A method for calculating shale gas well productivity

Abstract

This invention discloses a method for calculating shale gas well productivity. The method comprises: establishing a productivity calculation model applicable to different shale blocks based on steady-state seepage theory; and, in calculating shale gas well productivity using the productivity calculation model, replacing the pressure factor value obtained from initial field testing with the pressure factor value obtained when the pressure decreases to a stable production pressure differential based on unsteady-state seepage theory. Compared to existing technologies, the method according to the invention can obtain more accurate shale gas well productivity, thereby providing reliable theoretical and technical support for shale gas development evaluation and plan formulation.

Description

Technical Field

[0001] The present invention relates to the field of geological exploration and development, and in particular to a method for calculating the productivity of shale gas wells. Background Art

[0002] Shale gas refers to unconventional natural gas that exists in organic-rich mudstone and its interlayers and mainly exists in adsorption and free states.

[0003] Due to the dense nature of shale gas reservoirs, pressure decreases rapidly during the initial stages of production, making it difficult to quickly and accurately evaluate gas well productivity on-site. Currently, the Chen Yuanqian one-point method, used for conventional gas wells, is still commonly used to calculate and evaluate shale gas well productivity. This method uses pressure and production data from testing. These results are often overly optimistic and differ significantly from actual conditions, resulting in investments and benefits in shale gas wells falling short of design requirements, leading to significant economic losses. Therefore, a productivity calculation method suitable for shale gas wells is needed to provide reliable theoretical and technical support for shale gas development evaluation and plan formulation. Summary of the Invention

[0004] The present invention provides a method for calculating the productivity of a shale gas well, the method comprising:

[0005] Based on the steady-state seepage theory, a productivity calculation model suitable for different shale blocks is established;

[0006] In the process of calculating the productivity of shale gas wells using the productivity calculation model, based on the unsteady-state seepage theory, the pressure factor value obtained by the initial field test is replaced by the pressure factor value when the pressure decreases to a stable production pressure difference.

[0007] In one embodiment, the pressure factor value obtained during the initial field test is replaced by the pressure factor value when the pressure decreases until the production pressure differential stabilizes, where:

[0008] The pressure drop during gas well production is predicted based on the unsteady-state equation. The pressure factor value when the pressure drops to a stable production pressure difference is calculated based on the pressure factor value obtained from the initial field test.

[0009] In one embodiment, calculating the value of the pressure factor when the pressure decreases to a stable production pressure difference includes:

[0010] Establish a non-steady-state seepage model to simulate and calculate the changes in pressure factors over production time under different production rates;

[0011] The pressure factor value when the production differential pressure tends to be stable is calculated based on the pressure factor value obtained from the initial field test based on the simulation results.

[0012] In one embodiment, a non-steady-state seepage model is established to simulate and calculate the changes in pressure factors over production time at different production rates, where:

[0013] The pressure drop percentage of the pressure factor is linearly related to the production rate.

[0014] In one embodiment, the pressure factor value when the production differential pressure tends to be stable is calculated based on the simulation results and the pressure factor value obtained from the initial field test, where:

[0015] A pressure factor value linear variation model based on the pressure factor values ​​obtained from the initial field test is established according to the simulation results, wherein the linear variation constant in the pressure factor value linear variation model is related to the seepage characteristics of the reservoir.

[0016] In one embodiment, the method further includes obtaining the linear change constant through regression calculation.

[0017] In one embodiment, the pressure factors include formation pressure and bottom hole flow pressure.

[0018] In one embodiment, the capacity calculation model includes:

[0019]

[0020] in:

[0021] α is a dynamic calculation factor that changes with output;

[0022] P r is the formation pressure, MPa;

[0023] P wf is the bottom hole flowing pressure, MPa;

[0024] Q g is the gas production, 10 4 m 3 / d;

[0025] Q AOF is the gas well production capacity, which is unobstructed flow, 10 4 m 3 / d.

