A petrophysical model and dictionary combined driving physical property parameter prediction method
By using a method that combines rock physics models and dictionaries, the problems of difficult model selection and low accuracy in linearized rock physics inversion methods are solved, and reservoir property parameter prediction with higher accuracy and adaptability is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2022-12-01
- Publication Date
- 2026-06-02
AI Technical Summary
In existing technologies, linearized rock physics inversion methods are difficult to select models, have low inversion accuracy, and the joint dictionary method ignores subsurface physical characteristics, resulting in inaccurate prediction results.
A method combining rock physics model and dictionary is adopted. By establishing a pre-stack forward model and linearization relationship, and learning a joint dictionary by combining well logging data, a joint inversion objective function is constructed and decomposed into multiple sub-problems for iterative solution.
It improves the accuracy and adaptability of reservoir physical parameter prediction, and the inversion results are more consistent with the geological laws and well logging data characteristics of actual underground strata.
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Figure CN116089908B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of rock physics inversion, and specifically relates to a reservoir physical parameter prediction technology. Background Technology
[0002] Reservoir physical properties, such as porosity, water saturation, and clay content, are crucial for directly locating underground oil and gas reservoirs. Seismic data obtained from seismic exploration contains abundant information on seismic elastic parameters and reservoir physical properties. Generally, the prediction of reservoir physical properties involves two steps: first, seismic inversion is performed using well logging data and seismic data to obtain subsurface elastic parameters, such as wave impedance, P-wave and S-wave velocities, and density; second, based on the obtained elastic parameters, rock physics inversion is performed to obtain the reservoir physical properties.
[0003] Seismic inversion technology has matured and become increasingly sophisticated over the past few decades. Depending on the type of input seismic signal, it can be divided into pre-stack seismic inversion and post-stack seismic inversion, each retrieving different elastic parameters. Among these, the AVO inversion technique based on the convolution model in pre-stack seismic inversion plays a crucial role in predicting reservoir physical parameters. The theoretical basis of AVO inversion is the Zoeppritz equation, which reveals the propagation law of seismic waves underground, namely the process of reflected and transmitted waves generated when incident waves encounter interfaces. However, due to the complexity of the Zoeppritz equation and its lack of intuitive physical interpretation, more easily calculated and physically meaningful approximations are often used in practical applications, such as the Aki-Richards approximation, the Shuey approximation, the Smith & Gidlow approximation, and the Fatti approximation. With these approximate formulas, combined with the convolution model, the objective function for seismic inversion can be constructed. To reduce the 'illness' of the inversion problem, regularization constraints need to be added to the objective function. Research on regularization terms is a major area of interest in seismic signal inversion. Existing regularization techniques include TK regularization based on smoothness constraints, TV regularization based on block constraints, and dictionary learning constraint methods that adaptively learn features from well logging data and add them to the inversion objective function. These regularization methods improve the accuracy of seismic inversion.
[0004] Rock physics inversion first requires establishing a theoretical or empirical rock physics model to connect the relationship between elastic parameters and physical property parameters, and then using an inversion algorithm to solve for the target result. The rationality and applicability of the rock physics model play a crucial role in rock physics inversion. Among rock physics models, the contact cementation model has a relatively simple mathematical form and is widely used in rock physics inversion. However, due to the highly complex relationship between elastic parameters and physical property parameters in reality, inclusion models or empirical models, such as the Xu-White model, Raymer's improved formula, and Gassmann equations, are often used. However, when using these models with complex relationships, due to their high nonlinearity, it is necessary to choose an inversion algorithm with probabilistic statistical methods, such as Bayesian methods or Monte Carlo algorithms. But using these algorithms can lead to low computational efficiency.
