Characterization of carbon dioxide leakage process along faults in the laboratory

Lifeng Xu, Qi Li,*, Yongsheng Tan, Xiaochun Li

a State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics,Chinese Academy of Sciences, Wuhan,430071,China

b University of Chinese Academy of Sciences, Beijing,100049, China

Keywords:Carbon dioxide (CO2) leakage Fault strain Temporary pseudo-sealing (TPS)Pressure front Fiber bragg grating (FBG) sensor Risk management

A B S T R A C T

1. Introduction

One of the most promising, cost-effective, and readily available technologies for reducing greenhouse gas emissions to the atmosphere is the capture and separation of carbon dioxide (CO2) from large stationary sources and storage in geological formations(Vernooij et al., 2020). To limit global warming to below 2°C, Wei et al. (2021) proposed a global layout of carbon capture and storage(CCS)in line with the 2°C climate target.A critical component of any successful CCS project will be to assure stakeholders and regulators that the risk of leakage out of the sequestration reservoir is very low and,if a leakage event occurs,it can be detected(Keating et al., 2014). Faults are widespread in geological structures and provide possible channels for CO2leakage (Jing et al., 2021). Understanding the role of faults and fractures as fast fluid pathways through overburden strata to the surface is critical to ensure storage verification for engineered CCS sites (Bond et al., 2017). Quantitative characterization of CO2leakage process in faults is a key scientific problem and technical difficulty in the risk assessment of CCS projects.

Pressure monitoring is a common method to characterize the process of CO2leakage in faults.To investigate how faults affect the migration of fluids in petroleum reservoirs, Wiprut and Zoback(2002) evaluated the stress state and pore pressure acting on the major faults in four oil and gas fields in the northern North Sea.They proposed that locally elevated pore pressure due to buoyant hydrocarbons in reservoirs abutting the faults is one of the factors causing fault reactivation and hydrocarbon leakage in that area. Li et al. (2006) proposed a sequential coupling approach in the numerical study to investigate the thermo-hydro-mechanical behavior of the CO2sequestration system concerning the temperature,initial geological stress,injection pressure and CO2buoyancy.Their numerical results show that injection pressure sensitively affects the relative slip change of the fault. Xu et al. (2021) monitored the strain characteristics and permeability evolution of faults under stress disturbance by fiber Bragg grating (FBG) sensors and pressure pulses.To characterize the leakage channels(such as faults and wells),Hosseini(2019)analytically detected and characterized the vertical leakage from a fault of finite length using pressure data collected from monitoring zones. The closed-form analytical solution proposed by Hosseini(2019)allows us to estimate the leakage rate,length of leaky section of the fault and relative position of the fault with respect to the location of the monitoring well. Understanding the leakage detected by pressure monitoring from a leaking well or a leaking fault is a challenge in the risk assessment of CCS leakage.To solve this problem,Mosaheb and Zeidouni(2017)proposed a method based on pressure transient analysis to distinguish the leaking wellhead from the leaking fault and finally determined the location and hydraulic characteristics of the leaking point. Based on the common pressure transient analysis method and the normalized treatment of the observed pressure according to the time variable leakage rate, it is possible to determine whether features causing leakage are induced by a fault or semipervious caprock Mosaheb and Zeidouni (2018).

Another common method used to characterize the CO2leakage process in faults is temperature monitoring. CO2injection into saline aquifers induces temperature changes owing to processes such as Joule-Thomson cooling, endothermic water vaporization, and exothermic CO2dissolution, in addition to the temperature discrepancy between injected and native fluids (Zeidouni et al.,2014), which may induce a detectable temperature signal in the above-zone monitoring interval. Therefore, temperature can be used to detect the leakage of fluids from the CO2storage zone(Mao et al., 2017). Michael et al. (2020) carried out a controlled-release test at the in situ laboratory project in Western Australia by injecting 38 t of gaseous CO2into a fault zone with 336-342 m depth, and CO2arrival was detected by distributed temperature sensing at the monitoring well(7 m away)after approximately 1.5 d and an injection volume of 5 t. Mao et al. (2017) investigated the strength of the temperature signals for two scenarios in which leakage occurs either through a leaky well or through a leaky fault.In addition, Mao et al. (2017) analyzed two major mechanisms contributing to the temperature signal and obtained two mechanisms: a larger pressure drops at shallower depths and thinner caprock thickness will enhance the temperature signal, and the effect of capillary pressure will reduce the temperature signal.

Some CCS projects also use deformation or strain to monitor CO2leakage in faults. The CO2leakage or stress changes in advance of fault slip will be accompanied by in situ strains, so strain monitoring may contribute to ensuring safe storage. In this case, small strains have the potential to be a useful signal for monitoring(Murdoch et al., 2020). By monitoring the fault displacement during the fluid injection test of the Mont Terri clay-rich fault zone,transmissivity variations in the fault damaged zone were found to be associated with the highest slip value being observed at the interface between the low permeable fault core and the damaged zone, and this finding is important when evaluating the loss of natural seal integrity of CO2sequestration sites (Guglielmi et al.,2017). Methods for measuring in situ strain reviewed by Murdoch et al. (2020) include instruments that are grouted in the annulus between casing and wall rock (strain resolution of 1 × 10-7),portable strain sensors that are temporarily clamped to the borehole wall(strain resolution of 1×10-8),and strainmeters that are grouted in place (strain resolution of 1 ×10-9). Those in situ strain data measured with emerging instruments promise to fill an important gap between the episodes of fast strain rates measured by seismic data, and the slow strains measured over relatively long periods of time by interferometric synthetic aperture radar(InSAR)and global position system(GPS)(Murdoch et al.,2020). InSAR deformation monitoring successfully detected a surface uplift of magnitude of 5 mm per year above active CO2injection wells,and the uplift pattern extended several kilometers from the injection wells in the Salah Gas Project (Rutqvist et al., 2010).The InSAR data showed that surface deformation monitoring measured using differential InSAR has also proven to be one of the more useful monitoring methods deployed at Krechba (Davis,2011).

