Refractured well yield time series data decomposition method based on minimum absolute deviation loss

Abstract

The invention provides a refracturing well yield time series data decomposition method based on minimum absolute deviation loss. The method comprises the following steps: (S1) collecting and arranging original data; (S2) denoising the input data by using bilateral filtering; (S3) stably extracting a trend by solving minimum absolute deviation regression with sparse regularization; (S4) using non-local seasonal filtering to obtain seasonal components; (S5) adjusting the trend and the season; and (S6) repeating the steps 2-5 until the calculation result converges. According to the method, the seasonality and the trend can be stably extracted from long-season period and high-noise data, and a solid foundation can be provided for fitting prediction of subsequent refracturing yield data.

Description

Technical Field

[0001] The invention relates to the technical field of reservoir production enhancement and transformation, and in particular to a method for decomposing time series data of repeated fracturing well production based on minimum absolute deviation loss. Background Art

[0002] Repeated fracturing production data samples often present high-dimensional, non-stationary characteristics, and usually contain too much noise, anomalies or missing values, which brings challenges to the modeling of production time series data. Real-world time series data usually consists of three parts: seasonality, trend, and residuals. Time series decomposition can decompose complex time series data into independent and interpretable components. Researchers can reveal potential trends and patterns that may be hidden in the original analysis, thereby gaining a deeper understanding of the data, which is especially useful when dealing with data with inherent seasonal changes or focusing on long-term trends. Take the production data of oil wells repeated fracturing as an example: if the original data is used directly for production forecasting, the noise and random fluctuations in the original data series will interfere with the production forecast. Therefore, first decomposing the time series into basic components and matching relatively simple professional models for each component may achieve 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 of the reasons is that the underlying sum-of-squares loss function needs to assume that the error is normally distributed, and squaring will exponentially amplify the contribution of outliers to the total loss, reducing the robustness of the algorithm. Summary of the invention

[0004] In view of the above problems, the present invention provides a method for decomposing the production time series data of re-fracturing wells based on minimum absolute deviation loss. The data cleaning effect is good, and seasonality and trends can be stably extracted from long seasonal cycles and high-noise data, providing a solid foundation for the fitting prediction of subsequent re-fracturing production data.

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

[0006] A method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss comprises the following steps:

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

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

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

[0010] Step 4: Use non-local seasonal filtering to obtain seasonal components;

[0011] Step 5: Adjust for trends and seasons;

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

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

[0014] Step 101: Collect and organize the oil well re-fracturing production data of the target block;

[0015] Step 102: Record the observed value of the oil well re-fracture production at time t as y t ,y t It can be expressed as:

[0016] y t =τ t +s t +r t ,t=1,2,...,N (1)

[0017] In formula (1), τ t Indicates the trend in a time series; t represents the seasonal component with a period of T; r t Represents the residual component. The residual component contains all components except trend and seasonality, and can be further decomposed into:

[0018] r t =a t +n t (2)

[0019] In formula (2), a t Indicates peak or valley value; n t Represents white noise.

[0020] Furthermore, the 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:

[0022]

[0023] In formula (3), J represents a filter window with a length of 2H+1, and the filter weight is:

[0024]

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

[0026] Step 202: updating the decomposition model for the first time;

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

[0028] y t ′=τ t +s t +r t ′ (5)

[0029]

[0030] Among them, y t ′ is the time series data after the first update; r t ′ is the remaining term after the first update; is the noise after filtering.

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

[0032] Step 301: seasonal difference;

[0033] Assuming that the seasonal component changes slowly, we first perform t 'Perform seasonal differences to reduce the impact of seasonality:

[0034]

[0035] In formula (7), represents the seasonal difference operation, is a first-order difference operation,

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

[0037] remember Since seasonal differencing will make s t and r t ' is significantly reduced, so Will dominate t , in order to t To recover the first-order difference of the trend component, it is necessary to construct a weighted sum objective function:

[0038]

[0039] In formula (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 target;

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

[0042]

[0043] In formula (9), ||x||1=∑ i |x i | represents the l1-norm of vector x; g and is the corresponding vector representation, g = [g T+1 ,g T+2 ,...,g N ] T ; M and D are Toeplitz matrices of (NT)×(N-1) and (N-2)×(N-1) order, respectively, and have the following form:

[0044]

[0045] For the convenience of solving, the three l1 norms in equation (9) are further expressed as a single l1 norm:

[0046]

[0047] In formula (10), the matrix P and vector q are:

[0048]

[0049] Step 304: Obtaining a relative trend;

[0050] Minimization of the single l1-norm in equation (10) is equivalent to the following linear programming:

[0051]

[0052] In formula (11), v is an auxiliary variable.

[0053] The output of equation (11) is in In actual operation, we usually have So we get the relative output based on τ1:

[0054]

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

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

[0057]

[0058] In formulas (12) and (13), y t ″ is the time series data after the second round of update; r t ″ is the remaining item after the second round of updating.

