Seismic frequency-dependent q-value estimation method based on rock physics mechanism

Abstract

The application discloses a seismic frequency-variable Q value estimation method based on a rock physical mechanism, and comprises the following steps: selecting an effective mesoscopic scale rock physical model, determining a Q(f) curve and a velocity dispersion relation in the model; improving the selected mesoscopic scale rock physical model by using a pre-established viscoelastic model, and analyzing attenuation characteristics of the mesoscopic rock physical model in describing a reservoir; and calculating a frequency-variable Q value of the improved mesoscopic scale rock physical model by using a double-parameter spectral ratio method of an SLS model. The above scheme is based on a WIGED multi-scale rock physical model of a fluid and a DKT model of dry rock, and proposes a new frequency-related Q estimation method, i.e. the double-parameter spectral ratio method. Compared with a conventional estimation method, the method establishes a connection among a mesoscopic rock physical model, logging data and seismic data, can give more accurate and reliable seismic data Q value results, and better explains reservoir physical properties.

Description

TECHNICAL FIELD

[0001] The present application relates to a Q value estimation method, in particular to a seismic frequency-dependent Q value estimation method based on rock physics mechanism. BACKGROUND

[0002] Saturated subsurface regions, such as shale reservoirs, can exhibit high attenuation at seismic frequencies (<100 Hz) (Chapman et al., 2006). Therefore, attenuation can be used as an aid in seismic data interpretation to directly probe for natural gas and oil. To better link the attenuation attribute to reservoir characteristics, it is necessary to: 1. increase the research on mesoscopic-scale seismic wave attenuation mechanisms, 2. propose more accurate estimation methods of frequency-dependent Q value based on real seismic data, and 3. establish the link between Q value and reservoir characteristics, such as fluid type or oil and gas saturation.

[0003] For dry rocks with frequencies between 0.1 and 100 Hz, the most important attenuation mechanisms are: matrix viscoelasticity (Nolick, 1972); dissipation due to wave-induced friction between mineral grains or cracks (Walsh, 1966); and thermoelastic mechanisms (Kjansson, 1980). In fluid-saturated rocks, the wave-induced fluid flow (WIFF) mechanism can often explain the attenuation and dispersion phenomena due to the presence of fluids in the rock pore space (Muller et al., 2010). At the macroscopic scale, Biot's poroelastic theory (Biot, 1956b, a; White, 1986; Pride, 2005) explains the attenuation and dispersion due to macroscopic fluid flow. However, the frequency of macroscopic fluid flow is usually above 10,000 Hz, much higher than the seismic exploration frequency band. At the microscopic scale, WIFF or squirt flow can often explain the attenuation in the ultrasonic frequency band, but can also be applied in the seismic and acoustic frequency bands (Johnston et al., 1979; Sams et al., 1997; Pride et al., 2004). At the mesoscopic scale, flow occurs in spatial variations of rock and / or fluid properties that are much larger than typical pore sizes, but much smaller than the wavelength. White (1975) first proposed an approximate "patchy-saturation" model based on Biot's theory. Further studies of this mesoscopic attenuation mechanism have shown that it can produce very large attenuation peaks in the seismic frequency band (Dutta and Odé, 1979; Gurevich et al., 1997; Shapiro and Muller, 1999; Johnson, 2001; Muller and Gurevich, 2004; Pride et al., 2004). Pride et al. (2004) explained the seismic response of patchy-saturated media in gas-water-saturated pores by introducing a "dual-porosity" theory that was able to explain the attenuation of measured data in the 1-104Hz frequency range (10 -2 <Q -1 <10 -1). In microbubble-saturated rocks (low gas saturation in the gas phase), the wave-induced gas dissolution out of solution (WIGED) mechanism can explain the apparent attenuation of seismic waves (Onuki, 1991; Collier et al., 2006; Tisato et al., 2015). Theoretical studies of the attenuation mechanism have been carried out, and experiments have been conducted on core samples (Wang et al., 2012; Tisato and Quintal, 2014). Practical data (Fielitz and Wegler, 2015; Pisi et al., 2015) show that the Q value is frequency-dependent. Therefore, the attenuation estimation method for field seismic data should consider the frequency-dependent attenuation. However, in most Q estimation methods, such as the log spectral ratio method (Tonn, 1991), the centroid frequency shift method (Quan and Harris, 1997), and the peak frequency shift method (Zhang and Ulrych, 2002), it is generally assumed that Q is independent of the frequency band. Gurevich and Pevzner (2015) discussed the error in estimating Q using the log spectral ratio method and concluded that the log spectral ratio method for estimating Q would cause systematic bias due to the introduction of linear regression.

