Method for combined characterization of pore structure

Abstract

A method for combined characterization of pore structure includes steps as follows. Firstly, CO2, N2 and high-pressure mercury intrusion porosimetry characterization curves are plotted based on actual measurement data, then, average values of the overlapping range of the CO2 and N2 characterization curves are calculated, and a function yi′=ƒ(x) is fitted. Each pore volume yi′ corresponding to each pore diameter xi is calculated, and a curve is plotted with xi as a horizontal coordinate and yi′ as a vertical coordinate, thereby obtaining a characterization curve of the overlapping range between CO2 and N2 adsorptions. The same data processing is used to process the overlapping range data of the N2 and high-pressure mercury intrusion porosimetry characterization curves, to obtain the characterization curve between them. The characterization curves are spliced with the original CO2, N2, and high-pressure mercury intrusion porosimetry characterization curves to obtain a combined characterization curve.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Chinese patent application No. CN 202311277481.6, filed to China National Intellectual Property Administration (CNIPA) on Sep. 28, 2023, which is herein incorporated by reference in its entirety.

TECHNICAL FIELD

The disclosure relates to the technical field of shale gas field development, and particularly to a method for combined characterization of a pore structure.

BACKGROUND

Shale gas is a typical type of unconventional natural gas. A matrix pore network in shale is composed of pores ranging from nanometer to micrometer diameters. Within a shale gas system, these pores, which are accompanied by natural fractures, form a seepage network that allows gas to flow from the shale to induced fractures during a development process. Currently, advanced research methods such as nano computed tomography focused ion beam scanning electron microscopy (nano-CT FIB-SEM), gas adsorption, high-pressure mercury intrusion porosimetry (MIP), and nuclear magnetic resonance are widely used to conduct extensive microscopic observations and analyses of the shale pore structure. Micropores refer to pores smaller than 2 nanometers (nm), mesopores refer to pores between 2 nm and 50 nm, and macropores refer to pores larger than 50 nm. Carbon dioxide adsorption experiments can characterize pores smaller than 3 nm, nitrogen adsorption experiments can characterize pores ranging from 1.6 nm to 200 nm, and high-pressure MIP experiments can characterize pores from 20 nm to 100,000 nm. Previous studies on the carbon dioxide adsorption experiments only took data smaller than 2 nm to represent the micropores; for the nitrogen adsorption experiments, only data between 2 nm and 50 nm were taken to represent the mesopores; for the high-pressure MIP experiments, only data larger than 50 nm were taken to represent the macropores. However, for overlapping parts of pore diameter ranges represented by the three methods, they were not processed properly and were simply deleted, which affected the accuracy of the combined characterization results.

SUMMARY

Addressing the issue that the current combined characterization method for pore structure, which simply deletes the overlapping parts in the characterization ranges of micropores, mesopores, and macropores, leads to large errors in the combined characterization results, the disclosure provides a method for combined characterization of pore structures.

The method for combined characterization of pore structures includes steps as follows.

S1, collecting actual measurement data of pore diameter ranges characterized by a carbon dioxide (CO₂) adsorption, a nitrogen (N₂) adsorption, and a mercury intrusion porosimetry; wherein the actual measurement data comprises a pore diameter and a pore volume;

• • for the CO₂ adsorption, taking the actual measurement data for the pore diameter less than 3 nanometers (nm), for the N₂ adsorption, taking the actual measurement data for the pore diameter in a range of 1.6-200 nm, and for the mercury intrusion porosimetry, taking the actual measurement data for the pore diameter in a range of 20-100,000 nm.

S2, plotting pore characterization curves with the pore diameter as a horizontal coordinate and the pore volume as a vertical coordinate based on the actual measurement data to obtain a CO₂ characterization curve, a N₂ characterization curve, and a mercury intrusion porosimetry characterization curve, respectively.

S3, performing data processing on an overlapping range of the pore diameter between the CO₂ characterization curve and the N₂ characterization curve, wherein the pore diameter in the overlapping range is in a range of 1.6 nm-3 nm.

