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Competitive Effects of Permeability and Gravity on the Drying- Out Process during CO2 Geological Sequestration in Saline Aquifers

Salt precipitation from the drying-out process has a profound effect on the well injectivity during the storage of carbon dioxide (CO2) in deep saline aquifers. Both gravity and reservoir heterogeneity have a significant impact on CO2-plume behavior and CO2 storage capacities. The collective effect of gravity and heterogeneity on the drying-out process by site-scale numerical simulation based on the Sleipner project had been investigated. Three site-scale permeability heterogeneous models and a fracture model had been built; simulation results showed that the gravity effect significantly increased the solid saturation at the injection well in the homogeneous model; changing the position of the injection well can change the distance that gravity can act and affect the amount of salt precipitation near the injection well. A novel conclusion is gravity and heterogeneity showed a mutual resistance relationship when considering the collective effect of gravity and heterogeneity on solid saturation. Gravity effects reduced the amount of salt deposited in the fracture model; at low CO2 injection rate, gravity force dominated CO2 flow; increased rock heterogeneity suppressed the production of salt precipitates; at high CO2 injection rate, viscous force dominated flow; and increased heterogeneity increased salt precipitation. This research is of important guiding significance for the design of site screening and injection schemes from the perspective of avoiding a large amount of salt precipitation and pressure build-up.


Introduction
It has been reported that unless there are immediate, rapid, and large-scale reductions in greenhouse gas emissions, limiting warming to close to 1.5°C or even 2°C will be beyond reach [1]. Greenhouse gases (GHG) mainly include carbon dioxide (CO 2 ), nitrous oxide (N 2 O), methane (CH 4 ), perfluorocarbons (PFCs), sulphur hexafluoride (SF 6 ), and hydrofluorocarbons (HFCs). Among all the greenhouse gases, CO 2 stands out as the most important GHG due to its excessive amount in the atmosphere compared to others [2]. The atmospheric concentration of CO 2 as of 2021 was at about 414 ppm, growing 100 ppm compared to that of 1958 [3]. In the near term, the effect of controlling the greenhouse effect by shifting the energy mix to less carbon-intensive alternative fuels and improving energy efficiency is limited [2]. Carbon-neutral and net-zero carbon emissions are a consensus long-term goal to reduce "global warming" [4,5]. Carbon Capture and Storage (CCS) is one of the effective technologies to mitigate the global warming effect [6,7]. CCS involves capturing CO 2 from energyrelated sources, compressing it, transporting it to a suitable storage location, and storing it in deep geological formations [8,9]. CCS is currently the only technology that allows the continued use of fossil fuels while reducing CO 2 emissions to the atmosphere [10].
The suitable geological formations that can carry out the CCS project include deep ocean, saline aquifers, depleted oil and gas reservoirs, unmineable coal seams, oil and gas reservoirs, and carbonation [10][11][12][13][14][15]. Deep saline aquifers are the most effective storage site due to their high storage capacity [16][17][18]. When CO 2 is injected into deep saline aquifers, the mutual solubility of the CO 2 -brine system increases the complex drying-out (water loss due to evaporation) and salting-out (salt precipitation begins to form due to the increase in brine saturation) process, once salts precipitate, the porosity and permeability diminish [19]. Salt precipitation can influence injectivity in a geological formation; monitoring pressure build-ups is a common method to evaluate the impact of CO 2 injection on well injectivity [20]. Some site tests [21][22][23] demonstrated the influences of salt precipitation on well injectivity.
Several laboratory studies have been performed by many scholars on the formation drying-out and salt precipitation with CO 2 sequestration. Of these studies, the position of salt precipitation in pores and the influence law of salt precipitation in pores on rock porosity and permeability are obtained by selecting cores with similar sites, changing fluid salinity, and the CO 2 injection strategy [24][25][26][27][28]. On the other hand, some scholars also use microfluidic models to study the mechanism of salt precipitation, especially the effect of the structure of the pore space on the location of salt precipitation and the process of accumulating salt precipitation generation [29][30][31][32]. However, it is found that the results of these experiments are controversial. Some scholars believe that salting has a great impact on CO 2 injection [25,27,33], while others believe that it has little impact [34] and even improves injectivity [35]. Ott et al. [36] believe that the reason for the dispute is that experimental domains have a limited volume and mass of salt that can be transported and precipitated within the domain, most of the experiments were carried out in a single primary drainage process, and small-scale tests underestimated the effect of precipitation. What is more, due to the limitation of scale, it is difficult for laboratory tests to consider the effects of gravity and the real heterogeneity of rock on the distribution of multiphase in the CO 2 -brine system [37]. In fact, according to the monitoring data of the site, when CO 2 is injected into the deep saline aquifers, the salt precipitation range can be tens of meters, and the gas migration front can reach hundreds of meters to kilometers [21,22]. Therefore, the fieldscale numerical experiment is helpful to overcome the scale defects of laboratory research.
