Orthotropic rock physical modeling method

Abstract

The invention discloses an orthotropic rock physical modeling method. The method comprises the following steps: S1, obtaining tight reservoir parameters; s2, estimating the elastic modulus of the mixed minerals; s3, enabling the mixed mineral to be equivalent to a VTI background rock matrix caused by a thin layer; s4, matrix pores are added into a VTI background rock matrix; s5, embedding the vertical crack into the VTI background'dry 'rock skeleton to obtain an OA medium'dry' rock skeleton; s6, calculating the bulk modulus and saturated rock density of the mixed fluid; s7, adding the mixed fluid into the OA medium'dry 'rock skeleton to obtain OA medium saturated rock; s8, calculating longitudinal and transverse wave velocities and anisotropy parameters of OA medium saturated rocks; and S9, calculating OA medium saturated rock. According to the method, the tight reservoir with the orthotropic characteristic can be simulated, the Thomsen parameter and the fracture weakness parameter of the tight reservoir can be obtained, and data support is provided for fracture evaluation, anisotropic parameter inversion, permeability prediction and the like of the tight reservoir.

Description

Technical Field

[0001] The present invention belongs to the technical field of rock physics, and particularly relates to a method for modeling orthotropic rock physics. Background Art

[0002] The causes of rock anisotropy are relatively complex, mainly including thin interbeds formed due to differences in sedimentary environments, as well as factors such as diagenesis and fracture development. These many factors interact with each other, resulting in the rock exhibiting typical transversely isotropic (TI) medium characteristics. The Young's modulus in different directions is proportional to the confining pressure, but the Poisson's ratio shows no obvious change. The Thomsen anisotropy parameters ε, γ, and δ coefficients decrease with the increase of the effective pressure, and there is a certain linear relationship among the parameters. The anisotropy in tight reservoirs (such as tight sandstone, shale, etc.) is manifested in many aspects, which has various impacts on oil and gas exploration and development. In terms of mechanical properties, anisotropy causes differences in mechanical parameters such as the compressive strength and tensile strength of the rock in different directions, which will cause uneven wear of the drill tool and problems with wellbore stability during the drilling process. In terms of permeability, anisotropy makes the flow resistance of oil and gas different in different directions, affecting the migration and accumulation of oil and gas, and thus having an important impact on the productivity and development strategy of the oil and gas reservoir. In terms of seismic wave propagation characteristics, anisotropy will cause changes in parameters such as seismic wave velocity and amplitude in different directions, posing challenges to the interpretation of seismic data and reservoir prediction.

[0003] Rock physics methods have unique advantages in obtaining anisotropy parameters of tight reservoirs. Rock physics is a bridge connecting the physical properties of rocks and seismic elastic properties. By establishing a rock physics model, the microscopic structure, mineral composition, etc. of the rock can be related to the macroscopic physical properties, providing a theoretical basis for obtaining anisotropy parameters. In recent years, many scholars have carried out relevant rock physics research on tight reservoirs and proposed rock physics models suitable for tight reservoirs. Smith et al. found that microcracks with different pore aspect ratios in tight sandstone can be used to explain the relationship between the longitudinal and transverse wave velocities and pores, and the sensitivity to pressure will change with the presence of microcracks. Keys and Xu established a rock physics model suitable for sandstone based on different pore aspect ratios of sandstone and mudstone. Ruiz et al. established the SPM model suitable for tight sandstone gas reservoirs, simulating the tight reservoir situation by assuming cracks with an aspect ratio of 0.01 and spherical pores with an aspect ratio of 1. Liu Qian et al. innovatively introduced the pore connectivity parameter in the Raymer formula into the equivalent medium model for the low-connected pore characteristics of the reservoir, effectively quantifying the influence mechanism of isolated pores on elastic modulus anisotropy and fluid sensitivity. In addition, Wang Daxing established a rock physics inversion model based on multi-attribute constraints by systematically analyzing the correlation between the measured porosity, fluid saturation, and elastic parameters of the core, significantly improving the reliability of seismic prediction of gas-bearing properties of the reservoir.

