Artificial intelligence virtual well sample expansion method based on geostatistics

Abstract

The invention provides an artificial intelligence virtual well sample expansion method based on geostatistics. The sample expansion method comprises the following steps: performing statistical analysis according to logging data to obtain prior information; a sequential indication simulation algorithm simulates lithology conforming to prior information; checking statistical parameters of the simulated lithofacies and dividing the lithofacies of the virtual well; performing sequential Gaussian simulation on the fractal phase, and simulating physical properties and elastic parameters by a sequential Gaussian co-simulation algorithm; combining each well to obtain lithology, physical property and elastic parameters of the complete well; and physical properties and elastic parameters of the simulated lithofacies are checked by using the statistical magnitude and the variation function. The accuracy of the simulation data is verified through statistical analysis, the consistency of the simulation data and actual well data is ensured, and the credibility of the virtual well sample is enhanced.

Description

Technical Field

[0001] This invention relates to the field of oil and gas exploration, and in particular to an artificial intelligence virtual well sample expansion method based on geostatistics. Background Technology

[0002] In recent years, artificial intelligence has shown great potential in the field of seismic exploration. In 2001, Hampson et al. used neural networks to quantitatively predict elasticity and rock properties from seismic data. This supervised learning technique derived a statistical relationship between well logging data and seismic data. This relationship was then applied to seismic data to estimate the logging properties at other locations in seismic exploration. However, a limiting factor for this analysis is the need for sufficient labeled data (i.e., well control) to train and validate this relationship. In seismic exploration, however, due to high drilling costs, well logging data is scarce, while the amount of data from the work area is enormous. Several researchers have adopted various methods to increase the amount of training data. Wang et al. (2019) performed a series of transformations on labeled data to increase the amount of available data. Although previous researchers have explored the idea of ​​supplementing the training set with synthetic data (Wang et al., 2019), it cannot be guaranteed that the pseudo-logging curves generated using these techniques follow the same rock physics laws as the original logging curves. Summary of the Invention

[0003] In view of the above problems, the present invention is proposed to provide a geostatistical-based artificial intelligence virtual well sample expansion method to overcome or at least partially solve the above problems.

[0004] According to one aspect of the present invention, an artificial intelligence virtual well sample expansion method based on geostatistics is provided, the sample expansion method comprising:

[0005] Prior information is obtained through statistical analysis of well logging data;

[0006] Sequential indicator simulation algorithms simulate lithology that conforms to prior information;

[0007] Examine the statistical parameters of the simulated lithofacies and classify the lithofacies of the virtual well;

[0008] Sequential Gaussian simulation and sequential Gaussian co-simulation algorithms were used to simulate physical properties and elastic parameters based on lithofacies.

[0009] By combining the data from each well, the lithology, physical properties, and elastic parameters of the complete well are obtained.

[0010] Statistical measures and variograms were used to examine the physical and elastic parameters of the simulated lithofacies.

[0011] Optionally, the step of obtaining prior information through statistical analysis of well logging data specifically includes:

[0012] The original well data were divided according to lithofacies type;

[0013] The statistical parameters required to analyze the spatial model of each variable in each lithofacies.

[0014] Optionally, the step of dividing the original well data according to lithofacies type specifically includes:

[0015] To address the non-stationarity of well logging data, the original well data is divided according to lithofacies type, so that statistical data within the same lithofacies are considered stationary.

[0016] Optionally, the statistical parameters required for the spatial model of each variable in each lithofacies include: histogram, spatial continuity model, and correlation between variables.

[0017] Optionally, the statistical parameters required for the spatial model of each variable in each lithofacies include:

[0018] The variogram assesses how data changes at multiple distances and measures the spatial correlation between data.

[0019] The formula for the function of variation mentioned in the description is as follows:

[0020]

[0021] γ(h) is the variogram value with lag distance h, and N(h) is the number of data pairs z(μ) at distance h. α ),z(μ α +h) are the spatial sampled values ​​of the head and tail with a lag distance of h, respectively.

[0022] Optionally, the sequential indication simulation algorithm for simulating lithology that conforms to prior information specifically includes:

[0023] Calculate the probabilistic mass function of lithofacies;

[0024] Calculation of lithofacies probability based on the indicative kriging method;

[0025] Based on the lithofacies probability, a lithofacies sequence is generated by sampling.

[0026] Optionally, the probabilistic mass function for calculating lithofacies specifically includes:

[0027] Based on prior information and statistical analysis, calculate the probability mass function for each lithofacies.

