Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO<sub>2</sub> Geological Storage Process

Ren, Jie; Feng, Di

doi:https://doi.org/10.1155/2021/2809467

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Volume 2021 | Article ID 2809467 | https://doi.org/10.1155/2021/2809467

Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO₂ Geological Storage Process

Jie Ren¹and Di Feng²

Academic Editor: Zhanbo Cheng

Received01 Nov 2021

Accepted10 Dec 2021

Published21 Dec 2021

Abstract

The sensitivity analysis of the salting-out effect on well injectivity is a significant work in the research of geological storage of CO₂ in deep saline aquifers, which is helpful in the selection of storage sites and the design of the injection strategy. We conduct a detailed sensitivity analysis about the salting-out process using the local sensitivity method and two global sensitivity methods. Sensitivity coefficients showed that brine salinity (X_NaCl) has the highest sensitivity and interaction effect, the CO₂ injection rate (Q_CO2) has a greater influence in the early stage of the salting-out process and a smaller influence in the end stage, and the other three parameters (empirical parameters related to the pore distribution m, the liquid residual saturation in the relative permeability function S_plr, and the liquid residual saturation in the capillary pressure function S_clr) have a smaller sensitivity. This paper also analyzes the calculation amount of different sensitivity methods and suitable ways of obtaining the sensitivity coefficient and reveals the following. (1) The sensitivity coefficient changes dynamically with time, if only the sensitivity of the final state is taken into account on a long-time physical process, and some sensitive parameters during the process may be neglected. (2) The selection of the sample size should be based on the convergence of multiple calculations, and the results of the empirical calculation are uncertain. (3) The calculation of Sobol sensitivity is complicated, the results calculated by surrogate model depend on whether the sample is representative enough; on the other hand, it is feasible to use S_ti-S_i approximation to characterize the second-order sensitivity to reduce the computation. The research results not only reveal the sensitivity of the parameters related to the injection well salting-out problem during CO₂ storage in deep saline aquifers but also guide the calculation of global sensitivity analysis with a similar physical process.

1. Introduction

Geological storage of carbon dioxide (CO₂) is an effective way to mitigate the effect of global warming [1]. Because of its wide distribution and large storage capacity, the deep saline aquifer is considered as an effective site for large-scale CO₂ geological storage [2]. In the near and medium-term, the main interest of carbon sequestration technology is to solve the problem of low storage capacity, and in the future, deep saline aquifers are the main technology of carbon sequestration [3]. Currently, CO₂ geological storage has not been commercialized due to the high construction cost. There are broad prospects for CO₂ geological sequestration in deep saline aquifers because lots of countries have formulated strict carbon emission reduction plans [4] and the implementation of carbon pricing makes CO₂ sequestration profitable.

The dissolution of CO₂ in water and the dissolution of water in CO₂ occur at the same time in the CO₂-brine system [5]. Although the solubility of water in CO₂ is low under site conditions, this dehydration process cannot be ignored when a large amount of dry CO₂ fluid is continuously injected into the rock formation [6]. When CO₂ is injected into the deep saline aquifer with higher salinity, it removes the water from the brine and increases the concentration of the brine; in turn, salt crystallization occurs when the concentration of the brine reaches the saturation limit [6–9].

At present, there are few site projects sealed in deep saline aquifers. According to statistics, large-scale site projects will enter the explosive period after 2020 [3]. Most of the current research on the geological storage of CO₂ in deep saline aquifers focuses on the exploration of CO₂ migration law, storage mechanisms, and risk assessment of leakage [10–14]. The monitoring data from the site project show that the salt precipitation near the well is part of the low permeability zone, which causes the accumulation of injection pressure and reduces the CO₂ injectivity [15]. Therefore, with the development of a large number of CO₂ storage projects in the deep saline aquifers, it is necessary to screen and evaluate the potential sites from the point of view of the impact of salting out, to provide a basis for site storage potential evaluation and site selection.

The main purpose of studying the phenomenon of salting out is to study the effect of salt precipitation on the permeability of rock formation. Verma and Pruess [16] proposed to transform the relationship between porosity and permeability into the relationship between solid saturation (S_s) and permeability, and the value of S_s indicates the percentage of volume of NaCl crystals in the pores of the rock. According to the conservation of mass, Pruess [17] gives a method for calculating the S_s value, so that the study of salting out can be transformed into quantitative research of S_s.

