl River Mouth Basin (see Figure 7), the Shenhu area covers an area of more than 20,000 km² with a water depth of 200 to 2000 m [26]. It is located between the continental shelf and the continental slope, and the seabed slopes to the southwest. The results of gas hydrate drilling show that the seafloor temperature in the Shenhu area is about 4 °C, and the geothermal gradient is 44–67 °C/km [27,28]. The gravity flow on the continental slope leads to an increase in the sedimentation rate and is conducive to forming gas hydrate [29,30]. The primary sources of the gravity flow come from the sediments characterized as the facies of high porosity delta front, subaqueous fan, channel, and slump deposits [31]. The gas hydrates are chiefly accumulated in the unconsolidated mudstone silt of the late Miocene Pliocene sediments [32,33]. The gas-hydrate distribution has a general depth range from about 150 to 400 m below the sea floor (mbsf) [34,35].

In the regional geological map of the study area (see Figure 7), the locations of the two wells, SH2 and SH17, are indicated. Figure 8 illustrates well logs from the aforementioned two wells, including the curves of gamma-ray, resistivity, P-wave velocity (V_P), porosity (φ), and bulk density (ρ), respectively. The interpreted gas hydrate-bearing intervals extend from approximately 190−230 mbsf in the SH2 well and approximately 205−245 mbsf in the SH17 well. The resistivity logging data provide qualitative estimates of the gas hydrate saturation, with higher resistivity values indicating more gas hydrate accumulated in sediments. As indicated by gamma-ray logging, the gas hydrate formations in the two wells exhibit lithological inhomogeneity, with the gas hydrate interval in the SH17 well presenting more heterogeneity than that in the SH2 well. The plot of V_P reveals that the P-wave velocity is positively correlated with resistivity in the two wells, indicating higher elastic wave velocities in the presence of gas hydrates. The plot of the porosity represents the volumetric fraction of the pores saturated with gas hydrates and water, and the porosity is negatively correlated with ρ.

3.3. Modeling P-Wave Velocity of Marine Sediments Containing Gas Hydrates

As shown in Figure 9, the impact of gas hydrates on the V_P of the marine sediments was investigated. A series of V_P curves for constant S_gh values were modeled and plotted for the two wells based on the proposed model (schematically displayed in Figure 2). The core sample analyses suggest that the solid minerals of the marine formations in the two wells predominantly comprise quartz, clay, and calcite. The volume percentages of quartz, clay, and calcite were assumed to be 60%, 35%, and 5%, respectively, based on considerations of Liu et al. [36]. The porosity was obtained from Figure 8. The elastic moduli of constituents are given in

Table 1. Properties of the constituents used in rock physics modeling [37,38].

	Clay	Quartz	Calcite	Hydrate	Brine
K (GPa)	20.90	36.60	76.80	5.60	2.25
µ (GPa)	6.85	45.00	32.00	2.40	0.00
ρ (g/cm3)	2.58	2.65	2.71	0.92	1.04

. The value of S_c was adjusted to be 0.1 and 0.2 for the SH2 and SH17 wells, respectively. Here, S_c values were empirically determined to give more rational predictions of S_gh. The influence of S_c on S_gh estimation is discussed in detail in Section 3.5.

In Figure 9a, a nomogram of modeled V_P curves for various levels of S_gh suggests that the presence of gas hydrates can notably elevate V_P of the marine sediments. Moreover, in Figure 9a, the modeled V_P at constant zero-S_gh in the SH2 well acts as a baseline to infer the depth interval with relatively higher gas hydrate content. According to Figure 9a, the constant zero-S_gh line intersects the measured V_P log at depths ~190 and ~220 mbsf, respectively. The elevated V_P values within this depth interval suggest the presence of gas hydrates. The measured V_P values lie between the constant 0 and 0.4 S_gh lines and are consistent with the core measurements of gas hydrate saturation presented in Figure 9b.

Figure 9c,d reveals similar results obtained for the SH17 well. The V_P curves at constant 0 and 0.2 S_gh can be regarded as the baselines to indicate gas hydrate accumulation for the depth intervals below and above ~236 mbsf. In Figure 9c, the constant 0.4 S_gh line perfectly agrees with the core measurement results in Figure 9d, validating our modeling method presented in Figure 2. However, the V_P modeled for the constant 0.4 S_gh (see Figure 9c) is much higher than the measured results at the lower interval centered around 240 ~mbsf (see Figure 9d). As mentioned in the analysis of Figure 8, this discrepancy may be relevant to the lithological heterogeneity indicated by the gamma-ray logging.

Figure 10a,b illustrates the modeled V_P of the marine sediments in the SH2 and SH17 wells, varying with S_gh for different φ. The core measured results in Figure 9 were color-coded by φ and overlaid in the plots with colorful dots. Similar to the case for modeling V_P in Figure 9a,c, S_c values of 0.1 and 0.2 in Figure 10a,b can appropriately interpret core measurement data.

