A method and system for calculating bubble size in reservoirs around oil and gas wells

Abstract

The present invention provides a method and system for calculating bubble size in a reservoir surrounding an oil and gas well, belonging to the field of bubble drive technology for reservoirs surrounding a well. The method comprises the following steps: obtaining rock physical parameters of the reservoir surrounding the well; calculating the pressure gradient of the reservoir surrounding the well based on the rock physical parameters; obtaining the major axis and minor axis of the largest elliptical area formed by the bubble projection based on the pressure gradient; calculating the distance from any point of the bubble to the plane containing the largest elliptical area based on the major axis and minor axis of the largest elliptical area and in combination with the rock physical parameters; and calculating the coordinates of any point on the bubble surface based on the major axis and minor axis of the largest elliptical area and the distance from any point of the bubble to the plane containing the largest elliptical area, thereby determining the size of the bubble. The present invention ensures the accuracy of the obtained bubble size by quantitatively calculating the rock physical parameters of the reservoir surrounding the well, the pressure gradient, the size of the projected area when the bubble floats, and the distance from any point on the bubble surface to the projected area.

Description

Technical Field

[0001] The present invention belongs to the technical field of bubble drive in peri-well reservoirs, and in particular relates to a method and system for calculating bubble size in peri-well reservoirs of oil and gas wells. Background Art

[0002] Variations in bubble size in reservoirs surrounding oil and gas wells have a significant impact on reservoir parameters, directly related to the flow characteristics of gas-liquid two-phase flow, reservoir development efficiency, and well production optimization. Variations in bubble size influence fluid driving behavior. Smaller bubbles enhance momentum transfer and liquid carrying capacity between gas and liquid, improving reservoir oil and gas recovery. Larger bubbles, however, can block flow pathways, increase flow resistance, and reduce development efficiency. Therefore, studying the patterns of bubble size can help optimize reservoir flow patterns and improve gas-liquid flow characteristics.

[0003] In addition, bubble size also has a significant impact on the pressure distribution and liquid-carrying properties of the reservoir surrounding the well. Appropriate bubble size can enhance liquid carrying efficiency and avoid the risk of liquid plugging, thereby maintaining pressure balance in the reservoir surrounding the well and maintaining efficient development. Bubble size is particularly important in low-permeability reservoirs (such as shale gas reservoirs), as properly regulating bubble characteristics can help optimize fracturing schemes and gas injection strategies in unconventional gas reservoirs, further improving recovery. Bubble size research also provides a scientific basis for numerical simulations of gas wells, enabling the construction of more accurate fluid flow models. It also has guiding significance for technological innovations such as foaming agent design and gas injection process optimization. Therefore, paying attention to the changing patterns of bubble size can not only improve reservoir development efficiency but also provide a theoretical and practical basis for the long-term stability of gas well operations.

[0004] Currently, methods for calculating bubble size in reservoirs surrounding oil and gas wells primarily include pressure and fluid dynamics analysis, downhole imaging, dynamic gas measurement, and foaming agent experiments. These methods, through direct measurement or indirect inference, combined with experimental analysis and data modeling, provide a variety of technical means for studying the characteristics of gas-liquid two-phase flow in reservoirs. Pressure and fluid dynamics analysis is simple and easy to use, but its accuracy depends on model parameters and is suitable for preliminary assessment of gas-liquid flow patterns. Downhole imaging technology is intuitive and highly accurate, allowing direct observation of bubble size but primarily limited to the wellbore. Dynamic gas measurement indirectly infers reservoir bubble characteristics through gas-liquid separation data. While the technology is mature, its accuracy is highly dependent on parameter inversion. Foaming agent experiments accurately analyze bubble generation patterns in the laboratory, but this differs significantly from field conditions and requires practical verification.

