Research Status, Existing Problems, and the Prospect of New Methods of Determining the Lower Limit of the Physical Properties of Tight Sandstone Reservoirs

Abstract

At present, many methods are used to determine the lower limits of physical properties (PPLLs) of tight sandstone reservoirs, such as empirical statistics, oil occurrence, and logging parameter crossplots, but the accuracy with which these methods obtain the lower limit of physical properties depends entirely on the number of test production data, and they are not suitable for tight sandstone reservoirs with a low degree of exploration and a lack of prediction. Compared to these mature methods, it can be concluded that the water-film-thickness-based method, which integrates factors such as formation temperature, formation pressure, mineral wettability, and formation water salinity, can characterize PPLLs using the minimum pore throat radius for hydrocarbon migration, which has a better theoretical basis and technical advantages. However, the water-film thickness is not a fixed value and cannot be directly measured in the laboratory. The molecular simulation method, known as a computational microscope, has become an effective means of investigating nano effects. By accurately investigating the interactions between rock minerals and the formation of water on atomic and molecular scales based on increasingly improved studies of the molecular force field, this method can overcome the deficiencies of the laboratory study of water films and precisely characterize the water films’ thickness. The intersection of molecular simulation and geology can bring about new methods and new research ideas for determining the lower limit of the physical properties of tight sandstone reservoirs and has broad application prospects.

1. Introduction

Compared with other unconventional reservoirs, such as shale reservoirs, tight sandstone reservoirs have higher seepage capacity and fracability. Therefore, tight sandstone oil and gas resources are one of the best choices to replace conventional oil and gas resources and realize the transition from conventional oil and gas exploitation to unconventional oil and gas exploitation [1,2,3,4,5]. With the continual efforts of oil and gas geologists and the strong support of national policies, China’s exploration and development of tight sandstone oil and gas resources have made great progress in both the theoretical basis and the production practice, and a stage of rapid development has now been entered, and China has become the international leader in some technical aspects of tight oil and gas exploration and development [6,7,8,9,10]. Breakthroughs have been made in tight sandstone gas recovery in basins such as Ordos, Songliao, Junggar, and Sichuan in China by referencing successful experiences in the exploration and development of hydrocarbons in North America [11,12,13,14,15]. However, there are many difficulties with the determination of PPLL since tight reservoirs are generally characterized by low compositional maturity, high lithium content, and strong compaction due to their large burial depth and complex diagenesis.

It is necessary to determine PPLLs for the classification, evaluation, and calculation of reserves of reservoirs, with the PPLLs including the lower limits of porosity and permeability and the upper limit of water saturation [16,17]. The lower limit of porosity refers to the minimum porosity of hydrocarbon reservoir rocks at which oil and gas can be produced, and it is closely related to the properties of fluids in the reservoirs, the connectivity of rock pores, and permeability. The lower limit of permeability refers to the minimum permeability of hydrocarbon reservoir rocks at which oil and gas can be produced, and it is closely related to the properties of fluids in the reservoirs, saturation, and the connectivity of rock pores. The upper limit of water saturation refers to the maximum permeability of hydrocarbon reservoirs, above which water rather than oil and gas can be produced. According to the concept of relative permeability, the upper limit of water saturation is 70%. The accurate determination of the PPLLs of tight reservoirs is of great significance for the prospecting of new strata and new fields.

Presently, the most widely used methods for determining PPLLs include the empirical statistical method and those based on well tests, oil occurrence, drilling fluid invasion, the parameters of mercury injection capillary pressure (MICP), and irreducible water saturation [18,19,20,21]. These traditional methods are effective for conventional reservoirs with good pore structure and abundant oil-testing data. When applied to tight sandstone reservoirs with poor physical properties, micro-fracture development, and little oil and gas testing data, the accuracy of the prediction depends more on the number of samples [22,23,24]. When the existing methods cannot solve this problem, we put forward the following considerations. Considering the characteristics of high clay content and the complex pore structure of tight sandstone reservoirs, can we establish a set of methods for determining the PPLLs with high accuracy and strong predictability? Based on this problem, this paper introduces the water-film-thickness method and introduces molecular simulation technology to study the complex physical and chemical interactions between rock and mineral surfaces and underground saline ions at the molecular and atomic scales [25,26] from multiple perspectives, such as basic mineralogy and material chemistry [27,28]. The water-film thickness is accurately characterized and provides a new idea and method for determining the lower limit of the physical properties of tight reservoirs.

2. Research Status of Determining the PPLLs

There are two classes of commonly used methods for determining PPLLs. One class is used to determine the PPLLs of tight reservoirs based on massive statistical data on actual production. This class of methods includes those based on empirical statistics, oil occurrence, and log-parameter cross-plots. The other class is used to determine the PPLLs of tight reservoirs based on the analytical results from various experiments on samples, including those based on the minimum flow-pore-throat radius and irreducible water saturation [29,30,31].

