Linear flow-elliptical flow analysis method for coalbed methane fractured vertical well single-phase water production data

Abstract

The present invention discloses a linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fracture vertical wells, takes zero intercept as the termination cycle condition, and establishes an L-type linear flow production data analysis method based on the linear flow production data analysis method. f ·k 0.5 With the stress sensitivity coefficient inversion method; given the original permeability initial value and substituted into the elliptical flow production data analysis method, the original permeability initial value and the inversion permeability value of the method are matched as the termination cycle condition, and the original permeability, fracture half-length and skin coefficient of the coal seam are determined iteratively. Based on the principle of coal seam parameter consistency, the linear flow analysis method and the elliptical flow analysis method are based on L f ·k 0.5 Linked to the stress sensitivity coefficient, both methods incorporate built-in iteration, looping, and feedback processes to collaboratively invert basic coal seam properties and coal seam transformation parameters, ensuring the reliability of the inversion results. This invention can provide a theoretical basis for subsequent sweet spot identification, production capacity forecasting, and development plan formulation in coalbed methane wells.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of oil and gas field development engineering and unconventional oil and gas reservoir development, and particularly relates to a linear flow-elliptical flow analysis method for single-phase water production data of a coalbed methane fractured vertical well. BACKGROUND

[0002] Oversaturated coalbed methane reservoirs are generally developed in China and even the whole world. The original coalbed pressure of such gas reservoirs is higher than the critical desorption pressure, and it needs to go through a long single-phase water drainage stage to realize coalbed pressure reduction and desorption, and then form gas-water two-phase flow in the coalbed and finally form wellhead gas production. At present, the production data analysis methods established around coalbed methane development are mainly based on the middle and late single-phase gas flow, and a small amount of research explores the production data analysis method based on coalbed methane gas-water two-phase flow. The production data analysis method research of the early single-phase water stage of coalbed methane wells is weak. The production evolution of oversaturated coalbed methane wells generally includes three stages of early single-phase water drainage, middle gas-water two-phase flow and late single-phase gas flow. Compared with the production data analysis of the middle and late stages to invert the basic reservoir properties and transformation parameters, the early data inversion can determine the above key parameters earlier, which is more conducive to the allocation of coalbed methane wells, the design of drainage system and the subsequent production optimization, etc. In addition, the characteristics of coalbed methane gas-water two-phase flow are complex, which are affected by many factors such as gas desorption, two-phase capillary force, gas-water two-phase flow capacity difference, etc. The existing production data analysis methods for coalbed methane gas-water two-phase flow are still in the initial stage, and the reliability and accuracy of the inversion results are still not ideal. For the single-phase gas stage of the late development stage of coalbed methane wells, the main analysis method is to use the conventional gas well analysis method, considering the unique dynamic permeability of coalbed and gas desorption effect, which can accurately invert the basic reservoir properties and control reserves. However, only the coalbed methane wells with good physical property conditions, reasonable drainage system and no connection with external water body can reach the single-phase gas stage for a long time, and most of the coalbed methane wells do not have the single-phase gas stage. Therefore, the applicability of the single-phase gas stage production data analysis method to coalbed methane wells is weak. The single-phase water stage has the advantages of single flow state, relatively few influencing factors of daily water production, and easy linearization of water production equation, which can effectively reduce the multi-solution of the method inversion results and ensure the inversion accuracy. The initial inversion results can effectively support the design of the middle and late production allocation and drainage system, so it is of great practical significance to develop the production data analysis of the single-phase water stage of coalbed methane wells.