The physical properties of the matrix and fluid and the interaction of various forces in the displacement process are the main factors controlling fluid flow in porous media [38]. In recent years, it has been widely studied to explore the influence of different parameters on the spatial distribution of CO 2 and brine [39]. The influence of different parameters on the salting-out process can be analyzed when the phase change involving the (dis)appearance of solid salt is recognized and the permeability changes from precipitation and salt dissolution [40]. These numerical simulation studies consider the sensitivity parameter including injection rate, initial brine saturation, salinity, water content, capillary pressure, relative permeability, temperature, and permeability [19,[41][42][43][44][45][46]. Recent research shows that capillary-driven backflow is considered a key mechanism that determines regimes of salt precipitation [47][48][49]. Norouzi et al. [50] per-formed a comprehensive sensitivity analysis on a wide range of parameters, including relative permeability and capillary pressure curves; injection flow rate and temperature; and initial salinity, porosity, and reservoir temperature to support the role of capillary pressure and capillary-driven backflow in salt precipitation.
The conditions for capillary-driven backflow are capillary pressure gradient larger than the viscous pressure gradient [36,51]. Therefore, how to break the balance between capillary pressure and viscous pressure is the key point for salting out. Capillary number (C a ) is used to quantify the influence of capillary dispersion, and it is defined as different expressions [11,[52][53][54]; changing parameters in the capillary number equation (such as injection rate of nonwetting phase and fluid viscous) has been shown to affect the stability of the two-phase displacement patterns [55,56].
The gravitational effect regulated by density difference becomes highly essential in the real porous media system since it is not flat and horizontal [57]. The pore-scale study conducted by Suekane et al. [58] finds that the effect of buoyancy on fingering growth activity in immiscible twophase flow displacements and buoyancy stabilizes or destroys fluid motion depending on fluid characteristics, injection direction, and capillary-viscous force competition. The gravity number (N gv ) is used to quantify the influence of the gravitational effect [38,54]. In the CO 2 -brine system, buoyancy-dominated flow between CO 2 and brine indicated increased vertical CO 2 migration and brine counterflow, as well as localized salt precipitation; the buoyancy effect is one of the most critical parts in affecting the distribution of both the CO 2 plume and the salt precipitation associated with it [59].
Reservoir heterogeneity has an impact on CO 2 -plume migration and trapping capacity [60]. Han et al. [61] conducted numerical simulations to explore the systematic effects of permeability heterogeneity on CO 2 trapping mechanisms and found that permeability heterogeneity influences buoyancy-driven CO 2 migration. The research by Green and Ennis-King [62] finds that the heterogeneity in the reservoir rock acts to retard buoyant migration by increasing the tortuosity of the migration pathways.
In summary, gravity and formation heterogeneity have been shown to have a substantial impact on saturation in deeper regions [37]. Both gravity and reservoir heterogeneity significantly impact CO 2 injectivity and migration and need to be incorporated into reservoir simulations to provide accurate predictions of both CO 2 -plume behavior and CO 2 storage capacities. This is of important guiding significance for site screening and injection scheme design from the perspective of avoiding a large amount of salt precipitation and pressure build-up. In this paper, the collective effect of gravity and heterogeneity on the drying-out process will be investigated by site-scale numerical simulation. The Sleipner site project was used as a research background for numerical simulations. In Section 2, different permeability heterogeneous models are built. In Section 3, numerical simulations are performed based on the models in Section 2. The results of the numerical simulation are given in Section 4.  [63]. The system was idealized as a symmetric two-dimensional (2D) domain perpendicular to the horizontal injection well with a screen length of 100 m ( Figure 1) [40]. Two sand layers and two shale layers were chosen to do the simulation (the area enclosed by a dashed line in Figure 1), and the thickness of the formation site was idealized at 88 m. Three different models were set to characterize the sandstone layer formation, and "sand" was used to simplify the meaning of "sandstone" (homogeneous model, fracture model, and three permeability heterogeneous models). The gas phase can rarely invade into cap rock (shale layer) due to the low permeability; the shale layer formation was kept as a homogeneous model. The homogeneous model in this research was the 52 m thick homogeneous sand formation overlaid by the 36 m thick homogeneous shale caprock. Hydrogeological parameters of sand formation and shale formation are given in Table 1. A 500 m horizontal fracture was built near the well in the sand formation to express the simple fracture model (Figure 2). In this paper, the fracture was set as a solid unit to represent the fracture characteristics by setting as large porosity as possible and certain permeability; hydrogeological parameters of the fracture are given in Table 1.
