Well testing analysis and interpretation method for single-medium different-boundary oil reservoir inclined shaft

Abstract

The invention belongs to the technical field of oil reservoir development dynamic monitoring data interpretation and analysis, and particularly relates to a well testing analysis and interpretation method for a single-medium different-boundary oil reservoir inclined shaft. A well testing analysis and interpretation method for a single-medium different-boundary oil reservoir inclined shaft comprises the following steps that according to the characteristics of a single-medium oil reservoir, an instantaneous point source diffusion equation of the single-medium oil reservoir is listed in combination with different types of boundary conditions; according to a mirror image reflection rule, carrying out infinite multiple times of symmetry along top and bottom boundaries through a LordKelvin basic solution, and superposing sources to obtain a single-medium oil reservoir instantaneous point source function basic solution under different types of boundary conditions; and integrating along the track of the mirror image inclined shaft in combination with the track of the mirror image inclined shaft, and obtaining the bottom hole pressure response of the inclined shaft in the single medium oil reservoir under different types of boundary conditions through dimensionless. Compared with a conventional vertical shaft theory for explaining inclined shaft data, the method has the advantage that the adaptability and precision of analysis and explanation can be greatly improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of oil reservoir development dynamic monitoring data interpretation and analysis, and particularly relates to a well test analysis and interpretation method for a single medium different boundary inclined well. BACKGROUND

[0002] As an important method for understanding reservoir dynamics, well test data interpretation and analysis is mainly used to evaluate the response characteristics of oil and gas wells or reservoirs and obtain relevant dynamic parameters according to the test data of oil and gas wells. With the continuous development of drilling technology, complex structure wells such as inclined wells, horizontal wells, and branch wells are increasing, and their testing methods and interpretation methods have also developed to meet production needs. The completion, well testing, and interpretation of inclined wells are usually more complex than that of straight wells.

[0003] At present, there are more studies on well test technology for horizontal wells and straight wells, and relatively less studies on pressure test data interpretation and research for inclined wells, especially for inclined well test interpretation and analysis technology under complex geological conditions and complex boundary conditions, which are rarely published. Patent CN202211593363.1 discloses an improved MDH well test analysis method (MDH well test analysis method is a well test analysis method proposed by Miller, Dyes, and Hutchinson in 1950, mainly used to analyze the radial flow section of pressure buildup data, and analyze the formation permeability and skin factor data), which optimizes the MDH method by the difference of the shut-in pressure at different times, and uses the new model established by the optimized formula to output the optimal solution. This method effectively eliminates the effects of wellbore afterflow and oil layer skin factor, maintains the stability of the slope and the accuracy of the test flow pressure before shut-in, but this method is only limited to the pressure test data interpretation and research of straight wells, and is not suitable for inclined well interpretation. Patent CN202010615379.2 discloses a single well test analysis method, which unifies the circular closure and circular constant pressure boundary conditions of the Darcy seepage well test model of homogeneous deposits, and establishes a new well test interpretation model. However, this method is only limited to the unification of circular closure and circular constant pressure boundary conditions, and does not consider other types of boundary conditions. Patent CN200810019198.2 proposes a well test analysis method based on small signal extraction technology, which makes an interpretation of pressure data well test analysis without radial flow straight line segment, but this method is more inclined to early well test interpretation optimization, and has little relevance to the present application method. SUMMARY

[0004] In view of the above problems, the purpose of the present application is to provide a well test analysis and interpretation method for inclined wells in single medium different boundary reservoirs, which establishes a single medium different boundary reservoir well test model by using a point source function and determines its basic solution, obtains a numerical solution of the bottom hole pressure response equation of the inclined well by using the mirror reflection principle, the Duhamel superposition principle and the Stehfest inversion algorithm, and draws a double logarithmic typical curve of the bottom hole pressure and the pressure derivative of the inclined well, so as to establish an interpretation and analysis method for the well test data of the inclined well in the single medium different boundary reservoir, and compared with the interpretation of the inclined well data by using the conventional straight well theory, the adaptability and accuracy of the analysis and interpretation can be greatly improved.

