A function description method of rock resistivity

Abstract

The application provides a function description method of rock resistivity, which comprises the following steps: selecting at least two rock samples of the same type of rock, performing a saturated water experiment and a centrifugal experiment on the rock samples, and measuring the pore water resistivity of the rock samples, the rock resistivity corresponding to the saturated water saturation, and the rock resistivity under different partial water saturations; according to the rock porosity, the pore water resistivity, the rock resistivity corresponding to the saturated water saturation, and the rock resistivity under different water saturations, the first function coefficient and the second function coefficient of a saturated water rock resistivity description function equation are obtained, the third function coefficient of a partial saturated water rock resistivity and bound water saturation relationship equation corresponding to different effective water saturations, and the fourth function coefficient and the fifth function coefficient of a partial saturated water rock resistivity description function are obtained, and finally, the function description of the rock resistivity is obtained, and the accuracy of the rock resistivity description is improved.

Description

Technical Field

[0001] This application relates to the field of rock physics technology, and in particular to a method for describing the function of rock resistivity. Background Technology

[0002] The functional description of rock resistivity under different water-bearing states is one of the core contents of rock carbide physics and reservoir evaluation under water-bearing states. The accuracy of its functional description determines the accuracy of the description of rock conductivity and the precision of the estimated oil saturation of the reservoir, which is of great significance to reservoir evaluation research.

[0003] In existing technologies, the Archie formula and modified models based on the Archie formula are typically used to describe the rock resistivity under different water-bearing conditions.

[0004] However, the inventors have discovered that the existing technology has at least the following technical problems: due to the non-Archie phenomenon in rock resistivity, the accuracy of describing rock resistivity under different water conditions using the Archie formula will be low when the rock resistivity is in a non-Archie state. Summary of the Invention

[0005] This application provides a method for describing the function of rock resistivity to overcome the problem that the accuracy of describing rock resistivity under different water-bearing conditions using the Archie formula is low when the Archie phenomenon is not present.

[0006] In a first aspect, this application provides a method for describing the resistivity of rocks as a function, comprising:

[0007] Select at least two rock samples of the same type, conduct saturated water test and centrifugation test on the rock samples, and measure the pore water resistivity, rock resistivity corresponding to saturated water saturation, and rock resistivity at different partial water saturation, where different partial water saturation includes: partial saturated water saturation and bound water saturation.

[0008] Based on the rock porosity, pore water resistivity, and rock resistivity corresponding to saturated water saturation, the first and second function coefficients in the description function equation of saturated water rock resistivity are calculated using the least squares method.

[0009] Based on different partial water saturation and rock resistivity under different partial water saturation, the rock resistivity of each rock sample under the same effective water saturation was determined by interpolation.

[0010] Based on the bound water saturation and the rock resistivity of each rock sample under the same effective water saturation, the third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation at different effective water saturations is calculated using the least squares method.

[0011] Based on the effective water saturation and the third function coefficient corresponding to the effective water saturation, the fourth and fifth function coefficients of the partially saturated water rock resistivity description function are calculated using the least squares method;

[0012] Based on the first, second, fourth, and fifth function coefficients, determine the rock resistivity description function for the rock type.

[0013] In one possible design, saturated water and centrifugation experiments are performed on rock samples, and the pore water resistivity, rock resistivity at saturated water saturation, and rock resistivity at different partial water saturation levels are measured, including:

[0014] Select at least two rock samples of the same type, conduct a saturated water experiment on the rock samples, and measure the pore water resistivity of the rock samples and the rock resistivity corresponding to the saturation degree of saturated water.

[0015] Then, the rock samples were centrifuged, and the rock resistivity was measured at different water saturation levels in different parts of the rock sample during the centrifugation experiment.

[0016] In one possible design, after conducting a saturated water experiment on the rock sample, the following is also included:

[0017] Measure and record the porosity of the rock samples.

[0018] In one possible design, based on different partial water saturation levels and rock resistivity at different partial water saturation levels, an interpolation method is used to determine the rock resistivity of each rock sample at the same effective water saturation level, including:

[0019] The effective water saturation corresponding to different partial water saturation is determined based on the bound water saturation.

[0020] Based on the effective water saturation and the corresponding rock resistivity, the rock resistivity of each rock sample under the same effective water saturation is determined by interpolation.