[0005] Linearized rock physics inversion methods can improve computational efficiency, but they are only applicable to rock physics models with low nonlinearity. Furthermore, different rock physics models need to be selected for different work areas to improve inversion accuracy, thus linearized inversion methods lack strong adaptability. However, the inversion framework constructed using this method can reflect the actual physical distribution of subsurface strata. To address the shortcomings of linearized rock physics inversion methods, such as difficulty in model selection and low inversion accuracy, we propose a reservoir property parameter prediction method jointly driven by a rock physics model and a dictionary. This method, based on the framework of linearized rock physics inversion, learns the feature information in well logging data and the correlation between elastic parameters and physical property parameters through a joint dictionary, obtaining a joint dictionary of elastic and physical property parameters. This learned joint dictionary is then added to the linearized rock physics inversion process, thereby extracting the actual subsurface physical distribution patterns from the rock physics model, weakening the influence of the rock physics model, and thus improving the accuracy of reservoir property parameter prediction.
[0006] The relevant existing technologies are as follows:
[0007] 1. A method for inverting physical property parameters based on linearized rock physics inversion
[0008] To address the low computational efficiency of probability and statistics, some scholars have proposed a linearized rock physics inversion method. The process involves first linearizing the selected rock physics model, then directly using this linearized model to construct the objective function, and finally performing the inversion operation to obtain the rock physics inversion result. The linearization process of the rock physics model originates from the rock physics inversion problem, which can generally be written in the following form:
[0009] d=f(m) (1)
[0010] Where d represents the elastic parameter, f(·) represents the selected rock physics model, and m is the target physical property parameter for inversion. The method for linearizing this problem is to perform a Taylor expansion of equation (1) and cut off at the first order, thus obtaining a linearized formula. Assuming that equation (1) is Taylor expanded at m0, the following formula is obtained:
[0011]
[0012] Where f′(m0) is the value of the first derivative of f(m) when m0 is taken. If f(·) is a form with multiple equations and multiple variables, then f′(m0) corresponds to the form of the Jacobian matrix. Combining the constant terms in equation (2), we can obtain the following linearized rock physics inversion model:
[0013]
[0014] The physical property parameters can be obtained by directly using the optimization solution method for the above model.
[0015] 2. A porosity inversion method based on a joint dictionary
[0016] For complex underground geological structures, geostatistical methods can only provide a general macroscopic prediction, failing to capture detailed trends. Linear fitting porosity prediction methods can only fit local features, unable to describe the overall relationship. Neural network prediction methods are time-consuming because they require retraining the neural network for each prediction location. To address the shortcomings of these existing methods, such as poor adaptability and low computational efficiency, some scholars have proposed using a joint dictionary method for porosity inversion. This method is based on research findings that reservoir parameters within the same work area exhibit a certain degree of consistency and lateral continuity, and that there is a strong correlation between underground elastic and physical property parameters. Starting with well logging curves and combining relevant geological background, the joint dictionary method learns the relationship between underground elastic and physical property parameters, and then uses the resulting joint dictionary to predict porosity. The steps of this method are as follows:
[0017] (1) After dividing the well logging curves into blocks and splicing samples with different attributes, a training sample Y = [Y] is formed for the joint dictionary. Ip ,Y por ],in
[0018] (2) The joint dictionary is obtained by training the training samples using the K-SVD algorithm.
[0019] (3) Construct the objective function for seismic inversion using the seismic convolution model:
[0020]
[0021] (4) Using the joint dictionary obtained from training, combined with the objective function of seismic inversion, first use the impedance dictionary D Ip By incorporating a regularization constraint into the seismic inversion objective function, an optimization algorithm is used to solve the seismic inversion objective function, and the sparse coefficients α of the impedance are obtained simultaneously. i Using this sparsity coefficient α i Dictionary of porosity por Multiplying these results yields the predicted porosity. Therefore, the objective function for the final joint impedance and porosity inversion is as follows:
[0022]
[0023] While inversion methods based on linearized rock physics models can improve computational speed to some extent, they also present several challenges when using Taylor expansion for linearization. For instance, the expansion point m0 needs to be determined, as different m0 points yield different linearization results, making it difficult to identify an optimal expansion point. Furthermore, because the Taylor expansion for linearization is only truncated at the first order, it is only suitable for linearization within a small range and requires the rock physics model to be linear or slightly nonlinear. Failure to meet these requirements will reduce the accuracy of the linearization inversion. The selection of the rock physics model also presents an issue. Different models are needed for regions with different rock physics properties. For example, a model combining the critical porosity model and the Gassmann equation is suitable for modeling argillaceous sandstone reservoirs, but the model needs to be changed when the work area is different.