[0028] There are N lithofacies, each lithofacies being F1, F2, ..., F N ;

[0029] For a certain lithofacies F iIts probability mass function is expressed as:

[0030]

[0031] Optionally, the calculation of lithofacies probability based on the indicator kriging method specifically includes:

[0032] At simulated location v, the lithofacies probability of a given location is calculated based on the lithofacies values ​​of previously simulated locations;

[0033] Assume the previous simulated locations near P are P1, P2, ..., P m The corresponding lithofacies value is

[0034] The indicated kriging method is used to calculate the lithofacies F at a given location P. i The probability of:

[0035]

[0036] in, It is an indicator function, when The value is 1 if it is true, and 0 otherwise.

[0037] Based on the calculated lithofacies probabilities, lithofacies sequences are generated through sampling.

[0038] At the simulated location P, the lithofacies with the highest probability is selected as the simulation result.

[0039] Optionally, the step of checking the statistical parameters of the simulated lithofacies and classifying the lithofacies of the virtual well specifically includes:

[0040] Perform statistical analysis on the simulated virtual well data to check whether it meets the lithofacies distribution ratio of the actual well data;

[0041] Calculate the virtual well transition matrix, which represents the probability of transitioning from one given lithofacies to another.

[0042] When the simulated virtual lithofacies matches the distribution of real lithofacies, the virtual lithofacies are divided.

[0043] Optionally, the simulation of physical properties and elastic parameters by sequential Gaussian simulation and sequential Gaussian co-simulation algorithms for different lithofacies specifically includes:

[0044] Normal transformation property parameters:

[0045] Perform a normal transformation on the physical property parameters to ensure that the data follows a normal distribution;

[0046] Assuming the original physical property parameter is X, the transformed parameter Y obtained after normal transformation is expressed as:

[0047]

[0048] Where, μ X and σ X These are the mean and standard deviation of the original physical property parameters;

[0049] Simulated physical property distribution and variation function of rock physical properties:

[0050] For each lithofacies F i The physical property distribution is obtained based on the corresponding well logging curves;

[0051] Assume the physical properties corresponding to the well logging curve are Using a Gaussian distribution to simulate the distribution of physical properties, it can be represented as:

[0052]

[0053] When simulating the variation function of rock physical properties, a similar Gaussian function is used to consider the spatial correlation of geological properties:

[0054] γY(h)=C Y ·e -aY·e

[0055] Sequential Gaussian simulation of filled reservoir properties:

[0056] Sequential Gaussian simulations were used to populate each lithofacies with the simulated physical property values;

[0057] For each simulated location P, the transformed physical property values ​​are obtained by randomly sampling from the physical property distribution. The physical properties at the simulated location P are obtained by inverse normal transformation.

[0058]

[0059] reservoir physical properties Fill into the corresponding lithofacies F i middle.

[0060] Optionally, the method for generating the elasticity parameter includes:

[0061] Based on reservoir properties and a rock physics model, elastic properties are generated, realizing the generation of labeled and trained geophysical constraint data;

[0062] Based on statistical data, elastic properties are directly simulated within a predefined lithofacies range.

[0063] This invention provides an artificial intelligence virtual well sample expansion method based on geostatistics. The sample expansion method includes: obtaining prior information through statistical analysis of well logging data; simulating lithology that conforms to the prior information using a sequential indicator simulation algorithm; checking the statistical parameters of the simulated lithofacies and classifying the lithofacies of the virtual well; performing sequential Gaussian simulation and sequential Gaussian co-simulation algorithms to simulate physical and elastic parameters for each lithofacies; merging the lithology, physical properties, and elastic parameters of each well to obtain the complete well's lithology; and checking the physical properties and elastic parameters of the simulated lithofacies using statistics and variograms. Statistical analysis verifies the accuracy of the simulated data, ensuring its consistency with actual well data and enhancing the credibility of the virtual well sample.

[0064] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 A flowchart of an artificial intelligence virtual well sample expansion method based on geostatistics provided for an embodiment of the present invention. Detailed Implementation

[0067] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0068] The terms "comprising" and "having," and any variations thereof, in the specification, embodiments, claims, and drawings of this invention are intended to cover non-exclusive inclusion, such as including a series of steps or units.

[0069] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0070] like Figure 1As shown, the purpose of this invention is to provide an artificial intelligence virtual well sample expansion method based on sequential indicator simulation to establish lithofacies and sequential Gaussian simulation to generate corresponding physical property parameters for each lithofacies.