Each method has some limitations in monitoring the CO2leakage process in the fault. (1) Pressure monitoring is not sensitive to all leakages (Narendran et al.,1991; Yao et al., 2019). To evaluate the detection sensitivity of deep subsurface pressure monitoring, a baseline (nonleaky) model run was compared against ten different leakage scenarios,where the permeability of caprock was increased by factors of 2-100 (from 10-3to 10-1millidarcy) (Azzolina et al., 2014). The results of Azzolina et al.(2014) suggested that pressure monitoring would not be able to distinguish small leakage rates (i.e. less than 50 × baseline) from baseline conditions and that only large leakage rates (i.e. more than 100 × baseline) would be discriminated with sufficient statistical power (>99%). The study of Hosseini and Alfi (2016) also found that small leakages may not be detected by simple monitoring of absolute changes in pressure. (2) Unlike the pressure monitoring, which increases in response to both CO2and brine leakage, the temperature signal may differentiate between the leaking fluids. The strength of the temperature signal correlates with the leakage velocity, unlike the pressure signal, whose strength depends on the leakage rate(Zeidouni et al.,2014).Thus,temperature data will be more useful if collected along potential leaky wells and/or wells intersecting potential leaky faults.However, in field applications, the pressure and temperature of the storage reservoir and the temperature of the surface are known, while whether and where CO2leakage occurs are generally unknown and need to be determined, and the permeability and cross-sectional area of the vertical leakage path are also unknown (Zeng et al., 2012). Furthermore, the sensitivity of the temperature monitoring is not high, and this defect will greatly affect its monitoring effect at a low leakage rate. To evaluate the sensitivity of distributed temperature sensing(DTS)data to detect CO2leakage, Zhang et al. (2018) described the relationship between the CO2leakage rate and temperature response at DTS locations and found that the minimum detectable leakage rate was estimated to be 0.1 kg/s, limiting the applicable scope of the temperature monitoring. (3) Verdon et al. (2013) compared the geomechanical deformation induced by megatonne-scale CO2storage at Sleipner, Weyburn, and Salah, and found that the geomechanical responses of these sites are significantly different,highlighting the importance of systematic geomechanical appraisal prior to injection and comprehensive, multifaceted monitoring during injection at any future large-scale CCS operations(Verdon et al.,2013).In addition,the feasibility of obtaining useful strain signals during CO2injection cannot be established from available field data(Murdoch et al.,2020).There is an urgent need for comprehensive and multifaceted monitoring methods to be integrated organically in CCS projects.

Therefore,in this study,pressure sensors,FBG temperature and strain sensors were organically combined to monitor the CO2leakage characteristics in faults under different initial pressures by experiments. In particular, the internal strain response due to CO2leakage on the fault plane within the fault is first monitored in real time by FBG sensors. The conceptual model for the field setting in this experiment is the monitoring of temperature, pressure, and fault deformation when CO2leaks from a reservoir along a fault at a given initial pressure. Starting at the laboratory scale, this study quantitatively characterized the characteristics of reservoir CO2leakage along the fault to provide technical and theoretical support for on-site monitoring of CO2geological storage. From the experimental results, we found an interesting experimental phenomenon: CO2continued to leak in the fault, but the pressure and temperature of CO2remained unchanged,which continued for the first 1/3 of total leakage time (tall). This phenomenon is named temporary pseudo-sealing (TPS). Then, TPS behaviors were analyzed.Finally,we concluded that the TPS phenomenon is caused by the phase transition energy formed during liquid CO2leakage.Several factors contribute to TPS behavior generation: a small leakage aperture, a fault intermeshing zone and a compression zone caused by the Bernoulli effect.These results will be related to or extended to more realistic scenarios in a full-scale field setting from the following points. On the one hand, the discovery of TPS behavior can avoid some misjudgments for the leakage monitoring of CO2geological sequestration on site. On the other hand, the monitoring results of pressure, temperature and strain in this experiment show the advantages and disadvantages of each monitoring method. For example, this study found that when the TPS effect occurs, it is not reliable to monitor leakage solely by temperature and pressure.However,FBG strain sensing monitoring remains sensitive to CO2leaks in TPS behavior.

