An experimental study of the elastic properties of the sandstone flooded with supercritical CO₂: the influences of saturation, pressure and temperature

SUMMARY

Geological storage of captured CO₂ is essential for reducing anthropogenic greenhouse gas emissions and ensuring the sustainable use of fossil fuels. Understanding the influence of saturation, pressure and temperature on the elastic properties of brine-saturated sandstone flooded with supercritical CO₂ is critical for interpreting seismic and sonic logging data, which aids in monitoring and quantifying subsurface changes associated with CO₂ injection. The experimental results indicate that as scCO₂ saturation increases (0–60 per cent), the P-wave velocity decreases significantly with an average of 14 per cent drop, while the S-wave velocity increases slightly. Temperature variations (80–110 °C) have a minimal effect on both velocities (1–2 per cent), whereas elastic features show notable sensitivity to the variation of confining pressure (20–30 MPa) and pore pressure (10–20 MPa). Ignoring the effects of pore pressure might lead to the bias of interpreting seismic data for monitoring scCO₂ saturation change. The constructed rock physics models well capture the coupled effects of porosity and scCO₂ saturation on the P-impedance and P- and S-wave velocity ratio, which show good agreement with the experimental results. These findings are crucial for improving monitoring methods and enhancing the accuracy of predictive models for CO₂ geological storage.

1 INTRODUCTION

Geological sequestration of CO₂ is considered to be an indispensable technical approach to reducing anthropogenic greenhouse gas emissions, which also play an imperative role in green low-carbon development. Understanding the elastic properties of the rock-CO₂-brine system is essential for seismic monitoring of the flow of CO₂ plumes and quantitative estimate of the amount of CO₂ stored in place (Tura & Lumley 2000; Lumley 2010; Robinson & Davis 2011; Daley & Harbert 2019).

The phase status of CO₂ depends on the temperature and pressure conditions. At temperature and pressure at or above critical point (7.38 MPa, 31.1 °C), CO₂ becomes supercritical fluids, which typically exhibit the physical properties of low viscosity and high density (Span & Wagner 1996). It is more viable and economical to inject CO₂ into geological formation at a supercritical state since the higher density allows for a larger storage capacity (Prasad et al. 2021). When scCO₂ is injected into saline aquifers, brine and scCO₂ are often considered as two immiscible fluids. Due to the unique physical properties and active chemical reactivity of scCO₂, the dynamic elastic responses of the rock-brine-scCO₂ system are notably affected by the saturation, temperature and pressure conditions.

Some experimental studies are conducted to understand the effects of phase behaviours of CO₂, pressure and saturation effects on the velocity and attenuation characteristics of porous rocks injected by CO₂ (Wang & Nur 1989; Xue & Ohsumi 2004; Shi et al. 2007, 2011; Yam & Schmitt 2011; Adam & Otheim 2013; Lebedev et al. 2013). Lei & Xue (2009) investigated the influences of CO₂ saturation on the P-wave velocity and attenuation using laboratory-based seismic measurements with dense sensor arrays at ultrasonic frequencies. Njiekak et al. (2013) performed ultrasonic measurements on carbonates fully saturated with CO₂ for a geological storage project in the Weyburn field, and they found that both the P- and S-wave velocity notably decreased as the CO₂ transformed from gas to either liquid or supercritical phase. Mikhaltsevitch et al. (2014) conducted an experimental study to measure Young's modulus and extensional attenuation of low-permeability sandstone flooded with supercritical CO₂ at seismic frequencies (0.1–100 Hz). They mainly compare sandstone's elastic and anelastic properties in dry conditions, fully water-saturated conditions, and partially saturated status with the maximum amount of scCO₂. Nevertheless, there is still a lack of systematical study of the coupling effects of rock's porosity, clay content and microstructures with CO₂ saturation on the rock's elastic and anelastic properties under varying temperature and pressure conditions.

In addition to the saturation level, the fluids distribution pattern also notably influence the elastic and attenuation behaviour of partially saturated rocks (Cadoret et al. 1995, 1998; Kobayashi & Mavko 2016; Zhu et al. 2017; Li et al. 2020; Chapman et al. 2021). Nakagawa et al. (2013) conducted elastic and attenuation measurements for sandstones during supercritical CO₂ injection using Resonant Bar methods, and the saturation and distribution of supercritical CO₂ were simultaneously estimated using X-ray CT scans. They concluded that, the CO₂-brine distribution pattern affect the velocity and attenuation of the extension wave during the CO₂ injection test and the subsequent brine re-injection test. Using the outcrop sandstone sample with moderate laying, Alemu et al. (2013) investigated the effect of sub-core scale heterogeneity on CO₂ fluid distribution pattern, and hence how those affect the elastic and electrical responses. Based on the simultaneous measurements of ultrasonic waveforms and X-ray computed tomography images, Zhang et al. (2015) investigated the influences of saturation paths on the P-wave velocity and attenuation in low-permeability sandstone during drainage (CO₂ injection) and imbibition (brine injection).

