Calculation of specific surface area for tight rock characterization through high-pressure mercury intrusion

As one of the unconventional oil and gas resources, tight oil is of great development prospect all over the world. The characterization of tight reservoir has important guiding significance for overcoming the problems in exploration as well as improving the development effect. As one of the characteristics of reservoir cores, the specific surface area is very important for the characterization of tight reservoirs. In this study, based on mercury injection data of tight reservoir core from Changqing Oilfield, through the establishment of equal diameter pore model, the specific surface area of pores corresponding to different radii is calculated, respectively, and the overall specific surface area of the core is obtained. Through the comprehensive evaluation of themercury injection data and the calculation results, it is found that the pores with the medium radius (0.009–0.178 μm) have the greatest contribution to the pore volume, followed by the pores with smaller radius (0.004–0.007 μm), and the pores with larger radius (0.268–53.835 μm) have the least contribution to the pore volume. However, the pores with smaller radius (0.004–0.089 μm) have the greatest contribution to the specific surface area, followed by the pore with larger radius (0.133–6.666 μm), and the specific surface area of individual pores in the middle range (8.917 μm) has the least contribution. Therefore, the adsorption loss of surfactant and so on must be considered in the process of tight oil development. In the development process, a series of main technologies such as fracturing, new water/gas injection, and horizontal well development should be explored. Through the overall design and scale implementation of reservoir scale, the investment cost of unit-producing reserves can be effectively reduced, and ultimately, the maximum benefit of tight oil development can be realized.


Introduction
As one of the unconventional oil and gas resources in the new century, tight oil and gas have become the main targets for increasing reserves and production of fossil energy [1,2]. Tight oil is a kind of unconventional oil resource, which is formed in the tight reservoir sandwiched in or adjacent to the high-quality source rocks without large-scale long-distance migration. It has the characteristics of low porosity and low permeability. Compared with the ultra-low permeability and ultra-low permeability reservoirs developed in the past, its reservoir-forming mechanism is more complex and exploration is more difficult. Therefore, the development of tight oil and gas has also encountered many challenges [3][4][5][6][7] and scholars have conducted lots of research to improve the development of these resources. In view of the technical difficulties in the exploration and development of Linxing-Shenfu Gas Field, Du et al. [8] established a set of supporting technologies for the exploration and development of tight sandstone gas and systematically carried out research on the geological controlling factors and main development technologies of tight gas. The research results effectively support the increase of reserves and production of Linxing-Shenfu Gas Field. By summarizing the important progress of PetroChina in tight oil exploration and development, Du et al. [9] put forward suggestions for the country to increase policy support. The research is of great significance for accelerating the development of tight oil in China and ensuring the national energy security. Li [10] introduced the general situation of tight oil development in SINOPEC, analyzed the main problems faced by tight oil development, and proposed five development directions of tight oil development technology in China, including hydrocarbon accumulation rule research, development mechanism research, tight oil production engineering technology research, enhanced oil recovery technology research, development mode, and management mode research. The research has good guiding significance for realizing the beneficial development of tight oil in China and ensuring the national energy supply and energy security. These studies show that in order to solve the problems in the development of tight oil and gas reservoirs, it is necessary to carry out core analysis experiments of tight reservoirs and make fine characterization of reservoir characteristics.
Specific surface area refers to the total area of unit mass of material, and the unit is generally m 2 /g. The content of core specific surface area is of great significance for understanding development effects of reservoirs. On the basis of analyzing the influencing factors of irreducible water saturation in clastic rock reservoir, Kang et al. [11] calculated the irreducible water saturation of clastic rock by using core analysis items such as clastic rock grain size, bulk density, and clay mineral content to determine the specific surface area and other parameters of clastic rocks. Therefore, the calculation method of irreducible water saturation based on core analysis parameters is established. This method lays a theoretical foundation for the evaluation of irreducible water saturation of clastic rocks and has a good application value for the determination of irreducible water saturation with low cost and high accuracy. Mao et al. [12] studied the reservoir characteristics and formation mechanism of the dolomitic limestone reservoir in Tahe Oilfield by using core observation, thin section identification, energy spectrum analysis, and other technical methods. Bi et al. [13] studied the retention characteristics and influencing factors of two typical microbial strains for oil recovery, Pseudomonas aeruginosa WJ 1 and Bacillus subtilis SLY 3, in the migration process of porous media through isothermal adsorption experiments and flow experiments. This study can provide an important reference for improving the numerical simulation of microbial-enhanced oil recovery. Taking the delta reservoir of Shengtuo Oilfield as an example, Deng and Xu [14] studied the variation law of percolation parameters with water injection development by means of core analysis and established the variation model of percolation parameters. The results show that the pore and throat radius increase and the average specific surface area of rock decreases with the increase of water injection degree and composite water cut. Li [15] summarized the different viewpoints on non-Darcy percolation, discussed the relationship between specific surface area and permeability and its influence on start-up pressure from the aspects of pore structure of porous media and interaction between rock and fluid based on the geological characteristics of low permeability reservoirs, and proposed measures to reduce the start-up pressure gradient. Based on the characteristics of complex pore structure and large specific surface area in low permeability reservoirs, Yang et al. [16] developed a new anionic surfactant foaming agent and systematically evaluated the basic properties of the new foaming agent. The results show that the new foaming agent system has superior performance and can be applied to Yanchang shallow and medium-deep ultralow permeability reservoirs.
In fact, a large number of scholars have carried out research on the calculation method of specific surface area of porous media. Liu [17] proposed a calculation method for the specific surface area of foam metal by using the corresponding relationship between the specific surface area of foam metal and the porosity and pore diameter. Then, the specific surface area of the foam metal was successfully calculated based on the relevant experimental data. Based on fractal theory, Yin et al. [18] analyzed the particle size distribution, volume, and surface area of aggregate and deduced a calculation method of specific surface area of aggregate. Combined with physical aggregate, the specific surface area of finished aggregate with different particle sizes was calculated. The calculated results are in good agreement with the measured results, indicating that the fractal theory can be used to accurately calculate the specific surface area of artificial aggregate. Liu [19] analyzed the pore structure of samples with different pore sizes by the N 2 adsorption method and calculated the specific surface area of the samples by the BET method. The results show that in the application of the BET method, the range of relative pressure should be determined according to the pore size of the sample. Based on fractal theory, Ji et al. [20] proposed a method for calculating the specific surface area of stones and proved the applicability of the method by using experimental data. The research results can provide good reference for concrete proportioning. Chen et al. [21] introduced various adsorption isothermal equations based on various adsorption theories. The specific surface area of many kinds of activated carbon was calculated. The results show that the difference between different calculation methods is within a reasonable range.
In this study, the AutoPore IV 9500 mercury porosimeter is used to test the tight formation core from Changqing oilfield in Northwest China. The formation buried depth of the core is about 1,660 m, the dry weight of core is 30.011 g, the porosity of the core is 8.98%, and the permeability is 0.49 × 10 −3 μm 2 . Based on the review of the research on the specific surface area calculation of porous media, the method for calculating the specific surface area of tight cores is given in combination with the core mercury intrusion data. Then, based on the original data, the specific surface area of the tight core is calculated by using this method. In order to further characterize the pore structure, the distribution of specific surface area with pore radius is also plotted and analyzed.