2. Experimental method

2.1. Experimental preparation

The shale rock sampled from the Longmaxi Formation in Sichuan Province, China, is shown in Fig. 1. The density, permeability and other physical parameters and mineral composition of the intact sample are shown in Table 1.The rock sample was processed into a cylinder with a height of 99.96 mm and a diameter of 49.97 mm,as shown in Fig. 2a. The remaining oil stains of rock were washed off with alcohol. The rock samples were dried at 60°C for 48 h and weighed every 8 h.When the difference between the two weighing values was less than 10 mg,the rock sample was considered to reach the drying standard.To obtain the rough fracture plane,we used the Brazilian splitting method to split the sample. Then, a threedimensional (3D) scanner was used to obtain the digital surface elevation data of the two fault planes,as shown in Fig.2b.According to the elevation data, the overall roughness coefficient of the fault plane was 23.2. In our calculation, the first derivative (Z2) of the average root-mean-square roughness (RMS) was used to calculate the joint roughness coefficient (JRC) of the fault surface. The calculation formula isJRC=32.2+32.47log10Z2,which is proposed by Tse and Cruden (1979). Then, high-precision, corrosion-resistant, and antistatic FBG sensors were used to monitor changes in temperature and strain during CO2leakage.These two grooves were 0.5 mm wide and 0.5 mm deep and were used to bury the FBG sensor string, as shown in Fig.2c.The grooves were carved by a fine cutting machine.The width of the blade is approximately 0.3 mm.A single cutting can form a groove of 0.5-mm width.The carving depth was controlled to approximately 0.5 mm when moving the blade. Thus, a 0.2-mm diameter FBG sensor can be embedded in grooves with a width and depth of 0.5 mm.Gaps between grooves and FBG sensors were filled with epoxy glue. The roughness coefficients of fault surface channels were 23.4 and 25.6, respectively (see Fig. 3). The FBG sensors were buried in the groove with epoxy glue, and then the original topography of the fault surface was restored, as shown in Fig. 2d. Then, the two rock samples were closed. The hoop FBG sensors and axial FBG sensors were pasted on the outside surface of the sample,as shown in Fig.2e and f.Then,silica gel was used to seal the rock sample,as shown in Fig.2g.Finally,the sample was placed in the experimental equipment. The FBG sensors and the FBG demodulator were connected, as shown in Fig. 2h. The instrument model of our demodulator is OPM-T1620.The FBG sensors have been calibrated by our group before being used in this study (Sun et al.,2017a,b;Fan et al.,2019).

Fig.1. The source location,photos and size of the rock sample: (a)Samples were taken from the Sichuan Basin,China; (b)The specific location of the rock samples in the Sichuan Basin; (c) A large and unprocessed block of rock; (d) The diameter of the cylindrical sample; and (e) The height of the cylindrical sample.

Table 1 The physical parameters and mineral composition of the sample.

Fig.2. Schematic diagrams of sample preparation:(a)The Longmaxi Formation shale sample with a diameter of 49.97 mm and height of 99.96 mm;(b)Split the sample using the Brazilian splitting method;(c)High-precision cutting:two thin grooves of 0.5-mm width and 0.5-mm depth were obtained;(d)The axial FBG sensors buried with epoxy glue in the groove and backfilled to the original shape;(e)Close the faulted sample,and paste the hoop FBG sensors at the middle height of the sample;(f)Paste axial FBG sensors on the outer surface; (g) Coat its outer surface with silica gel; and (h) The FBGs were welded with an optical fiber of the demodulator, and the sample was placed in the core holder.

2.2. Experimental procedure

The whole experiment was carried out at an initial temperature of 20.7°C and a static water confining pressure of 10.5 MPa.The setting of temperature, pore pressure and confining pressure in this experiment basically refers to the setting of relevant papers of the IEA-GHG Weyburn-Midale CO2monitoring and storage project. (1) The selection of confining pressure of 10.5 MPa in this experiment refers to the in situ net stress in the Weyburn reservoir, which ranges from 7 MPa to 15 MPa (Wilson et al., 2004). Hawkes and Gardner (2013) performed pressure transient testing for the assessment of wellbore integrity in the IEA-GHG Weyburn-Midale CO2monitoring and storage project.(2) The initial pore pressure in the rock formation surrounding their test interval was assumed to be equal to the hydrostatic pressure(12.66 MPa)in the well of Weyburn VIT#1(Hawkes and Gardner 2013). According to the initial pore pressure selected by Hawkes and Gardner (2013), we set an initial CO2pressure of 110 MPa. (3) When studying the CO2rock physics of the Weyburn-Midale geological storage project,the results of Njiekak et al. (2013) presented are all from measurements made at constant temperatures(23°C and 50°C)with pore pressures varying from 1 MPa to 25 MPa in each case. In addition, a controlled CO2release experiment in a fault zone at the in situ laboratory in Western Australia showed that the temperature of in situ CO2was in the range of 18-55°C (Michael et al., 2020). According to the CO2temperature and pressure settings of Njiekak et al.(2013)and Michael et al. (2020), our complete study involves temperatures ranging from 20.7°C, 25°C, 30°C, 35°C, 40°C, 45°C,50°C and 55°C, and the pressure range involves 1-10 MPa.However, due to the limitation of manuscript length and the principle of research topic uniqueness, the main finding of this study is that TPS occurs when liquid CO2leaks atPp0= 7-10 MPa. Therefore, only the experimental results of CO2leakage at 1-10 MPa and 20.7°C are included in this study. The experimental results under other temperatures will be sorted out and analyzed later and will strive for publication. The experimental equipment is shown in Fig. 4, which includes mainly a pressure loading system,temperature control system,permeability testing system, core holder, pressure acquisition system, and FBG strain and temperature data acquisition system. The maximum confining pressure of the equipment can be increased to 55 MPa,and the temperature control range is 0-100°C. The key parameters of the FBG sensors are shown in Table 2.