[0021] In one possible design, the effective water saturation corresponding to different partial water saturations is determined based on the bound water saturation, and the calculation formula is as follows:

[0022]

[0023] In the formula, S we Effective water saturation, in units of v / v;

[0024] S w This represents partial water saturation, expressed in v / v.

[0025] S wi The bound water saturation is expressed in v / v.

[0026] In one possible design, the resistivity description function of saturated water rock is as follows:

[0027]

[0028] In the formula, R c The resistivity of pore water is expressed in Ω·m.

[0029] R0 is the rock resistivity corresponding to the degree of water saturation, in Ω·m;

[0030] φ represents the porosity of the rock, which is dimensionless.

[0031] c and m are the first and second function coefficients in the equation describing the resistivity of saturated water rock, respectively, and are dimensionless.

[0032] In one possible design, the equation relating the partially saturated water rock resistivity to the bound water saturation is as follows:

[0033]

[0034] In the formula, R t The water saturation is S w Rock resistivity, in Ω·m;

[0035] R0 is the rock resistivity corresponding to the degree of water saturation, in Ω·m;

[0036] S wi This is the bound water saturation, expressed in v / v.

[0037] χ is the third function coefficient in the equation relating partially saturated water rock resistivity to bound water saturation, and is dimensionless.

[0038] In one possible design, the equation for the resistivity function of partially saturated water rock is:

[0039] χ=d(1-S we η )

[0040] In the formula, χ is the third function of the equation relating partially saturated water rock resistivity to bound water saturation, and is dimensionless;

[0041] S we Effective water saturation, in units of v / v;

[0042] d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless.

[0043] In one possible design, the rock resistivity description function for the rock type is:

[0044]

[0045] In the formula, R t The water saturation is S w Rock resistivity, in Ω·m;

[0046] R c The resistivity of pore water is expressed in Ω·m.

[0047] S we Effective water saturation, in units of v / v;

[0048] S wi This is the bound water saturation, expressed in v / v.

[0049] c and m are the first and second function coefficients in the equation describing the resistivity of saturated water in rock, respectively, and are dimensionless.

[0050] d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless.

[0051] In one possible design, rocks of the same type are rocks with one or more of the following properties:

[0052] Lithology, mineral composition type, and rock pore type.

[0053] This application provides a method for describing the function of rock resistivity. By measuring the rock porosity, pore water resistivity, and rock resistivity under different water saturation states of rock samples, the first and second function coefficients of the function equation describing the resistivity of saturated water rock are obtained. The third function coefficient of the equation relating the partially saturated water rock resistivity to the bound water saturation under different effective water saturation states, as well as the fourth and fifth function coefficients of the function describing the resistivity of partially saturated water rock, are obtained. Finally, a function description of rock resistivity is obtained, overcoming the problem of low accuracy of the existing Alzer formula in non-Alzer phenomena, and conforming to the understanding of rock physics. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1A schematic flowchart illustrating a method for describing the function of rock resistivity according to an embodiment of this application;

[0056] Figure 2 Comparison of the results obtained from the saturated water rock resistivity coefficient describing equation determined for the embodiments of this application with the results obtained from Archie's formula;

[0057] Figure 3 The results are the third function coefficients of the equation relating partially saturated water rock resistivity to bound water saturation for different effective water saturation levels as determined in the embodiments of this application.

[0058] Figure 4 A comparison is made between the rock resistivity values ​​corresponding to saturated water saturation calculated for the embodiments of this application and the rock resistivity values ​​corresponding to saturated water saturation calculated by Archie's formula.

[0059] Figure 5 A comparison is made between the rock resistivity values ​​corresponding to partially saturated water saturation calculated for the embodiments of this application and the rock resistivity values ​​corresponding to partially saturated water saturation calculated using the Archie formula. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] To address the technical problem that the Archie formula is insufficiently accurate in describing rock resistivity under different water saturation conditions in non-Archy phenomena, this application proposes the following technical solution: A descriptive function for rock resistivity is obtained by measuring rock porosity, pore water resistivity, and rock resistivity under different water saturation conditions in rock samples. Detailed embodiments are described below.

[0062] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0063] Figure 1 This is a schematic flowchart illustrating a method for describing the function of rock resistivity according to one embodiment of this application. Figure 1 As shown, the method includes:

[0064] S101: Select at least two rock samples of the same type, conduct saturated water and centrifugation experiments on the rock samples, and measure the pore water resistivity, rock resistivity corresponding to saturated water saturation, and rock resistivity at different partial water saturation levels. The different partial water saturation levels include partial saturated water saturation and bound water saturation.