[0004] In recent years, Yadav et al. (2008) proposed a method based on wave propagation models and travel time curves to calculate the frequency-dependent Q value. Li et al. (2016) proposed a two-parameter regression method based on the power-law attenuation model to estimate the frequency-dependent Q value. Beckwith et al. (2017) improved the spectral ratio method based on the PSQI framework and combined the frequency-dependent Q. By introducing the power-law attenuation model, the frequency-dependent attenuation was accurately calculated from field seismic data.

[0005] Although attenuation has been proven to be helpful in detecting oil and gas directly from seismic data, the low accuracy of Q estimation results and the gap between Q value and reservoir properties have reduced its performance in reservoir interpretation.

[0006] However, scientists have shown that attenuation (the inverse of the quality factor, 1 / Q) is related to frequency, but most Q estimation methods are still based on the assumption that Q is constant. Although mesoscopic rock physics models bridge the gap between seismic attenuation and reservoir properties (such as porosity and fluid saturation), existing mesoscopic rock physics models have not been effectively applied to frequency-dependent Q estimation. A compromise method for estimating frequency-dependent Q is to apply viscoelastic models (such as GSLS) in Q estimation methods (such as the log spectral ratio method), but the physical meaning of viscoelastic models is less, which leads to errors in Q estimation. SUMMARY

[0007] In view of the defects in the prior art, the method for estimating seismic frequency-dependent Q value based on rock physical mechanism provided by the application is a new frequency-dependent Q estimation method, i.e., a double-parameter spectral ratio method, based on the WIGED_DKT model. Compared with conventional estimation methods, the method establishes the connection between the mesoscopic rock physical model, logging data and seismic data, can give more accurate and reliable seismic data Q value results, and better explain the reservoir physical properties.

[0008] To achieve the above object, the technical scheme of the application is as follows:

[0009] The method for estimating seismic frequency-dependent Q value based on rock physical mechanism comprises the following steps:

[0010] An effective mesoscopic scale rock physical model is selected to determine the Q(f) curve and velocity dispersion relationship in the model;

[0011] The selected mesoscopic scale rock physical model is improved by using a pre-established viscoelastic model, and the attenuation characteristics of the mesoscopic rock physical model in describing the reservoir are analyzed;

[0012] The double-parameter spectral ratio method of the SLS model is used to calculate the frequency-dependent Q value of the improved mesoscopic scale rock physical model.

[0013] Preferably, the step of selecting the effective mesoscopic scale rock physical model comprises:

[0014] Logging data and rock sample experimental data are used to select an effective mesoscopic scale rock physical model, and the selected WIGED multi-scale rock physical model is evaluated for effectiveness in relation to a shale reservoir;

[0015] The mesoscopic scale rock physical model is composed of a WIGED multi-scale rock physical model of fluid and a DKT model of dry rock.

[0016] Preferably, the step of determining the Q(f) curve and velocity dispersion relationship in the model comprises:

[0017] The quantitative relationship between the seismic attenuation, velocity and fluid properties of the mesoscopic scale rock physical model is obtained, and reservoir parameters are defined according to the effective mesoscopic scale rock physical model, and the corresponding Q(f) curve and velocity dispersion are calculated.

[0018] The reservoir parameters include porosity, fluid type and saturation.

[0019] Preferably, the step of improving the selected mesoscopic scale rock physical model by using a pre-established viscoelastic model comprises:

[0020] The scale of the Q(f) curve in the mesoscopic rock physics model is coarsened, and an explicit expression of Q is obtained by minimizing the error between the viscoelastic model and the mesoscopic rock physics model;

[0021] The frequency-dependent Q(f) curve is considered, and the optimal viscoelastic parameter of the frequency-dependent Q(f) curve is calculated;

[0022] The attenuation characteristics of the mesoscopic rock physics model reservoir are analyzed.

[0023] Further, the Q(f) curve expression in the mesoscopic rock physics model is coarsened using the viscoelastic model, and the following explicit expression of Q is determined:

[0024]

[0025] Further, the frequency-dependent Q(f) curve is:

[0026]

[0027] Where f is the frequency, G is the frequency-independent attenuation factor due to spherical diffusion, reflection and transmission loss, and Δt is the difference in travel time.

[0028] Further, the optimal viscoelastic parameter of the Q(f) curve can be obtained by minimizing the following objective function:

[0029]

[0030] Further, the analysis of the attenuation characteristics of the mesoscopic rock physics model reservoir includes:

[0031] The volume of the bubble and water is obtained according to the volume change rate of the bubble, and the bulk modulus of the corresponding fluid is determined;

[0032] The attenuation coefficient is calculated according to the bulk modulus of the fluid;

[0033] The GSLS model is used to approximate the attenuation effect based on the WIGED theory, and the frequency-dependent Q value curve simulated by the GSLS model from different relaxation mechanisms and the attenuation curve obtained from the WIGED theory are obtained.