It is necessary to point out that the elastic responses of geological formation injected by scCO₂ are jointly affected by various factors such as pressure, temperature and saturation conditions. Without fully considering the various physical factors on the elastic signature, the interpretation of seismic data for CO₂ storage monitoring can be possibly biased. For example, quantifying the saturation from seismic data is essential to map the CO₂ plum migration path, while predicting the pressure variation is critical to detect the possible leak risks. Therefore, it is important to clarify the sensitive elastic attributes to the variation of pressure and saturation. Nevertheless, the influences of pore pressure on the elastic responses during scCO₂ injection are sparsely reported.

The primary objective of this study is to systematically investigate the influences of pressure, temperature and saturation on the elastic signatures of porous sandstone injected by CO₂, therefore offering insights into reliable seismic monitoring of CO₂ sequestration into brine aquifer.

2 MATERIALS AND METHODS

2.1 Geological background and samples description

The rock samples used for experimental study were obtained from the drilling wells of Guantao Formation strata at depths ranging from 1916 to 2234 m in the Bohai Bay Basin (Eastern offshore China), which are the potential sites for CO₂ sequestration. The Guantao Formation consists of medium-coarse sandstones. The axis of the core sample is oriented horizontally to the layering, and sample appears to be relatively homogeneous without subscale heterogeneities. Fig. 1 shows the cross-plot of porosity and permeability for the measured rock samples, with the porosity range of 15 to 30 per cent (average porosity of 21.61 per cent), and permeability range of 1–220 mD (average permeability of 24.15 mD). Overall, the relatively high porosity and permeability characteristics, make the target formation a good candidate for CO₂ injection and storage. The overlying formation is mainly composed of fine-grained mudstones, with low porosity and permeability, serving as a good sealing layer.

Fig. 2(a) shows the 3-D Micro CT (computerized tomography) scanning image of a typical porous sandstone sample, which is colour-coded by the mean pore radius. As we can see, the pore radius can reach up to 178 μm. Figs 2(b) and (c) show the pore equivalent radius and throat equivalent radius distribution of the rock sample, with an average pore size of 39.80 μm and pore throat radius of 35.46 μm indicating that the samples are predominantly characterized by intergranular pores with large pore sizes. In addition, the scanned CT image also shows the investigated sandstone exhibits good pore connectivity, which is also important for the scCO₂ flooding efficiency.

The XRD (X-ray Diffraction) analysis results of the nine typical rock samples are presented in Fig. 3. The samples primarily consist of quartz, feldspar and clay minerals. Quartz dominates the composition, ranging from 42 to 65 per cent. Generally, the feldspar content varies from 11.9 to 52.7 per cent, while clay mineral content ranges from 3.7 to 20.6 per cent. These results indicate that the samples are predominantly composed of quartz, with varying amounts of feldspar and clay minerals.

2.2 Experimental setup and procedure

2.2.1 Experimental setup

The schematic diagram of the experimental setup used for measuring elastic wave velocities for sandstone flooded with supercritical CO₂ is illustrated in Fig. 4.

The experimental setup employs a high-temperature and high-pressure rock core clamp. The ISCO65D pumps used can deliver pressures ranging from 0 to 90 MPa, ensuring precise control and monitoring. Temperature control within the rock core clamp is achieved through an integrated electrical heating system, which can be managed via an operation panel or dedicated software. This system can regulate temperatures from ambient conditions up to 150 °C. The plungers at both ends of the core holder contain piezoelectric ceramic transducers, which can generate and receive compressional waves (P waves) at a frequency of 1 MHz and shear waves (S waves) at a frequency of 0.5 MHz.

The pressure injection system is designed with fluid injection and outflow ports located at both ends of the clamp. In this experiment, CO₂ is directly injected using a CO₂ pump, while saline water is injected by connecting a water pump to a container holding saline water. During the experiment, the temperature of both the autoclave and rock samples was consistently maintained above 80 °C, while the pore pressure was sustained above 10 MPa and the confining pressure was kept above 20 MPa. These conditions ensured that the CO₂ remained in its supercritical state throughout the experiment. Displaced fluids are collected through transparent pipes connected to the clamp's outflow port.