As for different heterogeneous models, the Sequential Gaussian Simulation (SGS) method was used to generate spatially correlated property fields [64]. The values generated by GSLIB (var) represent the logarithm (base 10) of the property, var = log 10 ðkÞ, where k means permeability [65]. The "var = 0" means that there is no modifier for the original rock permeability, a positive number means that the permeability increases, and a negative number means that the permeability decreases. In this study, three different permeability change intervals were set to characterize the strength of heterogeneity. Interval (-1.6, 1.2) indicated low heterogeneity of the sand layer, interval (-3.5, 2.5) indicated medium heterogeneity, and interval (-5, 4) indicated high heterogeneity. Permeability distributions of three models are given in Figure 3. The specific method was shown in Finsterle and Kowalsky's [66] research. In Figure 3, the homogeneous shale layer remains unchanged, the red circled area indicates a low-permeability zone near the injection well.

Space Discretization.
The model grid was generated with the MESHMAKER module of TOUGH2 as a horizontal (X -Z) grid [67]. The geological model had an X and Z dimension of 6,000 m × 88 m. The drying-out phenomenon is not expected to occur throughout the reservoir, but only close to the injection point. Therefore, the mesh of the model was only densified near the injection well. The space discretization for the 2D grid is presented in

Modeling Approach
For the boundary conditions, the right boundary was fixed at constant pressure to allow flow in and out; the other three boundaries were set as no-flow boundaries ( Figure 1). For the initial conditions, the formation temperature (T) was set at 37°C to maintain the isothermal condition. The injection well was 1,020 m below the ground, so the pressure was approximately 11 MPa in the injection well. The q in the field project was approximately 10 6 tons per year, corresponding to q = 0:3170 kg/s in the simulation, and q was 0.1585 kg/s for the half space in this study [40]. The total simulation time is specified as 1 year. Other parameters used in this simulation are listed in Table 1. Relative permeability function, capillary function, and porosity-permeability relationship were three governing equations of salt transport Var:  Table 2.
In Table 2, k rl is the liquid relative permeability, λ is the empirical parameter related to core size distribution, S l is the liquid saturation, S ls is the liquid saturation when saturated, S gr is the residual gas saturation, S lr is the residual liquid saturation, k rg is the gas relative permeability, P cap is the capillary pressure, P 0 is the air entry pressure, P max is the maximum capillary pressure, k 0 is the initial permeability, Γ is the fractional length of the pore bodies, and ϕ r is the fraction of original porosity at which permeability is reduced to zero.
In this paper, the gravity effect and the heterogeneity effect were two main factors of sensitivity analysis (SA) during case studies; solid saturation (S s ) was used as the response variable for SA. Descriptions of different simulation cases are given in Table 3. Parameter D means the distances between the injection well and the caprock; it is related to the gravity effect on S s ; the specific content is given in Section 4.1.1.

Simulation Results and Discussion
Numerical simulations were performed using the TOUGH2 code and the related fluid characteristic module ECO2N [40,67]. The TOUGH2-ECO2N module was used to simulate the value of S s in the injection well when CO 2 was injected into deep saline aquifers. ECO2N represents a mixture of three phases: a liquid phase rich in water, a gas phase rich in CO 2 , and a solid salt. The simulation time was 3:1536 × 10 7 s (1 year) and did not consider temperature changes in the system. The results of the numerical simulation are given below.

4.1.
Effect of Gravity on S s . Case 1 and Case 1-1 were contrasted together to research the effect of gravity. Gas saturation (S g ) (mainly gas CO 2 saturation) and S s were given as contour maps after 3:1536 × 10 7 s simulation. The injection well was chosen as the monitoring point, the time evolution of S s and the mass of salt at the injection well were picked up from the simulation output file by [66], and the mass of salt denotes salt mass in the aqueous phase and solid phase. Figure 5 shows the simulation result of Case 1; Figure 6 shows the simulation result of Case 1-1. Due to the saltingout phenomenon that occurs particularly in and close to the borehole [24], Figure 7 shows the comparison result of two cases at the monitoring point (injection well).