Sensitivity analysis of the parameters affecting S_s of the injection well is the focus of the research on the salting-out effect at present. Miri and Hellevang [18] summarize the research results using simulation studies for the salt precipitation induced by CO₂ injection. These numerical simulation studies consider sensitivity parameters including injection rate, initial brine saturation, salinity, water content, capillary pressure, relative permeability, temperature, and permeability. [19–25]. The above studies are all local sensitivity analysis considering a single factor and cannot give the sensitivity comparison among the parameters and cannot get the effect of the interaction between the parameters on the S_s.

The global sensitivity analysis method can not only examine the influence of input variables on response variables but also examine the interaction of input parameters and the influence of multiparameters on response variables. The commonly used global sensitivity analysis methods include the Morris method [26] and the Sobol method [27] based on variance analysis. Jung et al. [28] and Wainwright et al. [29] conducted a global sensitivity analysis using the Morris method to evaluate the sensitivity of the leakage signal (pressure disturbance) to the parameters of the geological storage model of CO₂. Zheng et al. [30, 31] carried out a global parameter sensitivity analysis of the CO₂ migration process in deep saline aquifers and compared the Morris method, the Sobol method, and other sensitivity analysis methods. It is found that the sensitivity arrangement of the input variables is different when different response variables are selected. Sobol’s method has high accuracy, but the amount of calculation is too large. Wang et al. [32] conducted a global sensitivity analysis to evaluate the sensitivity of clogging signals (S_s) to model parameters, but they use the kriging surrogate model to simplify the migration dissolution process of CO₂ injection into the deep saline aquifers to simplify the calculation of Sobol’s method.

In this study, we conduct a more detailed analysis, using the same salting-out forward model developed by Wang et al. [32]. Firstly, we conduct a sensitivity analysis based on the local sensitivity method and two global sensitivity methods. Then, the influence of the selection of calculation parameters on the results of sensitivity analysis is discussed. An additional interpretation is provided for the local and global sensitivity methods. Finally, differences between the Sobol methods calculated from hydrogeological forward simulation and surrogate model are compared. The research results not only reveal the sensitivity of the parameters related to the injection wells salting-out problem during CO₂ storage in deep saline aquifers but also guide the selection of calculation parameters for similar sensitivity analysis, such as the process of heat extraction, energy storage, and evolution analysis of geological parameters [33–36].

2. Methodology

2.1. Modeling Approach of the Salting-Out Process

A radial geological model was built to simulate the salting-out process. The model used for sensitivity analysis is the same as Wang et al.’s model [32]. Assume that supercritical carbon dioxide (scCO₂) is injected into a homogeneous, anisotropic deep saline aquifer at a constant injection rate (Q_CO2). The thickness of the storage layer is 100 m, and the horizontal distance is 2,500 m. The radius of the injection well is 0.3 m, and it is 11.5 m from the bottom of the model. The one-quarter concept model is shown in Figure 1. In the horizontal direction, the injection well is the first unit with a unit size of 0.3 m, followed by 50 logarithmic size increasing units; in the vertical direction, the injection well is 11.5 m above the center of the bottom boundary element with a thickness of 1 m, and the thickness of the bottom and top units is 2 m. Other parts are evenly divided into units with a thickness of 5 m. The specific divided grid is shown in Figure 2; the upper and lower borders and right borders are sealed as no-flow boundary conditions. The parameters of the model used for simulation are given in Table 1.

The TOUGH2/ECO2N module is used to simulate CO₂ migration in deep saline aquifers and the salting-out process due to the miscibility of water and CO₂ [17], and the injection time is set at 100 days. In the sensitivity analysis, we choose five parameters as input parameters: CO₂ injection rate (Q_CO2), salinity (X_NaCl), empirical parameters related to pore distribution (m), liquid residual saturation in the relative permeability function (S_plr), and liquid residual saturation in the capillary pressure function (S_clr). Table 2 shows the ranges of reference parameter for sampling during sensitivity analysis. We assume a uniform distribution within the range of each parameter. From current researches, the salting-out problem can clog the gas flow path and reduce the CO₂ injectivity [24, 39, 40]. According to the VP model, the gas injectivity in the salting zone varies with the solid saturation value S_s [16], so S_s is used to map the CO₂ injectivity and as the response variable for the sensitivity analysis. We set the injection unit as an observation point and S_s as a function of time in the reference case shown in Figure 3.

