A New CO2-EOR Methods Screening Model Based on Interdependency Parameters

The successful implementation of carbon dioxide-enhanced oil recovery (CO2-EOR) is crucial in increasing oil production and reducing carbon emissions. For this reason, screening criteria are needed for the initial characterization of a suitable CO2-EOR reservoir. The existing screening model treats the screening parameters independently. Therefore, each parameter has its criteria limit and does not relate to the others. However, in reality, several screening parameters are interdependent, so we need a method that treats the interdependent parameters simultaneously. This research develops a new simultaneous screening model using the interdependency of the parameters. Quantitative and actual data were collected from CO2-EOR field documentation worldwide with a comprehensive analysis. A statistical approach with a correlation analysis method was used to determine the interconnected screening parameters. The results were synchronized with the expert domain to match actual physical conditions. The limit of simultaneous screening criteria was acquired by multivariate quality control (MQC) based on the principal component analysis (PCA) method. The proposed screening model was compared with 13 actual projects, and demonstrated improvements to previous models. The results match actual operations and follow the expert domain rules. If the miscible CO2-EOR is met, then the immiscible should also be appropriate but not vice versa. Nevertheless, four different immiscible projects are predicted to be slightly optimistic as miscible or immiscible.


Introduction
One of the enhanced oil recovery (EOR) methods is carbon dioxide injection, which directly utilizes CO 2 from unwanted industrial operations because of its harmful impact on climate change. Currently, this method has attracted the attention of petroleum industries because it provides dual benefits. Firstly, it prevents the release of excess CO 2 in the atmosphere by re-injecting it into reservoirs. Secondly, it increases the oil recovery to meet energy needs [1]. Correspondingly, CO 2 -EOR has been considered as one of the primary EOR methods in the US [2]. The CO 2 -EOR projects in the US have increased in the last than 20 years, despite oil prices fluctuation. Therefore, they have good prospects for continuous implementation [3].
In the oil recovery process, CO 2 is injected into the reservoir, and it creates an interaction with the rock and the oil. This interaction alters the oil and rock properties with its mechanism including oil swelling, reduction in oil viscosity and CO 2 -oil interfacial tension, extraction of light/intermediate oil components, and wettability changes [4]. The  The screening model in the previously mentioned research analyzed the parameters independently. Therefore, they did not affect one another. As a result, each parameter has its respective criteria limit in this individual screening model. For example, porosity has its screening criteria limit, as do permeability and other parameters. However, in reality, these parameters are interdependent because they influence and relate to one another. Therefore, a screening model capable of considering these parameters simultaneously is needed. A new screening model utilizing the interdependency among the parameters called the simultaneous screening model was developed in this research.
Essentially, the present research aims to develop a combined screening model that is between simultaneous and individual models for the CO 2 -EOR methods. Two approaches were simultaneously applied to achieve this purpose, namely statistics and expert domain. The statistical approach is used to model physical phenomena. The expert domain approach is used to correct the results of statistical correlations adjusted to the real physical phenomena. The updated data on the miscible and immiscible CO 2 -EOR was the basis for supporting this goal. Nine significant screening parameters were used, including porosity, permeability, oil viscosity, oil gravity, depth, temperature, oil saturation, net thickness, and MMP.