Before the experiment, the pressure data acquisition system and the FBG data acquisition system were debugged to ensure normal operation. Then, a vacuum pump was used to remove air and other impurity gases from the entire experimental system.Next, the pressure data acquisition system and FBG data acquisition system were turned on, and the pressure, temperature and strain data were collected. Then, a hydrostatic confining pressure of 10.5 MPa was applied. After the confining pressure was stabilized, a metering pump was used to inject CO2at the set pressure. CO2was stored in an upstream pressure vessel with a volume of 100 mL. When the upstream pressure vessel was filled with CO2at the set pressure, valve No. 4 was closed, as shown in Fig. 4. Finally, valve No. 3 was opened, and the leakage test was initiated. The outlet was connected to the atmosphere during the entire leakage experiment. To monitor the temperature, the FBG sensors were pasted on the surface of the downstream steel pipe near the core holder. Because the downstream was directly connected to the atmosphere, the pressure in the downstream steel pipeline was zero, so there was no strain caused by pressure. Although temperature and strain were recorded by FBG sensors, only the temperature changes but no strain changes in the downstream of the steel pipe. Therefore, a single set of temperature data was available in downstream steel pipes. Moreover, the FBG sensor data pasted on the sample were reduced due to the effect of temperature,and finally, single strain data were obtained. During the test,pressure sensors, FBG temperature sensors and FBG strain sensors were monitored in real time. The specific experimental conditions are shown in Table 3.

Fig.4. Schematic diagram of equipment.A high-precision metering pump injected CO2 at a specific pressure into a 100-mL storage container.Valve 3 was opened to allow CO2 to enter the fault and leak.The exit end of the fault is always connected to the atmosphere.The pressure was measured by the pressure sensor at the entrance and exit.The strain and temperature changes were monitored using FBG sensors.

Table 2 Key parameters of FBG sensors.

Table 3 Test conditions.

3. Experimental results

3.1. Pressure and temperature changes during CO2 leakage

When gaseous CO2with an initial pressure (Ppu0) of 1-5 MPa leaked,the upstream pressure decayed exponentially with elapsed time, as shown in Fig. 5a. AsPpu0increased, the rate of leakage increased.The slopes ofPpu0=1-5 MPa att=1 s were 0.9,3.7,8.4,16.3, and 25.8. The slope here refers to the inclination of the pressure-time curve with respect to the abscissa axis. The relationship between pressure and time can be expressed in the form of a unified exponential function:

wherePiis the real-time upstream pressure(MPa),and parametersaandbcan be calculated by the initial pressurePpu0:

When the initial phase of CO2was liquid(Ppu0=7-10 MPa),the relationship between upstream pressure and time showed multistage characteristics, as shown in Fig. 5b, which can be divided into five stages. That is, the pressure in stage I dropped sharply; the pressure in stage II showed a parabolic function that first increased and then decreased; the pressure in stage III remained unchanged; the pressure in stage IV dropped linearly;and the pressure in stage V decayed exponentially. Specifically, in stage I, the four pressure curves all dropped from the initial pressure to approximately 6 MPa within 5 s. Then, the four pressure curves all increased rapidly and then decreased slowly to 5.75 MPa.The increase in pressure at this stage was rare in CO2leakage in fault experiments. After the end of stage II, CO2continued to leak,but the pressure remained unchanged,and the four pressure curves were maintained at 5.75 MPa.Stage II was also a very special stage.Here,stages II and III were defined as fault“TPS”behavior.This TPS behavior refers to the pressure value remaining nearly unchanged,but CO2continues to leak. The fault appeared to be closed and no longer leaked CO2.However,the fault was actually still leaking CO2at this stage. At the end of stage III, the curve returned to normal,entering stage IV, in which the pressure decreased linearly with increasing leakage time. All four curves in stage IV were reduced from 5.75 MPa to approximately 3.5 MPa. Then, the curve finally entered the stage V of exponential decay.This stage was similar to the leakage curve when the initial phase of CO2was gaseous (i.e.Ppu0= 1-5 MPa). The pressure reduced from approximately 3.5 MPa-0 MPa in stage V. Among the four curves, the fault TPS stage(stages II and III),stage IV,and stage V respectively accounted for 1/3 oftall. The pink line (Ppu0= 10 MPa) dropped to a smaller value than the blue and yellow lines(Ppu0= 8 MPa, 9 MPa) in the stage I.So the pink line has a smaller amount of CO2than the blue and yellow lines after the stage I.These results in the pink line are lower than the blue and yellow lines.The lowest pressure reached by the pressure drop in the stage I of the pink line is because the maximum initial pressure difference(10 MPa)of the pink line leads to the largest fault opening. At this point, the pressure reached by the pressure drop in the stage I appears inflection point dominated by fault opening.WhenPpu0is less than 10 MPa,the initial pressure is dominant to control the pressure reached by the pressure drop in the stage I.In that time,the pressure value of the stage I increases slightly with the increase of the initial pressure.WhenPpu0equals to 10 MPa, the fault opening is dominant to control the pressure reached by the pressure drop in the stage I. At this point, the pressure value of the stage I decreases with the increase of the initial pressure.

The initial phase ofPpu0= 6 MPa was liquid but close to the critical pressure (5.75 MPa) of the gas-liquid phase. Therefore,whenPpu0= 6 MPa, the pressure leakage curve was between the leakage characteristics of gaseous and liquid CO2. The pressuretime curve atPpu0= 6 MPa also included stages I-V. As the duration of each stage was much shorter thanPpu0= 7-10 MPa,the five stages were not clearly divided in Fig. 5b. Therefore,Ppu0= 6 MPa was taken as the critical initial pressure. When the initial pressure is less than 6 MPa,the CO2pressure shows a smooth exponential decay.When the initial pressure is greater than 6 MPa,the pressure attenuation curve presents an obvious constant pressure stage.