3.4. Estimation of the Gas Hydrate Concentration from the P-Wave Velocity Log

The modeling procedure in Section 3.3 somehow validated our proposed method in accounting for the P-wave velocity of sediments for varied gas hydrate saturation. Subsequently, using the method described in Figure 3, we can conduct the quantitative prediction of S_gh from well-log data of SH2 and SH17 wells, with estimated results presented in Figure 11a,b, respectively. The rock properties used here are the same as those in Section 3.3.

In Figure 11a, concerning the plotted results associated with the SH2 well, the modeled V_P exhibits a good agreement with the measured V_P log data, and the estimated S_gh curve almost perfectly matches the S_gh values measured from the core samples. Then, the gas hydrate concentration (C_gh) was evaluated by using C_gh = S_gh × φ. The same results were obtained for the SH17 well, as illustrated in Figure 11b. Well-fitted V_P and a good match between estimated and measured S_gh validate our proposed methodology for accurate estimations of the gas hydrate concentration in marine sediments.

However, several discrepancies between the estimated S_gh results and the corresponding measured values can be observed at ~204 mbsf in the SH2 well (see Figure 11a), around ~223 mbsf, and centered at ~243 mbsf in the SH17 well (see Figure 11b). A source of such deviations may come from the heterogeneity in lithology, as explained in Section 3.2. Another reason for such discrepancy may be associated with the variation in S_c, which is discussed in the following Section 3.5.

3.5. Influence of the S_c Value on S_gh Estimation

Figure 12 illustrates the impact of different prescribed S_c values on S_gh estimation. The S_c values of 0.1 and 0.2 can provide rational estimations of S_gh for the SH2 and SH17 wells, as mentioned in Section 3.3 and Section 3.4. However, several local deviations of the estimated curves from their corresponding core measured results, such as those at ~204 mbsf in the SH2 well, around ~223 mbsf, and centered at ~243 mbsf in the SH17 well, can be explained by the growth of S_c values. The obtained results indicate that the critical status described in Figure 1 may vary with burial depths in the gas hydrate formations. Note that the predicted S_gh values in an interval centered at ~243 mbsf in the SH17 well are still much lower than the core measurement results, even for a relatively higher S_c (i.e., S_c = 0.5). As discussed in Section 3.4, lithological heterogeneity may also be responsible for such discrepancies.

In the model-based workflow demonstrated in Figure 3, S_c can be regarded as another parameter ready to be predicted besides S_gh. Mathematically, however, it is impossible to reliably estimate two unknowns (S_gh and S_c) from the objective function involving only one source of information (V_P). Simultaneous estimations of S_gh and S_c could be feasible in the case of the availability of the shear-wave velocity for wellbores.

3.6. Correlation Analyses of V_P versus S_gh, φ, and C_gh

In Figure 13, exploring the correlations between V_P and S_gh, φ, and C_gh is of interest. The plotted results reveal that V_P notably correlated with S_gh and C_gh (see Figure 13a,b), implying that P-wave velocity can be employed as a reliable indicator of the gas hydrate concentration in the study area. Accordingly, the linear correlation equations can be given as follows:

$$V_P=1.08S_{gh}+1.76$$

(12)

$$V_P=1.90C_{gh}+1.80$$

(13)

In contrast, V_P shows no observable correlation with φ (see Figure 13c), which is different from the case in conventional oil and gas reservoirs.

4. Discussion

Due to specific occurrence status, marine sediments containing gas hydrates exhibit particular elastic responses different from oil- and gas-bearing hydrocarbon resources. Therefore, an appropriate RPM was established to describe the elastic characteristics of gas hydrate deposits. Accordingly, a method was developed to predict hydrate concentrations using the P-wave velocity of well-log data. The predicted results are encouraging where the estimated gas hydrate saturation rationally agrees with the core measured data.

The proposed model (see Figure 2) quantifies the elastic responses of marine sediments based on the assumption of the gas hydrate occurrence (see Figure 1). One of the advantages is estimating the elastic properties of gas hydrate deposits where the gas hydrates exist as pore fillings and form part of the solid matrix according to various occurrence statuses or concentrations. Thus, the model provides insights into the elastic properties of marine sediments associated with the accumulation process of gas hydrates. The other merit of the model is to evaluate the non-zero stiffnesses of the pore-filled mixture composed of gas hydrates and water. It is emphasized that the procedure for modeling the pore filling moduli should not be confused with the original applications of the corresponding methods in estimating the moduli of the entire unconsolidated rock, as presented by Helgerud et al. [15]. As demonstrated in Figure 2, the elastic properties of the gas hydrate deposits were obtained from the dry sediment frame (composed of minerals and gas hydrates) and pore fillings (mixture of water and gas hydrates) with the solid substitution theory [25]. In comparison, the elastic properties associated with the dynamic variation in gas hydrate occurrence cannot be described by commonly used average equations [6,9,11] or the original form of the effective medium model [15].

