Linear flow-elliptical flow analysis method for single-phase water production data of coal bed gas fracturing vertical well

Abstract

The invention discloses a linear flow-elliptical flow analysis method for single-phase water production data of a coalbed methane fracturing vertical well, which comprises the following steps of: establishing an Lf.k0.5 and stress sensitivity coefficient inversion method based on a linear flow production data analysis method by taking zero intercept as a termination cycle condition; giving an original permeability initial value, substituting the original permeability initial value into an elliptical flow production data analysis method, and iteratively determining the original permeability, the fracture half length and the skin coefficient of the coal seam by taking the condition that the original permeability initial value is consistent with a method inversion permeability value as a termination cycle condition. Coal seam parameter consistency is taken as a principle, a linear flow analysis method and an elliptical flow analysis method take Lf.k0.5 and a stress sensitivity coefficient as links, iteration, circulation and feedback processes are built in each of the linear flow analysis method and the elliptical flow analysis method, coal seam basic physical properties and coal seam modification parameters are subjected to collaborative inversion, and the reliability of an inversion result is jointly guaranteed. The method can provide a theoretical basis for subsequent sweet spot area identification, productivity prediction, development scheme formulation and the like of the coal-bed gas well.

Description

Technical Field

[0001] The invention relates to oil and gas field development engineering and unconventional oil and gas reservoir development, and in particular to a linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fractured vertical wells. Background Art

[0002] Undersaturated coalbed methane reservoirs are widely developed in my country and even in the world. The original coalbed pressure of such gas reservoirs is higher than the critical desorption pressure. It takes a long period of single-phase drainage to achieve coalbed decompression 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 mid- and late-stage single-phase gas flow. A small number of studies have explored production data analysis methods based on coalbed gas-water two-phase flow, and the research on production data analysis methods in the early single-phase water stage of coalbed methane wells is weak. The production evolution of undersaturated coalbed methane wells generally includes three stages: early single-phase drainage, mid-stage gas-water two-phase flow, and mid- and late-stage single-phase gas flow. Compared with the inversion of reservoir basic physical properties and transformation parameters through mid- and late-stage production data analysis, the above key parameters can be determined earlier through early data inversion, which is more conducive to coalbed methane well production allocation, drainage system design, and subsequent production optimization. In addition, the characteristics of coalbed methane-water two-phase flow are complex and are affected by multiple factors such as gas desorption, two-phase capillary force, and differences in gas-water two-phase seepage capacity. The existing production data analysis methods for coalbed methane-water two-phase flow are in their infancy, and the reliability and accuracy of the inversion results are still unsatisfactory. For the single-phase gas stage in the late stage of coalbed methane well development, the main body of the analysis method uses conventional gas well analysis methods, taking into account the unique dynamic permeability and gas desorption effect of coal seams, and can more accurately invert the basic physical properties of the reservoir and control reserves. However, only coalbed methane wells with good physical conditions, reasonable drainage and production systems, and no connection with external water bodies can reach the single-phase gas stage after a long production period. Most coalbed methane wells do not have a single-phase gas stage, so the single-phase gas stage production data analysis method is less applicable to coalbed methane wells. The single-phase water stage has the advantages of a single flow state, relatively few factors affecting daily water production, and easy linearization of the water production equation. It can effectively reduce the multi-solution nature of the inversion results of the method and ensure the inversion accuracy. The initial inversion results can effectively support the design of mid- and late-stage production allocation and drainage systems. Therefore, conducting production data analysis in the single-phase water stage of coalbed methane wells has important practical significance.

[0003] The existing single-phase water stage production data analysis method for coalbed methane wells mainly follows the conventional oil and gas wells, without fully considering the dynamic permeability of coal seams and the long-term "moving boundary" caused by low permeability characteristics. The single-phase water analysis method used essentially cannot 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 specific flow type, and there is a general problem of a limited number of inverted physical properties. For example, the existing production data analysis method based on linear flow can only obtain the mathematical relationship between the fracture half field and permeability (L f ·k0.5 ), but cannot determine the fracture half-length and coal seam permeability; the production data analysis method based on boundary control flow can obtain some physical properties of the coal seam and the oil and gas well control area, but cannot determine the coal seam transformation parameters. The actual oil and gas well production data fluctuates greatly. The data processed by the single flow type production data analysis method often has multiple linear segments, which leads to strong multi-solution inversion results. The inherent reason is that the application process of the single flow type method lacks verification and feedback links, and cannot guarantee the reliability of the inversion results. Aiming at the problems of the inadaptability of the existing single-phase water stage production data method to coalbed methane wells, limited inversion parameters, and strong multi-solution, Summary of the invention

