Method and system for calculating bubble size of reservoir around oil and gas well

Abstract

The invention provides a method and system for calculating the bubble size of a reservoir around an oil and gas well, and belongs to the technical field of bubble driving of the reservoir around the well, and the method comprises the following steps: obtaining rock physical parameters of the reservoir around the well; calculating the pressure gradient of the reservoir around the well according to the rock physical parameters; based on the pressure gradient, acquiring a long axis and a short axis of a maximum elliptical region formed by bubble projection; calculating the distance from any point of the bubble to the plane where the maximum elliptical region is located according to the long axis and the short axis of the maximum elliptical region and in combination with rock physical parameters; and calculating the coordinate of any point on the surface of the bubble according to the long axis and the short axis of the maximum elliptical region and the distance from any point of the bubble to the plane where the maximum elliptical region is located, thereby determining the size of the bubble. According to the method, the accuracy of the obtained bubble size can be ensured by quantitatively calculating the rock physical parameters of the reservoir around the well, the pressure gradient, the size of the projection area during bubble floating and the distance from any point on the bubble surface to the projection area.

Description

Technical Field

[0001] The present invention belongs to the technical field of bubble-driven wellbore peripheral reservoirs, and particularly relates to a method and system for calculating the bubble size of wellbore peripheral reservoirs in oil and gas wells. Background Art

[0002] The change of bubble size in the wellbore peripheral reservoir of an oil and gas well has an important impact on the reservoir parameters, which is directly related to the flow characteristics of the gas-liquid two-phase flow, the reservoir development efficiency, and the production optimization of the oil and gas well. The change of bubble size affects the driving behavior of the fluid. Smaller bubbles can enhance the momentum transfer and liquid-carrying capacity between gas and liquid, improve the oil and gas utilization degree of the reservoir, while large bubbles may block the seepage channels, increase the flow resistance, and reduce the development efficiency. Therefore, studying the law of bubble size helps to optimize the flow pattern management of the reservoir and improve the gas-liquid seepage characteristics.

[0003] In addition, the bubble size also has an important impact on the pressure distribution and liquid-carrying performance of the wellbore peripheral reservoir. Appropriate bubble size can enhance the liquid-carrying effect, avoid the risk of liquid blockage, thus maintaining the pressure balance of the wellbore peripheral reservoir and maintaining efficient development. In low-permeability reservoirs (such as shale gas reservoirs), the bubble size is particularly important because reasonable regulation of bubble characteristics can help optimize the fracturing scheme and gas injection driving strategy of unconventional gas reservoirs, and further improve the recovery rate. The study of bubble size also provides a scientific basis for the numerical simulation of gas wells, thus constructing a more accurate fluid flow model, and has guiding significance for technological innovations such as the design of foaming agents and the optimization of gas injection processes. Therefore, paying attention to the change law of bubble size can not only improve the reservoir development efficiency, but also provide theoretical and practical basis for the long-term stability of gas well operation.

[0004] At present, the calculation methods of bubble size in the wellbore peripheral reservoir of oil and gas wells mainly include pressure and hydrodynamic analysis, downhole camera, dynamic gas measurement, and foaming agent experiment, etc. These methods provide various technical means for the study of the characteristics of gas-liquid two-phase flow in the reservoir through direct measurement or indirect calculation, combined with experimental analysis and data modeling. The pressure and hydrodynamic analysis method is simple and easy to use, but its accuracy depends on model parameters and is suitable for preliminary judgment of gas-liquid flow pattern characteristics. The downhole camera technology is intuitive and has high accuracy, and can directly observe the bubble size, but it is mainly limited to the wellbore range. The dynamic gas measurement indirectly calculates the reservoir bubble characteristics through gas-liquid separation data. The technology is mature but the accuracy depends more on parameter inversion. The foaming agent experiment accurately analyzes the bubble generation law in the laboratory, but there is a large difference from the field and actual verification is needed.

[0005] In summary, the accuracy of the bubble size obtained by the existing bubble size acquisition methods is relatively low, and there is a large difference from the field. Summary of the Invention

[0006] To overcome the deficiencies of the above-mentioned existing technologies, the present invention provides a method for calculating the bubble size of the reservoir around an oil and gas well, comprising the following steps: Obtain the petrophysical parameters of the reservoir around the well; Calculate the pressure gradient of the reservoir around the well according to the petrophysical parameters; Based on the pressure gradient, obtain the major axis and minor axis of the largest elliptical region formed by the bubble projection; Calculate the distance from any point on the bubble to the plane where the largest elliptical region is located according to the major axis and minor axis of the largest elliptical region and in combination with the petrophysical parameters; calculate the coordinates of any point on the bubble surface according to the major axis, minor axis of the largest elliptical region and the distance from any point on the bubble to the plane where the largest elliptical region is located, and determine the size of the bubble according to the coordinates of any point on the bubble surface.