2.1. Empirical Statistical Method

The empirical statistical method is based on the core porosity and permeability data obtained by analyzing a large number of existing core samples and determining reservoir PPLLs using the proportion of the cumulative loss of the storage and seepage capacities caused by samples with low porosity and permeability. The proportion of the cumulative loss of the storage and seepage capacities refers to the percentage of cumulative porosity (permeability) multiplied by the thickness of the samples with physical properties below the PPLLs in the storage and seepage capacities of the total samples. In a nutshell, the basic principle of the method is to use large amounts of core porosity and permeability data to find a lower limit below which the loss of reservoir capacity and permeability is negligible. Generally, the porosity and permeability corresponding to the 5% cumulative loss of the storage and seepage capacities are assumed to be PPLLs. Generally, the porosity and permeability values corresponding to the loss ratio of cumulative storage and permeability of 5% are taken as the PPLLs. In practical application, the porosity and permeability corresponding to the 5% cumulative loss of the storage and seepage capacities are also used as the limit in different areas [32,33,34].

At present, this method is widely used to determine reservoir PPLLs in various oil fields at home and abroad. Although the empirical statistical method is a relatively mature method to obtain the reservoir PPLLs, it must be based on huge numbers of core data and will be mixed with some subjectivity when determining the proportion of the cumulative loss of the storage and seepage capacities. In addition, the empirical statistical method has a better application effect on reservoirs with a good correlation between porosity and permeability, and the actual use should take into account the reservoir permeability characteristics of different reservoirs rather than blindly “rigid”.

Lv, X.Y. et al. [35] determined the PPLLs of the tight sandstone gas reservoirs in the middle to lower sections of the third member of the Shahejie Formation (Es3) in the Duzhai area of the Dongpu sag using the empirical statistical method. With the proportion of the cumulative loss of the storage and permeability capacities of 5% as the limit, they determined the PPLLs of effective reservoirs, including the lower limit of permeability of 0.037 × 10⁻³ μm² and the lower limit of porosity of 3.92%, which corresponded to the cumulative frequency of porosity of 16.50%. The reservoirs have a small loss in storage and seepage capacities under these low limits, which are therefore reasonable (Figure 1).

2.2. Oil-Occurrence-Based Method

According to the previous development experience of tight sandstone reservoirs in China, the physical properties of effective reservoirs have a good correlation with their oiliness, and in the study of underground oil-bearing reservoirs, the core is the most primitive and closest to the real situation of the reservoir. The research shows that the physical properties of effective reservoirs have a good correlation with their oil content, so we can determine the reservoir PPLLs according to the oil-bearing occurrence of the core. On the basis of the oil test results, the oil-bearing characteristics of the core (oil saturation, oil immersion, oil spots, or oil traces) are defined, and the reservoir is divided into two types, namely oil-bearing and dry layers. According to the oil-bearing characteristics, the permeability and porosity data of the core of the oil-bearing and dry layers are statistically classified, the physical property boundary of the two types of reservoirs is divided, and then the physical property parameters of the core samples are tested, the corresponding relationship between oil occurrence and physical property parameters of core is established, and the relationship between oil-bearing characteristics and porosity parameters is drawn. Finally, the PPLLs are determined according to the relationship diagram [36,37]. This method only needs single-layer oil test results and corresponding porosity and permeability values to obtain the PPLLs and does not require formation pressure, flow pressure, or other data. This method has the advantages of simplicity and strong operability and is especially suitable for areas with few formation test data.

Zhang, B.S. et al. [38] investigated the PPLLs of the tight sandstone gas reservoirs in the Dibei area of the Tarim Basin using the oil-occurrence-based method. Based on the oil occurrence, they divided the gas reservoirs into effective reservoirs (with fluorescence) and dry layers and then determined the PPLLs of the reservoirs by combining the porosity–permeability cross plot. As shown in Figure 2, when the porosity was below 2% and the permeability was below 0.03 × 10⁻³ μm², no fluorescence was displayed in the core samples; the lower limit of the porosity of the reservoir was assumed to be 2%, and the lower limit of the permeability was assumed to be 3%. In the course of the application of this method, it was found that the oil-bearing occurrence method is only applicable to oil-bearing reservoirs and cannot be applied to natural gas reservoirs. In the process of obtaining PPLLs, the properties of the crude oil and human factors will have a certain influence on the results obtained.