It is necessary to point out that, in order to quantify the fluid saturation by CO₂ flooding, the collection container contains anhydrous CaCl₂ to capture the displaced saline water. The mass of the displaced brine is monitored using a high-precision balance to accurately calculate the brine saturation at each saturation point. This setup allows for quantification of fluid saturation within the rock sample.

2.2.2 Experimental procedure

The core sample is first evacuated for a minimum of 2 hr. Following the evacuation, the core sample is immersed in an NaCl solution with a salinity of 13 g L⁻¹ for 2 hr, reflecting the typical saline formation water. The sample is then weighed to record its initial mass.

The core sample is placed in the core holder, and the system is heated to 80 °C. A confining pressure of 20 MPa is applied using a water pump, and brine is injected into the sample at a fluid pressure of 10 MPa. The end valve is closed once continuous, air-bubble-free brine flows from the outlet. The confining pressure, fluid pressure and temperature are maintained for at least 30 min to ensure full brine saturation and to balance the system conditions.

Pressure, temperature and saturation cycling experiments are then performed on the sample. The confining pressure varied between 20 and 30 MPa in 10 MPa increments, while the pore pressure was fixed at 10 MPa. When the pore pressure was increased from 10 MPa to 20 MPa in 10 MPa increments, the confining pressure was fixed at 30 MPa. The temperature was adjusted between 80 and 110 °C in 10 °C increments. These ranges for temperature, confining pressure and pore pressure are based on the insitu conditions of the target formation for CO₂ sequestration. The sample is achieved six saturation points during the CO₂ flooding experiment, from fully brine-saturated status to CO₂ breakthrough status.

During the experimental procedure, we first adjusted the saturation, and then changed the temperature and pressure conditions under that specific saturation level. Once all temperature and pressure conditions for that saturation were tested, we moved on to the next saturation condition. This implementation strategy was to maintain the stability of saturation level and reduce the overall time of the whole experimental procedure. At each saturation level, temperature and pressure cycling were performed ultrasonic measurements are performed under these varying conditions, recording both P-wave and S-wave waveforms. After picking the onsets on the waveforms, ultrasonic velocities are obtained ultrasonic velocities are obtained by

where |${L_\mathrm{ s}}$| is the sample length, |$\Delta t$| is the traveltime of ultrasonic waves through the sample. The traveltimes |$\Delta t$| of both P and S wave are recorded and are calibrated with the effect of the end buffers. The estimated errors for P-wave and S-wave velocities are 1 and 3 per cent, respectively. The primary source of error is the ambiguity in manually picking the first arrivals of the waveforms. Furthermore, we calculated the P-wave impedance using the following equation:

where ​|${v_p}$| is the P-wave velocity of the CO₂-partially saturated sandstone, and |$\rho $| ​is the density of the CO₂-partially saturated sandstone, which can be calculated using the following equation:

Here, |${\rho _{\mathrm{ dry}}}$|​ represents the density of the dry rock sample, which is calculated from the precisely measured mass and volume of the dry sample. |${S_{\mathrm{ C}{\mathrm{ O}_2}}}$|​​ denotes the CO₂ saturation, while |${\rho _{\mathrm{ C}{\mathrm{ O}_2}}}$|​ and |${\rho _{\textrm{brine}}}$|​ are the densities of CO₂ and brine under the experimental temperature and pressure conditions, respectively. Their calculation formulas are provided by (Batzle & Wang 1992) and (Hassanzadeh et al. 2008). |$\varphi $| represents the porosity of the rock sample.

Before recording waveform at each fixed measuring condition, the system is stabilized by balancing pressure changes for 15 min, temperature changes for 30 min, and saturation changes for 20 min. These equilibrium time intervals are roughly estimated based on experimental experience and reference (Zhang et al. 2015). For example, temperature is highly sensitive to electrical resistance, and through electrical resistance monitoring of temperature variations, it tends to stabilize within 30 min. Before each CO₂ flooding displacement, the volume of brine required to reach the next saturation level is roughly estimated. To maintain the stable pore pressure, we manually controlled the valve at the end of the holder to ensure that CO₂ was injected at a slow rate. Typically, the volume of displaced brine did not exceed 0.5 ml within two minutes, and the displaced brine is collected in a container with anhydrous CaCl₂.

