Permeability inversion method and device and storage medium

Abstract

The invention provides a permeability inversion method and device and a storage medium, and belongs to the technical field of seismic exploration. The method comprises the following steps: S1, acquiring a transmission stoneley wave and a reflection stoneley wave; s2, synthesizing the stoneley waves under different well conditions into forward waveforms; and S3, carrying out permeability inversion. According to the method, the simplified Biot-Rosenbaum pore medium model is utilized, the attenuation characteristics of the actual stratum are considered, the permeability of the stratum is obtained through the global optimization method according to the total frequency deviation and time delay generated by stoneley waves in the permeability attenuation stratum relative to the impermeable completely elastic stratum, and the method has the advantages of being efficient, accurate and precise.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic exploration, and in particular relates to a permeability inversion method, device and storage medium. Background Art

[0002] Permeability is an important parameter that describes the ability of fluids (including groundwater, oil, natural gas, etc.) in underground media to flow in rock pores. In the field of oil and gas exploration, the measurement and estimation of permeability is a very important link. Traditional permeability measurement methods mainly include ground observation, well observation, seismic exploration, etc. Using seismic data to estimate permeability is an economical and feasible method.

[0003] Stoneley wave is a kind of fluid-guided wave propagating between the fluid in the well and the wellbore formation. It has the characteristics of low frequency and large amplitude in the full wave train of acoustic waves. The propagation speed is slightly lower than the sound speed of the fluid in the well, and the propagation direction is parallel to the well axis. Due to the expansion and contraction of the wellbore wall, when the formation exists in the permeable fractures where the wellbore intersects, the fluid in the wellbore and the fluid in the fracture exchange energy, resulting in the attenuation of the Stoneley wave energy and reflection at the fracture. It can be seen that the better the formation permeability, the slower the Stoneley wave propagation speed and the more serious the energy attenuation. When the Stoneley wave propagates in the permeable porous formation, its propagation speed and energy attenuation will change. The waveform characteristics show that the propagation time of the direct Stoneley wave is delayed and the center frequency is shifted to a lower level. Based on this feature, the propagation characteristics and energy attenuation of the Stoneley wave can be used to estimate the permeability of the formation. However, the measured Stoneley wave is often affected by factors unrelated to permeability, such as lithology, wellbore collapse, and mud cake, which leads to deviations in the estimated permeability.

[0004] China's open document Well Logging Technology, 2002 (4) discloses a method for estimating formation permeability using Stoneley waves. The dispersion and energy attenuation of low-frequency Stoneley waves in permeable formations are closely related to the original permeability of the formation. The Stoneley wave information in the full acoustic wave train can be used to estimate the permeability of the formation. The multipole array acoustic logging (MAC) data is separated by wave fields, the Stoneley wave waveform is synthesized, and the Stoneley wave arrival delay and main frequency shift are calculated to obtain the formation permeability, which is then compared with the permeability calculated by core analysis and nuclear magnetic resonance logging. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problems existing in the prior art and to provide a permeability inversion method, device and storage medium, which effectively eliminates the influence of well diameter and lithology on Stoneley waves, simplifies the calculation process and improves the inversion accuracy.

[0006] The present invention is achieved through the following technical solutions:

[0007] A first aspect of the present invention provides a permeability inversion method, which specifically comprises the following steps:

[0008] S1, obtaining transmitted Stoneley waves and reflected Stoneley waves;

[0009] S2, synthesizing the Stoneley waves under different well conditions into forward waveforms;

[0010] S3. Permeability inversion.

[0011] A further improvement of the present invention is:

[0012] In step S1, the transmitted Stoneley wave and the reflected Stoneley wave are obtained, and the specific operations include:

[0013] Stoneley waves are extracted from the full wave train data of acoustic waves, and then the transmitted Stoneley waves and reflected Stoneley waves are obtained using the wave field separation method.