[0003] The existing production data analysis method of the single-phase water stage of coalbed methane wells mainly follows the conventional oil and gas wells, and does not fully consider the long-time "moving boundary" caused by the dynamic permeability of coalbed and low permeability characteristics. The followed single-phase water analysis method cannot essentially meet the analysis needs of coalbed methane wells. In addition, the existing single-phase water stage production data analysis method is often established around a certain specific flow pattern, and generally has the problem of limited inversion properties. For example, the existing production data analysis method based on linear flow can only obtain the mathematical relationship between fracture half-field and permeability (L f ·k0.5 ), but the crack half-length and the coal seam permeability cannot be determined; the production data analysis method based on the boundary control flow can obtain part of the coal seam properties and the oil and gas well control area, but the coal seam reconstruction parameters cannot be determined. The actual oil and gas well production data fluctuates greatly, and the data processed by the single flow type production data analysis method often has multiple linear segments, resulting in strong multi-solution of the inversion result, and the internal reason is that the single flow type method application process lacks a verification feedback link, and cannot guarantee the reliability of the inversion result. In view of the inadaptability of the existing single-phase water stage production data method to the coalbed methane well and the problems of limited inversion parameters and strong multi-solution, SUMMARY

[0004] In view of the above technical deficiencies, the purpose of the present application is to provide a coalbed methane fractured vertical well single-phase water production data linear flow-elliptical flow analysis method. Compared with the existing single-phase water stage production data analysis method, it has obvious advantages in the number of inversion parameters and solving accuracy, and can efficiently invert the key properties of the coal reservoir and the reservoir reconstruction parameters, providing a theoretical basis for the mid-late stage productivity prediction, drainage scheme development and gas well recovery rate calibration of the coalbed methane well.

[0005] To solve the above technical problems, the technical scheme adopted by the present application is as follows:

[0006] The present application provides a coalbed methane fractured vertical well single-phase water production data linear flow-elliptical flow analysis method, which comprises linear flow analysis and elliptical flow analysis; wherein the linear flow analysis comprises the following steps:

[0007] S1, collecting the production data of the target coalbed methane well; including daily water production, bottom hole pressure and production days;

[0008] S2, giving the initial value of the coal rock stress sensitivity coefficient αo in the range of the coal rock stress sensitivity coefficient variation of the research block;

[0009] S3, obtaining the daily X linear , Y linear of the coalbed methane well according to the formula (11), (12);

[0010]

[0011] X linear = exp [α (p i -p w )] - 1 (12)

[0012]

[0013] Wherein, q w represents daily water production, m 3 / d; t represents the production time of the coalbed methane well, days; Φ represents the coal rock porosity, dimensionless; μw represents the coal seam water viscosity, cp; C t represents the coal rock comprehensive compression coefficient, which is the sum of the coal rock pore compression coefficient and the coal seam water compression coefficient, MPa -1 ; α represents the coal rock stress sensitivity coefficient, MPa -1 ; p i represents the original reservoir pressure of the coal seam, MPa; k represents the original permeability of the coal seam, mD; L f represents the fracture half-length, m; h represents the coal reservoir thickness, m; p w represents the bottom hole pressure, MPa; X linear , Y linear respectively represent the daily abscissa and ordinate expressions of the linear flow water production equation after linearization processing.

[0014] S4, draw the (X linear , Y linear ) scatter plot in the rectangular coordinate system, identify and fit the linear segment to obtain m linear and the intercept; m linear is the slope of the above linear relationship;

[0015] S5, if the intercept is greater than 10 -5 , then re-define the initial value of the coal rock stress sensitivity coefficient α o and repeat the above steps S2-S4 until the intercept is less than 10 -5 , then implement step S7;

[0016] S6, determine the coal rock stress sensitivity coefficient α and m linear ; based on formula (14) and m linear , obtain the correct L f ·k 0.5 value;

[0017]

[0018] The elliptical flow analysis includes the following steps:

[0019] S7, according to the stress sensitivity coefficient α and the L f ·k 0.5 value obtained by linear flow production data analysis, define the initial value of the original permeability of the coal rock in the target block k o ;

[0020] S8, calculate L f based on the L 0.5 ·k f value obtained by linear flow;

[0021] S9, calculate Y ellipse and X ellipse of each day according to formulas (19), (20);

[0022]

[0023]

[0024] L y represents the position of the pressure wave front expanding constantly in the direction perpendicular to the artificial fracture direction; L x represents the position of the pressure wave front in the direction along the artificial fracture direction; X ellipse , Y ellipse are the daily horizontal coordinate and vertical coordinate expressions of the linearized elliptical flow equation.

