Shale gas production decline rule analysis method and system based on rational function
By fitting the law of decreasing shale gas output based on rational functions, the problems of insufficient fitting accuracy and poor adaptability in the existing technology are solved, and accurate prediction of the dynamics of the output changes of shale gas wells throughout the life cycle are achieved.
Patent Information
- Application Number
- CN202311097660.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-08-29
- Publication Date
- 2025-02-28
AI Technical Summary
In the prior art, the analysis model of shale gas yield decreases in the law of shale gas production has problems such as insufficient fitting accuracy and poor adaptability.
The method based on rational function is used to analyze the law of decreasing shale gas output. By obtaining and processing the historical data of shale gas production, the average daily gas output of a single well, the monthly average daily gas output of a single well and the annual average daily gas output of a single well are fitted using a rational function.
The accuracy of prediction of the decreasing trend of shale gas production has been improved, and an accurate reflection of the dynamics of the output changes of shale gas wells throughout the life cycle is achieved.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of shale gas development, and in particular to a method and system for analyzing shale gas production decline law based on rational functions. Background Art
[0002] For shale gas reservoirs, due to the compactness of the reservoir and the adsorption of organic matter, they have a special seepage mechanism and the gas well production cycle is as long as several decades. A shale gas well will mainly go through two production stages since it is put into production: (1) the initial production is high but the decline is fast, and the main produced gas is free gas in the fracture system; (2) the production gradually tends to be stable, and the main produced gas is free gas and adsorbed gas in the matrix pores. Due to the long-term non-steady-state flow stage, shale gas wells generally have a long decline period, especially in the early stage of production, when the production is high but the decline is fast. The proportion of produced gas in EUR in this stage is relatively high, which is an important stage for shale gas wells to contribute to production. Therefore, it is of great significance to understand the law of shale gas production decline. On the one hand, it can grasp the production dynamics of a single well and the entire shale gas reservoir. On the other hand, it can carry out production prediction and final recoverable reserves prediction for a certain production stage in the future, so as to provide a basis for the formulation of development plans and the deployment and adjustment of the next development decision.
[0003] As a method for analyzing the decline law of shale gas production, the empirical method is widely used because of its advantages such as low data requirements, simple operation and reliable results. Its main principle is to match the historical production dynamics of gas wells through models to achieve the purpose of understanding their production decline laws. The empirical models commonly used for shale gas production decline analysis include the Arps model, SEPD model, Duong model and YM-SEPD model. Since various decline models have certain applicable conditions, they cannot achieve accurate fitting of the production decline of shale gas wells throughout their life cycle. Therefore, a combined decline model based on two or more basic models has been derived to improve the fitting accuracy.
[0004] The existing empirical decline models cannot accurately fit the production history of shale gas in actual application due to the limitation of applicable conditions. The Arps decline model is established based on medium and high permeability reservoirs with pseudo-radial boundary control flow, and its applicability in shale gas reservoirs is poor. The SEPD model has a low degree of consistency with the actual production in the early stage of shale gas well decline, and the model decline rate is greater than the actual production decline rate, resulting in poor applicability at this stage; in the middle and late stages of production, the decline rate of the model is close to the actual decline rate, but due to the large decline rate in the early stage, the predicted production in this stage is lower than the actual production, and the final predicted EUR is small. In contrast to the SEPD model, the predicted production trend of the Duong model in the early stage of gas well decline is highly consistent with the actual production, but in the middle and late stages of production, the model predicted production is higher than the actual production of the gas well, resulting in a large final predicted EUR. The YM-SEPD model and the SEPD model are different manifestations of the same model, and the model prediction results of the two are similar. Compared with the basic single model, the fitting accuracy of the combined model is relatively higher, but the determination of segmentation points becomes a new difficulty. At the same time, the model fitting accuracy has room for improvement. Summary of the invention
[0005] The present invention aims to solve the problems of insufficient fitting accuracy and poor adaptability of the shale gas production decline law analysis model in the prior art, and proposes a shale gas production decline law analysis method and system based on rational functions. The method and system use rational functions to achieve high-precision fitting of shale gas production decline, thereby improving the prediction accuracy of shale gas production decline trend.
[0006] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is as follows:
[0007] A method for analyzing shale gas production decline law based on rational functions, characterized by comprising the following steps:
[0008] Obtain historical shale gas production data for a single well or multiple wells, including production days and corresponding daily gas production;
[0009] Filter out abnormal data points in historical production data to obtain single well effective production days and daily gas production data;
[0010] The obtained data are aligned with the production time, and the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve and the annual average single-well daily gas production decline curve are obtained respectively;
[0011] Rational functions are used to fit the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve, and the annual average single-well daily gas production decline curve;
[0012] Based on the fitting results, the daily, monthly and annual gas production decline laws of shale gas are analyzed.