2.3. Log-Parameter Cross-Plot-Based Method

Porosity and permeability are the most basic and important physical parameters used to evaluate reservoirs. They are usually correlated with each other and are often accompanied by the statistical distribution of the power function. First, the porosity and permeability data are obtained by analyzing the core. Then, the cross plot of porosity and permeability is drawn. Finally, the inflection point of the porosity distribution curve with drastic changes is determined. The corresponding porosity and permeability data at this point can be used as a basis for judging the PPLLs. The variation in permeability with porosity can be divided into three categories: (1) the permeability does not vary significantly with an increase in the porosity, indicating ineffective pores with poor connectivity; (2) the permeability shows a certain upward trend with an increase in the porosity, indicating effective pores with a certain flow capacity; and (3) the permeability increases significantly with an increase in the porosity, indicating effective pores with a high and stable flow capacity. Duan, Y.N. et al. [39,40,41] pointed out, when studying the PPLLs of tight sandstone reservoir in the Sugali gas field, that, based on the pore-permeability cross plot, oil and gas test results could be combined with other related logging parameters, and the statistical relationship with the PPLLs of the reservoir could be further determined according to the characteristics of different logging parameters, which would make the obtained results more close to the actual formation conditions.

Li, Y. et al. [42] investigated the PPLLs of the gas reservoirs in the second member of the Upper Triassic Xujiahe Formation in the Sichuan Basin using the porosity–permeability cross plot and massive data on porosity and permeability. They found that the permeability varied slightly and increased significantly with an increase in the porosity when the core porosity was 6% and greater than 6%, respectively. Therefore, the PPLLs are estimated to be 6%. Based on the functional relationship (the equation is shown at the top of Figure 3) corresponding to the trend of the pore permeability of the sample, the lower limit of permeability was 0.038 × 10⁻³ μm². Li, Y. et al. [42] found that determining the inflection point is subjective and there will be some errors, but this method is still a practical method to determine the reservoir PPLLs.

2.4. Minimum Flow-Pore-Throat Radius-Based Method

The macroscopic seepage capacity of the reservoir is strongly influenced by the microscopic pore structure and the throat of tight sandstone reservoirs. The pore size determines the ability of the rock to store oil and gas, and the radius and shape of the throat determine the seepage capacity of oil and gas [43,44,45]. For a given pressure difference, the smaller the throat radius, the higher the capillary pressure, and the greater the resistance to the flow of oil and gas, and the flow rate of oil and gas will be smaller. The minimum throat radius that can ensure the movement of oil and gas in the pores is called the minimum flow-pore-throat radius. Usually, in a calculation, the capillary pressure curve and the other data can be obtained according to the MICP test and other methods to analyze the pore structure of rocks. Then, the minimum pore-throat radius of the reservoir is calculated by using the Purcell method or the Wall method formula, and the pore-throat radius corresponding to the cumulative permeability contribution that reaches 99.99% is the minimum flow-pore-throat radius, and the corresponding reservoir PPLLs are determined [46,47].

During the experiment, it was found that the capillary curve obtained from the mercury injection test of a single core sample can only reflect a very small dispersion point in the reservoir and cannot represent the whole reservoir due to the heterogeneity of the reservoir. Therefore, in the process of practical application, researchers average and synthesize all the measured data and derive the J function for calculation according to the capillary formula and pore radius formula [48]. This function comprehensively considers the interfacial tension of fluid and reservoir wettability and more accurately characterizes the characteristics of the capillary force curve.

The expression of the J-function is as follows:

$$J(S_w)=\frac{P_c}{\sigma \cos \theta }\sqrt{\frac{K}{\phi }}$$

(1)

where J is the J-function J, dimensionless; S_w is the water saturation, %; P_c is the capillary pressure, MPa; K is the permeability, 10⁻³ μm²; φ is the porosity, %; $\sigma$ is the interfacial tension, mN/m; and θ is the wetting angle, °. As the MICP experiment adopts the mercury–air system, it is practical to take $\sigma$ = 0.048 × 10⁻³ mN/m and θ = 140°.

The Purcell method reflects the cumulative contribution of pore-throat radii to permeability through the relationship between mercury injection pressure and the volume of mercury injected. Specifically, this method divides the logarithms of the pore throat radii into several units and then calculates the contribution of each unit to the permeability [49]. The specific calculation equations are as follows:

$${\sum }_{i=1}^n∆K_i=∆K_1+∆K_2+\cdots ∆K_n$$

(2)

$$∆K_i=\frac{∆K_{mi}}{{\sum }_{i=1}^n∆K_{mi}}$$

(3)

$$∆{\mathrm{K}}_{\mathrm{m}\mathrm{i}}=\frac{1}{2}(\frac{1}{{\mathrm{P}}_{\mathrm{c}\mathrm{i}}^2}+\frac{1}{{\mathrm{P}}_{\mathrm{c}\mathrm{i}+1}^2})·∆{\mathrm{S}}_{\mathrm{i}+1}$$

(4)

where ${\sum }_{i=1}^n∆K_i$ is the cumulative contribution of all units to permeability, %; $∆K_i$ is the contribution of a unit interval to permeability, %; $∆S_{i+1}$ is the volume of mercury injected of a unit interval, %; and i is the number of the unit interval of the pore throat radius.