Fig.5. Curve of upstream pressure over elapsed time during CO2 leakage:(a)The five curves from A to E represent gaseous CO2 leakage in the fault when Ppu0=1-5 MPa.The five tables in the figure are the specific parameters of the exponential fitting function;and(b)Pressure-time curve of 10 sets of leakage tests.When Ppu0=7-10 MPa,the pressure-time curve can be divided into five stages. The most special stages were stages II and III, where the fault exhibited TPS behavior.

When CO2leaks through faults, a nonisothermal effect, known as the Joule-Tom effect, will occur due to pressure reduction (the temperature of most gases will drop when freely diffused gas enters a low-pressure vessel from a high-pressure vessel) (Hosking et al., 2020). Therefore, temperature changes throughout the process should be monitored. As shown in Fig. 6a, whenPpu0= 1-5 MPa, the temperature change was very small within 1.2°C. The temperature change trend was closely related withPpu0.The largerPpu0is,the greater the temperature change(ΔT)is.The maximum temperature drops (ΔTmax) ofPpu0=1-5 MPa were 0.5°C, 0.6°C,0.65°C, 0.7°C, and 0.9°C, respectively. Each curve reached ΔTmaxwhen the leakage completed 1/3 oftall. After reaching ΔTmax, the temperature began to increase gradually, but the rate of temperature increase was significantly lower than when it decreased.

As shown in Fig.6b,the temperature change was more dramatic when liquid CO2leaked atPpu0= 7-10 MPa, with a maximum temperature drop of 2.5°C. The temperature drop curve and the pressure drop curve showed a stronger correlation. In stage I, the temperature dropped as the pressure dropped. In stages II and III,the pressure drop curve remained unchanged at 5.75 MPa,and the temperature curve was also stable at 20.156°C. Stages II and III were the stages defining TPS behavior. Interestingly, the temperature and pressure values at this time were exactly the critical temperature and pressure of the gas-liquid phase. Almost 85% of the temperature reduction was completed in stage IV. In stage V,the temperature drop continued for a certain time, and then the temperature rose to the initial value.

The temperature atPpu0=6 MPa was reduced by a maximum of 1.3°C during the leakage process,and the shape of the temperature drop curve was similar to the shape of the temperature drop curve atPpu0=7-10 MPa.

3.2. Fault strain response during CO2 leakage

Under differentPpu0, the hoop strain characteristics were tensile strain first,as shown in Fig.7.Then,the compressive strain zone appeared and gradually disappeared along with the tensile strain zone. In particular, whenPpu0= 7-10 MPa, liquid CO2leaked, the tensile strain zone reappeared at stage IV and disappeared at stage V after the first disappearance in the fracture area, as shown in Fig. 7a(7-10) and Fig. 7b(7-10). The compression zone did not disappear until the leakage was completed.Spatially, the tensile strain always appeared at the boundary between the fault plane and column side face,while the strain state on column side face at the non-boundary was always compressive strain. WhenPpu0increased from 1 MPa to 6 MPa, the extreme strain values increased significantly with increasingPpu0, as shown in Fig.7a(1-6)and Fig.7b(1-6).However,when the liquidPpu0increased from 7 MPa to 10 MPa, the extreme strain values were almost unchanged. Fig. 7 shows that at any value ofPpu0of liquid CO2, pressure and temperature will all enter the critical temperature (20.156°C) and pressure (5.75 MPa) at an instant when the leakage starts. As a result, the strain value hardly increased when thePpu0of liquid CO2increased from 7 MPa to 10 MPa.

The 3D spatiotemporal evolution diagrams of axial strain outside the fault and its corresponding two-dimensional (2D)strain cloud diagrams are shown in Fig. 8. When gaseous CO2leaked, the tension at the fault entrance led to fault opening, and the following compression at the exit led to fault exit closure. The phenomenon was most obvious whenPpu0=5 MPa.Theoretically,when gas enters the fault, the effective stress on the fault is reduced, and the entire fault is subjected to relative tensile strain.However, the Bernoulli effect occurred when CO2leaked through the fault, as shown in Fig. 9.

Fig. 6. Temperature changes during CO2 leakage. The temperature-time curves were highly correlated with the pressure-time curve: (a) When Ppu0 = 1-5 MPa, the maximum temperature drop during gaseous CO2 leakage was 1.2 °C; and (b) When Ppu0 = 6-10 MPa, the maximum temperature drop during liquid CO2 leakage is 2.5 °C.

Fig.8. (a)The 3D spatiotemporal evolution diagrams of the axial strain outside the fault and(b)Its corresponding 2D strain cloud diagrams.Compared with gaseous CO2(Ppu0=1-5 MPa) leakage, the compression zone of liquid CO2 (Ppu0 = 7-10 MPa) was obviously moved back to the outlet.

The Bernoulli equation can be written as

wherepis the pressure,ρ is the fluid density,v is the fluid velocity,gis the gravitational acceleration,his the height, andCis constant.