[0065] Specifically, at least two rock samples of the same type were selected, and a saturated water experiment was conducted on the rock samples to measure the pore water resistivity and the rock resistivity corresponding to the saturated water level. Then, a centrifugation experiment was conducted on the rock samples, and the rock resistivity at different water saturation levels in different parts of the rock samples was measured during the centrifugation experiment.

[0066] Among them, rocks of the same type are rocks that have one or more of the following rock properties: lithology, mineral composition type, and rock pore type.

[0067] For example, eight sandstone samples were selected, and saturated water tests were conducted on the eight rock samples. The pore water resistivity and the rock resistivity corresponding to the saturated water saturation were measured according to the procedures specified in the standard "Laboratory Measurement and Calculation Methods for Rock Resistivity Parameters SYT5385-2007". Then, the rock samples were centrifuged. During the centrifugation test, the bound water saturation of the rock samples was measured according to the procedures specified in the standard "Laboratory Measurement Specifications for Nuclear Magnetic Resonance Parameters of Rock Samples SY / T 6490-2014". The rock resistivity of the rock samples at different partial water saturation levels was measured according to the procedures specified in the standard "Laboratory Measurement and Calculation Methods for Rock Resistivity Parameters SYT5385-2007".

[0068] In this embodiment, the rock resistivity can be measured using either the two-electrode method or the four-electrode method.

[0069] S102: Based on the rock porosity, pore water resistivity, and rock resistivity corresponding to saturated water saturation, the first and second function coefficients in the description function equation of saturated water rock resistivity are calculated using the least squares method.

[0070] The equation describing the resistivity of water-saturated rocks is shown below:

[0071]

[0072] In the formula, R c The resistivity of pore water is expressed in Ω·m.

[0073] R0 is the rock resistivity corresponding to the degree of water saturation, in Ω·m;

[0074] φ represents the porosity of the rock, which is dimensionless.

[0075] c and m are the first and second function coefficients in the equation describing the resistivity of saturated water rock, respectively, and are dimensionless.

[0076] Specifically, the rock porosity, pore water resistivity, and rock resistivity corresponding to saturated water saturation of the eight rock samples were substituted into the saturated water rock resistivity description equation. The first and second function coefficients of the saturated water rock resistivity description equation were calculated using the least squares method. The first function coefficient c = -0.26045, and the second function coefficient m = 2.06129. The saturated water rock resistivity description equation is shown below:

[0077]

[0078] Figure 2 The results obtained from the saturated water rock resistivity coefficient description equation determined for the embodiments of this application are compared with the results obtained from the Archie formula.

[0079] S103: Based on different partial water saturation and rock resistivity under different partial water saturation, the rock resistivity of each rock sample under the same effective water saturation is determined by interpolation.

[0080] Specifically, the effective water saturation corresponding to different partial water saturation is determined based on the bound water saturation; based on the effective water saturation and the rock resistivity corresponding to the effective water saturation, the rock resistivity of each rock sample under the same effective water saturation is determined by interpolation.

[0081] The formula for calculating the effective water saturation corresponding to different partial water saturations based on the bound water saturation is as follows:

[0082]

[0083] In the formula, S we Effective water saturation, in units of v / v;

[0084] S w This represents partial water saturation, expressed in v / v.

[0085] S wi The bound water saturation is expressed in v / v.

[0086] In this embodiment, the effective water saturation of eight rock samples at different partial water saturation levels is obtained; based on the eight different effective water saturation levels and the resistivity under effective water saturation, the rock resistivity of the eight rock samples under the same effective water saturation level is determined by interpolation.

[0087] In this embodiment, the rock resistivity of each rock sample under the same effective water saturation can be determined according to a quadratic interpolation function.

[0088] S104: Based on the bound water saturation and the rock resistivity of each rock sample at the same effective water saturation, the third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation at different effective water saturations is calculated using the least squares method.

[0089] The equation relating the resistivity of partially saturated water rocks to the degree of bound water saturation is as follows:

[0090]

[0091] In the formula, R t The water saturation is S w Rock resistivity, in Ω·m;

[0092] R0 is the rock resistivity corresponding to the degree of water saturation, in Ω·m;

[0093] S wi This is the bound water saturation, expressed in v / v.

[0094] χ is the third function coefficient in the equation relating partially saturated water rock resistivity to bound water saturation, and is dimensionless.