The modeling results (Figure 4 and Figure 5) indicate that wave velocities exhibit different variation trends with gas hydrate saturation (S_gh), where the introduced critical gas hydrate saturation (S_c) acts as a turning point. The P- and S-wave velocities (V_P and V_S) of the rock slowly grow with S_gh for values lower than S_c, while these velocities sharply magnify with S_gh for values greater than S_c. The obtained results coincide with the laboratory measurements observed by Berge et al. [39], justifying the assumption of the dynamic accumulation process of gas hydrates (see Figure 1). The dramatic rise in wave velocities with increasing S_gh beyond S_c can be explained such that the gas hydrates configure part of the dry sediment frame beyond the critical saturation and thus enhance the stiffnesses of the sediment.

In the calibration of the modeling results using realistic data, elevated V_P in gas hydrate formations can be interpreted by the increased gas hydrate saturation in the sediments (see Figure 9), matching with the results in existing studies [15,17,18]. The merit of our study is incorporating appropriate physical parameters (S_gh and S_c) into the model for a detailed description of the dynamic accumulation process of gas hydrates. However, due to the lack of the shear wave velocity in the wellbores, only S_gh was estimated in the present study (see Figure 11), where S_c was treated as an adjusting factor and empirically chosen for better prediction results. When sufficient log data (V_P and V_S) is available in the future, both S_gh and S_c can be estimated simultaneously, providing more insights into the in situ properties of gas hydrates.

Our proposed method provides reasonable estimates for S_gh, agreeing with core measurement results in the SH2 and SH17 wells (see Figure 11). However, uniform lithology was considered for the involved depth intervals in the two wells because detailed information on mineralogical fractions is unavailable. In future investigations, the constraint of sufficient mineralogical information would reduce uncertainty in S_gh estimation. Meanwhile, further explorations on the petrophysical and geochemical properties that provide more in situ information on gas hydrate formations facilitate rock physics modeling and improve the estimation of the gas hydrate concentration. Meanwhile, correlation analyses of the obtained results indicate that the predicted V_P is positively correlated with the gas hydrate saturation and corresponding concentration (see Figure 13a,b), indicating that compressional wave velocity is a useful indicator for gas hydrate identification. However, the V_P of the gas hydrate formation exhibits a less obvious correlation with porosity (see Figure 13c), which is different from the case in oil and gas reservoirs.

Finally, the proposed model can be extended to investigate the attenuation and dispersion associated with gas hydrate occurrence by incorporating relevant poroelastic theories [22,40,41,42,43]. Another application is establishing rock physics templates based on the proposed model for quantitative seismic interpretation of gas hydrate reservoir properties [44]. Moreover, based on the improved understanding of the elastic responses of gas hydrate deposits, we can develop a new seismic inversion method specifically for the characterization of marine sediments containing gas hydrates, which will be explored in the accompanying paper (Part 2).

5. Conclusions

This study aimed to propose an efficient RPM to model the elastic wave velocities of marine sediments containing gas hydrates. The theoretical modeling based on the RPM examined the impact of the gas hydrate saturation and corresponding modes of occurrence on the elastic properties of marine sediments. The proposed RPM model was calibrated using well-log data to interpret elevated wave velocities in marine sediments. Finally, the RPM was extended to evaluate the gas hydrate concentration in boreholes, and the estimated results were successfully validated by employing the core measured data. The primary inclusions are as follows:

• A critical value of the gas hydrate saturation was introduced to the proposed RPM as a key parameter for different modeling schemes. In this way, the proposed RPM is capable of considering the impact of gas hydrates on the sediment stiffnesses during the dynamic accumulation process of the gas hydrates, including being pore fillings and forming part of the solid components.
• The proposed model takes into account the pore-filled gas hydrate fabric to exhibit non-zero bulk and shear moduli. Therefore, gas hydrates and water mixture was regarded as solid pore fillings saturated in the dry sediment frame.
• Theoretical modeling illustrates the elastic properties of the marine sediments exhibit various variation trends determined by S_c. The increase in S_gh considerably elevates the values of V_P and vs. of sediments, with the velocities increasing more rapidly for S_gh values beyond the S_c value. This issue is mainly attributed to the fact that gas hydrates become part of the solid component of sediments and noticeably affect sediment stiffness for S_gh higher than S_c.
• The numerical experiment of the RPM using well-log data validates that the proposed model can be employed to estimate the gas hydrate saturation based on the elastic properties of marine sediments. The elevated V_P values within target depth intervals can be utilized to infer the gas hydrate saturation.
• The quantitative gas hydrate saturation estimation leads to results agreeing with the core measurement data, confirming the applicability of the proposed method for reliable estimation of the gas hydrate saturation based on the elastic properties.

The RPM proposed in the present study provides a powerful tool for describing the physical relationships between elastic parameters and the sedimentary properties associated with gas hydrates. The proposed model improves the understanding of elastic behaviors of gas hydrates and suggests a practical way to estimate gas hydrate concentration using well-log data. The RPM can be employed in future investigations to construct rock physics templates for quantitative seismic interpretation or be incorporated into seismic inversion methods for directly characterizing gas hydrate–bearing sediments.