Deformation Characteristics of Hydrate-Bearing Sediments

DONG Lin , LI Yanlong , , ZHANG Yajuan , HU Gaowei , LIAO Hualin,CHEN Qiang , and WU Nengyou ,

1) Key Laboratory of Gas Hydrate, Ministry of Natural Resources, Qingdao Institute of Marine Geology, Qingdao 266237, China

2) Laboratory for Marine Mineral Resources, Laoshan Laboratory, Qingdao 266237, China

3) College of Oceanography, Hohai University, Nanjing 210098, China

4) College of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266555, China

Abstract The safe and efficient development of natural gas hydrate requires a deep understanding of the deformation behaviors of reservoirs. In this study, a series of triaxial shearing tests are carried out to investigate the deformation properties of hydrate-bearing sediments. Variations of volumetric and lateral strains versus hydrate saturation are analyzed comprehensively. Results indicate that the sediments with high hydrate saturation show dilative behaviors, which lead to strain-softening characteristics during shearing. The volumetric strain curves have a tendency to transform gradually from dilatation to compression with the increase in effective confining pressure. An easy prediction model is proposed to describe the relationship between volumetric and axial strains. The model coefficient β is the key dominating factor for the shape of volumetric strain curves and can be determined by the hydrate saturation and stress state.Moreover, a modified model is established for the calculation of lateral strain. The corresponding determination method is provided for the easy estimation of model coefficients for medium sand sediments containing hydrate. This study provides a theoretical and experimental reference for deformation estimation in natural gas hydrate development.

Key words gas hydrate; deformation characteristics; volumetric strain; lateral strain; prediction model

1 Introduction

As an alternative energy resource, natural gas hydrate(NGH) has great potential for development due to its wide distribution, abundance, and less pollution (Chonget al.,2016; Cuiet al., 2018; Donget al., 2023a). However, the unreasonable development of NGH can also lead to crucial issues, such as landslides (Liuet al., 2020), wellbore stability (Donget al., 2022b, 2023b), sand production (Wuet al., 2021), and other problems (Yanget al., 2017; Wanet al., 2018). Therefore, the deformation behaviors of hydrate-bearing sediments (HBS) are of practical value for the estimation, prediction, and control of geological problems during NGH development.

The deformation characteristics of HBS have been deeply studied using combined numerical modeling, experimental tests and theoretical analysis (Liuet al., 2017; Lijithet al., 2019). The deformation characteristics of sand, silt,and clay containing tetrahydrofuran hydrate were investigated and compared, and the results indicate that the deformation behaviors of sediments, including volumetric and lateral strains, are affected by the soil type, stress state, and hydrate concentration (Yunet al., 2007; Priest and Hayley,2019; Nakashimaet al., 2021; Huet al., 2023). Furthermore, the variation laws of deformation behaviors of hydrate-bearing silica sand (Miyazakiet al., 2011), Toyoura sand (Hyodoet al., 2013), and Ottawa sand (Pinkert and Grozic, 2014) were studied based on laboratory tests. The results show a slight contraction at the start of shearing,followed by dilative behaviors at the end. High dilation was observed due to the small porosity of specimens. The volumetric and lateral strains of HBS can be estimated efficiently based on constitutive models (Uchidaet al., 2012;Sánchezet al., 2017; Liuet al., 2021), numerical simulation (Zhouet al., 2018; Sunet al., 2019), and empirical models (Kulhawy, 1975; Miyazakiet al., 2012; Yanet al.,2017). The key parameters of models and determination methods are introduced to ensure the accuracy of calculations (Shaibuet al., 2021). However, these calculation models have limited applications due to the determination of model parameters and assumptions. Therefore, developing an easy and efficient way to estimate the deformation properties of HBS is necessary.

In this study, the deformation behaviors of HBS are investigated through a series of triaxial shearing tests. The effect of hydrate saturation on volumetric and lateral strains is discussed in detail. Moreover, a prediction model is established to estimate the volumetric strain of specimens.The lateral strain is discussed based on the proposed modified model. This study is important in evaluating and predicting the deformation behaviors of reservoirs during NGH development.

2 Experimental Methods

2.1 Experimental Setup

Fig.1 depicts the triaxial shearing test apparatus for HBS illustrated in our previous work (Liet al., 2018, 2021a;Donget al., 2022a). This equipment can provide high-pressure and low-temperature conditions for hydrate formation and further realize triaxial shearing. The volumetric and lateral displacements can be obtained based on test data to reflect the deformation behaviors of specimens.

Fig.1 Triaxial shearing test apparatus for hydrate-bearing sediments.

The specimens are prepared with 192 g quartz sand and 99.9％ pure methane gas. The particle size distribution is shown in Fig.2. The sample is mainly composed of clay-free medium sand with a porosity of 40.0％.

Fig.2 Particle size distribution of the specimens.