The S3 specifically includes:

• • S31, taking an average value of pore volume data in the overlapping range of the pore diameter between the CO₂ characterization curve and the N₂ characterization curve, specifically, calculating an average value of a CO₂ pore volume and a N₂ pore volume corresponding to a same pore diameter, then forming a discrete point list of data points [x_i, y_i] based on the average value of the pore volume and the pore diameter in the overlapping range, wherein x_i represents the pore diameter, y_i represents the average value of the pore volume, and i represents a number of the data points in the overlapping range, with i taking a value greater than or equal to 8;
  • S32, fitting a curve of y_i′=ƒ(x) passing through all the data points in the discrete point list based on the discrete point list of the data points [x_i, y_i], thereby obtaining the function of y_i′=ƒ(x);
  • the S32 specifically includes:
    • letting an equation passing through a first point (x_i, y_i) be defined as follows:y=y_i  (equation 1),
    • letting an equation passing through a second point (x₂, y₂) be defined as follows:y=y₁+a₀(x−x₁)  (equation 2),
    • substituting the second point (x₂, y₂) into the equation 2 to obtain a₀;
    • letting an equation passing through a third point (x₃, y₃) be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)  (equation 3),
    • substituting the third point (x₃, y₃) into the equation 3 to obtain a₁;
    • letting an equation passing through a third point (x₄, y₄) be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)  (equation 4),
    • substituting the third point (x₄, y₄) into the equation 4 to obtain a₂;
    • sequentially obtaining a₃, a₄, a₅ . . . a_i-2 based on the S32 based on the above equation defined means; and
    • followed by obtaining the function of y_i′=ƒ(x) between the overlapping range of the CO₂ adsorption and the N₂ adsorption based on the obtained a₀, a₁, a₂ . . . a_i-2 as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)+a₃(x−x₁)(x−x₂)(x−x₃)(x−x₄)+ . . . +a_i-2(x−x₁)(x−x₂)(x−x₃)(x−x₄) . . . (x−x_i-2)(x−x_i-1)  (equation 5);
  • S33, substituting each pore diameter x_i into the function y_i′=ƒ(x) to calculate the corresponding pore volume y_i′ of each pore diameter x_i, plotting the curve with the pore diameter x_i as the horizontal coordinate and the pore volume y_i′ as the vertical coordinate to obtain a characterization curve of the overlapping range of the pore diameter between the CO₂ characterization curve and the N₂ characterization curve.

S4, performing data processing on an overlapping range of the pore diameter between the N₂ characterization curve and the mercury intrusion porosimetry characterization curve, wherein the overlapping range of the pore diameter between the N₂ characterization curve and the mercury intrusion porosimetry characterization curve is in a range of 20 nm-200 nm, processing steps are the same in the steps S31 to S33, thereby to obtain a characterization curve of the overlapping range of the pore diameter between the N₂ characterization curve and the mercury intrusion porosimetry characterization curve.

S5, splicing and combining the characterization curve of the overlapping range of the pore diameter between the CO₂ characterization curve and the N₂ characterization curve, the characterization curve of the overlapping range of the pore diameter between the N₂ characterization curve and the mercury intrusion porosimetry characterization curve, with the CO₂ characterization curve, the N₂ characterization curve, and the mercury intrusion porosimetry characterization curve, thereby obtaining a combined characterization curve of the pore structure based on the CO₂ adsorption, the N₂ adsorption, and the mercury intrusion porosimetry.

In this situation, the combined characterization curve of the pore structure based on the adsorption results of the CO₂ adsorption, the N₂ adsorption, and the high-pressure mercury intrusion porosimetry is used to characterize the pore structure of shale to detect and determine a gas content in the shale, and then extract a natural gas in the shale.

Compared to the related art, the beneficial effects of the disclosure are as follows.

(1) In the related art, the overlapping ranges in the characterization pore diameters of the CO₂ adsorption, the nitrogen N₂ adsorption, and the mercury intrusion porosimetry are not processed. Instead, the overlapping ranges among them are simply deleted, which affects the accuracy of the combined characterization results. The method for data processing of the disclosure fits the overlapping ranges of the CO₂ characterization curve and the N₂ characterization curve from two curves into one curve, and also fits the overlapping ranges of the N₂ characterization curve and the high-pressure mercury intrusion porosimetry characterization curve into one curve. By employing the method for data processing of the disclosure, the overlapping ranges in the characterization pore diameter of the CO₂ adsorption, the nitrogen N₂ adsorption, and the mercury intrusion porosimetry can be processed, thereby enhancing accuracy.