[0025] S10, plot the (X ellipse , Y ellipse ) scatter plot in the rectangular coordinate system, identify and fit the linear segment to obtain m ellipse and b ellipse ; m ellipse is the slope of the linear relationship of the elliptical flow, and b ellipse is the intercept of the linear relationship of the elliptical flow;

[0026] S11, according to m ellipse and formula (24), calculate the coal rock permeability k, and compare the relative error σ between the initial value of the coal rock permeability k o and the coal rock permeability k;

[0027] The expression of the coal rock permeability and the skin factor is:

[0028]

[0029] S = -b ellipse (25)

[0030] S12, if σ is greater than 1%, then the initial value of the coal rock permeability k a is given again and the above steps S7-S11 are repeated until σ is less than 1%, and the coal rock permeability and b ellipse are determined;

[0031] S14, calculate the skin factor according to formula (25) and b ellipse .

[0032] Preferably, in step S2, the fluid mainly flows into the wellbore along the direction perpendicular to the artificial fracture direction to form production under the linear flow pattern, and the flow velocity under the linear flow of single-phase water is expressed as:

[0033]

[0034] wherein v linearrepresenting coal seam water flow velocity under linear flow, m / s; k(p) represents coal seam permeability considering stress sensitivity, mD; p represents coal seam pressure, MPa; μ represents coal seam water viscosity, cp; l represents distance along water flow direction, m; w representing coal seam water viscosity, cp; l represents distance along water flow direction, m;

[0035] During the process of pressure relief drainage, coal seam pressure gradually decreases, and coal seam permeability also gradually decreases under the effect of stress sensitivity, and its representation equation is as follows:

[0036] k(p) = k·exp[α(p i -p)] (2)

[0037] wherein, k represents original coal seam permeability, mD; α represents coal rock stress sensitivity coefficient, MPa -1 ; p i represents original coal seam reservoir pressure, MPa; p represents current coal reservoir pressure, MPa;

[0038] Due to the low permeability characteristics of coal seams, the pressure wave front caused by coalbed methane well production continuously expands outward, when the flow type is linear flow, the propagation direction of the pressure wave front is perpendicular to the artificial fracture, and the overall pressure drop area is a rectangular geometry continuously expanding outward, wherein the moving boundary perpendicular to the artificial fracture is characterized by the following equation:

[0039]

[0040] wherein, L y represents the position of the pressure wave front continuously expanding perpendicular to the artificial fracture, m; Φ represents coal rock porosity, dimensionless; C t represents the comprehensive compression coefficient of coal rock, which is the sum of the coal rock pore compression coefficient and the coal seam water compression coefficient, MPa -1 ; t represents the production time of the coalbed methane well, days;

[0041] C t =C f +C w (4)

[0042] According to the linear flow water flow velocity and flow cross-sectional area, the water production equation of the fractured vertical well under linear flow can be further derived based on formula (1):

[0043]

[0044] wherein, q w represents daily water production, m 3 / d; L f represents fracture half-length, m; h represents coal reservoir thickness, m.

[0045] Considering the stress sensitivity of coal rock, formula (2) is brought into formula (5), and the following formula (6) is obtained:

[0046]

[0047] Formula (6) is expanded and integrated, and the following formula (7) is obtained:

[0048]

[0049] Further derivation is made, and the following formula (8) is obtained:

[0050]

[0051] Formula (3) is brought into formula (8), and the unit system is switched to the unit system commonly used in the mine, and the following formula (9) is obtained:

[0052]

[0053] Both sides of formula (9) are divided by k 0.5 , and the following formula (10) is obtained:

[0054]

[0055] Based on formula (10), linearization is made to the linear flow water production equation, and the following formula (11) and formula (12) are obtained.

