Efficient construction and analysis method for relative permeability curves of water-drive gas reservoirs

Abstract

The present invention discloses an efficient method for constructing and analyzing relative permeability curves of water-drive gas reservoirs. The method includes establishing a capillary pressure function relational expression; a gas-water relative permeability function relational expression; obtaining a normalized capillary pressure curve; obtaining the undetermined coefficients in the capillary pressure function relational expression and the gas-water relative permeability curve; calculating and comparatively analyzing the fitting errors of different capillary pressure function relational expressions and the differences in relative permeability curves calculated by different methods; and comparing and verifying the relative permeability curves indirectly calculated from the mercury injection experiment test results with the relative permeability curves obtained by direct experiment tests. The present invention has significant advantages and application values under the circumstances of great difficulty in laboratory relative permeability curve tests, high requirements for equipment, and insufficient current relative permeability curve test results. It can provide reliable basic relative permeability data for work in aspects such as water-drive gas reservoir engineering calculations, productivity prediction, and numerical simulation, and at the same time provide theoretical guidance for the indirect calculation of relative permeability curves of similar water-drive gas reservoirs.

Description

Technical Field

[0001] The present invention relates to the application field of an indirect acquisition method for the gas-water relative permeability curve of a water drive gas reservoir, and specifically relates to a method for efficiently constructing and analyzing the relative permeability curve of a water drive gas reservoir. Background Technique

[0002] As an important type of oil and gas resource, water drive gas reservoirs are widely distributed globally. In China, water drive gas reservoirs are mainly distributed in basins such as Ordos, Sichuan, and Tarim, accounting for a relatively high proportion of the gas reservoirs in China. Efficient development of such gas reservoirs is of great significance for alleviating China's urgent demand for clean energy. In-depth understanding of the pore structure characteristics and fluid seepage laws of the reservoirs in water drive gas reservoirs is the prerequisite and foundation for developing such oil and gas resources.

[0003] The gas-water relative permeability curve (hereinafter referred to as the "relative permeability curve") is an essential basic data for the design of gas reservoir development plans and adjustment plans. Usually, the indoor displacement experiment is the most direct means to obtain the relative permeability curve. For deep water drive gas reservoirs, the reservoir temperature and pressure are generally high. Conducting relative permeability curve test experiments under high temperature and high pressure conditions requires high requirements for experimental equipment, high experimental test costs, and is time-consuming and laborious. If the number of experimental groups for relative permeability curve testing is too small or the representativeness of the relative permeability test results is insufficient, the test results will be difficult to truly reflect the seepage characteristics of the gas-water two-phase fluid in the gas reservoir (or development interval). Using an unrepresentative and inaccurate relative permeability curve for gas reservoir dynamic analysis, numerical simulation, production capacity prediction, etc. will lead to large deviations in the calculation results, and further lead to incorrect understanding of the gas reservoir development status by gas reservoir developers.

[0004] The present invention provides a method for efficiently constructing and analyzing the relative permeability curve of a water drive gas reservoir. Especially in the case where the relative permeability curve test is difficult and the test results are insufficient, this method provides a reliable technical idea and solution for obtaining a representative relative permeability curve of a water drive gas reservoir. Summary of the Invention

[0005] In view of the above problems, the present invention provides a method for efficiently constructing and analyzing the relative permeability curve of a water drive gas reservoir, aiming to solve the problem of indirectly and efficiently obtaining the gas-water relative permeability curve of a water drive gas reservoir.

[0006] To solve the above at least one technical problem, the present invention provides a method for efficiently constructing and analyzing the relative permeability curve of a water drive gas reservoir, and this method includes:

[0007] (1) Establish a capillary pressure function relationship. Specifically, collect the laboratory mercury injection test results, analyze the mercury injection curves of each core, and establish a capillary pressure function relationship according to the morphological characteristics of the mercury injection curves;

[0008] (2) Establish the functional relationship of gas-water relative permeability. Specifically, combining the fluid seepage theory of porous media and the capillary pressure function, and adopting the Purcell method and the Burdine correction method, establish the functional relationship of gas-water relative permeability for characterizing the displacement and imbibition processes in porous media.

[0009] (3) Obtain the normalized capillary pressure curve. Specifically, based on the understanding of reservoir, gas well, and gas reservoir properties, clarify the pore permeability parameters of the core, classify the cores, and use the capillary pressure curve normalization method to obtain the normalized capillary pressure curves of different types of reservoirs, gas wells, and the entire gas reservoir. The obtained normalized capillary pressure curves can reflect the overall pore structure and seepage characteristics of different types of reservoirs, gas wells, and gas reservoirs.

[0010] (4) Obtain the undetermined coefficients in the capillary pressure function relationship and the gas-water relative permeability curve. Specifically, adopt the non-linear regression method to obtain the undetermined coefficients in the capillary pressure function relationship, and substitute the undetermined coefficients into the gas-water relative permeability function relationship derived from the capillary pressure function relationship to obtain the gas-water relative permeability curve that can reflect the overall pore structure and seepage characteristics of different types of reservoirs, gas wells, and the target gas reservoir.

[0011] (5) Calculate and compare the fitting errors of different capillary pressure function relationships and the differences in the gas-water relative permeability curves calculated by different methods. Specifically, respectively adopt the capillary pressure function relationship and the gas-water relative permeability function relationship of the present invention, the Corey capillary pressure function relationship and the Brooks&Corey relative permeability function relationship widely used in the industry, and use the numerical integration method based on the Burdine correction method, combined with the laboratory mercury injection test results, to calculate and compare the fitting errors of different capillary pressure function relationships, and then analyze the differences in the quantitative characterization of capillary pressure curves by different function relationships, as well as the differences in the relative permeability curves calculated by different methods, and give usage suggestions.

[0012] (6) Compare and verify the gas-water relative permeability curve indirectly calculated from the laboratory mercury injection test results with the gas-water relative permeability curve obtained by direct experimental tests, discuss the applicability of the method proposed in the present invention, and give usage suggestions.

[0013] The method provided in the embodiments of the present application can help technicians obtain the gas-water relative permeability curve that can accurately and reliably reflect the true seepage characteristics of the target gas reservoir, different types of reservoirs, and gas wells, and provide reliable basic relative permeability data for engineering calculations, numerical simulations, dynamic analyses, etc. of water drive gas reservoirs.

[0014] In one embodiment, the capillary pressure function relationship includes:

[0015]

[0016] Or it is the capillary pressure function relational expression as described below:

[0017]

[0018] Where: p c is the capillary pressure, MPa; p c,max is the maximum capillary pressure, MPa; p c,min is the minimum capillary pressure, MPa; S wn is the normalized wetting phase saturation; a, b, c, α, β, γ are undetermined coefficients or experimental fitting coefficients of the fitting function, and α = (p c,max / p c,min ) a .

[0019] In one embodiment, the gas-water relative permeability function relational expression includes:

[0020] The gas-water relative permeability function relational expression based on the Purcell method is as follows:

[0021]

[0022]

[0023] The above gas-water relative permeability function relational expression is corrected based on the Burdine method as follows:

[0024]

[0025]

[0026] Where, K rw , K rg are the relative permeabilities of the liquid phase and the gas phase respectively, dimensionless; b, c are undetermined coefficients or experimental fitting coefficients of the fitting function; S wn is the normalized wetting phase saturation.

[0027] In one embodiment, for the capillary pressure curve normalization method, by using the Leverett dimensionless J(S wn ) function to calculate the J(S wn ) function values at different normalized wetting phase saturations S wn in each core mercury injection curve, and then using the following equation to nonlinearly fit the J(S wn ) function values to obtain the nonlinearly fitted curve of the J(S wn ) function, and the expression is as follows:

[0028]

[0029] In the formula: J(S wn ) is the Leverett dimensionless "J(S wn ) function"; ε1 and ε2 are the undetermined coefficients of the fitting equation or the experimental fitting coefficients; S wn is the normalized wetting phase saturation.