[0007] Preferably, the pressure gradient of the reservoir around the well is specifically calculated by the following formula: ; In the formula, is the production of the oil and gas well, with the unit of is the effective permeability, with the unit of ; is the fluid viscosity, with the unit of ; h is the formation depth, with the unit of m; r 0 is the distance from the reservoir around the well to the wellbore, with the unit of m.

[0008] Preferably, the major axis of the largest elliptical region where the bubble is located is specifically calculated by the following formula: ; In the formula, is the critical value of the stress intensity factor; is the elliptic modulus, ; is the ratio parameter of the major axis to the minor axis of the elliptical region formed by the bubble projection, , and the value range is , a is the major axis of the largest elliptical region; c is the minor axis of the largest elliptical region; and are the first kind of complete elliptic integral and the second kind of complete elliptic integral respectively; is the pressure gradient of the reservoir around the well.

[0009] Preferably, the distance from any point on the bubble to the plane where the largest elliptical region is located is calculated according to the major axis and minor axis of the largest elliptical region and in combination with the petrophysical parameters, specifically by the following formula: ; ; In the formula, is the distance from any point on the bubble surface to xoz plane; is the Poisson's ratio; is the Young's modulus of the rock; is the pressure gradient of the reservoir around the well; and are the first kind of complete elliptic integral and the second kind of complete elliptic integral respectively; is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection; is the elevation angle of the spherical coordinate system characterizing the spatial position of the bubble; φ is the azimuth angle of the spherical coordinate system characterizing the spatial position of the bubble; is the elliptic modulus, , , and the value range is ; a is the major axis of the largest elliptical area; c is the minor axis of the largest elliptical area; r is the distance from any point on the bubble surface to the origin of the spherical coordinate system.

[0010] Preferably, the petrophysical parameters include formation depth, effective permeability, fluid viscosity, well production, Young's modulus of the rock, Poisson's ratio, pore throat length, and pore throat width.

[0011] The present invention also provides a system for calculating the bubble size of the reservoir around an oil and gas well, including: A first parameter acquisition module for acquiring the petrophysical parameters of the reservoir around the well; A pressure gradient calculation module for calculating the pressure gradient of the reservoir around the well according to the petrophysical parameters; A second parameter acquisition module for acquiring the major axis and the minor axis of the largest elliptical area formed by the bubble projection based on the pressure gradient; A bubble size calculation module for calculating the distance from any point of the bubble to the plane where the largest elliptical area is located according to the major axis and the minor axis of the largest elliptical area and in combination with the petrophysical parameters; calculating the coordinates of any point on the bubble surface according to the major axis, the minor axis of the largest elliptical area, and the distance from any point of the bubble to the plane where the largest elliptical area is located, and determining the size of the bubble according to the coordinates of any point on the bubble surface.

[0012] The method for calculating the bubble size of the reservoir around an oil and gas well provided by the present invention has the following beneficial effects: The present invention can calculate the pressure gradient of the reservoir around the well based on rock physical parameters. By combining the calculation of the pressure gradient of the reservoir around the well, the major axis and minor axis of the maximum elliptical area formed by the bubble projection can be obtained. Through the major axis and minor axis of the maximum elliptical area formed by the bubble projection, the distance from any point on the bubble to the plane where the maximum elliptical area is located can be calculated. According to the major axis, minor axis of the maximum elliptical area and the distance from any point on the bubble to the plane where the maximum elliptical area is located, the coordinates of any point on the bubble surface can be calculated, thereby determining the size of the bubble. By quantitatively calculating the rock physical parameters, pressure gradient of the reservoir around the well, the size of the projection area when the bubble floats, and the distance from any point on the bubble surface to the projection area, the present invention can ensure the accuracy of the obtained bubble size. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the embodiments of the present invention and their design solutions, the drawings required for the present embodiments will be briefly introduced below. The drawings in the following description are only partial embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0014] Figure 1 is the optimization control flow chart of the bubble shape in the reservoir around the well; Figure 2 is the schematic diagram of the projection shape of the bubble on the xoy coordinate plane; Figure 3 is the schematic diagram of the projection shape of the bubble on the xoz coordinate plane; Figure 4 is the schematic diagram of the projection shape of the bubble on the yoz coordinate plane. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] In order to enable those skilled in the art to better understand the technical solutions of the present invention and implement them, the present invention will be described in detail below with reference to the drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be used to limit the protection scope of the present invention.