The Wall method reflects the cumulative contribution of pore throat radii to permeability through the relationship between pore throat radii and the volume of mercury injected. Specifically, this method calculates the cumulative contribution of each pore volume permeability based on the equal pore volume increment. The specific calculation equation is as follows:

$$∆{\mathrm{K}}_{\mathrm{i}}=\left[\right.(2\mathrm{i}-1){\mathrm{r}}_{\mathrm{i}}^2/{\sum }_{\mathrm{i}=1}^{\mathrm{n}}(2\mathrm{i}-1){\mathrm{r}}_{\mathrm{i}}^2\left.\right]\times 100$$

(5)

where r_i is the pore throat radius, μm.

Ye, C. et al. [49] plotted the curve of the J-function for reservoirs of the first member of the Shanxi Formation in the Longdong area, Ordos Basin, based on the data from the MICP analysis (Figure 4). Moreover, they determined that the MICP samples from this area had an average porosity and permeability of 5.1% and 0.058 × 10⁻³ μm², respectively. Then, they determined that the pore-throat radius at and above which the pore throat radii cumulatively contribute 99% of permeability was 0.0164 μm using the Wall method. By establishing the cross plots of the pore throat radius vs. porosity and permeability, they calculated that the lower limits of porosity and permeability were 4.2% and 0.062 × 10⁻³ μm, respectively (Figure 5). In summary, this method is a relatively accurate method of obtaining the PPLLs of reservoirs, but whether this method can be applied depends on the number of core data. If the number of cores is small, the capillary pressure characteristics of the reservoir cannot be well characterized, and the accuracy of the results of obtaining PPLLs will be greatly affected.

2.5. Irreducible-Water-Saturation-Based Method

Compared to conventional reservoirs, the rock particles in tight sandstone reservoirs have a higher surface energy. This allows them to adsorb more water, known as irreducible water [50,51]. The pore space of a reservoir can be divided into the pore space that allows fluid to flow freely and the pore space that holds irreducible water. When irreducible water occupies all the pore space of a reservoir, oil and gas cannot be stored and flow, and the pores are considered invalid. In theory, the porosity and permeability values corresponding to the irreducible water saturation of 100% are the PPLLs of the reservoir [52,53,54,55]. Due to the different definitions of dry layers in practical applications, the lower charging limit corresponding to 100% irreducible-water saturation is often less than the PPLLs of an effective reservoir. Previous studies have shown that when irreducible-water saturation exceeds 80%, the reservoir space is microporous, and its storage and permeability performance is poor. Therefore, the porosity corresponding to the irreducible water saturation of 80% is usually used as the reservoir PPLL. When determining the irreducible-water saturation of tight sandstone reservoirs, the results will be influenced by factors including the pore radius, the mass fraction of clay minerals, the pore type, and the wettability, resulting in the deterioration of the functional relationship between permeability and bound water saturation, which will further cause errors in the results of obtaining the PPLLs. Therefore, multiple methods for obtaining the PPLLs should be combined for verification.

With the porosity corresponding to the irreducible water saturation of 80% as the lower limit of porosity, Wang, Y.Z. et al. [56] established the functional relationship between the porosity and irreducible water saturation of the Paleogene reservoirs at a depth of 3.0–3.2 km in the Dongying sag. Then, they verified the results by combining other methods for determining PPLLs and determined the lower limit of porosity at 9.09% (Figure 6).

3. Analysis of the Applicability of Determining the PPLLs

Different methods of determining PPLLs require different geological data and apply to different stages, and their results have different meanings. Some methods, such as the empirical statistical method and the methods based on oil occurrence and log-parameter cross plots, are simple and easy to operate. However, their results are not accurate enough, although they agree well with the actual production. These methods are based on principles of statistics, and thus their results tend to be greatly affected by subjectivity and sample quality. The methods based on the minimum flow-pore-throat radius and irreducible water saturation are based on the analysis and testing of cores and can be employed to derive the PPLLs by establishing corresponding mathematical and physical models. The two methods take into account the effects of the microscopic pore-throat structure on the PPLLs and provide a new direction for research on PPLLs. However, they encounter the difficulties of a lack of data on samples and unified criteria and scales for relevant analyses and tests.

Table 1. Methods for determining the lower limits of physical properties of reservoirs.