[0004] In view of the above-mentioned technical deficiencies, the purpose of the present invention is to provide a linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fracturing vertical wells. Compared with the existing single-phase water stage production data analysis method, it has obvious advantages in the number of inversion parameters and solution accuracy, and can efficiently invert the key physical properties of coal reservoirs and reservoir transformation parameters, providing a theoretical basis for the mid- and late-stage production capacity prediction of coalbed methane wells, the formulation of drainage and production plans, and the calibration of gas well recovery rates.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] The present invention provides a linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fracturing vertical wells, including linear flow analysis and elliptical flow analysis; wherein the linear flow analysis includes the following steps:

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

[0008] S2. Given the initial value of the coal rock stress sensitivity coefficient αo within the range of the coal rock stress sensitivity coefficient in the study area;

[0009] S3. According to formulas (11) and (12), we can get the daily X linear , Y linear And obtain the linear relationship formula (13);

[0010]

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

[0012]

[0013] Among them, q w Represents daily water production, m 3 / d; t represents the production time of coalbed methane well, day; Φ represents the porosity of coal rock, dimensionless; μw Represents the viscosity of coal seam water, cp; C t Represents the comprehensive compression coefficient of coal rock, which is the sum of the pore compression coefficient of coal rock and the water compression coefficient of coal seam, 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 linear abortion water equation after linearization.

[0014] 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;

[0015] 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 S7;

[0016] 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;

[0017]

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

[0019] 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 ;

[0020] S8, L based on linear flow f ·k 0.5 Value calculation L f ;

[0021] S9. Calculate the daily Y according to formulas (19) and (20): ellipse and X ellipse ;

[0022]

[0023]

[0024] L y represents the position of the pressure wave front extending 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 It is the daily horizontal and vertical coordinate expressions of the linearized elliptic flow abortion water equation.

[0025] 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 elliptic streamline relationship;

[0026] 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;

[0027] Coal rock permeability and skin coefficient expression:

[0028]

[0029] S=-b ellipse (25)

[0030] S12. If σ is greater than 1%, the initial value k of coal rock permeability 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 ;

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

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

[0033]

[0034] Among them, v linearrepresents 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 water flow direction, m;

[0035] During the depressurization and drainage process, the coal seam pressure gradually decreases, and the coal seam permeability will gradually decrease due to the stress sensitivity effect. The characterization equation is as follows:

[0036] k(p)=k·exp[α(p i -p)] (2)

[0037] Among them, 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;

[0038] 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 flow, 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, in which the moving boundary perpendicular to the direction of the artificial fracture is characterized by the following equation:

[0039]

[0040] Among them, L y represents the position of the pressure wave front extending 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 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, day;

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

[0042] 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):

[0043]

[0044] 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.

[0045] Considering the stress sensitivity effect of coal rock, substituting formula (2) into formula (5), we get:

[0046]

[0047] Expand formula (6) and integrate it to obtain:

[0048]

[0049] Further deduction, we get:

[0050]

[0051] Substituting formula (3) into formula (8) and switching the unit system to the commonly used unit system in the mine, we get:

[0052]

[0053] Divide both sides of equation (9) by k 0.5 ,have to:

[0054]

[0055] Based on formula (10), the water production equation under linear flow is linearized to obtain formula (11) and formula (12).

[0056] Preferably, see Figure 2 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. 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):

[0057]

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

[0059] Substituting formula (3) into formula (15), we get:

[0060]

[0061] 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:

[0062]

[0063] Among them, S is the skin coefficient of coalbed methane well, which represents the imperfection of gas well and is dimensionless;

[0064] Further transforming formula (17), we get:

[0065]

[0066] Based on formula (18), the water production equation under elliptical flow is linearized and set as follows:

[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, 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 with Y ellipse is the Y axis, X ellipse Draw a scatter plot for the X-axis, identify and fit a linear relationship, the slope and intercept of which are:

[0071] m ellipse =0.543kh (22)

[0072] b ellipse =-S (23)

[0073] Among them, m ellipse is the slope of the elliptical streamline relationship, b ellipse is the intercept of the elliptic streamline relationship;

[0074] Further transforming formulas (22) and (23), we can obtain the expressions of coal rock permeability k and skin coefficient s:

[0075]

[0076] S=-b ellipse (25).