[0005] The technical scheme of the present application is as follows: a well test analysis and interpretation method for inclined wells in single medium different boundary reservoirs, comprising the following steps:

[0006] S1: according to the characteristics of the single medium reservoir, combining different types of boundary conditions, listing the instantaneous point source diffusion equation, the different types of boundary conditions include top and bottom closed boundary, top and bottom constant pressure boundary, top and bottom mixed boundary, circular closed outer boundary and circular constant pressure outer boundary;

[0007] S2: according to the mirror reflection rule, through the Lord_Kelvin basic solution, along the top and bottom boundary, make infinite times of symmetry, after superposition of the source, get the basic solution of the single medium reservoir instantaneous point source function under different types of boundary conditions;

[0008] S3: combine the mirror inclined well trajectory with the basic solution of the single medium reservoir instantaneous point source function under different types of boundary conditions obtained in step S2, integrate along the mirror inclined well trajectory, and get the bottom hole pressure response of the inclined well in the single medium reservoir under different types of boundary conditions through non-dimensionalization.

[0009] The instantaneous point source diffusion equation is specifically:

[0010]

[0011] In the formula, M D is the pressure response observation point; M' D is the point source; s is the Laplace variable; M D is the pressure response observation point; M' D is the point source; s is the Laplace variable;

[0012] The boundary condition of the top and bottom closed boundary is:

[0013]

[0014] In the formula, z D is a point on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0015] The boundary conditions for the top and bottom isobaric boundaries are as follows:

[0016]

[0017] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0018] The boundary conditions for the top-bottom hybrid boundary are as follows:

[0019]

[0020] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0021] The boundary conditions for the circular closed outer boundary are as follows:

[0022]

[0023] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; r D r eD The response of a unit intensity source; z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0024] The boundary conditions for the circular isobaric outer boundary are as follows:

[0025]

[0026] In the formula, z D Points on the well trajectory; M D pressure response of a unit strength transient point source located at M D r D , r eD is the response of a unit strength source; z e is the dimensionless formation thickness, and l is the characteristic length,

[0027] The step S2 is to obtain the basic solution of the transient point source function of a single medium reservoir under different types of boundary conditions after superimposing the source is:

[0028]

[0029] wherein, M D pressure response of a unit strength transient point source located at M D ; p is the fluid density, kg / m 3 ; and s is the Laplace variable.

[0030] The specific process of obtaining the bottom hole pressure response of a deviated well in a single medium reservoir under different types of boundary conditions in the step S3 is as follows:

[0031] S31: First, the trajectory equation of the deviated well is listed according to the boundary conditions, and the trajectory equation is differentiated and combined with the basic solution of the transient point source function of a single medium reservoir under different types of boundary conditions obtained in the step S2 to obtain the bottom hole pressure response of the deviated well in a single medium reservoir under corresponding boundary conditions

[0032] S31: The bottom hole pressure response of the deviated well in a single medium reservoir under corresponding boundary conditions obtained in the step S31 is introduced into the dimensionless pressure to obtain the dimensionless bottom hole pressure response of the deviated well in a single medium reservoir under corresponding boundary conditions:

[0033] wherein, k is the rock permeability, m 2 ; p is the fluid viscosity, mPa·s; p is the pressure, MPa; q is the volume flow rate, m 3 / s; x, y, z are point coordinates; z e is the dimensionless formation thickness; and l is the characteristic length,

[0034]

[0035] ​​The technical effect of the present application is that the present application establishes a single medium different boundary reservoir well testing model by a point source function and determines the basic solution thereof, on the basis of which, by using the mirror reflection principle, the Duhamel superposition principle and the Stehfest inversion algorithm, the numerical solution of the bottom hole pressure response equation of the deviated well is calculated and the double logarithmic typical curve of the bottom hole pressure and the pressure derivative of the deviated well is drawn, so that the interpretation and analysis method of the deviated well testing data of the single medium different boundary reservoir is established, and compared with the conventional straight well theory for interpreting the deviated well data, the adaptability and the accuracy are greatly improved.

[0036] Further illustration will be made below in combination with the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 A flow chart of a well testing analysis and interpretation method for a single medium different boundary reservoir deviated well according to an embodiment of the present application.