Methods
The mercury intrusion data measured by the test instrument AutoPore IV 9500 are used as the raw material. As the injection pressure is gradually increased during the experiment, mercury will continuously enter the core pores. Volumes of mercury injected at different injection pressures were recorded in turn. According to the mathematical relationship between capillary pressure, pore radius, and other parameters, the pore radius corresponding to different injection pressures can be calculated. Interval injected volume is obtained by the difference between the mercury injected volume corresponding to the current recording point and the mercury injected volume corresponding to the previous recording point. We set the interval injected volume under the first pressure recording point to 0. Obviously, the interval injected volume represents the pore volume to the corresponding pore radius. In the calculation method of the specific surface area involved in this study, it is assumed that the rock pores are uniformly cylindrical, and the bottom radius of the cylindrical is the pore radius converted by the injection pressure. The cross-sectional area of the corresponding pore can be calculated from the area formula for a circle. The total pore length at the corresponding pore radius can be obtained by dividing the pore volume by the corresponding pore cross-sectional area. Therefore, the specific surface area of the corresponding pore can be obtained by dividing the area of the cylindrical surface by the total weight of the core. As the intrusion pressure increases, the mercury continuously enters the pores with different radii. The specific surface area corresponding to each radius level can be calculated in turn by this method. The total specific surface area of the core can be obtained by summing the specific surface areas at different radius levels. This calculation process and its key parameters can be reflected by the data in Table 1. Of course, enough attention should be paid for the conversion of units in the calculation and check carefully to obtain the accurate value.

