A method for simulating the effect of wetting on dispersion and attenuation in partially saturated sand

Abstract

The application belongs to the field of rock physics and geophysical exploration, and relates to a simulation method for wettability affecting dispersion and attenuation of partially saturated sandstone, which comprises the following steps: S1. establishing a relationship between capillary pressure and water saturation for wettability correction; S2. calculating equivalent pore throat radius and effective permeability according to the relationship between capillary pressure and water saturation; S3. calculating characteristic frequency and complex bulk modulus under different wettability conditions based on a partially saturated patchy medium model; S4. simulating and comparing the characteristics of longitudinal wave velocity and attenuation under different wettability and water saturation conditions, analyzing the modulation law of frequency-dependent acoustic response caused by wettability change, and realizing quantitative characterization of the wettability effect. The step-by-step modeling method proposed in the application, combined with the wettability correction parameter represented by the contact angle, can systematically calculate the continuous coupling process from capillary pressure to equivalent pore throat structure and equivalent permeability to acoustic response, and realize quantitative analysis of the wettability change on the dispersion and attenuation law.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of rock physics and geophysical exploration, and particularly relates to quantitative calculation and analysis of acoustic response to wettability. BACKGROUND

[0002] Fossil energy will still bear the basic energy supply for a long period of time. After long-term development, a large amount of remaining oil still remains in the reservoir, which is difficult to be efficiently produced by conventional methods. Chemical displacement can change the wettability of rock from hydrophobic to hydrophilic, reduce the interaction energy between oil phase and rock surface, and make the oil adhering to the pore wall into a flowable phase, thereby improving the recovery efficiency. The change of wettability changes the fluid distribution and connectivity of pore size, and further affects the frequency-dependent acoustic properties of reservoir rock. Based on this, the dynamic monitoring of key parameters such as velocity and attenuation by using acoustic method has become an important technical means for identifying fluid redistribution and optimizing reservoir development. In seismic interpretation and practical application, clarifying the influence of wettability change on acoustic response is the key to accurate reservoir characterization.

[0003] A large number of studies have shown that under certain wettability conditions, there is a typical nonlinear relationship between P-wave velocity and water saturation. The overall trend is that in the low saturation interval, the velocity changes little; when close to the critical saturation, the velocity increases rapidly; and in the high saturation stage, it tends to be stable. At the same time, the attenuation usually has a significant peak near the medium saturation, and its amplitude and peak position are jointly controlled by the pore geometry, patchy fluid distribution and fluid connectivity, which reflects the viscous coupling effect and pressure relaxation process under the wave-induced flow. Further studies have shown that the change of wettability will significantly modulate the connectivity and interface boundary conditions of pore fluid. Under the hydrophilic condition, the wetting phase forms a continuous film along the pore wall, which enhances the connectivity of the fluid channel, so that the velocity gradually increases with the saturation, and the attenuation peak is low and biased to a smaller saturation interval. In contrast, under the hydrophobic condition, the wetting phase is dispersedly distributed, the connectivity is weakened, and the fluid movement is limited, which leads to a sharp rise in velocity near the critical saturation, and the attenuation peak amplitude increases and shifts to the high saturation direction.