[0034] Further, the volume change rate of the bubble is determined by the following formula:

[0035]

[0036] In the formula, P is the pressure in the bubble (Pa), R is the gas constant (8.31446 m 3 Pa K -1 mol -1 ), and T is the temperature (K).

[0037] According to the volume strain of the bubble and water, that is, ε=dV / V, the volume modulus of the corresponding fluid can be calculated, that is, K=F(dP) / F(ε), and the attenuation coefficient is calculated according to the volume modulus of the fluid by the following formula:

[0038] Q -1 =Re(K) / Im(K)

[0039] The three parameters L, τ and τ of the SLS model are obtained by solving the following least square problem: σ and the approximate attenuation curve of τ:

[0040]

[0041] Wherein, Q WIGED (w) is the numerical solution of Q value based on WIGED theory, w is frequency, τ σ is relaxation time, and τ can be expressed as:

[0042]

[0043] Wherein, τ ε is strain relaxation time.

[0044] Further, the two parameters of the SLS model are used to model the frequency-dependent Q, according to the expression of the Q(f) curve of the SLS model, the two-parameter spectral ratio method is established, and the two parameters τ σ and τ of the SLS model are calculated:

[0045] The frequency-dependent Q value is determined according to the two parameters τ σ and τ of the SLS model;

[0046] Wherein, the two parameters τ σ and τ of the SLS model are determined by the following formula:

[0047]

[0048] Compared with the prior art, the beneficial effects of the present application are reflected in:

[0049] The present application emphasizes the importance of estimating Q value based on the knowledge of specific reservoir properties and corresponding rock physical mechanism. It is found for the first time that the traditional wave fluid flow mechanism cannot describe the attenuation characteristics of the fluid saturated with micro-scale bubbles in the seismic frequency band. On this basis, the effective model is selected by combining the WIGED multi-scale rock physical model of the fluid and the DKT model of the dry rock. Considering that the theoretical parameters of the WIGED model are not available in practice, the viscoelastic model (SLS model) with fewer parameters is used to coarsen the Q value curve from the WIGED_DKT model.

[0050] The application provides a double-parameter spectral ratio method based on a WIGED_DKT model, which is used for frequency-variable Q estimation. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the drawings needed in the specific embodiments or the prior art description will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, each element or part is not necessarily drawn according to the actual proportion.

[0052] Figure 1 A flow chart of a seismic frequency-variable Q value estimation method based on a rock physical mechanism is provided for the present application.

[0053] Figure 2 A rock physical model modeling method flow chart is provided for the present application.

[0054] Figure 3 A rock physical model optimization and evaluation standard schematic diagram is provided for the present application.

[0055] Figure 4 A velocity dispersion (a) and attenuation (b) relationship schematic diagram of a WIGED model and a White model is provided for the present application.

[0056] Figure 5 A WIGED-DKT model simulation oil and water velocity dispersion (a) and attenuation (b) schematic diagram is provided for the present application.

[0057] Figure 6 A WIGED-DKT model simulation velocity dispersion (a) and attenuation (b) schematic diagram under different gas saturation is provided for the present application.

[0058] Figure 7 A rock physical template schematic diagram of different frequencies of gas saturation and porosity is provided for the present application.

[0059] Figure 8 A rock physical quantity plate schematic diagram based on Tau and ts cross-plot is provided for the present application.

[0060] Figure 9 A model 1 schematic diagram for calculating constant Q and frequency-variable Q values by using a traditional LSR method and a double-parameter LSR method is provided for the present application.

[0061] Figure 10 A model 2 schematic diagram for calculating constant Q and frequency-variable Q values by using a traditional LSR method and a double-parameter LSR method is provided for the present application.

[0062] Figure 11 Figure 3 is a schematic diagram of a model for calculating constant Q and frequency-dependent Q values using a traditional LSR method and a two-parameter LSR method according to the present application. DETAILED DESCRIPTION

[0063] The embodiments of the technical solutions of the present application will be described in detail below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and therefore only serve as examples, and cannot limit the protection scope of the present application.

[0064] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present application should be understood as the usual meanings understood by the skilled person in the field of the present application.

[0065] The embodiments of the present application provide a seismic frequency-dependent Q value estimation method based on rock physical mechanism, as shown in the following formula: Figure 1 The method comprises the following steps:

[0066] S1: selecting an effective mesoscale rock physical model to determine the Q(f) curve and velocity dispersion relationship in the model;

[0067] S2: improving the selected mesoscale rock physical model using a pre-established viscoelastic model to analyze the attenuation characteristics of the mesoscale rock physical model in describing the reservoir;

[0068] S3: calculating the frequency-dependent Q value of the improved mesoscale rock physical model using a two-parameter spectral ratio method of the SLS model.

