Storing CO 2 as solid hydrate in shallow aquifers: Electrical resistivity measurements in hydrate-bearing sandstone

. A recent proposed carbon dioxide (CO 2 ) storage scheme suggests solid CO 2 hydrate formation at the base of the hydrate stability zone to facilitate safe, long-term storage of anthropogenic CO 2 . These high-density hydrate structures consist of individual CO 2 molecules confined in cages of hydrogen-bonded water molecules. Solid-state storage of CO 2 in shallow aquifers can improve the storage capacity greatly compared to supercritical CO 2 stored at greater depths. Moreover, impermeable hydrate layers directly above a liquid CO 2 plume will significantly retain unwanted migration of CO 2 toward the seabed. Thus, a structural trap accompanied by hydrate layers in a zone of favorable kinetics are likely to mitigate the overall risk of CO 2 leakage from the storage site. Geophysical monitoring of the CO 2 storage site includes electrical resistivity measurements that relies on empirical data to obtain saturation values. We have estimated the saturation exponent in Archie’s equation, n ≈ 2.1 (harmonic mean) for CO 2 and brine saturated pore network, and for hydrate-bearing seal (S H < 0.4), during the process of storing liquid CO 2 in Bentheimer sandstone core samples. Our findings support efficient trapping of CO 2 by sedimentary hydrate formation and show a robust agreement between saturation values derived from PVT data and from modifying Archie’s equation.


Introduction
Carbon capture and storage (CCS) technologies are expected to play a substantial role in the transformation of the energy sector toward reduced emissions of anthropogenic greenhouse gases [1]. Captured CO2 is typically injected and stored in a supercritical state [2] in aquifers and depleted reservoirs at great depths. Once injected, CO2 is retained in the sediments by physicochemical processes including structural trapping, capillary trapping, fluid dissolution, and mineral reactions. The contribution from each trapping process varies greatly with time [3]. Structural and capillary trapping are highly relevant from the onset of injection, while fluid dissolution and mineral reaction are believed to have a significant impact at a later stage.
More recently, an additional trapping mechanism suggests liquid CO2 stored and contained by an upper CO2 hydrate layer located at the base of the gas hydrate stability zone (GHSZ). This self-sealing hydrate layer makes an artificial cap rock that can prevent upward migration of CO2 [4,5]. Cooler storage conditions enhances the CO2 storage capacity due to increased CO2 density, increased mobility control (important if long inter-well distance), and increased CO2 solubility in water compared to storage of supercritical CO2.
Experimental work has verified that CO2 hydrate can form at the base of the GHSZ and reduce the CO2 diffusion rate significantly in unconsolidated media [6]. Furthermore, high-density storage of CO2 hydrate in silica sand has been demonstrated [7], as well as CO2 hydrate acting as permeability barriers and successfully sealing off the pore space [8,9]. CO2 immobilization by hydrate formation was directly visualized using MRI and micromodels [10]. A substantial GHSZ is ideal to make sure escaped liquid CO2 is immobilized and converted to solid hydrate before reaching the seabed, and thus extending the hydrate sealing layer. Predicted thickness of the GHSZ for offshore Western Europe is nearly 0.5 km of the upper sediments [11], showing great potential for liquid CO2 storage at shallow depths.
Resistivity measurements are routinely used to determine presence of sedimentary hydrates both in the field and in the laboratory. However, relevant empirical data are needed for saturation quantifications. These can be obtained and calibrated based on controlled laboratorial experiments. For a medium with uniform cross-section transmitting a uniform flow of electric current, resistivity is found from: where Rt is the bulk resistivity, Z is the measured impedance, A is the cross-sectional area of the sample, L is the length of the sample, and θ is the phase angle. The Formation Factor (F) relates empirically to porosity through [12]: where R0 is the resistivity of a fully brine-saturated sample, Rw is the resistivity of the brine, ϕ is the porosity of the sample, m is the cementation exponent and a is the tortuosity factor. Rw is calculated using a standard conversion [13]: where C is the ion content of brine. The Rw value is corrected for temperature variations by [14]: where T1 is ambient temperature and T2 is sample temperature. The Resistivity Index (RI) that applies to sediments partially saturated with a non-conductive material such as oil, gas, or hydrate, is defined as: where Rt is the measured bulk resistivity, Sw is the brine saturation and n is the saturation exponent.