[0056] Preferably, referring to Figure 2 , regarding the elliptical flow analysis, as the coalbed methane well is further developed, the pressure wave front continues to expand, the flow pattern gradually evolves from linear flow to elliptical flow, and the pressure wave front expands outward in an elliptical geometric shape, wherein the position of the pressure wave front in the direction perpendicular to the artificial fracture is still characterized by formula (3), and the position of the pressure wave front along the direction of the artificial fracture is characterized by the following formula (15):

[0057]

[0058] Wherein, L x represents the position of the pressure wave front along the direction of the artificial fracture, m;

[0059] Formula (3) is substituted into formula (15), and the following formula (16) is obtained:

[0060]

[0061] Considering the stress sensitivity and the moving boundary, the coalbed methane well water production equation in the unit system of the mine under elliptical flow is as follows:

[0062]

[0063] Wherein, S is the skin factor of the coalbed methane well, representing the imperfection of the gas well, and is dimensionless;

[0064] Further transform formula (17) to obtain:

[0065]

[0066] Based on formula (18), linearize the water production equation of elliptical flow to make:

[0067]

[0068] The linear relationship after processing is:

[0069] Y ellipse =0.543khX ellipse -S (21)

[0070] Similar to the data processing of linear flow, according to the daily report data of coalbed methane well, the daily water production, production days and bottom hole pressure, the Y ellipse and X ellipse of each day are calculated, the scatter plot is drawn in the rectangular coordinate system with Y ellipse as the Y axis and X ellipse as the X axis, the linear relationship is identified and fitted, and the slope and intercept of the linear relationship are:

[0071] m ellipse =0.543kh (22)

[0072] b ellipse =-S (23)

[0073] Wherein, m ellipse is the slope of the linear relationship of elliptical flow, and b ellipse is the intercept of the linear relationship of elliptical flow;

[0074] Further transform formula (22) and (23) to obtain the expressions of coal rock permeability k and skin factor s:

[0075]

[0076] S=-b ellipse (25)。

[0077] The beneficial effects of the present application are: ① a linear flow production data analysis method with zero intercept as the iteration termination condition is established, which can determine the coal rock permeability sensitivity coefficient and L f ·k 0.5 , the existing research does not consider the damage effect of coal rock stress sensitivity on permeability; ② the synergistic mechanism of linear flow analysis and elliptical flow analysis is clarified, the linear flow determines and provides L f ·k 0.5The elliptical flow analysis sets the initial value of coal rock permeability and inverts the coal rock permeability through data processing and linear segment analysis. The initial permeability value and the inverted permeability error are compared. Based on the principle of coal rock permeability consistency, if the error is large, the initial permeability value is reset and the elliptical flow analysis process is iterated until the error is within a controllable range. Finally, the coal rock permeability and fracture half-length are determined at the same time. The existing single flow pattern method can only clearly determine L f ·k 0.5 ;③ A complete set of linear flow-elliptical flow one-click collaborative production data analysis processes has been formed, and the cyclic iteration conditions of linear flow analysis and elliptical flow analysis as well as L f ·k 0.5 This method uses the permeability sensitivity coefficient as an intermediate parameter, and through a collaborative analysis process, it can directly output coal rock permeability, fracture half-length, stress sensitivity coefficient, and skin coefficient. Overall, this method has significant advantages over existing single-phase water production data analysis methods in terms of the number of inversion parameters and solution accuracy. It can efficiently invert key coal reservoir properties and reservoir stimulation parameters, providing a theoretical basis for mid-to-late-stage coalbed methane well production capacity prediction, drainage plan formulation, and gas well recovery rate calibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0079] Figure 1 A schematic flow chart of a linear flow-elliptical flow analysis method for single-phase water production data of a coalbed methane fractured vertical well provided by an embodiment of the present invention;

[0080] Figure 2 This is a characteristic diagram of reservoir flow pattern evolution in the single-phase water stage of coalbed methane fractured vertical wells. DETAILED DESCRIPTION

[0081] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0082] like Figure 1 As shown, the linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fractured vertical wells includes linear flow analysis and elliptical flow analysis; wherein the linear flow analysis includes the following steps:

[0083] S1, collecting target coalbed methane well production data; including daily water production, well bottom pressure and production days;

[0084] S2, giving a coal rock stress sensitivity coefficient initial value αo in the range of coal rock stress sensitivity coefficient variation in the study block;

[0085] S3, obtaining X linear , Y linear of each day according to formula (11), (12);

[0086]

[0087] X linear = exp[α(p i -p w )]-1 (12)

[0088]