[0095] Specifically, the least squares method was used to fit the water content states with effective saturation of 0, 0.2, 0.4, 0.6, 0.8, and 1.0, and the fitting results are shown below:

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] It can be seen that when the effective saturation is 0, 0.2, 0.4, 0.6, 0.8, and 1.0, the corresponding third function coefficients of the equation relating partially saturated water rock resistivity to bound water saturation are 1.39995, 0.97842, 0.65533, 0.38902, 0.15988, and 0, respectively. Figure 3The result is the third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation for different effective water saturation levels as determined in the embodiments of this application.

[0103] S105: Based on the effective water saturation and the third function coefficient corresponding to the effective water saturation, the fourth and fifth function coefficients of the partially saturated water rock resistivity description function are calculated using the least squares method.

[0104] The equation for the resistivity function of partially saturated water rock is as follows:

[0105] χ=d(1-S we η )

[0106] In the formula, χ is the third function of the equation relating partially saturated water rock resistivity to bound water saturation, and is dimensionless;

[0107] S we Effective water saturation, in units of v / v;

[0108] d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless.

[0109] In this embodiment, the fourth and fifth function coefficients of the partially saturated water rock resistivity function were obtained in 6 sets. The fourth and fifth function coefficients were obtained by using the least squares method and were d = 0.98029 and η = 0.68283.

[0110] S106: Determine the rock resistivity description function for the rock type based on the first function coefficient, the second function coefficient, the fourth function coefficient, and the fifth function coefficient.

[0111] The rock resistivity description function for each rock type is:

[0112]

[0113] In the formula, R t The water saturation is S w Rock resistivity, in Ω·m;

[0114] R c The resistivity of pore water is expressed in Ω·m.

[0115] S we Effective water saturation, in units of v / v;

[0116] S wi This is the bound water saturation, expressed in v / v.

[0117] c and m are the first and second function coefficients in the equation describing the resistivity of saturated water in rock, respectively, and are dimensionless.

[0118] d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless.

[0119] Figure 4 This paper compares the rock resistivity value corresponding to saturated water saturation calculated in this application embodiment with the rock resistivity value corresponding to saturated water saturation calculated using the Archie formula. The rock resistivity value corresponding to saturated water saturation calculated in this application embodiment is 0.99931, with an error of 8.43%; the rock resistivity value corresponding to saturated water saturation calculated using the Archie formula is 0.98704, with an error of 14.11%.

[0120] Figure 5 This paper compares the rock resistivity values ​​corresponding to partially saturated water saturation calculated in this application's embodiments with those calculated using the Archie formula. The rock resistivity value calculated in this application's embodiments is 0.99388, with an error of 5.13%; the rock resistivity value calculated using the Archie formula is 0.87181, with an error of 8.43%. It can be seen that the accuracy of the rock resistivity results calculated in this application's embodiments for both saturated and partially saturated water saturation is significantly higher than the results calculated using the Archie formula.

[0121] The rock resistivity description method provided in this embodiment obtains the first and second function coefficients of the rock resistivity description function equation by measuring the rock porosity, pore water resistivity, and rock resistivity under different water saturation states of rock samples. It also obtains the third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation at different effective water saturation levels, and the fourth and fifth function coefficients of the partially saturated water rock resistivity description function. Based on these coefficients, a functional description of rock resistivity is finally obtained, overcoming the problem of low accuracy of the existing Alzer formula in non-Alzer phenomena and conforming to rock physics understanding.

[0122] In the embodiments of this application, Figure 1 Based on the provided embodiments, a detailed explanation is given of the specific implementation method for measuring the porosity of rock samples after conducting a saturated water experiment on the rock samples in S101. This method includes:

[0123] S601: Measure and record the porosity of rock samples.

[0124] Specifically, the porosity of the rock samples was measured according to the procedure specified in the standard "Standard for Determination of Porosity and Permeability of Rocks under Overburden" (SY T6385-1999).

[0125] In this embodiment of the application, the porosity of the ground is measured; the atmospheric pressure and experimental temperature data for rock porosity measurement are set, the number of rock samples to be analyzed and the basic parameters are input, the rock samples are measured, and the triaxial porosity of the rock samples is obtained; the triaxial porosity of the rock samples is corrected according to the porosity of the ground.

