A method for calculating longitudinal wave velocity in a gas-water system

Abstract

The present application belongs to the technical field of rock physics, and is especially a longitudinal wave velocity calculation method under a gas-water system. The method comprises the following steps: S1: obtaining longitudinal and transverse wave velocities of a sample under normal pressure and under a limit high pressure through experiments; S2: calculating a skeleton bulk modulus and a clay water relaxation time according to a sample XRD mineral analysis result; S3: converting the wave velocities into moduli; S4: calculating saturated volcanic lava longitudinal wave velocities considering frequency dispersion according to a Gurevich formula; S5: measuring a nuclear magnetic T2 spectrum of the sample under a saturated state; S6: calculating bulk moduli under different saturation degrees; and S7: converting to obtain longitudinal wave velocities under different saturation degrees. The present application explains the reason why the volcanic lava saturation degree-longitudinal wave velocity rule presents a "convex" shape from a mechanism, and effectively calculates volcanic lava longitudinal wave velocities under different saturation degrees.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rock physics, in particular to a method for calculating P-wave velocity in gas-water system. BACKGROUND

[0002] Due to the large difference in bulk modulus between gas and liquid, P-wave velocity is very sensitive to the gas content of the rock. Therefore, acoustic methods are important tools for fine evaluation of reservoir logging. Understanding the acoustic properties of gas-bearing volcanic lava is of great significance for the development of low resistivity volcanic lava gas reservoirs and the safety evaluation of CO2 storage caprocks.

[0003] However, the understanding of the influencing factors and mechanisms of volcanic lava acoustic parameters is not enough at present. Volcanic lava usually has low porosity and permeability, contains high content of clay minerals formed by alteration, and has completely different pore structure from sandstone due to genetic differences. These characteristics result in different acoustic velocity rules from conventional sandstone.

[0004] Mavko and Jizba proposed a granular rock jet flow dispersion quantitative model (Mavko-Jizba model). This model can calculate the elastic wave velocity of fluid-saturated rock at high frequency, and is a high-frequency modified version of the Gassmann model. However, it is only applicable to liquid-saturated rock, and the calculation accuracy of the model is insufficient when the pores are filled with low-modulus fluids such as natural gas. To solve this problem, Gurevich et al. modified the model and proposed a modified version of the Mavko-Jizba model that can calculate the high-frequency bulk modulus of dry and water-saturated rock. This study refers to it as the Gurevich model.

[0005] The above-mentioned models are only applicable to single fluid conditions and cannot be used to calculate P-wave velocity in gas-water systems.

[0006] However, based on the analysis of a large number of different rock physics experiments, we found that volcanic lava pores are mainly dissolution pores, with special pore structure, and the fluid distribution state also shows obvious differences from conventional sandstone in nuclear magnetic T2 spectrum. These special rock physics conditions make the P-wave velocity of rock samples change with saturation in a "convex" curve. Therefore, none of the existing models can effectively explain and calculate the P-wave velocity of volcanic lava. In order to solve these problems, we provide a method for calculating P-wave velocity in gas-water system considering the special pore structure and fluid distribution of partially saturated volcanic lava. SUMMARY

[0007] This section is intended to summarize some aspects of the embodiments of the present application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the summary of the application and the title of the application in order to avoid obscuring the purpose of this section, the summary of the application and the title of the application, and such simplifications or omissions are not to be construed as limiting the scope of the present application.

[0008] To solve the above technical problems, according to one aspect of the present application, the present application provides the following technical solutions:

[0009] A longitudinal wave velocity calculation method under a gas-water system, comprising the following steps:

[0010] S1: measuring the longitudinal and transverse wave velocities of the dry state of the volcanic lava sample under different pressures, or obtaining the velocities according to the wave velocity-porosity-pressure relationship of the same batch of samples, and recording the longitudinal and transverse wave velocities under normal pressure and the longitudinal and transverse wave velocities under the limit high pressure;

[0011] S2: calculating the skeleton bulk modulus and clay water relaxation time according to the XRD mineral analysis result of the sample;

[0012] S3: converting the wave velocity into modulus;

[0013] S4: calculating the saturated volcanic lava longitudinal wave velocity considering dispersion according to the Gurevich formula;

[0014] S5: measuring the nuclear magnetic T2 spectrum of the sample in the saturated state to obtain the clay water relaxation time, calculating the clay water porosity, and recording it as ;

[0015] S6: calculating the bulk modulus under different saturations:

[0016]

[0017] wherein is the bulk modulus of the mixed fluid, which is obtained by the Brie formula:

[0018]

[0019] wherein is the bulk modulus of the gas, which is taken as 0.000142 GPa, is the bulk modulus of the water, which is taken as 2.2 GPa, is the unrelaxed state bulk modulus, which is obtained by substituting into the Gurevich formula for calculation;

[0020] S7: converting the bulk modulus back to wave velocity, so as to obtain the longitudinal wave velocity under different saturations.