[0069] In step S1, the selecting an effective mesoscale rock physical model comprises:

[0070] Using logging data and rock sample experimental data, an effective mesoscale rock physical model is selected, and the selected WIGED multi-scale rock physical model is evaluated for effectiveness for shale reservoirs;

[0071] The mesoscale rock physical model is composed of a WIGED multi-scale rock physical model of fluid and a DKT model of dry rock.

[0072] In step S1, determining the Q(f) curve and velocity dispersion relationship in the model comprises:

[0073] Obtaining the quantitative relationship between seismic attenuation, velocity and fluid properties of the mesoscale rock physical model, and defining reservoir parameters according to the effective mesoscale rock physical model to calculate the corresponding Q(f) curve and velocity dispersion;

[0074] The reservoir parameters include porosity, fluid type and saturation.

[0075] In step S2, improving the selected meso-scale rock physics model by using the pre-established viscoelastic model comprises:

[0076] coarse-graining the scale of the Q(f) curve in the meso-scale rock physics model, obtaining an explicit expression of Q by minimizing the error between the viscoelastic model and the meso-scale rock physics model;

[0077] considering the frequency-dependent Q(f) curve, calculating the optimal viscoelastic parameters of the frequency-dependent Q(f) curve;

[0078] analyzing the attenuation characteristics of the meso-scale rock physics model reservoir.

[0079] Specifically, the coarse-graining of the Q(f) curve expression in the meso-scale rock physics model by using the viscoelastic model determines the following explicit expression of Q:

[0080]

[0081] The consideration of the frequency-dependent Q(f) curve is as follows:

[0082]

[0083] where f is the frequency, G is the frequency-independent attenuation factor due to spherical diffusion, reflection and transmission loss, and Δt is the difference in travel time.

[0084] The optimal viscoelastic parameters of the Q(f) curve can be obtained by minimizing the following objective function:

[0085]

[0086] The analysis of the attenuation characteristics of the meso-scale rock physics model reservoir comprises:

[0087] According to the volume change rate of the bubble, the volumes of the bubble and water are obtained, and the bulk modulus of the corresponding fluid is determined;

[0088] According to the bulk modulus of the fluid, the attenuation coefficient is calculated;

[0089] The GSLS model is used to approximate the attenuation effect based on the WIGED theory, and the frequency-dependent Q value curve simulated by the GSLS model with different relaxation mechanisms and the attenuation curve obtained by the WIGED theory are obtained.

[0090] where the volume change rate of the bubble is determined by the following formula:

[0091]

[0092] In the formula, P is the internal pressure of the bubble (Pa), R is the gas constant (8.31446 m3 Pa K -1 mol -1 ), T is temperature (K);

[0093] According to the volume strain of bubble and water ε = dV / V, the volume modulus of the corresponding fluid K = F(dP) / F(ε) can be calculated, and the attenuation coefficient is calculated according to the volume modulus of the fluid by the following formula:

[0094] Q -1 = Re(K) / Im(K)

[0095] The three parameters L, τ σ and τ of the SLS model are obtained by solving the following least squares problem:

[0096]

[0097] Where Q WIGED (w) is the numerical solution of Q value based on WIGED theory, w is frequency, τ σ is relaxation time, and τ can be expressed as:

[0098]

[0099] Where τ ε is strain relaxation time.

[0100] The two parameters of the SLS model are used to model the frequency-dependent Q, and the two-parameter spectral ratio method is established according to the expression of Q(f) curve of the SLS model, to calculate the two parameters τ σ and τ of the SLS model:

[0101] The frequency-dependent Q value is determined according to the two parameters τ σ and τ of the SLS model;

[0102] Where the two parameters τ σ and τ of the SLS model are determined by the following formula:

[0103]

[0104] Example 1:

[0105] The importance of estimating Q value based on the knowledge of specific reservoir properties and corresponding petrophysical mechanisms is emphasized in this example. Taking shale reservoirs as an example, it is found for the first time that the traditional wave-induced fluid flow mechanism cannot describe the attenuation characteristics of micro-scale bubble-saturated fluid in the seismic frequency band. On this basis, combined with the WIGED (Wave induced gas exsolution and dissolution) multi-scale petrophysical model of fluid and the DKT model of dry rock. Considering that the theoretical parameters of the WIGED model are not available in practice, a viscoelastic model (SLS model) with fewer parameters is used to promote the Q curve from the WIGED_DKT model. A two-parameter spectral ratio method based on the WIGED_DKT model is proposed for frequency-dependent Q estimation. The proposed idea and method bridge the gap between petrophysical models and seismic data Q value estimation, and can obtain more accurate and reliable Q value and velocity dispersion, so as to better detect oil and gas in the reservoir.