According to the Bernoulli equation, the pressure is low where the velocity is high, and the pressure is high where the velocity is low. When CO2flows through the fault plane, the pressure on the fault plane is reduced,which makes the fault plane closed together and forms a compression zone.The greater thePpu0of CO2was,the greater the outlet velocity was, and the greater the pressure drop on the fault surface. Therefore, a larger compression area formed.Because the outlet speed will increase with increasingPpu0, the center point of the compression zone will also move to the outlet end whenPpu0increases. Therefore, the Bernoulli effect not only led to the appearance of the compression zone, but also made the compression zone move toward the outlet asPpu0increased.When liquid CO2leaked, the tensile force at the fault entrance and its distribution were significantly wider than the tensile force at the fault entrance and its distribution of gaseous CO2. As shown in Fig. 9b-d, with the initial CO2leakage phase from the gaseous phase (5 MPa) to the gas-liquid critical phase (6 MPa) and then to the liquid phase(7-10 MPa),the fault compression zone obviously offset toward the exit. The center of the compression zone moved fromX=50-62 mm and 100 mm,whilePpu0increased from 5 MPa to 6 MPa and 7-10 MPa,respectively.The axial strains first showed tension at the inlet and no strain at the outlet because CO2did not completely penetrate the fault,and leakage was not initiated at the beginning of leakage. CO2temporarily accumulated at the fault entrance, which reduced the effective stress (tension strain occurred). When the effective pressure accumulated to the breakthrough pressure, the fault opening increased to the critical value.At this point, CO2quickly leaked from the inlet to the near outlet.Due to the Bernoulli effect, the CO2leakage causes the pressure of the fault plane near the exit to decrease and the two fault planes to close together and compress (the compression zone appears). The appearance of the compression zone led to tighter fault closure and smaller leakage apertures,which was an important reason that the pressure curves in stages II and III remained unchanged. In addition, the compression zone formed by the Bernoulli effect was similar to the lever fulcrum.The fulcrum will move back to the exit with the increase ofPpu0, and the lever effect will be more significant with the increase of the length of the front arm. As a result,when the front-end pressure is reached, the back end of the fulcrum will produce greater compression deformation.In addition,thePpu0of liquid CO2itself was larger than thePpu0of the gaseous phase, so the liquid compressive strain value was 3.5 times the compressive strain value of the gaseous phase.

The 3D spatiotemporal evolution diagrams of monitoring line 1 strain on the fault surface and its corresponding 2D strain cloud diagrams are shown in Fig.10. The roughness of monitoring line 1 was 23.4, which was close to the average of 23.2. The strain of monitoring line 1 showed that the tensile strain appeared at the inlet first,and then compression occurred at the outlet,which was similar to the space-time evolution of axial strain. However, the fault compressive strain at the outlet was nearly twice the fault compressive strain of the axial strain, which manifested that the fault plane outlet was the key position where the liquid CO2phase changed to the gas phase. Additional small compressive strain zones(X=25 mm andX=75 mm)were observed.All this suggests that the strain inside the fault is much more intense than the strain outside and that CO2is leaked mainly from the fault surface.

Fig. 7. 3D and 2D spatio-temporal evolution diagrams of strain (a) The 3D evolution diagrams of the hoop strain outside the fault and (b) Its corresponding 2D strain cloud diagrams.From bottom to top,they are the evolution diagrams of strain with time and position coordinates for Ppu0=1-10 MPa.Color icons were used to indicate the magnitude of strain. Warm colors, such as red, represent tensile strain, while cool colors, such as blue and purple, represent compressive strain. Along the X-axis, the strain change with the leakage time can be obtained. Along the Y-axis, the change characteristics of strain with the circumferential position can be obtained. The Z-axis represents strain.

Fig.10. (a) The 3D spatio-temporal evolution diagrams of strain in the monitoring line 1 on the fault surface and (b) Its corresponding 2D strain cloud diagrams.

The 3D spatio-temporal evolution diagrams of the monitoring line 2 strain on the fault surface and its corresponding 2D strain cloud diagrams are shown in Fig. 11. The roughness of monitoring line 2 on the fault surface was 25.6, which is larger than the roughness of monitoring line 1 (23.4). Fig.11a(1-6) and Fig. 11b(1-6) show the strain spatio-temporal diagrams of monitoring line 2 whenPpu0= 1-6 MPa, which was similar to the strain in Figs. 8 and 10. The fault inlet was under tension,and the exit was under compression. However, the distribution range and size of the compressional strain zone were larger than the distribution range and size of the compressional strain zone in Figs. 8 and 10 because the roughness of monitoring line 2 was larger, especially the intermeshing zone at the junction of 39 mm, and monitoring line 2 was more significant, as shown in Fig. 3. The fault intermeshing zone is “fault barrier”, which consists of a raised area and a depression area. As monitoring line 2 was rougher, it was a disadvantageous leakage channel compared with monitoring line 1. CO2needed to have a higher breakthrough pressure to leak from monitoring line 2 so that the strain variable was severe. During the subsequent leakage period, the leakage channel was rapidly established due to pressure breakthrough. At this time, the fault leakage rate was high, and the fault compression affected by the Bernoulli effect was more significant. The quantitative statement was that the compressive strain value of monitoring line 2 was twice the compressive strain value of monitoring line 1 and 4 times the compressive strain value of external axial strain, as shown in Fig. 11a(7-10) and Fig. 11b(7-10). The strain characteristics on the fault surface were strictly affected by the fluctuation of the fault surface.

Fig.3. Elevation curve of the position of two monitoring lines:(a)3D structure reconstruction based on elevation data obtained by a 3D scanner and(b)The elevation curves of the two monitoring lines arranged on the fault plane.There is a peak at X=35-40 mm in the lower half of the fault.The peak extends from monitoring line 2 to monitoring line 1 and gradually decreases.

Fig.11. (a) The 3D spatiotemporal evolution diagrams of strain in the monitoring line 2 strain on the fault surface and (b) Its corresponding 2D strain cloud diagrams.