2.2.3 Quantitative scCO₂ saturation estimation

Determining the precise saturation at each saturation point during the experiment is a considerable challenge. To address this, a container filled with anhydrous CaCl₂ is used to collect the displaced brine during each step of saturation change. The anhydrous CaCl₂ ensures that any water vapour displaced at high temperatures is captured effectively. By monitoring the mass change, the volume of displaced brine can be accurately calculated. The CO₂ saturation at each point can be determined using the following formula:

where ΔV is the cumulative volume of displaced brine. |${V_{\textrm{pipe}}}$| is the volume of the equipment's piping. Through the pump, brine is injected into the dead volume pipes at the front and back ends at a fixed low flow rate. The dead volumes at the front and back ends are estimated by considering the volume change of the fluid in the pump, the flow rate and the injection time. Multiple measurements are taken and averaged to reduce errors. |${V_{\mathrm{ por}}}$| is the pore volume of the rock sample, which can be calculated based on the sample's volume and porosity. In this study, we assume that the pore volume of the rock samples remains constant and does not change with variations in confining pressure and pore pressure.

It is worth mentioning that the estimation of the dead volumes at the valve points and the contact surfaces between the rock sample and the equipment possibly introduces uncertainties for the saturation calculations. Before the experiment, brine was injected at a constant low flow rate into the pipeline until water flowed out from the other end. After closing the valves, the water in the pipeline was expelled. By comparing the mass difference between the injected and expelled water, we found that the mass difference was consistently within 0.2 g after multiple measurements. Thus, we concluded that the dead volume should be less than 0.2 ml. In addition, note that the 10 MPa pore pressure variation (10–20 MPa) can cause the maximum 0.02 ml volume change of brine within the pore volume, and hence the estimation of supercritical CO₂ saturation may introduce an error of 0.5 per cent.

The rock samples need to achieve maximum residual saturation after the final CO₂ displacement with brine. During this last displacement process, minimal brine was observed in the transparent outlet pipe, indicating the samples reached maximum residual saturation. After concluding the experiment, we need to verify whether all displaceable brine has been expelled from the rock sample by CO₂ to ensure that the sample has reached its maximum residual saturation. CO₂ was injected into the rock sample for approximately 5 min to displace any remaining brine. The CO₂ flow rate during the verification phase was higher than that during the experimental phase, which could cause some trapped brine in valve dead zones to also be expelled. The mass change of the CaCl₂ container was recorded, and the change in mass was found to be within 0.1 g. The total amount of brine that could be displaced from the rock sample was approximately 2 g. Therefore, there may be a 2.5 per cent error in achieving the maximum CO₂ saturation state.

Interestingly, the final scCO₂ saturations of the 30 rock samples were consistently less than 60 per cent, aligning with the limited scCO₂ saturations observed in other relevant studies (Caspari et al. 2011; Alemu et al. 2013; Lebedev et al. 2013; Zhang et al. 2015). A large number of capillary pressure experiments have shown that sandstone is wet, and CO₂ will preferentially displace brine from the macropores before invading other pores, and the brine will be retained in the smaller pores as a wetting phase, which results in the brine with a large irreducible saturation (Espinoza & Santamarina 2010; Zhang et al. 2014; Iglauer et al. 2015).

3 RESULTS

3.1 The influences of temperature, pressure and scCO₂ saturation on wave velocities

Figs 5(a)–(h) show the influences of temperature, effective pressure, pore pressure and scCO₂ saturation on the P and S waveforms of the investigated rock samples, respectively. The effective pressure is defined as the difference between confining pressure (⁠|${P_\mathrm{ c}}$|⁠) and pore pressure (⁠|${P_\mathrm{ f}}$|⁠). The impacts of temperature, effective pressure, pore pressure and saturation on P-wave and S-wave velocities are depicted in Fig. 6, corresponding to the waveform changes shown in Fig. 5.

As shown in Figs 5(a) and (b), the first arrivals of both P waves and S waves are delayed with increasing temperature, though the delay is marginal, indicating only slight postponement. This is consistent with Figs 6(a) and (b), where P- and S-wave velocities decrease by approximately 2 per cent as the temperature increases from 80 to 110 °C. This also suggests that both of the bulk and shear moduli are affected by temperature variation.

In contrast, confining pressure and pore pressure significantly affect the first arrival times of the P and S waves. As confining pressure increases from 20 to 30 MPa (with pore pressure at 10 MPa), the first arrivals of P and S waves show a notable advancement (Figs 5c and d). Conversely, as pore pressure increases from 10 to 20 MPa (with confining pressure at 30 MPa), the first arrivals of P and S waves exhibit significant delays (Figs 5e and f). Figs 6(c) and (d) illustrate that both P-wave and S-wave velocities significantly increase with higher confining pressure. Conversely, Figs 6(e) and (f) show that increased pore pressure leads to a notable decrease in P- and S-wave velocities. This is mainly because the increased pore pressure likely loosens grain contacts, thereby reducing overall rock elasticity (Biot 1941; Nur & Byerlee 1971; Dvorkin et al. 1991).