[0021] As a preferred scheme of the method for calculating the longitudinal wave velocity under a gas-water system according to the present application, in step S2, if the wave velocity-saturation curve under normal pressure needs to be calculated, the bulk modulus of the mixed mineral is calculated according to the Voigt-Reuss-Hill modulus model, denoted as GPa; if the wave velocity-saturation curve under different pressures or different temperatures needs to be calculated, the intercept of the reciprocal wave velocity-porosity curve of the same batch of samples needs to be referred to.

[0022] As a preferred scheme of the method for calculating the longitudinal wave velocity under a gas-water system according to the present application, in step S3, the formula for converting the wave velocity into the modulus is:

[0023]

[0024]

[0025] wherein, is the bulk modulus, GPa; is the shear modulus, GPa; is the bulk density, g / cm 3 ; and are the longitudinal wave velocity and the transverse wave velocity, m / s, respectively.

[0026] As a preferred scheme of the method for calculating the longitudinal wave velocity under a gas-water system according to the present application, in step S4, the Gurevich formula is:

[0027]

[0028] wherein is the bulk modulus under high frequency and unrelaxed state, GPa; is the longitudinal wave velocity under the limit high pressure obtained in S1 and the bulk modulus under the limit high pressure calculated in S2, GPa; is the longitudinal wave velocity under normal pressure obtained in S1 and the bulk modulus under normal pressure calculated in S2, GPa; is the bulk modulus of water, taken as 2.2 GPa; is the bulk modulus of the volcanic lava when the porosity is zero, obtained in S3; is the soft pore porosity of the sample.

[0029] Compared with the prior art, the present application has the beneficial effect that the present application explains the reason why the saturation-longitudinal wave velocity rule of the volcanic lava presents a “convex” shape from the mechanism, and effectively calculates the longitudinal wave velocity of the volcanic lava under different saturation conditions. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the present application will be described in detail below with reference to the drawings and detailed embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor on the basis of these drawings. Among them:

[0031] Figure 1 Flow chart of the longitudinal wave velocity calculation method under the gas-water system of the present application;

[0032] Figure 2 Curve graph of the longitudinal wave velocity of the dry sample changing with confining pressure in the embodiment of the longitudinal wave velocity calculation method under the gas-water system of the present application;

[0033] Figure 3 Inverse of the wave velocity (time difference) of the same batch of samples-porosity curve graph in the embodiment of the longitudinal wave velocity calculation method under the gas-water system of the present application;

[0034] Figure 4 NMR T2 spectrum of two samples under different saturations in the embodiment of the longitudinal wave velocity calculation method under the gas-water system of the present application;

[0035] Figure 5 Comparison graph of the modulus calculation effect of several classical models and the model of the present application in the embodiment of the longitudinal wave velocity calculation method under the gas-water system of the present application. DETAILED DESCRIPTION

[0036] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings.

[0037] Secondly, the present application is described in detail in combination with the schematic diagram. In the detailed description of the embodiments of the present application, the cross-sectional view of the device structure will be partially enlarged without the general proportion for the convenience of description, and the schematic diagram is only an example, which should not limit the scope of protection of the present application here. In addition, the three-dimensional spatial dimensions of length, width and depth should be included in the actual manufacture.

[0038] In order to make the purposes, technical solutions and advantages of the present application more clear, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0039] Please refer to Figure 1 The present application provides a longitudinal wave velocity calculation method under a gas-water system, comprising the following steps:

[0040] S1: Measure the P-wave and S-wave velocities of the dry volcanic lava sample at different pressures, or obtain the velocities from the P-wave-S-wave-porosity-pressure relationship of the same batch of samples, and record the P-wave and S-wave velocities at normal pressure and the P-wave and S-wave velocities at the limit high pressure (the upper limit of the P-wave-S-wave-pressure relationship);

[0041] S2: Obtain the XRD mineral analysis results of the sample, if it is necessary to calculate the P-wave-saturation curve at normal pressure, calculate the bulk modulus of the mixed mineral according to the Voigt-Reuss-Hill (V-R-H) modulus model (formula (3)), and record it as , GPa; if it is necessary to calculate the P-wave-saturation curve at different pressures or different temperatures, the intercept of the reciprocal of the P-wave velocity (time difference) -porosity curve (Whilly formula) of the same batch of samples needs to be referred to.