[0089] Wherein, q w represents daily water production, m 3 / d; t represents the production time of the coalbed methane well, days; Φ represents the coal rock porosity, dimensionless; μ w represents the coalbed water viscosity, cp; C t represents the coal rock comprehensive compression coefficient, which is the sum of the coal rock pore compression coefficient and the coalbed water compression coefficient, MPa -1 ; α represents the coal rock stress sensitivity coefficient, MPa -1 ; p i represents the original reservoir pressure of the coalbed, MPa; k represents the original permeability of the coalbed, mD; L f represents the fracture half length, m; h represents the coal reservoir thickness, m; p w represents the well bottom pressure, MPa; X linear , Y linear respectively represent the daily horizontal coordinate and vertical coordinate expressions of the linear flow water production equation after linearization processing.

[0090] S4, drawing (X linear , Y linear ) scatter plot in the rectangular coordinate system, identifying and fitting the linear segment to obtain m linear and intercept; m linear is the slope of the above linear relationship;

[0091] S5, if the intercept is greater than 10 -5 , then the coal rock stress sensitivity coefficient initial value α o is given again and the above steps S2-S4 are repeated until the intercept is less than 10 -5 , then step S7 is implemented;

[0092] S6, determine the stress sensitivity coefficient a and m of coal rock linear ; based on formula (14) and m linear Get the correct L f ·k 0.5 Value;

[0093]

[0094] The elliptical flow analysis includes the following steps:

[0095] S7, according to the stress sensitivity coefficient a and L f ·k 0.5 Value obtained by linear flow production data analysis, given the target block coal rock original permeability initial value k o

[0096] S8, calculate L f Based on the L f ·k 0.5 Value obtained by linear flow L f

[0097] S9, according to formula (19), (20) to calculate Y ellipse And X ellipse Per day;

[0098]

[0099] L y Represent the position of the pressure wave front perpendicular to the direction of artificial fracture and continuously expanding; L x Represent the position of the pressure wave front along the direction of artificial fracture; X ellipse , Y ellipse It is the daily horizontal coordinate and vertical coordinate expression of the linearization treatment of elliptical flow water production equation.

[0100] S10, draw (X ellipse , Y ellipse ) scatter plot in rectangular coordinate system, identify and fit linear segment, get m ellipse And b ellipse ; m ellipse It is the slope of the linear relationship of elliptical flow, and b ellipse It is the intercept of the linear relationship of elliptical flow;

[0101] S11, according to m ellipse And formula (24), calculate the permeability k of coal rock, compare the relative error σ between the initial value k o And the permeability k of coal rock;

[0102] The expression of coal rock permeability and skin factor is:

[0103]

[0104] S = -b ellipse (25)

[0105] S12, if σ is greater than 1%, then re-define the initial coal permeability k a and repeat the above steps S7-S11 until σ is less than 1%, determine the coal permeability k and b ellipse ;

[0106] S14, calculate the skin factor according to formula (25) and b ellipse .

[0107] In step S2, under linear flow flow pattern, the fluid mainly flows into the wellbore along the direction perpendicular to the artificial fracture to form production, and the flow velocity under single-phase water linear flow is expressed as:

[0108]

[0109] where v linear represents the flow velocity of coal seam water under linear flow, m / s; k(p) represents the coal seam permeability considering the stress sensitivity effect, mD; p represents the coal seam pressure, MPa; μ w represents the viscosity of coal seam water, cp; l represents the distance along the water flow direction, m;

[0110] During the process of pressure reduction and water drainage, the coal seam pressure gradually decreases, and the coal seam permeability also gradually decreases under the effect of stress sensitivity effect, and its characterization equation is as follows:

[0111] k(p) = k·exp[α(p i -p)] (2)

[0112] where k represents the original permeability of coal seam, mD; α represents the stress sensitivity coefficient of coal and rock, MPa -1 ; p i represents the original reservoir pressure of coal seam, MPa; p represents the current coal reservoir pressure, MPa;