Method	Data Used	Content	Advantages and Disadvantages
Empirical statistical method	Porosity and permeability	The porosity and permeability corresponding to the cumulative loss of the storage and seepage capacities of 5% are taken as the PPLLs.	Advantages: simple and easy to operate, and the yielded PPLLs agree with the actual production when there are a large number of samples; Disadvantages: involving certain subjective judgment, and accurate results can be obtained only when there are plenty of samples [32,33,34].
Oil-occurrence-based method	Well test results, porosity, and permeability	The reservoir PPLLs above the criteria for dry layers are obtained based on well test results and corresponding porosity and permeability.	Advantages: can determine the boundary of commercial hydrocarbon flow based on the criteria for dry layers; applies to crude oil with high viscosity; Disadvantages: not suitable to determine low production reservoirs since the oil occurrence of cores is greatly affected by well test technology and human factors [36,37].
Log-parameter cross-plot-based method	Porosity, permeability, and other log data	Based on a large number of samples, the inflection point of permeability varying with porosity is determined using the porosity–permeability cross plot. The reservoir PPLLs can be determined based on the inflection point, as well as other log parameters.	Advantages: easy to operate; Disadvantages: the inflection point is difficult to determine, and massive sample data are required [39,40,41].
Minimum flow-pore-throat-radius-based method	Porosity, permeability, and data from MICP analysis	The porosity and permeability corresponding to the pore-throat radius at and above which pore-throat radii cumulatively contribute 99.9% of the permeability are taken as the reservoir PPLLs.	Advantages: reflecting the effects of microscopic pore-throat radii on the physical properties of reservoirs based on MICP tests and yielding relatively objective PPLLs; Disadvantages: insufficient data on MICP samples and high requirements for the representativeness of the samples [43,44,45].
Irreducible-water-saturation-based method	Irreducible-water saturation, porosity, and permeability	The porosity and permeability corresponding to the irreducible water saturation of 80% are considered the reservoir PPLLs.	Advantages: simple; Disadvantages: the results are not accurate enough, with the irreducible-water saturation of 80% as the limit since different experiments yield different values of irreducible water saturation [51,52,53].

summarizes the applicability and limitations of several methods for determining PPLLs. According to this table, most of these methods are based on the storage and permeability capacities of reservoirs and determine the reservoir PPLLs through the statistical analysis of parameters such as porosity and permeability. Moreover, their results are influenced by factors such as the quantity and representativeness of samples and human judgment. The PPLLs of effective reservoirs refer to the lower limits at which commercial hydrocarbon flow can be obtained using existing techniques. However, as tight oil- and gas-production techniques and processes improve, PPLLs are getting closer to the lower limits of hydrocarbon accumulation and charging, with the latter reflecting the hydrocarbon charging process under the formation temperature and pressure by using the minimum pore-throat radius for hydrocarbon migration. Therefore, there is a lack of a method to determine the in situ PPLLs of tight reservoirs while considering temperature and pressure under the reservoir conditions.

4. Analysis of the Theoretical and Technical Advantages of the Water-Film-Thickness-Based Method to Determine the PPLLs

The study of the PPLLs for hydrocarbon accumulation and charging is a very important link in the decision making and implementation of tight oil and gas development. Compared with conventional methods, the water-film-thickness-based method takes into account the process of hydrocarbon charging through tiny pore throats and reflects factors such as temperature, pressure, mineral wettability, and the salinity of formation water (e.g., composition and pH). The reservoir PPLLs determined using this method can reflect the in situ porosity and permeability under actual reservoir conditions. Moreover, this method enjoys unique theoretical and technical advantages.

4.1. Research Advances in Water-Film Thickness

The formation and presence of water films are the result of complex physical and chemical processes between solids and liquids. The water-film thickness is not a fixed value and is affected by many factors such as temperature, pressure, minerals, curvature, and formation water [57]: (1) regarding the effect of temperature, a higher temperature is associated with more intense molecular thermal motion, leading to a smaller water-film thickness. (2) Regarding the effect of formation pressure, Wang, W.M. et al. [58] conducted a case study on the tight sandstones of the fourth member of the Shahejie Formation in the Damintun sag, Liaohe Basin, and concluded that higher formation pressure is associated with a more compact arrangement of water molecules, which leads to a smaller water-film thickness. This result indicates that there is a negative correlation between formation pressure and the water-film thickness. (3) Regarding the effect of mineral surfaces, water films are the thickest on concave surfaces, and a higher curvature of the concave surface is associated with a greater water-film thickness; water films are the thinnest on convex surfaces, and a higher curvature of the convex surface corresponds to a lower water-film thickness; water films are moderately thick on a flat surface [59]. (4) Regarding the effect of mineral wettability, a more hydrophilic rock surface is associated with a greater water-film thickness. (5) Regarding the effect of the salinity of formation water, the repulsive force between both interfaces of a water film in the formation brine decreases as the electrolyte compresses the electrical double layer, leading to a decrease in the water-film thickness. In the case of relatively high salinity of formation water, the electrolyte concentration exceeds the demand for negative charges on the surface of clay minerals. Therefore, the electrolyte compresses the electrical double layer, and the repulsive force between the two interfaces of the water film decreases, which causes the water-film thickness to decrease. In the case of relatively low formation, water salinity and the water film-thickness increase accordingly. Meanwhile, the effective pore-throat radius decreases, reducing the seepage capacity of fluids. In other words, the reservoir permeability decreases [60,61,62].