(2) The disclosure utilizes mathematical methods to characterize the pore structure of the shale, which is used for predicting the production of the shale gas fields, enhancing the understanding of developed blocks, and allowing for timely adjustments to the overall development level and development effectiveness of the gas field based on predictions.

The other advantages, objectives, and features of the disclosure will be partially demonstrated through the following description, and partially understood by those skilled in the art through research and practice of the disclosure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates a CO₂ characterization curve plotted based on actual data of a CO₂ adsorption.

FIG. 2 illustrates a N₂ characterization curve plotted based on actual data of a N₂ adsorption.

FIG. 3 illustrates a high-pressure mercury intrusion porosimetry characterization curve plotted based on actual data of a high-pressure mercury intrusion porosimetry.

FIG. 4 illustrates a characterization curve combined the CO₂ adsorption and the N₂ adsorption in a pore diameter range of 1.6 nm to 3 nm.

FIG. 5 illustrates a characterization curve combined the N₂ adsorption and the high-pressure mercury intrusion porosimetry in a pore diameter range of 20 nm to 200 nm.

FIG. 6 illustrates a characterization curve of a full pore diameter range combined the CO₂ adsorption, the N₂ adsorption, and the high-pressure mercury intrusion porosimetry.

DETAILED DESCRIPTION OF EMBODIMENTS

An illustrated embodiment of the disclosure is described below in conjunction with the attached drawings. It should be understood that the illustrated embodiment described herein is only for illustrating and explaining the disclosure, and are not intended to limit the disclosure.

In an embodiment of the disclosure, firstly, actual measurement data representing pores diameter range of a CO₂ adsorption, a N₂ adsorption, and a high-pressure mercury intrusion porosimetry are collected, and the pores diameter range of the CO₂ adsorption, the N₂ adsorption, and the high-pressure mercury intrusion porosimetry are key data. The pore diameter range characterized by the CO₂ adsorption is less than 3 nm, and the pore diameter range characterized by the N₂ adsorption is 1.6-200 nm. The pore diameter range characterized by the high-pressure mercury intrusion porosimetry is 20-100,000 nm. It can be observed that the overlapping range of the pore diameters between the CO₂ adsorption and the N₂ adsorption is 1.6 nm to 3 nm, and the overlapping range of the pore diameters between the N₂ adsorption and high-pressure mercury intrusion porosimetry is 20 nm to 200 nm. The pore volumes measured by the CO₂ adsorption, the N₂ adsorption, and the high-pressure mercury intrusion porosimetry correspond to the pore diameters in a one-to-one manner, with the pore diameters as a horizontal coordinate and the pore volume as a vertical coordinate to plot characterization curves, thereby obtaining a CO₂ characterization curve, a N₂ characterization curve, and a high-pressure mercury intrusion porosimetry characterization curve, respectively.

FIG. 1 illustrates the CO₂ characterization curve plotted based on actual data of the CO₂ adsorption. The pore diameter range is from 0.25 nm to 3 nm. The trend is that as the pore diameter increases, the pore volume also increases, thereby obtaining the results of the pore volume of the CO₂ adsorption characterization.

FIG. 2 illustrates the N₂ characterization curve plotted based on actual data of the N₂ adsorption. The pore diameter range is from 1.6 nm to 200 nm. The trend is that as the pore diameter increases, the pore volume also increases, thereby obtaining the results of the pore volume of the N₂ adsorption characterization.

FIG. 3 illustrates the high-pressure mercury intrusion porosimetry characterization curve plotted based on actual data of the high-pressure mercury intrusion porosimetry. The pore diameter range is from 20 nm to 100,000 nm. The trend is that as the pore diameter increases, the pore volume also increases, thereby obtaining the results of the pore volume of the high-pressure mercury intrusion porosimetry characterization.

A data processing is performed on an overlapping range of the pore diameters between the CO₂ characterization curve in FIG. 1 and the N₂ characterization curve in FIG. 2.

The overlapping range of the pore diameters of 1.6 nm to 3 nm are selected to calculate an average pore volume for CO₂ and N₂ pore volumes corresponding to the same pore diameter, followed by forming a discrete point list of data points [x_i, y_i] for the overlapping range of the pore diameter data, where x_i represents the pore diameter, y_i represents the average value of the pore volume, and i represents a number of the data points in the overlapping range, with i taking a value of 8. The specific data of the discrete point list [x_i, y_i] is shown in Table 1.