[0030] In one embodiment, based on the J(S wn ) function value, the non-linear fitting curve is obtained by using the non-linear fitting method to obtain the undetermined coefficients of the J(S wn ) function fitting equation, and then substituting them into the J(S wn ) fitting function equation to plot the non-linear fitting curve of the J(S wn ) function. Then, according to the non-linear fitting curve of the J(S wn ) function, the normalized wetting phase saturation S wn is equally divided into n parts. The arithmetic mean method is used for each equal division point to obtain the average J(S wn ) function values at different normalized wetting phase saturations S wn . The calculation formula is as follows:

[0031]

[0032] Based on the average J(S wn ) function values described above, using the J(S wn ) function equation proposed by Leverett, the capillary pressure is calculated, and the normalized wetting phase saturation S wn is denormalized to obtain the wetting phase saturation S w . The denormalization formula is as follows:

[0033] Mercury injection:

[0034]

[0035] Mercury withdrawal:

[0036]

[0037] In the formula: S w is the wetting phase saturation, %; S wn is the normalized wetting phase saturation, %; i is the i-th equal division point of the normalized wetting phase saturation S wn on the J(S wn ) function fitting curve, number; k is the number of core samples, number; is the average value of the J(S wn ) function corresponding to the i-th equal division point of the normalized wetting phase saturation S wn ; Sw,i For the normalized wetting phase saturation S wn S corresponding to the value at the i-th equal division point w Value, %; S wn,i For the normalized wetting phase saturation S wn Value at the i-th equal division point, %; Is the average value of the residual wetting phase saturation (or the minimum wetting phase saturation) of all core samples, %;

[0038] Is the average value of the maximum wetting phase saturation of all core samples, %.

[0039] In one embodiment, the obtaining of the capillary pressure and relative permeability function equations and curves includes: 1) According to quantitative indicators (main porosity and permeability), supplemented by qualitative indicators (observation and judgment of lithology and pore structure characteristics), classify the core samples to obtain representative cores of different types of reservoirs. When screening representative core samples of the reservoir, it is necessary to observe whether the lithology of the core sample conforms to the lithology characteristics understanding of the development horizon, and the tested physical properties should cover the main physical property range of the specific reservoir and the mean difference is not large to ensure the representativeness and reliability of the samples. Based on the core classification results, combined with the mercury injection experiment data of representative cores of various types of reservoirs, using the method established in the present invention, non-linearly fit the experimental data to obtain the undetermined coefficients in the capillary pressure function and relative permeability function of different types of reservoirs, and then draw the corresponding representative capillary pressure curve and relative permeability curve; 2) According to the average physical properties (main porosity and permeability) calculated by the gas well thickness weighted average method, screen and adjust the core samples so that the calculated results of the average pore permeability parameters of the core samples are not much different from the gas well thickness weighted average pore permeability parameters, and ensure a certain number of core samples as representative cores (as many core samples as possible), then it can be determined as the representative core of the gas well.

[0040] Based on the understanding of the results of logging interpretation, core analysis, formation group division, etc., master the pore permeability distribution of the gas well, and use the thickness weighted average method to calculate the average pore permeability parameter range of different gas wells. The calculation formula is as follows:

[0041]

[0042]

[0043] In the formula: K1, K2, K n Are the permeabilities of the 1st, 2nd, n-th layer segments (or sub-layers) respectively, mD; h1, h2, h n Are the thicknesses of the 1st, 2nd, n-th layer segments (or sub-layers) respectively, m; Is the average permeability of the gas well, mD; φ1, φ2, φ n Are the porosities of the 1st, 2nd, n-th layer segments (or sub-layers) respectively, %; is the average porosity of the gas well, %.

[0044] When the diameters of the experimental cores are the same, the average pore permeability parameters of the selected representative cores are calculated using the following formula:

[0045]

[0046]

[0047] When the diameters of the experimental cores are different, the average pore permeability parameters of the selected representative cores are calculated using the following formula:

[0048]

[0049]

[0050] Where: K L,1 , K L,2 , K L,n are the permeabilities of the 1st, 2nd, and nth cores, respectively, mD; L1, L2, L n are the lengths of the 1st, 2nd, and nth cores, respectively, mD; d1, d2, d n are the diameters of the 1st, 2nd, and nth cores, respectively, %; is the average permeability of the selected core samples, mD; φ L,1 , φ L,2 , φ L,n are the porosities of the 1st, 2nd, and nth cores, respectively, %; is the average porosity of the selected core samples, %.

[0051] By screening and adjusting the core samples, the difference between the average pore permeability parameters of the core samples and the calculation results of the weighted average pore permeability of the gas well thickness is made small. After the physical property gap reaches the expectation, the selected cores can be used as the representative cores of the gas well. To ensure the representativeness and reliability of the analysis results of the core samples, the number of core samples should be increased as much as possible according to the actual situation.

[0052] (3) On the premise of ensuring data quality, a large number of mercury injection test results of cores (as many as possible) can be used to obtain the normalized capillary pressure curve and gas-water relative permeability curve of the entire gas reservoir.

[0053] In one embodiment, the comparative analysis of the calculation results of different models includes:

[0054] The model and method proposed in the embodiments of the present application, the Corey (1954) capillary pressure function and the Brooks & Corey (1966) relative permeability function, which are widely used in the industry, are respectively adopted to calculate and comparatively analyze the fitting errors of different capillary pressure functions, analyze the differences of different equations in the quantitative characterization of capillary pressure curves, and calculate the mean absolute error, mean relative error and goodness of fit R of the capillary pressure predicted values and experimental values of the two methods 2 to evaluate the prediction error of the model.

[0055] In one embodiment, the method further includes:

[0056] Screen test core samples with physical properties similar to those of the cores used in the previous mercury injection experiment, conduct gas-water relative permeability experiments under the same simulated reservoir conditions, and compare the test results with the relative permeability curves indirectly calculated from the mercury injection data to check the quality of the relative permeability curves.

[0057] In summary, compared with the relative permeability experiment, the indoor mercury injection experiment has the advantages of short time, low cost, easy control of test temperature and pressure, etc. The mercury injection test results can not only reflect the pore structure characteristics of the reservoir, but also reveal the seepage characteristics of fluids under specific formation conditions. By establishing a method for mutual conversion of the test results of the above two experimental means, the mercury injection experiment data can be indirectly used to calculate the relative permeability curve. This means that the traditional method of directly obtaining the relative permeability curve through indoor experiments can be converted into an alternative solution with lower cost and relatively easier test process. The present invention provides an efficient method for constructing and analyzing the relative permeability curve of a water drive gas reservoir. Especially in the case where the relative permeability curve test is difficult and the test results are insufficient, this method provides a reliable technical idea and solution for obtaining the representative relative permeability curve of a water drive gas reservoir.