[0014] A further improvement of the present invention is:

[0015] The permeability inversion in step S3 is specifically as follows:

[0016] According to the simplified Biot-Rosenbaum porous medium model, the global variable particle swarm optimization algorithm is used to invert the objective function to obtain the permeability of the formation.

[0017] A further improvement of the present invention is:

[0018] According to the simplified Biot-Rosenbaum porous media model, in permeable formations, the wave number of Stoneley waves is approximately expressed as:

[0019]

[0020] Among them, k e is the wave number of Stoneley wave in the equivalent elastic formation wellbore, ω is the angular frequency, R and a are the wellbore radius and the instrument radius respectively, ρ pf is the borehole fluid density, κ(ω) and D are the permeability and diffusivity of the porous formation, η is the viscosity of the formation pore fluid, K 0 and K 1 denote the 0th-order and 1st-order imaginary Bessel functions respectively.

[0021] A further improvement of the present invention is:

[0022] For the measured or simulated Stoneley wave waveform, the spectrum is obtained by Fourier transform, and its center frequency and variance are calculated using the following formula:

[0023]

[0024] In the formula, W represents the power spectrum, f represents the frequency, and its relationship with the wave velocity is f=kV, where V is the wave velocity.

[0025] A further improvement of the present invention is:

[0026] For the Stoneley wave waveform, the center time is calculated using the following formula:

[0027] T c =∫t(W(t)) 2 dt / ∫(W(t)) 2 dt (3)

[0028] Get the frequency shift and time delay between the measured and simulated waveforms:

[0029]

[0030] In formula (4), the superscript syn represents the simulated waveform, and the superscript msd represents the measured waveform.

[0031] A further improvement of the present invention is:

[0032] Since the actual stratum is not completely elastic, after considering the inherent attenuation of the stratum, the wave number of the Stoneley wave is:

[0033]

[0034] Where Q is the formation attenuation factor;

[0035] The theoretical center frequency is calculated from the above attenuation formation model and the simulated waveform:

[0036]

[0037] The frequency shift and time delay between the simulated waveform and the theoretical waveform are:

[0038]

[0039] Equation (7) gives the total frequency offset and time delay of Stoneley waves in permeable attenuated formations relative to impermeable perfectly elastic formations, where d is the formation thickness and ω is the angular frequency.

[0040] A further improvement of the present invention is:

[0041] According to the frequency offset and time delay, the following inversion objective function is constructed:

[0042]

[0043] Where:

[0044] Q -1 Inelastic decay index;

[0045] Δf c msd , ΔT c msd After the measured waveform is separated by wave field, the frequency shift and time lag of the Stoneley wave direct wave are calculated by formula (4);

[0046] Δf c theo , ΔT c theo The frequency shift and time lag calculated theoretically by equations (6, 7) are used to simulate the non-permeable and non-attenuating formation in the measured environment;

[0047] σ syn , σ theo The center frequency variance between the measured and theoretical simulation is calculated by formula (2);

[0048] For the inversion objective function given by formula (8), in order to avoid the influence of local maximum value on the result, the particle swarm optimization algorithm of global variables is used to perform multivariable joint inversion to obtain the permeability of the formation.

[0049] A second aspect of the present invention provides a permeability inversion device, comprising:

[0050] an acquisition unit, for acquiring the transmitted Stoneley wave and the reflected Stoneley wave;

[0051] A synthesis unit, used to synthesize Stoneley waves under different well conditions into forward modeling waveforms;

[0052] Inversion unit, used for permeability inversion.