[0026] In one embodiment, in the production capacity calculation formula, α is a dynamic calculation factor that changes with production, where:

[0027] The relationship between α value and gas production of gas wells that have undergone systematic well testing in the statistical block;

[0028] The α value is obtained through regression calculation.

[0029] In one embodiment, the capacity calculation model further includes:

[0030]

[0031] The selection of the function and the determination of the a and b values ​​are determined by the seepage characteristics of the shale reservoir, and the a and b values ​​are obtained through regression calculation.

[0032] Compared with the existing technology, the method according to the present invention can obtain more accurate shale gas well production capacity, thereby providing reliable theoretical and technical support for shale gas development evaluation and plan formulation.

[0033] Other features and advantages of the present invention will be described in the following description. Furthermore, some features and advantages of the present invention will become apparent from the description or may be learned through practice of the present invention. The objectives and some advantages of the present invention may be achieved or obtained by the steps particularly pointed out in the description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0035] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0036] Figure 2 2. It is a schematic diagram of the relationship between the α value and gas production of a shale gas well according to an embodiment of the present invention;

[0037] Figure 3 is a graph showing changes in formation pressure and bottom hole flowing pressure over time according to one embodiment of the present invention;

[0038] Figure 4 is a formation pressure drop ratio curve according to an embodiment of the present invention;

[0039] Figure 5 FIG. 4 is a bottom hole flow pressure drop ratio curve according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The following will describe in detail the implementation methods of the present invention in conjunction with the accompanying drawings and embodiments, so that practitioners of the present invention can fully understand how the present invention applies technical means to solve technical problems and achieve the implementation process of technical effects, and can specifically implement the present invention based on the above implementation process. It should be noted that as long as no conflict arises, the various embodiments of the present invention and the various features in each embodiment can be combined with each other, and the resulting technical solutions are all within the scope of protection of the present invention.

[0041] Due to the dense nature of shale gas reservoirs, pressure decreases rapidly during the initial stages of production, making it difficult to quickly and accurately evaluate gas well productivity on-site. Currently, the Chen Yuanqian one-point method, used for conventional gas wells, is still widely used to calculate and evaluate shale gas well productivity. This method uses pressure and production data from testing. These results are often overly optimistic and differ significantly from actual conditions. This results in both investment and benefits falling short of design requirements, leading to significant economic losses.

[0042] To address the problems existing in the prior art, the present invention proposes a method for calculating shale gas well productivity. In the prior art, shale gas well productivity is typically calculated based on the pressure obtained from initial field testing (directly derived from the well's field testing). However, for shale gas wells, the initial pressure decreases rapidly, and the pressure obtained from initial field testing is often too high. This results in the final calculated shale gas well productivity being higher than the actual value.

[0043] Based on the above analysis, the method of the present invention adopts a method combining steady-state and unsteady-state seepage theories.

[0044] Next, a detailed description of the method according to an embodiment of the present invention will be provided based on the accompanying drawings. The steps shown in the flowcharts of the accompanying drawings can be executed in a computer system including, for example, a set of computer-executable instructions. Although the flowcharts show a logical order of the steps, in some cases, the steps shown or described may be executed in a different order than that shown or described herein.

[0045] Specifically, such as Figure 1 As shown, in one embodiment, based on the steady-state seepage theory, a productivity calculation model applicable to different shale blocks is established (S110); in the process of calculating the productivity of shale gas wells using the productivity calculation model (S120), based on the unsteady-state seepage theory, the pressure factor value obtained by the initial field test is replaced by the pressure factor value when the pressure decreases to a stable production pressure difference (S121).

[0046] Specifically, in one embodiment, the pressure factors include formation pressure and bottom hole flow pressure.

[0047] Furthermore, in one embodiment, the pressure decline during gas well production is predicted based on a non-steady-state equation, and the pressure factor value when the pressure declines to a stable production pressure difference is calculated based on the pressure factor value obtained from the initial field test.