Figure 3 presents the time evolution of S_s at the observation point, from 10 seconds to 100 days after injection of scCO₂, the value of S_s keeps constant, which means a complete salting-out situation. It takes saline in the well unit 1.6 × 10⁵ s to reach the saturation limit, and the salt precipitation accumulation process keeps about 1.2 × 10⁵ s.

2.2. Sensitivity Analysis of the Salting-Out Problem

The sensitivity coefficients show the impact of parameter change on the calculated system behavior at the observation point. We perturb five parameters: Q_CO2, X_NaCl, m, S_plr, and S_clr; the number of parameters (n_k) equals 5. S_s is used as the response variable for sensitivity analysis, we consider a set of n_k parameters denoted by {x_i|i = 1, …, n_k}, and the forward simulation output y = f({x_i}), where f represents a forward model calculated by the TOUGH2 simulator [41], as shown in Section 2.1.

We discuss three sensitivity analysis methods, including the local sensitivity method, the Morris global sensitivity method, and the Sobol global sensitivity method. Forward simulation is taken by the TOUGH2 code; the inverse modeling capabilities for the TOUGH2 detailed calculation of the three models are developed by Wainwright et al. [29].

Local sensitivity analysis only tests the effect of a single parameter on the model; it can be calculated by the following equation:where is the local sensitivity coefficient for parameter i, is the reference parameter value, Δx_i is a parameter increment, τ_x,i is the parameter-scaling factor, and τ_y is the output-scaling factor [42]. This coefficient can be used to identify the parameters that most strongly affect the behavior of the system at the actual or potential observation points.

A global sensitivity analysis method can test the interaction between parameters, and it can test the effect of multiple parameters, which change concurrently with the response variable. The conventional approach to performing global sensitivity analysis is the Morris sensitivity test method and Sobol’s sensitivity test method. Morris [26] proposed a data screening method that can select parameters that have a low impact on the results and reduce the number of analysis variables.

The Morris method is one of the global sensitivity analysis methods. The elementary effect of parameter x_i is calculated by the following equation [29]:where EE_i is the elementary effect of parameter x_i, Δ = n_p/{2(n_p − 1)} is the fixed increment from the unit interval [0, 1], each parameter range is scaled to the interval [0, 1], partitioned into (n_p − 1) equally-sized intervals, and each parameter take on values from {0, 1/(n_p − 1), 2/(n_p − 1), …, 1}, where n_p is the number of sampling points in the interval [0, 1] [26], based on which the elementary effects (EE) and variance (STD of EE) are calculated; reflecting the relative parameter importance, as well as linearity and correlation, EE and STD of EE are two sensitivity coefficients in the Morris method. Nonlinear effects and interaction effects cannot be separated using this method [26].

The Sobol method is a quantitative global sensitivity analysis method based on a variance analysis first proposed by Sobol [27]. The sensitivity of a single input parameter can be evaluated by calculating the contribution of that parameter to the output variance, and the cross-sensitivity of multiple input parameters can also be evaluated by calculating the contribution of multiple input parameters to the output variance. The basic equations are given as follows:where S_i is the first-order sensitivity value, S_ti is the total sensitivity value, E[·] is the mean, V[·] is the variance, X_i is the random system parameter, Y is the random system response, and X_−i is all random system parameters except X_i. The calculation method was proposed by Sobol [27] and modified by Saltelli et al. [43].

3. Results and Discussions

3.1. Reasonable Calculation of Sample Size Using Different Sensitivity Methods

Forward analysis was implemented 6 times (the formula is n_k + 1) for the local sensitivity method. The Morris method can be considered as an extension of the local sensitivity method by comparing (1) and (2); one local sensitivity simulation is 1 path (n_B) in the Morris simulation. The Morris method requires multiple sampling frequencies to calculate the average value. Figure 4 shows the mean EE and STD of EE at 100 days for each parameter as a function of n_B with n_p = 4; the mean EE and the STD of EE appear to stabilize after 200 n_B. In the case of a lower path’s situation, although the value of the mean EE and the STD of EE is not stable, we can also distinguish the magnitude of the parameter’s sensitivity and assess the importance of parameters.

