Impacts of hydrate on the lateral stress in sediments

The ratio between the horizontal and the vertical effective stresses is defined as the coefficient of earth pressure at rest Ko. Ko in hydrate-bearing sediments is critical in understanding the stress states in hydrate-bearing sediments, yet has not been previously understood. An oedometer cell equipped with vertical and horizontal stress measurement sensors is used to measure the evolution of Ko in tetrahydrofuran hydrate- bearing sands during hydrate formation and dissociation and vertical stress changes. The results show that the response of Ko in hydrate-bearing specimens reflects the combined effects of hydrate cementation, the viscous nature of hydrate crystals, and the stress levels. These results can enhance the understanding of stress anisotropy and geomechanical behaviors of hydrate reservoirs during gas production.


Introduction
The coefficient of earth pressure at rest Ko indicates the in situ stress state in deposits, and can be defined as the ratio of vertical and horizontal effective stress, as expressed below,

=
(1) where σʹv and σʹh are the vertical and horizontal effective stresses. The value of Ko in soils can be influenced by many factors, including the effective stress, stress history, the over-consolidation ratio, cementation bonding and debonding, packing density, and particle shape and size [1][2][3][4][5].
For non-cemented soils, the values of Ko does not change significantly during loading, i.e., the lateral stress increases linearly with the increase in vertical stress [2,3]. The response of the Ko of cemented soils is different from that of the non-cemented soils. For cemented soils, the Ko is mainly governed by the cementation among particles during loading, leading to lower Ko values at low strain conditions [2,6].
The hydrate crystals in pore spaces can play an essential role in the stress-strain relation, strength, stiffness, permeability, and volume changes of hydratebearing specimens [7][8][9][10]. Especially, the increased effective stress caused by the depressurization method for gas production in deep-sea hydrate deposits can induce significant changes in the Ko of hydrate-bearing sediments. Therefore, it is essential to understand the affecting factors of the values of Ko in hydrate-bearing sediments.
The objective of this experimental study is to investigate the evolution of Ko in tetrahydrofuran (THF) hydrate-bearing specimens and to understand the effects of hydrate crystals on the stress state under zero lateral strain condition. Fig.1 shows a schematic drawing of a thick-wall oedometer cell (refer to [11,12] for more details of this setup). The vertical stress is controlled the hydraulic pump in a reaction frame, and a diaphragm pressure transducer installed at the middle height of the specimen monitors the lateral stress response. Porous bronze disks are embedded on the pedestals to allow uniform drainage of the pore fluid throughout the test. The whole experimental setup is placed into a freezer to control the experimental temperature with an accuracy of 0.1°C.

Experimental setup
F110 fine quartz sands (maximum void ratio emax = 0.85, minimum void ratio emin = 0.54, mean particle size d50 = 120 μm, and uniformity coefficient Cu = 1.21) are used in this experimental study. The specimens have a diameter of 50.8 mm, and a height of 30.5 mm with the relative packing density Dr = 40% and the corresponding void ratio e = 0.726. The ratio of specimen height and diameter (H/D) is limited to 0.6 to prevent the boundary effects from the top and bottom pedestals [13]. The F110 sands are mixed with a predetermined ratio of THF and deionized water. The mass ratio of THF and deionized water is 0:100 for Sh = 0 (water-saturated) and 20.3:79.7 for Sh = 0.96 specimens.
After packing, the specimen temperature is lowered to 0.1°C to trigger hydrate formation. During the hydrate formation, 25 kPa vertical stress, caused by the selfweight of the top pedestals, is applied to the specimens. Once a thermal peak indicating the initiation of hydrate nucleation is observed, the temperature is kept constant for at least additional 24 hours. Meanwhile, the vertical displacement, lateral stress, and P-wave velocity are continually monitored to confirm the completion of hydrate formation. After hydrate formation, additional vertical stress is applied stepwise to the specimens up to 25 MPa. Each loading step is applied at a rate of approximately 5 MPa per minute until the targeted vertical stress is achieved and then held constant. The lateral stress is measured throughout the hydrate formation and the loading processes.    The Sh = 0 sediment shows a slight decrease in K0 at the moment of each loading step and then stabilizes in minutes. For the Sh = 0.96 sediment, the temporary reduction followed by a gradual increase in Ko is observed during each loading step.

Discussion
The response of Ko during loading is summarized in Fig. 4. For Sh = 0 (water-saturated) specimen, Ko slightly decreases with increasing vertical stress. The minor reduction in Ko indicates a stiffer specimen, attributed to the compaction effects by the increased vertical stress. firstly decreases at the moment of vertical loading and then rises under a constant vertical load, indicating a viscous behavior in stress transfer. Since no such evident time-lapse behavior is detected in the Sh = 0 specimen, it can be concluded that the presence of hydrate crystals causes such a creep behavior in the Ko of the hydratebearing specimen. Since quarzitic sands do not present significant creep behaviors [14], the observed apparent time-delayed response of stress transfer in hydratebearing sediments highlights the critical role of hydrate crystals in the stress state of hydrate-bearing sediments. The hydrate crystals can enhance the strength and the stiffness of hydrate-bearing specimens [15][16][17]. The reduction of Ko for the Sh = 0.96 specimen under relatively low vertical stress (σv < 1 MPa) is primarily caused by the cementation between soil particles and hydrate crystals. The cementation supports and shares the applied verticals stress and causes less pronounced lateral stress transfer [2,4,7]. Also, hydrate crystals can act as part of the skeletal structure that carries the load together with soil particles [16]. At relatively high vertical stress (1 MPa < σv < 25 MPa), the Ko of the hydrate-bearing specimen is mainly governed by the sand skeleton after losing the majority of cementation.

Conclusions
This study experimentally examines the evolution of the coefficient of earth pressure at rest Ko in hydratebearing specimens. The main findings follow.
• The Ko of the hydrate-free specimen (Sh = 0, watersaturated) decreases slightly from 0.63 to 0.51 as the vertical stress increases from 25 kPa to 25 MPa, mainly due to the compaction effect that stiffens the specimen. • The hydrate-bearing specimen (Sh = 0.96) shows a significant reduction in Ko, reflecting the role of hydrate crystals in bonding the sand particles and thus less stress transfer in the horizontal direction. • The presence of hydrate crystals plays a vital role in the viscous response of Ko during loading. • With further increases in the vertical stress, the Ko value increases, mainly governed by the sand skeleton after the debonding of hydrate cementation.
The work is supported by the DOE/NETL gas hydrate research program.