[0048] Specifically, in one embodiment, the non-steady-state seepage theory is adopted to consider the changes in formation pressure and bottom hole pressure over time under different production rates, so as to determine the formation pressure and bottom hole pressure when the production pressure difference is stable as the input values ​​for the production capacity calculation.

[0049] Furthermore, in one embodiment, calculating the value of the pressure factor when the pressure decreases to a stable production pressure difference includes:

[0050] Establish a non-steady-state seepage model to simulate and calculate the changes in pressure factors over production time under different production rates;

[0051] The pressure factor value when the production differential pressure tends to be stable is calculated based on the pressure factor value obtained from the initial field test based on the simulation results.

[0052] Specifically, in one embodiment, a non-steady-state seepage model is established that takes desorption and stress sensitivity into consideration.

[0053] Specifically, in one embodiment, the pressure determination includes the determination of the formation pressure and the bottom hole flow pressure. The steps are as follows:

[0054] ① Using the unsteady-state seepage model, based on the reservoir parameters and seepage characteristics of the block, the changes in formation pressure and bottom hole pressure over time under different production rates are simulated and calculated. The unsteady-state seepage model is as follows:

[0055]

[0056] x D 、y D 、z D is a dimensionless variable;

[0057]

[0058] Where:

[0059] Q sc is the gas well production under standard conditions, 10 4 m 3 / d;

[0060] is the dimensionless pseudo-pressure;

[0061] c gmi is the gas compressibility coefficient of the matrix system in the original state of the gas reservoir, Pa -1 ;

[0062] c gfi is the gas compressibility coefficient of the fracture system in the original state of the gas reservoir, Pa -1 ;

[0063] φ m 、φ f are the porosity of the matrix system and fracture system, respectively, in decimals;

[0064] K fh is the horizontal permeability of the reservoir, md;

[0065] K fv is the permeability of the reservoir in the vertical direction, md;

[0066] h is the effective thickness of the reservoir, m;

[0067] T sc is the temperature under standard conditions, K;

[0068] P sc is the formation pressure under standard conditions, MPa;

[0069] T is the formation temperature, K;

[0070] L is the effective length of the gas well production interval, m;

[0071] μi is the viscosity of natural gas, mPa·s;

[0072] K m is the permeability of the reservoir matrix system, md;

[0073] K fh is the horizontal permeability of the reservoir fracture system, md.

[0074] ② Numerical solution is performed on the unsteady seepage model established by equation (1), and a series of data on the formation pressure and bottom hole pressure changes with time under production are generated.

[0075] The pressure drop ratio is defined as:

[0076]

[0077] Among them, P i is the initial pressure of the well, P s The pressure at which the production pressure difference begins to stabilize. A series of data points are plotted with production as the horizontal axis and pressure drop ratio as the vertical axis for regression calculation to obtain a function of production and pressure drop ratio.

[0078] Specifically, in one embodiment, the pressure drop percentage of the pressure factor is linearly related to the production.

[0079] Furthermore, in one embodiment, a pressure drop ratio linear variation model based on the pressure factor values ​​obtained from the initial field test is established according to the simulation results, wherein the linear variation constant in the pressure drop ratio linear variation model is related to the seepage characteristics of the reservoir.

[0080] Specifically, in one embodiment, the linear change constant is obtained through regression calculation.

[0081] Specifically, in one embodiment:

[0082] Formation pressure drop ratio:

[0083] ΔPrD (Q g )=a1Q g +b1; (8)

[0084] Pressure drop ratio of bottom hole flowing pressure:

[0085] ΔP wfD (Q g )=a2Q g +b2. (9)

[0086] Therefore, the formation pressure when the production pressure difference is stable is:

[0087] P r '=(1-a1Q g -b1)P r ; (10)

[0088] Bottom hole flowing pressure when production differential pressure is stable:

[0089] P w ' f =(1-a2Q g -b2)P wf (11)

[0090] In formulas (10) and (11), P r 、P wf , Q g They are the formation pressure, bottom hole flow pressure and gas production during the test respectively.