[0013] Furthermore, the abnormal data points include data points with a daily gas production of 0 or data points with an abnormally low daily gas production before and after a corresponding time point.
[0014] Furthermore, the average daily gas production per well decline curve refers to a curve showing the change of the average daily gas production per well with the number of effective production days. The calculation method of the average daily gas production per well is as follows:
[0015]
[0016] Where: q at is the average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;q it is the daily gas production of the ith well on the tth day of effective production, in units of 10 4 m 3 / d; w is the number of wells whose actual effective production days are not greater than t.
[0017] Furthermore, the monthly average single-well daily gas production decline curve refers to a curve chart showing the change of the monthly average single-well daily gas production with the effective production days. The monthly average single-well daily gas production is obtained by calculating the average single-well daily gas production of the effective production days for 30 consecutive days.
[0018] Furthermore, the annual average single-well daily gas production decline curve refers to a curve chart showing the change of the annual average single-well daily gas production with the effective production days. The annual average single-well daily gas production is obtained by calculating the average single-well daily gas production of the effective production days for 365 consecutive days.
[0019] Furthermore, the rational function form used for fitting is as follows:
[0020]
[0021] Where: q t is the fitted average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;a 1 ,a 2 ,...,a m ,a m+1 is the coefficient of the numerator polynomial; m is the degree of the numerator polynomial; b 1 ,…,b n-1 ,b n is the coefficient of the denominator polynomial; n is the degree of the denominator polynomial.
[0022] Furthermore, the degrees of the numerator and denominator polynomials in the rational function fitting result can be freely selected under the premise of ensuring the fitting effect.
[0023] The present invention also provides a shale gas production decline law analysis system based on rational functions, comprising: a parameter acquisition module for acquiring shale gas production history data of a single well or multiple wells, including production days and corresponding daily gas production;
[0024] Data cleaning module, used to filter abnormal data points in production history data to obtain single well effective production days and daily gas production data;
[0025] A data processing module is used to align the data obtained by the data cleaning module with the production time, and respectively obtain the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve, and the annual average single-well daily gas production decline curve;
[0026] A function fitting module is used to use rational functions to fit the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve and the annual average single-well daily gas production decline curve;
[0027] The result analysis module is used to analyze the daily gas production decline law, monthly gas production decline law and annual gas production decline law of shale gas according to the fitting results.
[0028] Furthermore, the data cleaning module is used to remove abnormal data points including data points with a daily gas production of 0 or data points with abnormally low daily gas production before and after a corresponding time point.
[0029] Furthermore, the data processing module is specifically used for:
[0030] The average daily gas production of a single well is obtained, and a curve of the average daily gas production of a single well versus the number of effective production days is plotted to obtain a decreasing curve of the average daily gas production of a single well;
[0031] The monthly average single-well daily gas production is calculated by taking the average single-well daily gas production of 30 consecutive effective production days as the average value, and a curve of the monthly average single-well daily gas production versus the effective production days is plotted to obtain the monthly average single-well daily gas production decreasing curve;
[0032] The annual average single-well daily gas production was calculated by taking the average single-well daily gas production of 365 consecutive effective production days as the average value, and a curve of the annual average single-well daily gas production versus the effective production days was plotted to obtain the annual average single-well daily gas production decrease curve.
[0033] In summary, the present invention has the following advantages:
[0034] 1. The present invention innovatively proposes to use rational functions to achieve high-precision fitting of shale gas production decline, thereby achieving the purpose of analyzing the law of shale gas production decline. The method described in the present invention is flexible in form, and the degree of the numerator / denominator polynomial can be freely selected under the premise of ensuring the fitting accuracy, thereby achieving the highest precision fitting, which can truthfully reflect the production change dynamics of shale gas wells / platforms / blocks throughout their life cycle.
[0035] 2. The method of the present invention has a wide range of applications and can meet the analysis of shale gas production decline rules at any production stage of a single well or multiple wells, and is not limited to the analysis of the daily gas production decline rules of a single well of the conventional decline model. It can provide important technical support for developers to accurately grasp the shale gas production decline rules.