(a)

(b)

In the Sobol method, we only need to determine n_s, where n_s is the number of sets of n_k dimensional parameter vectors from Monte Carlo sampling. Figure 5 shows S_i and S_ti for each parameter at 100 days as a function of n_s. From the figure, we can see that S_i and S_ti require several thousand n_s to stabilize (larger than 2,000 sets).

(a)

(b)

Due to the randomness of the Morris method, it is easy to meet the error during the 1 path calculated, and it is necessary to do multiple paths calculations to reduce the error. Saltelli et al. [44] present an experienced range of paths 4∼10 to easily obtain Morris calculations. Most scholars did not consider the effects of the paths on the Morris sensitivity analysis, and they always use the experience paths, such as n_B = 4 (Wang et al. [32]), n_B = 10 (Zheng et al. [31]), n_B = 10 (Wainwright et al. [45]), and n_B = 25 (Finsterle [46]). This way would bring some errors in the Morris sensitivity analysis, and the error was discussed in Section 3.4. As to n_s in Sobol sensitivity analysis, most researchers also chose the experienced value of n_s to do the calculation, such as n_s = 300 in Wainwright et al. [45]; it is also important to study the effect of n_s on sensitivity coefficients and get the big enough n_s to keep the sensitivity coefficient converged.

For the global sensitivity analysis coefficient, the confidence intervals are shown so that we can evaluate the parameter coefficient uncertainty with the given number of simulations (draw error band). In the Morris method, the standard error of the mean (SEM) of EE, defined as SEM = STD/n_B^0.5 [26], is used to calculate the confidence interval of the mean EE. In the Sobol method, the confidence interval of S_i is given as tanh{arctanh(S_i) ± 1.96SE} [29], where SE is the standard error given by SE = (n_s − 3)^−0.5. We chose n_B = 200 and n_s = 1,000 according to Figures 4 and 5 to ensure that the sensitivity of the calculated values is stable; the 95% confidence intervals of mean EE and S_i are given below.

Figure 6(a) shows a minor error band of the parameter sensitivity coefficient. This is because of the large number of n_B in the equation SEM = STD/n_B^0.5. The width of the confidence interval increases for small S_i (Figure 6(b)), implying that more simulations are required to rank the low-sensitivity parameters. The relationship between the sensitivity coefficient and n_B, the relationship between sensitivity coefficient and n_s, and the plot of sensitivity coefficient with the confidence intervals help to get the credible sensitivity coefficient.

(a)

(b)

3.2. Times Evolution of Sensitivity Coefficient with Different Sensitivity Methods

3.2.1. Local Sensitivity Method

The relationship between the local sensitivity coefficient of each parameter and time is given in Figure 7.

(a)

(b)

Figure 7(a) shows the time evolution of the sensitivity coefficient of the local sensitivity analysis method. For easier comparison, Figure 7(b) shows the absolute values of the local sensitivity coefficient: ||, which could represent the magnitude of parameter effects. As shown in Figure 7, X_NaCl is the most influential parameter at the early time, and Q_CO2 has a dominant effect afterward, m has the smallest effect, and S_plr and S_clr have an intermediate effect. The sensitivity to Q_CO2, S_plr, and S_clr decreases later, the sensitivity to m increases later, but the sensitivity to X_NaCl stays constant. At the end of the injection process, X_NaCl is still the most influential, but S_clr occupies the second position. The sensitivity of Q_CO2, S_plr, and m remain at a lower sensitivity coefficient after 2.79 × 10⁵ s; the corresponding precipitation does not increase in Figure 3.

3.2.2. Morris Sensitivity Method

In the Morris method, the number of partitions (n_p) and the number of paths (n_B) are the two parameters that determine the result of the sensitivity analysis. The premise of getting an accurate global sensitivity analysis is to investigate the influence of these two parameters. The influence of n_B has been researched in Section 3.1. Figure 8 shows the influence of n_p, the mean EE, and the STD of EE stabilized from 4 to 40 partitions, which means that n_p has a small impact on the stability of both mean EE and STD of EE in this study. From the above studies, the mean EE and STD of EE would converge when n_B = 200 and n_p = 4. The Morris sensitivity analysis results are shown in Figure 9.