Figs 5(g) and (h) demonstrate that scCO₂ saturation has a notable effect on the first arrival time of P waves. As the scCO₂ saturation increases from 0 per cent to the point where CO₂ breaks through the rock sample, the first arrivals of P waves show systematic delays, indicating a systematic decrease in velocity with increasing scCO₂ saturation levels. This is further corroborated by Figs 6(g) and (h), which show that P-wave velocity decreases by as much as 12 per cent when scCO₂ saturation increases from 0 to 55.76 per cent.

It is also interesting to note that the wave amplitude and energy are significantly diminished as more scCO₂ is injected into the brine-saturated samples, likely due to wave energy attenuation between scCO₂ and brine. Nevertheless, the increase in scCO₂ saturation does not have a pronounced effect on the S-wave waveform. The rise in scCO₂ saturation leads to a slight delay in the first arrival of the S-wave waveform. This is mainly because fluid saturation does not change the shear modulus of partially saturated rocks but decreases the bulk density, resulting in an enhanced S-wave velocity with increased scCO₂ saturation. The shear wave velocity increases by approximately 2 per cent when scCO₂ saturation rises from 0 to 55.76 per cent. As expected, scCO₂ saturation has trivial effects on the waveform characteristics of S waves, which is distinct from the influence of scCO₂ saturation on the waveform characteristics of P waves.

3.2 Comparisons of various factors on elastic responses of scCO₂ partially saturated sandstone

Based on the experimental measurements of 30 rock samples, we used the box plot shown in Fig. 7 to illustrate the sensitivity of P-wave velocities, S-wave velocities, P impedance (the P-wave velocity times bulk density), and Vp/Vs ratio (the ratio between P- and S-wave velocities) to variations in saturation, confining pressure, pore pressure and temperature. The P impedance and Vp/Vs ratio, which respectively control the intercept and gradient of seismic amplitude-versus-offset, are two essential and commonly used elastic attributes for quantitative seismic interpretation (Avseth et al. 2005). Those two elastic parameters can be also relatively reliably inverted from pre-stack seismic angle gathers (Xu et al. 2022), and hence can be used for seismic monitoring of reservoir properties changes. In the box plot, the upper and lower edges of the box represent the upper and lower quartiles of the data, while the line in the middle of the box represents the median. The edges of the box are connected by dashed lines, which represent the maximum and minimum values of the data. The red dots indicate outliers in the data. The box plot provides a clear visual representation of the data's distribution. From the box plot in Fig. 7(a), it is observed that P-wave velocity exhibits higher sensitivity to CO₂ saturation. From fully brine-saturated to CO₂ breakthrough in rock samples, most samples exhibit P-wave velocity changes ranging between 11 and 17 per cent, with a median of around 14 per cent. The sensitivity of P-wave velocity to confining pressure and pore pressure is quite similar, approximately around 5 per cent. P-wave velocity shows slightly higher sensitivity to confining pressure compared to pore pressure, as the increase in pore pressure also enhances the bulk modulus of scCO₂, partially offsetting the effects of pore pressure on the rock frame. Additionally, it is evident that temperature has a minimal effect on P-wave velocity, around 1–2 per cent.

Fig. 7(b) illustrates the sensitivity of S-wave velocity to various factors. The S-wave velocity is more sensitive to variations in confining pressure and pore pressure than the P-wave velocity. For example, a 10 MPa change in pore pressure results in approximately a 9 per cent velocity change. Confining pressure increases by 10 MPa, leading to a slightly lower impact than pore pressure, around 8 per cent. This suggests that confining pressure and pore pressure exert stronger influences on shear grain contact than the bulk modulus. As expected, S-wave velocity shows no significant sensitivity to CO₂ saturation or temperature.

Figs 7(c) and (d) illustrate the sensitivity of P impedance and Vp/Vs ratio to variations in saturation, confining pressure, pore pressure and temperature. P-wave impedance and the Vp/Vs ratio are two crucial parameters in pre-stack inversion. The Vp/Vs ratio was calculated for each rock sample, and the density of the samples at different saturations was determined using CO₂ saturation, dry rock mass and the physical properties of CO₂ and saline water. As expected, P impedance is highly sensitive to supercritical CO₂ saturation, reaching about 15 per cent. Variations in confining pressure from 20 to 30 MPa can cause approximately 6 per cent changes in impedance, while an increase in pore pressure from 10 to 20 MPa results in a 4 per cent change in P-wave impedance. It is evident that CO₂ saturation has the greatest impact on the Vp/Vs ratio, causing changes of about 15 per cent. Confining pressure variations from 20 to 30 MPa result in approximately 4 per cent changes in the Vp/Vs ratio, while increasing pore pressure from 10 to 20 MPa results in a 5 per cent change in the Vp/Vs ratio.