[0004] The above rock physics research usually assumes that tight reservoirs are isotropic media, ignoring the anisotropic propagation characteristics of seismic waves in tight reservoirs. Anisotropic parameters are of great significance in characterizing the anisotropic characteristics of tight reservoirs. However, the methods for obtaining anisotropic parameters in the traditional logging field are costly, time-consuming, and have limited sample sizes. Moreover, most current rock physics models are based on the assumption of transversely isotropic media and are difficult to characterize the elastic characteristics of tight reservoirs with orthorhombic anisotropic characteristics. Summary of the Invention

[0005] The object of the present invention is to overcome the deficiencies of the prior art and provide an orthorhombic anisotropic rock physics modeling method, which can solve the problem of difficult prediction of orthorhombic anisotropic parameters in log interpretation and improve the efficiency of log interpretation.

[0006] The object of the present invention is achieved by the following technical solutions: An orthorhombic anisotropic rock physics modeling method includes the following steps:

[0007] S1. Obtain the tight reservoir parameters required for rock physics modeling through logging and rock physics core tests, including the types of mineral components and the volume percentages of mineral components, the types and volume percentages of fluids in the rock, water saturation, porosity, and fracture density;

[0008] S2. Select the VRH formula to estimate the elastic modulus of the mixed minerals formed after mixing of each mineral component according to the volume percentage of the mineral components;

[0009] S3. Use the Backus average theory to equivalent the mixed minerals to the VTI background rock matrix caused by thin layers;

[0010] S4. Add the matrix pores to the VTI background rock matrix through the anisotropic SCA-DEM model to obtain the VTI background "dry" rock skeleton;

[0011] S5. Under the condition of weak anisotropy assumption, embed the vertical fractures into the VTI background "dry" rock skeleton through the Schoenberg fracture model to obtain the OA medium "dry" rock skeleton;

[0012] S6. Select the Wood formula to calculate the bulk modulus of the mixed fluid and the saturated rock density;

[0013] S7. Add the mixed fluid to the OA medium "dry" rock skeleton constructed in S5 through the Brown-Korringa equation to obtain the OA medium saturated rock;

[0014] S8. Calculate the P-wave and S-wave velocities and anisotropic parameters of the OA medium saturated rock according to the Tsvankin formula;

[0015] S9. Based on the Tsvankin anisotropic parameters, the Thomsen parameters and fracture weakness parameters of the saturated rock in the OA medium are calculated using the Bakulin formula.

[0016] The beneficial effects of the present invention are as follows: Under the condition of weak anisotropy assumption, by adding vertical fractures to the VTI background rock matrix, the present invention can simulate a tight reservoir with orthorhombic anisotropic characteristics, obtain the Thomsen parameters and fracture parameters of the tight reservoir, and provide data support for fracture evaluation, anisotropic parameter inversion, permeability prediction, etc. of the tight reservoir. Description of the Drawings

[0017] Figure 1 is the rock physics modeling flow chart of the present invention.

[0018] Figure 2 is the well logging interpretation chart of parameters such as well logging mineral component content and fluid saturation in the example.

[0019] Figure 3 is the comparison chart of the P-wave and S-wave velocities obtained by fitting the rock physics model and the measured P-wave and S-wave velocities.

[0020] Figure 4 Comparison chart of the orthorhombic anisotropic parameters predicted by the rock physics model and the well logging curves.

[0021] Figure 5 is the comparison chart of the VTI anisotropic parameters and fracture weakness parameters predicted by the rock physics model and the well logging curves.