Hydrate growth is accompanied by an effective reduction of the pore space as well as a salinity increase of the remaining brine that is not converted to solid hydrate. Both of these processes results in a continuous change in R0 as hydrate grows, and a dynamic R0* needs to be implemented in eq. 5. This R0* is calculated from eq. 2 by adjusting Rw and ϕ as hydrate grows. Rw is found from eq. 3-4 by keeping track of the salinity increase during hydrate growth from PVT data. PVT data is also used to monitor the hydrate saturation during hydrate growth, and ϕeff is then found from the following relation: where SH is the hydrate saturation. The cementation exponent m is calculated by eq. 2 when the sample (with known porosity) is completely filled with brine. This m is then assumed constant as hydrate grows in the pore space [15]. The tortuosity factor a is set to 1 to ensure that Rw = R0 in the limiting case where ϕ → 1.
Finally, the saturation exponent n is derived during hydrate growth by a modified version of eq. 5: The n is found as the slope when plotting the left side of eq. 7 as a function of -log Sw.
The majority of hydrate resistivity studies presented are related to CH4 hydrate in the context of mapping and production of natural gas through various dissociation processes [15][16][17][18]. To the best of the authors' knowledge, this paper presents the first reported resistivity measurements on sedimentary CO2 hydrate. We provide the saturation exponent n during CO2 injection into brinefilled cores and subsequent CO2 hydrate formation. Saturation values derived from resistivity measurements are compared with PVT derived saturations to investigate the applicability of using resistivity measurements to monitor the evolving CO2 hydrate seal in subsurface carbon storage.

Materials and methods
Homogenous and quartz-dominated Bentheimer sandstone (95.5% quartz, 2.0% kaolinite, 1.7% Kfeldspar, 0.8% other [19]) was used in this study. Average porosity and absolute permeability were measured to 0.22 and 1.1 D, respectively. Twin samples, all with diameter of 5 cm and length 15 cm, were cleaned, dried at 70 °C for 24 hours, and fully saturated with brine (3.5 or 5.0 weight% NaCl) under vacuum. The brine-saturated cores were positioned in a core holder containing a rubber sleeve, fixed upstream end-piece, and floating downstream end-piece (see Fig. 1). A nitrogen-supported back-pressure regulator was connected downstream and an effluent sample collector measured brine production. A refrigerated circulator supplied the system with cooling fluid. Precise high-pressure pumps regulated overburden and pore pressure. The laboratory setup allowed pressure differences and bulk resistivity (Hewlett-Packard LCRmeter; 1 kHz, two-electrode setup) across the core sample to be logged.

Fig. 1.
Coreflooding laboratory setup including sandstone core sample, core holder, cooling system, pressure and temperature measurements, back-pressure regulator, and high-pressure pumps to regulate pore pressure and overburden. Modified from [20].
The pore space was pressurized with brine to 7.0 MPa, while the confinement pressure was set to 10.0 MPa. The core was then flooded with brine (µ=1.07 cP) over a range of injection rates and absolute permeability was calculated. The waterflood was followed by liquid CO2 (µ=0.07 cP) injection at constant volumetric flow rate (0.5, 5 or 10 cm 3 /min) to achieve a mixture of water and CO2 in the pore space mirroring CO2 invasion into an aquifer.
Two different hydrate growth conditions were designed in the laboratory: i) hydrate formation at constant pressure (CO2 pressurized from both core ends, bypass valve open) and ii) flow-induced hydrate formation during CO2 injection with constant volumetric flow rate. Onset of hydrate formation within the pore space was determined from the increase in resistivity, temperature, and differential pressure.