[0113] Due to the low permeability characteristics of coal seams, the pressure wave front caused by the production of coalbed methane wells expands outward continuously, when the flow pattern is linear flow, the propagation direction of the pressure wave front is perpendicular to the artificial fracture, and the overall pressure drop area is a rectangular geometry that expands outward continuously, and the moving boundary perpendicular to the artificial fracture is characterized by the following equation:

[0114]

[0115] where L y represents the position of the pressure wave front expanding vertically to the artificial fracture, m; Φ represents the porosity of coal and rock, dimensionless; C trepresenting the comprehensive compression coefficient of coal rock, is the sum of the pore compression coefficient of coal rock and the water compression coefficient of coal seam, MPa -1 ; t represents the production time of the coalbed methane well, days;

[0116] C t = C f +C w (4)

[0117] According to the linear flow velocity and the flow cross-sectional area, the linear flow downhole water production equation of the fractured vertical well is further derived based on formula (1):

[0118]

[0119] wherein q w represents the daily water production, m 3 / d; L f represents the half length of the fracture, m; and h represents the thickness of the coal reservoir, m.

[0120] Considering the stress sensitivity effect of coal rock, formula (2) is brought into formula (5), and the following formula (6) is obtained:

[0121]

[0122] Formula (6) is expanded and integrated, and the following formula (7) is obtained:

[0123]

[0124] Further derivation gives the following formula (8):

[0125]

[0126] Formula (3) is brought into formula (8), and the unit system is switched to the unit system commonly used in the field, and the following formula (9) is obtained:

[0127]

[0128] Dividing both sides of formula (9) by k 0.5 , the following formula (10) is obtained:

[0129]

[0130] Based on formula (10), the linear flow downhole water production equation is linearized to obtain formula (11) and formula (12).

[0131] Regarding the elliptical flow analysis, as the coalbed methane well is further developed, the pressure wave front continues to expand, and the flow pattern gradually evolves from linear flow to elliptical flow. The pressure wave front expands outward in an elliptical geometric shape, wherein the position of the pressure wave front in the direction perpendicular to the artificial fracture is still represented by formula (3), and the position of the pressure wave front along the direction of the artificial fracture is represented by the following formula (15):

[0132]

[0133] where, L x represents the position of the pressure wave front along the direction of artificial fracture, m;

[0134] Substitute formula (3) into formula (15), we get:

[0135]

[0136] Considering the stress sensitivity effect and the moving boundary, the water production equation of a unit coalbed methane well under elliptical flow is as follows:

[0137]

[0138] where, S is the skin factor of the coalbed methane well, representing the imperfection of the gas well, dimensionless;

[0139] Further transform formula (17), we get:

[0140]

[0141] Based on formula (18), linearize the water production equation under elliptical flow, let:

[0142]

[0143] The linear relationship after processing is:

[0144] Y ellipse = 0.543khX ellipse -S (21)

[0145] Similar to the data processing of linear flow, according to the daily water production, production days and bottom hole pressure of the coalbed methane well, calculate the Y ellipse and X ellipse of each day, draw a scatter plot in the rectangular coordinate system with Y ellipse as the Y axis and X ellipse as the X axis, identify and fit the linear relationship, and the slope and intercept of the linear relationship are:

[0146] m ellipse = 0.543kh (22)

[0147] b ellipse = -S (23)

[0148] where, m ellipse is the slope of the linear relationship of elliptical flow, and b ellipse is the intercept of the linear relationship of elliptical flow;

[0149] Further transformation of formula (22), (23) is made to obtain the expressions of coal permeability k and skin factor s:

[0150]

[0151] S = -b ellipse (25).

[0152] After the error satisfies the condition, the output permeability is considered to reflect the fluid seepage capacity of the coal reservoir, and the skin factor is further calculated according to the linear relationship intercept. Therefore, the elliptical flow analysis that carries the linear flow analysis result can determine the coal permeability and skin factor. Overall, the linear flow-elliptical flow analysis method can simultaneously determine the stress sensitivity coefficient, permeability, fracture half-length and skin factor of the coalbed methane fractured vertical well.