[0053] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores at least one computer-executable program, and when the at least one program is executed by the computer, the computer executes the steps in the permeability inversion method as described above.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The present invention discloses a permeability inversion method. According to previous theoretical research, when Stoneley waves propagate in permeable porous formations, their propagation speed and energy attenuation will change, which is manifested in the waveform characteristics that the propagation time of the direct Stoneley waves is delayed and the center frequency is shifted to a lower level. When the present invention uses Stoneley wave data to perform formation permeability inversion, the theoretical model with better application effect is currently a simplified Biot-Rosenbaum porous medium model, and the attenuation characteristics of the actual formation are considered. The total frequency offset and time delay generated by the Stoneley wave in the permeable attenuation formation relative to the non-permeable fully elastic formation is used to obtain the permeability of the formation using a global optimization method, which has the characteristics of high efficiency, accuracy and precision.

[0056] The present invention effectively eliminates the influence of well diameter and lithology on Stoneley waves, simplifies the calculation process, improves the inversion accuracy, and can provide strong support for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 The present invention provides a flow chart of a permeability inversion method;

[0058] Figure 2 This is a comparison chart of the estimated permeability and the logged permeability of Well A;

[0059] Figure 3 This is a comparison chart of the estimated permeability and the well logging permeability of Well B;

[0060] Figure 4 This is a comparison chart of the estimated permeability and the well logging permeability of Well C;

[0061] Figure 5 This is a comparison chart between the estimated permeability and the logged permeability of Well D. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0063] In general, one well logging can collect 8 groups of acoustic wave arrays at the same time. Through processing, information such as the time difference and amplitude of the formation longitudinal wave, transverse wave, and Stoneley wave can be obtained. After spectrum analysis and filtering of the collected waveform data, other waveforms such as the formation longitudinal wave and transverse wave are eliminated, and only the low-frequency Stoneley wave information is retained. At this time, the low-frequency Stoneley wave includes two parts: transmission (direct) and reflection wave, and the reflection wave includes up-going wave and down-going wave. The direct wave and the center frequency can be used for subsequent permeability inversion.

[0064] In the elastic formation model, the lithology of the formation and the wellbore have an impact on the propagation characteristics of Stoneley waves, especially the change of wellbore, but these effects are independent of the permeability of the formation. Therefore, when using Stoneley waves for permeability inversion, the effects of formation elastic properties and wellbore on Stoneley waves must be eliminated.

[0065] To this end, the present invention provides a permeability inversion method, such as Figure 1 As shown, the specific steps include:

[0066] S1, obtaining transmitted Stoneley waves and reflected Stoneley waves;

[0067] Stoneley waves are extracted from the full wave train data of the acoustic wave, and then the wave field separation method (least square method or median filtering method) is used to obtain the transmitted (or direct) Stoneley waves and reflected Stoneley waves (including upgoing waves and downgoing waves).

[0068] The transmitted (direct) Stoneley waves extracted here can be used for permeability inversion in step S3.

[0069] S2, synthesizing the Stoneley waves under different well conditions into forward waveforms;

[0070] During the propagation of waves, the elastic characteristics of the formation and the changes in the well environment will cause changes in the propagation time and amplitude of the Stoneley wave, as well as attenuation in the well fluid and formation, but these two factors are unrelated to the permeability. The transmitted (or direct) Stoneley wave after wave field separation contains the above two influencing factors. Therefore, it is necessary to remove the influence of these two factors and obtain the true attenuation and propagation speed related to the permeability, so as to carry out subsequent permeability inversion.

[0071] This process is mainly to eliminate the elastic properties of the formation and only consider the changes in well diameter and lithology (elastic properties of the formation) in the equivalent elastic formation.

[0072] S3, permeability inversion;

[0073] Permeability will affect the four-pass filter in terms of energy attenuation and slowing down the propagation speed. By comparing the waveform synthesized in step S2 with the measured Stoneley wave waveform, it can be used to estimate the permeability of the formation. The specific steps are as follows:

[0074] According to the simplified Biot-Rosenbaum porous medium model, the global variable particle swarm optimization algorithm is used to invert the relevant objective functions to obtain the permeability of the formation.