CO2 -brine system (outside GHSZ)
The CO2 injection rate into a porous media affects the displacement efficiency and fluid saturations within the pore network. Achieving substantial CO2 storage capacity in a multiple well scenario relies on an efficient displacement process from injector to producer(s). Though supercritical CO2 can recover about the same amount of water at core-scale, the more optimum mobility ratio between liquid CO2 and water is likely to be important at long interwell distances. Fig 2 shows the rate dependency on macroscopic sweep efficiency, which govern the initial fluid distribution before hydrate formation. Three experiments with CO2 injection rate of 0.5 cm 3 /min (circles), 5 cm 3 /min (diamonds) and 10 cm 3 /min (triangles) were conducted outside of the GHSZ (20 °C) at 7.0 MPa. Injection rate (capillary number) affects both overall Sw and pore-level fluid distribution. A linear production profile is valid before CO2 breakthrough (BT), supplemented with water production measurements. Delayed CO2 BT (indicated with broken vertical lines) for 5 and 10 cm 3 /min implies improved sweep compared to the low injection rate (0.5 cm 3 /min). However, doubling the injection rate from 5 to 10 cm 3 /min had insignificant effect on the displacement process, reaching a plateau where approximately 50% of the brine remained after injecting several pore volumes (PV) of liquid CO2. Though the experiments were designed to minimize capillary end effects by increasing the core length and using relatively high flow rates, the lowest rate (0.5 cm 3 /min) experiment is prone to a more heterogeneous saturation profile due to reduced displacement efficiency. At breakthrough, saturation fractions in the pore space were Sw= 0.77 and SCO2= 0.23 (0.5 cm 3 /min), Sw= 0.59 and SCO2= 0.41 (5 cm 3 /min), and Sw= 0.57 and SCO2= 0.43 (10 cm 3 /min).
The bulk resistivity increased with increasing CO2 saturation because electrically conductive brine was replaced by insulating CO2 in the pore space. Fig 3  presents a logarithmic cross plot of water saturation (Sw) and resistivity index (RI) during CO2 injection into the cores. The saturation exponent n was found as the slope of the curves, with emphasis on the first saturation point (Sw = 1) and the last saturation points (after CO2 BT in the cores) when determining the slope of the curves (solid filled markers). The use of Archie's equation is not applicable until CO2 has reached the end of the core, achieving a predominantly uniform two-phase saturation profile throughout the entire core length. This is illustrated by the data points (no fill) obtained before CO2 BT, which deviate from the linear trend lines in Fig. 3.
The saturation exponent n increased with decreasing CO2 flow rate, and was 1.9 for 10 cm 3 /min, 2.1 for 5 cm 3 /min, and 2.3 for 0.5 cm 3 /min. This again reflects the different macroscopic sweep efficiencies that were achieved for the different flow rates, and highlights that n is sensitive to the displacement history. The n values identified in our CO2-brine systems corroborate with n values reported for similar conditions [21,22]. CO2 is a highly reactive fluid that can influence resistivity measurements through i) dissolution and dissociation where new ions are provided to the solution, and ii) contribution of surface conductivity -even in clay free rocks [21,23]. Both processes lead to increased electrolytic conductivity and may thus overestimate the water saturation if not accounted for. These effects are negligible if the water is highly saline [24]. In the next section, we will compare the water saturation derived from Archie's using the estimated n values with measured PVT data, to find if these effects are relevant to our systems with seawater salinity or higher.