TABLE 1
Discrete point list of data points [xi, yi] for
the overlapping range of the pore diameter
of the CO2 and N2 characterization curves
pore     pore
diameter volume
xi       yi
(nm)     (μL/g)
1.6      0.00745
1.8      0.00736
2.0      0.00920
2.2      0.02010
2.4      0.02366
2.6      0.02801
2.8      0.03200
3.0      0.03823

(1) An equation passing through a first point (x₁, y₁)=(1.6, 0.00745) is let be defined as follows:y=y₁  (equation 1),

(2) An equation passing through a second point (x₂, y₂)=(1.8, 0.00736) is let be defined as follows:y=y₁+a₀(x−x₁)  (equation 2),

• • the second point (x₂, y₂) is substituted into the equation 2 to obtain a₀=−0.00045;

(3) An equation passing through a third point (x₃, y₃)=(2.0, 0.00920) is let be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)  (equation 3),

• • the third point (x₃, y₃)=(2.0, 0.00920) is substituted into the equation 3 to obtain a₁=0.024125;

(4) An equation passing through a fourth point (x₄, y₄)=(2.2, 0.02010) is let be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)  (equation 4),

• • the fourth point (x₄, y₄)=(2.2, 0.02010) is substituted into the equation 4 to obtain a₂=0.14854;

(5) An equation passing through a fifth point (x₅, y₅)=(2.4, 0.02366) is let be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x_i)(x−x₂)(x−x₃)+a₃(x−x₁)(x−x₂)(x−x₃)(x−x₄)   (equation 5),

• • the fifth point (x₅, y₅)=(2.4, 0.02366) is substituted into the equation 5 to obtain a₃=−0.61275;

(6) An equation passing through a sixth point (x₆, y₆)=(2.6, 0.02801) is let be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)+a₃(x−x₁)(x−x₂)(x−x₃)(x−x₄)+a₄(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)  (equation 6),

• • the sixth point (x₆, y₆)=(2.6, 0.02801) is substituted into the equation 6 to obtain a₄=1.25153;

(7) An equation passing through a seventh point (x₇, y₇)=(2.8, 0.03200) is let be defined as follows:y=y₁+a₀(x−x₁)+a₁(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)+a₃(x−x₁)(x−x₂)(x−x₃)(x−x₄)+a₄(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)+a₅(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)(x−x₆)  (equation 7),

• • the seventh point (x₇, y₇)=(2.8, 0.03200) is substituted into the equation 7 to obtain a₅=−1.77663;

(8) An equation passing through a eighth point (x₈, y₈)=(3.0, 0.03823) is let be defined as follows:y=y₁+a₀(x−x)+a(x−x₁)(x−x₂)+a₂(x−x₁)(x−x₂)(x−x₃)+a₃(x−x₁)(x−x₂)(x−x₃)(x−x₄)+a₄(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)+a₅(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)(x−x₆)+a₆(x−x₁)(x−x₂)(x−x₃)(x−x₄)(x−x₅)(x−x₆)(x−x₇)  (equation 8),

• • the eighth point (x₈, y₈)=(3.0, 0.03823) is substituted into the equation 8 to obtain a₆=1.99459.

A relationship equation of the final function y_i=ƒ(x) obtained by fitting the overlapping range of CO₂ adsorption and N₂ adsorption is as follows:y′=0.00745−0.00045(x−1.6)+0.24125(x−1.6)(x−1.8)−0.93708(x−1.6)(x−1.8)(x−2.0)+2.10089(x−1.6)(x−1.8)(x−2.0)(x−2.2)−3.26986(x−1.6)(x−1.8)(x−2.0)(x−2.2)(x−2.4)+3.87261(x−1.6)(x−1.8)(x−2.0)(x−2.2)(x−2.4)(x−2.6)−3.65096(x−1.6)(x−1.8)(x−2.0)(x−2.2)(x−2.4)(x−2.6)(x−2.8)   (equation 9).

Each pore diameter value is substituted in the overlapping range of 1.6 nm-3 nm between the CO₂ adsorption and the N₂ adsorption into the equation 9 to calculate the final pore volume of the overlapping range of the CO₂ adsorption and the N₂ adsorption, as shown in Table 2.