In Figure 5(a), gas phase (CO 2 ) invades into sand formation evenly in the horizontal direction when there is no gravity effect. In the vertical direction, the caprock blocks the gas invasion into the upper layer due to its low permeability. After 1-year simulation, the maximum CO 2 migration line is about 2,200 m from the injection well in the horizontal direction ( Figure 5(a)). Salt precipitation occurred mainly near the injection well (0~6 m in the horizontal direction, -72~-60 m in the vertical direction). The maximum value of S s is located in the injection well; the S s values in each element are in the range of 0 to 0.1056 ( Figure 5(b)). Like the S g contour map, the S s contour map also shows symmetrical features. In Figure 6(a), the distribution of the gas phase is asymmetric when it comes to the gravity situation, and the Table 2: Governing equations of salt transport and flow behavior.

Description Equation Parameters
Relative permebility function, van Genuchten-Mualem model [68,69] Porosity-permeability relationship for tube-in-series model [70]  5 Lithosphere distribution of CO 2 presents the shape of a funnel. CO 2 is gathering at the bottom of the shale formation due to the buoyancy and low permeability of the caprock. The maxi-mum CO 2 migration line is about 3,000 m from the injection well. The preferential flow of CO 2 and the gathering of CO 2 at the bottom of the shale formation can be attributed to the effect of gravity. The preferential flow caused by gravity leads to a higher salt accumulation near the injection well ( Figure 6(b)) compared to the case without gravity ( Figure 5(b)); S s values near the well are at the range of 0 to 0.1584. The contour map of S s also shows asymmetrical features; the S s distribution has an upward trend due to the gravity effect.
Specifically, the gravity effect caused additional salt precipitation in the injection well; the value of S s is increased ΔS sG (+0.0529) due to the gravity effect (Figure 7(a)). In this paper, positive values are used to indicate a rising trend, and negative values indicate a decreasing trend. In Figure 7(b), the mass of salt in the injection well is increased ΔM G (+22.8 kg) when considering the gravity effect. The consensus mechanism about the salt aggravating near the injection well is the brine backflow around the well caused by the capillary difference [43]. In Figure 7, the value of S s and the mass of salt are in the same trend of change; the change in the mass of salt can be observed by the change in S s .  In Figure 9, the gravity effect makes a significant increase of S s at the injection well in all four case studies. ΔS 1 sG , ΔS sG , ΔS 2 sG , and ΔS 3 sG mean the S s increment caused by gravity effect in four different D simulations. S s decreases with the decrease of parameter D when considering the gravity effect in homogeneous simulations (red line in Figure 9). However, the location of the well has a very small effect on S s when the gravity effect is ignored (blue line in Figure 9). The increment of S s caused by the gravity effect is weakened with the decrease of D (from ΔS 1 sG = +0:0677 to ΔS sG = +0:0529, ΔS 2 sG = + 0:0418, and ΔS 3 sG = +0:0056). Compared to Figure 6(a), the contour map of CO 2 is not changed obviously when the location of the injection well is changed, they all show the shape of the funnel, and the maximum migration line of CO 2 is about 3,000 m from the injection well ( Figure 10). The above results indicate that salt precipitation can be reduced by shortening the distance from the injection well to the caprock (D), without affecting the CO 2 storage efficiency.
In the laboratory experiment, the limit size of the sample would limit the flow caused by gravity, and it would obtain a much smaller S s value to compare to the real site situation.  Tables 1 and 2. This section only considers the effect of formation heterogeneity on S s and does not consider the gravity effect. The simulation results are given below after a 1-year simulation.