[0022] Figure 6 is the Pearson correlation coefficient matrix between the VTI anisotropic parameters and fracture weakness parameters in the prediction results and the well logging parameters. Detailed Embodiments

[0023] The anisotropic characteristics of the actual formation are complex and variable. Under the assumptions of seismic wavelength scale and long wavelength, a tight reservoir affected by factors such as vertical fractures and horizontal thin interbeds can be equivalent to an orthorhombic anisotropic medium. The present invention fully considers the causes and characteristics of reservoir anisotropy, equivalent the tight reservoir to an orthorhombic anisotropic medium, more accurately depicts the relationship between rock physical properties and seismic responses, and provides a theoretical basis and prior information for predicting anisotropic parameters of tight reservoirs using wide-azimuth seismic data. The technical solution of the present invention will be further described below with reference to the drawings.

[0024] As Figure 1 shown, an orthorhombic anisotropic rock physics modeling method of the present invention includes the following steps:

[0025] S1. Obtain the tight reservoir parameters required for rock physics modeling through logging and rock physics core tests. The physical properties parameters of the tight reservoir include the types of mineral components and the volume percentages of mineral components, the types and volume percentages of fluids in the rock, water saturation, porosity, and fracture density. The types of mineral components and the volume percentages of mineral components, as well as the types and volume percentages of the rock mixed fluids, can be directly obtained through rock physics core tests; the water saturation and porosity parameters are obtained by logging measurements. The fracture density is obtained by calculation.

[0026] In this embodiment, the logging parameters obtained from a certain well are as Figure 2 shown (including compressional wave velocity, fast shear wave velocity, density, natural gamma, porosity, permeability, water saturation, and the volume percentages of each mineral). The red shaded part is the depth range where the target layer is located. This area has a relatively high permeability and a relatively low water saturation, but the porosity has no significant characteristics.

[0027] To effectively describe the complex pore - fracture structure of the tight reservoir, the total porosity of the orthotropic tight reservoir rock physics model includes matrix porosity φ p and fracture porosity φ f , where the fracture porosity φ f is calculated according to the fracture porosity empirical formula:

[0028]

[0029] In the formula: ρ LLD is the deep lateral resistivity (Ω·m); ρ LLS is the shallow lateral resistivity (Ω·m); ρ mf is the mud filtrate resistivity (Ω·m), which is obtained by logging measurement; A1, A2, and A3 are constant coefficients, and their values depend on the fracture type, as shown in Table 1.

[0030] Table 1

[0031]

[0032]

[0033] The specific process of calculating the fracture porosity is as follows: First, calculate the discrimination index Y, and its formula is as follows:

[0034]

[0035] In the formula, Y is the crack type discrimination index; according to its value from high to low, it can be discriminated as high-angle cracks, inclined cracks, and low-angle cracks in sequence. During the calculation process, first calculate the crack type discrimination index Y, then judge the crack type according to Y, find the values of A1, A2, and A3 corresponding to this crack type from Table 1, and finally substitute them into formula (1) to calculate the crack porosity.

[0036] The crack density e can be further calculated based on the crack porosity, and the formula is as follows:

[0037]

[0038] Among them, χ is the aspect ratio of the crack (usually defaulted to 0.01 in the calculation).

[0039] S2. According to the volume percentage of mineral components, select the VRH (Voigt-Reuss-Hill) formula to estimate the elastic modulus of the mixed minerals formed after mixing of each mineral component (such as quartz, clay, etc.); the expression of the VRH formula is:

[0040]

[0041] In the formula, M VRH 、M V and M R are the elastic modulus of the mixed minerals estimated by the VRH formula, the elastic modulus of the mixed minerals estimated by the Voigt model, and the elastic modulus of the mixed minerals estimated by the Reuss model respectively. The calculation formulas for the elastic modulus of the mixed minerals estimated by the Voigt model and the Reuss model are as follows:

[0042]

[0043] In the formula, is the volume percentage of the i-th mineral component, N is the number of mineral components; M i is the elastic modulus of the i-th mineral component; M VRH 、M V 、M R and M i can select any one of the moduli, such as the bulk modulus, shear modulus, etc.

[0044] In this example, the elastic moduli of the tight sandstone rock minerals and fluids used are shown in Table 2.