Materials and Methods
Based on the collected data set, this research developed a screening model for miscible and immiscible CO 2 -EOR. The database was collected and documented according to references of actual fields worldwide to develop an improved and more realistic screening model. Data reference sources were taken from the Worldwide EOR Surveys reported by Oil and Gas Journal (OGJ) from 1986 to 2014, SPE publications, Elsevier publications, technical field reports, and AAPG bulletin. The workflow of the screening model is shown in Figure 1, which is divided into three stages.
Stage 1: Data preparation. The quality of the data greatly affects the final result. Therefore, this stage plays an essential role in controlling data quality. This stage was carried out by collecting, sorting, and filling in missing data. For the sorting phase, only the successful and profitable CO 2 -EOR project data were chosen for miscible CO 2 -EOR. However, this was not the case for immiscible CO 2 -EOR due to limited published data.  Stage 2: Processing and analysis. These are the main steps in developing the screening model in this research. The data required for the process was collected in Stage 1. Then, a correlation analysis was carried out to determine the relationship between screening parameters with the Pearson linear correlation method. The results of the correlation analysis were synchronized with the expert domain rules to match the fundamental physical phenomena. Furthermore, the PCA method reduced the data dimension into several principal components (PCs). The PCs were the input for the MQC method in determining the screening limit simultaneously. For uncorrelated screening parameters, the screening limit was determined by simple descriptive statistics to obtain the individual screening limit for each parameter. Stage 2 results in a simultaneous and individual combination screening model as a new screening model for CO2-EOR.
Linear assumptions were adopted in the statistical calculation methods, including Pearson correlation, PCA, and MQC. Figure 2 describes the relationship among the statistical methods used to create a simultaneous screening model. The first calculations on the covariance matrix measured changes in the two related variables linearly. The normalized covariance produced a correlation matrix that showed the strength and direction of the relationship among the screening parameters in a linear manner. The t-statistic test was used to check the significance of the correlation coefficients [15]. The collected data also had to be reorganized because of duplications and typos in unit measurements reported in the data source. For the incomplete data due to missing values, mean imputation based on the same type of formation was applied for screening parameters other than MMP. A fully expert domain approach of Yellig-Metcalfe empirical correlation as a function of temperature (T), as shown in the following, was used for determining MMP [13,14].
Stage 2: Processing and analysis. These are the main steps in developing the screening model in this research. The data required for the process was collected in Stage 1. Then, a correlation analysis was carried out to determine the relationship between screening parameters with the Pearson linear correlation method. The results of the correlation analysis were synchronized with the expert domain rules to match the fundamental physical phenomena. Furthermore, the PCA method reduced the data dimension into several principal components (PCs). The PCs were the input for the MQC method in determining the screening limit simultaneously. For uncorrelated screening parameters, the screening limit was determined by simple descriptive statistics to obtain the individual screening limit for each parameter. Stage 2 results in a simultaneous and individual combination screening model as a new screening model for CO 2 -EOR.
Linear assumptions were adopted in the statistical calculation methods, including Pearson correlation, PCA, and MQC. Figure 2 describes the relationship among the statisti-Appl. Sci. 2022, 12, 3937 5 of 17 cal methods used to create a simultaneous screening model. The first calculations on the covariance matrix measured changes in the two related variables linearly. The normalized covariance produced a correlation matrix that showed the strength and direction of the relationship among the screening parameters in a linear manner. The t-statistic test was used to check the significance of the correlation coefficients [15]. MQC is a method for simultaneously monitoring the variability of a multivariate case of two or more related quality characteristics. MQC method is suitable for a small number of process variables since the covariance matrix of MQC method will become singular when implemented in large and intercorrelated process variables [16]. A popular approach for reducing the dimensions of this variable is PCA [17]. The PCA method expresses information by constructing new variables in linear combinations called principal components (PC) without eliminating the original variables to minimize the excessive loss of information [18].
The condition is presumed to be statistically controlled, supposing the process variable is within the limit as specified in the control chart. This research uses the Hotelling control chart and, when associated with PCA, it is equivalent to: where is the ith principal component score, is the variance of , and A is the number of PC retained in the PCA model [16]. The upper and lower limits of the Hotelling control chart have an F distribution as follows [16].
When the number of samples n is large, i.e., n > 100, many practitioners use an approximate control limit given by [17]: = 0 The symbol is the upper control limit, is the lower control limit, n is the number of samples, q is the number of variables, and , is the 100(1 − α)% of the F-distribution with q and n − q degrees of freedom. This control chart limit is further used as the simultaneous screening limit. An ellipse can represent multivariate control limits for two variables.
Subsequently, the individual screening model examines the parameters independently, indicating that these parameters are uncorrelated to each other. Individual screening criteria limits use simple descriptive statistical methods for quantitative calculations. The box plot gives some information on value of the minimum, mean, median, maximum, and quartiles. The swarm plot describes the data distribution in the box plot. Integrating the box and swarm plots then provides information more clearly as shown in Figure 3. MQC is a method for simultaneously monitoring the variability of a multivariate case of two or more related quality characteristics. MQC method is suitable for a small number of process variables since the covariance matrix of MQC method will become singular when implemented in large and intercorrelated process variables [16]. A popular approach for reducing the dimensions of this variable is PCA [17]. The PCA method expresses information by constructing new variables in linear combinations called principal components (PC) without eliminating the original variables to minimize the excessive loss of information [18].
The condition is presumed to be statistically controlled, supposing the process variable is within the limit as specified in the control chart. This research uses the Hotelling T 2 control chart and, when associated with PCA, it is equivalent to: where PC 2 i is the ith principal component score, S 2 PCi is the variance of PC i , and A is the number of PC retained in the PCA model [16]. The upper and lower limits of the Hotelling T 2 control chart have an F distribution as follows [16].
When the number of samples n is large, i.e., n > 100, many practitioners use an approximate control limit given by [17]: The symbol T 2 UCL is the upper control limit, T 2 LCL is the lower control limit, n is the number of samples, q is the number of variables, and F 1−α(q,n−q) is the 100(1 − α)% of the F-distribution with q and n − q degrees of freedom. This control chart limit is further used as the simultaneous screening limit. An ellipse can represent multivariate control limits for two variables.
Subsequently, the individual screening model examines the parameters independently, indicating that these parameters are uncorrelated to each other. Individual screening criteria Appl. Sci. 2022, 12, 3937 6 of 17 limits use simple descriptive statistical methods for quantitative calculations. The box plot gives some information on value of the minimum, mean, median, maximum, and quartiles. The swarm plot describes the data distribution in the box plot. Integrating the box and swarm plots then provides information more clearly as shown in Figure 3. Stage 3: Implementation. The final stage involved the implementation of the combined simultaneous and individual screening model on the CO2-EOR field data asides from those analyzed data. If the reservoir parameters are appropriate for the screening criteria, then the field is a suitable target for applying the CO2-EOR methods.