[0058] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention are hereinafter specifically exemplified. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. And throughout the drawings, the same reference numerals are used to represent the same meaning. In the drawings:

[0060] Figure 1 shows a schematic flow chart of an efficient method for constructing and analyzing the relative permeability curve of a water drive gas reservoir provided by an embodiment of the present invention;

[0061] Figure 2Shows the classification diagram of reservoir representative cores provided by the embodiments of the present invention;

[0062] Figure 3 Shows the capillary pressure (p c -S w 、p c -S Hg ) curves of different types of reservoirs provided by the embodiments of the present invention;

[0063] Figure 4 Shows the capillary pressure (p c -S w 、p c -S Hg ) curves of two typical gas wells provided by the embodiments of the present invention;

[0064] Figure 5 Shows all the capillary pressure experimental data of cores provided by the embodiments of the present invention and their fitting curves;

[0065] Figure 6 Shows the capillary pressure experimental data of different types of reservoirs provided by the embodiments of the present invention and their fitting curves;

[0066] Figure 7 Shows the capillary pressure experimental data of two typical gas wells provided by the embodiments of the present invention and their fitting curves;

[0067] Figure 8 Shows the fitting results of all the capillary pressure experimental data of cores provided by the embodiments of the present invention;

[0068] Figure 9 Shows the comparison of fitting errors between the new model and the Corey model provided by the embodiments of the present invention;

[0069] Figure 10 Shows the normalized capillary pressure curves of different types of reservoirs provided by the embodiments of the present invention;

[0070] Figure 11 Shows the normalized capillary pressure curves of two typical gas wells provided by the embodiments of the present invention;

[0071] Figure 12 Shows the normalized capillary pressure curve of the entire gas reservoir provided by the embodiments of the present invention;

[0072] Figure 13 Shows the gas-water relative permeability curves of different types of reservoirs provided by the embodiments of the present invention;

[0073] Figure 14 Shows the gas-water relative permeability curves of two typical gas wells provided by the embodiments of the present invention;

[0074] Figure 15Shows the entire gas-water relative permeability curve provided by the embodiments of the present invention;

[0075] Figure 16 Shows the comparison chart of all core gas-water relative permeability curves provided by the embodiments of the present invention;

[0076] Figure 17 Shows the verification of the relative permeability curve provided by the embodiments of the present invention;

[0077] Figure 18 Shows the technical roadmap provided by the embodiments of the present invention. Detailed implementation manners

[0078] Hereinafter, the exemplary embodiments of the present invention will be described in more detail with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be completely conveyed to those skilled in the art.

[0079] The embodiments of the present invention provide a method for efficiently constructing and analyzing the relative permeability curve of a water-drive gas reservoir, as Figure 1 shown, the method includes:

[0080] S101. Collect the laboratory mercury injection test results, analyze the mercury injection curves of each core, and establish a capillary pressure function relationship according to the morphological characteristics of the mercury injection curves

[0081] Exemplarily, a large number of experimental studies have shown that the capillary pressure p c and the wetting phase saturation S w or the mercury saturation S Hg have a certain relationship, and this relationship depends to a large extent on the inherent properties of the porous medium, such as mineral composition, pore structure, wettability, and interfacial tension. Through the mercury injection experiment, the capillary pressure curve (p c ~S w curve) of the core can be obtained relatively easily. Affected by various factors such as the in-situ deposition environment, deposition history, and paleo-water flow action. Usually, cores obtained from different formation groups, different wells, and different positions are used for laboratory mercury injection tests, and the shapes of the mercury injection curves obtained are various. The complex morphology of the capillary pressure curve is the result of the combined action of various factors such as the physical properties of the permeable medium, pore structure characteristics, lithology, and experimental conditions. Many researchers have tried to establish an empirical relationship between the capillary pressure and the wetting phase saturation (p c ~S w or p c ~S Hg ) to describe the potential relationship between the capillary pressure and the wetting phase saturation (or mercury saturation) in the porous medium.

[0082] The most representative and widely used capillary pressure function relationship was proposed by Corey in 1954. The author established an empirical model for describing the relationship between capillary pressure and wetting phase saturation in unsaturated porous media, and the expression is as follows:

[0083] p c = p e (S wn ) -1 / λ (1)

[0084] where the normalized saturation S wn can be expressed by the following formula:

[0085]

[0086] In the formula: p c is the capillary pressure, MPa; p e is the capillary pressure at the core inlet (or threshold pressure, displacement pressure), MPa; S wn is the normalized wetting phase saturation, %; λ is the pore size distribution index (or Corey constant), and the parameter λ is usually obtained by fitting experimental data; S w is the wetting phase saturation, %; S wr is the residual wetting phase saturation (or minimum wetting phase saturation), %. The displacement pressure pe is the minimum pressure when the non-wetting phase starts to enter the core, and it corresponds to the capillary pressure of the largest pores in the rock sample. The pressure corresponding to the intersection of the extended line of the gentle middle section of the capillary pressure curve and the vertical axis at the non-wetting phase saturation of zero is the core displacement pressure. Usually, if the rock has good permeability and large pore radius, the displacement pressure is relatively low, indicating good physical properties of the rock; vice versa. Therefore, the size of the displacement pressure can be used to evaluate the permeability of the rock and determine the largest pore radius of the rock. However, for cores with certain special properties, relying solely on the displacement pressure to judge the physical properties of the reservoir has a certain degree of ambiguity.

[0087] In the actual application process of the traditional Corey capillary pressure function, the fitting effect of its mercury injection experimental data for various cores (such as cores with different lithologies, physical properties, and heterogeneities) is not good. For example, fitting the capillary pressure data at the normalized wetting phase saturation of 0 may lead to a sharp increase in the fitting error (theoretically, the negative exponential power of 0 is not defined in mathematics).

[0088] The embodiment of this application proposes a brand-new capillary pressure function relationship. This relationship fully considers the characteristics of the capillary pressure curve and makes a non-zero correction to the base term of the fitting equation to achieve a better fitting effect for experimental data. The initial capillary pressure function relationship is as follows:

[0089]

[0090] Or

[0091]

[0092] In the formula: p c,max is the maximum capillary pressure, MPa; p c,min is the minimum capillary pressure, MPa; a, b, c, α, β, γ are undetermined coefficients (or experimental fitting coefficients) of the fitting function, and α = (p c,max / p c,min ) a .

[0093] The above function is a typical multi - variable non - linear function. A large number of indoor mercury injection experiment test results were collected and sorted out. The new function was used for non - linear fitting of the experimental data, and the fitting curves and prediction errors of the new function and the traditional Corey model (1954) were compared and analyzed.

[0094] S102. Combining the porous medium fluid seepage theory and the capillary pressure function, the Purcell method and the Burdine correction method were used to establish a relational expression for the gas - water relative permeability function to characterize the displacement and imbibition processes in porous media.

[0095] Exemplarily, in the 1950s, foreign scholar Purcell established a theoretical integral expression based on the relationship between capillary force and wetting phase saturation. This expression reflects the functional relationship between relative permeability, wetting phase saturation, and capillary pressure. The specific derivation of the expression is as follows (the following derivations all use the SI unit system):

[0096] Poiseuille’s law describes the flow law of steady - state fluid in a cylindrical pipe. According to Poiseuille’s law, there is a relationship between the flow rate of fluid through the pipe, the geometric shape of the pipe, the properties of the fluid, and the pressure difference applied to the fluid. From Poiseuille’s law, the flow rate formula for a single capillary i is:[[]]

[0097]

[0098] In the formula: q i is the flow rate of a single capillary, m 3 ; r i is the capillary radius, m; Δp is the pressure difference across the core ends, Pa; μ is the fluid viscosity, Pa·s; L is the capillary length, m.

[0099] It can be seen from Poiseuille’s law that the flow rate is proportional to the pressure difference, proportional to the fourth power of the pipe radius, and inversely proportional to the pipe length and fluid viscosity.

[0100] The volume of the i-th capillary is:

[0101] V i = πr i 2 L (6)

[0102] Where: V i is the volume of the i-th capillary, m 3 .

[0103] Capillary pressure is usually calculated by the Young-Laplace equation, which describes the relationship between the pressure difference inside and outside the capillary, the capillary radius, the surface tension of the liquid, and the contact angle. The expression of this equation is as follows:

[0104]

[0105] Where: p c,i is the capillary pressure of the i-th capillary, Pa; σ is the interfacial tension between the two phases, N / m; θ is the wetting contact angle, rad.

[0106] By combining equations (5) to (7), we can obtain:

[0107]

[0108] Assuming that the core consists of n capillaries with different diameters, the total flow rate is:

[0109]

[0110] Where: Q is the total flow rate, m 3 .