[0042] S3: Convert the P-wave and S-wave velocities into moduli according to formula (1) and formula (2), wherein is the bulk modulus, GPa; is the shear modulus, GPa; is the bulk density, g / cm 3 ; and are the P-wave and S-wave velocities, m / s, respectively. As can be seen from the formula, the modulus and the wave velocity are positively correlated, and in order to facilitate the discussion, the modulus calculation will be mainly discussed in the subsequent description of the present application;

[0043] (1)

[0044] (2)

[0045] S4: Calculate the P-wave velocity of the saturated volcanic lava considering the dispersion according to the Gurevich formula, wherein is the bulk modulus at high frequency and in the unrelaxed state, GPa; is the P-wave velocity at the limit high pressure obtained in S1 and the bulk modulus at the limit high pressure calculated in S3, GPa; is the P-wave velocity at normal pressure obtained in S1 and the bulk modulus at normal pressure calculated in S3, GPa; is the bulk modulus of water, which is 2.2 GPa; is the bulk modulus of the volcanic lava when the porosity is zero, which is obtained from S2; is the soft pore porosity of the sample, and in the present application, the soft pore is mainly considered to exist in the clay pores, and considering the characteristics of the volcanic lava usually having high clay content, the empirical upper limit value of the soft pore porosity, 1% (Shapiro, 2003), is directly taken;

[0046] (3)

[0047] S5: measure the nuclear magnetic T2 spectrum of the sample in the saturated state, obtain the clay water relaxation time according to the clay type provided by the XRD information, and then calculate the clay water porosity, denoted as .

[0048] S6: calculate the bulk modulus under different saturations according to formula (4), which is the core formula of the application and is improved on the basis of the Gurevich formula and the Brie formula .

[0049] (4)

[0050] wherein is the bulk modulus of the mixed fluid, which is obtained from the Brie formula:

[0051]

[0052] wherein is the bulk modulus of the gas, which is taken as 0.000142 GPa. The model follows two basic assumptions: the soft pores that cause the rock dispersion are mainly present in the clay pores of the volcanic lava; and the water preferentially fills the volcanic lava clay pores.

[0053] S7: the application considers that one of the Gassmann basic assumptions, i.e., the shear modulus is not affected by the fluid, is established. Therefore, it is considered that , and finally the bulk modulus is converted back to the wave velocity according to formula (1) and formula (2), so that the longitudinal wave velocity under different saturations can be obtained.

[0054] Embodiment

[0055] Taking two andesite samples of a gas reservoir in a certain area of the Songliao Basin in China as examples, denoted as X_1 and X_2.

[0056] According to S1, the longitudinal and transverse wave velocities of the volcanic lava samples under different pressures in the dry state are measured, and the longitudinal and transverse wave velocities under the limit pressure are recorded. As shown in the longitudinal wave velocity curve of the X_1 sample with the confining pressure change, as an example, with the increase of the confining pressure, the longitudinal wave velocity continuously increases, and the extension line thereof shows that the limit pressure wave velocity is about 5500 m / s; Figure 2

[0057] Since the embodiment needs to calculate the longitudinal wave velocity of the sample under the reservoir temperature and pressure, according to S3, the reciprocal of the wave velocity (time difference △t) of the same batch of samples-porosity curve of the same batch of samples is measured, as shown in Figure 3 . Based on the time difference of the dry sample line intercept, the wave velocity is calculated, and then converted to modulus according to formula (1) and formula (2), to obtain .

[0058] ​According to S3, the wave velocity is converted into modulus to obtain , and ;

[0059] After the above key parameters are obtained, according to S4, the following is calculated ;

[0060] According to S5, the nuclear magnetic T2 spectrum of the two samples in a saturated state is measured, and the clay minerals of the two samples are mainly chlorite according to the XRD information, so that the clay water relaxation time is determined as 5 ms, and then a is obtained according to the nuclear magnetic T2 spectrum of the sample in a saturated state. Figure 4 The nuclear magnetic T2 spectrum of the two samples under different saturations (left X_1, right X_2) can be seen that when not fully saturated, the fluid in the two samples is preferentially distributed in the short relaxation time pore space, i.e. the clay pores, which is an important support for considering the fluid distribution in the method;