Extensive studies have been conducted to determine the thickness of water films. Nevertheless, the accurate water-film thickness cannot be measured directly at present but can only be determined indirectly through experiments combined with theoretical derivations. The calculated water-film thicknesses vary greatly, and in particular, the water-film thickness inferred using some methods is significantly greater than the pore-throat radius of tight reservoirs measured using other tests. A final conclusion is yet to be reached on the method that yields the results with the closest agreement with actual geological conditions [63,64]. Liu, D.X. et al. [65] determined the irreducible water-film thickness using the centrifugal method. With this method, the difference in volume between the liquid centrifuged from the hydrophilic surface and the lipophilic surface of grains is taken as the water absorption of adsorbed water films, which is then converted into the thickness of the adsorbed water films. Although this method is based on a feasible principle, it is applied on the premise that the remaining water after centrifugation is evenly distributed on the surface of solid grains. This assumption is significantly inconsistent with the complex pore-throat structures and the heterogeneity of uneven dissolution pore surfaces of tight sandstone reservoirs. Therefore, the results of this method cannot accurately characterize the thickness of adsorbed water films at the pore throats of tight sandstones. Wang, Y. et al. [65] derived the minimum flow-pore-throat radius of the study area from massive data and determined the capillary pressure of rocks in the laboratory. Then, they determined the water saturation of samples by combining the minimum flow-pore-throat radius and finally determined the PPLLs based on data such as the porosity and capillary pressure of different types of reservoirs. This method requires a large number of data and is subjected to large errors [66].

Therefore, the research into the factors influencing the water-film thickness are still in the stage of theoretical inference, while the transformation from qualitative to quantitative characterization is lacking. Moreover, there is no single method that can comprehensively take into account the influence of multiple factors such as temperature, pressure, and formation water under formation conditions.

4.2. Water-Film-Thickness-Based Method for Determining the PPLL of Tight Reservoirs

Through the combination of theories and tests, as well as the analysis of the force applied to water films, a computational method of water-film thickness that reflects factors such as temperature and pressure has been preliminarily developed. When gravity is ignored, a water film is subjected to the disjoining pressure (P_d) caused by the approach of its top and bottom interfaces, the formation pressure (P_i) perpendicular to the capillary wall, and the capillary pressure (P_c) opposite to the formation pressure. On this basis, the relationship between the water-film thickness and the throat radius under different formation pressures can be established (Figure 7).

The force applied to the water film is analyzed as follows:

$$P_d=P_i+P_c$$

(6)

$$P_c=2\sigma cos\theta /\mathrm{r}$$

(7)

$$P_d=2200/{\mathrm{h}}^3+150/{\mathrm{h}}^2+12/\mathrm{h}$$

(8)

where Pd is the disjoining pressure, MPa; r is the pore throat radius, m; Pi is the formation pressure, MPa; $\sigma$ is the gas-water interfacial tension, N/m; Pc is the capillary pressure, MPa; $\theta$ is the wetting angle, °; and h is the water-film thickness, m.

As shown in Figure 8, according to the relationship between water-film thickness and throat radius, natural gas accumulation can be divided into two regions, namely ineffective charging zone A and effective charging zone B. In zone A, the throat radius is less than the water-film thickness, and ineffective natural gas charging occurs under different formation pressures. In zone B, the throat radius is greater than the water-film thickness, and effective natural gas charging occurs under different formation pressures. Line C represents the critical PPLLs for natural gas charging when the throat radius is equal to the water-film thickness under different formation pressures. As shown by the intersection points of line C and the curves of different formation pressures, when the formation pressure rises from 30 MPa to 50 MPa, the critical water-film thickness shows the opposite trend, decreasing from 28 nm to 16 nm. Accordingly, the minimum throat radius for natural gas charging gradually decreases. This method has been applied to many oil fields in China. Compared with the conventional methods, this method incorporates certain innovations both in principle and experimentally. In particular, this method was applied to the deep, tight sandstone gas reservoirs in the Longfengshan area of the Songliao Basin, determining the PPLLs of the reservoirs in the Bei-210 well area and the reserves of the Bei-210 block. However, this method still has some problems in the calculation of some parameters (e.g., interfacial tension) and the analysis of its theoretical applicability. Therefore, it is necessary to further improve this method through fine-scale investigations based on the existing progress.

