A repeated fracturing well production time series data decomposition method based on minimum absolute deviation loss

Abstract

The application provides a repeated fracturing well production time series data decomposition method based on minimum absolute deviation loss, comprising the following steps: (S1) collecting and arranging original data; (S2) using bilateral filtering to denoise input data; (S3) robustly extracting a trend by solving minimum absolute deviation regression with sparse regularization; (S4) using non-local seasonal filtering to obtain a seasonal component; (S5) adjusting the trend and the season; (S6) repeating steps 2-5 until the calculation result converges. The application can stably extract a seasonality and a trend from a long seasonal cycle and high-noise data, and can provide a solid foundation for subsequent fitting and prediction of repeated fracturing production data.

Description

Technical Field

[0001] This invention relates to the field of reservoir production enhancement technology, specifically to a method for decomposing time series data of production from repeatedly fractured wells based on minimum absolute deviation loss. Background Technology

[0002] Repeated fracturing production data samples often exhibit high dimensionality and non-stationarity, and typically contain excessive noise, outliers, or missing values, posing challenges to modeling production time series data. Real-world time series data usually consists of three parts: seasonality, trend, and residuals. Time series decomposition can break down complex time series data into independent and interpretable components. Researchers can reveal potential trends and patterns that may be hidden in the original analysis, leading to a deeper understanding of the data. This is particularly useful when dealing with data with inherent seasonal variations or focusing on long-term trends. Taking repeated fracturing production data of oil wells as an example: if the raw data is used directly for production prediction, noise and random fluctuations in the original data series will interfere with the prediction. Therefore, first decomposing the time series into basic components and matching each component with a relatively simple specialized model may yield better results than simply building increasingly complex prediction models.

[0003] Existing time series data decomposition methods are not good at extracting seasonal and trend features from data with long seasonal cycles and high noise. One reason is that the underlying sum of squares loss function requires the assumption that the error is normally distributed, and the square will amplify the contribution of outliers to the total loss, reducing the robustness of the algorithm. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a method for decomposing time-series production data of repeatedly fractured wells based on minimum absolute deviation loss. The method exhibits excellent data cleaning performance, stably extracting seasonality and trends from long-term and high-noise data, thus providing a solid foundation for subsequent fitting and prediction of repeatedly fractured well production data.

[0005] The present invention adopts the following technical solution:

[0006] A method for decomposing time series data of production from repeatedly fractured wells based on minimum absolute deviation loss includes the following steps:

[0007] Step 1: Input the time series data of production from repeatedly fractured wells;

[0008] Step 2: Use bilateral filtering to denoise the input data;

[0009] Step 3: Robustly extract the trend by solving the minimum absolute deviation regression with sparse regularization;

[0010] Step 4: Use nonlocal seasonality filtering to obtain seasonal components;

[0011] Step 5: Adjust trends and seasons;

[0012] Step 6: Repeat steps 2-5 until the calculation results converge.

[0013] Furthermore, step 1 specifically includes the following sub-steps:

[0014] Step 101: Collect and organize the repeated fracturing production data of oil wells in the target block;

[0015] Step 102: Record the production output of repeated fracturing of the oil well at time [time]. The observed value is , This can be expressed as:

[0016] (1)

[0017] In equation (1), Indicates the trend in a time series; The period is represented as Seasonal components; This represents the remaining components. The remaining components include all components other than trend and seasonality, and can be further decomposed into:

[0018] (2)

[0019] In equation (2), Indicates peak or trough value; This represents white noise.

[0020] Furthermore, step 2 specifically includes the following sub-steps:

[0021] Step 201: Smooth the initial time series using neighboring points with similar values. The time series after bilateral filtering is as follows:

[0022] (3)

[0023] In equation (3), Indicates length is The filter window has the following filter weights:

[0024] (4)

[0025] In equation (4), It is a normalization factor; and It is a parameter that controls the smoothness of the output time series.

[0026] Step 202: Initial update of the decomposition model;

[0027] After denoising, the decomposition model in equation (1) is updated as follows:

[0028] (5)

[0029] (6)

[0030] in, This is the time series data after the first update; These are the remaining items after the initial update; It is filtered noise.

[0031] Furthermore, step 3 specifically includes the following sub-steps:

[0032] Step 301: Seasonal difference;

[0033] Assuming that seasonal components change slowly, the first step is to analyze the denoised data. Seasonal differencing is used to mitigate the effects of seasonality.

[0034] (7)

[0035] In equation (7), This represents seasonal difference operations. ; It is a first-order difference operation. .