Results and discussion
According to the aforementioned calculation method, the key parameters are calculated step by step, and the specific results are shown in the columns of Table 1. In order to clearly demonstrate the characteristics of the tight reservoir core, the relation between pore radius and corresponding specific surface area is plotted, as shown in Figure 1. From Table 1, it can be seen that the specific surface area in the last column is actually the specific surface area of the pores in the corresponding pore size range.
By adding the specific surface areas of all pore ranges, the specific surface area of all pores in the core can be obtained as 2.207889848 m 2 /g.
According to the data distribution, it can be seen that the pore radius of the core is distributed between 0.004 and 53.929 μm. In the process of mercury injection, the total volume of mercury injection is 0.9069683 mL. The pore volume corresponding to each radius can be reflected according to the corresponding interval injected volume. Therefore, the ratio of the interval injected volume to the total mercury volume is the percentage of the pore volume at the corresponding radius to the total pore volume. According to this principle, the pores with a radius of 0.089 μm account for 17.12% of the total pore volume, and the second is the pores with a radius of 0.067 μm, which account for 14.43% of the total pore volume. In general, the pores with a radius of 0.036-0.089 μm are the most frequent part of the pore distribution, accounting for more than 50% of the total pore volume. Radius 0.009-0.178 μm pores are the main part of the pore distribution, and their respective percentage of the total pore volume is more than 3%, and their total percentage of the total pore volume is more than 86.5%. The pore with a radius of 53.929 μm accounts for 2.97% of the total pore volume, which is relatively high, but this value is not accurate enough, mainly due to the influence of the cavity on the surface of the rock sample. From the overall distribution of pores, the pores with radii between 0.268 and 53.929 μm account for only about 5% of the total pore volume. However, the pores with radii between 0.004 and 0.007 μm account for about 6.4% of the total pore volume. This shows that the pores in the rock sample are still dominated by mesopores and small pores, and the volume fraction of macropores is very low.
The abscissa of Figure 1 represents the distribution of core pores in μm, and the ordinate represents the specific surface area of the pores corresponding to the pore radius in m 2 /g. In order to clearly show the trend of data change, the abscissa and ordinate in the figure are in the form of logarithmic coordinates. It can be seen from Figure 1 that, on the whole, with the increase of pore radius, the specific surface area corresponding to the pore shows a decreasing trend. Specifically, with the change of pore radius, the change trend of the corresponding specific surface area is also different. When the pore radius is distributed between 0.004 and 0.089 μm, the corresponding specific surface area is basically between 0.10 and 0.20 m 2 /g, which belongs to the range of larger specific surface area. With the increase of pore radius, the specific surface area shows a downward trend and shows an approximate linear downward trend in logarithmic coordinates. When the pore radius is 6.666 μm, the corresponding specific surface area is 1.21723 × 10 −5 m 2 /g. When the pore radius reaches 8.917 μm, the corresponding specific surface area begins to increase with the increase of pore radius. The corresponding specific surface area is 4.90145 × 10 −6 m 2 /g at pore radius of 8.917 μm. The last point is that when the pore radius is 105.461 μm, the corresponding specific surface area is 0 m 2 /g. This result is affected by the metering method in the measurement process, and the result is not suitable for direct analysis.
There is also an error in the calculation of specific surface area. First of all, it is assumed in the experiment that the mercury intake at the first pressure measuring point of 0.0070 MPa is zero, which may not be completely accurate. Second, in the experiment, it is assumed that the mercury intake at the second pressure measuring point of 0.0137 MPa is 0.0269803 mL. Considering that there are cavities on the surface of the rock sample, the mercury intake is not strictly accurate. Third, the pore radius is calculated according to the mercury injection pressure in the experiment, and the value of the pore radius is determined by the value of the mercury injection pressure. The actual pore radius is not distributed discretely in this way, which leads to the inaccurate characterization of the pore radius. Fourth, in the calculation process, it is assumed that the pore radius is uniformly distributed; that is to say, it is assumed that the amount of mercury in the same pore radius range enters the pores with uniform pore size. In fact, it is difficult to keep the uniform distribution of pore size, which leads to the error between the calculation results and the actual results. Fifth, in the process of measurement, the error of instrument measurement will also lead to insufficient accuracy of data and affect the final calculation results of specific surface area.

Conclusion
As can be seen from results above, there is no direct correlation among the pore volume contribution, the specific surface area contribution, and the pore radius distribution. The largest contribution made to the pore volume is the pore with the medium radius, followed by the pore with smaller radius, and the smallest contribution is made by the pore with larger radius. From the contribution of specific surface area, with the increase of radius, the contribution of the specific surface area is gradually decreasing. The largest contribution is made by the pore with smaller radius, followed by the pore with larger radius, and the contribution of some individual pores with medium radius is the smallest. Therefore, the adsorption loss of surfactant and so on must be considered in the process of tight oil development. Conventional chemical flooding methods often fail to achieve the desired results for tight oil development. In the development process, a series of main technologies such as fracturing, new type water/gas injection, and horizontal well development should be explored. Through fracturing to open the oil and gas seepage path, relying on new type water/gas injection to restore the flow pressure of oil and gas in the reservoir, horizontal wells are used to cross the reservoir to increase the area of oil and gas infiltration into the wellbore, so as to improve the single-well production. For the most important, the development of tight oil must take benefit as the center, adhere to the dynamic management mode of "integration" of exploration, development, engineering, and surface construction, and realize the effective reduction of investment cost per unit of producing reserves through the overall design and scale implementation of reservoir scale, so as to achieve the maximum benefit of tight oil development.