[0077] The beneficial effects of the present invention are as follows: ① A single-phase water stage linear flow production data analysis method with zero intercept as the iteration termination condition is established, which can simultaneously determine the coal rock permeability sensitivity coefficient and L f ·k 0.5 , the existing studies have not considered the harmful effect of coal rock stress sensitivity on permeability; ② The synergistic mechanism of linear flow analysis and elliptical flow analysis is clarified, and 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. The consistency of coal rock permeability is taken as the principle. If the error is large, the initial permeability value is reset and the elliptical flow analysis process is iterated until the error is within the controllable range. Finally, the coal rock permeability and the fracture half-length are determined at the same time. The existing single flow type method can only 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 loop iteration conditions of linear flow analysis and elliptical flow analysis as well as L f ·k 0.5 The transmission method of permeability sensitivity coefficient as an intermediate parameter can directly output coal rock permeability, fracture half-length, stress sensitivity coefficient and skin coefficient through a collaborative analysis process. In general, this method has obvious advantages over the existing single-phase water stage production data analysis method in terms of the number of inversion parameters and solution accuracy. It can efficiently invert the key physical properties of coal reservoirs and reservoir transformation parameters, and provide a theoretical basis for the mid- and late-stage production capacity prediction of coalbed methane wells, the formulation of drainage and production plans, and the calibration of gas well recovery rates. 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 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 be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0083] S1. Collect the production data of the target coalbed methane well, including daily water production, bottom hole pressure and production days;

[0084] S2. Given the initial value of the coal rock stress sensitivity coefficient αo within the range of the coal rock stress sensitivity coefficient in the study area;

[0085] S3. According to formulas (11) and (12), we can get the daily X linear , Y linear And obtain the linear relationship formula (13);

[0086]

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

[0088]

[0089] Among them, q w Represents daily water production, m 3 / d; t represents the production time of coalbed methane well, day; 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 pore compression coefficient of coal rock and the water compression coefficient of coal seam, 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 linear abortion water equation after linearization.

[0090] 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;

[0091] S5. If the intercept is greater than 10 -5 Then the initial value of the coal rock stress sensitivity coefficient α is given again o Repeat steps S2-S4 until the intercept is less than 10 -5 , then implement step S7;

[0092] 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;

[0093]

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

[0095] S7. Stress sensitivity coefficient α and L obtained from linear flow production data analysis f ·k 0.5 The initial permeability value k of the coal rock in the given target block is o ;

[0096] S8, L based on linear flow f ·k 0.5 Value calculation L f ;

[0097] S9. Calculate the daily Y according to formulas (19) and (20): ellipse and X ellipse ;

[0098]

[0099] L y represents the position of the pressure wave front extending 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 It is the daily horizontal and vertical coordinate expressions of the linearized elliptic flow abortion water equation.

[0100] 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 elliptic streamline relationship;

[0101] 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;

[0102] Coal rock permeability and skin coefficient expression:

[0103]

[0104] S=-b ellipse (25)

[0105] S12. If σ is greater than 1%, the initial value k of coal rock permeability 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 ;

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

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

[0108]

[0109] 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 water flow direction, m;

[0110] During the depressurization and drainage process, the coal seam pressure gradually decreases, and the coal seam permeability will gradually decrease due to the stress sensitivity effect. The characterization equation is as follows:

[0111] k(p)=k·exp[α(p i -p)] (2)

[0112] Among them, 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;

[0113] 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 flow, 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, in which the moving boundary perpendicular to the direction of the artificial fracture is characterized by the following equation:

[0114]

[0115] Among them, L y represents the position of the pressure wave front extending perpendicular to the direction of the artificial fracture, m; Φ represents the porosity of the coal rock, dimensionless; C tRepresents the comprehensive compression coefficient of coal rock, which 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, day;

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

[0117] 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):

[0118]

[0119] 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.