Results and Discussion
A total of 131 datasets on miscible CO2-EOR projects in the US were sorted from 1100 duplicating datasets into 145 datasets on project success and, finally, into 131 datasets for successful and profitable projects. There were some missing data in oil viscosity, oil saturation, net thickness, and MMP, as shown in Figure 4a.  Moreover, 37 project datasets of immiscible CO2-EOR were obtained from OGJ by constructing, extracting, and sorting 164 duplicated initial datasets. Furthermore, an additional 27 project datasets were collected from SPE and Elsevier publications, bringing a total of 64 project datasets originating from several countries. Afterward, 57 datasets from 1986 to 2020 were analyzed, and the remaining 7 datasets were used to implement the newly established screening model. Missing data in Figure 4b were identified for several screening parameters, including oil viscosity, temperature, oil gravity, oil saturation, net thickness, and MMP. The mean imputation and Yellig-Metcalfe empirical correlation were applied to fill the missing data.
The coefficients of correlation among screening parameters are shown in Figure 5a for miscible CO2-EOR and Figure 5b for immiscible CO2-EOR. A high coefficient value tends to have a significant correlation based on a p-value smaller than 5% of the t-statistic test shown in Figure 6. Statistically, the MMP screening parameter was significantly correlated to porosity, depth, oil gravity, viscosity, and temperature. Permeability was related substantially to porosity. Oil gravity correlated with porosity, depth, viscosity, and Stage 3: Implementation. The final stage involved the implementation of the combined simultaneous and individual screening model on the CO 2 -EOR field data asides from those analyzed data. If the reservoir parameters are appropriate for the screening criteria, then the field is a suitable target for applying the CO 2 -EOR methods.