[0111] According to Darcy's law, then

[0112]

[0113] Where: K is the absolute permeability of the core, m 2 ; A is the cross-sectional area of the core, m 2 .

[0114] By combining equations (9) and (10), the absolute permeability of the porous medium is obtained as

[0115]

[0116] According to the definition of saturation (the ratio of the volume of a certain phase fluid in the pore space to the total pore volume of the rock), the following equation holds

[0117]

[0118] Where: S iis the saturation of fluid phase i in the core, %; V i ′ is the volume of fluid phase i in the capillary, V p is the pore volume of the core, m 3 .

[0119] According to the definition of porosity (the proportion of pore space in the total volume of the rock), the following equation holds

[0120]

[0121] where: φ is the porosity, %.

[0122] By simple transformation, we can get

[0123] V i ′ = ALφS i (14)

[0124] Substitute equation (14) into equation (11) and after rearrangement, the absolute permeability of the porous medium is

[0125]

[0126]

[0127]

[0128] where: K w 、K nw are the phase permeabilities of the wetting phase and the non-wetting phase, m 2 .

[0129] According to the definition of relative permeability (K rw = K w / K, K rnw = K nw / K), the integral function relationship of the relative permeabilities of the wetting phase and the non-wetting phase in the two-phase seepage system of the porous medium is as follows:

[0130]

[0131]

[0132] where: K rw 、K rnw are the relative permeabilities of the wetting phase and the non-wetting phase respectively, dimensionless.

[0133] Burdine (1953) pointed out that the relative permeability integral function of Purcell (1949) could not fully reflect the complexity of the porous medium, and proposed to use the tortuosity ratio to reflect the complexity of the flow path in the porous medium, and established the modified Purcell equation as follows:

[0134]

[0135]

[0136]

[0137]

[0138] where: λ rw , λ rnw is the tortuosity ratio of the wetting phase to the non-wetting phase saturation, dimensionless; τ w (1), τ w (S w ) is the tortuosity when the wetting phase saturation is 100% and S w , dimensionless; τ nw (1), τ nw (S w ) is the tortuosity when the non-wetting phase saturation is 100% and S w , dimensionless.

[0139] Many researchers at home and abroad have established various empirical equations between capillary pressure and wetting phase (or mercury) saturation to describe the potential relationship between parameters. Theoretically, an empirical equation with a good fitting degree and capable of reflecting the non-linear characteristics of the capillary pressure curve can, to a certain extent, reflect the occurrence and seepage laws of two-phase fluids in porous media. However, as can be seen from Equations (20) to (23), from the perspective of solving the integral function, how to solve the integral of the capillary pressure function (find the primitive function of the integral function and obtain an accurate integral result), and then obtain a clear relative permeability (quasi) analytical model. This is a major difficulty in establishing a relative permeability (quasi) analytical model starting from the basic configuration and seepage mechanism of porous media from the perspectives of application and accuracy.

[0140] If the antiderivative of the relative permeability integral function cannot be found or the integral expression cannot be solved, it will be necessary to rely on specific numerical integration calculation techniques for the calculation. The use of numerical integration methods involves issues such as selecting appropriate integration algorithms, determining integration step sizes, and error control strategies. This requires researchers to have certain computer programming and numerical calculation knowledge, and also requires debugging and optimization of specific problems. In addition, due to the high computational complexity of numerical integration methods, when the amount of data is large, the calculation time may increase significantly. All these factors make numerical integration methods have certain limitations and challenges in practical applications. Especially in cases where model solving or parameter optimization needs to be performed frequently, the computational cost of numerical integration may limit the scope of use and popularization of the model. Although numerical integration is feasible in practice, it may increase the computational complexity, consume time and energy, and is not convenient to use. Such situations also bring difficulties to the application and popularization of relative permeability numerical models.

[0141] Therefore, choosing a reasonable capillary pressure function that can not only meet the specific requirements for the fitting error of mercury injection experiment data but also be substituted into the relative permeability integral function to solve for the analytical equation is a very challenging task. Solving the above problems is of great significance for improving the calculation efficiency and usability of relative permeability models. The embodiments of this application fully consider the characteristics of the capillary pressure curve and propose a brand-new capillary pressure function relationship (Equation 3 or Equation 4). Combining with the relative permeability integral relationship proposed by Purcell (1949), the relative permeability equation for the two-phase system is solved, and the expression is as follows:

[0142]

[0143]

[0144] Using the Burdine (1953) method to correct the Purcell (1949) integral expression, the target gas-water relative permeability function relationship is solved, and the expression is as follows:

[0145]

[0146]

[0147] Where, K rw 、K rg are the relative permeabilities of the liquid phase and the gas phase respectively, dimensionless; b and c are undetermined coefficients of the fitting function or experimental fitting coefficients; S wn is the normalized wetting phase saturation.

[0148] It can be seen from equations (24) to (27) that the relative permeability function expression only contains the unknown coefficients b and c in the new capillary pressure function, that is, the relative permeability function is directly related to only some parameters (b, c) in the capillary pressure function. The expression forms of equations (3) and (4) have a certain degree of similarity. From the perspective of function fitting, equation (4) can also be used to derive similar results (equations 24 to 27), that is, replace b with β and c with γ in equations (24) to (27), and the relative permeability function relationship corresponding to equation (4) can be obtained.

[0149] S103. Based on the knowledge of the properties of the reservoir, gas well and gas reservoir, the core porosity and permeability parameters are clarified, the cores are classified, and the capillary pressure curve normalization method is used to obtain the normalized capillary pressure curves of different types of reservoirs, gas wells and the entire gas reservoir.

[0150] For example, since factors such as rock lithology, wettability, interfacial tension and pore structure characteristics will affect the shape of the capillary pressure curve, the capillary pressure curves obtained from core samples with different permeabilities and porosities will have different shapes. Therefore, only normalized capillary pressure data can represent the reservoir characteristics. Normalization can eliminate potential differences between core samples, making the capillary pressure curves of different core samples comparable, thereby reflecting the reservoir properties.

[0151] Using the mercury injection curve results of a certain core, the theoretical relative permeability curve can be calculated using the method established in the embodiment of the present application. However, for different types of reservoirs, single wells and the entire gas reservoir, a large amount of mercury injection experimental data needs to be normalized. However, for deeply buried low-permeability and dense reservoirs, coring is difficult, the core integrity has high requirements on the coring process, and the coring yield is generally low. The approach adopted in the embodiment of the present application is to first conduct mercury injection experimental tests by screening multiple representative cores of the gas reservoir. Then, the mercury injection experimental data is processed by a normalization method to obtain a capillary pressure curve that can reflect the overall pore structure characteristics and seepage characteristics of the reservoir. Finally, the nonlinear regression method is used to obtain the undetermined coefficients of the capillary pressure function, and the relative permeability function equation is combined to draw the phase permeability curve.

[0152] In order to obtain the normalized capillary pressure function relationship of the reservoir, the dimensionless J(S) proposed by Leverett (1941) is usually used. wn ) function processing, J(S wn ) function combines the effects of fluid interfacial tension, wettability, rock permeability and porosity to characterize the capillary pressure curve characteristics of the reservoir. wn )The function calculation formula is as follows:

[0153]

[0154] In the formula: J(S wn ) is called the "J function", dimensionless; p c is the capillary pressure, MPa; δ is the interfacial tension, m·N / m; θ is the wetting contact angle, rad; k is the absolute permeability of the core, μm 2 ; φ is the porosity of the core, %.

[0155] By rewriting the units in Equation (28) into the commonly used units in the oilfield, Equation (28) can be rewritten as

[0156]

[0157] In the formula: p c is the capillary pressure, MPa; δ is the interfacial tension, N / m; θ is the wetting contact angle, rad; K is the absolute permeability of the rock sample, mD or 10 -3 μm 2 ; φ is the porosity of the core, %.