[0075] The details are as follows:

[0076] According to the simplified Biot-Rosenbaum porous media model, the wave number of Stoneley waves in permeable formations can be approximately expressed as:

[0077]

[0078] Among them, k eis the wave number of Stoneley wave in the equivalent elastic formation wellbore, ω is the angular frequency, R and a are the wellbore radius and the instrument radius respectively, ρ pf is the borehole fluid density, κ(ω) and D are the permeability and diffusivity of the porous formation, η is the viscosity of the formation pore fluid, K 0 and K 1 denote the 0th-order and 1st-order imaginary Bessel functions respectively.

[0079] After obtaining the synthetic Stoneley wave waveform under the wellbore condition of elastic formation by simulation method, the simulated transmitted Stoneley wave waveform can be obtained by wave field separation technology. At the same time, according to the measured waveform, the actual transmitted Stoneley wave can also be obtained by similar method.

[0080] Among them, the simulation method is an existing technical method, such as a simulated annealing method.

[0081] For the measured or simulated Stoneley wave waveform, the spectrum can be obtained by Fourier transform (FFT), and its center frequency and variance can be calculated using the following formula:

[0082]

[0083] In the formula, W represents the power spectrum, f represents the frequency, and its relationship with the wave velocity is f=kV, where V is the wave velocity.

[0084] For this series of Stoneley wave waveforms, the center time can be calculated using the following formula:

[0085] T c =∫t(W(t)) 2 dt / ∫(W(t)) 2 dt (3)

[0086] Based on the above, the frequency shift and time delay between the measured waveform and the simulated waveform can be obtained:

[0087]

[0088] In formula (4), the superscript syn represents the simulated waveform, and the superscript msd represents the measured waveform.

[0089] The permeability of the formation will increase the attenuation of the sound wave propagation energy and reduce the propagation speed. In the forward simulation of Stoneley waves, the elasticity of the formation is considered, and the permeability of the formation is not involved. Therefore, Δf c ,ΔT c will change. Using relevant inversion methods, such as particle swarm optimization, according to Δf c ,ΔT c The permeability of the formation can be obtained by the change in

[0090] Furthermore, since the actual stratum is not completely elastic, after considering the inherent attenuation of the stratum, the wave number of the Stoneley wave is:

[0091]

[0092] Where Q is the formation attenuation factor;

[0093] The theoretical center frequency can be calculated from the above attenuation formation model and the simulated waveform:

[0094]

[0095] The frequency shift and time delay between the simulated waveform and the theoretical waveform are:

[0096]

[0097] Equation (7) gives the total frequency offset and time delay of Stoneley waves in permeable attenuated formations relative to impermeable perfectly elastic formations, where d is the formation thickness and ω is the angular frequency.

[0098] According to the frequency offset and time delay, the following inversion objective function can be constructed:

[0099]

[0100] In formula (8):

[0101] The third term is a compensation function, and the coefficient α is very small. When the formation permeability κ varies within the allowed range, the contribution of the third term is basically zero; but if the formation permeability exceeds the allowed range, the contribution of the third term increases, thereby dragging the inversion parameters back to the allowed range.

[0102] Q -1 Inelastic decay index;

[0103] Δf c msd , ΔT c msd After the measured waveform is separated by wave field, the frequency shift and time lag of the Stoneley wave direct wave are calculated by formula (4);

[0104] Δf c theo , ΔT c theo The frequency shift and time lag calculated by equations (6, 7) are theoretically calculated for non-permeable and non-attenuating formations in simulated measured environments (considering only formation elasticity factor and well diameter changes);

[0105] σ syn , σ theoThe center frequency variance (correlated variable) of the measured and theoretical simulations is calculated by formula (2);

[0106] For the inversion objective function given by formula (8), in order to avoid the influence of local maximum value on the result, the particle swarm algorithm of global variables can be used to perform multivariable joint inversion to obtain the permeability of the formation.