4. Discussion

4.1. Causes of TPS behavior

As shown in Fig.5b,when liquid CO2leaked,the pressure curves appeared in five stages.In the stage I,the pressure and temperature curves dropped sharply to the critical pressure (5.75 MPa) and temperature point(20.156°C),as shown in Figs.5b and 6b.At this stage, high-density liquid CO2was directly leaked, which led to a rapid decrease in the pressure. Subsequently, CO2changed from a high-density liquid phase to a low-density multiphase.During CO2phase change, the density decreased and the volume of CO2increased (Tian et al., 2021). In the constant volume container for CO2storage, CO2phase change appeared as a pressure supply source, which is also called phase change energy. As the fault permeability was approximately 3 ×10-12m2, the leakage rate of CO2in the fault was very small. Part of the pressure supply source was in the mixed phase to maintain the current leakage rate,while the other parts kept the pressure in the upstream storage vessel unchanged, as shown in Fig. 5b. During the length of 1/3tall, the pressure and temperature curves remain constant at critical pressure and temperature, as shown in Figs. 5b and 6b. The pressure curves of stages II and III have not been observed in previous studies. We have taken the real gas effect into account when explaining the cause of the TPS behavior.Ppu0=10 MPa is selected as an example, and real-time compressibility factor is obtained from experimental temperature and pressure monitoring results,as shown in Fig. 12. The compressibility coefficient of CO2changed between liquid-CO2and gas-CO2during TPS period, and finally converted into the compressibility coefficient of gas-CO2. It also indicated that the compressibility coefficient of CO2increased gradually during this period.The following will demonstrate again that the compressibility factor of CO2will continue to increase in the TPS stage based on the real gas equation. We can see from the previous text,the CO2storage container in this study is a constant volume container (100 ml), so the volume (V) of CO2is a constant value.According to Fig.12,the temperature(T)and pressure(p)of CO2remain almost constant in the TPS stage.Therefore,in the real gas equationpV=ZnRT,p,V,RandTremain unchanged in the TPS stage, whereZis the compressibility factor and represents the degree to which the real gas deviates from the ideal gas behavior;nis substance amount(mol);andRis molar gas constant(also known as universal gas constant)(J/(mol k)). However, CO2leakage at the TPS stage will lead to a continuous decrease in the substance amount (n). In the TPS stage, due top,V,RandTin the real gas equation are constant,whilenis decreasing,Zneeds to be increased to maintain the equilibrium of the real gas equation. This is the conclusion that compressibility factor will increase in the TPS stage based on experimental results and theoretical analysis. As we know, the compressibility coefficient represents the volume deviation between an actual gas compressed and an ideal gas compressed at the same pressure. When the compressibility factor increases,the CO2pressure will increase when it is compressed into a constant volume container. The increased pressure and the pressure drop caused by the CO2leak just cancel each other out.Therefore, in the whole TPS process, the continuous decrease ofnand the continuous increase ofZmaintain the dynamic equilibrium of the real gas equation. This is the reason why the TPS behaviour occurs. At stage IV, liquid CO2had been completely transformed into the mixed phase, and then the mixed phase CO2was transformed into gaseous CO2. Pruess (2011) suggested that strongly nonisothermal effects can arise from decompression of gas-like subcritical CO2, which is the so-called Joule-Thomson effect.Fig.6b shows that 85%of the temperature drop is achieved in stage IV.The density of miscible CO2in stage IV was only slightly higher than the density of gaseous CO2. The phase transition from the miscible phase to the gas phase also resulted in the formation of a small pressure recharge source, which could only slow the rate of pressure drop but could not keep the pressure unchanged. As a result,the pressure-time curve of stage IV is in the form of a linear decline rather than a rapid exponential decay.All miscible CO2had been converted to gaseous CO2at stage V.At that time,the pressure drop curve was consistent with the gaseous CO2leakage curve,both in the form of exponential decay. At this stage, CO2leaks in the gaseous phase without phase transformation.

Fig. 9. Bernoulli effect of CO2 leakage in fault: (a) A common Bernoulli effect: the airflow inside the two pieces of paper was fast, the pressure was reduced, and the pressure difference between the inside and the outside was formed, making the pieces of paper close together. (b-d) Compression schematics of the fault plane drawn according to the position of the compression zone in Figs. 8-10 when Ppu0 = 5-10 MPa.

Fig.12. Real-time compressibility factor-time curve of CO2 when Ppu0 =10 MPa.

4.2. Conditions for TPS behavior

4.2.1. Aperture

The aperture size of the fault has a significant impact on the leakage rate in the fault (Liu et al., 2017). To understand the influence of different apertures on the TPS behavior, we compared the pressure monitoring results in the experiments with different apertures of Tian et al. (2021) and Ahmad et al. (2013a), as shown in Fig.13a.The detailed experimental designs of Tian et al.(2021)and Ahmad et al. (2013a) are shown in Table 4. Fig. 13a1 shows the experimental pressure curve of this study.The stage with a slope of 0 in the figure was the TPS stage. The experimental results of Ahmad et al.(2013a)are plotted in Fig.13a2.The initial temperature and pressure of his experiment were 20°C and 12 MPa, respectively, which were close to the temperature and pressure conditions of our experiment. The experiment of Ahmad et al. (2013a)studied CO2leakage with three nozzle diameters ofD= 3.2 mm,6.4 mm and 12.7 mm.Fig.13a2 shows that the smaller the diameter is, the closer the slope of the pressure curve at the intermediate stage is to zero.A more quantitative analysis is shown in Fig.14,and the relationship between slope and aperture in the shaded part of Fig.13a2 is expressed asyslope=-0.00115xaperture+0.00323.Fig.14 shows that the slope has a linear relationship with the aperture.When the aperture is 1.48 mm,TPS behavior will also be observed in the experiment of Ahmad et al. (2013a). The smaller the nozzle diameter is,the more likely the phenomenon of TPS will occur.Tian et al. (2021) also conducted experiments on CO2leakage characteristics under different nozzle diameters (1 mm and 3 mm), as shown in Fig.13a3.From their results,we can also observe that the smaller the nozzle diameter(1 mm)is,the closer the pressure curve slope in the intermediate stage is to zero, and the more likely TPS behavior is to occur.If only the pressure data were used to evaluate whether CO2leakage occurred,the CCS risk assessment during the TPS period would be misjudged.4.2.2. Initial leakage pressure

