1. Introduction
The increasing concentration of CO
2, a predominant greenhouse gas, has directly contributed to global warming and climate change, posing significant threats to human survival. Research indicates that the continuous emission of CO
2 from fossil fuel combustion into the atmosphere will persist as a pressing issue [
1,
2], exacerbating the likelihood of extreme heat events and significantly impacting the hydrological cycle [
3]. Therefore, reinjecting greenhouse gases into reservoirs offers a dual benefit of reducing CO
2 emissions and enhancing oil recovery. On the other hand, as conventional oil and gas resources gradually enter their later stages, the exploitation of tight oil and gas resources with rich geological reserves has emerged as a primary direction for future development [
4,
5]. However, due to the complexity of their pore structures, these resources exhibit poor production performance and rapid decline in yields, with current recovery remaining low. Moreover, conventional methods such as water flooding make it difficult to replenish reservoir energy due to the intricate pore structures.
The unique properties of supercritical CO
2, such as its density approximation to liquid and viscosity close to gas, along with its strong diffusivity, enable effective replenishment of reservoir energy. It also exhibits multiple effects, including energy enhancement, viscosity reduction, and phase mixing. Field trials have demonstrated that CO
2 injection significantly enhances oil recovery and reduces carbon emissions, making it the most promising and effective alternative development method for tight oil reservoirs [
6]. Previous researchers [
7] began studying CO
2 injection technology in the 1970s. Hawthorne S.B. [
8] conducted CO
2 injection experiments on Bakken tight reservoir rocks, verifying the feasibility of CO
2 injection in increasing oil recovery. Ma J. et al. [
9,
10,
11,
12] conducted CO
2 huff-n-puff experiments on tight rock cores with an average permeability of 2.3 mD, showing that three cycles could increase oil recovery to 30%.
The success rate of field applications varies between 50% and 70%, with the primary reason for failure being the blind well selection. Therefore, developing a rational evaluation method before implementing CO
2 injection in tight oil reservoirs is of significant importance. The process of selecting wells for CO
2 huff-n-puff among candidate wells is complex, involving various factors influencing the effectiveness of CO
2 injection and experts from different backgrounds [
13,
14]. While pressure indices are commonly used in chemical flooding to assess plugging effectiveness [
15], the development modes of CO
2 flooding and injection often rely on selecting blocks with strong adaptability based on reasonable ranges of certain basic physical parameters. Xiong [
16] and Yu [
17] evaluated the development effectiveness of the Mahu and Bakken oil fields based on their geological, engineering, and production dynamics.
Due to the inherent uncertainty in well selection evaluation methods, fuzzy methods are commonly employed to establish evaluation systems [
18,
19,
20]. This involves normalizing using membership functions and obtaining weighting factors for each influencing factor through expert scoring. Subsequently, a comprehensive assessment factor for decision-making is calculated, and the numerical ranking of this factor determines the order of decision-making. However, this well selection method has certain limitations, primarily concerning linear membership degrees and weight assignments. The establishment of membership functions often utilizes linear functions for normalization, which may have minimal impact on conventional reservoirs but fail to capture the nonlinearity of factors affecting unconventional reservoir development. Moreover, weighting factors obtained through expert scoring are significantly influenced by the composition of the expert pool and subjective experiential biases, leading to instability and potential bias in the decision process.
This paper addresses the CO2 huff-n-puff development process in unconventional oil reservoirs. Utilizing the widely applied fuzzy evaluation method, the nonlinear characteristics of each influencing factor on development are considered. A set of exponential-based membership degree expression models is established, which accurately improved fuzzy methods. Based on examples of unconventional reservoir development, with the oil exchange ratio as the target parameter, linear regression is employed to quantify the impact of various factors on CO2 huff-n-puff development effectiveness in a manner that is more realistic and reduces subjective biases. This method facilitates the rapid calculation of priority for CO2 huff-n-puff wells based on rock and fluid properties and enables the prediction of a relatively accurate oil exchange ratio. It effectively supports the implementation of CO2 huff-n-puff development in unconventional oil reservoirs at field sites.