Results and Discussion
A total of 131 datasets on miscible CO 2 -EOR projects in the US were sorted from 1100 duplicating datasets into 145 datasets on project success and, finally, into 131 datasets for successful and profitable projects. There were some missing data in oil viscosity, oil saturation, net thickness, and MMP, as shown in Figure 4a. Stage 3: Implementation. The final stage involved the implementation of the combined simultaneous and individual screening model on the CO2-EOR field data asides from those analyzed data. If the reservoir parameters are appropriate for the screening criteria, then the field is a suitable target for applying the CO2-EOR methods.

Results and Discussion
A total of 131 datasets on miscible CO2-EOR projects in the US were sorted from 1100 duplicating datasets into 145 datasets on project success and, finally, into 131 datasets for successful and profitable projects. There were some missing data in oil viscosity, oil saturation, net thickness, and MMP, as shown in Figure 4a.  Moreover, 37 project datasets of immiscible CO2-EOR were obtained from OGJ by constructing, extracting, and sorting 164 duplicated initial datasets. Furthermore, an additional 27 project datasets were collected from SPE and Elsevier publications, bringing a total of 64 project datasets originating from several countries. Afterward, 57 datasets from 1986 to 2020 were analyzed, and the remaining 7 datasets were used to implement the newly established screening model. Missing data in Figure 4b were identified for several screening parameters, including oil viscosity, temperature, oil gravity, oil saturation, net thickness, and MMP. The mean imputation and Yellig-Metcalfe empirical correlation were applied to fill the missing data.
The coefficients of correlation among screening parameters are shown in Figure 5a for miscible CO2-EOR and Figure 5b for immiscible CO2-EOR. A high coefficient value tends to have a significant correlation based on a p-value smaller than 5% of the t-statistic test shown in Figure 6. Statistically, the MMP screening parameter was significantly correlated to porosity, depth, oil gravity, viscosity, and temperature. Permeability was related substantially to porosity. Oil gravity correlated with porosity, depth, viscosity, and Moreover, 37 project datasets of immiscible CO 2 -EOR were obtained from OGJ by constructing, extracting, and sorting 164 duplicated initial datasets. Furthermore, an additional 27 project datasets were collected from SPE and Elsevier publications, bringing a total of 64 project datasets originating from several countries. Afterward, 57 datasets from 1986 to 2020 were analyzed, and the remaining 7 datasets were used to implement the newly established screening model. Missing data in Figure 4b were identified for several screening parameters, including oil viscosity, temperature, oil gravity, oil saturation, net thickness, and MMP. The mean imputation and Yellig-Metcalfe empirical correlation were applied to fill the missing data.
The coefficients of correlation among screening parameters are shown in Figure 5a for miscible CO 2 -EOR and Figure 5b for immiscible CO 2 -EOR. A high coefficient value tends to have a significant correlation based on a p-value smaller than 5% of the t-statistic test shown in Figure 6. Statistically, the MMP screening parameter was significantly correlated to porosity, depth, oil gravity, viscosity, and temperature. Permeability was related substantially to porosity. Oil gravity correlated with porosity, depth, viscosity, and temperature. Oil saturation had an insignificant correlation with all the screening parameters and so, the net thickness. Combining statistical methods and expert domains was needed to match the results from the correlations to the actual physical phenomena. Besides, the expert domain approach served as the basis for determining the correlation and dependency of the screening parameters shown in Figure 7 with the following explanation: 1.
MMP correlates with temperature, oil gravity, and depth, whereas oil gravity correlates with oil viscosity. Therefore MMP, temperature, oil gravity, depth, and oil viscosity are intercorrelated and depend on each other.