[0038] Figure 2 A top and bottom closed plate-shaped formation boundary schematic diagram according to an embodiment of the present application.

[0039] Figure 3 A top and bottom constant pressure plate-shaped formation boundary schematic diagram according to an embodiment of the present application.

[0040] Figure 4 A top and bottom mixed plate-shaped formation boundary schematic diagram according to an embodiment of the present application.

[0041] Figure 5 A boundary schematic diagram of an external boundary circular closed reservoir according to an embodiment of the present application.

[0042] Figure 6 A boundary schematic diagram of an external boundary circular constant pressure reservoir according to an embodiment of the present application.

[0043] Figure 7 A deviated well model in a top and bottom closed rectangular fault reservoir according to an embodiment of the present application.

[0044] Figure 8 A BA well pressure and pressure derivative double logarithmic curve fitting diagram according to an embodiment of the present application.

[0045] Figure 9 A BA well semi-log fitting diagram according to an embodiment of the present application. DETAILED DESCRIPTION

[0046] Embodiment 1

[0047] As shown in the drawings, a well testing analysis and interpretation method for a single medium different boundary reservoir deviated well includes the following steps: Figure 1

[0048] ​S1: according to the characteristics of single medium reservoir, combining different types of boundary conditions, including top and bottom closed boundary, top and bottom constant pressure boundary, top and bottom mixed boundary, circular closed outer boundary and circular constant pressure outer boundary, the transient point source diffusion equation is listed;

[0049] S2: according to the mirror reflection rule, through Lord_Kelvin basic solution, along the top and bottom boundary infinite times of symmetry, the source is superposed to obtain the single medium reservoir transient point source function basic solution under different types of boundary conditions;

[0050] S3: for the single medium reservoir transient point source function basic solution under different types of boundary conditions obtained in step S2, combined with the mirror inclined well trajectory, the integral is carried out along the trajectory of the mirror inclined well, and the bottom hole pressure response of the inclined well in the single medium reservoir under different types of boundary conditions is obtained through dimensionless.

[0051] The transient point source diffusion equation is specifically:

[0052]

[0053] In the formula, M D is the pressure response observation point; M' D is the point source; s is the Laplace variable; M D is the pressure response of the unit strength transient point source located at M' D , and ∞ is the infinite distance, and δ is the transient function.

[0054] As Figure 2 shown, the boundary condition of the top and bottom closed boundary is:

[0055]

[0056] In the formula, z D is the point on the well trajectory; M D is the pressure response of the unit strength transient point source located at M' D ; z e is the dimensionless formation thickness, and l is the characteristic length,

[0057] As Figure 3 shown, the boundary condition of the top and bottom constant pressure boundary is:

[0058]

[0059] In the formula, z D is the point on the well trajectory; M D is the pressure response of the unit strength transient point source located at M'D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0060] like Figure 4 As shown, the boundary conditions of the top-bottom hybrid boundary are:

[0061]

[0062] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0063] like Figure 5 As shown, the boundary conditions of the circular closed outer boundary are:

[0064]

[0065] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; r D r eD The response of a unit intensity source; z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0066] like Figure 6 As shown, the boundary conditions of the circular constant-pressure outer boundary are:

[0067]

[0068] In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; r D r eD The response of a unit intensity source; z e Let l be the dimensionless stratum thickness and l be the characteristic length.

[0069] In step S2, the source superposition is used to obtain the basic solutions of the instantaneous point source function of a single-medium reservoir under different types of boundary conditions. for:

[0070]

[0071] In the formula, At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; ρ is the fluid density, kg / m³. 3 ; s is a Laplace variable.

[0072] The specific process for obtaining the bottom hole pressure response of a deviated well in a single-medium reservoir under different boundary conditions in step S3 is as follows:

[0073] S31: First, list the trajectory equation of the deviated well based on the boundary conditions, and then differentiate it. Substitute the equation into the fundamental solution of the instantaneous point source function of a single-medium reservoir under different types of boundary conditions obtained in step S2. The bottom hole pressure response of a deviated well in a single-medium reservoir under the corresponding boundary conditions was obtained.