2. Evaluation of Individual Factors
The evaluation index system for CO
2 huff-n-puff is established based on mechanisms such as CO
2, causing oil expansion, viscosity reduction, extraction of light components from crude oil, improvement in the oil–water mobility ratio, and enhancement of reservoir permeability, in conjunction with reservoir petrophysical and fluid properties [
21,
22,
23]. The evaluation factors for CO
2 injection include reservoir thickness, formation pressure, reservoir temperature, porosity, permeability, water saturation, crude oil viscosity, and crude oil density. Subsequent production dynamics, including gas injection volume, injection rate, injection pressure, and soaking time, are controllable factors. The objective of this method is to screen wells suitable for CO
2 huff-n-puff; we do not discuss time-varying parameters such as water cut and gas–oil ratio within the scope of this paper. Therefore, the aforementioned production dynamic parameters are not considered in this study.
- (1)
Reservoir Thickness (h)
Reservoirs with a thickness greater than 10 m demonstrate relatively higher success rates for CO2 huff-n-puff. This is primarily attributed to the density and viscosity contrast between CO2 and crude oil, resulting in CO2 inducing volumetric expansion of crude oil while displacing it along with the overlying oil and water in the far zones of the well, thus creating elastic gas drive energy accumulation. Therefore, increasing reservoir thickness facilitates the occurrence of effective overlying action of CO2 in the near-well zone, thereby aiding in carrying residual mobile oil during well production. Thinner reservoirs are less prone to gas channeling, making it easier for CO2 to push residual oil toward the deeper parts of the reservoir, affecting the efficiency of enhanced oil recovery by CO2 huff-n-puff.
On the other hand, thicker reservoirs exhibit a non-uniform vertical distribution of CO2, leading to significant differences in CO2 dissolution concentrations within the fluid in the operational range. Consequently, the overall dissolution and viscosity reduction effects, as well as expansion capacity, tend to decrease with increasing reservoir thickness. Therefore, excessively thick reservoirs are not favorable for CO2 huff-n-puff.
- (2)
Reservoir Temperature (T)
Lower reservoir temperatures pose challenges for CO2 in achieving phase mixing with formation fluids. Conversely, higher reservoir temperatures facilitate CO2 expansion upon injection, enhancing its dissolution gas drive effect and improving the effectiveness of CO2 huff-n-puff in enhanced oil recovery.
- (3)
Formation Pressure (P)
CO2 effectively induces crude oil flow primarily due to factors such as viscosity reduction, light component extraction, and expansion to increase oil mobility. For a given reservoir temperature, higher pressure results in greater CO2 solubility and a closer approach to phase mixing. Phase mixing enhances the mobility of reservoir oil and allows CO2 to penetrate deeper into the reservoir, expanding the affected volume. However, excessively high formation pressure can lead to effective conventional depletion, diminishing the incremental production effect of CO2 huff-n-puff. Therefore, the effectiveness of CO2 huff-n-puff-enhanced production weakens as formation pressure continues to rise, and reasonable formation pressure should be maintained near the minimum miscibility pressure.
- (4)
Porosity (Φ)
The success rate of CO2 injection is highest when reservoir porosity is within the range of 10–20%. Excessive porosity can lead to CO2 channeling and bypassing, reducing the efficiency of carrying residual oil during CO2 huff-n-puff.
- (5)
Permeability (k)
The oil exchange ratio exhibits a logarithmic relationship with reservoir permeability levels. For ultra-low permeability reservoirs (permeability less than 1 × 10−3 μm2), permeability significantly influences the oil exchange ratio, with increasing permeability leading to a noticeable increase in oil recovery. However, for very low permeability reservoirs (permeability greater than 1 × 10−3 μm2 but less than 10 × 10−3 μm2), the influence of permeability on the oil exchange ratio is relatively minor. Excessively high permeability is susceptible to gas channeling, resulting in rapid gas diffusion to the far reaches of the reservoir, significantly reducing oil recovery efficiency. This is the primary reason why high-permeability reservoirs are not suitable for CO2 huff-n-puff in enhanced oil recovery.
- (6)
Water Saturation (Sw)
Higher water saturation leads to lower oil and gas production rates and a higher water cut, which is unfavorable for CO2 huff-n-puff development. Excessive water saturation hinders the formation of continuous oil bands during displacement, thus failing to achieve the expected CO2 injection effect. Lower water saturation is more conducive to CO2 huff-n-puff development.
- (7)
Crude Oil Density (ρ)
Crude oil density typically falls below 0.86 g·cm−3. Generally, lower crude oil density results in higher cumulative oil production. However, for CO2 huff-n-puff, the enhanced oil recovery compared to conventional depletion tends to decrease with lower crude oil density. This is because higher crude oil density, indicating higher heavy component content, enhances the CO2 extraction effect, resulting in better overall CO2 huff-n-puff effectiveness.