[0016] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the technical solutions of the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0017] In addition, terms such as "first" and "second" are for descriptive purposes only and should not be construed as indicating or implying relative importance. In the description of the present invention, it should be noted that unless otherwise clearly specified or limited, the terms "connected" and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. In the description of the present invention, unless otherwise stated, the meaning of "plurality" is two or more, which will not be elaborated here.

[0018] Embodiment For the convenience of describing the method for calculating the bubble size of the reservoir around the oil and gas well of the present invention, it is specifically illustrated by a certain oil and gas well in a certain shale gas reservoir, and the specific steps are as Figure 1 shown: Step 1: Obtain the petrophysical parameters of the reservoir around the well.

[0019] Through well logging and core analysis in the well, the following petrophysical parameters of the reservoir around the oil and gas well are obtained after detailed geological investigation: Formation depth: h = 2000 [m]; Radial distance from the reservoir around the well to the wellbore: = 1 [m]; Effective permeability: = 2×10 - ¹ 4 [m²]; Fluid viscosity: = 0.5×10 - ³ [Pa·s]; Production of the oil and gas well: = 100 [m³ / day]; Young's modulus of the rock: = 30 [GPa]; Poisson's ratio: = 0.25; Pore throat length: L = 6.72 [mm]; Pore throat width: W = 9.8 10 -4 [mm].

[0020] At the same time, the fracture mechanics parameters for bubble control are determined through on-site experiments as: Critical value of stress intensity factor: = 90 [Pa· .

[0021] The ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection is taken as: = 0.91 (the value range is [0.85, 0.95]).

[0022] The above parameters can provide a physical basis for the subsequent calculation of the pressure gradient of the reservoir around the well and the prediction of the bubble shape.

[0023] Step 2: Calculate the pressure gradient of the reservoir around the well according to the petrophysical parameters, specifically calculated by the following formula: ; In the formula, is the production of the oil and gas well, with the unit of ; is the effective permeability, with the unit of ; is the fluid viscosity, with the unit of ; h is the formation depth, with the unit of m; r 0 is the distance from the reservoir around the well to the wellbore, with the unit of m.

[0024] Substitute the known values into the formula for calculating the pressure gradient of the reservoir around the well to obtain the pressure gradient with a value of approximately 23 [Pa / mm], and the result provides a key parameter for the subsequent calculation of the bubble shape.

[0025] Step 3: Based on the pressure gradient, obtain the major axis and minor axis of the maximum elliptical region formed by the bubble projection.

[0026] According to the linear elastic fracture mechanics theory, under the condition of bubble floating, the maximum region formed by the bubble projection is an elliptical region, and the major axis of the elliptical region is calculated by the formula: ; In the formula, is the critical value of the stress intensity factor; is the elliptic modulus, ; is the ratio parameter of the major axis to the minor axis of the elliptical region formed by the bubble projection, , and the value range is , a is the major axis of the maximum elliptical region; c is the minor axis of the maximum elliptical region; and are the first kind of complete elliptic integral and the second kind of complete elliptic integral respectively; is the pressure gradient of the reservoir around the well.

[0027] Using the known parameters, the value of the major axis can be numerically solved to be 3.32 [mm], and the value of the minor axis is 3.02 [mm], so as to determine the size of the maximum expansion direction of the bubble. Among them, the minor axis is obtained through the major axis and Determined.

[0028] Step 4: Calculate the distance from any point on the bubble to the plane where the maximum elliptical region is located based on the major axis and minor axis of the maximum elliptical region and in combination with the rock physical parameters; calculate the coordinates of any point on the bubble surface based on the major axis, minor axis of the maximum elliptical region and the distance from any point on the bubble to the plane where the maximum elliptical region is located, and determine the size of the bubble based on the coordinates of any point on the bubble surface.

[0029] In the case of bubble floating, the maximum elliptical region formed by the bubble projection is located in the plane, and the coordinates of any point on the bubble surface can be expressed as: , , ; where c is the minor axis of the maximum elliptical region; a is the major axis of the maximum elliptical region; φ is the azimuth angle of the spherical coordinate system characterizing the spatial position of the bubble, φ ; is the elevation angle of the spherical coordinate system characterizing the spatial position of the bubble, ; b is the distance from any point on the bubble surface to the xoz plane.