[0074] S31: Bottomhole pressure response of a deviated well in a single-medium reservoir under the corresponding boundary conditions obtained in step S31. Introducing dimensionless pressure, the dimensionless bottom hole pressure response of a dimensionless deviated well in a single-medium reservoir under the corresponding boundary conditions is obtained:

[0075]

[0076] In the formula, k is the rock permeability, in μm 2 μ is the fluid viscosity (mPa·s); p is the pressure (MPa); q is the volumetric flow rate (m³ / s). 3 / s; x, y, z are the coordinates of the point; z e l represents the dimensionless stratum thickness; l represents the characteristic length.

[0077] This explanation uses a top-and-bottom sealed right-angle fault reservoir as an example. The deviated well model in a top-and-bottom sealed right-angle fault reservoir is shown below. Figure 7 Let the distances from the center of the deviated well to the two faults be L1 and L2, respectively. The right-angle fault is a completely impermeable fault. Let the midpoint of the deviated well be denoted by M′, and the midpoints of the mirrored wells be denoted by M″, M″′, and M″″, respectively. The deviated well is parallel to one of the faults. From the fundamental solution of the point source function, the fundamental solution of the point source function in the top-bottom closed right-angle fault reservoir is:

[0078]

[0079] In the formula, z D Points on the well trajectory; At time 0, MD pressure response of a point source with unit strength at M' D ; s is Laplace variable; R Di is boundary distance.

[0080]

[0081] where RDi is boundary distance; x, y, z are point coordinates; z e is dimensionless formation thickness; and l is characteristic length. By using Poisson formula, formula (12) is simplified as

[0082]

[0083] where R Di is boundary distance; z D is a point on well trajectory; x, y, z are point coordinates; z e e is dimensionless formation thickness; l is characteristic length; K0 is Bessel function; and s is Laplace variable.

[0084] As shown in formula (13), the well trajectory equation of a deviated well is: Figure 6

[0085] z-z' = cotθ(x-x') (14)

[0086] The mirror well trajectory satisfies formula (15):

[0087]

[0088] By combining formula (13) and formula (15), formula (16) is obtained:

[0089]

[0090] By substituting formula (16) into formula (13) and integrating along the deviated well trajectory, the bottom hole pressure response of a deviated well in a top-to-bottom sealing right-angle fault reservoir is obtained by dimensionless, as shown in formula (17):

[0091]

[0092] where k is rock permeability, m 2 ; μ is fluid viscosity, mPa·s; p is pressure, MPa; q is volume flow rate, m 3 / s; x, y, z are point coordinates; z e e is dimensionless formation thickness; K0 is Bessel function; and s is Laplace variable.

[0093] The bottom hole pressure responses of deviated wells under other types of boundary conditions can be obtained in the same way.

[0094] Example 2

[0095] The well test analysis and interpretation method for the inclined well of the single medium different boundary reservoir in example 1 is used to interpret and analyze the well test result of the BA well, and the specific process is as follows:

[0096] S1: The daily oil production of the BA well before shut-in is 0.753t, and then the shut-in pressure recovery is 27.18h, according to the drilling data of the well, firstly, the pressure and pressure derivative double logarithmic curve fitting graph is drawn, as shown in the figure, according to the end characteristics of the well curve fitting graph, it can be judged that there is a non-permeable fracture zone near the well, and the constant pressure characteristics are not obvious, which is consistent with the actual geological characteristics of the well, after comprehensive consideration, the model of top and bottom closed single medium homogeneous formation and boundary of right angle fault is selected for fitting; Figure 8

[0097] S2: According to the model type, the basic solution of the top and bottom closed right angle fault formation point source function is listed See formula (12);

[0098] S3: The well trajectory equation of the inclined well is listed, and its mirror image is listed, the mirror image well trajectory satisfies equation group formula (15); formula (12) and formula (15) are combined, the result is brought into Simplify the formula, and integrate along the inclined well trajectory, the bottom hole pressure response of the inclined well in the top and bottom closed right angle fault reservoir can be obtained by non-dimensionalization, see formula (17), finally, the fitting result is shown in table 1 and Figure 9 .