Fig. 8 shows the influence of porosity, CO₂ saturation, confining pressure, pore pressure and temperature on the crossplot of P impedance and the Vp/Vs ratio. As expected, the P impedance decreases as porosity and CO₂ saturation increase (Figs 8a and b). However, the Vp/Vs relationship is complicated by the coupling effects of porosity and saturation. For high brine saturation, high porosity corresponds to a high Vp/Vs ratio, while for high CO₂ saturation, high porosity corresponds to a low Vp/Vs ratio.

As illustrated in Fig. 8(c), increasing effective pressure (increase confining pressure while keeping pore pressure constant) leads to higher P impedance and a decrease in the Vp/Vs ratio. Conversely, as illustrated in Fig. 8(e), increasing pore pressure decreases P impedance and enhances the Vp/Vs ratio. The variation of the Vp/Vs ratio with pore pressure is mainly because the shear wave velocity is more sensitive to the pore pressure enhancement than the compressional wave velocity. The higher Vp/Vs ratio corresponds to larger porosity (Fig. 8e), implying that the shear wave velocity is more sensitive to pore pressure variation at larger porosity. These experimental results lay the foundation for seismic monitoring of pore pressure variations during CO₂ geological sequestration, which is also an important indicator for possible CO₂ leakage (Birkholzer et al. 2009; Szulczewski et al. 2011; Rutqvist 2012; Newell & Ilgen 2019). Temperature effects are shown in Fig. 8(d), where generally, with increasing temperature, both P-wave impedance and the Vp/Vs ratio exhibit a decreasing trend, though the changes are minimal.

Fig. 9 illustrates the coupled effects of porosity and scCO₂ saturation on the relative changes in P-wave impedance (⁠|$\Delta \mathrm{ PI}/\mathrm{ PI}$|⁠) and Vp/Vs ratio |$( {\Delta ( {\mathrm{ Vp}/\mathrm{ Vs}} )/( {\mathrm{ Vp}/\mathrm{ Vs}} )} )$|⁠. The relative changes of these two parameters are defined as the difference between the P- impedance and the Vp/Vs ratio at different scCO₂ saturation conditions with respect to the fully brine saturated conditions divided by the P impedance and Vp/Vs ratio at fully brine saturated conditions.

As scCO₂ saturation increases from 0 per cent to approximately 50 per cent, P-wave impedance can decrease by up to about 25 per cent, and Vp/Vs ratio can decrease by up to 20 per cent. It is necessary to point out that the scCO₂ saturation effect are strongly coupled together with porosity: the higher porosity, the scCO₂ saturation effects are stronger in deceasing P impedance and Vp/Vs ratio.

4 ROCK PHYSICS MODELLING TO QUANTIFY scCO₂ SATURATION EFFECTS ON ELASTIC PROPERTIES

Rock physics modelling is crucial for the quantitative interpretation of the elastic and attenuation properties of partially CO₂-saturated rocks, providing insights into seismic monitoring of geological CO₂ storage. In this section, rock physics modelling is applied to quantify the effects of scCO₂ saturation on the effective elastic properties. As previously mentioned, the effects of saturation are coupled with porosity, and therefore, porosity is also considered in rock physics modelling. The rock physics modelling workflow is illustrated through the schematic representation in Fig. 10.

The mineral composition includes quartz (45 per cent), plagioclase (20 per cent), feldspar (15 per cent), and clay (20 per cent) by volume, with a permeability of 100 mD. The equivalent bulk modulus |${K_0}$| and shear modulus |${\mu _0}$| of the mineral material making up rock are calculated by Hill average, while the equivalent bulk modulus |${K_\mathrm{ d}}$| and shear modulus |${\mu _\mathrm{ d}}$| of the dry rock matrix are computed through the application of a self-consistent model (Berryman 1980; Berryman & Wang 1995):

where N represents the number of inclusions. |${K_i}$| and |${\mu _i}$| represent the bulk modulus and shear modulus of the i-th inclusion, respectively, and the pores are treated as empty inclusions. |${x_i}$| represents the volume percentage of the i-th term, while |${P^i}$| and |${Q^i}$| are the geometric factors.