[0120] Considering the stress sensitivity effect of coal rock, substituting formula (2) into formula (5), we get:

[0121]

[0122] Expand formula (6) and integrate it to obtain:

[0123]

[0124] Further deduction, we get:

[0125]

[0126] Substituting formula (3) into formula (8) and switching the unit system to the commonly used unit system in the mine, we get:

[0127]

[0128] Divide both sides of equation (9) by k 0.5 ,have to:

[0129]

[0130] Based on formula (10), the water production equation under linear flow 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. 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):

[0132]

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

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

[0135]

[0136] 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:

[0137]

[0138] Among them, S is the skin coefficient of coalbed methane well, which represents the imperfection of gas well and is dimensionless;

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

[0140]

[0141] Based on formula (18), the water production equation under elliptical flow is linearized and set as follows:

[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, 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 with Y ellipse is the Y axis, X ellipse Draw a scatter plot for the X-axis, identify and fit a linear relationship, the slope and intercept of which are:

[0146] m ellipse =0.543kh(22)

[0147] b ellipse =-S(23)

[0148] Among them, m ellipse is the slope of the elliptical streamline relationship, b ellipse is the intercept of the elliptic streamline relationship;

[0149] Further transforming formulas (22) and (23), we can obtain the expressions of coal rock permeability k and skin coefficient s:

[0150]

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

[0152] After the error meets the conditions, the output permeability is considered to reflect the fluid seepage capacity of the coal-rock reservoir, and the skin coefficient is further calculated based on the linear relationship intercept. Therefore, the elliptical flow analysis based on the linear flow analysis results can determine the coal-rock permeability and skin coefficient. Overall, the linear flow-elliptical flow analysis method can simultaneously determine the stress sensitivity coefficient, permeability, fracture half-length and skin coefficient of coalbed methane fracturing vertical wells.

[0153] The method proposed in this embodiment coordinates two flow types that are adjacent in time sequence to jointly invert the key physical properties and transformation parameters of the coal reservoir, and has the remarkable characteristics of strong reliability of the inversion results and fast solution speed. The specific inversion process mainly linearizes the water production equation under different flow types, then processes the production data and identifies the fitted linear segments, and then inverts the target parameters based on the linear relationship (slope, intercept). Due to the complexity of the actual drainage parameters of coalbed methane wells, there are often multiple linear segments in the processed curves, which can easily cause the conventional production data analysis methods established around a single flow type to produce multiple solutions, reducing the reliability of the inversion. The linear flow and elliptical flow focused by this method are adjacent in time sequence. During the application of this method, the production data processing of different flow types presents a linear relationship that is adjacent in time sequence, which can better accurately identify the correct linear segment and reduce the multi-solution. In addition, the linear flow-elliptical flow collaborative production data analysis method is based on L f ·k 0.5 With stress sensitivity coefficient as the link, the system integrates the iterative cycle process of linear flow and elliptical flow analysis, which jointly ensures the reliability of rapid inversion and inversion results.

[0154] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. Linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fracturing vertical wells, characterized by: It includes linear flow analysis and elliptical flow analysis; the linear flow analysis includes the following steps: S1. Collect the production data of the target coalbed methane well, including daily water production, bottom hole pressure and production days; S2. Given the initial value of the coal rock stress sensitivity coefficient αo within the range of the coal rock stress sensitivity coefficient 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, day; 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 pore compression coefficient of coal rock and the water compression coefficient of coal seam, 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 abscissa and ordinate 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 given again 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 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 extending 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 coordinates of the linearized elliptic flow abortion water equation are expressed; 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 elliptic 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 expression: S=-b ellipse (25) S12. If σ is greater than 1%, the initial value k of coal rock permeability 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 fracturing vertical wells according to claim 1, characterized in that: In step S2, the fluid in the linear flow pattern mainly flows into the wellbore along the direction perpendicular to the artificial fracture to form production, and the flow velocity of the single-phase water linear flow 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 water flow direction, m; During the depressurization and drainage process, the coal seam pressure gradually decreases, and the coal seam permeability will gradually decrease due to the stress sensitivity effect. The characterization equation is as follows: k(p)=k·exp[α(p i -p)] (2) Among them, 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 flow, 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, in which the moving boundary perpendicular to the direction of the artificial fracture is characterized by the following equation: Among them, L y represents the position of the pressure wave front extending 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 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, day; 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, substituting formula (2) into formula (5), we get: 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 water production equation under linear flow is linearized to obtain formula (11) and formula (12).

3. The linear flow-elliptical flow analysis method for single-phase water production data of coalbed methane fracturing 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: Among them, S is the skin coefficient of coalbed methane well, which represents the imperfection of 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 follows: 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 with Y ellipse is the Y axis, X ellipse Draw a scatter plot for the X-axis, identify and fit a linear relationship, the slope and intercept of which are: 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 elliptic streamline relationship; Further transforming formulas (22) and (23), we can obtain the expressions of coal rock permeability k and skin coefficient s: S=-b ellipse (25)。

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