[0036] 3. The method of the present invention is simple, easy to understand, easy to use, easy to operate and convenient to apply. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 The flowchart of the analysis of shale gas production decline law based on rational function of the present invention;
[0038] Figure 2 It is a fitting diagram of the average daily gas production decline curve of a single well based on a rational function of the present invention;
[0039] Figure 3 It is a fitting diagram of the average monthly gas production decline curve of a single well based on a rational function of the present invention;
[0040] Figure 4 This is a fitting diagram of the average annual gas production decline curve of a single well based on a rational function of the present invention. DETAILED DESCRIPTION
[0041] In order to explain the present invention more clearly, the present invention is further described below in conjunction with preferred embodiments and drawings. It should be understood by those skilled in the art that the content described below is illustrative rather than restrictive, and should not be used to limit the scope of protection of the present invention.
[0042] The present invention provides a method for analyzing the shale gas production decline law based on rational functions, comprising the following steps:
[0043] Step 1: Prepare historical shale gas production data for a single well or multiple wells.
[0044] This step takes the production start time as the starting point and prepares all the single well production history data of the target well / platform / block, including the production days and their corresponding daily gas production.
[0045] Step 2: Filter out abnormal data points caused by factors such as well closure.
[0046] Based on the prepared data, abnormal data points are filtered, including data points with a daily gas production of 0 or data points with abnormally low daily gas production compared with the daily gas production before and after the corresponding time point. Furthermore, the daily gas production data points of each well remaining after filtering are recalibrated with effective production days, and finally the data preparation work is completed.
[0047] Step 3: Obtain the average daily gas production decline curve for a single well.
[0048] This step is for multiple wells such as platforms / blocks. According to the single well effective production days and daily gas production data prepared in step 2, the production time is aligned to obtain the average single well daily gas production decline curve. The average single well daily gas production calculation method is as follows:
[0049]
[0050] Where: q at is the average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;q it is the daily gas production of the ith well on the tth day of effective production, in units of 10 4 m 3 / d; w is the number of wells whose actual effective production days are not greater than t.
[0051] Furthermore, after all the data are calculated, a curve chart showing the average daily gas production of a single well versus the number of effective production days is drawn, that is, a curve chart showing the average daily gas production of a single well decreasing.
[0052] Step 4: Use rational functions to fit the average single well daily gas production decline curve and analyze the daily gas production decline law of shale gas.
[0053] The rational function in this step has the following form:
[0054]
[0055] Where: q t is the fitted average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;a 1 ,a 2 ,…,a m ,a m+1 is the coefficient of the numerator polynomial; m is the degree of the numerator polynomial; b 1 ,...,b n-1 ,b n is the coefficient of the denominator polynomial; n is the degree of the denominator polynomial.
[0056] In this embodiment, taking the analysis of the average daily gas production decline law of multiple wells in a shale gas block as an example, after completing data preparation and obtaining the average daily gas production decline curve of a single well according to steps one, two, and three, the rational function described in step four is used for fitting. The fitting coefficients when the numerator and denominator polynomials are of different orders are shown in Table 1 below. Figure 2 The fitting results for quintic polynomials in both numerator and denominator are shown.
[0057] Table 1 Numerator / denominator polynomial coefficients in the fitting results of average single well daily gas production
[0058]
[0059] Furthermore, the degrees of the numerator and denominator polynomials in the rational function fitting result can be freely selected under the premise of ensuring the fitting effect, such as:
[0060] The numerator is a cubic polynomial and the denominator is a quintic polynomial. The rational function is
[0061] Or the numerator is a quartic polynomial and the denominator is a quadratic polynomial, then the rational function is
[0062] It should be noted that as the degree of the numerator or denominator polynomial changes, the coefficients of the numerator and denominator polynomials of the rational function in the fitting results will change.
[0063] Furthermore, according to the fitting results, the average single-well daily gas production decline curve is recalculated, based on which the daily gas production decline law of the target well / platform / block production well is analyzed.
[0064] Furthermore, the average monthly gas production of a single well is calculated with 30 consecutive effective production days as one month, and a decreasing curve of the average monthly gas production of a single well is drawn. The rational function described in step 4 is used for fitting. The fitting coefficients when the numerator and denominator polynomials are of different orders are shown in Table 2 below. Figure 3 The fitting results for quintic polynomials in both numerator and denominator are shown.
[0065] Table 2 Numerator / denominator polynomial coefficients in the fitting results of average monthly gas production of a single well
[0066]
[0067] Similar to the fitting of the average daily gas production of a single well, the degrees of the numerator and denominator polynomials in the rational function fitting of the average monthly gas production of a single well can be freely selected under the premise of ensuring the fitting effect, but as the degree of the numerator or denominator polynomial changes, the coefficients of the numerator and denominator polynomials in the fitting result will change.