[0106] In order to better illustrate the present application, the following example 1 is described in detail by way of example to realize the frequency-dependent Q value estimation based on the mesoscale petrophysical model, and the specific implementation steps are as follows:

[0107] Only the change of amplitude spectrum is considered, and the phase change and dispersion are ignored. The amplitude of the seismic wavelet propagating in the viscoelastic medium can be expressed as:

[0108]

[0109] Where A is the frequency spectrum after propagating s distance, G is the frequency-independent attenuation term, and S is the initial wavelet spectrum.

[0110] In equation 1, according to the microscale petrophysical model, the Q value should change with frequency. However, these models do not give an explicit expression of Q(f). Scientists have used different expressions, such as power law model, etc. for application, and discussed the influence caused by selecting different models. However, there is no further suggestion on the selection of Q(f) curve expression, and the existing expressions lack physical meaning. Therefore, the relationship between Q value and frequency is not clear, which is not suitable for the interpretation of seismic attenuation.

[0111] In this example, we combine Q value estimation and petrophysical model to introduce the idea and process of developing an effective frequency-dependent Q value estimation method based on mesoscale petrophysical modeling and analysis. The following are the steps of Q value estimation:

[0112] 1. Select an effective mesoscale petrophysical model

[0113] Petrophysical model gives the quantitative relationship between seismic attenuation, velocity and fluid properties. The modeling process of petrophysical model is as follows Figure 2The fluid-mixture rock physics model is selected by understanding the geological background, and the P-wave and S-wave velocities can be predicted. The selected model is evaluated by using the well logging data and rock sample experimental data. Figure 3 The rock physics model selection and evaluation criteria are shown; wherein, ① fluid-mixture model selection: wave-induced gas exsolution model (WIGED), wave-induced fluid flow model (WIFF).

[0114] ② rock physics skeleton model selection: anisotropic soft-porosity model, anisotropic SCA model, anisotropic SCA model, anisotropic DEM model, anisotropic Eshelby-Cheng model, anisotropic Hudson model, isotropic SCA model, isotropic DEM model. The model selection and evaluation method establishes a double-standard evaluation method, that is, the P-wave, S-wave prediction results and anisotropic parameter prediction results are combined to jointly judge the pros and cons of the model, avoiding the errors and misunderstandings caused by measuring the model by the fitting degree of the S-wave prediction results alone.

[0115] 2. Q(f) curve and velocity dispersion relationship analysis

[0116] The rock physics model gives the quantitative relationship between seismic attenuation, velocity and fluid properties. Once the effective rock physics model is determined, the corresponding Q(f) curve and velocity dispersion can be calculated by giving the reservoir parameters such as specific porosity, fluid type and saturation.

[0117] 3. Scale coarsening of mesoscopic rock physics model

[0118] The Q(f) curve expression in the mesoscopic scale rock physics model is coarsened by using the viscoelastic model. By minimizing the error between them, the explicit expression of Q can be derived with fewer parameters, and it can be easily calculated or inverted from seismic data.

[0119]

[0120] 4. A new effective frequency-dependent Q estimation method is proposed

[0121] Once the viscoelastic model is selected for the Q(f) curve, the explicit expression of the Q(f) curve can be derived. On this basis, a new frequency-dependent Q estimation method is proposed. The traditional log spectral ratio (LSR) (Tonn, 1991) considers that the seismic wave propagates through the Futterman (1962) constant Q model characteristic of the attenuation medium. If the frequency-dependent Q(f) curve is considered as:

[0122]

[0123] where f is the frequency, G is the frequency independent attenuation factor due to spherical divergence, reflection transmission losses and other incoherent attenuation, and Δt is the difference in travel time.

[0124] The optimum viscoelastic parameters of the Q(f) curve can be obtained by minimizing the following objective function:

[0125]

[0126] The frequency dependent Q value can then be described by the above parameters.

[0127] 1. Effective mesoscopic rock physics model selection and attenuation property analysis

[0128] Take the micro-pore shale reservoir as an example, fill the micron-scale pore with bubble fluid. The fluid in the bubble is single-phase fluid, and the fluid in the liquid is single-phase fluid or equivalent single-phase fluid of two-phase fluid (calculated by Wood equation).

[0129] The volume change rate of the bubble is:

[0130]

[0131] where P is the pressure in the bubble (Pa), R is the gas constant (8.31446 m 3 Pa K -1 mol -1 ), and T is the temperature (K).

[0132] According to the volume strain of the bubble and water ε = dV / V, the volume modulus of the corresponding fluid K = F(dP) / F(ε) can be calculated, and thus the attenuation coefficient Q- 1 = Re(K) / Im(K). As Figure 4 , the velocity dispersion (a) and attenuation (b) relations of the WIGED model and the White model are applied, and the bubble radius is 3 microns.

[0133] The following numerical example of shale reservoir compares the attenuation and velocity dispersion predicted by our WIGED model and White model, and also shows the Gassmann Hill and Gassmann Wood boundaries. The parameters used by us are shown in Table 1. The carbon dioxide content in the saturated fluid is 15%, and the porosity of the shale is 0.2.