[0024] The porosity inversion method based on a joint dictionary mainly starts from existing well logging data, learns the relationship between impedance and porosity through dictionary learning, and then divides the dictionary into an impedance dictionary and a porosity dictionary. First, an impedance dictionary constraint term is added to the objective function of seismic inversion to obtain a joint sparse coefficient. Then, this sparse coefficient is directly multiplied by the porosity dictionary to obtain the porosity. Through this process, we can see that this method obtains porosity through data-driven prediction. Therefore, it inevitably ignores the physical characteristics of the underground layers, which will cause some deviation from reality in details. Summary of the Invention
[0025] To address the aforementioned technical problems, this invention proposes a reservoir property parameter inversion method jointly driven by a rock physics model and a dictionary. This method reduces the dependence of the linearized rock physics model inversion method on the linearization method and model selection, ultimately improving the adaptability of the method and the accuracy of the prediction results.
[0026] The technical solution adopted in this invention is: a method for inverting reservoir physical parameters driven by a rock physics model and a dictionary, comprising:
[0027] S1. Establish the pre-stack forward model:
[0028] d = Gm
[0029] Where d is the seismic signal formed by vectoring J seismic signals with different incident angles from the same angle gather, G is the forward modeling operator constructed from wavelet, P-wave and S-wave background velocities and fitting coefficients, and m is the model parameters obtained from P-wave and S-wave impedance and density.
[0030] S2. Establish the three elastic parameters V. p V s ρ and the three physical property parameters φ, C, S w Relationships;
[0031]
[0032] Among them, V p V represents the longitudinal wave velocity. s ρ represents transverse wave velocity, φ represents density, φ represents porosity, C represents clay content, and S represents... w V represents the degree of water saturation. P,mat and V P,fl These refer to the longitudinal wave velocities of the solid and fluid phases, respectively, V. S,mat This refers to the transverse wave velocity of the solid phase, ρ. mat and ρ fl These represent the densities of the solid and fluid phases, respectively;
[0033] S3. Expand and linearize the relation established in step S2 to obtain the Jacobian matrix and Taylor remainder e of each physical property parameter.
[0034] S4. Based on the Jacobian matrix of each physical property parameter and the Taylor remainder e, a linearized model for the forward modeling of rock physics of the physical property parameters is obtained.
[0035] S3. Learn a joint dictionary of elastic parameters and physical property parameters from well logging data;
[0036] S4. Based on the linearized model of rock physics forward modeling of physical property parameters and the joint dictionary of elastic and physical property parameters, construct a jointly driven inversion objective function:
[0037]
[0038] The joint-driven inversion objective function satisfies the following constraints:
[0039]
[0040] Among them, G φ The linear operator representing porosity, G C A linear operator representing the clay content, G Sw The linear operator representing water saturation, D E D is a dictionary of elasticity parameters. P A dictionary of physical property parameters, d φ For a linearized rock physics inversion model of porosity expansion, d C To develop a linearized rock physics inversion model for mud content, d Sw For a rock physics inversion model that linearizes water saturation, m P Let R be the set of physical property parameters, where n is the normalized elastic parameter. i Let α be a block matrix. i These are the joint sparse coefficients obtained from the joint dictionary, ψ(·) is the conversion formula between model parameters and elasticity parameters, and ζ... -1 (·) is the inverse normalization operator;
[0041] S5. Decompose the joint-driven inversion objective function into the following three sub-problems:
[0042] Subproblem 1: Considering only the model parameter m as a variable, the expression for subproblem 1 is:
[0043]
[0044] Subproblem 2: Considering the sparsity coefficient α i Physical property parameter m P As the variable, the expression corresponding to subproblem two is:
[0045]
[0046] Sub-problem 3: Considering the three physical parameters φ, S w C is a variable, and the expression corresponding to subproblem three is:
[0047]
[0048] By iteratively solving these three sub-problems, reservoir property parameter prediction can be achieved through a combination of rock physics model and dictionary-driven approach.