[0059] Furthermore, the step 4 specifically includes the following sub-steps:

[0060] Step 401: extract seasonality through non-local seasonal filtering;

[0061] For y t ″ -KT , whose neighborhood includes 2H+1 nearest neighbors y′ j ′=y t ″ -kT-H ,y t ″ -kT-H+1 ,…,y t ″ -kT ,y t ″ -kT+1 ,…,y t ″ -kT+H , the seasonal component extracted by non-local seasonal filtering It can be expressed as:

[0062]

[0063] In formula (12):

[0064]

[0065] Ω={(t′,j)(t′=tk×T,j=t′±h)}

[0066] k=1,2,...,K;h=0,1,...,H

[0067] Step 402: the third round of updating the decomposition model;

[0068] After removing the seasonal component, what remains is:

[0069]

[0070] Furthermore, the step 5 specifically includes the following sub-steps:

[0071] Step 501: Adjusting the seasonal component by removing the mean;

[0072] It is necessary to ensure that the sum of all seasonal components within a period is zero, so the seasonal component obtained from equation (12) is adjusted by removing its mean:

[0073]

[0074] Step 502: updating the decomposition model;

[0075] The estimates of trend and seasonal components are updated as:

[0076]

[0077] The estimate for the remainder is updated to:

[0078]

[0079] Furthermore, the 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 the present invention are that it can decompose complex long-term production time series of repeated fracturing into trend, seasonal and residual components, and has the ability to handle outliers, quickly respond to sudden trend changes, cope with seasonal changes and fluctuations and noise, and has efficient calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present invention, but are not intended to limit the present invention.

[0083] Figure 1 It is the technical roadmap of the present invention;

[0084] Figure 2 This is the time series decomposition effect of 8315 wells;

[0085] Figure 3 This is the time series decomposition effect of 8321 wells;

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

[0087] Figure 5 This is the time series decomposition effect of 8330 wells. DETAILED DESCRIPTION

[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

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

[0091] The production time series data of inefficient oil wells are collected from the production statistics system of the oil production plant. The data we collected include wells 8315, 8321, 8325, and 8330 in Block W of Xinjiang Oilfield (pseudonym). The production data spans from 1981 to 2023, with months as the time step unit (some months are closed for maintenance and no data). The collected basic data set is shown in Table 1:

[0092]

[0093] Table 1 Basic data set

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

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

[0096] (2) Update the decomposition model for the first time.

[0097] Step 3: Robustly extract trends by solving the least absolute deviation regression with sparse regularization, which includes the following steps:

[0098] (1)Seasonal difference;

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

[0100] (3) Determine the optimization goal;

[0101] (4) Obtaining relative trends;

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

[0103] Step 4: Use non-local seasonal filtering to obtain seasonal components, which includes the following steps:

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

[0105] (2) The third round of updating the decomposition model.

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

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

[0108] (2) Update the decomposition model.

[0109] Step 6: Repeat steps 2 to 5 until the calculation results converge. The time series decomposition effects of the four wells are as follows: Figure 2-Figure 5 Taking Well 8315 as an example, the model is updated and decomposed multiple times as shown in Table 2, and the final decomposition results are shown in Table 3

[0110]

[0111]

[0112] Table 2 Updated decomposition model of Well 8315

[0113]

[0114] Table 3 Time series decomposition results of well 8315

[0115] 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 that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss, characterized in that: The following steps are involved: Step 1: Input the production time series data of re-fractured wells; Step 2: Use bilateral filtering to denoise the input data; Step 3: Robustly extract trends by solving the least absolute deviation regression with sparse regularization; Step 4: Use non-local seasonal filtering to obtain seasonal components; Step 5: Adjust for trends and seasons; Step 6: Repeat steps 2 to 5 until the calculation results converge.

2. The method for decomposing the production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 1 specifically includes the following sub-steps: Step 101: Collect and organize the oil well re-fracturing production data of the target block; Step 102: Identify the components of the repeated fracturing production time series data.

3. The method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 2 specifically includes the following sub-steps: Step 201: smoothing the initial time series using adjacent points with similar values; Step 202: Update the decomposition model for the first time.

4. The method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 3 specifically includes the following sub-steps: Step 301: seasonal difference; Step 302: construct a weighted sum objective function based on minimum absolute deviation loss; Step 303: Determine the optimization target; Step 304: Obtaining a relative trend; Step 305: The second round of updating the decomposition model.

5. The method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 4 specifically includes the following sub-steps: Step 401: extract seasonality through non-local seasonal filtering; Step 402: The third round of updating the decomposition model.

6. The method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 5 specifically includes the following sub-steps: Step 501: Adjusting the seasonal component by removing the mean; Step 502: Update the decomposition model.

7. The method for decomposing production time series data of re-fracturing wells based on minimum absolute deviation loss according to claim 1, characterized in that: The step 6 specifically comprises the following steps: Step 601: Repeat steps 2 to 5 until the calculation results converge.

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