[0099] Table 1: Interpretation and fitting parameter results of BA well

[0100]

[0101]

[0102] By comparing the fitting results of the inclined well model and the straight well model, it can be seen that the fitting results of the inclined well model are more consistent with the actual geological characteristics of the well, and can better reflect the actual situation of the reservoir. And the calculation parameters of the inclined well interpretation model are more accurate, and the applicability is stronger.

[0103] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application.​

Claims

1. A well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, characterized in that: Includes the following steps: S1: Based on the characteristics of a single-medium reservoir, the instantaneous point source diffusion equation is listed in combination with different types of boundary conditions. The different types of boundary conditions include top and bottom closed boundary, top and bottom isobaric boundary, top and bottom mixed boundary, circular closed outer boundary and circular isobaric outer boundary. S2: According to the mirror reflection law, by performing infinitely many symmetries along the top and bottom boundaries using the Lord_Kelvin fundamental solution, the sources are superimposed to obtain the fundamental solutions of the instantaneous point source function of a single medium reservoir under different types of boundary conditions; S3: Combine the fundamental solutions of the instantaneous point source function of a single-medium reservoir under different boundary conditions obtained in step S2 with the trajectory of the mirrored deviated well, and integrate along the trajectory of the mirrored deviated well. By dimensionless transformation, the bottom hole pressure response of the deviated well in a single-medium reservoir under different boundary conditions is obtained.

2. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 1, is characterized in that: The instantaneous point source diffusion equation is specifically as follows: In the formula, M D M' is the pressure response observation point. D s is a point source; s is a Laplace variable; At time 0, M D For the location M' D The pressure response of a unit intensity instantaneous point source at a given location is given by ∞, where ∞ is at infinity and δ is an instantaneous function.

3. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: The boundary conditions for the top and bottom closed boundaries are as follows: In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

4. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: The boundary conditions for the top and bottom isobaric boundaries are as follows: In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

5. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: The boundary conditions for the top-bottom hybrid boundary are as follows: In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at z e Let l be the dimensionless stratum thickness and l be the characteristic length.

6. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: The boundary conditions for the circular closed outer boundary are as follows: In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; r D r eD The response of a unit intensity source; z e Let l be the dimensionless stratum thickness and l be the characteristic length.

7. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: The boundary conditions for the circular isobaric outer boundary are as follows: In the formula, z D Points on the well trajectory; At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; r D r eD The response of a unit intensity source; z e Let l be the dimensionless stratum thickness and l be the characteristic length.

8. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 2, is characterized in that: In step S2, the source superposition is used to obtain the basic solutions of the instantaneous point source function of a single-medium reservoir under different types of boundary conditions. for: In the formula, At time 0, M D For the location M' D Pressure response of a unit intensity instantaneous point source at a given location; ρ is the fluid density, kg / m³. 3 ; s is a Laplace variable.

9. The well test analysis and interpretation method for deviated wells in reservoirs with different boundaries in a single medium, as described in claim 8, is characterized in that: The specific process for obtaining the bottom hole pressure response of a deviated well in a single-medium reservoir under different boundary conditions in step S3 is as follows: S31: First, list the trajectory equation of the deviated well based on the boundary conditions, and then differentiate it. Substitute the equation into the fundamental solution of the instantaneous point source function of a single-medium reservoir under different types of boundary conditions obtained in step S2. The bottom hole pressure response of a deviated well in a single-medium reservoir under the corresponding boundary conditions was obtained. S31: Bottomhole pressure response of a deviated well in a single-medium reservoir under the corresponding boundary conditions obtained in step S31. Introducing dimensionless pressure, the dimensionless bottom hole pressure response of a dimensionless deviated well in a single-medium reservoir under the corresponding boundary conditions is obtained: In the formula, k is the rock permeability, in μm 2 μ is the fluid viscosity (mPa·s); p is the pressure (MPa); q is the volumetric flow rate (m³ / s). 3 / s; x, y, z are the coordinates of the point; z e l represents the dimensionless stratum thickness; l represents the characteristic length.

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