Analysis of Microscopic Main Controlling Factors for Occurrence of Movable Fluid in Tight Sandstone Gas Reservoirs Based on Improved Grey Correlation Theory

College of Sciences, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China College of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China Shaanxi Key Laboratory of Advanced Stimulation Technology for Oil & Gas Reservoirs, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China Changqing Downhole Technology Company, Petro China Chuanqing Drilling Engineering Company Limited, Xi’an 710065, Shaanxi, China Sinopec Green Source 1ermal Energy Development Co., Ltd, Xianyang 712000, Shaanxi, China Research Institute of Exploration and Development, Petro China Changqing Oilfield Company, Xi’an 710018, Shaanxi, China National Engineering Laboratory for Exploration and Development of Low Permeability Oil and Gas Fields, Xi’an 710018, Shaanxi, China


Introduction
e exploration and development of tight sandstone oil and gas in unconventional oil and gas occupy an increasingly important position in the field of oil and gas exploration in China [1][2][3]. Under the coupling action of time, temperature, pressure, and other factors, the creep characteristics of rock particles at different buried depths are different, resulting in different types of reservoirs with different pore structure characteristics, storage and seepage capabilities [4][5][6][7]. Pores and throats are the main channels for controlling fluid seepage [8,9]. e size and distribution of pores and throats affect the connectivity and seepage capacity of pores and throats [10,11]. A large number of studies have shown that the proportion set of movable fluids includes reservoir, storage capacity, and fluid storage characteristics, and it is more ideal to characterize the physical properties of ultra-low permeability reservoirs. However, the tight sandstone reservoirs have the characteristics of poor physical properties, small pore throats, and strong microheterogeneity [12][13][14][15] compared with conventional reservoirs, which leads to complex reservoirs of movable fluids and difficult mining. At present, new technologies and methodologies are introduced by many scholars to discuss the occurrence of movable fluids in tight reservoirs and their main controlling factors and have achieved certain results. For example, some scholars combine high-pressure mercury intrusion, nitrogen adsorption, image analysis, and other technical methods with nuclear magnetic resonance experiments to reveal the influence of microgeological factors on the occurrence of movable fluids in the reservoir. Studies have shown that the recoverability of oil and gas reservoirs is mainly affected by the pore structure and the occurrence characteristics of movable fluids; the microscopic pore structure characteristics have a significant impact on movable fluids [16][17][18][19].
However, their research mainly uses qualitative analysis methods to describe the impact of reservoir microgeological factors on the occurrence of movable fluids. e interaction between various factors has not been considered, and it is difficult to accurately quantify the impact of microgeological factors on the reservoir movable fluids, which has become one of the technical bottlenecks restricting the development of tight oil and gas reservoirs. erefore, taking the tight sandstone reservoir of He8 formation in Sulige gas field as an example, based on the physical properties of the reservoir, constant velocity mercury intrusion, and nuclear magnetic resonance experiments, the scientific determination resolution coefficient is introduced, and the improved gray correlation analysis model is established to determine the main controlling factors affecting the occurrence of movable fluids in tight sandstone gas reservoirs with near/similar physical properties. It provides reliable microscopic geological basis for finding the "sweet spot" of tight sandstone reservoir and its further efficient development.

Experimental Samples and Test Methods
(1) Before Testing, Wash the Sample With Oil. e sample was washed with methanol and dichloromethane mixture in the Soxhlet extracter. When the fluorescence of the washing fluid was very low and unchanged, the washing oil was considered to be finished, and the sample was dried continuously by microwave at 100°C for 24 h.
e experimental methods were strictly carried out in accordance with SY/T6385-1999 "Test method for porosity and permeability of overburden rocks" [20]. FYKS-1 porosity-permeability tester with high temperature and overburden pressure has tested the porosity and permeability.
e main technical parameters are as follow: e effective pressure of simulated formation is less than 70 MPa; the effective temperature of simulated formation is less than 150°C; applicable core is Φ25 × 25∼80 mm or Φ38 × 40∼80 mm; measuring range of permeability is (0.01∼8000) × 10 −3 μm 2 , measuring range of porosity is less than 50%; measurement precision of permeability is less than 10% for low permeability reservoir and 5% for medium and high permeability reservoir; measurement precision of porosity is 0.5%.
(3) NMR Experiment. e nuclear magnetic resonance T 2 spectrum was measured by MicroMR20-025 from Newmai Company. e main frequency intensity was 23 MHz, the core diameter was 25 mm, the length was 2-4 cm, the echo interval was 0.2 ms, the waiting time was 6 s, and the echo number was 8000. e experimental method is strictly in accordance with SY/T6490-2014 "Laboratory measurement specification for nuclear magnetic resonance parameters of rock samples" [21]. e experiment was carried out at 22°C.
(4) CVMI Experiment. e experimental method was strictly carried out in accordance with GB/T29171-2012 "Rock capillary pressure measurement" [22]. e maximum mercury injection pressure in the constant rate mercury injection test was 0.006895 MPa.