[0036] Step 302: Construct a weighted objective function based on minimum absolute deviation loss;

[0037] remember Because seasonal difference operations will cause and Significantly reduced, therefore Will lead In order to The first-order difference of the trend recovery component requires the construction of a weighted sum objective function:

[0038] (8)

[0039] In equation (8), represents the second-order difference operation. The first term in equation (8) represents the empirical error calculated using the minimum absolute deviation loss.

[0040] Step 303: Determine the optimization objective;

[0041] The equivalent matrix form of equation (8) is:

[0042] (9)

[0043] In equation (9), Representing vectors of Norm; and It is the corresponding vector representation. ; ; and They are Rank and The order Topletz matrix has the following form:

[0044]

[0045] To facilitate the solution, the three equations in equation (9) are... The norm is further represented as a single norm. Norm:

[0046] (10)

[0047] In equation (10), the matrix and vector They are respectively:

[0048]

[0049] Step 304: Obtain the relative trend;

[0050] In equation (10) a single Minimizing the norm is equivalent to the following linear programming problem:

[0051] (11)

[0052] In equation (11), It is an auxiliary variable.

[0053] The output of equation (11) is ,in In actual calculations, there are usually... Thus, we obtain the following based on Relative output:

[0054]

[0055] Step 305: Second round of updating the decomposition model;

[0056] Based on the relative trend obtained from the denoised time series, the decomposition model can be updated as follows:

[0057] (12)

[0058] (13)

[0059] In equations (12) and (13), This is the time series data after the second round of updates; These are the remaining items after the second round of updates.

[0060] Furthermore, step 4 specifically includes the following sub-steps:

[0061] Step 401: Extract seasonality using nonlocal seasonality filtering;

[0062] for Its neighborhood includes A neighbor Seasonal components extracted by nonlocal seasonality filtering This can be expressed as:

[0063] (14)

[0064] In equation (14):

[0065]

[0066] Step 402: Third round of updating the decomposition model;

[0067] After removing seasonal components, the remaining portion is:

[0068] (15)

[0069] Furthermore, step 5 specifically includes the following sub-steps:

[0070] Step 501: Adjust for seasonal components by removing the average value;

[0071] It is necessary to ensure that the sum of all seasonal components within a period is zero, therefore the seasonal components obtained from formula (14) are adjusted by removing their average:

[0072] (16)

[0073] Step 502: Update the decomposition model;

[0074] The estimates for the trend and seasonal components have been updated as follows:

[0075] (17)

[0076] (18)

[0077] The estimated value for the remaining portion is updated as follows:

[0078] (19)

[0079] Furthermore, step 6 specifically includes the following sub-steps:

[0080] Step 601: Repeat steps 2 to 5 until the calculation results converge.

[0081] The beneficial effects of this invention are: it can decompose complex long-term production time series of repeated fracturing into trend, seasonal and residual components, and at the same time has the ability to handle outliers, respond quickly to sudden trend changes, cope with seasonal changes and fluctuations and noise, and is computationally efficient. Attached Figure Description

[0082] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below. Obviously, the drawings described below only relate to some embodiments of the present invention and are not intended to limit the present invention.

[0083] Figure 1 This is a technical roadmap for the present invention;

[0084] Figure 2 The time series decomposition effect of well 8315;

[0085] Figure 3 The time series decomposition effect of well 8321;

[0086] Figure 4 The time series decomposition effect of well 8325;

[0087] Figure 5 The time series decomposition effect of well 8330. Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] like Figures 1 to 5 As shown, this invention provides a technical solution: a method for decomposing time series data of repeated fracturing well production based on minimum absolute deviation loss, comprising the following steps:

[0090] Step 1: Collect and organize the raw data, specifically including the following steps:

[0091] We collected time-series production data of inefficient oil wells from the production statistics system of the oilfield. The data we collected included wells 8315, 8321, 8325, and 8330 in Block W of Xinjiang Oilfield (pseudonym). The production data spanned from 1981 to 2023, with months as the time step unit (some months were shut down for maintenance and therefore had no data). The basic dataset we collected is shown in Table 1.

[0092]

[0093] Table 1 Basic Dataset

[0094] Step 2: Use bilateral filtering to denoise the input data, specifically including the following steps:

[0095] (1) Use neighboring points with similar values ​​to smooth the initial time series;

[0096] (2) First update of the decomposition model.

[0097] Step 3: Robustly extract the trend by solving the minimum absolute deviation regression with sparse regularization, specifically including the following steps:

[0098] (1) Seasonal difference;

[0099] (2) Construct a weighted objective function based on minimum absolute deviation loss;

[0100] (3) Determine the optimization objective;

[0101] (4) Obtain the relative trend;

[0102] (5) Second round of updating the decomposition model.