[0126] The rock resistivity function description method provided in this embodiment obtains a more accurate rock sample porosity by measuring the triaxial porosity of the rock sample and correcting the triaxial porosity of the rock sample based on the porosity of the ground, thereby further increasing the accuracy of the rock resistivity function description method.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for describing the resistivity of rocks as a function, characterized in that, include: At least two rock samples of the same type were selected, and saturated water and centrifugation experiments were performed on the rock samples. The pore water resistivity, rock resistivity corresponding to saturated water saturation, and rock resistivity at different partial water saturation were measured. The different partial water saturation included partial saturated water saturation and bound water saturation. Based on the rock porosity, the pore water resistivity, and the rock resistivity corresponding to the saturation of water, the first and second function coefficients in the description function equation of the saturated water rock resistivity are calculated using the least squares method. Based on the different partial water saturation and the rock resistivity under different partial water saturation, the rock resistivity of each rock sample under the same effective water saturation was determined by interpolation. Based on the bound water saturation and the rock resistivity of each rock sample under the same effective water saturation, the third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation corresponding to different effective water saturation is calculated using the least squares method. Based on the different effective water saturation and the third function coefficients corresponding to the different effective water saturation, the fourth and fifth function coefficients of the partially saturated water rock resistivity description function are calculated using the least squares method; Based on the first function coefficient, the second function coefficient, the fourth function coefficient, and the fifth function coefficient, determine the rock resistivity description function for the rock type; The rock resistivity description function for the rock type is: In the formula, The water saturation is Rock resistivity at time, unit ; The resistivity of pore water is expressed in units of... ; This represents partial water saturation, expressed in v / v. Effective water saturation, in units of v / v; This is the bound water saturation, expressed in v / v. c and m are the first and second function coefficients in the equation describing the resistivity of saturated water in rock, respectively, and are dimensionless. d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless. The porosity of the rock is dimensionless.

2. The method according to claim 1, characterized in that, The process of performing saturated water and centrifugation experiments on the rock samples, and measuring the pore water resistivity, the rock resistivity corresponding to saturated water saturation, and the rock resistivity at different partial water saturation levels, includes: Select at least two rock samples of the same type, conduct a saturated water experiment on the rock samples, and measure the pore water resistivity and the rock resistivity corresponding to the saturated water saturation level of the rock samples. The rock sample was then centrifuged, and the rock resistivity was measured at different water saturation levels during the centrifugation process.

3. The method according to claim 2, characterized in that, After performing a saturated water test on the rock sample, the method further includes: The porosity of the rock sample was measured and recorded.

4. The method according to claim 1, characterized in that, The method of determining the rock resistivity of each rock sample at the same effective water saturation using interpolation based on the different partial water saturation and rock resistivity at different partial water saturation includes: The effective water saturation corresponding to different partial water saturations is determined based on the bound water saturation. Based on the effective water saturation and the corresponding rock resistivity, the rock resistivity of each rock sample under the same effective water saturation is determined by interpolation.

5. The method according to claim 4, characterized in that, The formula for calculating the effective water saturation corresponding to different partial water saturations based on the bound water saturation is as follows: In the formula, Effective water saturation, in units of v / v; This represents partial water saturation, expressed in v / v. The bound water saturation is expressed in v / v.

6. The method according to claim 1, characterized in that, The equation describing the resistivity of saturated water in rocks is as follows: In the formula, The resistivity of pore water is expressed in units of... ; The rock resistivity corresponding to saturated water saturation, in units of ; Rock porosity, dimensionless; c and m are the first and second function coefficients in the equation describing the resistivity of saturated water rock, respectively, and are dimensionless.

7. The method according to claim 1, characterized in that, The equation relating the resistivity of partially saturated water rock to the degree of bound water saturation is as follows: In the formula, The water saturation is Rock resistivity at time, unit ; The rock resistivity corresponding to saturated water saturation, in units of ; This represents partial water saturation, expressed in v / v. This is the bound water saturation, expressed in v / v. The coefficient of the third function in the equation relating partially saturated water rock resistivity to bound water saturation is dimensionless.

8. The method according to claim 1, characterized in that, The equation for the resistivity function of partially saturated water rock is: In the formula, The third function coefficient of the equation relating partially saturated water rock resistivity to bound water saturation is dimensionless. Effective water saturation, in units of v / v; d and η are the fourth and fifth function coefficients of the partially saturated water rock resistivity description function, respectively, and are dimensionless.

9. The method according to any one of claims 1 to 8, characterized in that, The rocks of the same type are rocks that share one or more of the following rock properties: Mineral composition type, rock pore type.

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