5. A New Method for Determining the Water-Film Thickness Based on Molecular Simulation

5.1. The Necessity of Determining the Water-Film Thickness Based on Molecular Simulation

The preliminarily established water-film-thickness-based method for determining the PPLLs has been applied to multiple petroliferous basins such as Songliao, Bohaiwan, Junggar, Ordos, Tuha, and Santanghu. Some application results have been achieved in many target areas using this method. However, there are still many problems with this method in its specific applications, such as insufficient analysis of its theoretical basis and difficulties in selecting key parameters. Specifically, these problems primarily include the following. (1) The formation mechanisms of water films are unclear. The presence of adsorbed water films is the result of physical, chemical, and mechanical interactions among solid, water films, and air among grains. Moreover, the water films have significantly different properties from water in the liquid phase. Recent studies of water films on solid–liquid surfaces primarily focus on the macroscopical measurement of the interactions between rock minerals and fluids in oil reservoirs, while few researchers have investigated the complex interactions between the ionized surfaces of different lithologies and ions in brine from the perspective of essential mineralogy and surface chemistry. Therefore, there is an urgent need to establish the quantitative relationship between the wettability and the interactions among mineral surfaces, ions in brine, and active components in crude oil. Moreover, it is advisable to quickly investigate the effects of different clay minerals on the adsorption of water films by measuring the contact angles between pure minerals in different rock compositions and brine with different ions and crude oil from the perspective of dispersion, charges, and ion exchange. (2) Changes in curvature and roughness are not considered in the modeling of water films. The water film model applied in previous studies assumes that minerals have smooth surfaces and that water molecules are directionally distributed around spherical sandstone grains. Theoretically, this assumption applies only to well-sorted spherical sandstone grains with high sphericity and smooth surfaces after long-distance transportation. However, in low-permeability reservoirs with authigenic clay minerals, the clay minerals tend to envelop grains or directly divide pore throats, forming a large number of micropores with clay minerals as the wall. The clay minerals enveloping grains or filling pores are composed of multiple clay platelets, most of which grow in the direction perpendicular or nearly perpendicular to the relatively smooth framework grains, roughening pore surfaces. Therefore, the water film surfaces are not smooth but roughen to a certain degree. The degree of fluctuation of the water film’s roughening is the roughness of water film areas and requires further investigation. (3) Some key parameters are difficult to select. Parameters such as rock density, specific surface area, pore size, and irreducible-water saturation can be determined through mature geologic tests such as low-temperature nitrogen adsorption, MICP, and centrifugal nuclear magnetic resonance (NMR). However, the selection of parameters such as interfacial tension and the wetting angle of rocks is not rigorous enough. Among these parameters, the interfacial tension is substituted with a value approximating the reservoir depth based on relevant references. Meanwhile, the wetting angle is tested using distilled water without considering the components of actual formation water. As a result, both parameters are subject to large errors. (4) There are insufficient theoretical bases for the calculation of disjoining pressure. There is a lack of sufficient theoretical basis for determining the disjoining pressure when calculating the force applied to water films. Theoretically, disjoining pressure Pd consists of the electrostatic force, the Van der Waals force, and structural components, which consist of matrix suction and osmotic suction. Presently, disjoining pressure is still determined using the thickness of water films on hydrophilic quartz surfaces under different disjoining pressures measured by using spectroscopic ellipsometry. Therefore, the determination of disjoining pressure suffers from insufficient theoretical bases and large computational errors [58].

As shown by the investigation of the influencing factors and calculation methods of the water film’s thickness, the application of the water-film-thickness-based method in determining the PPLLs of tight reservoirs is still in its preliminary stage, such as through reference citation, theoretical estimation, or direct adoption. There is a great lack of studies on the formation mechanisms, influencing factors, and determination methods of water films.

5.2. A New Method for Determining the PPLLs of Tight Reservoirs Based on Molecular Simulation

Over the past few years, the rapid advancement of the molecular simulation technology has created favorable conditions for the detailed characterization of study objects and the in-depth understanding of the theories of micro/nano scales [67]. Molecular simulation is also known as a computational microscope [68] and has been widely applied in nanogeoscience. This method can overcome the disadvantage that water films cannot be directly measured in the laboratory. Moreover, it can accurately simulate the formation of water films on rock surfaces in reservoirs based on the increasingly improved research on the molecular force field. The basic principle of molecular simulation is as follows: first, based on the 3D characterization of the micro–nano-scale fissure—the pore-throat system developing in tight sandstones—the pore-throat structure that determines the hydrocarbon migration and charging is constructed using the modeling software Materials Studio; then, an appropriate molecular force field is selected to precisely describe the interactions between formation water and reservoir rocks and to investigate and simulate the adsorption behavior of formation water on the surfaces of reservoir rocks; finally, the evaluation method for the water-film thickness is determined through an analysis of relevant structures and physicochemical properties. As shown by the principle, molecular simulation has unique superiority over conventional methods in determining water films’ thicknesses: (1) unlike conventional methods, which yield inaccurate water-film thickness indirectly through macro averaging, molecular simulation can investigate the interactions between formation water and reservoir rocks on atomic and molecular scales and thus establish an accurate evaluation method for the water-film thickness; (2) molecular simulation considers broader geological factors and examines their influencing patterns on the water-film thickness by controlling the pore throat size, selecting typical types of clay minerals, constructing surface roughness, changing the formation water salinity, and adjusting temperature and pressure.