[0049] The beneficial effects of this invention are as follows: This invention employs a linearized rock physics inversion method as the inversion framework, and combines the advantages of a joint dictionary in learning features from existing data and mining the relationships between different parameters, resulting in higher accuracy of the inversion results and better conformity to the geological laws of actual subsurface strata. It is a data- and model-driven method for inverting reservoir physical parameters. The method of this invention has the following advantages:
[0050] (1) This invention makes full use of the geological laws in the rock physics model, and the distribution law of the inversion result is more in line with the actual situation of the underground strata.
[0051] (2) The inversion results of this invention combine the feature information learned from the well logging data and the correlation information between elastic parameters and physical property parameters, making the results more consistent with the actual data. Attached Figure Description
[0052] Figure 1 The flowchart shows the method for inverting reservoir property parameters based on rock physics models and joint dictionaries.
[0053] Figure 2 The process of obtaining dictionary training samples from well logging data;
[0054] Figure 3 For comparison of porosity prediction results;
[0055] Among them, (a) is the joint driving method, and (b) is the linear rock physics inversion method;
[0056] Figure 4 Comparison of predicted mud content results;
[0057] Among them, (a) is the joint driving method, and (b) is the linear rock physics inversion method;
[0058] Figure 5 For comparison of single-well test results;
[0059] Among them, (a) is the inversion of physical property parameters of the rock physics model, and (b) is the inversion of physical property parameters driven by the rock physics model and the dictionary. Detailed Implementation
[0060] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.
[0061] The method of the present invention includes the following steps:
[0062] 1. Establishing the forward model, including the following steps:
[0063] 11. Establishment of pre-stack seismic forward model
[0064] Pre-stack seismic forward modeling is mainly constructed based on the approximate equations established by Fatti et al., using wave impedance reflection coefficients as variables, and the seismic convolution model. The Fatti approximate equations are shown below:
[0065] R PP (θ)=c1R P +c2R S +c3R D (6)
[0066] in θ1 is the angle of the reflected longitudinal wave, and θ2 is the angle of the transmitted longitudinal wave; R PP (θ) is the PP wave reflection coefficient that varies with angle; c1=1+tan 2 θ, c2 = -8γ 2 tan 2 θ, γ = V S / V P c3 = -0.5tan 2 θ+2γ 2 sin 2 θ; R P R S R D These are the longitudinal wave impedance reflection coefficient, the transverse wave impedance reflection coefficient, the transverse wave impedance reflection coefficient, and the density reflection coefficient, respectively. They have the following relationships with the longitudinal and transverse wave velocities and densities:
[0067]
[0068]
[0069]
[0070] Where △V P , △V S Δρ and Δρ correspond to the differences in P-wave velocity, S-wave velocity, and density on both sides of the interface, respectively; V p V S Let ρ be the average values of the P-wave velocity, S-wave velocity, and density on both sides. Since the forward modeling of plane wave propagation underground can be considered a discretized process, it is assumed that the underground region consists of N... l It is constructed from several small layers, and two adjacent layers form a medium interface. Let i = 1, 2, ..., N l -1 represents the boundary between layer i and layer i+1. Let be the longitudinal wave impedance reflection coefficient of the i-th interface. Since the elastic difference between adjacent layers is small, some studies suggest the following approximation:
[0071]
[0072] Combining equation (7), we can deduce:
[0073]
[0074] in and Let be the longitudinal wave impedance of the i-th layer. For N... l With sampling points, equation (11) can be written in the following matrix form:
[0075]
[0076] The above formula can be simplified as:
[0077]
[0078] in, The vector of longitudinal wave impedance reflection coefficients. Represents the real number field; Represents the natural logarithm of the longitudinal wave impedance vector; The first difference matrix corresponds to the first matrix on the right-hand side of equation (12). Similarly, and Let represent the natural logarithms of transverse wave impedance and density, respectively. Combining equations (8) and (9), we can obtain:
[0079]
[0080] R D =TL D (15)
[0081] in, and These are the natural logarithms of the transverse wave impedance reflection coefficient vector and the transverse wave impedance vector, respectively. and Let represent the natural logarithm of the density reflectance coefficient vector and the density vector, respectively. Combining equations (13)-(15), equation (6) can be rewritten as:
[0082]
[0083] Where c1 = 1 + tan 2 θ, c2 = -8γ 2 tan 2 θ, γ = V S / V P c3 = -0.5tan 2 θ+2γ 2 sin 2 θ; assuming the logarithm L of the P-wave and S-wave impedance of the strata rocks P L S and the logarithm of density LD There is a weak linear relationship among the three:
[0084] L S =kL P +k c +△L S (17)
[0085] L D =mL P +m c +△L D (18)
[0086] Where k, k c m c and m c Let be the constant coefficient of the fitted linear relationship. Substituting equations (17) and (18) into equation (16), we get:
[0087]
[0088] in and According to the convolution model, the forward model from reflection coefficient to seismic signal can be expressed as the following formula:
[0089] d(θ)=W(θ)R PP (θ) (20)
[0090] in It refers to the synthetic seismic signal at an incident angle of θ. Represents a length of N d -N l +2(N d >N l The convolution matrix is constructed from the wavelets of the seismic signal. Let J be the number of incident angles of the seismic signal. Combining equations (19) and (20), the equations corresponding to all incident angles can be incorporated into one equation, resulting in the following pre-stack three-parameter forward model:
[0091]
[0092] The above yields the pre-stack forward model, which is used to invert V. p V s The three parameters ρ are abbreviated as:
[0093] d=Gm (22)
[0094] Where d represents the seismic signal formed by vectoring J seismic signals with different incident angles from the same angle gather, G is the forward modeling operator constructed from wavelet, P-wave and S-wave background velocities, and fitting coefficients, and m are the model parameters obtained from P-wave and S-wave impedance and density. Pre-stack seismic inversion can be achieved using this formula.
[0095] 12. Establishment of a linearized forward model for rock physics
[0096] In the rock physics model and joint dictionary method, this invention uses the Raymer improved formula, the Raymer-Dvorkin model, and the density equation to establish the three elastic parameters V. p V s ρ and the three physical properties: porosity φ, clay content C, and water saturation S w The relationship between them is shown in the following formula:
[0097]
[0098] Where V P,mat and V P,fl These refer to the longitudinal wave velocities of the solid and fluid phases, respectively, V. S,mat This refers to the transverse wave velocity of the solid phase, ρ. mat and ρ fl Let these represent the densities of the solid phase and the fluid phase, respectively. Their calculation formulas are as follows:
[0099] ρ mat =ρ c C+ρ q (1-C) (24)
[0100] Where the subscript c represents clay, the subscript q represents quartz, and ρ c ρ q These represent the density of clay and the density of quartz, respectively, and are generally taken as constants.
[0101] ρ fl =ρ w S w +ρ hc (1-S w (25)
[0102] Where ρ w ρ hc Let these represent the densities of water and the oil-gas mixture, respectively, and generally take constant values.