2.2 Experimental Procedure

The specimen is prepared using thein-situmethod by adding a certain volume of water into the sand for target hydrate saturation (Hyodoet al., 2013; Donget al., 2020).The pressure of methane gas is kept at 4.5 MPa (± 0.1 MPa),and the temperature is set as 1℃ (± 0.1℃) throughout the tests. The specimen preparation is considered completed after no methane gas pressure change is observed. The water in the pore of specimens is considered to be entirely consumed for hydrate formation (Liuet al., 2018). The volume of hydrate is identified from the initial volume of water (Ghiassian and Grozic, 2013; Lijithet al., 2019).The hydrate saturation can be determined through calculation (Liuet al., 2018).

After hydrate formation, the effective confining pressure is maintained at 1 MPa, 2 MPa, and 4 MPa to reflect the effect of stress states. The specimens containing hydrate are sheared at a speed of 0.9 mm min?1. The shearing process continues before the axial strain reaches 15％. Displacement and load are recorded throughout the shearing tests.

2.3 Calculations of Volumetric and Lateral Strains

Volumetric strain is defined as the ratio between the change in volume and the original specimen volume, which is given as

whereεvrepresents the volumetric strain (％);dandhare the diameter and height of the specimen, respectively (unit:mm); andVis the volume change, which equals the difference between the recorded inlet and outlet surrounding fluid (unit: mL).

Correspondingly, the lateral strain can be calculated by Eq. (2):

whereεlandεarepresent the lateral and axial strains, respectively (％).

3 Experimental Results

3.1 Volumetric Strain

Fig.3 illustrates the relationship between the volumetric and axial strains of HBS. The positive volumetric strain indicates that the HBS is in compression, and the negative volumetric strain indicates that dilative behaviors are observed.

Fig.3 Volumetric deformation behaviors of hydrate-bearing sediments. (a), σ3 = 1 MPa; (b), σ3 = 2 MPa; (c), σ3 = 4 MPa.

Under low effective confining pressure (σ3= 1, 2 MPa), the high hydrate-saturated specimens show compressive behaviors at small strains and shear dilative behaviors at increasing axial strain. The deformation behaviors during shearing are transformed from shear compression to dilatation with the increase in hydrate saturation. Moreover,the axial strain corresponding to the state transformation point increases with the decrease in hydrate saturation. The hydrate-free specimens show shear compressive behaviors during the shearing tests. Compression deformation is remarkably reduced with the increase in hydrate saturation.

The volumetric deformation shows a tendency to transform gradually from dilatation to compression with the increase in effective confining pressure. Compared with low hydrate saturation, high hydrate saturation brings in high dilatation. Owing to the inhibition effect of confining pressure on deformation, the dilatation degree decreases with the increase in effective confining pressure.

3.2 Lateral Strain

Fig.4 displays the lateral strain of HBS during the tests.The positive lateral strain indicates that the specimens show dilative behaviors during shearing, which is similar to previous studies (Yunet al., 2007; Miyazakiet al., 2011; Pinkert and Grozic, 2014). The maximum lateral strain shows a decreasing trend with the hydrate formation. In particular, the value decreases by about 29％ with the increase in hydrate saturation from 0 to 40.0％ at the effective confining pressure of 1 MPa. In addition, the confining pressure restrains the lateral expansion during deformation. The maximum lateral strain decreases with the increase in the effective confining pressure.

Fig.4 Lateral strain of hydrate-bearing sediments. (a), σ3 = 1 MPa; (b), σ3 = 2 MPa; (c), σ3 = 4 MPa.

3.3 Deformation Mechanism

The test results indicate that deformation behaviors mainly depend on the hydrate saturation and stress states. Sediment particle movements and hydrate cementation damage occur during shearing, which determines the variations of microstructures and deformation characteristics of HBS.

In general, deformation is rarely observed in the early axial loading stage and is dominantly triggered by the slight compaction of sediments (Miyazakiet al., 2011). Specimens under loading laterally expand, causing nonhomogeneous lateral expansion in the middle and later stages(Liet al., 2021b). Meanwhile, volumetric deformation shows various characteristics of dilatation and compression during shearing, as shown in Fig.5.

Fig.5 Deformation behaviors of hydrate-bearing sediments during shearing.

Hydrate formation enhances the cementation between sediment particles, thus increasing the movement resistance of particles and reducing the breakage of cementation bonds (Donget al., 2022a; Zhaoet al., 2022). Confining pressure can limit particle movement, especially lateral motion under loading (Donget al., 2020; Liet al., 2021a).Hydrate content and confining pressure affect the particle movement and cementation damage, altering the volumetric and lateral deformation of HBS, as depicted in Fig.6.

Fig.6 Micro-mechanisms controlling the deformation behaviors of hydrate-bearing sediments.

4 Strain Prediction

4.1 Volumetric Strain Prediction

On the basis of the above analysis of deformation behaviors, an easy and efficient prediction model is proposed to simulate the relationship between the volumetric and axial strains of HBS. The model can be expressed as follows:

whereεvandεarepresent the volumetric and axial strain(％);βis the coefficient related to hydrate saturation and the effective confining pressure, dimensionless;Shrepresents hydrate saturation (％); andσ3is the effective confining pressure (MPa).