(a)

(b)

(a)

(b)

(c)

Figure 9 shows the time evolution of the mean elementary effect from the Morris sensitivity analysis method. The number of simulations is 1,200 (the formula is n_B × (k + 1)). The mean EE represents the average effect of each parameter on the parameter space (Figure 9(a)), the mean |EE| is used to identify the noninfluential factors (Figure 9(b)), and the STD of EE is used to identify interaction effects (Figure 9(c)).

In Figure 9(b), Q_CO2 is the most influential at the early time, and X_NaCl has a dominant effect afterward. The sensitivity to X_NaCl, m, S_plr, and S_clr increases later, but the sensitivity to Q_CO2 decreases later. At the end of the injection process, X_NaCl still has a dominant effect. The effect of Q_CO2 is reduced to a similar extent as that of m, and the sensitivity of S_plr and S_clr keeps a lower sensitivity coefficient.

The sensitivity coefficient of Q_CO2 has different trends with other parameters. As seen in Figure 9(a), the sensitivity coefficient of Q_CO2 is positive at the early stage and then decreases to a negative value, which means that Q_CO2 has a positive correlation with S_s at the early time, and Q_CO2 has a negative correlation with S_s at the later stage. In the early time, dry CO₂ injection into deep saline aquifers would bring H₂O into the CO₂ flow, and the change of Q_CO2 leads to the same change trend of H₂O loss of brine water, which means the positive correlation. In the process of continuous injection of CO₂, the water saturation gradually decreases and the capillary pressure would increase; as seen in Figure 10, the capillary pressure in the pore would prevent further H₂O loss; this is the reason for the reduced sensitivity coefficient. The gas saturation of the rock formation gradually increases, generating a capillary pressure in the direction of the injection well, which causes the saline water to flow back to the injection well when the capillary pressure gradually increases and exceeds the displacement pressure (as shown in Figure 11). During the brine backflow process, the change in Q_CO2 leads to different changes in S_s, causing a negative correlation [25]. The research in this paper shows that the sensitivity coefficient can be changed with time before the salting-out process is stable and the influence of the parameter on the response variable is positive or negative. Researchers should consider the dynamic change of the sensitivity index when performing a similar sensitivity analysis, in particular, considering a long-time physical process.

3.2.3. Sobol Sensitivity Method

We take n_s = 2,000 to keep S_i and S_ti index stable and then conduct the Sobol global sensitivity analysis; the results are shown in Figure 12.

(a)

(b)

(c)

Figure 12 shows the time evolution of the sensitivity index of the Sobol method with 14,000 simulations (the formula is n_s × (k + 2)). Figure 12(a) shows the first-order effect excluding the interaction effect (S_i). Figure 12(b) shows the total sensitivity index of the X_i parameter, including the interaction effect, and is used to identify parameters with negligible effects (S_ti). Figure 12(c) shows the difference between S_ti and S_i as a function of time, identifying the interaction effects. Due to the variance based on (2) and (3), the sensitivity coefficient of S_i and S_ti will remain positive for all time (Figure 12(a) and Figure 12(b)). In Figure 12(a), the largest effect of Q_CO2 at early times can be seen, and X_NaCl has a dominant effect afterward. The sensitivity to Q_CO2 and X_NaCl increases later, and the sensitivity to Q_CO2 decreases to the stable value, but the sensitivity to X_NaCl increases to the stable value at the end of time. The patterns of the three low-influential parameters (m, S_plr, and S_clr) are similar to each other throughout the time. At the end of time, the patterns of Q_CO2 and X_NaCl are similar in Figure 12a and Figure 12(b), suggesting that a change in any of these two parameters would have a significant impact on S_s even without taking into account the effects of the interaction. The ranking of low sensitivity parameters (m, S_plr, and S_clr) importance is not easily recognized than in the local sensitivity analysis and mean EE in the Morris sensitivity analysis. According to the results of the confidence interval in Section 3.1, more simulations are required to rank the low-sensitivity parameters.