TABLE 2
Pore diameter and pore volume data for the
overlapping range between the CO2 and N2
characterization curves
pore     pore
diameter volume
(nm)     (μL/g)
1.6      0.00745
1.7      0.0136
1.8      0.00736
1.9      0.00535
2.0      0.00920
2.1      0.01527
2.2      0.02010
2.3      0.02255
2.4      0.02366
2.5      0.02520
2.6      0.02801
2.7      0.03101
2.8      0.03200
2.9      0.03113
3.0      0.03823

The characterization curve of the overlapping range between the CO₂ absorption and the N₂ absorption is plotted based on the data in Table 2, as shown in FIG. 4.

The same data processing is used to process the overlapping range of the pore diameters between the N₂ characterization curve and the high-pressure mercury intrusion porosimetry characterization curve.

The overlapping range of the pore diameters of 20 nm to 200 nm are selected to calculate an average pore volume for the N₂ adsorption and the high-pressure mercury intrusion porosimetry corresponding to the same pore diameter, followed by forming a discrete point list of data points [u_i, v_i] for the overlapping range of the pore diameter data, where u_i represents the pore diameter, v_i represents the average value of the pore volume, and the specific data of the discrete point list [u_i, v_i] is shown in Table 3.

TABLE 1
Discrete point list of data points [ui, vi] for the
overlapping range of the pore diameter of the
N2 and high-pressure mercury intrusion
porosimetry characterization curves
pore     pore
diameter volume
(nm)     (μL/g)
20       0.42653
40       0.48291
60       0.51302
80       0.54216
100      0.62865
120      0.69838
140      0.76387
160      0.81548
180      0.88295
200      0.90359

(1) An equation passing through a first point (u_i,v_i)=(20, 0.42653) is let be defined as follows:v=v₁  (equation 10),

(2) An equation passing through a second point (u₂,v₂)=(40, 0.48291) is let be defined as follows:v=v₁+b₀(u−u₁)  (equation 11),

• • the second point (u₂,v₂)=(40, 0.48291) is substituted into the equation 11 to obtain b₀=0.00282;

(3) An equation passing through a third point (u₃,v₃)=(60, 0.51302) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)  (equation 12),

• • the third point (u₃,v₃)=(60, 0.51302) is substituted into the equation 12 to obtain b₁=−3.28375×10⁻⁵;

(4) An equation passing through a fourth point (u₄,v₄)=(80, 0.54216) is let be defined as follows:v=v_i+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)  (equation 13),

• • the fourth point (u₄,v₄)=(80, 0.54216) is substituted into the equation 13 to obtain b₂=5.27083×10⁻⁷;

(5) An equation passing through a fifth point (u₅,v₅)=(100, 0.62865) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)   (equation 14),

• • the fifth point (u₅,v₅)=(100, 0.62865) is substituted into the equation 14 to obtain b₃=8.59895×10⁻⁹;

(6) An equation passing through a sixth point (u₆,v₆)=(120, 0.69838) is let be defined as follows:v=v+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)+b₄(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)  (equation 15),

• • the sixth point (u₆,v₆)=(120, 0.69838) is substituted into the equation 15 to obtain b₄=−4.30859×10⁻¹⁰;

(7) An equation passing through a seventh point (u₇,v₇)=(140, 0.76387) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)+b₄(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)+b₅(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)  (equation 16),

• • the seventh point (u₇,v₇)=(140, 0.76387) is substituted into the equation 16 to obtain b₅=8.34440×10⁻¹²;

(8) An equation passing through a eighth point (u₈,v₈)=(160, 0.81548) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)+b₄(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)+b₅(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)+b₆(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)  (equation 17),

• • the eighth point (u₈,v₈)=(160, 0.81548) is substituted into the equation 17 to obtain b₆=−1.10423×10⁻¹³;

(9) An equation passing through a ninth point (u₉,v₉)=(180, 0.88295) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)+b₄(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)+b₅(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)+b₆(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)+b₇(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)(u−u₈)  (equation 18),

• • the eighth point (u₉,v₉)=(180, 0.88295) is substituted into the equation 18 to obtain b₇=1.17279×10⁻¹⁵;