[0045] Table 2

[0046] Component Bulk modulus (GPa) Shear modulus (GPa) <![CDATA[Density (g / cm 3 )]]> Coal 7.400 4 1.65 Clay 21.000 7 2.60 Quartz 37.000 44 2.65

[0047] S3. Use the Backus average theory to equivalent the mixed minerals to the VTI background rock matrix caused by thin layers, and obtain its stiffness matrix C VTI; Calculate the stiffness matrix C of the VTI background rock matrix using the Backus average theory VTI The formula is as follows:

[0048]

[0049] where c ij represents the stiffness matrix element in a single layer; the subscripts i, j = 1, 2, …, 6 are the stiffness matrix element indices; <> indicates weighted averaging of the parameters within the parentheses according to the weighting coefficient, and here the weighting coefficient can be either the mineral volume percentage (narrow sense Backus average) or the layer thickness (broad sense Backus average).

[0050] In the calculation process, the broad sense Backus average assumption is adopted. Specifically, the weighting coefficient is replaced by the layer thickness, and the layer thickness of each layer is the same (equal to the depth interval of the logging sampling points). The total thickness during calculation is determined by the number of sampling points selected. The more sampling points, the smoother the calculation result. In this example, the number of calculation points selected is 41.

[0051] S4. Add the matrix pores to the VTI background rock matrix through the anisotropic SCA-DEM model to obtain the VTI background "dry" rock skeleton; and obtain the equivalent elastic stiffness matrix c SCA , which is expressed as:

[0052]

[0053] In the formula, c n is the stiffness tensor of the nth mineral component, v n is the volume percentage of the nth mineral component; K *n is the tensor connecting stress and strain; is the tensor related to the aspect ratio; I is the unit tensor.

[0054] Since the added pores are connected, to ensure the double-connectedness of the pores, the SCA model and the DEM model are usually used in combination. The DEM model is expressed by the difference equation as:

[0055]

[0056] where, c DEM is the stiffness tensor of the pore-containing equivalent medium; v is the content of the inclusions (inclusions generally refer to fluids or other minerals. Since the "dry" skeleton is calculated here, the modulus of the inclusions is set to zero to simulate a dry cavity, that is, the inclusions here are empty, and it can be simply understood that the inclusions are air); c i is the stiffness tensor of the ith inclusion.

[0057] S5. Under the condition of weak anisotropy assumption, the vertical fractures are embedded into the VTI background "dry" rock skeleton through the Schoenberg fracture model to obtain the OA medium "dry" rock skeleton. The stiffness matrix formula of the OA medium "dry" rock skeleton is as follows:

[0058]

[0059] where, Δ N is the normal weakness and T is the tangential weakness of the fractures, and their variation ranges are from 0 to 1.

[0060] S6. Select the Wood formula to calculate the bulk modulus K fl of the mixed fluid and the saturated rock density ρ. The Wood formula is expressed as:

[0061]

[0062] where, is the volume percentage corresponding to each fluid component; is the bulk modulus of each fluid component; M is the number of fluid components; is the density corresponding to each fluid component; is the density corresponding to each mineral component; the bulk modulus of the brine used in this calculation process is 2.5 GPa, and the density is 1 g / cm 3 ; the bulk modulus of the gas is 0.063 GPa, and the density is 0.11 g / cm 3 .

[0063] S7. Add the mixed fluid into the OA medium "dry" rock skeleton constructed in S5 using the Brown-Korringa equation to obtain the OA medium saturated rock, and obtain the stiffness matrix of the OA medium saturated rock.

[0064] Calculate the stiffness matrix of the OA medium saturated rock according to the Brown-Korringa equation. The formula is as follows:

[0065]

[0066] In the formula, is the stiffness matrix of the OA medium "dry" rock skeleton, that is, C OA in S5; K0 is the bulk modulus of the mixed minerals, obtained from S2; φ is the total porosity; K fl is the bulk modulus of the mixed fluid, obtained from S6.