[0091] Where a1, a2, b1, and b2 are related to the seepage characteristics of the reservoir and are obtained through regression calculation.

[0092] Furthermore, in one embodiment, the capacity calculation model includes:

[0093]

[0094] in:

[0095] P r is the formation pressure, MPa;

[0096] P wf is the bottom hole flowing pressure, MPa;

[0097] Q g is the gas production, 10 4 m 3 / d;

[0098] Q AOF is the gas well production capacity, which is unobstructed flow, 10 4 m 3 / d.

[0099] Furthermore, the value of α is not a fixed value, but a dynamic calculation factor that changes with production. Specifically, according to different seepage characteristics, the α function relationship can be divided into exponential, linear, logarithmic, polynomial, and power.

[0100] Specifically, in one embodiment, α is replaced by a function obtained by regression, where:

[0101] The relationship between α value and gas production of gas wells that have undergone systematic well testing in the statistical block;

[0102] The α value is obtained through regression calculation.

[0103] Specifically, in one embodiment:

[0104]

[0105] in:

[0106] A is the laminar flow coefficient, MPa 2 / 10 4 m 3 / d;

[0107] B is the turbulence coefficient, MPa 2 / (10 4 m 3 / d) 2 .

[0108] Based on the well test data within the block, including formation pressure, bottomhole flowing pressure, and open flow rate, the α value at different production rates is calculated according to the formula:

[0109]

[0110] The α value under different gas production rates was calculated by regression, and the functional relationship between α and production was obtained.

[0111] Specifically, in one embodiment, the capacity calculation model further includes:

[0112]

[0113] In formula (15), the selection of the function and the determination of the values ​​of a and b are determined by the seepage characteristics of the shale reservoir, and the values ​​of a and b are obtained through regression calculation.

[0114] Specifically, in one embodiment, based on formula (12), the formation pressure and bottom hole flowing pressure values ​​obtained when the pressure decreases to a stable production pressure difference are used to replace the formation pressure and bottom hole flowing pressure values ​​obtained in the initial field test (substituted into formulas (10) and (11)), and the function obtained by regression is used to replace α (substituted into formula (15)), and the production capacity calculation model is obtained as follows:

[0115]

[0116] The specific implementation process of the method according to an embodiment of the present invention will be described in detail below with reference to specific application scenarios.

[0117] In one embodiment, the dynamic calculation of shale gas well productivity in a certain block includes the following steps:

[0118] (1) Determination of dynamic α value

[0119] Based on the data of well test in the block, including formation pressure, bottom hole pressure and open flow rate, the α value under different production rates is calculated according to formula (14).

[0120] Regression calculation is performed on the α value under different gas production rates to obtain the functional relationship between α and production rate. Specifically, based on the seepage characteristics of the shale reservoir, the function type of formula (15) and the values ​​of a and b are determined by regression calculation. The test data (production and pressure) of the shale gas wells in the block are used to calculate the α value under different production rates according to formula (14), that is, one production rate corresponds to one α value. Then, with the horizontal axis being the gas production rate and the vertical axis being the α value, the points calculated by the above formula are plotted into a scatter plot. For example, the scatter plot of α value and gas production rate in the Weirong-Yongchuan block is shown as follows: Figure 2 As shown in an optional example, you can use exponential, linear, logarithmic, polynomial, power and other functions to fit from the Excel table, and judge which function type it belongs to from the correlation. Once the function is determined, the a and b values ​​are also determined. It can be seen that the α value and gas production meet the following conditions: Figure 2 The power function relationship shown.

[0121] (2) Determination of pressure

[0122] The determination of pressure includes the determination of formation pressure and bottom hole flow pressure. It is divided into the following steps:

[0123] ① Using the unsteady-state seepage model (Equations (1) to (6)), according to the reservoir parameters and seepage characteristics of the block, the changes of formation pressure and bottom hole pressure with time under different production rates are simulated and calculated.