[0004] Although a large number of experimental and theoretical studies have been conducted to investigate the influence of wettability on the acoustic properties of rocks, the current results still have obvious limitations. Most experimental studies are based on fully saturated samples or a single wetting state, making it difficult to reveal the systematic influence of wettability changes on acoustic behavior under partially saturated conditions. In addition, although the method of preparing hydrophobic samples through surface coating is convenient for comparison, it will also change the equivalent mechanical properties of the dry rock skeleton and the chemical characteristics of the pore interface, thereby intertwining the wettability effect and the skeleton modification effect, which weakens the physical comparability of the results. Partially saturated rock experiments Sutiyoso, H.S.; Sahoo, S.K.; North, L.J.; Minshull, T.A.; Falcon-Suarez, I.H.; Best, A.I. (2024). Laboratory measurements of water saturation effects on the acoustic velocity and attenuation of sand packs in the 1–20 kHz frequency range [J]. Geophysical Prospecting, 72(9): 3316-3337. show that the longitudinal wave velocity and attenuation both exhibit significant frequency dependence, but limited to fixed wetting conditions, it is still insufficient to reveal the control effect of wettability changes on the frequency domain acoustic response law. On the other hand, existing theoretical modeling methods are mostly based on the assumption of full saturation or fixed pore structure parameters, Li, J. X., Rezaee, R., and Müller, T. M. (2020). Wettability effect on wave propagation in saturated porous medium. Journal of the Acoustical Society of America, 147(2), 911-920. In this study, the model introduces a slip length parameter under the assumption of full saturation to quantitatively represent the modification effect of wettability on the boundary conditions of the pore fluid, and calculates the frequency response of the longitudinal wave velocity and attenuation by combining viscous coupling and fluid inertia effects. However, this type of model is based on the single-phase fluid assumption and cannot describe the multi-phase fluid distribution in partially saturated media. Overall, there is still no theoretical model that can quantitatively couple wettability and acoustic response processes within a unified physical framework, thus significantly limiting the applicability of the model for reservoir parameter inversion and acoustic monitoring. SUMMARY

[0005] To overcome the aforementioned technical deficiencies, this application proposes a simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone. This method addresses the problem in existing technologies where it is difficult to quantitatively describe the impact of wettability changes on the acoustic response of partially saturated sandstone. Based on a partially saturated porphyritic medium model, a step-by-step modeling method is proposed to obtain the frequency-related acoustic properties of partially saturated sandstone under different wettability conditions. Specifically, under the condition of wettability characterized by contact angle, continuous modeling is carried out from capillary pressure curves to pore throat structure and acoustic response. This enables a theoretical simulation method for the effect of wettability differences on the acoustic properties of partially saturated sandstone, and further allows for a comparative analysis of the differences in dispersion and attenuation responses between hydrophilic and hydrophobic systems under different saturation conditions.

[0006] To achieve the above design objectives, the simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone assumes that the background medium of the partially saturated sandstone is a homogeneous isotropic porous medium, with the fluid in the pores consisting of an aqueous phase and a gas phase, and wettability is characterized by the contact angle. Under hydrophilic conditions, the aqueous phase forms a continuous film along the pore walls to enhance fluid connectivity; under hydrophobic conditions, the aqueous phase exists in the form of isolated patches, and local pressure diffusion is restricted, thus affecting the velocity dispersion and attenuation characteristics. The method includes the following steps:

[0007] S1. Establish the relationship between capillary pressure and water saturation with wettability correction;

[0008] S2. Calculate the equivalent pore throat radius and effective permeability based on the relationship between capillary pressure and water saturation.

[0009] S3. Calculate the characteristic frequencies and complex bulk modulus under different wettability conditions based on the partially saturated patchy medium model;

[0010] S4. Simulate and compare the longitudinal wave velocity and attenuation characteristics under different wettability and water saturation conditions, analyze the modulation law of frequency-related acoustic response to wettability changes, and realize the quantitative characterization of wettability effect.

[0011] In summary, the simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone has the following advantages:

[0012] This application enables accurate simulation and calculation of the longitudinal wave velocity and attenuation characteristics of partially saturated sandstone under different wettability conditions, supplements and improves the frequency domain acoustic theory calculation methods applicable to partially saturated media, and provides a reliable theoretical basis for identifying reservoir wettability state based on acoustic response.

[0013] This application proposes a stepwise modeling method based on a partially saturated mottled medium model, and combines it with wettability correction parameters characterized by contact angle. This method can systematically calculate the continuous coupling process from capillary pressure to equivalent pore throat structure and equivalent permeability to acoustic response, and realize quantitative analysis of the effects of wettability changes on dispersion and attenuation.