2.
Porosity correlates with permeability based on reservoir rock properties. 3.
Oil saturation and net thickness insignificantly correlate to other screening parameters.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 16 temperature. Oil saturation had an insignificant correlation with all the screening parameters and so, the net thickness. Combining statistical methods and expert domains was needed to match the results from the correlations to the actual physical phenomena. Besides, the expert domain approach served as the basis for determining the correlation and dependency of the screening parameters shown in Figure 7 with the following explanation: 1. MMP correlates with temperature, oil gravity, and depth, whereas oil gravity correlates with oil viscosity. Therefore MMP, temperature, oil gravity, depth, and oil viscosity are intercorrelated and depend on each other. 2. Porosity correlates with permeability based on reservoir rock properties. 3. Oil saturation and net thickness insignificantly correlate to other screening parameters.
(a) (b)   temperature. Oil saturation had an insignificant correlation with all the screening parameters and so, the net thickness. Combining statistical methods and expert domains was needed to match the results from the correlations to the actual physical phenomena. Besides, the expert domain approach served as the basis for determining the correlation and dependency of the screening parameters shown in Figure 7 with the following explanation: 1. MMP correlates with temperature, oil gravity, and depth, whereas oil gravity correlates with oil viscosity. Therefore MMP, temperature, oil gravity, depth, and oil viscosity are intercorrelated and depend on each other. 2. Porosity correlates with permeability based on reservoir rock properties. 3. Oil saturation and net thickness insignificantly correlate to other screening parameters.

Miscible CO2-EOR Screening Model
The summary of simultaneous and individual combination screening models for miscible CO2 is provided in Table 3. Simultaneous screening model A includes five parameters: MMP, temperature, depth, oil gravity, and oil viscosity. Although the grouping only concerns the limits or boundary of data values, to the best of our knowledge, the model may relate to mixture miscibility and the fluids' composition, where the mixture, in this case, stands for oil mixed with CO2 within the reservoir during the injection. Indeed, the miscibility is sensitive to the pressure-related properties, i.e., MMP and depth, and also temperature. Furthermore, the composition of oil dictates the specific gravity and the viscosity, and affects the miscibility of CO2 into the oil as well. Based on this, those five parameters were grouped into the corresponding model.
The PCA method reduced the data dimensions to 2 PCs, explaining the total data diversity of 79.2%, as shown in Figure 8a. PC1 explains 59.1% and PC2 explains 20.1%. Figure 8b shows the magnitude of the eigenvectors for each PC. The equation in Table  3 is simultaneous screening model A, a quadratic function of PC1 and PC2. The limit obtained was 11.13 at a confidence level of 99.5%, as shown in Figure 9. If the value of is less than 11.13, the miscible CO2-EOR is the appropriate EOR method. The oil gravity and viscosity have a more significant effect on the value of .   Figure 7 shows four processes in the resulting screening model. The first calculation is done with the simultaneous model A, then, if appropriate, the process moves to the simultaneous model B and finally to the two individual models. If the four processes meet all the criteria, the reservoir is suitable for implementing CO 2 -EOR.
As mentioned, this research focused on developing a screening model for miscible and immiscible CO 2 -EOR. These two models are significantly different and have their own uniqueness. The following sections discuss the development and implementation of the screening model for different miscibility conditions of CO 2 -EOR.

Miscible CO 2 -EOR Screening Model
The summary of simultaneous and individual combination screening models for miscible CO 2 is provided in Table 3. Simultaneous screening model A includes five parameters: MMP, temperature, depth, oil gravity, and oil viscosity. Although the grouping only concerns the limits or boundary of data values, to the best of our knowledge, the model may relate to mixture miscibility and the fluids' composition, where the mixture, in this case, stands for oil mixed with CO 2 within the reservoir during the injection. Indeed, the miscibility is sensitive to the pressure-related properties, i.e., MMP and depth, and also temperature. Furthermore, the composition of oil dictates the specific gravity and the viscosity, and affects the miscibility of CO 2 into the oil as well. Based on this, those five parameters were grouped into the corresponding model. Table 3. Summary of the miscible CO 2 -EOR screening model.