[0103]
[0104]
[0105]
[0106] in
[0107]
[0108]
[0109] K fl =S w K w +(1-S w )K hc (31)
[0110] Where K and G represent the bulk modulus and shear modulus respectively, the subscript w indicates water, and the subscript hc indicates an oil-gas mixture. Therefore, K w K represents the bulk modulus of water. hc The bulk modulus of the oil-gas mixture is expressed as (3). Equation (23) is directly applied to equation (3) in (φ0, C0, S). w0 Expanding and linearizing (generally, the values of these points are taken as the statistical average of this work area) yields the Jacobian matrix and the Taylor remainder e, as shown below:
[0111]
[0112]
[0113] A linearized model for forward modeling of rock physics can be constructed using this Jacobian matrix:
[0114] d E =G p m p (34)
[0115] Here d E The meaning is the difference between the three elastic parameters and the Taylor expansion remainder e, as shown in equation (35):
[0116]
[0117] G p The Jacobian matrix obtained by equation (32) is m p These are physical properties, including porosity φ, clay content C, and water saturation S. w Three parameters. However, experiments show that when inverting all three parameters simultaneously, only the same forward operator G is used. p This would cause significant errors, so some improvements were made. Specifically, the physical property parameters were linearized one by one. When calculating a certain physical property parameter, a reasonable value was given to the other physical property parameters, and then their Jacobian matrices and Taylor expansion remainders were calculated separately, as shown below:
[0118]
[0119]
[0120] At this point, the Jacobian matrix of each parameter in equation (36) corresponds to the forward operator G in equation (32). p , respectively In equation (32), d E The meaning is that it becomes the difference between the remainder terms of the Taylor expansions of the three elastic parameters and different physical property parameters, and thus their d E The format is as follows:
[0121]
[0122] Where n is the number of inversion points. The objective function for rock physics inversion, which is linearly expanded parameter by parameter, can be constructed using the linearization method described above, as shown in equation (39):
[0123]
[0124] 2. Reservoir property parameter prediction driven by a combination of rock physics model and dictionary includes the following steps:
[0125] 21. Training of a joint dictionary of elastic parameters and physical property parameters
[0126] Before performing reservoir property parameter inversion using the rock physics model and joint dictionary, a joint dictionary of elastic and physical property parameters needs to be learned from well logging data. It's important to note that because well logging data values for different attributes have different scales and orders of magnitude, the well data needs to be normalized to its maximum and minimum values to bring them to the same scale for joint sparse representation. Furthermore, to fully utilize the well logging data, a sliding window is used to divide the existing well data into blocks, and then these blocks of different attribute values are pieced together to form a training sample. The operation process is as follows: Figure 2 As shown:
[0127] After the above block-based operations, the training samples of the dictionary Y = [Y1, Y2, ..., Y] can be obtained. n ], where n is the number of blocks obtained by the sliding window, and each training sample Y i =[VP i ,VS i ,ρ i ,φ i Sw i C i The K-SVD algorithm is applied to the obtained training sample Y to obtain a joint dictionary of elastic parameters and physical property parameters. in A dictionary of elastic parameters. This is a dictionary of physical property parameters.
[0128] 22. Construct and solve the joint objective function of rock physics and dictionary.
[0129] For the joint dictionary obtained from training, a joint-driven inversion objective function is constructed by combining the pre-stack seismic inversion model (22) and the sequentially expanded linearized rock physics inversion model (39) as shown in equation (40):
[0130]
[0131] And it satisfies the following constraint:
[0132]
[0133] Where ||0 represents the 0-norm, d is the seismic data, G is the pre-stack forward modeling operator, and m is the model parameter. These are the normalized elastic parameters. R is a set of physical property parameters. i Let α be a block matrix. i The joint sparse coefficients, ||α, are obtained from the joint dictionary. i ||0≤K α This indicates that the sparsity must be less than a certain small constant K. α ψ(·) is the conversion formula between model parameters and elasticity parameters, ζ -1 (·) is the inverse normalization operator. The minimization objective function described by equation (40) can be divided into three parts:
[0134] (1) Seismic inversion objective function term: i.e. This is used to minimize the fitting error between seismic data and pre-stack forward modeling synthesized signals, thereby obtaining high-fidelity elastic parameter data.
[0135] (2) Objective function term for rock physics inversion: i.e. Three parameters are used to minimize the elastic parameters and the physical properties obtained from rock physics forward modeling.
[0136] (3) Union dictionary constraints: This is used to minimize the error between the inversion results and the joint dictionary prediction results, so as to make the inversion results match the learned dictionary features.