[0067] S8. Calculate the P-wave and S-wave velocities and anisotropy parameters of the OA medium saturated rock according to the Tsvankin formula. The expression of the Tsvankin formula is as follows:

[0068]

[0069] In the formula, V P0 and V S0 are the longitudinal wave velocity and the shear wave velocity propagating in the vertical direction respectively; ε (1,2) , γ (1,2) , δ (1,2,3) represent the components of the Thomsen parameters in different symmetry planes, where "1, 2, 3" represent the x2Ox3, x1Ox3, and x1Ox2 planes respectively.

[0070] S9. Based on the Tsvankin anisotropic parameters, the Thomsen parameters and the fracture weakness parameters of the saturated rock in the OA medium are calculated using the Bakulin formula. The Bakulin formula is as follows:

[0071]

[0072] In the formula, ε and δ represent the Thomsen anisotropic parameters in the VTI background medium; g is the square of the shear-to-longitudinal wave velocity ratio, that is Δ N , Δ V and Δ H represent the normal fracture weakness, the vertical tangential fracture weakness, and the horizontal tangential fracture weakness respectively.

[0073] In this embodiment, the predicted P-wave and S-wave velocity results of the rock physics modeling are compared with the measured velocities as Figure 3 shown. Among them, the fitting result of the P-wave velocity is better. In addition, the S-wave velocity used here is the fast S-wave velocity, which has a certain error from the actual propagated S-wave velocity. Therefore, the fitting effect of the S-wave velocity here seems to have a larger error, but its general trend is consistent. Since there is a strong correlation between the permeability and the anisotropic parameters, this relationship can be used to verify the predicted anisotropic parameters. Figure 4 Shows the Tsvankin anisotropic parameters and the corresponding well logging curves (S-wave anisotropy, porosity, and permeability). It can be seen that there is a certain correlation between the absolute value of the anisotropic parameter and the permeability. Figure 5 Is a comparison chart of the VTI anisotropic parameters and the fracture weakness parameters with the well logging curves. As can be seen from the figure, there is an obvious correlation between the anisotropic parameters predicted by the orthorhombic anisotropic rock physics model and the permeability, and this feature is particularly significant within the depth range of the target layer, such as Figure 6 shown in the Pearson correlation coefficient matrix of the parameters. Among them, the correlation coefficients between the three fracture weaknesses and the permeability are greater than 0.7. This indirectly verifies the effectiveness and accuracy of the anisotropic parameters predicted by the model.

[0074] Those of ordinary skill in the art will realize that the embodiments described herein are provided to assist the reader in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on these technical revelations disclosed in the present invention, and these deformations and combinations are still within the scope of protection of the present invention.

Claims

1. An orthotropic rock physics modeling method, characterized in that: The steps include: S1. Obtain the tight reservoir parameters required for rock physics modeling through well logging and rock physics core testing, including the types and volume percentages of mineral components, the types and volume percentages of fluids in rocks, water saturation, porosity, and fracture density; S2. According to the volume percentage of the mineral components, the VRH formula is selected to estimate the elastic modulus of the mixed mineral formed after the mineral components are mixed; S3, using Backus average theory to equate mixed minerals to the VTI background rock matrix caused by thin layers; S4, adding matrix pores to the VTI background rock matrix through the anisotropic SCA-DEM model to obtain the VTI background "dry" rock skeleton; S5. Under the assumption of weak anisotropy, vertical fractures are embedded into the VTI background "dry" rock skeleton through the Schoenberg fracture model to obtain the OA medium "dry" rock skeleton; S6. Select Wood's formula to calculate the bulk modulus of the mixed fluid and the saturated rock density; S7, adding the mixed fluid into the OA medium "dry" rock skeleton constructed in S5 using the Brown-Korringa equation to obtain OA medium saturated rock; S8. Calculate the P- and S-wave velocities and anisotropy parameters of OA medium saturated rock according to Tsvankin formula; S9. Based on the Tsvankin anisotropy parameters, the Bakulin formula is used to calculate the Thomsen parameters and fracture weakness parameters of OA medium saturated rock.

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