[0068] Furthermore, according to the fitting results, the average single-well monthly gas production decline curve is recalculated, based on which the monthly gas production decline law of the target well / platform / block production well is analyzed.
[0069] Furthermore, the average annual gas production of a single well is calculated with 365 consecutive effective production days as one year, and a decreasing curve of the average annual gas production of a single well is drawn. The rational function described in step 4 is used for fitting. The fitting coefficients when the numerator and denominator polynomials are of different orders are shown in Table 3. Figure 4 The fit results for cubic polynomials in both numerator and denominator are shown.
[0070] Table 3 Numerator / denominator polynomial coefficients in the fitting results of average monthly gas production of a single well
[0071]
[0072] Similar to the fitting of the average daily / monthly gas production of a single well, the degrees of the numerator and denominator polynomials in the rational function fitting of the average annual gas production of a single well can be freely selected under the premise of ensuring the fitting effect, but as the degree of the numerator or denominator polynomial changes, the coefficients of the numerator and denominator polynomials in the fitting results will change.
[0073] Furthermore, according to the fitting results, the average annual gas production decline curve of a single well is recalculated, and the monthly gas production decline pattern of the target well / platform / block production well is analyzed based on this.
[0074] It should be noted that as the data points in the average daily / monthly / annual production decline curve of a single well decrease / increase, the degree of the numerator and denominator polynomials must decrease / increase during the rational function fitting process. The more data points there are, the higher the fitting accuracy will be.
[0075] It should be noted that this method can meet the analysis of shale gas production decline rules at any production stage of a single well or multiple wells, and is not limited to the above-mentioned analysis of daily gas production, monthly gas production, and annual gas production decline rules.
[0076] Example 2
[0077] This embodiment provides a shale gas production decline law analysis system based on rational functions, which corresponds to the implementation steps of the shale gas production decline law analysis method based on rational functions described in the above embodiment 1. The system includes:
[0078] Parameter acquisition module, used to obtain the historical data of shale gas production of a single well or multiple wells, including production days and corresponding daily gas production;
[0079] The data cleaning module is used to filter out abnormal data points in the production history data to obtain the effective production days and daily gas production data of a single well; abnormal data points include data points with a daily gas production of 0 or data points with abnormally low daily gas production before and after the corresponding time point.
[0080] A data processing module is used to align the data obtained by the data cleaning module with the production time, and respectively obtain the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve, and the annual average single-well daily gas production decline curve;
[0081] Specifically, the data processing module is used to:
[0082] The average daily gas production of a single well is obtained, and a curve of the average daily gas production of a single well versus the number of effective production days is plotted to obtain a decreasing curve of the average daily gas production of a single well;
[0083] The monthly average single-well daily gas production is calculated by taking the average single-well daily gas production of 30 consecutive effective production days as the average value, and a curve of the monthly average single-well daily gas production versus the effective production days is plotted to obtain the monthly average single-well daily gas production decreasing curve;
[0084] The annual average single-well daily gas production is calculated by taking the average single-well daily gas production of the effective production days for 365 consecutive days as the average value, and a curve of the annual average single-well daily gas production versus the effective production days is plotted to obtain the annual average single-well daily gas production decreasing curve.
[0085] The average daily gas production of a single well is calculated according to the following formula:
[0086]
[0087] Where: q at is the average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;q it is the daily gas production of the ith well on the tth day of effective production, in units of 10 4 m 3 / d; w is the number of wells whose actual effective production days are not greater than t.
[0088] A function fitting module is used to use rational functions to fit the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve and the annual average single-well daily gas production decline curve;
[0089] The function fitting module uses rational functions of the following form for fitting:
[0090]
[0091] Where: q tis the fitted average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;a 1 ,a 2 ,...,a m ,a m+1 is the coefficient of the numerator polynomial; m is the degree of the numerator polynomial; b 1 ,…,b n-1 ,b n is the coefficient of the denominator polynomial; n is the degree of the denominator polynomial.
[0092] The degrees of the numerator and denominator polynomials in the rational function fitting results can be freely selected while ensuring the fitting effect.
[0093] The result analysis module is used to recalculate the average single-well annual gas production decline curve, the monthly average single-well annual gas production decline curve, and the annual average single-well annual gas production decline curve according to the fitting results, and analyze the daily gas production decline law, monthly gas production decline law, and annual gas production decline law of shale gas.