CO2 hydrate -brine system (within GHSZ)
To simulate the conditions of shallow CO2 storage sites in offshore Western Europe, a temperature and pressure regime of 4 °C and 7.0 MPa pore pressure were chosen. This puts the system well within the GHSZ for CO2 hydrate. Two hydrate growth scenarios were tested; i) static hydrate formation at constant pressure and ii) flowinduced hydrate formation under continuous CO2 injection. Both approaches resulted in formation of CO2 hydrate and subsequently immobilization of the injected CO2 over a range of thermodynamic conditions. Fig 4 shows a logarithmic cross plot of water saturation (Sw) and resistivity index (RI) during CO2 hydrate formation in the pore space. The saturation exponent n is derived from the slope of the best-fit linear model to all measured data points during CO2 hydrate formation. Final hydrate saturation depended on initial displacement of water by CO2, and the more efficient displacement, the more hydrates were formed. Improved CO2 sweep led to higher number of interfaces that acted as potential nucleation sites, and reduced water shielding in the samples. Increasing the initial CO2 flow rate from 0.5 cm 3 /min to 10 cm 3 /min, increased the final hydrate saturation by almost a factor of 2.  When hydrates, water and CO2 were present simultaneously in the pore space, n corresponded to 1.7 for SH = 0.37 (Sw = 0.21), 2.1 for SH = 0.32 (Sw = 0.22), and 3.0 for SH = 0.21 (Sw = 0.53). Compared to the CO2brine system, hydrate formation changed the n value for the 0.5 cm 3 /min drainage experiment (least uniform saturation distribution) from 2.3 to 3.0, for 10 cm 3 /min from 1.9 to 1.7, while for 5 cm 3 /min n remained unchanged (2.1). In the case of very limited hydrate formation (SH = 0.21), low bulk resistivity measurements can be ascribed to substantial connectivity and increased ion content of the remaining free water. The obtained n values are nonetheless in good agreement with recent studies for natural gas hydrate in coarse-grained reservoirs [15], and for glass bead specimen [25].
The next three figures show a direct comparison of saturation values derived from Archie's and from measured PVT data. In Fig 5, saturation profiles during the initial displacement and the following hydrate nucleation and growth are displayed for flow rate 0.5 cm 3 /min. The aforementioned unsteady-state regime occurring before CO2 breakthrough, leads to severe deviation between the Archie saturation and correct linear displacement (mass balance) due to temporarily non-uniform saturation profiles. Once CO2 breaks through at the outlet end of the sample, the saturation values from Archie's match actual PVT values very well at the plateau (Sw≈0.7). The onset of hydrate formation is indicated with a vertical line (broken). At this point, Archie's overestimate the water saturation somewhat compared to actual measurements. This apparent increase in water saturation is likely due to a short drop in resistivity linked to hydrate nucleation as reported in the literature [8,16,26]. Another possibility is the aforementioned CO2 effects that may overestimate the water saturation, although the effects are most likely inhibited by the saline brine present. For the following hydrate growth process there is a very good agreement between the two water saturation profiles.
In Fig 6, drainage of water by CO2 at injection rate of 5 cm 3 /min and subsequent hydrate formation is displayed. Again, we observed a deviation in saturation profiles before CO2 BT, and a good agreement after the CO2 front reached the outlet end of the sample. The consistency continues from the onset of hydrate formation until hydrates occupy approximately 15% of the pore space. At this point the hydrate formation rate decreased substantially and the saturation profiles temporarily plateaued (for 0.2 hours). This period of hampered hydrate growth is not captured using Archie's saturation calculations, thus underestimating the water saturation here. Accelerated hydrate formation followed next and this "normalization" caused the end-point saturation values from PVT data and resistivity measurements to match once again. Fig 7 shows saturation profiles during the initial displacement, and the following hydrate nucleation and growth for flow rate of 10 cm 3 /min. The remaining water saturation in the core after CO2 breakthrough was almost identical to the 5 cm 3 /min experiment. There is a good agreement between the water saturation profiles after this point including the whole hydrate formation period in Fig  7. CO2 dissociation effects are highly sensitive to salinity. The 3.5 weight% NaCl solution used in Fig 5-7, belongs in a "high-salinity regime" where the conductivity was actually reduced by up to 15% due to reduced ion mobility [27]. This CO2 dissolution effect, if not accounted for, will underestimate the water saturation derived from resistivity measurements. At the time-scale investigated in our study, no consistent impact of CO2 dissociation on resistivity measurements was observed. Modifying Archie's equation by accounting for reduced effective porosity and increased salinity of the remaining water for each time step [16], resulted in resistivity saturation values agreeing very well with obtained PVT measurements.  