[0158] In summary, in the embodiments of the present application, by combining the results of mercury injection into the core, pore permeability, wetting contact angle, and interfacial tension tests, and using the J(S wn ) function formula, the J(S wn ) function value corresponding to the mercury injection data of each core sample can be calculated, and then the curve of the J(S wn ) function value versus the wetting phase saturation or the normalized wetting phase saturation can be plotted.

[0159] Exemplarily, by observing the characteristics of the above-mentioned normalized wetting phase saturation curve, the following equation is used to perform nonlinear fitting on the curve. The expression of the J(S wn ) function fitting equation is as follows:

[0160]

[0161] In the formula: ε1 and ε2 are undetermined coefficients (or experimental fitting coefficients) of the fitting equation.

[0162] Exemplarily, after calculating the J(S wn ) function value of each core sample, using the above equation and the nonlinear regression method, the undetermined coefficients of the equation are obtained, and the J(S wn ) function fitting curve (i.e., the above-mentioned reservoir capillary pressure function fitting curve) is plotted. Using the respective fitting equations of each core (i.e., the reservoir capillary pressure function fitting curves of each core sample), the curve S wn is equally divided into n parts, and at each equal division point, the arithmetic mean method is used for averaging to obtain the average J(S wn ) function value (i.e., the above-mentioned average reservoir capillary pressure function value). The calculation formula is as follows:

[0163]

[0164] where: i is the i-th equal division point of the normalized wetting phase saturation by the J(S wn ) function fitting curve, unit; k is the number of core samples, unit; is the average value of the J(S wn ) function corresponding to the i-th equal division point of the normalized wetting phase saturation S wn .

[0165] For the same development series, when the permeability K, porosity φ, wetting contact angle θ and interfacial tension δ of a certain specific horizon are known, by using the averaged J(S wn ) function value and combining with the definition expression (Equation 29) of the J(S wn ) function, the capillary pressure values at different normalized wetting phase saturations can be calculated, and the calculation formula is as follows:

[0166]

[0167] By anti-normalizing the normalized wetting phase saturation S wn , the representative capillary pressure curve of the reservoir can be obtained, and the anti-normalization formula is as follows:

[0168] Mercury injection:

[0169]

[0170] Mercury withdrawal:

[0171]

[0172] where: S w,i is the value of S wn corresponding to the i-th equal division point value of the normalized wetting phase saturation S w

[0173] , %, S wn,i is the value of the i-th equal division point of the normalized wetting phase saturation S wn , %, is the average value of the residual wetting phase saturation (or minimum wetting phase saturation) of all core samples, %, is the average value of the maximum wetting phase saturation of all core samples, %.

[0174] S104. By using the nonlinear regression method, obtain the undetermined coefficients in the capillary pressure function relation, and substitute the undetermined coefficients into the gas-water relative permeability function relation derived from the capillary pressure function relation, so as to obtain the gas-water relative permeability curve that can reflect the overall pore structure and seepage characteristics of different types of reservoirs, gas wells and target gas reservoirs.

[0175] (1) Capillary pressure and relative permeability equations and curves for different types of reservoirs

[0176] Considering the differences in the internal properties of reservoirs, in order to efficiently develop reservoirs with large property differences, it is usually necessary to classify the reservoirs and formulate reservoir classification criteria for specific gas reservoirs. The vast majority of oil and gas fields at home and abroad use a combination of qualitative and quantitative indicators for reservoir classification. Qualitative indicators provide descriptions of reservoir types and characteristics, while quantitative indicators provide quantitative evaluations of reservoir properties and parameters. The method of combining qualitative and quantitative indicators can make the reservoir classification results of different regions and oil and gas fields comparable. Combining the two can more accurately characterize the characteristics of the reservoir, providing a more accurate basis for subsequent gas reservoir reserve assessment, dynamic analysis, development decision-making, and measure transformation.

[0177] Reservoir classification can provide descriptions of gas reservoir reservoirs, including rock types, pore structures, permeability, porosity, and reservoir development and distribution. In the embodiments of this application, mainly based on quantitative indicators (main porosity and permeability), supplemented by qualitative indicators (lithology, observation and judgment of pore structure characteristics), the core samples are classified to obtain representative cores of different types of reservoirs. When screening representative core samples of the reservoir, it is necessary to observe whether the lithology of the core sample conforms to the understanding of the lithology characteristics of the development horizon, and the physical properties tested should cover the main physical property range of the specific reservoir and the mean values have little difference to ensure the representativeness and reliability of the samples. Core classification helps to reveal the characteristics and properties of specific reservoirs. Based on the core classification results, combined with the mercury injection experiment data of representative cores of various reservoirs, using the method established in the embodiments of this application, the experimental data is non-linearly regressed to obtain the undetermined coefficients in the capillary pressure function and relative permeability function of different types of reservoirs, and then the corresponding representative capillary pressure curves and relative permeability curves are drawn.

[0178] (2) Capillary pressure and relative permeability equations and curves for typical gas wells

[0179] For wells with a large number of cores taken and a high core recovery rate, a large number of mercury injection experiments can be carried out, and mercury injection curves can be obtained for subsequent analysis. However, in most cases, affected by factors such as coring costs and coring process requirements, it is difficult to meet this condition on site. Therefore, in this case, a small number of "high-quality" representative cores of the target layer can be screened for experimental testing to support subsequent analysis work. Based on the achievements of logging interpretation, core analysis, formation group division, etc., the pore permeability distribution of gas wells is mastered, and the thickness weighted average method is used to calculate the average pore permeability range of different gas wells. The calculation formula is as follows:

[0180]

[0181]

[0182] In the formula: K1, K2, K n are the permeabilities of the 1st, 2nd, and nth layers (or sub-layers) respectively, in mD; h1, h2, h n are the thicknesses of the 1st, 2nd, and nth layers (or sub-layers) respectively, in m; is the average permeability of the gas well, in mD; φ1, φ2, φ n are the porosities of the 1st, 2nd, and nth layers (or sub-layers) respectively, in %; is the average porosity of the gas well, in %.

[0183] When the diameters of the experimental cores are the same, the average physical properties of the selected representative cores are calculated using the following formula:

[0184]

[0185]

[0186] When the diameters of the experimental cores are different, the average physical properties of the selected representative cores are calculated using the following formula:

[0187]

[0188]

[0189] In the formula: K L,1 , K L,2 , K L,n are the permeabilities of the 1st, 2nd, and nth cores respectively, in mD; L1, L2, L n are the lengths of the 1st, 2nd, and nth cores respectively, in mD; d1, d2, d n are the diameters of the 1st, 2nd, and nth cores respectively, in %; is the average permeability of the selected core sample, in mD; φ L,1 , φ L,2 , φ L,n are the porosities of the 1st, 2nd, and nth cores respectively, in %; is the average porosity of the selected core sample, in %.

[0190] By screening and adjusting the core samples, the difference between the average pore-permeability parameters of the core samples and the calculation results of the thickness-weighted average pore-permeability parameters of the gas well can be made small. After the physical property difference reaches the expectation, the selected core can be used as the representative core of the gas well. To ensure the representativeness and reliability of the analysis results of the core samples, the number of core samples should be increased as much as possible according to the actual situation.

[0191] (3) Capillary pressure and relative permeability function equations and curves of the entire gas reservoir

[0192] First, collect and organize all the mercury injection experiment data of the cores. By using the capillary pressure curve normalization method, the comprehensive capillary pressure curve of the entire gas reservoir can be obtained. Then, by using the new capillary pressure function of the embodiment of the present application and adopting the non-linear regression method, the undetermined coefficients of the equation can be obtained. Finally, combining the relative permeability function relationship established in the embodiment of the present application, the relative permeability curve is plotted. It should be noted that the representativeness and reliability of the capillary pressure curve of the entire gas reservoir are jointly affected by the quantity and quality of the mercury injection experiments. When performing the normalization process, do not blindly increase the mercury injection experiment data of the cores to achieve a certain quantity accumulation while ignoring the influence of factors such as different batches of cores and experimental conditions on the mercury injection curve. On the premise of ensuring the data quality, continuously expand the data set for normalization analysis, that is, increasing the number of cores tested in the experiment is an inevitable choice to improve the reliability and representativeness of the calculation results.