[0107] Given that different wells and different depths correspond to different permeabilities, the permeability inversion method proposed in the present invention is used to compare the permeability measured by well logging. Since the method proposed in the present invention extracts the spectrum of Stoneley waves, this operation is equivalent to a data smoothing effect, so the overall peak value of the estimated permeability is lower than the data measured by well logging.

[0108] [Example 1]

[0109] like Figure 2 As shown, the logging depth is 518-620m, and the area with permeability close to 0.01 is considered as non-reservoir section, and the permeability range of reservoir section is 0.01-1.4μm 2 The dotted line is the logging permeability, and the black line is the permeability value estimated by this method. For each reservoir section, the estimated permeability is consistent with the measured permeability, indicating that the algorithm proposed by this invention has very good adaptability. In particular, the thin reservoirs between 540-550m and 570-580m also have a good response on the estimated permeability curve, indicating that this method can eliminate the influence of formation lithology and truly reflect the change of permeability.

[0110] [Example 2]

[0111] like Figure 3 As shown, the logging depth is 518-618m, and the area with permeability close to 0.01 is considered as non-reservoir section, and the permeability range of reservoir section is 0.01-1.5μm 2 The logging depth and permeability range are close to those in Example 1. The dotted line is the logging permeability, and the black line is the permeability value estimated by this method. For each reservoir section, the estimated permeability is consistent with the measured permeability, indicating that the algorithm proposed in this invention has very good adaptability.

[0112] [Example 3]

[0113] like Figure 4 As shown in the figure, the logging depth is 2000-2100m, and the permeability is close to 0.01, which is considered as the non-reservoir section. The permeability range of the reservoir section is 0.01-0.14μm. 2 Compared with the previous two embodiments, the logging depth is deeper, and the permeability is smaller due to the burial depth. The dotted line is the logging permeability, and the black line is the permeability value estimated by this method. Figure 4As shown, the estimated permeabilities of the four reservoir segments reflected in the figure are consistent with the measured permeabilities, but the peak values ​​are more different than those of the first two embodiments, indicating that the method proposed in the present invention has a certain adaptability to the estimated permeability of low-permeability reservoirs with lower permeability.

[0114] [Example 4]

[0115] like Figure 5 As shown, the logging depth is 2300-2400m, and the permeability is close to 0.01, which is considered as the non-reservoir section. The permeability range of the reservoir section is 0.01-0.16μm. 2 The logging depth is slightly deeper than that of Example 3, and the permeability range is close to that of Example 3. The dotted line is the logging permeability, and the black line is the permeability value estimated by this method. Figure 5 As shown in the figure, the estimated permeabilities of multiple reservoir sections are consistent with the measured permeabilities, but the error of the peak estimation is larger. In addition, for the reservoir section deeper than 2360m, the method of estimating permeability is easy to identify two thin reservoirs as one reservoir in the thin reservoir section. This also shows that for deeper reservoirs, when the permeability value itself is small, the estimated value of the method proposed in the present invention is used for permeability inversion, which has a certain reference value. But in general, this method is an effective, simple and accurate method for inverting permeability.

[0116] [Example 5]

[0117] An embodiment of the present invention provides a permeability inversion device, comprising:

[0118] an acquisition unit, for acquiring the transmitted Stoneley wave and the reflected Stoneley wave;

[0119] A synthesis unit, used to synthesize Stoneley waves under different well conditions into forward modeling waveforms;

[0120] Inversion unit, used for permeability inversion.

[0121] [Example 6]

[0122] An embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores at least one computer-executable program, and when the at least one program is executed by the computer, the computer executes the steps in the permeability inversion method as described above.

[0123] The above technical solution is only one implementation mode of the present invention. For those skilled in the art, it is easy to make various types of improvements or modifications based on the principles disclosed in the present invention, and it is not limited to the technical solution described in the above specific embodiments of the present invention. Therefore, the above description is only preferred and does not have a restrictive meaning.