Dimensionless Method.
It is necessary to standardize each parameter [25] for making the parameters comparable, due to the different dimensions of different parameters and the large difference in value. e method is as follows: (1) For the parameters (excluding parameters other than the effective pore-throat radius ratio) which are positively correlated with reservoir microscopic pore-throat structure characteristics and movable fluid saturation, divide directly by their maximum value. (2) For parameters that are negatively related to characteristic parameters of reservoir microscopic pore throat structure and saturation of movable fluid (effective pore-throat radius ratio), the maximum value is used to subtract the difference of the parameters and then divided by the maximum value.

Improved Grey Relevance eory.
e concept of relevance analysis is proposed by Grey system theory, which can provide mathematical analysis methods to clarify the relationship between various factors in the system and find the most influential factors [26][27][28]. In the traditional gray correlation analysis method, the resolution coefficient is not quantified but a fixed value 0.5, without considering the distortion of the correlation degree measurement caused by the abnormal value in the data. e improved gray correlation analysis method introduces the quantization process of the resolution coefficient, which makes the calculation process more reasonable [29][30][31]. e steps are as follows: e absolute value of reference sequence and the reference sequence subtraction at each point is Maximum range is Minimum range is Correlation coefficient is where ε 0i (k) is the relative difference between the comparison curve X i (k) and the reference curve In order to weaken the influence of the correlation coefficient distortion caused by too large size and enhance the significant difference between correlation coefficients, a coefficient or resolution is artificially introduced, and its value is between 0∼1. e quantization method is as follows: Assuming that ∇ θ is the average value of the absolute difference of indicators, then . e value of ρ follows the following principles: If 0 < 1/ε < 2 that is, the normal value, 2ρ > 1, let ρ ∈ (0.8, 1), and 1 is used in this paper.

Reservoir Physical Properties and Movable Fluid.
Porosity and permeability are not only indicators to characterize reservoir quality, but also closely related to the difficulty and effectiveness of oil and gas field exploitation [19]. It is show that, porosity is distributed in the range of 6.9%∼18.3%, with an average of 11.735%; permeability is with an average value of 0.291 × 10 −3 μm 2 , by physical testing and analysis of 10 representative cores in the reservoir of the He 8th member of the study area, and it belongs to a typical tight sandstone gas reservoir. Reservoir porosity has a positive linear correlation with permeability (Figure 1), but the correlation is not strong (R 2 � 0.488), which shows that the pore structure of the reservoir is complex, and the physical properties of the reservoir and the fluid flow capacity are controlled by a variety of microgeological factors.
It is found that the movable fluid saturation of the He 8th member in the study area is between 5.38%∼32.67%, with an average of 17.56% (Table 1), which based on some scholars' research on the movable fluid of He 8 formation in the east of Sulige gas field.
We have the conclusion that there is a different degree of overlap in information for a single characteristic parameter, by in-depth analysis of the constant velocity mercury intrusion and physical property analysis results of 10 core samples from He 8 reservoir. erefore, the reservoir quality factor is introduced, denoted by RQI � ��� � K/ϕ [19], and it divides the reservoir into two types: I (RQI ≥ 0.15) and II (RQI < 0.15) ( Table 1).

