Oil reservoir history fitting method based on ensemble Kalman filtering
By using the ensemble Kalman filtering method in the automatic historical fit of reservoirs, the reservoir geological model is updated in real time, and the limitations of gradient algorithms in automatic historical fit of reservoirs are solved, achieving effective inversion of reservoir parameters and high accuracy of the model.
Patent Information
- Application Number
- CN202311659107.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-05
- Publication Date
- 2025-06-06
AI Technical Summary
The existing gradient algorithms have problems such as local optimal solution traps, large calculation amounts, high requirements for historical data and complex parameter settings in the automatic historical fit of reservoirs, which are difficult to effectively solve the complexity and uncertainty of reservoir dynamic changes.
The gradient-free automatic historical fitting method based on ensemble Kalman filtering is adopted to update the reservoir geological model in real time through the prediction and assimilation steps of the state vector to avoid accompanying gradient calculations, and constrain static parameters.
Effective inversion of reservoir parameters is achieved, the differences in production dynamic data are reduced, the accuracy of the model is improved and the reflection of real reservoir characteristics is reduced, and the uncertainty of reservoir awareness is reduced.
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Figure CN120105652A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of oil and gas field development and proposes an oil reservoir history matching method based on ensemble Kalman filtering. Background Art
[0002] Reservoir simulation history matching refers to simulating the dynamic changes of the reservoir through computer models, and comparing the differences between the simulation results and the actual observation data, so as to correct and optimize the model. In the process of history matching, it is necessary to comprehensively consider geological, engineering, economic and other factors to determine reasonable model parameters and boundary conditions.
[0003] When performing history matching, it is first necessary to collect and organize actual observation data, including reservoir production, pressure, temperature and other data. Then, a reservoir model is established using computer simulation software and the model is initialized based on the collected data. During the simulation process, it is necessary to continuously adjust the model parameters and boundary conditions to make the simulation results as close to the actual observation data as possible.
[0004] The purpose of history matching is to improve the accuracy and precision of reservoir simulation and provide reliable prediction and analysis for the future development of reservoirs. Through history matching, we can understand the dynamic change law of reservoirs, optimize development plans and production strategies, and improve the recovery rate and economic benefits of reservoirs.
[0005] When performing history matching, the following points should be noted:
[0006] 1. Data quality: The actual observation data collected must be accurate and reliable, otherwise it will affect the accuracy and precision of the simulation results.
[0007] 2. Model selection: Select appropriate computer simulation software and model parameters based on the characteristics of the reservoir and actual needs.
[0008] 3. Parameter optimization: During the simulation process, model parameters and boundary conditions need to be continuously adjusted to obtain the best fitting effect.
[0009] 4. Error analysis: Analyze the differences between the simulation results and the actual observed data, understand the deficiencies of the model, and propose improvement measures.
[0010] 5. Update the model: With the continuous increase of actual observation data and changes in the reservoir development stage, the reservoir model needs to be updated and corrected in a timely manner to maintain its accuracy and precision.
[0011] In short, reservoir simulation history matching is one of the very important technical means in reservoir engineering, which can improve the efficiency and economic benefits of reservoir development.
[0012] The history fitting problem of reservoir simulation is a classic inverse problem, which mainly fits the actual production dynamic data by skipping the geological model parameters. Therefore, this problem is usually converted into an optimization problem for solution.
[0013] Gradient algorithm is a commonly used automatic history matching optimization method, but it has some shortcomings in solving the problem of automatic history matching of oil reservoirs. Gradient algorithm is a method based on mathematical optimization, which finds the optimal solution by calculating the gradient of the objective function. However, in the problem of automatic history matching of oil reservoirs, the objective function usually has multiple local optimal solutions, and there may be complex nonlinear relationships and uncertain factors. This makes the gradient algorithm fall into the local optimal solution when solving, and it is impossible to find the true global optimal solution.
[0014] In addition, gradient algorithms usually require a large amount of historical data for training and optimization, which increases the amount of computation and computing time. In the problem of automatic reservoir history matching, historical data may not be sufficient or of low quality, which further limits the performance and effect of gradient algorithms.
[0015] In addition, gradient algorithms usually require manual setting of some parameters, such as learning rate, number of iterations, etc., which have a significant impact on the performance and results of the algorithm. In the problem of automatic reservoir history matching, manual setting of these parameters may become very difficult and time-consuming due to the complexity and uncertainty of the problem.
[0016] In summary, gradient algorithms have some shortcomings in solving the problem of automatic history matching of reservoirs, and more effective and reliable methods are needed to improve and perfect them.