All parameters show interaction effects at the early time since S_ti-S_i is larger than 0 (Figure 12(c)). The S_ti-S_i decreases later and stabilizes at a low value, indicating a low interaction effect at the end times. The patterns of the S_ti-S_i in the Sobol method are different from the patterns of the STD of EE in the Morris method; this is because STD of EE includes both the nonlinear effects and interaction effects, but S_ti-S_i represents only the interaction effects [29]. Comparing Figure 9(c) with Figure 12(c), Q_CO2 and X_NaCl have an abnormal trend in Figure 9(c), and the sensitivity coefficient is much higher than the other three parameters, which indicate significant nonlinear effects of Q_CO2 and X_NaCl. Comparison of STD of EE and S_ti-S_i helps to get a deep understanding of the sensitivity coefficient of the parameter. The nonlinear effect of Q_CO2 can be seen in Wang et al. [32], it is mainly due to the critical value of Q_CO2, which controls the backflow phenomenon in the salting-out problem.

3.3. Uncertainly of Morris Results about Different Path Choice

Figure 13 shows the Morris global sensitivity analysis of S_s near the injection well, the traditional sensitivity coefficient is calculated by the equation d_i = Δf(Δx_i)/Δx_i (Figure 13(a)). The difference in coordinate values is due to the introduction of the scaling factor τ_x,i/τ_y during the sensitivity calculation of Figure 13(b), which helped to avoid a wide range of axes and plot closer and useful graphs [47].

(a)

(b)

The number of paths in Figure 13(a) is equal to 4, the descending order of the mean EE is X_NaCl, Q_CO2, m, S_clr, and S_plr, and the descending order of the STD of EE is Q_CO2, S_clr, S_plr, m, and X_NaCl [32]. Under the same path (equal to 4) and time (100 days) conditions, the results in Figure 13(b) are quite different from those in Figure 13(a), especially the STD of EE of the parameter X_NaCl. X_NaCl has a dominant interaction or nonlinear effect in Figure 13(b), but it has the lowest interaction or nonlinear effect in Figure 13(a). This is because the larger uncertainty of the initial parameters is selected because of the smaller number of paths. The sensitivity analysis result becomes more stable as the number of paths increases (Figure 13(b)). When the number of paths is 500, the descending order of the mean EE is X_NaCl, Q_CO2, S_clr, S_plr, and m and the descending order of the STD of EE is X_NaCl, Q_CO2, m, S_clr, and S_plr. This result is more accurate than Figure 13(a) carried out by Wang et al. [32].

3.4. Comparison of Sobol Results between the Physical Model and Surrogate Model

If the model has a simple and explicit mathematical expression f(x), the sensitivity of Sobol can be calculated by the analytic method. If the model does not have a simple mathematical expression, to be able to extract a large number of samples while reducing the amount of computation, in one manifold method, the surrogate model [48, 49] is used instead of the physical model to calculate the response variable S_s, and then the Sobol sensitivity is calculated by Monte Carlo method [44]. In this paper, the sensitivity coefficient is calculated by real forward simulations instead of the calculation of the sensitivity coefficient coming from the Kriging surrogate model in Wang et al. [32]. The results of the comparison are shown in Figure 14.

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(b)

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Figure 14(a) and Figure 14(b) show the first-order and total sensitivity coefficients of the salting-out model parameters, respectively. First of all, these two figures have a similar pattern about the sensitivity coefficient. X_NaCl has the greatest influence on the response variable S_s, much higher than the other parameters. The descending ranking of the sensitivity coefficient is X_NaCl, m, S_plr, Q_CO2, and S_clr in Figure 14(a); however, Figure 14(b) shows the different range of the sensitivity coefficient: X_NaCl, Q_CO2, S_plr, m, and S_clr. Q_CO2 has the second place in this article but the lowest position in Wang et al. [32]. In this paper, the Morris method and the Sobol method get a similar sensitivity coefficient; what else the sensitivity coefficient result from Sobol method in this paper can also correspond to the sensitivity coefficient of the Morris method in Wang et al. The difference in results can be attributed to the use of the surrogate model and the number of simulations, full of simplicity and experience.