[0153] The method proposed in this embodiment coordinates two types of flow patterns in sequence, and jointly inverts the key properties of the coal reservoir and the reconstruction parameters, and has the significant characteristics of strong reliability of inversion results and fast solving speed. The specific inversion process mainly linearizes the water production equation under different flow patterns, then processes the production data and identifies the linear segment, and then inverts the target parameters based on the linear relationship (slope, intercept). Due to the complexity of the actual drainage parameters of the coalbed methane well, the processed curve often has multiple linear segments, which easily causes the production data analysis method established around a single flow pattern to have multiple solutions, reducing the inversion reliability. The linear flow and the elliptical flow in this method are time-sequentially adjacent, and the linear relationship under the production data processing of different flow patterns in the application process of this method is time-sequentially adjacent, which can accurately identify the correct linear segment, reducing the multiple solutions. In addition, the linear flow-elliptical flow cooperative production data analysis method takes L f ·k 0.5 as the link of the stress sensitivity coefficient, and systematically integrates the linear flow and the elliptical flow analysis iterative cycle process, which jointly guarantees the fast inversion and the reliability of the inversion results.

[0154] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. Linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fractured vertical wells, characterized by: It includes linear flow analysis and elliptical flow analysis; the linear flow analysis includes the following steps: S1. Collect production data of target CBM wells, including daily water production, bottom hole pressure, and production days; S2. Given the initial value of coal rock stress sensitivity coefficient αo within the range of coal rock stress sensitivity coefficient variation in the study area; S3. According to formulas (11) and (12), we can get the daily X linear 、Y linear And obtain the linear relationship formula (13); X linear =exp[α(p i -p w )]-1 (12) Among them, q w Represents daily water production, m 3 / d; t represents the production time of coalbed methane well, days; Φ represents the porosity of coal rock, dimensionless; μ w Represents the viscosity of coal seam water, cp; C t Represents the comprehensive compression coefficient of coal rock, which is the sum of the coal rock pore compression coefficient and the coal seam water compression coefficient, MPa -1 ; α represents the stress sensitivity coefficient of coal rock, MPa -1 ;p i represents the original reservoir pressure of the coal seam, MPa; k represents the original permeability of the coal seam, mD; L f represents the half-length of the fracture, m; h represents the thickness of the coal reservoir, m; p w represents the bottom hole pressure, MPa; X linear 、Y linear They represent the daily horizontal and vertical expressions of the linearized abortion water equation respectively; S4. Draw (X linear , Y linear ) scatter plot, identify and fit the linear segment, and get m linear and intercept; m linear is the slope of the above linear relationship; S5. If the intercept is greater than 10 -5 Then the initial value of the coal rock stress sensitivity coefficient α is re-given o Repeat steps S2-S4 until the intercept is less than 10 -5 , then implement step S6; S6. Determine the stress sensitivity coefficient α and m of coal rock linear ; Based on formula (14) and m linear Get the right L f ·k 0.5 value; The elliptical flow analysis comprises the following steps: S7. Stress sensitivity coefficient α and L obtained from linear flow production data analysis f ·k 0.5 Value, given the initial value k of the original permeability of the target block coal rock o ; S8, L obtained based on linear flow f ·k 0.5 Value calculation L f ; S9. Calculate the daily Y according to formulas (19) and (20) ellipse and X ellipse ; L y represents the position of the pressure wave front that continues to expand perpendicular to the direction of the artificial fracture; L x represents the position of the pressure wave front along the direction of the artificial fracture; X ellipse , Y ellipse The daily horizontal and vertical coordinate expressions of the linearized elliptic flow abortion water equation; S10. Draw (X ellipse , Y ellipse ) scatter plot, identify and fit the linear segment, and get m ellipse and b ellipse ;m ellipse is the slope of the elliptical streamline relationship, b ellipse is the intercept of the elliptical streamline relationship; S11, according to m ellipse Calculate the coal rock permeability k with formula (24) and compare the initial value of coal rock permeability k o The relative error σ between the coal rock permeability k; Coal rock permeability and skin coefficient expressions: S=-b ellipse (25) S12. If σ is greater than 1%, the initial value of coal rock permeability k is re-given. a Repeat the above steps S7-S11 until σ is less than 1% to determine the relationship between coal rock permeability and b ellipse ; S14, according to formula (25) and b ellipse Calculate the skin factor.