[0017] Newton-type methods are the most widely used methods in gradient algorithms. The Gauss-Newton method is difficult to handle large-scale reservoir history matching problems. With the application of the limited storage BFGS method (LBFGS) to the problem of automatic reservoir history matching, it provides a new idea for solving large-scale reservoir history matching problems. Although the gradient algorithm is an effective method to solve the problem of automatic reservoir history matching, the gradient still needs to be calculated using the adjoint method. This requires reservoir workers to have professional numerical simulation knowledge. The adjoint method solves the gradient code and embeds it into the reservoir simulator code. The cost of dissecting and compiling the reservoir simulator alone is huge, so this method cannot be well transplanted to various general simulators. In view of the limitations of gradient algorithms, many foreign scholars have also conducted research on automatic reservoir history matching based on non-gradient optimization methods.
[0018] With the introduction of the stochastic perturbation gradient approximation (SPSA) algorithm into automatic history matching research, the application of the standard SPSA algorithm to reservoir case tests shows that although this method can fit the actual production data relatively well, its convergence speed is slow and the computational efficiency is low. Summary of the invention
[0019] The purpose of the present invention is to propose a reservoir history matching method based on ensemble Kalman filtering in view of the deficiencies in the prior art.
[0020] One of the technical solutions of the present invention:
[0021] An automatic reservoir fitting method based on ensemble Kalman filtering comprises the following steps:
[0022] a1. Obtain reservoir parameters;
[0023] a2. Set the state vector;
[0024] a3. Based on the automatic history fitting of the ensemble Kalman filter, the updated state vector at the current moment is obtained, and the predicted state vector at the next moment is calculated. It is continuously updated over time to gradually correct the system state vector.
[0025] Furthermore, the state vector is y n,j :
[0026]
[0027] Assume that the number of set members is N e y n,j represents the state vector of member j at time n; m, p n , d n Represent three types of parameters of the reservoir model; among them, m represents N m Static parameters of dimension; p n Represents N p Dynamic parameters of dimension; d n Represents N d Dimensional production data.
[0028] Furthermore, the step a3 includes two parts: a prediction step and an assimilation step.
[0029] Furthermore, the prediction step includes:
[0030] F(·) represents the reservoir simulator, i.e.
[0031]
[0032]
[0033] In the formula, f represents the predicted value; u represents the updated value; is the predicted state vector of set member j at time n; the updated state vector of a set member at time n-1 is
[0034]
[0035] Furthermore, the step a3 also includes observation of dynamic parameters and production data, and the observation equation is:
[0036]
[0037] Where O is N d ×(N m +N p )-dimensional zero matrix; I is N d ×N d dimensional identity matrix; v(n) is the observation error, and
[0038] Furthermore, the prediction step also includes:
[0039] Get a sample of observation data with perturbations For any set member j, the data can be realized as follows:
[0040]
[0041] Among them, C Dn is the covariance matrix of the production data, Decomposition of C using the square method Dn , the solution is the square root matrix L D ; Z D N d A ×1-dimensional polynomial random variable with mean 0 and standard deviation 1.
[0042] Further, the assimilation step comprises:
[0043] The collective Kalman gain matrix K is obtained by calculating formula (1.8) n ; The predicted state vector can be updated by formula (1.7);
[0044]
[0045]
[0046]
[0047] in, is the predicted covariance, Represents the mean of the state vector; the updated covariance matrix can be obtained by formula (1.10)
[0048]
[0049] Furthermore, the step a3 further includes:
[0050] Predicted state vector By absorbing production data through formula (1.7), the state vector updated at the current moment can be obtained: in The predicted state vector at the next moment can be calculated using formula (1.2): With the continuous updating over time, the system state vector is gradually corrected.
[0051] The second technical solution of the present invention:
[0052] An automatic reservoir fitting method based on ensemble Kalman filtering includes the following calculation steps:
[0053] b1. Give uncertain parameters and set the range of the parameters, including permeability, porosity and conductivity;
[0054] b2. Use Gaussian distribution to sample uncertain parameters so that the samples are representative;
[0055] b3. Generate certain trial calculation examples;
[0056] b4. Call the reservoir numerical simulation software to calculate the generated example and obtain complete calculation production data; b5. Define the evaluation objective function, calculate the objective function and judge the error between the calculated data and the observed data;
[0057] b6. Obtain the final static parameters and output the final updated calculation results.
[0058] Furthermore, the step b5 includes: if the maximum iteration step is reached, then the process ends; if not, then the static parameters are updated and the next step is performed.