Screening Model
Simultaneous A: • Porosity, % • Permeability, md The PCA method reduced the data dimensions to 2 PCs, explaining the total data diversity of 79.2%, as shown in Figure 8a. PC1 explains 59.1% and PC2 explains 20.1%. Figure 8b shows the magnitude of the eigenvectors for each PC. The T 2 A equation in Table 3 is simultaneous screening model A, a quadratic function of PC1 and PC2. The limit obtained was 11.13 at a confidence level of 99.5%, as shown in Figure 9. If the value of T 2 A is less than 11.13, the miscible CO 2 -EOR is the appropriate EOR method. The oil gravity and viscosity have a more significant effect on the value of T 2 A .
rameters: MMP, temperature, depth, oil gravity, and oil viscosity. Although the grouping only concerns the limits or boundary of data values, to the best of our knowledge, the model may relate to mixture miscibility and the fluids' composition, where the mixture, in this case, stands for oil mixed with CO2 within the reservoir during the injection. Indeed, the miscibility is sensitive to the pressure-related properties, i.e., MMP and depth, and also temperature. Furthermore, the composition of oil dictates the specific gravity and the viscosity, and affects the miscibility of CO2 into the oil as well. Based on this, those five parameters were grouped into the corresponding model. The PCA method reduced the data dimensions to 2 PCs, explaining the total data diversity of 79.2%, as shown in Figure 8a. PC1 explains 59.1% and PC2 explains 20.1%. Figure 8b shows the magnitude of the eigenvectors for each PC. The equation in Table  3 is simultaneous screening model A, a quadratic function of PC1 and PC2. The limit obtained was 11.13 at a confidence level of 99.5%, as shown in Figure 9. If the value of is less than 11.13, the miscible CO2-EOR is the appropriate EOR method. The oil gravity and viscosity have a more significant effect on the value of .
(a) (b)    Simultaneous screening model B includes two screening parameters, namely porosity and permeability. As commonly known in petroleum literatures, a dimension combining permeability and porosity parameters represents the measure of volumetric flow capacity. In the same sense, the screening model B may also have similar physical meaning. A simultaneous screening model was developed using the MQC method. Figure 10a,b indicate that the screening boundary is in ellipse form, and the Hotelling T 2 chart has an upper limit of 11.13 at a confidence level of 99.5%. The simultaneous screening model B is in the form of the T 2 B equation, a function of porosity and permeability. If the value of T 2 B is less than 11.13, it is suitable for the miscible CO 2  Oil saturation and net thickness parameters employ an individual screening model. Figure 11a shows the integration of box and swarm plots for oil saturation and Figure 11b for net thickness. The individual screening criteria of oil saturation have a minimum data value of 17%, as of that of Olive Field [19], and a maximum of 89%, as of that of Salt Creek Field [20]. Meanwhile, the minimum data of net thickness is 9 ft, as of that of Chester Field [21], and the maximum data is 472 ft, as of that of Citronelle Field [22].  Table 4 provides a complete simultaneous and individual combination screening model for immiscible CO2-EOR. Therefore, all five parameters in the simultaneous screening model A are covered in 2 PC and by 75% data diversity, as shown in Figure 12a. Figure  12b gives the eigenvectors for each PC. As shown in Figure 13, the limit of simultaneous model A is 12.1 with a confidence level of 99.5%. In other words, any value of less than 12.1 means that the immiscible CO2-EOR is amenable. Based on the correlation of expressed in Table 4, is more influenced by oil gravity and viscosity than the other three parameters. The simultaneous screening model B depends on the value of , as shown in Figure 14, which means immiscible CO2-EOR is suitable if is less than 12.1. In addition, the value is governed by porosity and permeability. Oil saturation and net thickness parameters employ an individual screening model. Figure 11a shows the integration of box and swarm plots for oil saturation and Figure 11b for net thickness. The individual screening criteria of oil saturation have a minimum data value of 17%, as of that of Olive Field [19], and a maximum of 89%, as of that of Salt Creek Field [20]. Meanwhile, the minimum data of net thickness is 9 ft, as of that of Chester Field [21], and the maximum data is 472 ft, as of that of Citronelle Field [22]. Oil saturation and net thickness parameters employ an individual screening model. Figure 11a shows the integration of box and swarm plots for oil saturation and Figure 11b for net thickness. The individual screening criteria of oil saturation have a minimum data value of 17%, as of that of Olive Field [19], and a maximum of 89%, as of that of Salt Creek Field [20]. Meanwhile, the minimum data of net thickness is 9 ft, as of that of Chester Field [21], and the maximum data is 472 ft, as of that of Citronelle Field [22].  Table 4 provides a complete simultaneous and individual combination screening model for immiscible CO2-EOR. Therefore, all five parameters in the simultaneous screening model A are covered in 2 PC and by 75% data diversity, as shown in Figure 12a. Figure  12b gives the eigenvectors for each PC. As shown in Figure 13, the limit of simultaneous model A is 12.1 with a confidence level of 99.5%. In other words, any value of less than 12.1 means that the immiscible CO2-EOR is amenable. Based on the correlation of expressed in Table 4, is more influenced by oil gravity and viscosity than the other three parameters. The simultaneous screening model B depends on the value of , as shown in Figure 14, which means immiscible CO2-EOR is suitable if is less than 12.1. In addition, the value is governed by porosity and permeability.  Table 4 provides a complete simultaneous and individual combination screening model for immiscible CO 2 -EOR. Therefore, all five parameters in the simultaneous screening model A are covered in 2 PC and by 75% data diversity, as shown in Figure 12a. Figure 12b gives the eigenvectors for each PC. As shown in Figure 13, the limit of simultaneous model A is 12.1 with a confidence level of 99.5%. In other words, any value of T 2 A less than 12.1 means that the immiscible CO 2 -EOR is amenable. Based on the correlation of T 2 A expressed in Table 4, T 2 A is more influenced by oil gravity and viscosity than the other three parameters. The simultaneous screening model B depends on the value of T 2 B , as shown in Figure 14, which means immiscible CO 2 -EOR is suitable if T 2 B is less than 12.1. In addition, the T 2 B value is governed by porosity and permeability. Table 4. Summary of the immiscible CO 2 -EOR screening model.