The properties of fluids, particularly CO₂, are influenced by variations in temperature and pressure. We use the empirical formulas given in Hassanzadeh et al. (2008) and Han et al. (2010) to calculate the density, bulk moduli and viscosity of the scCO₂ and brine at a pressure of 10 MPa and a temperature of 80 °C (Table 1).

To account for the partial saturation effects on the overall effective elastic properties, we employ the extended Gassmann equation to characterize the velocity dispersion characteristics in partially CO₂-saturated rocks (Zhao et al. 2021). Due to the complex pore throat size distribution (Fig. 2), the size of the scCO₂ patches also tends to distribute following a spectrum instead of following a uniform pattern. The extended Gassmann equation can compute frequency-dependent velocity due to wave-induced fluid flow between two immiscible fluids, where the size of the fluid patches might follow a complex distribution. The main limitation of the extended Gassmann equation is that physical interactions among the multiple sets of heterogeneities as well as the possible wave-induced fluid flow (WIFF) effects on shear dispersion are ignored. Based on the extended Gassmann equation, the frequency-dependent equivalent bulk modulus |${K^{\rm{*}}}$| can be expressed as:

where |${f_i}$| denotes the volume fraction of the i-th heterogeneous component, adhering to |$\mathop \sum \nolimits_i {f_i} = 1$|⁠. The term |${\varepsilon _{\textrm{WIFF}}}{( f )_i}$| signifies the dynamic volumetric strain induced in the i-th component as a result of pore pressure relaxation due to the two immiscible fluids of scCO₂ and brine, with |${\varepsilon _{\textrm{WIFF}}}{( 0 )_i}$| representing that at the low-frequency limit. The detailed expression for |${\varepsilon _{\textrm{WIFF}}}( f )$| is shown in Appendix  A. |$\mathrm{ d}{P_0}$| represents the applied stress. |${K_\mathrm{ G}}$| represents the equivalent bulk modulus of a fluid-saturated rock under low-frequency conditions, which can be calculated by the classical Gassmann equation (Gassmann 1951):

where |${K_\mathrm{ f}}$| is the bulk modulus of the filled scCO₂, as shown in Table 1, while |$\varphi $| represents the porosity.

In this study, we utilize ultrasonic frequency measurements (10⁶ Hz) of elastic wave velocities to construct a rock physics template. The main gas patch radius is set as 0.1 cm, which is roughly estimated based on the fluid patch characterization for the brine-CO₂ system in (Zhang et al. 2015).

Figs 11(a) and (b) compare the measured data of 30 samples with the constructed rock physics template based on the aforementioned equations, represented as a cross-plot of P impedance and Vp/Vs ratio, colour-coded by scCO₂ saturation and porosity, respectively. The template shows a strong agreement with the experimentally measured elastic properties, effectively capturing the data characteristics and accurately representing the two primary factors influencing P-wave impedance and the Vp/Vs ratio: saturation and porosity. Specifically, for a given porosity, increased scCO₂ saturation results in lower P-wave impedance and a lower Vp/Vs ratio, with the effect of varying saturation levels on the Vp/Vs ratio being more pronounced at higher porosities.

5 DISCUSSIONS

A key challenge in interpreting time-lapse post- or pre-stack seismic differences is decoupling the effects of saturation and pore pressure variation on the elastic responses. Based on previous experimental results, Fig. 12 schematically illustrates the influences of scCO₂ saturation and pore pressure on the P impedance and Vp/Vs ratio. For a given scCO₂ saturation, it is evident that an increase in pore pressure causes a further decrease in P impedance but slightly enhances the Vp/Vs ratio. Therefore, to reliably interpret scCO₂ saturation and monitor CO₂ migration, it is essential to account for pore pressure effects on the elastic responses. Ignoring pore pressure effects and using only P impedance to interpret saturation changes could result in significant overestimation of saturation.

Moreover, characterizing pore pressure evolution in CO₂ storage projects is crucial for potential leakage detection and risk evaluation. Thus, constructing a time-lapse rock physics template that considers the influence of scCO₂ saturation and pore pressure is essential, which should be considered in future work.

The main limitation of the experimental study is that the setup does not allow for the measuring ultrasonic velocity while simultaneously monitoring the fluid distribution (such as with X-ray CT), hindering our ability to gain a profound understanding of the relationship between elastic properties and fluids distribution. Moreover, we primarily consider the drainage scenario during the CO₂ flooding experiment, while the imbibition scenario is also important in a CO₂ storage site. More details regarding how the different fluids distribution patterns in the drainage and imbibition scenarios affect elastic wave velocities can be also found in Alemu et al. (2013) and Zhang et al. (2015).