[0014] The modeling method proposed in this application can systematically and comprehensively calculate the acoustic response characteristics under different porosity, permeability and fluid properties, and can be verified by experimental data. It has a high consistency with the actual observation results, and at the same time, it has high computational efficiency and clear physical meaning of parameters.

[0015] The simulation method proposed in this application can provide a theoretical basis for reservoir wettability characterization and fluid identification, and has important application value for improving the accuracy of reservoir parameter inversion and oil and gas development monitoring. Attached Figure Description

[0016] Fig. 1 This is a schematic diagram showing capillary pressure and water saturation under different wettability conditions.

[0017] Fig. 2 A comparison of the longitudinal wave velocity and attenuation with water saturation under different wettability conditions in the model and experiment;

[0018] Among them, (a) is a schematic diagram of longitudinal wave velocity and water saturation at different contact angles (model and experiment);

[0019] (b) is a schematic diagram of the relationship between longitudinal wave attenuation and water saturation at different contact angles;

[0020] Fig. 3 A comparison of the changes in P-wave velocity and attenuation with water saturation under different frequencies and wettability conditions for the same lithology;

[0021] in,

[0022] (a) Schematic diagram of longitudinal wave velocity and water saturation at a frequency of 100 Hz;

[0023] (b) Schematic diagram of longitudinal wave attenuation and water saturation at a frequency of 100 Hz;

[0024] (c) Schematic diagram of longitudinal wave velocity and water saturation at a frequency of 10 kHz;

[0025] (d) Schematic diagram of longitudinal wave attenuation and water saturation at a frequency of 10 kHz;

[0026] (e) Schematic diagram of longitudinal wave velocity and water saturation at a frequency of 1 MHz;

[0027] (f) Schematic diagram of longitudinal wave attenuation and water saturation at a frequency of 1 MHz. Detailed Implementation

[0028] The technical solutions in the embodiments will now be clearly and completely described with reference to the accompanying drawings.

[0029] like Figs. 1 to 3 As shown, this embodiment proposes a simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone, including the following implementation steps:

[0030] Assuming the reservoir is an isotropic porous medium composed of a water-gas two-phase fluid within the pores, and wettability is quantified by contact angle, the pore throat is approximated as a cylindrical capillary with a spherical cap-shaped interface to characterize the effect of wettability on pore throat pressure distribution and fluid connectivity. The residual water saturation is set to zero to focus on the dominant role of wettability in capillary pressure distribution and fluid connectivity.

[0031] S1. Establish the relationship between capillary pressure and water saturation with wettability correction;

[0032] Based on the van Genuchten equation proposed by M. Th. van Genuchten, 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils [J]. Soil Science Society of America Journal, 44(5): 892–898 (translation), this embodiment introduces a wettability correction term into the original equation to establish a wettability-corrected capillary pressure-saturation function, which is used to characterize the effect of contact angle variation on capillary pressure. The calculation formula is as follows:

[0033] (1)

[0034] in, For effective saturation, S W Water saturation The remaining water saturation level, and The shape parameter is usually taken as Wettability correction factor The expression is:

[0035] (2)

[0036] in, and It is an empirical constant. It represents the contact angle.

[0037] Specifically, assuming the reservoir pore space is completely movable, i.e., the remaining water saturation... Background medium porosity The parameter values ​​are as follows: Shape parameter , Scaling factor Pa, wettability adjustment coefficient The contact angle range is to (by (with intervals), covering wettability variations from completely hydrophilic to completely hydrophobic; and water saturation ranges. Calculated The curve reflects the systematic effect of the contact angle on the capillary pressure distribution.