[0124] ② Numerical solution is performed on the unsteady seepage model established by formula (1), and a series of data on the formation pressure and bottom hole pressure changes with time under production are generated. Figure 3 As shown, Figure 3 The curves of formation pressure and bottom hole flowing pressure changing with time at different production rates are simulated based on the characteristic parameters of the shale reservoir in the target block. Figure 3In the figure, curves 1, 2, 3, 4, 5, 6, and curves 7, 8, 9, 10, 11, and 12 correspond to formation pressure and bottomhole flowing pressure, respectively. Curves 1 and 7 correspond to 5,000 cubic meters per day; curves 2 and 8 correspond to 10,000 cubic meters per day; curves 3 and 9 correspond to 20,000 cubic meters per day; curves 4 and 10 correspond to 30,000 cubic meters per day; curves 5 and 11 correspond to 40,000 cubic meters per day; and curves 6 and 12 correspond to 50,000 cubic meters per day. After 500 hours of production, the differential pressure gradually stabilizes.

[0125] The pressure drop ratio is defined as formula (7). With the output as the horizontal axis and the pressure drop ratio as the vertical axis, a series of data points are drawn for regression calculation to obtain the function of output and pressure drop ratio.

[0126] The pressure drop ratio of the formation pressure is given by formula (8);

[0127] The pressure drop ratio of bottom hole flowing pressure is given by formula (9).

[0128] Therefore, the formation pressure when the production differential pressure is stable is expressed as (10), and the bottom hole flow pressure when the production differential pressure is stable is expressed as (11).

[0129] In formula (10) and formula (11), a1, a2, b1, and b2 are related to the seepage characteristics of the reservoir and are obtained through regression calculation.

[0130] Specifically, the target block is calculated by regression to obtain a1=0.0076, b1=0.0001, a2=0.096, b2=0.0017, as shown in the following example: Figure 4 、 Figure 5 shown. Figure 4 is the formation pressure drop ratio curve, Figure 5 It is a bottom hole flowing pressure drop ratio curve.

[0131] (3) Calculate production capacity

[0132] Based on formula (12) of the steady-state binomial capacity equation, formulas (10), (11) and (15) are substituted into formula (12) to obtain the capacity calculation formula (16). The capacity is calculated according to formula (16).

[0133] The method of the present invention targets the characteristic of rapid pressure decrease in shale gas. By combining steady-state and non-steady-state seepage theories, a dynamic calculation method for evaluating the productivity of shale gas wells is derived and established, solving the problem of large calculation errors in existing methods, which results in investment and benefits failing to meet design requirements and causing serious economic losses.

[0134] It should be understood that the embodiments disclosed herein are not limited to the specific structures, processing steps, or materials disclosed herein, but should extend to equivalent substitutions of these features understood by those skilled in the relevant art. It should also be understood that the terminology used herein is for the purpose of describing specific embodiments only and is not intended to be limiting.