Presently, molecular simulation has been preliminarily applied in the study of water films and their structures (Figure 9). De Almeida and Miranda found that the water films on quartz surfaces significantly affected water–oil displacement [69]. Specifically, the water films blocked the direct contact between the oil phase and pore surfaces but significantly reduced the displacement pressure, whereas pores without water films required extremely high displacement pressure. Afterward, De Almeida and Miranda compared the displacement effects of pores bearing pure water and those containing water with a certain salinity, discovering that salt ions in water led to thickened water films, which reduced the actual size of pore throats and blocked oil displacement [70]. Raiteri et al. and Sedghi et al. [71,72] discovered that the water molecules on calcite surfaces showed a highly ordered arrangement; their dense distribution indicated that the water films on calcite surfaces exhibited the characteristics of multilayer adsorption, and the water molecules in highly ordered arrangements blocked the electrostatic interactions between them and oil molecules and increased the interfacial tension between oil and water accordingly. Zhang et al. [73] found the effect of the pore size on the thickness of the adsorbed water films in quartz nanopores. In other words, the water-film thickness increased with an increase in the pore size. They also found that small quartz pores contained only a monolayer of absorbed water, while large quartz pores contained multilayers of absorbed water, and that the water-film thickness in quartz nanopores was significantly less than that determined in previous studies. Liao et al. [74] found that the water in clay nanopores also exhibited the characteristics of multilayer adsorption and that the water-film thickness could be characterized using the density distribution of water. As indicated by the above-mentioned studies, the molecular simulation method can reveal the characteristics of the occurrence of water films and water–rock interactions at the microscopic level, and the water-film thickness of tight reservoirs can be investigated by establishing an appropriate geologic model so as to gradually improve the problems existing in the water-film-thickness method and break through the existing limitations.

In addition, the change in rock wettability significantly affects the wetting angle and adsorption characteristics (Figure 10a) and inevitably has a great influence on the water-film thickness [75]. Underwood and Li et al. found that the density of water molecules in water- and oil-wet nanopores in kaolinites showed the characteristics of multilayer adsorption [76]. Compared with the oil-wet nanopores, the water-wet nanopores exhibited higher water-density peaks that varied over a wider range, indicating thicker water films in the water-wet nanopores. Based on the wetting angles of water on mineral surfaces, Mohammed and Gadikota found that the hydrophilicity of different minerals was in the order of quartz > calcite > illite [77]. However, Chang et al. [78] discovered that the hydrophilicity of mineral surfaces was in a different order: gypsum > calcite > quartz. The different orders might be related to the different molecular force fields they used. Temperature and pressure also affect the motion and distribution structure of water molecules, hydrogen bonding, and the structure of water films in sequence, thus changing the water films’ thickness. Almost all the recent studies of molecular simulation focus on atomic-scale smooth surfaces [79]. However, actual mineral surfaces exhibit varying degrees of roughness (Figure 10b). Some studies have shown that roughness significantly affects the viscosity and diffusivity of fluids [80]. Therefore, the effect of roughness on water films cannot be ignored. Overall, the study of water films based on molecular simulation still faces many critical problems, such as the modeling of typical rocks, the accurate selection of a force field, and the methods for determining water-film thickness. Therefore, there is an urgent need to conduct further relevant studies.

Overall, compared with conventional methods, the water-film-thickness-based method takes into account more geological factors and is more effective in determining the PPLLs of tight sandstone reservoirs with nanopores. However, the water-film thickness cannot be measured directly at present but can only be determined indirectly through experiments combined with theoretical derivations. Moreover, the water-film-thickness-based method still faces many basic problems, such as theoretical analysis, the selection of key parameters, and modeling. Given these problems, the molecular simulation method, which is known as the computational microscope, is applied to the water-film-thickness-based method. The aim is to fully utilize the unique advantages of molecular simulation in the study of water films to solve bottleneck problems (e.g., the formation mechanisms, stability analysis, and determination methods of water films) centering on geological problems and to develop new methods for determining the PPLLs of tight sandstone reservoirs with a high clay content, a complex mineral composition, and curved and tiny throats.

6. Conclusions

• Conventional methods for determining PPLLs, such as the empirical statistical method and the methods based on oil occurrence and log-parameter cross plots, mostly determine the PPLLs of reservoirs through the statistical analysis of parameters, including porosity and permeability. Their results are affected by the quantity and representativeness of samples and human judgment and have poor predictability. Therefore, the conventional methods are not applicable for tight sandstone reservoirs with complex pore structures and insufficient data from well tests.
• Compared with conventional methods, the water-film-thickness-based method integrates more factors, including temperature, pressure, mineral wettability, and formation water salinity, and the PPLLs determined using this method are closer to the actual geological conditions of oil reservoirs.
• The introduction of the molecular simulation method into the determination of the water-film thickness allows for investigating the interactions between rock minerals and formation water on atomic and molecular scales, revealing the microscopic formation mechanisms of water films, establishing an accurate evaluation method for water-film thickness, and ascertaining the law of change in the water-film thickness under different reservoir conditions. Compared with other methods, molecular simulation has greater theoretical advantages and is technically feasible. It can break through the technical bottlenecks in the study of the water film-thickness and provide a new study method for determining the PPLLs of complex reservoirs.