Effect of Formation
In Figure 11(a), the fast flow of CO 2 due to the horizontal fracture is visible and the fracture is filled with CO 2 after a 1-year simulation (S g = 1:0). The maximum migration line of CO 2 is about 2,800 m in the horizontal direction, which is larger than that in the homogeneous model in Figure 5(a). In Figure 11, the black circle areas show low S g zones. The low S g zones in Figure 11(a) indicate high liquid saturation (S l ) zones, and local high S l zones are formed in both the upper and lower parts of the fracture. In Figure 11(b), the local fast flow in the fracture makes the value of S s unusually high in the injection well. Except for injection wells, there is no salt precipitation in other areas (in Figure 11(b), the S s only appear in the injection well mesh). The S s value shows a linear rise to 0.746 in the injection well when the simulation ends (Figure 12(a)). However, the increase in salt precipitation did not reach a steady state. If the simulation time prolongs to t s , the S s value could rise to 1.0 and lead to the complete blocking of the pore space at the time of 4:4384 × 10 7 s (t e in Figure 12(b); t e means the time that salt precipitation no longer increases; t s means 2-year simulation time). The S s difference compared to the homogeneous model in the 1-year simulation is ΔS sF (+0.6400) (Figure 12(a)). In Figure 12(b), the increment of S s caused by the fracture in this study can reach the maximum ΔS sF2 value (+0.8940) if the simulation time has been extended. This complete blockage of the fracture structure is observed by several laboratory experiments, and solid precipitates mainly near the well where a high gas flow rate is maintained [30,71,72]. It is necessary to avoid fractures near the injection well when choosing the storage site although these fractures will not lead to CO 2 leakage.

Permeability Heterogeneous Models.
Case 2-1, Case 2-2, and Case 2-3 were joined together to research the effect of heterogeneity with three permeability heterogeneous models. Different grid permeabilities were used to display the formation heterogeneity. Three different permeability distributions are given in Figure 3. The different permeability change intervals indicate different heterogeneities. The parameters used for the simulation are given in Tables 1  and 2. The simulation results are given below.
Compared to Figure 5(a), contour maps of S g in Figure 13 are all showing asymmetrical properties. Compared to simulation conditions, the difference in CO 2 distribution is mainly 7 Lithosphere attributed to the influence of heterogeneity. In Figure 13(a), S g in the lower part of the sand formation is greater than that in the upper part of the formation, because there are highpermeability channels in the lower part (Figure 3(a)). More low-permeability zones will be formed with increasing formation heterogeneity (Figures 3(b) and 3(c)). These lowpermeability zones will be formed low S g areas, and more liquid is surrounded by gas, which indicates the preferential flow in the heterogeneous sand formation (Figure 13(b) and Figure 13(c)). Like the preferential flow caused by gravity, the preferential flow caused by the heterogeneity of the formation also increases the distance of CO 2 migration, from 2,200 m in the homogeneous model ( Figure 5(a)) to 2,800 m in the heterogeneity model ( Figure 13). Figure 14 shows the time evolution of S s in the injection well for three different heterogeneity models and one homo-geneous model. Compared with the S s value in the homogeneous model, the heterogeneous model causes a significant increase in S s at the injection well. As heterogeneity increases, the increase in S s increases from ΔS sH1 (+0.0045) to ΔS sH2 (+0.0077) and ΔS sH3 (+0.0080) (Figure 14). This means that the stronger the heterogeneity, the more salt precipitates at the injection well. This is consistent with previous research [73]. When the results of gravity effects are compared with the results of heterogeneity effects, the independent influence of formation heterogeneity on the S s value is much lower than that of gravity effect and fracture heterogeneity effect in this study.  Figure 3. The simulation results are given below after a 1-year simulation. In Figure 15, there are two significant preferential flows in the sand formation. The gathering of CO 2 at the bottom of shale formation means the preferential flow is caused by gravity; the local high S g flow passage in the horizontal direction means the preferential flow caused by fracture (Figure 15(a)), and the asymmetric sawtooth migration of CO 2 means the preferential flow caused by heterogeneity (Figures 15(b)-15(d)). The maximum CO 2 migration lines in these three different heterogeneity models are all more than 2,200 meters. However, this distance decreases with increasing heterogeneity, which shows the opposite result in Figure 13. Compared to Figure 6(a), the joining of gravity and heterogeneity decreases the CO 2 migration line in the horizontal direction; heterogeneity shows a resistance effect of the CO 2 migration line caused by the gravity effect.