[0038] like Fig. 1 The figure shows the capillary pressure and water saturation under different contact angles. The capillary pressure varies with the contact angle. from Gradually increase to At the same saturation Under certain conditions, the capillary suction required to maintain the interface curvature decreases significantly; while at the same capillary pressure... The corresponding saturation level is significantly increased. This result indicates that the shift from hydrophilic to hydrophobic wettability weakens the adhesion of the liquid to the pore wall, causing the capillary equilibrium to change from being dominated by wetting potential to being jointly controlled by pore throat geometry and pressure.

[0039] S2. Calculate the equivalent pore throat radius and effective permeability based on the relationship between capillary pressure and water saturation.

[0040] Furthermore, the difference in capillary pressure can be transformed into a change in the geometry of the pore throat through the capillary equilibrium equation, thereby establishing a quantitative mapping relationship between wettability and the pore throat radius. This invention employs the validated Young–Laplace capillary equation form (Leverett, MC, 1941. Capillary behavior in porous solids [J]. Transactions of the AIME, 142(1): 152–169; Bear, J., 1972. Dynamics of Fluids in Porous Media [M]. New York: Elsevier) to calculate the equivalent radius of curvature in a cylindrical pore throat model.

[0041] Assuming the reservoir pore throat is approximately a cylindrical capillary and the interface is spherical, with its curvature determined by interfacial tension... Contact angle and capillary pressure Determined jointly. Based on geometric relationships. in Where is the throat radius, Let the radius of curvature of the interface be substituted. The expression for capillary pressure can be obtained as follows:

[0042] (3)

[0043] When wettability is incorporated into the capillary pressure-saturation relationship, it can be further written in the form of an equivalent pore throat radius:

[0044] (4)

[0045] in, The equivalent radius of curvature (m). interfacial tension (N·m) −1 ), The wettability correction van Genuchten relationship is calculated from Equation (1).

[0046] Equivalent pore throat radius under different wettability conditions To further characterize the effect of wettability on fluid permeability, this study introduces an empirical permeability function to describe the relationship between pore throat geometry and permeability. This relationship is derived from the empirical pore flow model proposed by Bear, J., 1972. Dynamics of Fluids in Porous Media [M]. New York: Elsevier and Kozeny, J. and Carman, PC, 1956. Flow of Gases Through Porous Media [M]. London: Butterworths, and is suitable for describing the proportional relationship between pore throat radius distribution and effective permeability.

[0047] Based on the geometric assumptions of pore flow, permeability is proportional to the square of the pore throat radius, therefore:

[0048] (5)

[0049] in, For effective penetration, For reference throat radius, This is the baseline penetration rate.

[0050] Specifically, assuming a homogeneous reservoir pore-throat structure, the reference pore-throat radius is... μm, baseline permeability m 2 ; Interface tension N·m −1 And substitute it into equation (3) It can calculate the effective permeability under different contact angle conditions. ;

[0051] S3. Calculate the characteristic frequencies and complex bulk modulus under different wettability conditions based on the partially saturated patchy medium model;

[0052] Effective permeability under different wetting conditions Then, the influence of wettability on acoustic dispersion and attenuation behavior can be further analyzed. This study is based on the partially saturated White model proposed by JE White, 1975. Computed seismic speeds and attenuation in rocks with partial gas saturation [J]. Geophysics, 40(2):224–232, and combined with the Cole–Cole broadening form proposed by Cole, KS and Cole, RH, 1941. Dispersion and absorption in dielectrics [J]. Journal of Chemical Physics, 9(4): 341–351, to establish a calculation framework for frequency-dependent complex bulk modulus under wettability correction.

[0053] According to the White model, fluid pressure relaxation within small-scale pore throats is controlled by viscous diffusion, and its characteristic angular frequency is... Determined by both permeability and pore parameters, it can be expressed as:

[0054] (6)

[0055] in, The viscosity is the fluid viscosity (Pa·s). Porosity (dimensionless) The bulk modulus of the fluid is Pa. The characteristic diffusion length (m) can be taken to be on the order of the pore throat characteristic size (approximately 10). −5 m).