[0005] In summary, the bubble size obtained by the existing bubble size acquisition method has low accuracy and is significantly different from the on-site data. Summary of the Invention

[0006] In order to overcome the above-mentioned shortcomings of the prior art, the present invention provides a method for calculating the bubble size of the reservoir around an oil and gas well, comprising the following steps:

[0007] Obtaining petrophysical parameters of the reservoir around the well;

[0008] Calculate the pressure gradient of the reservoir around the well based on rock physical parameters;

[0009] Based on the pressure gradient, obtaining the major axis and minor axis of the largest elliptical area formed by the bubble projection;

[0010] The distance from any point on the bubble to the plane where the maximum elliptical area is located is calculated based on the major and minor axes of the maximum elliptical area and combined with rock physical parameters. The coordinates of any point on the bubble surface are calculated based on the major and minor axes 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 size of the bubble is determined based on the coordinates of any point on the bubble surface.

[0011] Preferably, the pressure gradient of the reservoir around the well is specifically expressed by the following formula:

[0012] ;

[0013] Where, is the production of oil and gas wells, in units of is the effective permeability, in units of ; is the fluid viscosity, in units of ; h is the depth of the formation, in m; r 0 is the distance from the reservoir around the well to the well wall, in meters.

[0014] Preferably, the major axis of the largest elliptical area where the bubble is located is obtained by the following formula:

[0015] ;

[0016] Where, is the critical value of stress intensity factor; is the ellipse modulus, ; is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection, , 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 They are the complete elliptic integrals of the first and second kinds respectively; is the pressure gradient of the reservoir around the well.

[0017] Preferably, the distance from any point of the bubble to the plane where the maximum elliptical area is located is calculated based on the major axis and minor axis of the maximum elliptical area and combined with petrophysical parameters, specifically by the following formula:

[0018] ;

[0019] ;

[0020] Where, From any point on the bubble surface to xoz Distance of the plane; is Poisson's ratio; is the Young's modulus of rock; is the pressure gradient of the reservoir around the well; and They are the complete elliptic integrals of the first and second kinds respectively; 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 representing the spatial position of the bubble; φ is the azimuth angle of the spherical coordinate system representing the spatial position of the bubble; is the ellipse modulus, , , 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.

[0021] Preferably, the rock physical parameters include formation depth, effective permeability, fluid viscosity, well production, rock Young's modulus, Poisson's ratio, pore throat length and pore throat width.

[0022] The present invention also provides a system for calculating bubble size in a reservoir around an oil and gas well, comprising:

[0023] The first parameter acquisition module is used to obtain the petrophysical parameters of the reservoir around the well;

[0024] Pressure gradient calculation module, used to calculate the pressure gradient of the reservoir around the well based on rock physical parameters;

[0025] A second parameter acquisition module is used to acquire the major axis and minor axis of the largest elliptical area formed by the bubble projection based on the pressure gradient;

[0026] The bubble size calculation module is used to calculate the distance from any point on the bubble to the plane where the maximum elliptical area is located based on the major and minor axes of the maximum elliptical area and combined with rock physical parameters; calculate the coordinates of any point on the bubble surface based on the major and minor axes of the maximum elliptical area and the distance from any point on the bubble to the plane where the maximum elliptical area is located, and determine the size of the bubble based on the coordinates of any point on the bubble surface.

[0027] The method for calculating bubble size in the reservoir around an oil and gas well provided by the present invention has the following beneficial effects:

[0028] The present invention can calculate the pressure gradient of the reservoir around the well based on the rock physical parameters, and in combination with the pressure gradient calculation of the reservoir around the well, can obtain the major axis and minor axis of the maximum elliptical area formed by the bubble projection; through the major axis and minor axis of the maximum elliptical area formed by the bubble projection, the distance from any point of the bubble to the plane where the maximum elliptical area is located can be calculated; the coordinates of any point on the bubble surface are calculated based on the major axis and 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, thereby determining the size of the bubble; the present invention can ensure the accuracy of the obtained bubble size through quantitative calculation of the rock physical parameters of the reservoir around the well, the pressure gradient, the size of the projection area when the bubble floats, and the distance from any point on the bubble surface to the projection area. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] To more clearly illustrate the embodiments of the present invention and its design, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0030] Figure 1 Optimize the control flow chart for the bubble shape of the reservoir around the well;

[0031] Figure 2 Schematic diagram of the bubble projection shape on the xoy coordinate plane;

[0032] Figure 3 Schematic diagram of the bubble projection shape on the xoz coordinate plane;

[0033] Figure 4 Schematic diagram of the bubble projection shape on the yoz coordinate plane. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0035] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "axial", "radial", "circumferential" and the like to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are 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 understood as limiting the present invention.

