Geomechanical effects of carbon sequestration as CO2 hydrates and CO2-N2 hydrates on host submarine sediments

Over the past 10 years, more than 300 trillion kg of carbon dioxide (CO2) have been emitted into the atmosphere, deemed responsible for climate change. The capture and storage of CO2 has been therefore attracting research interests globally. CO2 injection in submarine sediments can provide a way of CO2 sequestration as solid hydrates in sediments by reacting with pore water. However, CO2 hydrate formation may occur relatively fast, resulting decreasing CO2 injectivity. In response, nitrogen (N2) addition has been suggested to prevent potential blockage through slower CO2-N2 hydrate formation process. Although there have been studies to explore this technique in methane hydrate recovery, little attention is paid to CO2 storage efficiency and geomechanical responses of host marine sediments. To better understand carbon sequestration efficiency via hydrate formation and related sediment geomechanical behaviour, this study presents numerical simulations for single well injection of pure CO2 and CO2-N2 mixture into submarine sediments. The results show that CO2-N2 mixture injection improves the efficiency of CO2 storage while maintaining relatively small deformation, which highlights the importance of injectivity and hydrate formation rate for CO2 storage as solid hydrates in submarine sediments.


Introduction
CO2 emission from burning fossil fuels and industry processing traps heat in the atmosphere, which has grown from 30.4 Gigatonnes (Gt) in 2010 to 33.3 Gt in 2019 resulting global concern of climate change [1]. With unbalanced high CO2 concentration in the atmosphere, temperature could keep rising and cause global warming, which may change water cycle, melt glacier, increase the mean sea level, etc. [2]. Recent extreme weather patterns have been linked with CO2 emission, and if true, this could end up a vicious circle as the increase in the energy use could result in more CO2 emission and this in return could trigger greater energy consumption to accommodate extreme hot or cold weather [3]. Growing CO2 emission combined with its long-stay nature in the atmosphere requires the process of capture and storage of CO2 from the atmosphere.
Different CO2 sequestration concepts are brought up including CO2 injection into deep geological formations of low permeability and carbon mineralization via reaction with metal oxides. Nevertheless, the former may involve leakage issue due to the mobility of CO2 fluid and the latter usually requires long time for producing stable carbonates, thus limiting CO2 storage efficiency [4].
Gas hydrate formation in marine sediments provides a promising way of sequestering CO2 in solid phase [5], effectively reducing the possibility of CO2 escape from storage reservoir. When injected CO2 is mixed with free water in marine sediments, CO2 hydrates can form under suitable conditions of pressure and temperature. CO2 hydrates are ice-like solids enclosing CO2 molecules within the lattice cage of water molecules. Studies on CO2 hydrate kinetics found relatively fast formation rate of CO2 hydrates [6]. As gas hydrates grow rapidly in the pore space of marine sediments, the permeability can be largely reduced and thus adversely affect the CO2 injectivity and transportation. In response, N2 is suggested as an additive to reduce the rate of hydrate formation [7][8][9]. This is because N2 hydrate is less thermodynamically stable and hence the mixed N2 and CO2 can propagate further into the sediments. However, these studies seldomly consider CO2 storage efficiency and little attention is paid to deformation of the sediment and its effect on fluid flow.
To investigate gas hydrate-based carbon storage efficiency and associated geomechanical response, this paper presents two cases of pure CO2 injection and CO2-N2 mixture (90-10 mol%) injection into water saturated marine sediments. The following section describes new components of hydrate mixture and fluid mixture that are required to capture behaviour of CO2-N2 hydrate mixture. Next, model geometry and the initial conditions are presented before discussing the advantage of CO2-N2 mixture injection in detail.
2 Equations for CO2-N2 fluid mixture and hydrate mixture in sediments CO2 and N2 injection in marine sediments could lead to the generation of CO2-N2 fluid mixture and hydrate mixture (via reacting with free water). Built on the coupled thermo-hydro-chemo-mechanical formulation for single gas and hydrate developed by Klar et al. [10], equations are implemented for CO2 and N2 components including fluid mixture flow, diffusion of fluid mixture and partial pressure-based hydrate mixture formation.
Mass storage of CO2 and N2 in marine sediments is related to CO2-N2 fluid mixture flow, diffusion and hydrate reaction. The flow of CO2-N2 fluid mixture is governed by the Darcy's law, similar to conventional twophase flow such that water being wet fluid and CO2-N2 mixture being dry fluid. The density of dry fluid consists of both CO2 and N2, which is defined as: where ρ is density and subscripts f, cf and nf denotes fluid mixture, CO2 fluid and N2 fluid, respectively. Diffusion of CO2 and N2 within the dry fluid mixture, caused by difference in molar concentration, is determined by Fick's law: where j and ∇ are diffusive flux and vector differential operator, respectively, D is diffusion coefficient, and xcf is the molar fraction of CO2 in the dry fluid mixture. When single CO2 or N2 fluid is injected into marine sediment, CO2 hydrates or N2 hydrates can form under suitable pressure and temperature conditions (as shown in Fig. 1). The difference between hydrate equilibrium pressure and fluid pressure drives single hydrate formation. When CO2-N2 fluid mixture is present with free water, partial pressure difference between fluid phase and hydrate phase is assumed to govern the hydrate reaction of each component. In ideal fluid mixture, the partial pressure is given by: where P is fluid pressure. Partial hydrate equilibrium in a homogeneous solution is given by Chen and Guo [11]: where P eq is partial equilibrium hydrate equilibrium of CO2 or N2 in hydrate mixture and P eq0 is pure CO2 or N2 hydrate equilibrium, xch is molar fraction of CO2 in hydrate mixture, and subscripts ch and nh denote CO2 hydrate and N2 hydrate, separately. The rate of hydrate reaction for each component is then given as: Combining the above three processes, incremental mass change of CO2 or N2 is obtained as: where qf is flow flux vector of CO2-N2 gas mixture governed by Darcy's law, t is time, M is molecular mass, R is hydrate formation (R>0) or dissociation rate (R<0). Similarly, equations of incremental water and hydrates mass can be obtained. Finally, taking into account the saturation summation in the pore space and capillary pressure between water and fluid mixture, incremental pressure, saturation and temperature can be derived, which are related to coupled processes of heat transfer, fluid flow and diffusion, hydrate reaction and mechanical deformation during gas hydrate formation of injected CO2 and CO2-N2 in sediments. These are not expanded in this paper and please refer to the mentioned literature for reference.