- (8)
Crude Oil Viscosity (μ)
Similarly, higher crude oil viscosity leads to better CO2 huff-n-puff development effectiveness. The viscosity reduction during CO2 injection depends on CO2 solubility in crude oil. Higher crude oil viscosity enhances the dissolution and viscosity reduction effect of CO2, thereby increasing CO2 huff-n-puff effectiveness.
3. Dimensionless Processing
Based on the analysis of the eight influencing factors discussed in
Section 2, the factor set
Ui for evaluating the
i-th well can be established as follows:
The factor set U can be represented as a matrix of m × n, where m is the number of influencing factors, and n represents the number of wells to be evaluated.
Previous studies have traditionally categorized factors into positive and inverse correlations and often employed linear processing models. However, the impact of some factors on development exhibits nonlinear characteristics. For instance, increasing purity from 90% to 90.1% is relatively easy, but further improving purity from 99% becomes exceedingly difficult. Moreover, linear membership calculation methods commonly set the fuzzy value of the minimum to 0, eliminating the influence of this factor on the object. This approach is questionable, as shown in
Appendix A. Thus, this study considers the nonlinear nature of factors affecting development effectiveness and employs exponential functions to normalize the factor set. It also retains the impact of each factor’s minimum value on development, even though it may be relatively minor. The influencing factors are categorized into positive, inverse, and moderate indicators.
- (1)
Positive indicator
Positive indicators correspond to factors that are more favorable for CO
2 huff-n-puff as their values increase. These include permeability, reservoir temperature, crude oil density, and crude oil viscosity, totaling four parameters. A fuzzy quantification model for these indicators is established using exponential functions as follows:
In the equation, xi represents the parameter value of the i-th indicator, xi,min denotes the minimum value of the indicator, and xi,max represents the maximum value of the indicator.
- (2)
Inverse indicator
Inverse indicators require lower values for better CO
2 huff-n-puff development effectiveness, contrasting with positive indicators. As the values decrease, they become more beneficial for CO
2 huff-n-puff development. This category includes two parameters: porosity and water saturation. The fuzzy quantification model for inverse indicators is defined as follows:
- (3)
Moderate indicator
In contrast to positive and inverse indicators, when a factor has an optimal value, it exhibits characteristics of both positive and inverse indicators. Specifically, when the indicator value is less than the optimal value, it aligns with positive indicator characteristics, while it aligns with inverse indicator characteristics when the value exceeds the optimal value. This category includes two parameters: formation pressure and reservoir thickness. The fuzzy quantification model for moderate indicators can be expressed as
We calculate the membership degree of each factor for each well. This entails identifying the distribution type of each factor (positive, inverse, and moderate indicators). Then, the factor set
U (a matrix of
m ×
n) of the evaluation objects is normalized and transformed into a fuzzy comprehensive judgment matrix
R(
ri,j).
where
rij represents the dimensionless coefficient of the
i-th influencing factor for the
j-th well, ranging from 0 to 1. A higher value indicates greater suitability for CO
2 huff-n-puff development.
4. Inverse Calculation of the Weighting Factors
The impact of various factors on development effectiveness varies, with some parameters having a greater effect while others have a lesser impact. Therefore, it is necessary to allocate weight coefficients to each factor. The widely used method for determining weight coefficients is the expert scoring method, where multiple experts anonymously score the factors to calculate their weight coefficients. However, this method is significantly influenced by the composition of the experts and subjective biases, making it difficult to accurately reflect the actual development outcomes.
This study investigated some reported practical cases to collect data reflecting the CO
2 flooding development effectiveness, particularly focusing on the oil exchange ratio as an indicator. Based on the oil exchange ratio, combined with the factor set
U, weighting factors are calculated. Firstly, the oil exchange ratios of practical cases are statistically analyzed to establish the judgment set vector
V, such as Equation (5).
Subsequently, a set of weighting factors, denoted as
w, is established for each corresponding influencing factor.
The multiplication of the fuzzy comprehensive judgment matrix
R and the weighting factors yields a vector of n elements, representing the comprehensive decision factor
C reflecting the CO
2 huff-n-puff development effectiveness of each well.