Fig.7 shows the comparison between the test and calculated values ofβ.The results indicate thatβincreases with hydrate saturation and is affected by the effective confining pressure. This empirical model forβprediction can be obtained by fitting the above test data. The model error is determined through Eqs. (5) – (7). The error range ofβis 0.99％ – 4.96％, and the average error is 2.72％. In general, the error satisfies the engineering requirements.

Fig.7 Comparison of experimental and calculated value of β.

whereemin,emax, andeaveare the minimum, maximum, and average errors, respectively (％);βexpandβcalrepresent the test and calculation values ofβ, dimensionless; andnis the number of groups, dimensionless.

Fig.8 exhibits the effect ofβon volumetric strain curves.With the increase inβ, the degree of compression increases and that of dilatation decreases. The volumetric strain exhibits a steady trend of increasingversusaxial strain withβless than 0.9, indicating dilatant behaviors during shearing. By contrast, the volumetric strain continues to decrease whenβis greater than or equal to 0.9. Behaviors with shear contraction are observed during the triaxial shearing tests.

Fig.8 Effect of β on volumetric strain curves.

The predicted volumetric strain of HBS is obtained based on the above-proposed empirical model, as shown in Fig.9. Comparisons between the test and calculated results prove that this model can be used to predict the volumetric strain of NGH reservoirs with high accuracy.

Fig.9 Prediction of volumetric strain. (a), σ3 = 4 MPa; Sh = 0 – 40.0％; (b), Sh = 40.0％, σ3 = 1, 2, 4 MPa.

4.2 Lateral Strain Prediction

Kulhawy (1975) assumed that the relationship between lateral and axial strains can be described by hyperbolic function. Yanet al. (2017) then used this hyperbolic model to simulate the lateral deformation of HBS while considering the effect of hydrate formation. In general, the lateral strain of HBS can be calculated through Eq. (8).

wherehandDrepresent the model parameters related to hydrate saturation and effective confining pressure, respectively.

Furthermore, Eq. (8) can be converted into Eq. (9), showing that the valueεa/εlis linear with axial strainεa.

Fig.10 demonstrates the variation of model parametershandDversushydrate saturation. With the increase in hydrate formation,hincreases andDdecreases. A high effective confining pressure increasesDand decreasesh.handDshow significant correlations with hydrate content and confining pressure and can be obtained through data fitting,as shown in Eqs. (10) and (11).

Fig.10 Prediction of model coefficient h and D. (a), parameter h; (b), parameter D.

whereShrepresents hydrate saturation (％); andσ3represents the effective confining pressure (MPa).

Errors in prediction results can be identified through Eqs. (5) – (7). The error range ofhis 0.11％ – 4.75％, and the average error is 2.35％. The error range ofDis 0.15％– 4.93％, and the average error is 3.13％. By bringing these model parameters into Eq. (14), the lateral strain curves of HBS can be obtained efficiently, as shown in Fig.11. This modified model for lateral strain calculation has advantages such as high accuracy, good applicability, and high simplicity, providing a way to describe and estimate the deformation behaviors of reservoirs during NGH develop- ment.

Fig.11 Prediction of lateral strain based on the modified Kulhawy’s model. (a), σ3 = 1 MPa; (b), σ3 = 2 MPa; (c), σ3 = 4 MPa.

Poisson’s ratioνtand initial Poisson’s ratioνican be determined through Eqs. (12) and (13).

The initial Poisson’s ratio from previous experimental data is 0.24 – 0.55 (Miyazakiet al., 2011, 2012), and the calculated initial Poisson’s ratio based on the proposed model is 0.23 – 0.56. According to the discussion above,the initial Poisson’s ratio models can be calculated efficiently using this modified model by considering the effect of hydrate saturation and stress states, as shown in Fig.12.

Fig.12 Prediction of the initial Poisson’s ratio based on the modified model.

5 Conclusions

The evaluation and prediction of deformation characteristics are necessary precursors to the safe and efficient development of NGH. The deformation characteristics of HBS are investigated through a series of triaxial shearing tests. Volumetric and lateral strains are evaluated and estimated using the proposed prediction model. Correlations between the model coefficients and key factors are discussed in detail. The main conclusions are described as follows:

The higher the hydrate saturation, the more evident the expansion behaviors. Volumetric deformation shows a tendency to transform gradually from dilatation to compression with an increase in effective confining pressure.

The deformation behaviors of HBS are mainly controlled by sediment particle movements and hydrate cementation damage. Hydrate formation enhances the cementation between particles. A high confining pressure limits the particle displacements.

Correlations between volumetric and axial strains can be characterized through the proposed prediction model, which is simple, practical, and convenient. Its coefficientβis the dominating factor for the shape of volumetric strain curves.

The modified Kulhawy’s model can be used to predict the lateral strain of HBS with high precision. Its coefficients,handD, can be calculated based on the test data to determine the variation of lateral strain curves.

Acknowledgements

This research was supported by the Qingdao Natural Science Foundation (No. 23-2-1-54-zyyd-jch), the National Natural Science Foundation of China (Nos. 42076217, 41 976074), the Laoshan Laboratory (No. LSKJ202203506),and the Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University(No. KLE-TJGE-G2202).