Screening Model
Simultaneous A: • Porosity, % • Permeability, md        Figure 15 provides data distribution on the individual screening parameters of immiscible CO2-EOR, namely oil saturation and net thickness. Individual screening criteria for oil saturation have a minimum data of 22%, as of that of Weeks Island Field [23], and a maximum data of 83.5%, as of that of Ponte Dirillo Field [24]. Net Thickness screening criteria have a minimum data of 5.2 ft, as of that of Yaoyingtai Field [12], and a maximum data of 300 ft, as of that of Huntington Beach Field [12].

Implementation
The simultaneous and individual combination screening model was implemented and the results were compared with the real conditions in the corresponding fields. The model for miscible CO2-EOR was implemented only in Canadian fields. The reservoir properties and reference sources are shown in Table 5. The MMP values were obtained from the application of the Yellig-Metcalfe empirical correlation, whereas the other reservoir properties were collected from references and missing data were filled by mean imputation.
The combination screening models for miscible and immiscible CO2-EOR were reviewed and compared with the screening model presented by Taber et al. [10], Al Adasani and Bai [11], and Zhang et al. [5]. Table 6 shows the implementation results of several screening methods in miscible CO2-EOR fields. The proposed simultaneous and individual combination screening model recommended the injection of both miscible and immiscible CO2 for the six fields. The screening results match the actual conditions and meet the real physical phenomena. The reservoir that is suitable for miscible CO2 injection should also be appropriate for immiscible CO2-EOR.  Figure 15 provides data distribution on the individual screening parameters of immiscible CO 2 -EOR, namely oil saturation and net thickness. Individual screening criteria for oil saturation have a minimum data of 22%, as of that of Weeks Island Field [23], and a maximum data of 83.5%, as of that of Ponte Dirillo Field [24]. Net Thickness screening criteria have a minimum data of 5.2 ft, as of that of Yaoyingtai Field [12], and a maximum data of 300 ft, as of that of Huntington Beach Field [12].  Figure 15 provides data distribution on the individual screening parameters of immiscible CO2-EOR, namely oil saturation and net thickness. Individual screening criteria for oil saturation have a minimum data of 22%, as of that of Weeks Island Field [23], and a maximum data of 83.5%, as of that of Ponte Dirillo Field [24]. Net Thickness screening criteria have a minimum data of 5.2 ft, as of that of Yaoyingtai Field [12], and a maximum data of 300 ft, as of that of Huntington Beach Field [12].