[0071] Traditional methods often neglect the interrelationships between geological parameters when generating virtual well samples, resulting in simulation results that are not consistent with the actual situation.

[0072] This invention achieves a more accurate simulation of the correlation between geological properties by using the sequential instruction simulation method for discrete property (lithology) simulation, the sequential Gaussian simulation method for continuous property (physical properties, elastic parameters) simulation, and a precise combination of the two, demonstrating innovation in model consistency.

[0073] Specific technical solution of the present invention:

[0074] (1) Prior information is obtained by statistical analysis based on known well logging data.

[0075] This process yields statistical regularities for the vertical distribution of lithofacies (lithhofacies type, proportion of each lithofacies, etc.) and reservoir properties (such as porosity, water saturation, clay volume, etc.) or elastic properties (velocity, density, impedance, etc.), including averages, standard deviations, and correlation coefficients. Statistical analysis using known well logging data not only obtains prior information but also reveals the statistical regularities of the vertical distribution of lithofacies and reservoir properties (or elastic properties). The integration of prior information provides a practical geological basis for subsequent simulation processes.

[0076] 1) Classification of lithofacies

[0077] To address the non-stationarity of well logging data, this invention employs a unique method to categorize the raw well data according to lithofacies type, thus treating statistical data within the same lithofacies as stationary. This unconventional approach emphasizes sensitivity to data characteristics and innovation. Through this step, the invention bypasses traditional assumptions and more accurately captures the actual characteristics of geological data. The statistical parameters of each lithofacies are analyzed.

[0078] 2) Analyze all the statistical parameters required for the spatial model of each variable in each lithofacies. This typically includes histograms, spatial continuity models, and correlations between variables.

[0079] The variogram assesses how data changes at different distances, thus measuring the spatial correlation between data points. The formula for the variogram mentioned in the description is as follows:

[0080]

[0081] γ(h) is the variogram value with a lag distance of h, and N(h) is the number of data pairs z(μ) at a distance of h. α ),z(μ α +h) represent the spatial sampled values ​​at the head and tail of the data with a lag distance of h, respectively. The variogram provides useful information about the spatial continuity and variance of the data. It applies random function theory and considers not only the relationship between the location of the point to be estimated and the location of the known data, but also the spatial correlation of the variables.

[0082] (2) Sequential indicator simulation algorithm simulates lithology that conforms to prior information.

[0083] This invention introduces a sequential indicator simulation method to simulate discrete geological properties such as lithofacies, eliminating the reliance on the Gaussian assumption in traditional methods. By calculating lithofacies probabilities using the indicator kriging method, based on values ​​from previously simulated locations rather than a Gaussian distribution, a novel approach to lithofacies simulation is provided.

[0084] 1) Calculate the probabilistic mass function of the lithofacies:

[0085] First, based on prior information and statistical analysis, the probability mass function for each lithofacies is calculated. Assume there are N lithofacies, each labeled F1, F2, ..., F... N For a certain lithofacies F i Its probability mass function is expressed as:

[0086]

[0087] 2) Calculation of lithofacies probability based on the indicator kriging method:

[0088] At simulated location P, the lithofacies probability for a given location is calculated based on lithofacies values ​​from previous simulated locations. Assume the previous simulated locations near P are P1, P2, ..., P... m The corresponding lithofacies value is The indicator kriging method can be used to calculate the lithofacies F at a given location P. i The probability of:

[0089]

[0090] in, It is an indicator function, when It is 1 if it is true, otherwise it is 0.

[0091] Based on the calculated lithofacies probabilities, a lithofacies sequence is generated through sampling. At the simulation location P, the lithofacies with the highest probability is selected as the simulation result.

[0092] 3) Generation of lithofacies sequence:

[0093] Based on the calculated lithofacies probabilities, lithofacies sequences are generated through sampling.

[0094] At the simulated location P, the lithofacies with the highest probability is selected as the simulation result.

[0095] (3) Check the statistical parameters of the simulated lithofacies and classify the lithofacies of the virtual well.

[0096] Statistical analysis is performed on simulated virtual well data to check whether it matches the lithofacies distribution ratio of actual well data. Simultaneously, the virtual well transformation matrix (the core of the Markov chain) can be calculated, which represents the probability of transitioning from one given lithofacies to another. The transformation matrix reflects the proportion of lithofacies, the average thickness of the lithofacies, and the frequency of transitions. When the simulated virtual lithofacies match the distribution of real lithofacies, the virtual lithofacies are classified.