[0103] Step 4: Obtain the seasonal components using nonlocal seasonality filtering, which includes the following steps:

[0104] (1) Extract seasonality through non-local seasonality filtering;

[0105] (2) Third round of updating decomposition model.

[0106] Step 5: Adjust trends and seasons, specifically including the following steps:

[0107] (1) Adjusting for seasonal components by removing the average value;

[0108] (2) Update the decomposition model.

[0109] Step 6: Repeat steps 2-5 until the calculation results converge. The time series decomposition results for the four wells are as follows: Figures 2-5 As shown in Table 2, taking well 8315 as an example, the model was updated and decomposed multiple times, and the final decomposition results are shown in Table 3.

[0110]

[0111] Table 2. Updated decomposition model for well 8315

[0112]

[0113] Table 3 Time series decomposition results of well 8315

[0114] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for decomposing time series data of production from repeatedly fractured wells based on minimum absolute deviation loss, comprising the following steps: Step 1: Input the time series data of production from repeatedly fractured wells; Step 2: Use bilateral filtering to denoise the input data; Step 3: Robustly extract the trend by solving the minimum absolute deviation regression with sparse regularization; Step 4: Use nonlocal seasonality filtering to obtain seasonal components; Step 5: Adjust trends and seasons; Step 6: Repeat steps 2-5 until the calculation results converge; Step 1 specifically includes the following sub-steps: Step 101: Collect and organize the repeated fracturing production data of oil wells in the target block; Step 102: Record the production output of repeated fracturing of the oil well at time [time]. The observed value is , This can be expressed as: （1） In equation (1), Indicates the trend in a time series; The period is represented as Seasonal components; This represents the remaining components; the remaining components include all components other than trend and seasonality, and can be further decomposed into: （2） In equation (2), Indicates peak or trough value; Represents white noise; Step 2 specifically includes the following sub-steps: Step 201: Smooth the initial time series using neighboring points with similar values. The time series after bilateral filtering is as follows: （3） In equation (3), Indicates length is The filter window has the following filter weights: （4） In equation (4), It is a normalization factor; and It is a parameter that controls the smoothness of the output time series; Step 202: Initial update of the decomposition model; After denoising, the decomposition model in equation (1) is updated as follows: （5） （6） in, This is the time series data after the first update; These are the remaining items after the initial update; It is filtered noise; Step 3 specifically includes the following sub-steps: Step 301: Seasonal difference; Assuming that seasonal components change slowly, the first step is to analyze the denoised data. Seasonal differencing is used to mitigate the effects of seasonality. （7） In equation (7), This represents seasonal difference operations. ; It is a first-order difference operation. ; Step 302: Construct a weighted objective function based on minimum absolute deviation loss; remember Because seasonal difference operations will cause and Significantly reduced, therefore Will lead In order to The first-order difference of the trend recovery component requires the construction of a weighted sum objective function: （8） In equation (8), represents the second-order difference operation. The first term in equation (8) represents the empirical error calculated using the minimum absolute deviation loss. Step 303: Determine the optimization objective; The equivalent matrix form of equation (8) is: （9） In equation (9), Representing vectors of Norm; and It is the corresponding vector representation. ; ; and They are Rank and The order Topletz matrix has the following form: To facilitate the solution, the three equations in equation (9) are... The norm is further represented as a single norm. Norm: （10） In equation (10), the matrix and vector They are respectively: Step 304: Obtain the relative trend; In equation (10) a single Minimizing the norm is equivalent to the following linear programming problem: （11） In equation (11), It is an auxiliary variable; The output of expression (11) is ,in In actual calculations, there are usually Thus, we obtain the following based on Relative output: Step 305: Second round of updating the decomposition model; Based on the relative trend obtained from the denoised time series, the decomposition model can be updated as follows: （12） （13） In equations (12) and (13), This is the time series data after the second round of updates; These are the remaining items after the second round of updates; Step 4 specifically includes the following sub-steps: Step 401: Extract seasonality using nonlocal seasonality filtering; for Its neighborhood includes A neighbor Seasonal components extracted by nonlocal seasonality filtering This can be expressed as: （14） In equation (14): Step 402: Third round of updating the decomposition model; After removing seasonal components, the remaining portion is: （15） Step 5 specifically includes the following sub-steps: Step 501: Adjust for seasonal components by removing the average value; It is necessary to ensure that the sum of all seasonal components within a period is zero, therefore the seasonal components obtained from formula (12) are adjusted by removing their average: （16） Step 502: Update the decomposition model; The estimates for the trend and seasonal components have been updated as follows: （17） （18） The estimated value for the remaining portion is updated as follows: （19） Step 6 specifically includes the following sub-steps: Step 601: Repeat steps 2 to 5 until the calculation results converge.

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