Fig.13. (a)Relationship curves of pressure and time at different leakage apertures.The smaller the leakage aperture is,the more likely it is to have TPS behavior during CO2 leakage.(b)Relationship curves of pressure and time under different initial leakage pressures.The pressure-time curves always coincided after the pressure dropped rapidly at the moment of the leak began.

Fig.14. Relationship curve of aperture and slope (pressure-time curve in shaded area in Fig.13a2).

The initial leakage pressure of CO2will determine the initial phase and viscosity of CO2,which will affect the initial leakage rate.Here,the influence of the initial pressure on the TPS behavior was also analyzed. Ahmad et al. (2013b) studied the pressure-time curve of CO2under different initial pressures when the nozzle diameter was 6.4 mm(see Fig.13b).The figure shows that after the pressure drops sharply, three different initial pressure curves overlap in the study of Ahmad et al. (2013b). In our study, whenPpu0= 7-10 MPa, the pressure curves also overlapped in the TPS stage. Based on the experimental results of Ahmad et al. (2013b)and this study, when the initial phase is a stable liquid, the initial leakage pressure cannot determine whether TPS behavior can appear. The pressure-time curves always overlapped after the pressure dropped rapidly. In the study of Ahmad et al. (2013b),Ppu0=8.5 MPa was within the initial pressure range in which TPS behavior occurred in this study,but TPS behavior was not found in their study. Therefore, when liquid CO2leaks, its initial pressure cannot determine whether TPS behavior can occur.

4.2.3. Fault intermeshing zone and the compression zone caused by the Bernoulli effect

There are faults/fractures or high permeability zones in the main capping layer of CO2reservoirs, which can cause CO2leakage(Namhata et al., 2017). There is some difference between CO2leaking through a fault and leaking through a pipe nozzle.Therefore, it is necessary to understand the influence of the particularity of fault structure on leakage separately. The main difference between fault leakage and pipe leakage is that the shape and pore size of the pipeline will not change during leakage,while the degree of fault opening and closing can change. According to the description of the compression zone in Section 3.2, the compression zone is distributed near the outlet, while the tension zone is distributed at the entrance. Therefore, the whole fault presents a state of open entrance and closed exit.The CO2leakage in the fault will be affected by fault closure at the exit and the leakage rate will be reduced.When the CO2leakage rate is slow,the pressure supply source (phase change energy) generated by the liquid CO2phase transition can maintain the balance between the CO2leakage rate and the unchanged pressure. Therefore, the appearance of the compression region will promote the appearance of TPS behavior.We know from Figs.2 and 3 that there is a large fault“barrier”plane aty= 40-50 mm along the fault. Fault intermeshing at the fault“barrier”area will make it difficult for CO2to flow,which makes the CO2leakage rate slower. Therefore, the phase transition energy formed by the phase change of liquid CO2in the TPS period can sufficiently fill the pressure drop caused by the leakage.

5. Conclusions

In this study, CO2leakage tests in faults at different initial pressures were carried out. The parameters such as pressure,temperature and strains were recorded throughout the whole process. The following conclusions can be drawn:

(1) When gaseous CO2leaked with an initial pressure of 1-5 MPa, the pressure and temperature will change dynamically during leakage.However,when liquid CO2leaked with an initial pressure of 7-10 MPa, the pressure and temperature in the first 1/3 oftallremained unchanged, i.e. the socalled TPS behavior defined in this study. This TPS behavior is observed only in this experiment, and whether the field setting can be observed remains to be further studied.

(2) This TPS behavior shows that CO2can leak through the fault even if the pressure and temperature are not reduced. The main reason for the TPS behavior occurs when the phase change energy generated by the liquid CO2phase transition can maintain the balance between the CO2leakage rate and the unchanged pressure.

(3) The following factors also contribute to the emergence of TPS behavior: (i) The smaller the leakage aperture is, the smaller the leakage rate is, and the more likely TPS behavior will appear.This small leak aperture size is approximately 0.2 mm in this study.(ii)There is fault“barrier”on the fault plane,so CO2leakage is blocked here, and the overall leakage rate is reduced. (iii) The compression zone created by the Bernoulli effect again slows the leakage rate. The combined effect of thesefactors leads to a small overall leakage rate,and the phase change energy formed by the phase transition of CO2is sufficient to fill the pressure drop.

Data availability

The experimental data used in our research are available from the corresponding author on request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The research was partially supported by the Major Project of Inner Mongolia Science and Technology (Grant No. 2021ZD0034)and the National Natural Science Foundation of China (Grant Nos.41872210 and 41274111).The equipment and methodology we have developed for this research have applied for a national invention patent (ZL 202110708668.1).