Model description
Two cases are considered in this study: Case I is CO2 injection and Case 2 is CO2-N2 mixture (90-10 mol%) injection. Fig. 2 presents an axisymmetric marine sediment model adopted in this study. Initial intrinsic permeability is 10 -13.5 m 2 with the horizontal permeability (=10 -13 m 2 ) being 10 times of the vertical permeability (=10 -14 m 2 ). When injected CO2 and CO2-N2 form gas hydrates in marine sediments, the sediment permeability reduces and is considered to follow the permeability model of hydrate-bearing sediment Kh=K(1-Sh) N [16] with N being assumed as 5.74 in this study. The geomechanical behaviour of sediments is modelled by the methane hydrate critical state model [17], which considers the effect of hydrate contribution through hydrate-dependent strength, stiffness and dilatancy. In this study, the sediments around the well is subjected to unloading and its volumetric behaviour is presented in Fig. 3. For simplicity, this study assumes that CO2 hydrate-bearing sediments and CO2-N2 hydrate-bearing sediments have the same geomechanical properties.   Fig. 4 presents pore pressure profile of CO2 injection for both Case I and Case II at t = 4 months. As the injection pressure is only 500 kPa greater than the initial pore pressure, the effect of pore pressure changes appears to be limited within the vicinity of well. However, the injected fluid travels much further than it appears from Fig. 4, and it forms CO2 hydrate by reacting with pore water as shown in Fig. 5. Since injected fluid has lower density than the water, it tends to migrate upwards. In addition, due to lower temperature, upper area has more favourable condition for CO2 hydrate formation and therefore greater amount of CO2 hydrate forms in the upper area. Comparing between Case I and Case II, due to higher concentration of CO2 in the injected fluid, higher CO2 hydrate saturation is evident in Case I (Fig. 5a). This is also noticeable by higher temperature in Fig. 6, as CO2 hydrate formation is exothermic process, implying that Case I forms a greater amount of hydrate near the well. However, because of higher CO2 hydrate saturation, Case I eventually decreases injectivity due to reduction in the permeability. This is shown in Fig. 7. As a result, Case I has a slightly smaller region that injected fluid has propagated, resulting in lower CO2 storage. In order to highlight the effect of permeability reduction on CO2 storage, Fig. 8 shows the development of overall amount of CO2 stored as hydrate over a period of 4 months. As can be seen, although Case II has lower concentration of CO2, Case II achieves a greater amount of CO2 storage. In terms of geomechanical behaviour, Fig.  9 shows the development of averaged vertical strains (negative denotes extension) in the vicinity of injection zone, in specific, between r = 0.15 m and r = 1 m in radius and between z = 807.5 m and 812.5 m in depth. Because injection of fluid induces increase in the pore pressure, it induces vertical extension strain, implying heave of the sediments. Comparing the two cases, there is no significant difference and thus Case II has a greater advantage for geomechanical stability at a given amount of CO2 storage. It is interesting to note that the heave occurs almost immediately after fluid injection, but with time, the sediment slowly compresses, which can be seen by the increase in the vertical strain. This is caused by the slow process of CO2 hydrate formation as shown in Fig.  10, which presents the development of CO2 hydrate in the vicinity of the injection well. Since the volume of water and CO2 fluid required to form CO2 hydrate is larger, hydrate formation reduces pore pressure. This increases the effective stress and thus the sediment compresses. The slow process of CO2 hydrate formation is caused by the limited heat transfer. Since the injection pressure is constant, for CO2 hydrate to keep forming, it needs to lower temperature. Under this condition, the temperature reduction can only occur by conduction, which is relatively slow process. Nonetheless, the trend of the results implies that CO2 hydrate can keep forming while reducing the heave, which may help to achieve permanent CO2 storage with geomechanically-stable method, especially when mixture of CO2 and N2 is injected.

Conclusions
CO2 storage can be achieved by formation of solid hydrates in marine sediments. To consider the CO2 storage efficiency and geomechanical response of host sediments, two cases of CO2 and CO2-N2 injection (90-10 mol%) into marine sediment are simulated with the implementation of gas mixture and hydrate mixture in the coupled formulation. Three key findings as of 4-month injection are presented below: • CO2-N2 injection case has more CO2 amount being sequestered as hydrates in marine sediments due to moderate reduction of permeability from relatively slow CO2-N2 hydrate mixture formation.
• Vertical extension near the well is observed immediately after fluid injection in both cases because of increased pore pressure.
• Vertical strain near the well then gradually decreases as CO2 hydrate forms which depends on heat transfer. Although this study considers only one pressuretemperature condition, the favourable effects of CO2-N2 injection on geomechanical stability and CO2 storage efficiency are likely to stand for different pressure and temperature of marine setting as N2 hydrate remains less stable. The preliminary finding is promising, and future study includes the effect of different concentrations of the CO2-N2 mixture.