Microscopic Pore Structure Characteristics of Reservoir.
According to the analysis of casting thin sections and scanning electron microscope data (Figure 2), it can be seen that the reservoir space types of tight sandstone reservoir in He 8 in the study area only include residual intergranular pores, dissolution pores, and intercrystalline pores. It is shown that the pores of the tight sandstone reservoirs in He 8 formation of the study area are macropores, and the pore size and distribution interval are similar, the main pore radius distribution interval is between 120 μm∼150 μm and most of the throats belong to the fine throat-thin throat, and the pore throat radius is relatively large ( Table 2), based on previous research and analysis of Wang Daofu's pore classification standard and Li Daopin's throat classification standard. e pore-throat configuration relationship of different types of reservoirs is analyzed by mercury margin, which can be denoted by β, and the calculation formula of mercury ingress margin is where S t (%) is throat Saturation of Mercury, S p (%) is pore mercury saturation, and S (%) is total mercury saturation. It is found that the mercury ingress margin for type I reservoirs is 0.24∼1.47, the average value is 0.837; the mercury ingress margin of type II reservoirs is 2.09∼3.7, and the average value is 2.958; the percentage of mercury ingress in the throat of type I and II reservoirs is gradually increasing, and the reservoir is gradually controlled by the throat, based on the constant velocity mercury intrusion experiment results of 10 rock samples from the He 8th reservoir in the study area and using formula (1) to calculate the mercury ingress margin of each sample. At the same time, the analysis of the relationship between each microscopic pore structure characteristic parameter and movable fluid saturation found ( Figure 3) showed that only mercury intake margin and effective pore throat radius ratio were negatively correlated with movable fluid saturation, while other parameters were positively correlated with movable fluid saturation, and the correlation was significantly different.

Grey Correlation Degree between Micropore Structure Characteristic Parameters and Movable Fluid Saturation.
e movable fluid and micropore characteristic parameters of 10 samples from the He 8 tight sandstone reservoir in Sulige Gas Field were selected as the research object (Tables 1  and 2), Based on the results of reservoir classification, the same type of reservoir is used and the improved grey correlation theory is selected to quantitatively characterize the influence of the microscopic pore structure characteristic parameters of near/similar reservoirs on the occurrence of movable fluids.
According to the relevant data of each parameter in Tables 1 and 2, the movable fluid saturation and the characteristic parameters of the micropore are regarded as the parent sequence and the subsequence, respectively Taking the improved gray correlation theory, determine the gray correlation degree ranking between the microscopic pore structure characteristic parameters of the near/similar reservoirs and the movable fluid saturation, as shown in Table 3.
It can be seen from Table 3 that the relationship between the characteristic parameters of microscopic pore throats and the movable fluid saturation and their rankings show that the movable fluid saturation of Type I reservoirs is mainly affected by the effective pore-throat radius ratio, the total throat mercury saturation, and the effective pores radius. ese three characteristic parameters reflect the pores, throat size, and pore-throat configuration relationship and determine the effective way of fluid passage and the degree of restraint in the pores, indicating that the existence law of movable fluid in this type of reservoir is restricted by the connection of effective pore throats. Movable fluid saturation in Type II reservoirs is mainly affected by three factors:    effective throat volume per unit volume, total throat mercury saturation, and mainstream throat radius. We can get the conclusion that the presence of fluid in the effective throat of this type of reservoir has absolute control over the distribution of movable fluid.

Results and Conclusions
(1) e average value of pores in He 8 tight sandstone reservoir of the study area is 11.735%, and the average of permeability is 0.291×10 −3 μm 2 , which is a typical tight sandstone reservoir. Taking the size of the reservoir quality factor as the evaluation criterion, the reservoir is divided into two types, I and II, and the quality of the reservoir gradually deteriorates, and the physical properties of similar reservoirs are similar. (2) Using different types of reservoirs as data sets, the improved grey correlation theory was used to quantitatively characterize the influence of the microscopic pore structure of reservoirs with near/similar physical properties on the occurrence of movable fluids. Among them, the movable fluid saturation of Type I reservoirs is mainly affected by the effective pore-throat radius ratio, the total throat saturation of mercury, and the effective pore radius. e movable fluid saturation of Type II reservoirs is mainly affected by the effective throat volume per unit volume, the influence of the mercury saturation of the total throat and the radius of the mainstream throat. erefore, the occurrence state of movable fluids in Type II reservoirs is controlled by the throat radius stronger than in Type I reservoirs. (3) It is shown that the reservoirs in He 8 tight sandstone reservoir of the study area are mainly of throat type, and the mercury ingress margin of type I reservoirs is significantly less than that of type II reservoirs; the proportion of mercury in the throats of type I and II reservoirs is gradually increasing, and the reservoirs are affected by throats. e control effect is gradually increasing. Based on the constant velocity mercury injection experiment, the "mercury ingress margin" was introduced to analyze the pore-throat configuration relationship of different types of reservoirs in He 8 tight sandstone reservoir of the study area.

Data Availability
e data used to support the results of this study are included within the manuscript.

Conflicts of Interest
e authors declare that there are no conflicts of interest. Mathematical Problems in Engineering 7