[0193] Optionally, the above method further includes:

[0194] S105. Respectively adopt the capillary pressure function relation and the gas-water relative permeability function relation, the Corey capillary pressure function relation and the Brooks&Corey relative permeability function relation, and adopt the numerical integration means based on the Purcell method and the Burdine correction method. Combining the laboratory mercury injection test results, calculate, compare and analyze the fitting errors of different capillary pressure function relations and the differences in the gas-water relative permeability curves.

[0195] Exemplarily, based on the core physical properties and mercury injection test results data, respectively adopt the models and methods proposed in the embodiments of the present application, as well as the Corey (1954) capillary pressure function and the Brooks&Corey (1966) relative permeability function that are widely used in the industry, calculate, compare and analyze the fitting errors of different capillary pressure functions. Then, plot the comparison diagrams of the capillary pressure fitting curves, relative permeability curves and error comparison diagrams of different core samples. Finally, analyze the differences in the quantitative characterization of the capillary pressure curves by different equations and give usage suggestions.

[0196] The mean absolute error (MAE), mean relative error (MRE) and goodness of fit R of the capillary pressure predicted values and experimental values of the two equations can be calculated respectively. 2 The calculation formula is as follows:

[0197] ① Goodness of fit (coefficient of determination) R 2 is

[0198]

[0199] Where: SSR, SSE, and SST are the regression and residual sum of squares, and the total sum of squared deviations, respectively. The role of the goodness of fit is to measure the fitting quality of the regression equation to the sample data, that is, to measure the explanatory power of the prediction model for the actual data. When R 2 is close to 1, it indicates that the regression equation can explain most of the variability in the data, that is, the prediction model can well fit the sample data, the prediction result has a high degree of coincidence with the actual observed value, indicating that the model can better explain and predict the sample data. On the contrary, when R 2 is close to 0, it means that the regression equation cannot explain the variability of the data, that is, the fitting ability of the prediction model to the sample data is low, the prediction result has a poor degree of coincidence with the actual observed value, indicating that the model may have underfitting or other problems and needs to be further improved or another model needs to be selected.

[0200] ② The mean absolute error (MAE) is

[0201]

[0202] ③ The mean relative error (MRE) is

[0203]

[0204] For MAE and MRE, generally, the closer to 0, the better the performance of the prediction model. MAE is the average absolute value of the difference between the predicted value and the actual observed value. Its role is to measure the prediction accuracy of the prediction model and evaluate the overall error level of the model based on the actual observed value. The smaller the MAE, the smaller the average error of the prediction model, the smaller the difference between the prediction result and the actual observed value, and the better the prediction ability of the model. And MRE is the average relative value of the difference between the predicted value and the actual observed value. Its role is to measure the relative accuracy of the prediction model, that is, the relative difference between the predicted value and the actual observed value. MRE can help evaluate the relative error level of the model under different data ranges. For MAE and MRE, generally, the closer to 0, the better the performance of the prediction model. However, the interpretation of these two indicators also needs to be combined with the specific application background and data characteristics. When comparing different models, MAE and MRE can be used simultaneously to evaluate their prediction abilities, and the model with smaller MAE and MRE can be selected as a better prediction model.

[0205] Optionally, the above method further includes:

[0206] S106. Compare and verify the gas-water relative permeability curve indirectly calculated from the mercury intrusion test results in the laboratory with the gas-water relative permeability curve obtained by direct experimental testing.

[0207] Select test core samples with physical properties similar to those of the cores used in the preliminary mercury injection experiment. Conduct gas-water relative permeability experiments under the same simulated reservoir conditions, and compare the test results with the relative permeability curves indirectly calculated from mercury injection data to verify the quality of the relative permeability curves.

[0208] In summary, the beneficial effects of the embodiments of the present application are as follows:

[0209] 1. The embodiments of the present application provide a new idea for obtaining relative permeability curves in the laboratory, that is, in some special cases, such as when the laboratory relative permeability test results are relatively lacking or the relative permeability test is difficult, the mercury injection experiment test results that are relatively easy to obtain can be used, and the new method provided by the embodiments of the present application can be used to obtain relative permeability curves that can reflect the pore structure characteristics and fluid seepage characteristics of the reservoir.

[0210] 2. The method provided by the embodiments of the present application has the significant advantage that the proposed new capillary pressure function can better capture the changing trends and characteristics in the mercury injection experiment data, thereby providing more accurate model fitting results. In addition, the proposed functional equation has stronger inclusiveness and adaptability to data, can better adapt to core characteristics of different types, physical properties and heterogeneity degrees, and can be widely applied to the analysis of mercury injection experiment data of cores under various reservoir conditions.

[0211] 3. The embodiments of the present application propose a new two-phase system relative permeability functional equation. In the actual application process, this equation not only meets the calculation accuracy requirements, but also is convenient and practical, and is easy to promote and apply.

[0212] 4. Through experiments and analyses on a limited number of core samples, the properties and characteristics of different types of reservoirs, different wells, and even the entire gas reservoir can be inferred. The research method reflects the characteristics of "seeing the big from the small" and "showing the whole from the part". The experiment and analysis process is relatively efficient, and the comprehensive cost investment is relatively low, which is closer to the actual field situation.

[0213] Furthermore, the following shows a specific example implemented by the embodiments of the present application:

[0214] S1 Basic Overview of the Gas Reservoir

[0215] Take a water drive gas reservoir as an example. The reservoir lithology of this gas reservoir is mainly lithic sandstone and feldspathic lithic sandstone. The gas reservoir temperature is about 132 °C, the original formation pressure is between 68 and 85 MPa (average 76.5 MPa), and the current formation pressure is about 70 MPa. The average porosity of the reservoir is 9.7%, and the average permeability is 7.07×10 -3 μm 2, with strong heterogeneity. The main type of reservoir space is pore type, and there are well-developed microfractures. Previously, a reservoir classification standard was established based on the sedimentary microfacies, lithology, physical properties, and microscopic pore-throat characteristics of the gas reservoir, further clarifying the reservoir distribution characteristics of different horizons. Overall, it shows strong heterogeneity and rapid lateral changes. The classification and evaluation table of the gas reservoir reservoir is shown in Table 1.

[0216] Table 1 Classification and Evaluation Table of Gas Reservoir Reservoir

[0217]

[0218] S2 represents core screening and classification

[0219] The burial depth of the main layers of the target gas reservoir is generally around 4700 - 5200 m, with relatively high formation temperature and pressure (pressure coefficient 1.58). The coring difficulty is great and the coring cost is high. At present, the core recovery rate of the whole well section of the main layer is relatively low. Plug samples are drilled from the full-diameter core, and the method proposed in the embodiments of the present application is used to screen representative cores that can reflect the lithology, physical properties, and pore structure characteristics of different types of reservoirs. The core screening principle: When screening representative core samples of the reservoir, it is necessary to observe whether the lithology of the core sample conforms to the lithology characteristics understanding of the development horizon, and the physical property test should cover the main physical property range of the specific reservoir and the mean values have little difference to ensure the representativeness and reliability of the sample. By conducting experiments and analyses on limited core samples, the properties and characteristics of different types of reservoirs can be inferred.