Claims

1. A permeability inversion method, It is characterized in that The specific steps include: S1, obtaining transmitted Stoneley waves and reflected Stoneley waves; S2, synthesizing the Stoneley waves under different well conditions into forward waveforms; S3. Permeability inversion.

2. The permeability inversion method according to claim 1, It is characterized in that In step S1, the transmitted Stoneley wave and the reflected Stoneley wave are obtained, and the specific operations include: Stoneley waves are extracted from the full wave train data of acoustic waves, and then the transmitted Stoneley waves and reflected Stoneley waves are obtained using the wave field separation method.

3. The permeability inversion method according to claim 1, It is characterized in that The permeability inversion in step S3 is specifically as follows: According to the simplified Biot-Rosenbaum porous medium model, the global variable particle swarm optimization algorithm is used to invert the objective function to obtain the permeability of the formation.

4. The permeability inversion method according to claim 3, It is characterized in that According to the simplified Biot-Rosenbaum porous media model, in permeable formations, the wave number of Stoneley waves is approximately expressed as: Among them, k e is the wave number of Stoneley wave in the equivalent elastic formation wellbore, ω is the angular frequency, R and a are the wellbore radius and the instrument radius respectively, ρ pf is the borehole fluid density, κ(ω) and D are the permeability and diffusivity of the porous formation, η is the viscosity of the formation pore fluid, K 0 and K 1 denote the 0th-order and 1st-order imaginary Bessel functions respectively.

5. The permeability inversion method according to claim 4, It is characterized in that For the measured or simulated Stoneley wave waveform, the spectrum is obtained by Fourier transform, and its center frequency and variance are calculated using the following formula: In the formula, W represents the power spectrum, f represents the frequency, and its relationship with the wave velocity is f=kV, where V is the wave velocity.

6. The permeability inversion method according to claim 5, It is characterized in that For the Stoneley wave waveform, the center time is calculated using the following formula: T c =∫t(W(t)) 2 dt / ∫(W(t)) 2 dt (3) Get the frequency shift and time delay between the measured and simulated waveforms: In formula (4), the superscript syn represents the simulated waveform, and the superscript msd represents the measured waveform.

7. The permeability inversion method according to claim 6, It is characterized in that Since the actual stratum is not completely elastic, after considering the inherent attenuation of the stratum, the wave number of the Stoneley wave is: Where Q is the formation attenuation factor; The theoretical center frequency is calculated from the above attenuation formation model and the simulated waveform: The frequency shift and time delay between the simulated waveform and the theoretical waveform are: Equation (7) gives the total frequency offset and time delay of Stoneley waves in permeable attenuated formations relative to impermeable perfectly elastic formations, where d is the formation thickness and ω is the angular frequency.

8. The permeability inversion method according to claim 7, It is characterized in that According to the frequency offset and time delay, the following inversion objective function is constructed: Where: Q -1 Inelastic decay index; Δf c msd , ΔT c msd After the measured waveform is separated by wave field, the frequency shift and time lag of the Stoneley wave direct wave are calculated by formula (4); Δf c theo , ΔT c theo The frequency shift and time lag calculated theoretically by equations (6, 7) are used to simulate the non-permeable and non-attenuating formation in the measured environment; σ syn , σ theo The center frequency variance between the measured and theoretical simulation is calculated by formula (2); For the inversion objective function given by formula (8), in order to avoid the influence of local maximum value on the result, the particle swarm optimization algorithm of global variables is used to perform multivariable joint inversion to obtain the permeability of the formation.

9. A permeability inversion device, It is characterized in that include: an acquisition unit, for acquiring the transmitted Stoneley wave and the reflected Stoneley wave; A synthesis unit, used to synthesize Stoneley waves under different well conditions into forward modeling waveforms; Inversion unit, used for permeability inversion.

10. A computer-readable storage medium, It is characterized in that The computer-readable storage medium stores at least one computer-executable program, and when the at least one program is executed by the computer, the computer executes the steps in the permeability inversion method according to any one of claims 1 to 8.

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