[0061] According to S6, the bulk modulus under different saturations is calculated. In order to more directly compare the effect of the method, the measured wave velocity is converted into modulus according to formula (1) and formula (2), and the modulus is directly compared, Figure 5 The comparison chart of the modulus calculated by several classical models and the model of the application (left X_1, right X_2) can be seen that the classical Gassmann model is established under the assumption that the fluid is fully relaxed, without considering the enhancement of soft pores on the modulus of the rock at high frequency, i.e. frequency dispersion, so the modulus calculation result under the saturated state is low. The Gurevich model is a supplement to the Gassmann equation at high frequency, which accurately calculates the modulus of the volcanic lava sample under the saturated state, but the modulus under the partially saturated state needs to be calculated by combining the Brie formula, which cannot accurately describe the "convex" modulus-saturation curve of the volcanic lava. The method of the application is optimized by combining the Gurevich model, which accurately calculates the modulus of the volcanic lava sample, and then accurately calculates the longitudinal wave velocity of the volcanic lava sample;

[0062] Finally, according to S7, the calculated bulk modulus is converted into wave velocity to obtain the calculated wave velocity of the volcanic lava sample.

[0063] Although the application has been described with reference to the embodiments above, various improvements can be made thereto and equivalents can be substituted therefor without departing from the scope of the application. In particular, each of the features disclosed in the embodiments of the application can be used in any combination with each other, and the combinations of these features are not exhaustively described in the specification, which is only for the purpose of omitting the length and saving resources. Therefore, the application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for calculating the velocity of a longitudinal wave in a gas-water system, characterized by, The method comprises the following steps: S1: measuring the longitudinal and transverse wave velocities of the dry volcanic lava sample under different pressures, or obtaining the velocities according to the velocity-porosity-pressure relationship of the same batch of samples, and recording the longitudinal and transverse wave velocities under normal pressure and the longitudinal and transverse wave velocities under the limit high pressure; S2: calculating the skeleton bulk modulus and clay water relaxation time according to the XRD mineral analysis result of the sample; S3: Convert wave velocity to modulus, obtain dry rock bulk modulus , limit pressure under dry rock bulk modulus ; S4: Saturated volcanic lava bulk modulus accounting for dispersion according to Gurevich formula ; S5: Measure the nuclear magnetic T2 spectrum of the sample in the water-saturated state, obtain the clay water relaxation time, calculate the clay water porosity, and record it as ; S6: calculating the bulk modulus under different saturations: ； where is the water saturation, is the porosity, is the bulk modulus of the mixture fluid, which is obtained from Brie formula: ； wherein is the gas bulk modulus, taken as 0.000142 GPa, is the water bulk modulus, taken as 2.2 GPa; S7: converting the bulk modulus back to the wave velocity, so as to obtain the longitudinal wave velocity under different saturations.

2. The method of claim 1, wherein, The formula for converting the wave velocity to the modulus in S3 is: ； ； wherein, Gp is the bulk modulus, GPa; Gs is the shear modulus, GPa; Gp is the bulk density, g / cm 3 ; and Vp and Vs are the longitudinal and transverse wave velocities, m / s, respectively.

3. The method of claim 1, wherein, In the step S2, if the wave velocity-saturation curve under normal pressure needs to be calculated, the bulk modulus of the mixed mineral is calculated according to the Voigt-Reuss-Hill modulus model, denoted as , GPa; if the wave velocity-saturation curve under different pressures or different temperatures needs to be calculated, the intercept of the reciprocal wave velocity-porosity curve of the same batch of samples needs to be referred to.

4. The method of claim 1, wherein, The Gurevich formula in S4 is: ； where G0 is the bulk modulus in the high-frequency unrelaxed state, GPa, from G0 is the bulk modulus in the high-frequency unrelaxed state, GPa, from V0 is the bulk modulus at the limit of high pressure obtained from S3, GPa, and V1 is the longitudinal wave velocity at the limit of high pressure obtained from S1; V0 is the bulk modulus at the limit of high pressure obtained from S3, GPa, and V1 is the longitudinal wave velocity at the limit of high pressure obtained from S1; V0 is the bulk modulus at the limit of high pressure obtained from S3, GPa, and V1 is the longitudinal wave velocity at the limit of high pressure obtained from S1; V0 is the bulk modulus at the limit of high pressure obtained from S3, GPa, and V1 is the longitudinal wave velocity at the limit of high pressure obtained from S1; V0 is the bulk modulus at the limit of high pressure obtained from S3, GPa, and V1 is the longitudinal wave velocity at the limit of high pressure obtained from S1;

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