The comprehensive decision factor
Cj for the
j-th well is obtained by summing the products of all factors and their corresponding weighting factors for that well. Since both the decision factor and the oil exchange ratio can reflect the effectiveness of CO
2 huff-n-puff development, we reverse the process by using the statistically obtained oil exchange ratio parameters and the fuzzy comprehensive judgment matrix
R to calculate the combined weighting factors. This is expressed as
Furthermore, the calculated set of weighting factors is adjusted to ensure that the sum of them equals 1.
The weighting factors derived from actual production parameters eliminate or reduce human factors and have a certain theoretical basis. In the subsequent CO2 huff-n-puff well selection work, these weighting factors can be directly utilized as the basis for identification.
Finally, based on Equation (8), the comprehensive decision factor is calculated. The calculated decision factor represents the evaluation results of each factor and serves as the basis for well selection and prioritization for CO
2 huff-n-puff operations. A higher numerical value indicates a higher priority for CO
2 huff-n-puff operations. The specific calculation process is shown in
Figure 1.
5. Case Analysis
Due to the predominant use of depletion-driven development in unconventional reservoirs, there are limited cases of CO
2 huff-n-puff, and they have not generally reached a significant scale. This study systematically surveyed and compiled data on eight key parameters and oil exchange ratios (
Roe) from seven successful cases, establishing a set of factors for CO
2 huff-n-puff well selection, as presented in
Table 1.
The table includes permeability, temperature, crude oil density, and crude oil viscosity, where higher values are considered more favorable, while porosity and water saturation are optimal at lower values. Reservoir thickness and formation pressure are considered suitability indicators with optimal values. The membership degrees for each factor are calculated separately, transforming the table into a fuzzy matrix, as shown in
Table 2. The optimal values for formation pressure and reservoir thickness are taken as 25 MPa and 20 m, respectively. We mainly emphasize this method, and the selection of the optimal value is not representative. The determination of optimal values necessitates careful analysis in conjunction with specific issues encountered in indoor experimental setups or field applications within mines.
Using the statistically obtained oil exchange ratios as the target parameter and the parameters of seven blocks, namely Bakken, Eagle Ford, Chattanooga, Appalachian, Lost Soldier, Fuyu, and Mahu, and based on the literature survey-derived oil exchange rate parameters, the weighting factors are calculated in reverse, as shown in
Table 3.
The weighting factors also reflect the relative importance of each factor in influencing the effectiveness of CO
2 huff-n-puff development. The priority order of the weighting factors is porosity, reservoir temperature, water saturation, formation pressure, reservoir thickness, crude oil density, crude oil viscosity, and permeability. By incorporating the weighting factors and the fuzzy evaluation matrix into Equation (8), the comprehensive decision factors are calculated, as shown in
Table 4.
The relationship between the oil exchange ratio response and the comprehensive well selection decision factors is plotted in
Figure 2. It is evident that the oil exchange ratios of the seven blocks exhibit a clear positive correlation with the comprehensive decision factors, validating the accuracy of the weighting factors. The well selection decision method established in this study accurately reflects the effectiveness of CO
2 huff-n-puff.
In the practical application of this method, the relevant parameters of the target wells can first be statistically gathered, as shown in
Table 1. Using the membership degree calculation method, the data from
Table 1 can be transformed into dimensionless data in
Table 2. Subsequently, the comprehensive decision factors for each well are calculated based on the weighting factors we have determined, representing the priority of CO
2 huff-n-puff. The wells are then prioritized for CO
2 injection operations based on the magnitude of these factors. By considering the linear relationship between the comprehensive decision factors and the oil exchange ratio, the oil exchange ratio of this scheme can be predicted based on actual data. Taking the tight oil reservoirs in the Ordos Basin as an example, the basic model parameters are presented in
Table 5.
Utilizing the nonlinear membership degree calculation method, each parameter is separately made dimensionless, and the parameter matrix is transformed into a fuzzy matrix. Among them, the maximum and minimum values of each parameter are based on the data in
Table 1.
Substituting the coefficients from
Table 6 and the weighting factors into Equation (8) yields the comprehensive decision factor for CO
2 huff-n-puff of the tight oil reservoirs in the Ordos Basin, with a value of 0.617. From the data in
Table 4, this value falls between the Chattanooga and Eagle Ford reservoirs. Using the linear trend line in
Figure 1, it can be predicted that the oil exchange rate of CO
2 huff-n-puff in Ordos Basin is approximately 0.354 t/t.