[0056] To characterize the frequency broadening effect under partially saturated conditions, a complex bulk modulus of the Cole–Cole form is introduced. :

[0057] (7)

[0058] in, It represents the high-frequency limiting bulk modulus (Pa). The difference in volumetric modulus relaxation amplitude (Pa). The broadening index (0-1) characterizes the spectral width. Wettability is determined by... and Coupling, affecting and The value of is used to control the position and spectral width of the relaxation peak.

[0059] Complex bulk modulus It can be further used to calculate the longitudinal wave complex modulus, phase velocity, and attenuation coefficient:

[0060] (8)

[0061] (9)

[0062] (10)

[0063] in, This is the shear modulus (Pa). Total density of rock (kg·m³) −3 ).

[0064] Specifically, assuming the reservoir pore-throat structure is uniform and the porosity is... shear modulus Pa, fluid bulk modulus Pa, density of the rock skeleton kg / m 3 Fluid viscosity Pa·s, diffusion length m. Interfacial tension N·m −1 And the results calculated by combining equations (3) and (4) and The characteristic frequencies under different contact angles and water saturation conditions can be obtained. With complex bulk modulus distributed.

[0065] S4. Simulate and compare the longitudinal wave velocity and attenuation characteristics under different wettability and water saturation conditions, analyze the modulation law of frequency-related acoustic response to wettability changes, and realize the quantitative characterization of wettability effect.

[0066] Based on the calculation chain established in steps 1–3, the equivalent pore throat radius and effective permeability are first calculated using Pc(Sw,θ) corrected for wettability according to equations (1)–(3); then the characteristic angular frequency and broadening parameter are determined according to equations (5)–(7); finally, the frequency-related longitudinal wave velocity and attenuation are obtained according to equations (8)–(10). Referring to the glass bead experimental data of Chen, Y., Fu, L.-Y., Müller, TM, Han, T., and Li, JX (2025). Laboratory insights on acoustics of granular porous media with wettability changes. Geophysics, 90(6), MR429–MR440, the porosity-permeability and fluid property range consistent with that experiment is selected: porosity approximately 0.368, dry rock bulk modulus approximately 0.95 - 1.23 GPa, shear modulus approximately 0.31-0.38 GPa, and baseline permeability approximately 3.4 × 10⁻⁶. −11 m 2 The pore-throat scale is on the order of 3 × 10⁻⁶. −5 m; fluid bulk modulus K w =2.2 GPa, viscosity η = 1.0 × 10 −3 Pa·s, interfacial tension σ=0.072N·m −1 The confining pressure is approximately 0.75 MPa. van Genuchten used common ranges for the shape parameters n and m (e.g., n≈2 - 3, m=1−1 / n), and selected the scale terms α0 and β within a reasonable physical range (e.g., α0~10). −5 -10 −3 Pa −1 ,β~0.5 − 2 ); Residual moisture content setting S wr =0. The wettability angles were consistent with the experiments (θ = 25.2°, 75.8°).

[0067] like Fig. 2As shown, the P-wave velocity and attenuation under different wettability conditions are compared with the experimental results as a function of water saturation. The left figure (a) shows the relationship between P-wave velocity and water saturation under different contact angles (θ=25.2°, 75.8°). The solid line represents the model, and the dots and triangles represent the velocity data from Yangpu Chen, Li-Yun Fu, Tobias M. Müller, TongchengHan, Jimmy Xuekai Li, 2025. Laboratory insights on acoustics of granularporous media with wettability changes [J]. Geophysics. The overall trend of velocity with saturation is consistent with the experiment, verifying the mechanism by which wettability modulates velocity dispersion through permeability and characteristic frequencies. The right figure (b) shows the relationship between P-wave attenuation and water saturation under the same contact angle. The attenuation is broadened by the White model using the Cole–Cole exponent, exhibiting a single-peak shape, with the peak value being higher under hydrophobic conditions.