Implementation
The simultaneous and individual combination screening model was implemented and the results were compared with the real conditions in the corresponding fields. The model for miscible CO2-EOR was implemented only in Canadian fields. The reservoir properties and reference sources are shown in Table 5. The MMP values were obtained from the application of the Yellig-Metcalfe empirical correlation, whereas the other reservoir properties were collected from references and missing data were filled by mean imputation.
The combination screening models for miscible and immiscible CO2-EOR were reviewed and compared with the screening model presented by Taber et al. [10], Al Adasani and Bai [11], and Zhang et al. [5]. Table 6 shows the implementation results of several screening methods in miscible CO2-EOR fields. The proposed simultaneous and individual combination screening model recommended the injection of both miscible and immiscible CO2 for the six fields. The screening results match the actual conditions and meet the real physical phenomena. The reservoir that is suitable for miscible CO2 injection should also be appropriate for immiscible CO2-EOR.

Implementation
The simultaneous and individual combination screening model was implemented and the results were compared with the real conditions in the corresponding fields. The model for miscible CO 2 -EOR was implemented only in Canadian fields. The reservoir properties and reference sources are shown in Table 5. The MMP values were obtained from the application of the Yellig-Metcalfe empirical correlation, whereas the other reservoir properties were collected from references and missing data were filled by mean imputation.
The combination screening models for miscible and immiscible CO 2 -EOR were reviewed and compared with the screening model presented by Taber et al. [10], Al Adasani and Bai [11], and Zhang et al. [5]. Table 6 shows the implementation results of several screening methods in miscible CO 2 -EOR fields. The proposed simultaneous and individual combination screening model recommended the injection of both miscible and immiscible CO 2 for the six fields. The screening results match the actual conditions and meet the real physical phenomena. The reservoir that is suitable for miscible CO 2 injection should also be appropriate for immiscible CO 2 -EOR.
In the meantime, Zhang  The combination screening model for immiscible CO 2 -EOR was implemented in seven fields located in Trinidad, US, Turkey, and Brazil. These fields have been proven as successful in implementing immiscible CO 2 -EOR. The physical properties of the nine reservoir screening parameters are presented in Table 7. The screening parameter values were obtained from references and mean imputation was done for the missing data. In addition, the Yellig-Metcalfe correlation was used to determine the MMP. The results of implementing several screening models in the seven fields are shown in Table 8. The combination screening model recommended that the fields that are suitable for miscible CO 2 injection are also appropriate for immiscible CO 2 injection. However, a field that can be injected with immiscible CO 2 is not necessarily a field that can be injected with miscible CO 2 . The results of implementing this combination screening method followed the rules of the expert domain. Differences are notable when these results are compared to those of Al Adasani and Bai [11], Zhang et al. [5], and Taber et al.'s [10] screening methods. Their results showed that the reservoirs in the Bayou Sale and West Hasting fields are suitable for miscible CO 2 injection but not for immiscible CO 2 -EOR. As shown by the table, in reality, the fields have successfully implemented immiscible CO 2 -EOR.

Conclusions
Understanding the interdependence among screening parameters has resulted in developing a new model capable of handling the correlating parameters, namely the simultaneous screening model. The integration of simultaneous and individual screening models resulted in a combination screening model. This model is used to screen CO 2 -EOR methods and is a successful improvement on the previous models. The results obtained follow the expert domain rules. Assuming the field meets the miscible CO 2 -EOR criteria, the immiscible CO 2 -EOR is also implementable, but not vice versa. The combination screening model was implemented using several CO 2 -EOR field datasets and matched the real operations. This model also reduced screening time by determining several parameters simultaneously and not individually. Accordingly, applying the combination screening model in other fields should provide good, fast, realistic, and representative results. However, further research is still needed to develop a more reliable screening method that integrates economic aspects in order to fully assess CO 2 -EOR projects.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.