[0220] In the embodiments of the present application, a total of 20 pieces of core basic data (including core physical property and mercury injection test results) are collected and sorted out, and a semi-logarithmic graph of core porosity and permeability parameters is drawn. On this basis, combined with the reservoir classification and evaluation results and geological understanding, representative cores of various reservoirs (mainly development layers I - III) are screened. The classification diagram of reservoir representative cores is as Figure 2 . Based on the understanding of the results of logging interpretation, core analysis, small layer division, etc., the thickness weighted average method is used to calculate the average porosity and permeability parameters of two typical gas wells, and the method proposed in the embodiments of the present application is used to screen representative cores, calculate the average porosity and permeability parameters of the representative cores of the gas wells, and compare the parameter errors, such as absolute error (AE) and relative error (RE), as shown in Table 2.

[0221] Table 2 Comparison of Average Porosity and Permeability Parameters and Errors between Typical Gas Wells and Representative Cores

[0222]

[0223] By comparing the average physical properties obtained from the comprehensive analysis of logging and a large number of cores of typical gas wells with the average physical properties of representative cores (Table 2), it can be seen that the average physical properties of the representative cores of the two typical gas wells are not much different from the physical property results obtained from the comprehensive analysis of geology and cores, and the representativeness is good.

[0224] Classification of Mercury Injection Test Results of S3 Core

[0225] According to the mercury injection test data of different types of reservoirs and typical gas wells, combined with the representative core screening results, the capillary pressure (p c -S w 、p c -S Hg ) curves of different types of reservoirs and two typical gas wells are plotted (such as Figure 3 、 Figure 4 ). It can be seen from Figure 3 、 Figure 4 that the characteristics of the mercury injection curves of different types of reservoirs and different gas wells are significantly different. The physical properties of Class I reservoirs are the best, the mercury injection curve is generally smooth, and the pore size distribution is relatively uniform. The mercury injection curves of Class II and Class III reservoirs have multiple plateau segments, indicating that the pore structure of the reservoirs is complex and the heterogeneity is strong.

[0226] S4 Determination of Core Capillary Pressure Function Equation and Fitting Error

[0227] Combined with the mercury injection test results of the core, using the new capillary pressure function and the traditional Corey capillary pressure function proposed in the embodiments of the present application, and adopting the non-linear regression method, the mercury injection test data is fitted to obtain the undetermined coefficients of the two equations. The capillary pressure test data and their fitting curves of the entire gas reservoir, different types of reservoirs, two typical gas wells, and each core are shown in Figures 5 - 8 . The embodiments of the present application propose two new capillary pressure functions (Equations 3 to 4). The two equation forms are similar, and the fitting error differences are not significant. For the sake of simplicity, the embodiments only show the calculation results of Equation 3.

[0228] The undetermined coefficients obtained by the non-linear regression of the new capillary pressure function and the traditional Corey model in the embodiments are shown in Table 3. From Equations 40 to 42, the evaluation indexes (R 2 、MAE、MRE) are calculated as shown in Figure 9 .

[0229] Table 3 Undetermined Coefficients of Each Model

[0230]

[0231]

[0232] It can be seen from the analysis of the fitting results that( Figures 5 - 9) Compared with the Brooks and Corey capillary pressure function, the new function proposed in the embodiments of the present application can better fit the non-linear variation law in the experimental data, which means that the new function can better capture the complex variation trends and characteristics in the data, thereby providing more accurate model fitting results. In addition, the proposed equation has stronger inclusiveness and adaptability to the data. The new function can better adapt to core characteristics of different types, physical properties, and heterogeneity levels, and can be more widely applied to various actual scenarios. This improvement in data inclusiveness and adaptability makes the new function a more comprehensive and practical model choice.

[0233] Normalization of the capillary pressure curve

[0234] According to the previous experimental test results, the average interfacial tension of this gas reservoir is about 480 N / m, and θ is the wetting contact angle, about 80°. Using Equation 30, the J(S wn ) function values are fitted by the non-linear regression method. From Equations 29 to 31, combined with the fitting results of the J(S wn ) function values, the capillary pressure curve is normalized to obtain the normalized capillary pressure curves of different types of reservoirs, two typical gas wells, and the entire gas reservoir, as Figures 10 - 12 shown. As Figure 10 can be seen, the irreducible wetting phase saturation of Class I reservoirs is the smallest, and the irreducible wetting phase saturations of Class II and Class III reservoirs gradually increase, which is consistent with the overall understanding of the capillary pressure curves of different types of reservoirs. As Figure 11 can also be seen, the irreducible wetting phase saturation of Well CX560 is less than that of Well CH138, and the capillary pressure corresponding to this saturation is also smaller, indicating that the physical properties of Well CX560 are much better than those of Well CH138.

[0235] S6 Plot the gas-water relative permeability curve

[0236] Combined with the calculation results of the undetermined coefficients of the new capillary pressure function obtained by non-linear regression in Section S4 and the relative permeability function equation deduced in the embodiments of the present application, the gas-water relative permeability curves of different types of reservoirs, two typical gas wells, and the entire gas reservoir are plotted. The gas-water relative permeability curves (displacement and imbibition processes) of different types of reservoirs, two typical gas wells, and the entire gas reservoir are as Figures 13 - 15 shown.

[0237] As Figures 13 - 14It can be seen that the gas-water relative permeability curves of different types of reservoirs and different gas wells exhibit different variation characteristics. Generally speaking, the better the reservoir physical properties, the larger the co-permeability zone range, the higher the co-permeability point, and the larger the co-permeability zone area of the gas-water relative permeability curve. At the same saturation, the relative permeability of the gas phase and the liquid phase is also higher, and the gas-water two-phase seepage capacity is stronger. For water-wet reservoirs, the mercury injection curve corresponds to the process of the non-wetting phase displacing the wetting phase in the two-phase system, and gas displacing water causes the wetting phase saturation in the formation to gradually decrease. The mercury withdrawal curve corresponds to the process of the wetting phase imbibing the non-wetting phase in the two-phase system (such as during the gas production stage of a gas well). Due to the "imbibition" effect of the formation on the edge water (or formation water), under the drive of the pressure difference and capillary pressure, the edge water (or formation water) gradually migrates into the formation, displacing the natural gas stored in the pores, resulting in a gradual increase in the wetting phase saturation in the formation. Therefore, in different application scenarios, different gas-water relative permeability curves should be selected to meet the needs of engineering calculations.

[0238] Comparison of the relative permeability function of the embodiment of this application with the Corey relative permeability function and the numerical integration results

[0239] Using the method proposed in the embodiment of this application, combined with the fitting results of mercury injection experiment data, the relative permeability curves are plotted using the traditional Corey relative permeability function and the new relative permeability function established in the embodiment of this application. Then, using the Burdine modified relative permeability integral function and the numerical integration method, the mercury injection experiment data is transformed into the corresponding relative permeability calculated values. Finally, the above two equation functions are plotted and compared with the relative permeability calculated values obtained by numerical integration to evaluate the gap between the two equation functions and the numerical integration results.

[0240] It should be noted that, compared with the fitting equation, numerical integration directly calculates based on experimental data without the need for function fitting of the data, avoiding the smoothing effect of the fitting equation on experimental data and being able to more accurately reflect the true characteristics of experimental data. If a certain function is closer to the numerical integration result, it means that this function can better fit the experimental data and more accurately reflect the characteristics of experimental data. Although it is impossible to determine whether the equation conforms to physical laws from a theoretical perspective, from the perspective of the fitting degree to experimental data or the true reflection, this fitting equation obviously contains most of the information of experimental data. The numerical integration method is closer to the original data, but when reflecting the true change law of objective phenomena, it may be affected by experimental errors. However, the existence of experimental errors does not mean that there are problems with the proposed new method or that it is not applicable. Experimental errors are an inevitable part of the experimental process, and they reflect the uncertainties in actual phenomena and the measurement process. No matter what equation is used, all the efforts of scientific researchers lie in using more reasonable equations to characterize or describe various complex phenomena and problems. When evaluating the advantages and disadvantages of an equation, it is necessary to comprehensively consider the calculation results of the equation and the numerical integration calculation results. By comparing the consistency and differences between the two, the applicability and effectiveness of the equation can be evaluated. Such a comprehensive judgment can help us better understand the characterization ability and prediction ability of the equation and select the most suitable equation to solve practical problems.