[0135] The phrase "one embodiment" mentioned in the specification means that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least one embodiment of the present invention. Therefore, the phrase "one embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0136] Although the embodiments disclosed in the present invention are as described above, the contents described are merely embodiments adopted to facilitate understanding of the present invention and are not intended to limit the present invention. The method according to the present invention may also have various other embodiments. Without departing from the essence of the present invention, those skilled in the art may make various corresponding changes or modifications according to the present invention, and such corresponding changes or modifications shall all fall within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating shale gas well productivity, characterized in that: The method comprises: Based on the steady-state seepage theory, a productivity calculation model applicable to different shale blocks is established. In the process of establishing the productivity calculation model applicable to different shale blocks, the productivity calculation model established includes: Among them: α is the dynamic calculation factor that changes with output; P r is the formation pressure; P wf is the bottom hole pressure; Q g is the gas production; Q AOF is the gas well productivity; In the process of calculating the productivity of shale gas wells using the productivity calculation model, based on the theory of unsteady-state seepage, the pressure factor value obtained by the initial field test is replaced by the pressure factor value when the pressure decreases to a stable production pressure difference; Calculating the pressure factor value when the pressure decreases to a stable production pressure difference includes the following operations: Establish a non-steady-state seepage model to simulate and calculate the changes in pressure factors with production time under different production rates; the pressure factors include formation pressure and bottom hole flow pressure; Based on the simulation results and the pressure factor values ​​obtained from the initial field test, the pressure factor value when the production differential pressure tends to be stable is calculated; The pressure factor value when the production differential pressure tends to be stable is calculated based on the simulation results and the pressure factor value obtained from the initial field test according to the following logic: Based on the simulation results, a pressure factor value linear variation model is established based on the pressure factor values ​​obtained from the initial field test. The linear variation constant in the pressure factor value linear variation model is related to the seepage characteristics of the reservoir. Based on this, a linear relationship formula for the pressure drop ratio of the pressure factor is determined, including: Formation pressure drop ratio △P rD (Q g ): △P rD (Q g )=a1Q g +b1 The pressure drop ratio of bottom hole flow pressure △P wfD (Q g ): △P wfD (Q g )=a2Q g +b2 Where Qg is the gas production, a1, a2, b1, and b2 are linear constants respectively; Then, combined with the following definition of pressure drop ratio, the value of the pressure factor when the production pressure difference tends to be stable is determined: Among them, △P D Indicates the pressure drop ratio, P i is the initial pressure of the well, P s The pressure at which the production differential pressure begins to stabilize; Determine the value of the pressure factor when the production pressure difference tends to be stable according to the following formula: Formation pressure P when production pressure difference is stable r ': P r '=(1-a1Q g -b1)P r ; Bottom hole pressure P′ when production pressure difference is stable wf : P′ wf =(1-a2Q g -b2)P wf ; Where, P r is the formation pressure, the current formation pressure is the formation pressure during the test, P wf is the bottom hole flowing pressure, and the current bottom hole flowing pressure is the bottom hole flowing pressure during the test.

2. The method according to claim 1, characterized in that The pressure factor value obtained during the initial field test is replaced by the pressure factor value when the pressure decreases to a stable production pressure differential, where: The pressure drop during gas well production is predicted based on the unsteady-state equation. The pressure factor value when the pressure drops to a stable production pressure difference is calculated based on the pressure factor value obtained from the initial field test.

3. The method according to claim 1, characterized in that A non-steady-state seepage model was established to simulate and calculate the changes in pressure factors over production time under different production rates, including: The pressure drop percentage of the pressure factor is linearly related to the production rate.

4. The method according to claim 1, wherein The method further includes obtaining the linear change constant through regression calculation.

5. The method according to claim 1, wherein In the capacity calculation model, α is a dynamic calculation factor that changes with output, where: The relationship between α value and gas production of gas wells that have undergone systematic well testing in the statistical block; The α value is obtained through regression calculation.

6. The method according to claim 5, characterized in that The α value is obtained by regression calculation according to the following formula: Among them, α is a dynamic calculation factor that changes with output; P r is the formation pressure, and the current formation pressure is the formation pressure during the test; P wf is the bottom hole pressure, and the current bottom hole pressure is the bottom hole pressure during the test; Q g is the gas production; Q AOF is the gas well productivity; The calculated points are plotted into a scatter plot, and different function types are used for fitting. The function type that matches the gas production and the dynamic calculation factor is determined based on the correlation between the scatter plot distribution and the function curve. The function types include exponential function, linear function, logarithmic function and power function. Calculate α according to the determined function type: Among them, a and b are function operation parameters, respectively. The determination of a and b values ​​is determined by the seepage characteristics of the shale reservoir, and the a and b values ​​are obtained through regression calculation.

Images