As illustrated in Fig. 5, the waveform of P waves demonstrates significant sensitivity to variations in scCO₂ saturation levels. In contrast, the influence of scCO₂ saturation on S waves appears comparatively minor. This observation highlights P-wave attenuation is notable in the presence of partial CO₂ saturation, which has been also confirmed by other laboratory investigations (Lei & Xue 2009; Zhang et al. 2015). Since the experimental results clearly demonstrate that the velocity of the rock is strongly influenced by CO₂ saturation, it suggests that seismic waves do not propagate strictly along the fastest path (brine patch) or fall within the ray theory domain. This also implies that the two immiscible fluids of scCO₂ and brine tend to have a non-uniform distribution pattern in the porous sandstone, where the wave-induced fluid flow and scattering effects possibly contribute to the wave attenuation. In this study, we mainly focus on the elastic properties (velocity, impedance and Vp/Vs ratio) rather than wave attenuation. Future research endeavours will aim to explore the quantitative relationship between attenuation and scCO₂ saturation.

It is important to note that the quantified scCO₂ saturation (eq. 4) is primarily based on the assumption that CO₂ is in a free state. However, when CO₂ comes into contact with brine, it commonly undergoes dissolution, a process influenced by factors such as temperature, pressure and the chemical composition of the brine (Takenouchi & Kennedy 1965; Duan & Sun 2003). The dissolved CO₂ within the brine may introduce uncertainty of the saturation quantification. Besides, from the perspective of chemical reaction, the rock composition (in particular the carbonate mineral) can alter due to the CO₂ injection (Gherardi et al. 2007), and hence affect the overall elastic responses. Considering the relatively low calcite and clay content in the sandstone used, the chemical reaction impacts on the overall physical properties of the rock sample should be limited. In the future, more experimental and rock physics modelling work are necessary to investigate the potential influence of CO₂ dissolution and chemical reaction with rock minerals on the saturation-dependent elastic properties.

6 CONCLUSIONS

By carrying out ultrasonic measurement during scCO₂ injection into the porous sandstone, the elastic properties of 30 samples were experimentally investigated under varying saturation, pressure and temperature conditions. The P- and S-wave velocities are significantly affected by effective pressure, while the influences of temperature change are very limited. It is also found that as pore pressure changes from 10 to 20 MPa, the P- and S-wave velocities can drop by approximately 4 and 10 per cent, respectively. The scCO₂ saturation levels significantly affect the elastic responses of partially saturated sandstone. As CO₂ saturation increases from 0 per cent to approximately 50 per cent, there is a pronounced decrease in P-wave velocity (average 14 per cent), while S-wave velocity shows a slight increase. For a given porosity, higher scCO₂ saturation produces lower P impedance and a lower Vp/Vs ratio, with stronger influences at higher porosity.

The constructed rock physics template effectively captures the saturation and porosity effects on the P impedance and Vp/Vs ratio, thereby offering insights for seismic monitoring of CO₂ geological sequestration in the target saline sandstone formation. Additionally, to reliably interpret scCO₂ changes using time-lapse seismic data, it is important to decouple the pore pressure effects on the elastic responses.

ACKNOWLEDGMENTS

This work was supported by the National Key R&D Program of China (2023YFB4104202), Youth Innovation Promotion Association CAS (2021286), and Fundamental Research Funds for the Central Universities.

DATA AVAILABILITY

The data associated with this paper are available online https://zenodo.org/records/14591169.

REFERENCES

Appendix A

The expression for the dynamic volumetric strain |${\varepsilon _{\textrm{WIFF}}}( f )$| due to patchy saturation of the two immiscible fluid at the mesoscale is (Zhao et al. 2021):

with

and

Here, |${K_{\mathrm{ HF}}}$|​ is the equivalent bulk modulus at high frequencies, v is the fluid velocity through the inner boundary due to pressure difference, and a and b are radii for gas patch and ideal spheroidal rock unit. The inner sphere and outer shell are denoted by subscripts 1 and 2, respectively. |${P_1}$| and |${P_2}$| denote the pressures under external pressure |$d{P_0}$|⁠, respectively. |$\ {Z_1}$| and |${Z_2}$|​ are acoustic impedances, |${K_1}$| and |${K_2}$| represent saturated bulk moduli from the Gassmann equation, |${\mu _1}$| and |${\mu _2}$|​ are shear moduli, |$\eta $| is fluid viscosity, |${S_\mathrm{ g}}$|​ is gas saturation and k is permeability. The constant Q for each region must be calculated using its specific rock physical parameters.