[0241] Using the new gas-water relative permeability function, the integral expressions of the traditional Corey relative permeability function and the Burdine relative permeability function in the embodiments of the present application, calculate all the gas-water relative permeability curves of core samples (during the displacement and imbibition processes). The comparison diagrams of all the gas-water relative permeability curves of core samples are as Figure 16 shown. As Figure 16 can be seen, compared with the traditional Corey relative permeability function, the gas-water relative permeability curve drawn by the new relative permeability function in the embodiments of the present application has a higher degree of coincidence with the calculation result of the numerical integration method, indicating that the new model has better prediction performance and can obtain smaller engineering calculation errors.

[0242] Inspection of the S8 gas-water relative permeability curve

[0243] Based on the pore permeability data of the core samples from the previous mercury injection tests, multiple natural core samples are selected for pore permeability parameter tests, and finally four natural core samples with physical properties similar to those of the previous mercury injection core samples are screened for testing and inspection. The physical property parameters of the core samples are shown in Table 4.

[0244] Table 4 Summary of the test results of the physical properties of core samples

[0245]

[0246] By comparing the relative permeability curve indirectly calculated from the mercury intrusion test results with the relative permeability curve obtained from direct experimental tests (as shown in Figure 17 ), the experimental data points and the model calculation results have a good degree of coincidence. Compared with Class I and Class II reservoirs, due to the relatively poor physical properties, complex pore structures, and significant "multi-peak" characteristics of Class III reservoirs, the conversion effect of the mercury intrusion curve is generally average.

[0247] It should be noted that it is very difficult to find natural cores with exactly the same physical properties and pore structure characteristics in the world. The purpose of comparing the relative permeability curves of experimental tests and theoretical calculations is mainly to roughly measure the differences in the characteristics of the relative permeability curves obtained by the two methods under specific physical property conditions. The smaller the difference, the more reliable the relative permeability curve indirectly calculated by the mercury intrusion experiment, but it does not mean that the difference is only caused by the methods used. It does not rule out the possible systematic and random errors of the "before and after" different experiments, the differences in the individual internal properties (physical properties, pore structure, wettability, interfacial tension, etc.) of the cores used before and after, and the deviation between the test experimental values and the relative permeability curve converted from the mercury intrusion results caused by the damage of the cores during the experiment. The technical roadmap provided in the embodiments of the present invention is as shown in Figure 18 .

[0248] The above, the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. An efficient method for constructing and analyzing relative permeability curves of water - drive gas reservoirs, characterized in that, Including: Collect the laboratory mercury injection test results, analyze the mercury injection curves of each core, and establish the capillary pressure function relationship according to the morphological characteristics of the mercury injection curves; Combining the fluid seepage theory of porous media and the capillary pressure function, using the Purcell method and the Burdine correction method, establish the gas-water relative permeability function relationship for characterizing the displacement and imbibition processes of porous media; Based on the understanding of the reservoir, gas well, and gas reservoir properties, clarify the pore permeability parameters of the core, classify the core, and use the capillary pressure curve normalization method to obtain the normalized capillary pressure curves of different types of reservoirs, gas wells, and the entire gas reservoir; Using the non-linear regression method, obtain the undetermined coefficients in the capillary pressure function relationship, and substitute the undetermined coefficients into the gas-water relative permeability function relationship derived from the capillary pressure function relationship to obtain the gas-water relative permeability curve that can reflect the overall pore structure and seepage characteristics of different types of reservoirs, gas wells, and the target gas reservoir; Respectively use the capillary pressure function relationship and the gas-water relative permeability function relationship, the Corey capillary pressure function relationship and the Brooks&Corey relative permeability function relationship, and use the numerical integration method based on the Burdine correction method, combined with the laboratory mercury injection test results, to calculate and compare the fitting errors of different capillary pressure function relationships and the differences in the gas-water relative permeability curves calculated by different methods; Compare and test the gas-water relative permeability curve indirectly calculated from the laboratory mercury injection test results with the gas-water relative permeability curve obtained directly from the experimental test.

2. The method according to claim 1, characterized in that, The capillary pressure function relationship includes: Or is the capillary pressure function relationship described as follows: where p c is the capillary pressure, MPa; p c,max is the maximum capillary pressure, MPa; p c,min is the minimum capillary pressure, MPa; S wn is the normalized wetting phase saturation; a, b, c, α, β, γ are undetermined coefficients or experimental fitting coefficients of the fitting function, and α = (p c,max / p c,min ) a .

3. The method according to claim 1, characterized in that, The gas-water relative permeability function relationship includes: The gas-water relative permeability function relationship based on the Purcell method is as follows: Based on the Burdine correction method, the above gas-water relative permeability function relationship is as follows: Among them, K rw , K rg are the relative permeabilities of the liquid phase and the gas phase respectively, dimensionless; b and c are the undetermined coefficients of the fitting function or the experimental fitting coefficients; S wn is the normalized wetting phase saturation.

4. The method according to claim 1, characterized in that, The capillary pressure curve normalization method calculates the values of the J(S wn ) function at different normalized wetting phase saturations S wn in the mercury injection curves of each core by using the Leverett dimensionless J(S wn ) function, and then non-linearly fits the values of the J(S wn ) function by using the following equation to obtain the non-linear fitting curve of the J(S wn ) function, and the expression is as follows: Where: J(S wn ) is the Leverett dimensionless "J(S wn ) function"; ε1 and ε2 are coefficients to be determined in the fitting equation or experimentally fitted coefficients; S wn is the normalized wetting phase saturation.

5. The method according to claim 4, characterized in that, Based on the non-linear fitting curve of the J(S wn ) function, the undetermined coefficients of the fitting equation of the J(S wn ) function are obtained by using the non-linear fitting method, and then substituted into the J(S wn ) fitting function equation to plot the non-linear fitting curve of the J(S wn ) function. Then, according to the non-linear fitting curve of the J(S wn ) function, the normalized wetting phase saturation S wn is equally divided into n parts, and the arithmetic mean method is used for each equal division point to obtain the average J(S wn ) function values at different normalized wetting phase saturations S wn . The calculation formula is as follows: Based on the average J(S wn ) function value described above, using the J(S wn ) function equation proposed by Leverett, calculate the capillary pressure, and de-normalize the normalized wetting phase saturation S wn to obtain the wetting phase saturation S w . The de-normalization formula is as follows: Mercury injection: Mercury withdrawal: where: S w is the wetting phase saturation, %; S wn is the normalized wetting phase saturation, %; i is the i-th equally divided point on the fitting curve of the J(S wn ) function for the normalized wetting phase saturation S wn , where the unit of i is number; k is the number of core samples, where the unit of k is number; is the average value of the J(S wn ) function corresponding to the i-th equally divided point of the normalized wetting phase saturation S wn ; S w,i is the value of S wn corresponding to the value of the i-th equally divided point of the normalized wetting phase saturation S w , where the unit of S wn,i is %; S wn is the value of the i-th equally divided point of the normalized wetting phase saturation S , where the unit of S is %; is the average value of the residual wetting phase saturation or the minimum wetting phase saturation of all core samples, where the unit of S is %; is the average value of the maximum wetting phase saturation of all core samples, where the unit of S 6. The method according to claim 1, characterized in that, Also included: Screen test core samples with physical properties similar to those of the cores used in the previous mercury injection experiment, conduct gas-water relative permeability experiments under the same simulated reservoir conditions, and compare the test results with the relative permeability curves indirectly calculated from the mercury injection data to test the quality of the relative permeability curves.

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