[0030] Among them, the calculation formula for the distance from any point on the bubble surface to the xoz plane is: ; ; In the formula, is the distance from any point on the bubble surface to the xoz plane; is the Poisson's ratio; is the Young's modulus of the rock; is the pressure gradient of the reservoir around the well; and are the first kind of complete elliptic integral and the second kind of complete elliptic integral respectively; is the ratio parameter of the major axis to the minor axis of the elliptical region formed by the bubble projection; is the elevation angle of the spherical coordinate system characterizing the spatial position of the bubble; φ is the azimuth angle of the spherical coordinate system characterizing the spatial position of the bubble; is the elliptic modulus, , , and the value range is ; a is the major axis of the maximum elliptical region; cis the minor axis of the largest elliptical region; r is the distance from any point on the bubble surface to the origin of the spherical coordinate system.

[0031] Through this formula, using the known parameters, the geometric shape of the entire bubble surface can be numerically simulated, so as to obtain the accurate position information of the plane where the bubble is located at different positions. The contours of the projections of the bubble on the three coordinate planes are shown in Figure 2 , Figure 3 and Figure 4 , where = 4.4 10 -4 [mm].

[0032] Step 5: Dynamic parameter optimization and process control.

[0033] During the actual well operation, to ensure that the bubble does not get blocked when passing through the reservoir pore throats, the size of the bubble must be controlled. The length and width of the reservoir pore throats are L and W , see the known parameters. It can be calculated that the constraint conditions are satisfied: 2 c ≤0.9 L ; 2 ≤0.9 W ; When the projected size of the bubble on the plane is less than 85% of the pore throat size, the production of the oil and gas well meets the requirements, enabling the bubble to pass through the pore throat smoothly, ensuring both the gas-liquid two-phase transportation efficiency and preventing local blockage or reservoir damage caused by an overly large bubble. Through real-time feedback of on-site data, further adjust q , thereby changing the bubble size c and to achieve the best bubble shape control effect.

[0034] The present invention utilizes the principle based on linear elastic fracture mechanics, combined with the calculation of the pressure gradient of the reservoir around the well, to achieve precise control of the bubble size and shape. By quantitatively calculating the rock parameters around the well, the pressure gradient, the projected area during bubble floating, and the distance from any point on the bubble surface, the transfer efficiency of the gas-liquid two-phase flow can be improved, the carrying effect of the liquid can be enhanced, and it is ensured that the bubble has an appropriate size when passing through the pore throat, effectively adjusting the reservoir pressure around the well. In addition, this method is applicable to low-permeability reservoirs and complex reservoir environments, providing a scientific basis for optimizing the gas injection drive and fracturing schemes in oil and gas development.

[0035] The present invention also provides an oil and gas well reservoir bubble size calculation system around the well, including: A first parameter acquisition module for acquiring the petrophysical parameters of the reservoir around the well; A pressure gradient calculation module for calculating the pressure gradient of the reservoir around the wellbore according to petrophysical parameters; A second parameter acquisition module for obtaining the major axis and minor axis of the maximum elliptical region formed by the bubble projection based on the pressure gradient; A bubble size calculation module for calculating the distance from any point of the bubble to the plane where the maximum elliptical region is located according to the major axis and minor axis of the maximum elliptical region and in combination with petrophysical parameters; calculating the coordinates of any point on the bubble surface according to the major axis, minor axis of the maximum elliptical region and the distance from any point of the bubble to the plane where the maximum elliptical region is located, and determining the size of the bubble according to the coordinates of any point on the bubble surface.

[0036] The technical advantages of the present invention are as follows: 1. Solid theoretical basis.

[0037] By combining the linear elastic fracture mechanics theory with the pressure gradient calculation, it is ensured that the prediction of bubble behavior has high accuracy and scientificity.

[0038] 2. Improve the driving effect.

[0039] By precisely controlling the bubble size, smaller bubbles can enhance the momentum transfer between gas and liquid, improve the reservoir productivity, and at the same time avoid the liquid blockage problem caused by large bubbles.

[0040] 3. Simple and fast calculation.

[0041] Compared with the traditional numerical simulation and on-site experimental methods, this method has a lower calculation cost and a faster operation speed, and can provide real-time assistance for on-site dynamic regulation.

[0042] 4. Wide adaptability.