The fracture is full of gas, and the upper and lower parts of the fracture are areas of high water saturation (Figure 15(a)). The black circle area in the figure is the area of high water saturation; the phenomenon of residual trapping of liquid is more obvious in the case of stronger heterogeneity (Figure 15(d)). These high water saturation zones could supply the additional mass of salt to the injection well and cause the accumulation of salt deposits [71,72]. Figure 16 shows the time evolution of S s at the injection well for four different heterogeneity models. In Figure 16(a), the increase in S s in the fracture model is ΔS sF1 (+0.6400); the increase in S s in the joined model is ΔS sFG (+0.6230). This reduction can be attributed to the only difference between the two cases (gravity). In Figure 16(b), the independent effect of gravity makes S s increase ΔS sG (+0.0520). However, the S s value shows a downward trend when considering grav-ity and heterogeneity together. Among these three different heterogeneity simulations, the reduction of S s compared to the homogeneous simulation is ΔS sGH1 (-0.0220), ΔS sGH2 (-0.0410), and ΔS sGH3 (-0.0480), respectively. It means that the stronger the heterogeneity, the fewer salt precipitates. This is a new relationship about salt precipitation with heterogeneity and shows the opposite result to Figure 14 and previous research [73,74]. The only difference between Figures 14 and 16(b) is the presence or absence of gravity.
The gravity effect increases S s in the homogeneous model but decreases S s in the fracture model. The value of S s increases with the heterogeneity when the model is without gravity effect but decreases with the heterogeneity when the model is with gravity. These two different influent ways of heterogeneity are not studied before, and it should be given an in-depth understanding of heterogeneity and gravity.

Mutual Relationship of Gravity and Heterogeneity.
In the last part of research, the value of S s would be increased if there is only one influential factor. The S s increment caused by gravity is ΔS sG (+0.0520); the S s increment caused by fracture heterogeneity is ΔS sF2 (+0.8940); the maximum S s increment caused by formation heterogeneity is ΔS sH3 (+0.0080). In this study, gravity will have a dominant effect on the value of S s when considering both gravity and formation heterogeneity, and fracture heterogeneity will have a dominant effect on the value of S s when considering both gravity and fracture heterogeneity. It is a key point to study the importance of gravity for salt precipitation compared to the importance of heterogeneity.
Flow behavior in porous media is controlled by gravity force, viscous force, and capillary force [38]. The capillary/ viscous ratio (N cv ) controlled the backflow of the brine and affected the amount of salt precipitation [47,75]. The gravity/viscous ratio (N gv ) indicates the relative importance of the viscous and gravity forces; N gv is also called the gravity number [38]: where k v is vertical permeability, L is the length of the storage aquifer, Δρ is the density difference, g is the acceleration of gravity, H is the width of the storage formation, q is the total flow velocity, and μ is the viscosity. Zhou et al. [38] express immiscible displacements without gravity effect as N gv ≈ 0. In Equation (1), N gv will decrease with the increasing q. The small value of N gv means the small dominant in gravity flow. Two ways can be used to change the effect of gravity on S s : (1) change the dominant of gravity force; (2) keep the gravity as the dominant force (low q) but change the acting distance of the gravity (Section 4.1.1). According to Equation (1), the gravity dominant flow could be decreased by increasing the injection rate q. Case 4 series, Case 5 series, and Case 6 series were joined together to research this problem (Table 4). Except for q, other parameters were consistent  Figure 17 is the S s value at the injection well for different injection rates in three different models; the minimum heterogeneity model is used here (permeability change interval is -1.6~1.2). ΔS sG , ΔS 4 sG , ΔS 5 sG , and ΔS 6 sG indicate the S s increment caused by gravity effect; ΔS sH1 , ΔS 4 sH1 , ΔS 5 sH1 , and ΔS 6 sH1 mean the S s increment caused by the minimum heterogene-ity effect. The value of S s decreased as q increased in all three models; this is a common result of many scholars [19,43,44,73,76]. The gravity effect and the heterogeneity effect both can cause the S s to increase at the injection well in all four q simulations. However, the increase of q would reduce the S s value increment caused by the gravity effect (from ΔS sG = +0:0520 to ΔS 6 sG = +0:0010) and heterogeneity effect (from ΔS sH1 = +0:0045 to ΔS 6 sH1 = +0:0012). The increase in 10 Lithosphere S s value caused by gravity is greater than that caused by heterogeneity in situations of 0.1585 kg/s, 0.22 kg/s, and 0.28 kg/ s, which means that gravity has a dominant effect on solid aggravation. The difference in increment caused by gravity and heterogeneity in each q simulation is slowly shrieking.