[0068] Further based on the physical properties of Berea sandstone published in Wang, 2000, "Rock physical properties of Berea sandstone," porosity of approximately 0.20, dry bulk modulus and shear modulus typical of sandstone, and benchmark permeability and pore throat scale were taken as commonly used parameters within a reasonable range; other fluid and interface parameters were set using glass beads. The contact angles for hydrophilic and hydrophobic surfaces were taken as θ=30° and θ=120°, respectively. Comparisons were performed in three representative frequency bands: seismic band (100 Hz), well logging band (10 kHz), and laboratory ultrasound (1 MHz).

[0069] like Fig. 3 The figure shows a comparison of the P-wave velocity and attenuation with water saturation under different frequencies and wettability conditions for the same lithology; correspondingly, the velocity curves in the seismic band (100 Hz) change with water saturation. w The hydrophobicity decreases almost monotonically, and the hydrophobicity increases slightly in the medium-high saturation region before falling back. In the logging frequency band (10 kHz), the hydrophilicity shows a "bulge" and falls back at the high saturation end, while the hydrophobicity generally increases and turns around before and after the high saturation end. In laboratory ultrasound (1 MHz), both continue to rise with Sw and show a sharp downward turn at the high saturation end (close to full saturation).

Claims

1. A simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone, characterized in that: Includes the following steps, S1. Establish the relationship between capillary pressure and water saturation after wettability correction; The capillary pressure-water saturation relationship is described using the whey-corrected van Genuchten model, and the calculation formula of the model is as follows: ， in, For effective saturation, S W This represents the water saturation level. The remaining water saturation level, and For shape parameters; Wettability correction factor The expression is: ， in, and It is an empirical constant. Contact angle; Using the above formula, the corresponding capillary pressure-water saturation relationship curves can be obtained under different wettability conditions; S2. Calculate the equivalent pore throat radius and effective permeability based on the relationship between capillary pressure and water saturation. S3. Calculate the characteristic frequencies and complex bulk modulus under different wettability conditions based on a partially saturated patchy medium model; S4. Simulate and compare the longitudinal wave velocity and attenuation characteristics under different wettability and water saturation conditions, analyze the modulation law of frequency-related acoustic response to wettability changes, and realize the quantitative characterization of wettability effect.

2. The simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone according to claim 1, characterized in that: In step S2, the equivalent throat radius is calculated using the Young-Laplace relation.

3. The simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone according to claim 2, characterized in that: The formula for calculating the equivalent throat radius is as follows: ， The effective permeability is then determined by combining the pore-throat geometry. ， in, For interfacial tension, For reference aperture, The baseline permeability; when the wettability changes from hydrophilic to hydrophobic, Reducing capillary pressure leads to a decrease in capillary pressure. Enlarge This increases, thus affecting fluid connectivity.

4. The simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone according to claim 3, characterized in that: In step S3, the characteristic angular frequency of wave-induced flow is determined based on the effective permeability and pore parameters, and the complex bulk modulus is calculated using the Cole-Cole broadening method.

5. The simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone according to claim 4, characterized in that: The formula for calculating the complex bulk modulus is as follows: ， ， in, For fluid viscosity, Porosity Characteristic diffusion length, The broadening index is defined as follows: ， in, , , For control coefficients, For confining pressure, This is the lower limit value; Wettability through and The coupling affects the relaxation spectrum width and the position of the characteristic frequencies.

6. The simulation method for the influence of wettability on the dispersion and attenuation of partially saturated sandstone according to claim 2, characterized in that: In step S4, the longitudinal wave complex modulus, velocity, and attenuation characteristics are calculated based on the complex bulk modulus. The calculation formula is as follows: ， ， ， in, Shear modulus The total density of the rock; Under the same pore structure and saturation conditions, the frequency response of hydrophilic and hydrophobic systems can be compared and analyzed by changing the contact angle, thereby obtaining quantitative results on the effect of wettability on acoustic response.

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