[0043] The method of the present invention has strong engineering applicability and can play a good role in complex reservoirs such as shale gas and tight sandstone, improving the recovery rate.

[0044] In this embodiment, by combining geological survey, pressure gradient calculation, bubble shape prediction and dynamic parameter optimization, precise control of the bubble size and shape in the reservoir around the wellbore is achieved. Numerical calculation and on-site monitoring results show that this method can effectively regulate the bubble size, optimize the gas-liquid flow characteristics, ensure the safety and efficiency of oil and gas well production operations, and provide a reliable technical means for improving the reservoir productivity.

[0045] The above embodiments are only preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope disclosed by the present invention all belong to the protection scope of the present invention.

Claims

1. A method for calculating the bubble size of a reservoir around an oil and gas well, characterized in that, It includes the following steps: Obtain the petrophysical parameters of the reservoir around the well; Calculate the pressure gradient of the reservoir around the well according to the petrophysical parameters; Based on the pressure gradient, obtain the major axis and minor axis of the maximum elliptical area formed by the bubble projection; According to the major axis and minor axis of the maximum elliptical area, and in combination with the petrophysical parameters, calculate the distance from any point of the bubble to the plane where the maximum elliptical area is located; calculate the coordinates of any point on the bubble surface according to the major axis, minor axis of the maximum elliptical area and the distance from any point of the bubble to the plane where the maximum elliptical area is located, and determine the size of the bubble according to the coordinates of any point on the bubble surface.

2. The method for calculating the bubble size of the reservoir around the oil and gas well according to claim 1, wherein The pressure gradient of the reservoir around the well is specifically obtained through the following formula: ； In the formula, is the production of the oil and gas well, with the unit of ; is the effective permeability, with the unit of ; is the fluid viscosity, with the unit of ; h is the formation depth, with the unit of m; r 0 is the distance from the reservoir around the well to the wellbore, with the unit of m.

3. The method for calculating the bubble size of the reservoir around the oil and gas well according to claim 1, characterized in that, The major axis of the maximum elliptical area formed by the bubble projection is specifically obtained through the following formula: ； Wherein, is the critical value of the stress intensity factor; is the elliptic modulus, ; is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection, , and the value range is , a is the major axis of the largest elliptical area; c is the minor axis of the largest elliptical area; and are the complete elliptic integral of the first kind and the complete elliptic integral of the second kind respectively; is the pressure gradient of the reservoir around the well.

4. The method for calculating the bubble size of the reservoir around the oil and gas well according to claim 1, characterized in that The calculation of the distance from any point of the bubble to the plane where the maximum elliptical area is located according to the major axis and minor axis of the maximum elliptical area and in combination with the petrophysical parameters is specifically obtained through the following formula: ； ； In the formula, is the distance from any point on the bubble surface to xoz the plane; is the Poisson's ratio; is the Young's modulus of the rock; is the pressure gradient of the reservoir around the well; and are the first kind of complete elliptic integral and the second kind of complete elliptic integral respectively; is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection; is the elevation angle of the spherical coordinate system characterizing the spatial position of the bubble; φ is the azimuth angle of the spherical coordinate system characterizing the spatial position of the bubble; is the elliptic modulus, , , and the value range is ; a is the major axis of the largest elliptical region; c is the minor axis of the largest elliptical region; r is the distance from any point on the bubble surface to the origin of the spherical coordinate system.

5. The method for calculating the bubble size of the reservoir around the oil and gas well according to claim 1, characterized in that, The petrophysical parameters include formation depth, effective permeability, fluid viscosity, well production, Young's modulus of the rock, Poisson's ratio, pore throat length and pore throat width.

6. A system for calculating the bubble size of a reservoir around an oil and gas well, characterized in that, It includes: The first parameter acquisition module is used to obtain the petrophysical parameters of the reservoir around the well; The pressure gradient calculation module is used to calculate the pressure gradient of the reservoir around the well according to the petrophysical parameters; The second parameter acquisition module is used to obtain the major axis and minor axis of the maximum elliptical area formed by the bubble projection based on the pressure gradient; The bubble size calculation module is used to calculate the distance from any point of the bubble to the plane where the maximum elliptical area is located according to the major axis and minor axis of the maximum elliptical area and in combination with the petrophysical parameters; calculate the coordinates of any point on the bubble surface according to the major axis, minor axis of the maximum elliptical area and the distance from any point of the bubble to the plane where the maximum elliptical area is located, and determine the size of the bubble according to the coordinates of any point on the bubble surface.

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