[0137] The combination of the above three parts can make the physical property parameters obtained by inversion match the elastic parameters obtained by seismic inversion, and at the same time, it can also match the relationship between the two obtained by joint dictionary learning, thus obtaining a physical property parameter result that conforms to the actual rock physics model and is faithful to the characteristics of existing well logging data. However, directly solving equation (40) is difficult, firstly because there are many variables to be optimized, and secondly because the nonlinearity of the equality constraint ψ(·) involved is difficult to solve. Therefore, the block coordinate descent optimization strategy is adopted to iteratively solve equation (40), which is decomposed into the following three sub-problems:
[0138] (1) When only the model parameter m is considered as a variable, equation (38) can be simplified to:
[0139]
[0140] Where n are three normalized elasticity parameters. The constraints can be removed by adding a penalty term, letting... The approximate subproblem regarding the model parameter m can then be obtained as follows:
[0141]
[0142] It can be seen that this formula includes both the data fidelity term for seismic inversion and the constraint results of dictionary learning, which is mainly achieved through... It is reflected because It is obtained by dictionary encoding of previous data.
[0143] (2) When considering the sparsity coefficient α i Physical property parameter m P When the variable is used, equation (38) can be simplified to:
[0144]
[0145] At the same time, it can be observed in this step that, since a joint dictionary is used, the elastic parameters and physical property parameters share the same sparsity coefficient α. i Furthermore, since the physical properties are derived from the elastic parameters, this step first involves sparse encoding of the elastic parameters to obtain α. i Then α i With the physical property parameter dictionary D P Multiplying them yields the physical property parameters, as shown in the following formula:
[0146]
[0147] (3) When considering the three physical properties φ, S w When C is a variable, equation (38) simplifies to:
[0148]
[0149] Because m P Since sparse coding has already been used in subproblem (2), the equation optimization problem can be obtained by adding a penalty function term, as shown in the following equation:
[0150]
[0151] m P That is, φ,S w The set of C The result is obtained by dictionary encoding. By solving equation (44), the relationship between elastic parameters and physical property parameters extracted from well logging data by the joint dictionary is obtained, which conforms to both the rock physics model and the rock physics model.
[0152] Iteratively solving subproblems (1) to (3) realizes the reservoir property parameter prediction method driven by the rock physics model and dictionary.
[0153] The method of this invention was applied to a gas field in the Sichuan Basin to verify its effectiveness. The field included pre-stack seismic data obtained from sampling, as well as well logging data of elastic parameters (P-wave and S-wave velocities, density) and physical property parameters (porosity, permeability, saturation), totaling data from 5 wells, with a sampling time of 1 ms.
[0154] Two wells in the work area were selected for testing, and the inversion effects of the linearized rock physics inversion method and the joint driving method of this invention were compared. In the linearized rock physics inversion method, the Taylor expansion points of each physical property parameter were selected as the average values obtained from well logging data. In the joint driving method of this invention, the joint dictionary training part was tested and selected with an atom length of 40 and a number of atoms of 1600. The training samples were the P-wave and S-wave velocities, densities, and porosity saturation of the two wells, resulting in the trained joint dictionary D. 160×1600 Ultimately, the result is as follows: Figure 3 , 4 The comparison shows the inversion effect of porosity and clay content.
[0155] Depend on Figure 3 , Figure 4 The porosity and clay content profile inversion results from both methods show that the inversion results using the combined driving method exhibit stronger continuity overall compared to the linearized rock physics inversion method, and demonstrate more detailed variations in the vertical direction, thus better reflecting the actual physical distribution of underground strata. Furthermore, the inversion profile results show that the combined driving method of this invention is more similar in morphology to well data than the linearized rock physics inversion method, illustrating the advantages of combining data-driven approaches in this method.
[0156] To further verify the inversion effect of the method of the present invention, a single well was selected from the inversion profile for testing. The results are as follows: Figure 5 As shown.
[0157] The comparison chart of single-well test results shows that while the linearized rock physics inversion method may resemble the actual well data in terms of morphological trends, the inverted values largely deviate from the actual well data. Furthermore, the frequency band of the inversion results is lower. This is because linearized rock physics inversion is derived from elastic parameters obtained from seismic data, which inherently have a low frequency band; therefore, the frequency band of the linearized inversion results is also low. In contrast, the inversion results of the joint-drive method not only inherit the advantages of rock physics inversion in terms of trends but also closely match the actual data in terms of details. Therefore, this verifies that the joint-drive method of this invention is not only more consistent with geological laws but also has higher accuracy in the inversion results.