[0134] Table 1 Physical parameters of attenuation and velocity used in the model

[0135]

[0136]

[0137] Existing mesoscale models, such as the White model, assume that the inclusion size is on the order of millimeters. Figure 4 (a) It can be seen that the attenuation of fluid flow can be neglected at the same seismic frequency, while the attenuation of gas out-diffusion and dissolution is the main seismic attenuation mechanism. In the case of considering the rock's multiple porosity and high porosity, the WIGED model can be combined with the DKT model to predict the attenuation of saturated rock. In the following example, the rock matrix contains 30% sand and 55% clay, and the porosity is 15%. The pore size ratio is 0.1. The gas saturation is 1%. The saturated rock containing methane and oil has different attenuation patterns and velocity dispersion than the saturated rock containing carbon dioxide and water. The attenuation peak of the oil and methane saturated rock appears in the seismic frequency band (10 Hz-100 Hz), while the attenuation peak of the carbon dioxide and water saturated rock is relatively low (below 10 Hz), as shown in Figure 4 (b) It can be seen that the attenuation of fluid flow can be neglected at the same seismic frequency, while the attenuation of gas out-diffusion and dissolution is the main seismic attenuation mechanism. In the case of considering the rock's multiple porosity and high porosity, the WIGED model can be combined with the DKT model to predict the attenuation of saturated rock. In the following example, the rock matrix contains 30% sand and 55% clay, and the porosity is 15%. The pore size ratio is 0.1. The gas saturation is 1%. The saturated rock containing methane and oil has different attenuation patterns and velocity dispersion than the saturated rock containing carbon dioxide and water. The attenuation peak of the oil and methane saturated rock appears in the seismic frequency band (10 Hz-100 Hz), while the attenuation peak of the carbon dioxide and water saturated rock is relatively low (below 10 Hz), as shown in Figure 5 .

[0138] Then the WIGED-DKT model is used to predict the attenuation and dispersion caused by different gas saturation, as shown in Figure 5 With the increase of gas content in the fluid, the attenuation tends to be at a relatively high frequency, and when the saturation is greater than 0.5%, the attenuation speed decreases significantly, as shown in Figure 6 .

[0139] When considering the TOC (total organic carbon) content in shale, the next example simulates the attenuation and velocity dispersion of different total organic carbon content. The change of total organic carbon content does not change the attenuation peak, but only increases the attenuation with the increase of total organic carbon content, so that the attenuation speed decreases and the dispersion becomes obvious.

[0140] The rock physics template of gas saturation and porosity at different frequencies is shown in Figure 7 Specifically, the WIGED-DKT model constructs the rock physics template at 40 Hz (a) and 12500 Hz (b), with porosity between 0.15 and 0.2 and gas saturation between 0.1 and 1.

[0141] Figure 7 The frequency of (a) is 40 Hz, Figure 7 The frequency of (b) is 12500 Hz, corresponding to seismic frequency and logging frequency. The scale board shows the V p / V s and P-wave impedance. It can be seen from the two templates that there is a significant difference in the distribution of the theoretical values due to the existence of velocity dispersion. The templates give similar P-wave impedance ranges, but the V p / V s values are lower at seismic frequencies.

[0142] 2. Scale-up of meso-scale rock physics model with explicit Q(f) expression

[0143] Viscoelastic models can give the expression of Q with frequency, but have no explicit physical meaning. Viscoelastic models match the meso-scale rock physics model and can be used for frequency-dependent Q estimation.

[0144] Take the Q curve in the WIGED-DKT model as an example, and apply the GSLS model for improvement. In order to approximate the attenuation effect based on the WIGED theory with the GSLS model, three parameters L, τ σ and τ can be solved by solving the following least squares problem:

[0145]

[0146] where Q WIGED (w) is the numerical solution of Q based on the WIGED theory, w is the frequency, τ σ is the relaxation time, and τ can be expressed as

[0147]

[0148] where τ ε is the strain relaxation time.

[0149] The approximate attenuation curves represented by the GSLS model and those obtained from WIGED theory are compared and analyzed. The frequency-varying Q-value curves simulated by the GSLS model with different relaxation mechanism numbers and the dispersion Q-value curves obtained by WIGED theory are compared and analyzed. Assuming the relaxation mechanism numbers in the GSLS model are 1, 2, and 3 (L = 1, 2, 3), three approximate attenuation curves are obtained, which are very close to the results of WIGED theory. The attenuation curve with L = 2 has the smallest error, 2.9e-3. The errors for L = 1 and 3 are 6.6e-3 and 3.4e-3, respectively. However, when the relaxation mechanism number increases to 4 (L = 4), the error is large and deviates significantly from the WIGED theoretical value, with an error of 8.8e-2. Therefore, among the results that meet the error requirements, choosing a relaxation mechanism number of 1 (L = 1) yields a more reasonable approximation of the attenuation curve and saves computation time.