[0059] The beneficial effects of the present invention are:
[0060] The ensemble Kalman filter method adopted in the present invention is a gradient-free automatic history fitting method, which is implemented based on a group of reservoir models. By continuously absorbing actual production observation data, the reservoir geological model is updated in real time. It avoids accompanying gradient calculation, facilitates program development, debugging and maintenance, and the updated reservoir model can reflect the uncertainty of the real reservoir to a certain extent. The state vector in the initial set is normalized, and the static parameters of the reservoir such as permeability are constrained, and the static parameter field of the reservoir such as the permeability field is estimated. The results show that the difference in production dynamic data achieved by each reservoir model is significantly reduced and is consistent with the real observation value. It can effectively perform parameter inversion on the reservoir and provide guiding suggestions for adjusting production measures. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] Figure 1 Flowchart for automatic history matching calculation of ensemble Kalman filter;
[0062] Figure 2 This is the result of 10-step iteration of the ENKF algorithm;
[0063] Figure 3 This is the result of 30 iterations of the ENKF algorithm;
[0064] Figure 4 This is the 30-step iteration result of the bottom hole flowing pressure of Well W1;
[0065] Figure 5 This is the result of 30 iterations of the bottom hole flowing pressure of Well W2. DETAILED DESCRIPTION
[0066] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.
[0067] Embodiment 1:
[0068] An automatic reservoir fitting method based on ensemble Kalman filtering comprises the following steps:
[0069] (1) Set the state vector. To use the state vector to represent the model parameters and observations, we first need to set the state vector y n,j .
[0070]
[0071] Assume that the number of set members is N e y n,j Represents the state vector of member j at time n. m, pn , d n Represent three types of parameters of the reservoir model. Among them, m represents N m Static parameters of dimension; p n Represents N p Dynamic parameters of dimension; d n Represents N d Dimensional production data.
[0072] (2) Automatic history fitting method based on ensemble Kalman filtering.
[0073] The method as a whole consists of two parts: prediction step and assimilation step.
[0074] First is the prediction step, where F(·) represents the reservoir simulator INSIM connection unit software, i.e.
[0075]
[0076]
[0077] In the formula, f represents the predicted value; u represents the updated value; is the state vector of the set member j after being updated by the reservoir simulator at time n. The state vector of a set member after being updated at time n-1 is
[0078]
[0079] In the prediction step, as shown in formula (1.4), the static parameters updated at the previous moment are equal to the static parameters predicted at the current moment. However, dynamic parameters and production data change over time.
[0080] The observation equation is:
[0081]
[0082] Where O is N d ×(N m +N p )-dimensional zero matrix; I is N d ×N d dimensional identity matrix; v(n) is the observation error, and
[0083] Get a sample of observation data with perturbations For any set member j, the data can be realized as follows:
[0084]
[0085] Among them, C Dn is the covariance matrix of the production data, Decomposition of C using the square method Dn , the solution is the square root matrix L D ; Z D N d A ×1-dimensional polynomial random variable with mean 0 and standard deviation 1.
[0086] Next is the assimilation step. First, we need to calculate formula (1.8) to obtain the collective Kalman gain matrix K n The predicted state vector can be updated by formula (1.7).
[0087]
[0088]
[0089]
[0090] in, is the predicted covariance, Represents the mean of the state vector. The updated covariance matrix can be obtained by equation (1.10).
[0091]
[0092] Predicted state vector By absorbing production data through formula (1.7), the state vector updated at the current moment can be obtained: in The predicted state vector at the next moment can be calculated using formula (1.2): With the continuous updating over time, the system state vector is gradually corrected.
[0093] Embodiment 2:
[0094] The specific process of an automatic reservoir fitting technology based on ensemble Kalman filtering is as follows:
[0095] 1. In step 1, the uncertain parameters are given and the range of the parameters is set. These are mainly parameters such as permeability, porosity, and conductivity;
[0096] 2. In step 1, use Gaussian distribution to sample uncertain parameters so that the samples are representative;
[0097] 3. In step 1, generate certain trial calculation examples;
[0098] 4. As in step 2, perform ensemble Kalman filter update, call reservoir numerical simulation software to calculate the generated example, and obtain complete calculation production data;
[0099] 5. After each update of the state variables in step 2, calculate the objective function and determine the error between the calculated data and the observed data. If the maximum iteration step is reached, the process ends; if not, update the static parameters and proceed to the next step;
[0100] 6. Obtain the final static parameters and output the final updated calculation results, and step 2 ends.
[0101] Embodiment three:
[0102] Using the INSIM reservoir numerical simulation software based on the connection unit system, the EnKF method was used to perform historical fitting on the two-dimensional heterogeneous reservoir model. The 30 models generated in the previous sequential Gaussian simulation were selected as the initial model realizations, and the dynamic data of the first 1800 days were used to assimilate the data of each model realization. The conductivity distribution of some model realizations before and after data assimilation is shown in the figure. As can be seen from the figure, the permeability distribution between the initial model realizations is quite different, but after data assimilation, the difference in the conductivity distribution of each connection unit is significantly reduced, and compared with the permeability of the real reservoir model, each realization has a good grasp of the real characteristics of the reservoir, especially more accurately reflects the location of the high permeability strip. Therefore, it can be seen that the essence of using the EnKF method for historical fitting is to further reduce the differences between the model realizations on the basis of the inversion reservoir model parameters, so as to improve the understanding of the uncertainty of future reservoir prediction effects.