In addition to the constant pressure experiments, a series of flow-induced CO2 hydrate formation experiments were tested for various thermodynamic conditions (within the GHSZ). CO2 was injected into fully brine-saturated core samples at 7.0 MPa pore pressure and aquifer temperature of 4 °C or 6 °C. In Fig 8, resistivity profiles for different CO2 flow rates, and salinity and temperature regimes are compared as a function of time. Here, increased flow rate (from 0.5 to 5 cm 3 /min) accelerated hydrate formation and subsequent CO2 trapping and immobilization. However, in terms of pore volumes (PV) CO2 injected, we observed no effect of injection rate on hydrate induction time. The initial displacement of brine by liquid CO2 increased the bulk resistivity from approximately 5 Ωm to 10 Ωm in all four corefloods. Two experiments were flooded with CO2 at a constant rate of 5 cm 3 /min at 7.0 MPa and 4 °C, where one core contained 3.5 weight% NaCl (red curve) and the other 5 weight% NaCl (yellow) -to demonstrate the effect of salinity increase on hydrate formation. Furthermore, two experiments were flooded with CO2 at a constant rate of 0.5 cm 3 /min at 7.0 MPa and salinity of 3.5 weight% NaCl, one experiment at 4 °C (blue) and the other at 6 °C (light blue) -to demonstrate the effect of temperature increase. Resistivity profiles for various temperature and salinity conditions. Arrows indicate hydrate nucleation detected by a combination of pressure, resistivity, and temperature readings. Increase in salinity/temp caused a delayed CO2 hydrate seal formation during continuous flow experiments.
The 5 cm 3 /min constant rate experiment at lowest salinity (Fig 8 -red curve) started forming solid hydrates in the pore space shortly after CO2 breakthrough (nucleation indicated with black arrows). By increasing the brine salinity from 3.5 to 5 weight% (yellow curve), we observed a prolonged induction time of approx. 1.5 hours (factor 9 increase) from flow-induced hydrate formation. When injecting CO2 at 0.5 cm 3 /min at 3.5 weight%, the effect of increasing the sandstone temperature from 4 °C to 6 °C was a factor 2 increase in induction time from 3.8 hours (blue) to 7.6 hours (light blue -resistivity data beyond this point is missing, however point of hydrate nucleation was identified from pressure and temperature logs).
The flow-induced hydrate induction time was evidently sensitive to salinity and temperature variations, and must be taken into consideration when screening for potential carbon storage sites. All four experiments led to solid CO2 hydrate formation eventually. The steady increasing resistivity profiles after nucleation demonstrated hydrate growth in the pore network and decreased effective porosity and permeability. All corefloods experienced significant differential pressure build-up across the samples after hydrate formation, effectively stopping the CO2 production at the outlet. These observations suggest that the injected CO2 phase is made discontinuous by pore-spanning hydrate layers acting as permeability barriers, and thus successfully obstruct viscous CO2 flow in the core sample for the time investigated.

Conclusions
Electrical resistivity measurements providing fluid saturations relevant for CO2 hydrate storage, resulted in the following key experimental observations: For two-phase CO2-brine systems, the saturation exponent n ranged from 1.9 -2.3 (harmonic mean n ≈ 2.1) depending on the CO2 injection rate used during the drainage process. Because the saturation exponent is sensitive to the saturation profile along the core length, it is not recommended to rely on saturation values derived from resistivity measurements using a 2-electrode setup in non-uniform fluid distribution processes.
During CO2 hydrate formation, the saturation exponent n ranged from 1.7 -3.0 (harmonic mean n ≈ 2.1) depending on the initial distribution of brine, which resulted in different final CO2 hydrate saturations. The estimated values of n may be used to map the brine saturation Sw and the CO2 hydrate saturation (SH = 1 -Sw) in excess water conditions, and are in good agreement with previously measured n values during methane hydrate growth. Resistivity measurements are increasingly important for SH < 0.4, as acoustic methods currently cannot obtain sufficient velocity contrasts in zones of low hydrate saturation.