[0150] Once the Q-curve model is established, it is possible to construct a t-based model. au and t s A cross-plot of a rock physics scale. The variables in the scale are gas saturation and porosity. Based on the scale, the estimated physical meanings of Tau and ts can be further interpreted. In the scale, gas saturation is between 0.03 and 0.12, and porosity is between 0.08 and 0.16. Theoretical curves for two cases were calculated (oil and methane-saturated rocks versus carbon dioxide and water-saturated rocks). By comparing the Q-1 curves for the two cases, it can be seen that the two Q-1 regions basically overlap within the corresponding gas saturation and porosity ranges. The t values ​​for the two cases... au and t s The scope can be easily distinguished, such as Figure 8 As shown on the measuring plate. Estimated t au and t s The value is more sensitive to the liquid in the pores, thus acquiring physical significance. t au The value increases with increasing porosity, t s The value decreases as the gas saturation increases. For different fluid properties, t... s The range of values ​​varies significantly, which is beneficial for reservoir interpretation.

[0151] 3. Establishment of a novel two-parameter spectral ratio method for frequency-correlated Q estimation

[0152] Based on the Q(f) expression of the SLS model in the above formula, the two-parameter spectral ratio method can be established:

[0153]

[0154] Among them, the two parameters τ are calculated σ And τ; then these two parameters can be used to model the frequency-dependent Q.

[0155] A four-layer model was used for testing, considering both constant Q and frequency-varying Q to verify the feasibility of the proposed two-parameter LSR method. A Ricker wavelet with a peak frequency of 60 Hz was selected as the source. The shot gather was simulated in the frequency domain using convolution according to Equation 1. Futterman's (1962) frequency-independent Q-value model also considered velocity dispersion. Three models were considered. In the first model, the attenuation (1 / Q) of the first, third, and fourth layers was constant, while the second layer contained a two-phase fluid (water + CO2 bubbles), causing the attenuation to vary with frequency. The second layer had a gas saturation of 0.12 and a porosity of 0.08, with corresponding t... au and t s The values ​​are 0.1936 and 0.0075, respectively. Constant Q and frequency-varying Q values ​​were calculated using the traditional LSR method and the two-parameter LSR method, and the results are as follows: Figure 11 As shown. Q in the first layer -1 The estimated values ​​agree well with the actual values, although the results for the third and fourth layers contain minor errors. However, in the second layer, the conventional LSR cannot provide the frequency-dependent Q. -1 The curve is not accurately represented, and the estimation results have significant errors. The two-parameter spectral ratio method can more accurately estimate the frequency-varying Q value, corresponding to t. au and t s The values ​​are 0.1939 and 0.0075, respectively. Based on the measurement plate, the water content, gas saturation, and porosity of the second layer are as follows: Figure 9 As shown (approximately saturation 0.012, porosity 0.08).

[0156] Keeping the Q values ​​in other layers constant, changing the fluid in the second layer to oil + CH4 caused a frequency-varying Q value in the low-frequency range, with the attenuation peak occurring at a higher frequency, approximately 60Hz. In the second layer, the gas saturation is 0.1, and the porosity is 0.1, corresponding to t... au and t s The values ​​are 0.2628 and 0.0025, respectively. The constant Q value was estimated using the traditional spectral ratio method, and the frequency-varying Q value was estimated using the two-parameter spectral ratio method, respectively. From the Q value estimation results in the figure, it can be seen that the traditional spectral ratio method can accurately estimate the Q value in the first layer. The Q value estimation results in the third and fourth layers have some errors but are acceptable, which is due to the strong frequency-varying attenuation in the second layer. However, for the strong frequency-varying attenuation in the second layer caused by the presence of fluid, the constant Q estimation method cannot provide a frequency-varying Q value curve. The two-parameter spectral ratio method can accurately estimate the frequency-varying Q value, corresponding to t... au and t s The values ​​are 0.2628 and 0.0025, respectively. According to the measurement, the second layer contains water, and the gas saturation and porosity are as follows: Figure 10The saturation and porosity are shown in Table 1 (saturation 0.1, porosity 0.1).