(10) An equation passing through a tenth point (u₁₀,v₁₀)=(200, 0.90359) is let be defined as follows:v=v₁+b₀(u−u₁)+b₁(u−u₁)(u−u₂)+b₂(u−u₁)(u−u₂)(u−u₃)+b₃(u−u₁)(u−u₂)(u−u₃)(u−u₄)+b₄(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)+8.344401×10⁻¹²(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)+b₆(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)+b₇(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)(u−u₅)+b₅(u−u₁)(u−u₂)(u−u₃)(u−u₄)(u−u₅)(u−u₆)(u−u₇)(u−u₈)(u−u₉)  (equation 19),

• • the eighth point (u₁₀,v₁₀)=(200, 0.90359) is substituted into the equation 19 to obtain b₈=−1.11543×10⁻¹⁷.

A relationship equation of the final function y_i′=ƒ(x) obtained by fitting the overlapping range of the N₂ adsorption and the high-pressure mercury intrusion porosimetry is as follows:v′=0.42653+0.00282(u−20)−3.28375×10⁻⁵(u−20)(u−40)+5.27083×10⁻⁷(u−20)(u−40)(u−60)+8.59895×10⁻⁹(u−20)(u−40)(u−60)(u−80)−4.30859×10⁻¹²(u−20)(u−40)(u−60)(u−80)(u−100)+8.34440×10⁻¹²(u−20)(u−40)(u−60)(u−80)(u−100)(u−120)−1.10423×10⁻¹³(u−20)(u−40)(u−60)(u−80)(u−100)(u−120)(u−140)+1.17279×10⁻¹⁵(u−20)(u−40)(u−60)(u−80)(u−100)(u−120)(u−140)(u−160)−1.11543×10⁻¹⁷(u−20)(u−40)(u−60)(u−80)(u−100)(u−120)(u−140)(u−160)(u−180)   (equation 20).

Each pore diameter value is substituted in the overlapping range of 20 nm-200 nm between the N₂ adsorption and the high-pressure mercury intrusion porosimetry into the equation 20 to calculate the final pore volume of the overlapping range of the N₂ adsorption and the high-pressure mercury intrusion porosimetry, as shown in Table 4.

TABLE 4
Pore diameter and pore volume data for
the overlapping range between the N2
and high-pressure mercury intrusion
porosimetry characterization curves
pore     pore
diameter volume
(nm)     (μL/g)
20       0.42653
30       0.39595
40       0.48291
50       0.51632
60       0.51302
70       0.51588
80       0.54216
90       0.58459
100      0.62865
110      0.66615
120      0.69838
130      0.73049
140      0.76387
150      0.79368
160      0.81548
170      0.83739
180      0.88295
190      0.95398
200      0.90359

The characterization curve of the overlapping range between the N₂ absorption and the high-pressure mercury intrusion porosimetry is plotted based on the data in Table 4, as shown in FIG. 5.

Finally, the characterization curves of the overlapping range of the pore diameters between the CO₂ characterization curve and the N₂ characterization curve as shown in FIG. 4, the characterization curve of the overlapping range of the pore diameters between the N₂ characterization curve and the high-pressure mercury intrusion porosimetry characterization curve as shown in FIG. 5, as well as the original CO₂ characterization curve (FIG. 1), the N₂ characterization curve (FIG. 2), and the high-pressure mercury intrusion porosimetry characterization curve (FIG. 3) are combined and spliced together to ultimately form a combined characterization curve of the pore structure based on the results of the CO₂ adsorption, the nitrogen N₂ adsorption, and the mercury intrusion porosimetry, as shown in FIG. 6.

The above description is merely a preferred embodiment of the disclosure, and does not in any way limit the disclosure. Although the disclosure has been disclosed in detail through the preferred embodiment, it is not intended to limit the disclosure. Those skilled in the art, without departing from the scope of the technical solution of the disclosure, can make minor modifications or amendments that are equivalent to the equivalent embodiments based on the technical content disclosed above. Any simple modifications, equivalent changes, and amendments made to the above embodiment in accordance with the technical essence of the disclosure still fall within the scope of the technical solution of the disclosure.