Figure 14(c) shows the contribution of the parameter interaction to the sensitivity, which is called the second-order sensitivity coefficient [32]. Interaction parameters that can be considered include X_NaCl and m, X_NaCl and S_plr, and Q_CO2 and m. In Figure 14(d), the difference between S_ti and S_i identifies the interaction effect. X_NaCl has the biggest interaction effect, m and S_plr have a dominant interaction effect afterward, and Q_CO2 has the smallest interaction effect. The results in Figure 14(c) and Figure 14(d) are consistent, but the difference between S_ti and S_i is much easier to get than the second-order sensitivity coefficient.

4. Conclusions

The sensitivity analysis of the salting-out effect on well injectivity is a significant work in the study of geological storage of CO₂ in deep saline aquifers, which is helpful in the selection of storage sites and the design of the injection strategy. In this study, we conduct a more detailed sensitivity analysis using the salting-out model, which includes the local sensitivity method and two global sensitivity methods. The main conclusions obtained from this study are as follows:(1)Morris sensitivity coefficient requires several hundred and Sobol’s sensitivity coefficient requires several thousand sampling matrices to stabilize in this study. The stability and accuracy of sensitivity calculation are related to the selection of calculation times, which cannot be selected according to experience but should be chosen to make the sensitivity coefficient converge.(2)The sensitivity coefficient would change with the evaluation time. X_NaCl has always been the most important factor affecting salting out, and the parameters m, S_plr, and S_clr have low sensitivity. However, the less sensitive parameter Q_CO2 at the end of the evaluation time has a dominant effect during the evaluation process. This indicated that the law of time evolution cannot be ignored when studying the physical process of the problem, which is a long-time accumulation process, such as the salting-out process in this study.(3)Local sensitivity is a simplification of Morris, which can quickly select the most sensitive parameters. The Morris method is suitable for qualitatively selecting the most sensitive parameters and can obtain the interaction effect or the nonlinear effect. Sobol can quantify the sensitivity coefficient and cross-sensitivity coefficient, and it can help to compare with the Morris method to understand the nonlinear effect. The ranking of low sensitivity parameters (m, S_plr, and S_clr) importance is not easily recognized using Sobol’s method; more simulations are required to rank low sensitivity parameters.(4)Using the surrogate model to calculate the Sobol coefficient may cause some errors and uncertainty. Possible errors and uncertainties should be evaluated before the surrogate model is adopted to simplify the computation. On the other hand, the interaction sensitivity expressed by the S_ti-S_i approximation without calculating the second-order coefficient is effective.

Nomenclature

d_i:	Sensitivity coefficient in traditional sensitivity calculated method
k_x, k_y, k_z:	Permeability in three directions
m:	Parameter related to pore size distribution
n_B:	The number of parameter paths
n_k:	The number of parameters
n_p:	The number of sampling points
n_s:	The number of parameters sets
P:	Pressure
P₀:	Gas entry pressure
P_max:	Maximum capillary pressure
Q_CO2:	Injection rate of CO₂
S_gas:	Gas saturation
S_gr:	Residual gas saturation
S_i:	First-order sensitivity coefficient in Sobol method
:	Local sensitivity coefficient
S_lr:	Residual liquid saturation
S_ls:	Liquid saturation in the saturated state
S_s:	Solid saturation
S_ti:	Total sensitivity coefficient in Sobol method
T:	Temperature
x_i:	Input parameter
X_NaCl:	Salinity
ϕ:	Porosity.

Data Availability

All the data generated or analyzed during this study are included in this published article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The research was supported by the Jiangsu Planned Projects for Postdoctoral Research Funds (no. 2020Z006).

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Copyright © 2021 Jie Ren and Di Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO2 Geological Storage Process

Abstract

1. Introduction

2. Methodology

2.1. Modeling Approach of the Salting-Out Process

2.2. Sensitivity Analysis of the Salting-Out Problem

3. Results and Discussions

3.1. Reasonable Calculation of Sample Size Using Different Sensitivity Methods

3.2. Times Evolution of Sensitivity Coefficient with Different Sensitivity Methods

3.2.1. Local Sensitivity Method

3.2.2. Morris Sensitivity Method

3.2.3. Sobol Sensitivity Method

3.3. Uncertainly of Morris Results about Different Path Choice

3.4. Comparison of Sobol Results between the Physical Model and Surrogate Model

4. Conclusions

Nomenclature

Data Availability

Conflicts of Interest

Acknowledgments

References

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Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO₂ Geological Storage Process