[0157] In Model Three, the Q value of other layers is kept unchanged, and the fluid in the second layer is changed to oil + CH4, which causes the frequency-dependent Q value in the low frequency range, and the fluid in the third layer is water + CO2. The gas saturation and porosity in the second and third layers are consistent with those in Models One and Two. The conventional spectral ratio method is used to estimate the constant Q value, and the double-parameter spectral ratio method is used to estimate the frequency-dependent Q value. From the Q value estimation results in the figure, it can be seen that the conventional spectral ratio method can accurately estimate the Q value in the first layer, and the Q value estimation result in the fourth layer has some error but can be accepted, which is caused by the strong frequency-dependent attenuation in the second layer. However, the constant Q estimation method cannot give the frequency-dependent Q value curve due to the strong frequency-dependent attenuation caused by the fluid in the second and third layers. The double-parameter spectral ratio method can accurately estimate the frequency-dependent Q value result of the second layer, which corresponds to t au and t s values of 0.2652 and 0.0025, respectively, and the third layer corresponds to t au and t s values of 0.1934 and 0.0075, respectively. According to the table, it can be known that the second layer contains oil, the third layer contains water, and the gas saturation and porosity are shown in Table 1 (oil: saturation 0.1, porosity por 0.1, water: saturation 0.12, porosity 0.08). Figure 11

[0158] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the description of the present application.​

Claims

1. A method for estimating frequency-dependent Q values from seismic data based on rock physics mechanisms, characterized in that, The method comprises: selecting an effective mesoscale rock physics model, determining the Q(f) curve and the velocity dispersion relation in the model; improving the selected mesoscale rock physics model by using a pre-established viscoelastic model, and analyzing the attenuation characteristics of the mesoscale rock physics model in describing the reservoir; calculating the frequency-dependent Q value of the improved mesoscale rock physics model by using the double-parameter spectral ratio method of the SLS model; the improvement of the selected mesoscale rock physics model by using the pre-established viscoelastic model comprises: coarsening the scale of the Q(f) curve in the mesoscale rock physics model, and obtaining an explicit expression of Q by minimizing the error between the viscoelastic model and the mesoscale rock physics model; considering the frequency-dependent Q(f) curve, calculating the optimal viscoelastic parameters of the frequency-dependent Q(f) curve; analyzing the attenuation characteristics of the mesoscale rock physics model in describing the reservoir; the analysis of the attenuation characteristics of the mesoscale rock physics model in describing the reservoir comprises: obtaining the volumes of bubbles and water according to the volume change rate of the bubbles, and determining the bulk modulus of the corresponding fluid; calculating the attenuation coefficient according to the bulk modulus of the fluid; approximating the attenuation effect based on the WIGED theory by using the GSLS model, and obtaining the frequency-dependent Q value curve simulated by different relaxation mechanism numbers in the GSLS model and the attenuation curve obtained by the WIGED theory.

2. The method of claim 1, wherein, the selection of the effective mesoscale rock physics model comprises: selecting an effective mesoscale rock physics model by using logging data and rock sample experimental data, and evaluating the effectiveness of the selected WIGED multi-scale rock physics model for shale reservoirs; wherein the mesoscale rock physics model is composed of a WIGED multi-scale rock physics model of fluid and a DKT model of dry rock.

3. The method of claim 1, wherein, the determination of the Q(f) curve and the velocity dispersion relation in the model comprises: obtaining the quantitative relationship among seismic attenuation, velocity and fluid properties of the mesoscale rock physics model, defining reservoir parameters according to the effective mesoscale rock physics model, and calculating the corresponding Q(f) curve and velocity dispersion; wherein the reservoir parameters comprise porosity, fluid type and saturation.

4. The method of claim 1, wherein, the coarsening of the Q(f) curve expression in the mesoscale rock physics model by using the viscoelastic model determines the following explicit expression of Q:

5. The method of claim 1, wherein, the frequency-dependent Q(f) curve is as follows: wherein f is frequency, G is a frequency-independent attenuation factor caused by spherical diffusion, reflection and transmission loss, and Δt is the difference in travel time.

6. The method of claim 1, wherein, the optimal viscoelastic parameters of the Q(f) curve can be obtained by minimizing the following objective function:

7. The method of claim 1, wherein, the volume change rate of the bubbles is determined by the following formula: where P is the pressure Pa within the bubble, R is the gas constant with a value of 8.31446 m 3 PaK -1 mol -1 and T is the temperature in K. according to the volume strain ε=dV / V of the bubbles and water, the bulk modulus K=F(dP) / F(ε) of the corresponding fluid can be calculated, and the attenuation coefficient can be calculated according to the bulk modulus of the fluid by the following formula: Q -1 = Re(K) / Im(K) The three parameters L, τ of the SLS model are obtained by solving the following least squares problem σ and the approximate decay curve of τ: where Q WIGED (w) is the numerical solution of Q based on the WIGED theory, w is the frequency, τ σ is the relaxation time, and τ can be expressed as: where τ ε is the strain relaxation time.

8. The method of claim 7, wherein, The two parameters of SLS model are used to model the frequency-dependent Q. According to the expression of Q(f) curve of SLS model, the two-parameter spectral ratio method is established to calculate the two parameters τ σ and τ: Two parameters τ σ and τ determine the frequency-dependent Q value; where the two parameters τ σ and τ are determined by the following equations:

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