When it comes to the situation of 0.35 kg/s, the increase in the S s value caused by gravity (ΔS 6 sG = +0:0010) becomes smaller than that caused by heterogeneity (ΔS 6 sH1 = +0:0012); the gravity no longer has a dominant effect on solid aggravation. This is mainly due to the high q that decrease gravity dominant, and the viscous force began to show a dominant force.   Figure 16: Time evolution of S s at the injection well for four different heterogeneous models: (a) time evolution of S s for fracture heterogeneity; (b) time evolution of S s at the injection well for three different heterogeneous models when considering the gravity effect.

Lithosphere
In Figure 18, ΔS 6 sGH1 , ΔS 6 sGH2 , and ΔS 6 sGH3 mean the S s increment in three heterogeneous models compare to the homogeneous model when the gravity is considered. The S s value is increased with the heterogeneity enhancement (from ΔS 6 sGH1 = +0:0022 to ΔS 6 sGH2 = +0:0037 and ΔS 6 sGH3 = +0:0039). This means that the stronger the heterogeneity, the more salt precipitates, which is similar to Figure 14 and opposite to Figure 16(b). The only difference between Figures 18 and 16(b) is the value of q.

Conclusions
This paper researched the effect of gravity and heterogeneity on salt precipitation by using the numerical simulation method. The effect of gravity on salt precipitation was studied by changing the position of the injection well and determining whether to consider gravity. The effect of heterogeneity on S s was studied by building four different heterogeneous models. The collective effect of gravity and heterogeneity on S s was studied, which provides more information on the effect of formation heterogeneity. The main conclusions obtained from this study are as follows: (i) Gravity has a great effect on preferential flow, which would influence the accumulation of salt precipitation near the injection well. The preferential flow caused by the gravity effect increased the S s value in the injection well and changed the solid distribution in the sand layer compared to the simulation without the gravity effect. The influence of gravity could be reduced by changing the position of the injection well, that is, reducing the distance from the injection well to the caprock. Furthermore, in  Figure 17: S s value at the injection well for different injection rates. 12 Lithosphere the laboratory experiment, the limited size of the sample would underestimate the effect of gravity on S s . This would underestimate the effect of salt precipitation compared to actual site conditions (ii) Formation heterogeneity has a significant effect on S s . The fracture model is the most common heterogeneous model used in both laboratory experiments and site-scale simulations. The fracture near the injection well caused an abnormal increase in salt precipitation when not considering the gravity effect. If the injection time is long enough, the maximum S s value can increase to 1.0. Three different permeability heterogeneous models had been built according to the permeability range. When the gravity effect is not considered, the preferential flow of the formation increased with increasing heterogeneity; the stronger the heterogeneity, the greater the amount of precipitation near the well (iii) There is a competitive effect between gravity and heterogeneity on the value of S s . The gravity effect decreases S s in the fracture model. When it comes to heterogeneous models with gravity, salt precipitation decreases with increasing heterogeneity. This conclusion is opposite to simulation results without gravity effect in heterogeneous models. Fracture heterogeneity would always keep a dominant effect on S s due to the high S s increase at the single effect simulation; gravity effect can limit preferential flow caused by the fracture. Formation heterogeneity has a low effect on S s compared to the gravity effect in a low q situation. The heterogeneity effect can limit the preferential flow caused by gravity (iv) In addition to reducing the distance from the injection well to the caprock, the gravity effect can be also reduced by changing the dominant flow caused by gravity. At high q, viscous forces will control fluid distribution, and gravity forces will not dominate the flow. When heterogeneity becomes the dominant effect on S s , the amount of salt precipitation and the intensity of heterogeneity are positively correlated, which means that the S s value will increase with the increases in heterogeneity (v) The results of this article can give some inspiration to the site project. Reducing the distance from the injection well to the caprock can effectively reduce salt precipitation at the injection well. Fractures near injection wells must be avoided, and they can lead to large accumulations of salt deposits. At low q, gravity forces will dominate CO 2 flow; heterogeneity, in turn, inhibits the growth of salt precipitation in injection wells. Regions with strong heterogeneity can be chosen to inject when the q cannot be increased. At high q, viscous forces dominate the CO 2 flow, and selecting a relatively homogeneous formation injection helps reduce salt precipitation. If possible, increased q can effectively reduce salt precipitation under certain formation conditions Nomenclature D: Distances between the injection well and caprock g: Gravity k: Permeability k 0 : Initial permeability k a : Absolute permeability k r : Relative permeability k rg : Gas relative permeability k rl : Liquid relative permeability N gv : Gravity/viscous ratio p: Porosity