Claims

1. A method for combined characterization of a pore structure, comprising: S1, collecting actual measurement data of pore diameter ranges characterized by a carbon dioxide (CO2) adsorption, a nitrogen (N2) adsorption, and a mercury intrusion porosimetry; wherein the actual measurement data comprises a pore diameter and a pore volume;for the CO2 adsorption, taking the actual measurement data for the pore diameter less than 3 nanometers (nm), for the N2 adsorption, taking the actual measurement data for the pore diameter in a range of 1.6-200 nm, and for the mercury intrusion porosimetry, taking the actual measurement data for the pore diameter in a range of 20-100,000 nm;S2, plotting pore characterization curves with the pore diameter as a horizontal coordinate and the pore volume as a vertical coordinate based on the actual measurement data to obtain a CO2 characterization curve, a N2 characterization curve, and a mercury intrusion porosimetry characterization curve, respectively;S3, performing data processing on an overlapping range of the pore diameter between the CO2 characterization curve and the N2 characterization curve, wherein the pore diameter in the overlapping range is in a range of 1.6 nm-3 nm;wherein the step S3 specifically comprises: S31, taking an average value of pore volume data in the overlapping range of the pore diameter between the CO2 characterization curve and the N2 characterization curve, specifically, calculating an average value of a CO2 pore volume and a N2 pore volume corresponding to a same pore diameter, then forming a discrete point list of data points [xi, yi] based on the average value of the pore volume and the pore diameter in the overlapping range, wherein xi represents the pore diameter, yi represents the average value of the pore volume, and i represents a number of the data points in the overlapping range, with i taking a value greater than or equal to 8;S32, fitting a curve of yi′=ƒ(x) passing through all the data points in the discrete point list based on the discrete point list of the data points [xi, yi], thereby obtaining the function of yi′=ƒ(x);wherein the step S32 specifically comprises: letting an equation passing through a first point (xi, yi) be defined as follows: y=y1  (equation 1),letting an equation passing through a second point (x2, y2) be defined as follows: y=y1+a0(x−x1)  (equation 2),substituting the second point (x2, y2) into the equation 2 to obtain a0;letting an equation passing through a third point (x3, y3) be defined as follows: y=y1+a0(x−x1)+a1(x−x1)(x−x2)  (equation 3),substituting the third point (x3, y3) into the equation 3 to obtain a1;letting an equation passing through a third point (x4, y4) be defined as follows: y=y1+a0(x−x1)+a1(x−x1)(x−x2)+a2(x−xi)(x−x2)(x−x3)  (equation 4),substituting the third point (x4, y4) into the equation 4 to obtain a2;sequentially obtaining a3, a4, a5 . . . ai-2 based on the S32 based on the above equation defined means; andfollowed by obtaining the function of yi′=ƒ(x) between the overlapping range of the CO2 adsorption and the N2 adsorption based on the obtained a0, a1, a2 . . . ai-2 as follows: y=y1+a0(x−x1)+a1(x−x1)(x−x2)+a2(x−x1)(x−x2)(x−x3)+a3(x−x1)(x−x2)(x−x3)(x−x4)+ . . . +ai-2(x−xi)(x−x2)(x−x3)(x−x4) . . . (x−xi-2)(x−xi-1)  (equation 5);S33, substituting each pore diameter xi into the function yi′=ƒ(x) to calculate the corresponding pore volume yi′ of each pore diameter xi, plotting the curve with the pore diameter xi as the horizontal coordinate and the pore volume yi′ as the vertical coordinate to obtain a characterization curve of the overlapping range of the pore diameter between the CO2 characterization curve and the N2 characterization curve;S4, performing data processing on an overlapping range of the pore diameter between the N2 characterization curve and the mercury intrusion porosimetry characterization curve, wherein the overlapping range of the pore diameter between the N2 characterization curve and the mercury intrusion porosimetry characterization curve is in a range of 20 nm-200 nm, processing steps are the same in the steps S31 to S33, thereby to obtain a characterization curve of the overlapping range of the pore diameter between the N2 characterization curve and the mercury intrusion porosimetry characterization curve; andS5, splicing and combining the characterization curve of the overlapping range of the pore diameter between the CO2 characterization curve and the N2 characterization curve, the characterization curve of the overlapping range of the pore diameter between the N2 characterization curve and the mercury intrusion porosimetry characterization curve, with the CO2 characterization curve, the N2 characterization curve, and the mercury intrusion porosimetry characterization curve, thereby obtaining a combined characterization curve of the pore structure based on the CO2 adsorption, the N2 adsorption, and the mercury intrusion porosimetry.