2. The linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fractured vertical wells according to claim 1, characterized in that: In step S2, under the linear flow pattern, the fluid mainly flows into the wellbore in a direction perpendicular to the artificial fracture to generate production. The flow velocity of the single-phase water under the linear flow pattern is expressed as: Among them, v linear represents the water velocity of the coal seam under linear flow, m / s; k(p) represents the permeability of the coal seam considering the influence of stress sensitivity, mD; p represents the coal seam pressure, MPa; μ w represents the viscosity of coal seam water, cp; l represents the distance along the direction of water flow, m; During the depressurization and drainage process, the coal seam pressure gradually decreases, and the coal seam permeability will also gradually decrease due to the stress sensitivity effect. The characterization equation is as follows: k(p)=k·exp[α(p i -p)] (2) Where k represents the original permeability of the coal seam, mD; α represents the stress sensitivity coefficient of the coal rock, MPa -1 ;p i represents the original reservoir pressure of the coal seam, MPa; p represents the current reservoir pressure of the coal seam, MPa; Due to the low permeability of coal seams, the pressure wave front caused by coalbed methane well production continues to expand outward. When the flow pattern is linear, the propagation direction of the pressure wave front is perpendicular to the artificial fracture, and the overall pressure drop area is a continuously expanding rectangular geometric shape. The moving boundary perpendicular to the artificial fracture direction is represented by the following equation: Among them, L y represents the position of the pressure wave front that continues to expand perpendicular to the direction of the artificial fracture, m; Φ represents the porosity of the coal rock, dimensionless; C t Represents the comprehensive compression coefficient of coal rock, which is the sum of the coal rock pore compression coefficient and the coal seam water compression coefficient, MPa -1 ; t represents the production time of CBM well, days; C t =C f +C w (4) According to the linear flow velocity and flow cross-sectional area, the water production equation of a fractured vertical well under linear flow can be further derived based on formula (1): Among them, q w Represents daily water production, m 3 / d;L f represents the half-length of the fracture, m; h represents the thickness of the coal reservoir, m; Considering the stress sensitivity effect of coal rock, we can substitute formula (2) into formula (5) and obtain: Expand formula (6) and integrate it to obtain: Further deduction, we get: Substituting formula (3) into formula (8) and switching the unit system to the commonly used unit system in the mine, we get: Divide both sides of equation (9) by k 0.5 ,have to: Based on formula (10), the linear flow water production equation is linearized to obtain formulas (11) and (12).

3. The linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fractured vertical wells according to claim 1, characterized in that: With the further development of coalbed methane wells, the pressure wave front continues to expand, and the flow pattern gradually evolves from linear flow to elliptical flow. The pressure wave front expands outward in an elliptical geometric shape. The position of the pressure wave front perpendicular to the artificial fracture direction is still represented by formula (3), and the position of the pressure wave front along the artificial fracture direction is represented by the following formula (15): Among them, L x represents the position of the pressure wave front along the direction of the artificial fracture, m; Substituting formula (3) into formula (15), we get: Considering the stress sensitivity effect and moving boundary, the water production equation of the unit coalbed methane well in the mine under elliptical flow is as follows: Where S is the skin coefficient of the coalbed methane well, which represents the imperfection of the gas well and is dimensionless; Further transforming formula (17), we get: Based on formula (18), the water production equation under elliptical flow is linearized and set as: The linear relationship after processing is: Y ellipse =0.543khX ellipse -S (21) Similar to the data processing of linear flow, the daily water production, production days and bottom hole pressure of the coalbed methane well are used to calculate the daily Y ellipse and X ellipse , in the rectangular coordinate system, Y ellipse is the Y axis, X ellipse Draw a scatter plot for the X-axis and identify and fit a linear relationship with the slope and intercept being: m ellipse =0.543kh (22) b ellipse =-S (23) Among them, m ellipse is the slope of the elliptical streamline relationship, b ellipse is the intercept of the elliptical streamline relationship; Further deformation of formulas (22) and (23) yields the expressions for coal rock permeability k and skin coefficient s: S=-b ellipse (25)。

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