[0094] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the present invention.
Claims
1. A method for analyzing the decline law of shale gas production based on rational functions, characterized in that: The steps include: Obtain historical shale gas production data for a single well or multiple wells, including production days and corresponding daily gas production; Filter out abnormal data points in historical production data to obtain single well effective production days and daily gas production data; The obtained data are aligned with the production time, and the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve and the annual average single-well daily gas production decline curve are obtained respectively; Rational functions are used to fit the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve, and the annual average single-well daily gas production decline curve; Based on the fitting results, the daily, monthly and annual gas production decline laws of shale gas are analyzed.
2. The method for analyzing shale gas production decline law based on rational function according to claim 1, characterized in that: The abnormal data points include data points with a daily gas production of 0 or data points with an abnormally low daily gas production before and after a corresponding time point.
3. The method for analyzing shale gas production decline law based on rational function according to claim 1, characterized in that: The average daily gas production decline curve of a single well refers to the curve of the average daily gas production of a single well versus the number of effective production days. The calculation method of the average daily gas production of a single well is as follows: Where: q at is the average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d;q it is the daily gas production of the ith well on the tth day of effective production, in units of 10 4 m 3 / d; w is the number of wells whose actual effective production days are not greater than t.
4. The method for analyzing shale gas production decline law based on rational function according to claim 3 is characterized in that: The monthly average single-well daily gas production decline curve refers to a curve chart showing the change of the monthly average single-well daily gas production with the effective production days. The monthly average single-well daily gas production is obtained by calculating the average single-well daily gas production of the effective production days for 30 consecutive days.
5. The method for analyzing shale gas production decline law based on rational function according to claim 3 is characterized in that: The annual average single-well daily gas production decline curve refers to a curve chart showing the change of the annual average single-well daily gas production with the effective production days. The annual average single-well daily gas production is obtained by calculating the average single-well daily gas production of the effective production days for 365 consecutive days.
6. A method for analyzing shale gas production decline law based on rational functions according to any one of claims 1 to 5, characterized in that: The rational function form used for fitting is as follows: Where: q t is the fitted average daily gas production of a single well on the tth day of effective production, in units of 10 4 m 3 / d; a1, a2, …, a m ,a m+1 are the coefficients of the numerator polynomial; m is the degree of the numerator polynomial; b1,...,b n-1 ,b n is the coefficient of the denominator polynomial; n is the degree of the denominator polynomial.
7. The method for analyzing shale gas production decline law based on rational function according to claim 6, characterized in that: The degrees of the numerator and denominator polynomials in the rational function fitting results can be freely selected under the premise of ensuring the fitting effect.
8. A shale gas production decline law analysis system based on rational functions, characterized in that: include: Parameter acquisition module, used to obtain the historical data of shale gas production of a single well or multiple wells, including production days and corresponding daily gas production; Data cleaning module, used to filter abnormal data points in production history data to obtain single well effective production days and daily gas production data; A data processing module is used to align the data obtained by the data cleaning module with the production time, and respectively obtain the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve, and the annual average single-well daily gas production decline curve; A function fitting module is used to use rational functions to fit the average single-well daily gas production decline curve, the monthly average single-well daily gas production decline curve and the annual average single-well daily gas production decline curve; The result analysis module is used to analyze the daily gas production decline law, monthly gas production decline law and annual gas production decline law of shale gas according to the fitting results.
9. A shale gas production decline law analysis system based on rational functions according to claim 8, characterized in that: The data cleaning module is used to remove abnormal data points including data points with a daily gas production of 0 or data points with abnormally low daily gas production before and after a corresponding time point.
10. A shale gas production decline law analysis system based on rational functions according to claim 8, characterized in that: The data processing module is specifically used for: The average daily gas production of a single well is obtained, and a curve of the average daily gas production of a single well versus the number of effective production days is plotted to obtain a decreasing curve of the average daily gas production of a single well; The monthly average single-well daily gas production is calculated by taking the average single-well daily gas production of 30 consecutive effective production days as the average value, and a curve of the monthly average single-well daily gas production versus the effective production days is plotted to obtain the monthly average single-well daily gas production decreasing curve; The annual average single-well daily gas production is calculated by taking the average single-well daily gas production of the effective production days for 365 consecutive days as the average value, and a curve of the annual average single-well daily gas production versus the effective production days is plotted to obtain the annual average single-well daily gas production decreasing curve.