[0097] (4) Sequential Gaussian simulation and sequential Gaussian co-simulation algorithm are used to simulate physical properties and elastic parameters according to the lithofacies.

[0098] Simulations of physical property parameters often only consider global trends, with limited ability to simulate details and local variations. The innovative method introduced in this invention extends the simulation of physical properties from the global to the detailed through sequential Gaussian simulation, more realistically reflecting the complexity and heterogeneity of geological attributes. It not only simulates the distribution of physical properties based on well logging curves but also considers the spatial correlation within the reservoir through sequential Gaussian simulation. This process encompasses the microscopic variations of geological attributes, further reflecting the heterogeneity of the reservoir. The refined simulation can better capture the true changes in geological attributes.

[0099] 1) Normal transformation property parameters:

[0100] First, the physical property parameters are transformed normally to ensure that the data follows a normal distribution.

[0101] Assuming the original physical property parameter is X, the transformed parameter Y obtained after normal transformation is expressed as:

[0102]

[0103] Where: μ X and σ X These are the mean and standard deviation of the original physical property parameters.

[0104] 2) Simulation of physical property distribution and variation function of rock physical properties:

[0105] For each lithofacies F i The physical property distribution is obtained based on the corresponding well logging curves (such as porosity curves, permeability curves, etc.). Assume the physical property corresponding to the well logging curve is... Using a Gaussian distribution to simulate the distribution of physical properties, it can be represented as:

[0106]

[0107] When simulating the variation function of rock physical properties, a similar Gaussian function is used to consider the spatial correlation of geological properties:

[0108] γY(h=C Y ·e -aY·h

[0109] 3) Sequential Gaussian simulation of filled reservoir properties:

[0110] Sequential Gaussian simulations were used to fill the simulated physical property values ​​into each lithofacies.

[0111] For each simulated location P, the transformed physical property values ​​are obtained by randomly sampling from the physical property distribution. The physical properties at the simulated location P are obtained by inverse normal transformation.

[0112]

[0113] Ultimately, the reservoir physical properties will be... Fill into the corresponding lithofacies F i middle.

[0114] There are two methods to generate elasticity parameters:

[0115] Based on reservoir properties, elastic properties are generated using a rock physics model, enabling the generation of labeled and trained geophysical constraint data.

[0116] Based on the obtained statistical data, elastic properties can be directly simulated within a predefined lithofacies range without generating reservoir properties. The method of this invention is consistent with the method for simulating physical property parameters.

[0117] By combining the data from each well, the lithology, physical properties, and elastic parameters of the complete well are obtained.

[0118] Statistical measures and variograms were used to examine the physical properties and elastic parameters of the simulated lithofacies.

[0119] This invention not only generates lithological, physical, and elastic parameters, but also verifies the accuracy of the simulated data through statistical analysis, ensuring its consistency with actual well data. This innovation in verifying and refining simulation results further enhances the credibility of the virtual well samples. In the final generation of complete well data, this invention emphasizes the focus on and guarantee of the quality of the simulated data.

[0120] Beneficial effects: First, it conforms to prior knowledge. This method is based on known logging data and utilizes prior information from the logging data, such as the proportion of lithology, the corresponding physical properties of each lithology, the distribution of elastic parameters and their mean and variance, etc. Therefore, the synthesized virtual well sample has the characteristic of being consistent with the actual logging data.

[0121] Second, it possesses random diversity. Geostatistical simulation is a stochastic algorithm that uses spatial correlation models to sample random fields to simulate expected spatial variability, thereby generating a highly detailed realization of the attribute parameters of interest. It can reflect the structure of regionalized variables through randomness and better reflect the spatial variation characteristics of geological variables.

[0122] Third, the number of virtual well samples is unlimited. This method simulates based on prior knowledge of known logging data, producing a large number of virtual well samples. Compared to actual drilling, this method is not limited by drilling costs and generates a large number of samples for machine learning.

[0123] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for expanding virtual well samples based on geostatistics using artificial intelligence, characterized in that, The sample augmentation method includes: Prior information is obtained through statistical analysis of well logging data; Sequential indicator simulation algorithms simulate lithology that conforms to prior information; Examine the statistical parameters of the simulated lithofacies and classify the lithofacies of the virtual well; Sequential Gaussian simulation and sequential Gaussian co-simulation algorithms were used to simulate physical properties and elastic parameters based on lithofacies. By combining the data from each well, the lithology, physical properties, and elastic parameters of the complete well are obtained. Statistical measures and variograms were used to examine the physical and elastic parameters of the simulated lithofacies.

2. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The prior information obtained through statistical analysis of well logging data specifically includes: The original well data were divided according to lithofacies type; The statistical parameters required to analyze the spatial model of each variable in each lithofacies.

3. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The specific division of each raw well data according to lithofacies type includes: To address the non-stationarity of well logging data, the original well data is divided according to lithofacies type, so that statistical data within the same lithofacies are considered stationary.

4. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The specific statistical parameters required for the spatial model of each variable in each lithofacies include: histogram, spatial continuity model, and correlation between variables.

5. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The statistical parameters required for analyzing the spatial model of each variable in each lithofacies specifically include: The variogram assesses how data changes at multiple distances and measures the spatial correlation between data. The formula for the function of variation mentioned in the description is as follows: γ(h) is the variogram value with a lag distance of h, and N(h) is the number of data pairs z(μ) at a distance of h. α ),z(μ α +h) are the spatial sampled values ​​of the head and tail with a lag distance of h, respectively.

6. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The sequential indicator simulation algorithm simulates lithology that conforms to prior information, specifically including: Calculate the probabilistic mass function of lithofacies; Calculation of lithofacies probability based on the indicative kriging method; Based on the lithofacies probability, a lithofacies sequence is generated by sampling.

7. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 6, is characterized in that... The probabilistic mass function for calculating lithofacies specifically includes: Based on prior information and statistical analysis, calculate the probability mass function for each lithofacies. There are N lithofacies, each lithofacies being F1, F2, ..., F N ; For a certain lithofacies F i Its probability mass function is expressed as:

8. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 6, is characterized in that... The calculation of lithofacies probability based on the indicator kriging method specifically includes: At simulated location P, the lithofacies probability of a given location is calculated based on the lithofacies values ​​of previously simulated locations. Assume the previous simulated locations near P are P1, P2, ..., P m The corresponding lithofacies value is Indicative Kriging method is used to calculate lithofacies F at a given location P. i The probability of: in, It is an indicator function, when The value is 1 if it is true, and 0 otherwise. Based on the calculated lithofacies probabilities, lithofacies sequences are generated through sampling. At the simulated location P, the lithofacies with the highest probability is selected as the simulation result.

9. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The process of checking the statistical parameters of the simulated lithofacies and classifying the lithofacies of the virtual well specifically includes: Perform statistical analysis on the simulated virtual well data to check whether it meets the lithofacies distribution ratio of the actual well data; Calculate the virtual well transition matrix, which represents the probability of transitioning from one given lithofacies to another. When the simulated virtual lithofacies matches the distribution of real lithofacies, the virtual lithofacies are divided.

10. A method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, characterized in that, The simulation of physical properties and elastic parameters by sequential Gaussian simulation and sequential Gaussian co-simulation algorithms for different lithofacies specifically includes: Normal transformation property parameters: Perform a normal transformation on the physical property parameters to ensure that the data follows a normal distribution; Assuming the original physical property parameter is X, the transformed parameter Y obtained after normal transformation is expressed as: Where, μ X and σ X These are the mean and standard deviation of the original physical property parameters; Simulated physical property distribution and variation function of rock physical properties: For each lithofacies F i The physical property distribution is obtained based on the corresponding well logging curves; Assume the physical properties corresponding to the well logging curve are Using a Gaussian distribution to simulate the distribution of physical properties, it can be represented as: When simulating the variation function of rock physical properties, a similar Gaussian function is used to consider the spatial correlation of geological properties: γY(h)=C Y ·e -aY·h Sequential Gaussian simulation of filled reservoir properties: Sequential Gaussian simulations were used to fill in the simulated physical property values ​​into each lithofacies; For each simulated location P, the transformed physical property values ​​are obtained by randomly sampling from the physical property distribution. The physical properties at the simulated location P are obtained by inverse normal transformation. reservoir physical properties Fill into the corresponding lithofacies F i middle.

11. The method for expanding virtual well samples based on geostatistics using artificial intelligence, as described in claim 1, is characterized in that... The method for generating the elastic parameters includes: Based on reservoir properties and a rock physics model, elastic properties are generated, enabling the generation of labeled and trained geophysical constraint data. Based on statistical data, elastic properties are directly simulated within a predefined lithofacies range.

Images