[0158] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.
Claims
1. A petrophysical model and dictionary jointly driven reservoir property parameter inversion method, characterized in that, include: S1. Establish the pre-stack forward model: ； wherein a seismic signal composed of a post-group of seismic signal vectors of different incidence angles of the same angle gather, a forward operator constructed by a wavelet, P-SV background velocity and fitting coefficients, a model parameter constructed by P-SV and P-P impedances and density; S2. Establish the three elastic parameters. , , With physical property parameters Relationships; ； in, Indicates the longitudinal wave velocity. Indicates the transverse wave velocity. Indicates density, Indicates porosity. and These refer to the longitudinal wave velocities of the solid and fluid phases, respectively. This refers to the transverse wave velocity of the solid phase. and These represent the densities of the solid and fluid phases, respectively; S3. Expand and linearize the relation established in step S2 to obtain the Jacobian matrix and Taylor remainder of each physical property parameter. ; S4. Based on the Jacobian matrix and Taylor remainder of each physical property parameter. A linearized model for forward modeling of rock physics properties is obtained; S3. Learn a joint dictionary of elastic parameters and physical property parameters from well logging data; S4. Based on the linearized model of rock physics forward modeling of physical property parameters and the joint dictionary of elastic and physical property parameters, construct a jointly driven inversion objective function: ； The joint-driven inversion objective function satisfies the following constraints: ； in, Linear operators representing porosity, Linear operators representing clay content, Linear operators representing water saturation, A dictionary of elastic parameters. A dictionary of physical property parameters. A rock physics inversion model with linearized porosity expansion. A linearized rock physics inversion model was developed for mud content. A linearized rock physics inversion model for water saturation is developed. It is a set of physical property parameters. These are the normalized elastic parameters. It is a block matrix. The joint sparse coefficients are obtained from the joint dictionary. Here is the conversion formula between model parameters and elasticity parameters. For inverse normalization operator; S5. Decompose the joint-driven inversion objective function into the following three sub-problems: Sub-problem 1: Considering only model parameters As the variable, the expression corresponding to subproblem one is: ； Subproblem 2: Considering sparsity coefficients Physical properties As the variable, the expression corresponding to subproblem two is: ； Sub-problem 3: Considering the three physical parameters As the variable, the expression corresponding to subproblem three is: ； By iteratively solving these three sub-problems, reservoir property parameter prediction can be achieved through a combination of rock physics model and dictionary-driven approach.
2. The method for inverting reservoir property parameters driven by a rock physics model and dictionary as described in claim 1, characterized in that, The linearized model for the forward rock physics model of physical property parameters is as follows: ； in, Taylor expansion remainder of elastic parameters and rock physics model The difference, elastic parameters include: , , Three parameters, For Jacobian matrices, Specifically, it includes: , , Three parameters, Indicates the clay content, Indicates water saturation.
3. The method for inverting reservoir property parameters driven by a rock physics model and dictionary as described in claim 2, characterized in that, The expression is: ； in, , .
4. The method for inverting reservoir property parameters driven by a rock physics model and dictionary as described in claim 3, characterized in that, The expression is: ； in, , The bulk modulus of water. The bulk modulus of the oil-gas mixture is represented.
5. The reservoir property parameter inversion method jointly driven by rock physics model and dictionary as described in claim 4, characterized in that, The expression is: 。 6. The method for inverting reservoir property parameters driven by a rock physics model and dictionary as described in claim 5, characterized in that, The expression is: ； in, , These represent the density of clay and the density of quartz, respectively.
7. The method for inverting reservoir property parameters driven by a rock physics model and dictionary as described in claim 6, characterized in that, The expression is: ； in, , These represent the density of water and the density of the oil-gas mixture, respectively.