[0103] The model was optimized for 30 steps in total. The calculation results of the model are as follows: Figure 3 As shown in the figure, compared with the calculated production dynamic data of the initial model, the difference in production dynamic data achieved by each reservoir model based on the EnKF method is significantly reduced, and it is consistent with the actual observation value. After the update, each model has a better grasp of the future production dynamic changes of the reservoir, effectively reducing the uncertainty of reservoir understanding.
[0104] With the development of digital computing technology and modern algorithms, the ensemble Kalman filter method has been widely used in recent years as a new type of automatic history matching method. The state vector in the initial set is normalized, and the static parameters of the reservoir such as conductivity are constrained to estimate the static parameter field of the reservoir such as the permeability field. The results show that the difference in production dynamic data achieved by each reservoir model based on the EnKF method is significantly reduced, and it is consistent with the real observation value. Finally, a new method for inversion of large-scale fracturing models is proposed. First, the conductivity and other inversion parameters are preset, and a certain initial set is generated by a random algorithm within the set value range of the parameters to meet the distribution characteristics of the reservoir parameters. Experiments show that the automatic history matching of the ensemble Kalman filter method can effectively perform parameter inversion on the reservoir.
[0105] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims.
Claims
1. An automatic reservoir fitting method based on ensemble Kalman filtering, It is characterized in that The steps include: a1. Obtain reservoir parameters; a2. Set the state vector; a3. Based on the automatic history fitting of the ensemble Kalman filter, the updated state vector at the current moment is obtained, and the predicted state vector at the next moment is calculated. It is continuously updated over time to gradually correct the system state vector.
2. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 1, It is characterized in that The state vector is y n,j : Assume that the number of set members is N e y n,j represents the state vector of member j at time n; m, p n , d n Represent three types of parameters of the reservoir model; among them, m represents N m Static parameters of dimension; p n Represents N p Dynamic parameters of dimension; d n Represents N d Dimensional production data.
3. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 2, It is characterized in that The step a3 includes two parts: a prediction step and an assimilation step.
4. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 3, It is characterized in that The prediction step includes: F(·) represents the reservoir simulator, i.e. In the formula, f represents the predicted value; u represents the updated value; is the predicted state vector of set member j at time n; the updated state vector of a set member at time n-1 is 5. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 4, It is characterized in that The step a3 also includes observation of dynamic parameters and production data, and the observation equation is: Where O is N d ×(N m +N p )-dimensional zero matrix; I is N d ×N d dimensional identity matrix; v(n) is the observation error, and 6. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 5, It is characterized in that The prediction step also includes: Get a sample of observation data with perturbations For any set member j, the data can be realized as follows: Among them, C Dn is the covariance matrix of the production data, Decomposition of C using the square method Dn , the solution is the square root matrix L D ; Z D N d A ×1-dimensional polynomial random variable with mean 0 and standard deviation 1.
7. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 6, It is characterized in that The assimilation step comprises: The collective Kalman gain matrix K is obtained by calculating formula (1.8) n ; The predicted state vector can be updated by formula (1.7); in, is the predicted covariance, Represents the mean of the state vector; the updated covariance matrix can be obtained by formula (1.10) 8. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 7, It is characterized in that The step a3 further comprises: Predicted state vector By absorbing production data through formula (1.7), the state vector updated at the current moment can be obtained in The predicted state vector at the next moment can be calculated using formula (1.2): With the continuous updating over time, the system state vector is gradually corrected.
9. An automatic reservoir fitting method based on ensemble Kalman filtering, It is characterized in that The calculation steps include: b1. Give uncertain parameters and set the range of the parameters, including permeability, porosity and conductivity; b2. Use Gaussian distribution to sample uncertain parameters so that the samples are representative; b3. Generate certain trial calculation examples; b4. Call the reservoir numerical simulation software to calculate the generated example and obtain complete calculation production data; b5. Define the objective function of the evaluation, calculate the objective function and determine the error between the calculated data and the observed data; b6. Obtain the final static parameters and output the final updated calculation results.
10. The automatic reservoir fitting method based on ensemble Kalman filtering according to claim 9, It is characterized in that The step b5 includes: if the maximum iteration step is reached, then the process ends; if not, then the static parameters are updated and the process proceeds to the next step.