[0036] In addition, the terms "first", "second", etc. are used for descriptive purposes only and are not to be understood as indicating or implying relative importance. In the description of the present invention, it should be noted that, unless otherwise expressly 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 a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meaning of the above terms in the present invention can be understood according to the specific circumstances. In the description of the present invention, unless otherwise specified, "plurality" means two or more, which will not be described in detail here.

[0037] Example

[0038] In order to conveniently describe the method for calculating the bubble size of the reservoir around the oil and gas well of the present invention, a specific oil and gas well in a shale gas reservoir is used for illustration. The specific steps are as follows: Figure 1 As shown:

[0039] Step 1: Obtain the petrophysical parameters of the reservoir around the well.

[0040] Through well logging and core analysis, the following petrophysical parameters were obtained after detailed geological investigation of the reservoir around the oil and gas well:

[0041] Depth of formation: h =2000[m]; Radial distance from the reservoir around the well to the well wall: =1[m]; effective permeability: =2×10 - ¹ 4 [m²]; fluid viscosity: =0.5×10 - ³[Pa·s]; Oil and gas well production: =100[m³ / day]; Young's modulus of rock: =30[GPa]; Poisson’s ratio: =0.25; pore throat length: L=6.72[mm]; pore throat width: W =9.8 10 -4 [mm].

[0042] At the same time, the fracture mechanics parameters used for bubble control were determined through field experiments as follows: critical value of stress intensity factor: =90[Pa· ].

[0043] The ratio parameters of the major axis and minor axis of the elliptical area formed by the bubble projection are: =0.91 (value range is [0.85,0.95]).

[0044] The above parameters can provide a physical basis for subsequent calculation of the pressure gradient of the reservoir around the well and prediction of bubble shape.

[0045] Step 2: Calculate the pressure gradient of the reservoir around the well based on the rock physical parameters, specifically using the following formula:

[0046] ;

[0047] Where, is the production of oil and gas wells, in units of ; is the effective permeability, in units of ; is the fluid viscosity, in units of ; h is the depth of the formation, in m; r 0 is the distance from the reservoir around the well to the well wall, in meters.

[0048] Substitute the known values into the formula for calculating the pressure gradient of the reservoir around the well to obtain the pressure gradient The value is about 23 [Pa / mm], and the result provides key parameters for subsequent bubble morphology calculations.

[0049] Step 3: Based on the pressure gradient, obtain the major axis and minor axis of the largest elliptical area formed by the bubble projection.

[0050] According to the theory of linear elastic fracture mechanics, under the condition of bubble floating, the largest area formed by bubble projection is the elliptical area, and the long axis of the elliptical area is The calculation formula is:

[0051] ;

[0052] Where, is the critical value of stress intensity factor; is the ellipse modulus, ; is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection, , 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 They are the complete elliptic integrals of the first and second kinds respectively; is the pressure gradient of the reservoir around the well.

[0053] Using known parameters, the major axis can be numerically solved The value is 3.32[mm], the short axis The value of is 3.02 [mm], which determines the size of the bubble in the direction of maximum expansion, where the short axis Through the long axis and Sure.

[0054] Step 4: Calculate the distance from any point on the bubble to the plane of the largest elliptical area based on the major and minor axes of the largest elliptical area and combined with rock physical parameters; calculate the coordinates of any point on the bubble surface based on the major and minor axes of the largest elliptical area and the distance from any point on the bubble to the plane of the largest elliptical area; and determine the size of the bubble based on the coordinates of any point on the bubble surface.

[0055] In the case of bubble floating, the largest elliptical area formed by the bubble projection is located at plane, the coordinates of any point on the bubble surface can be Expressed as:

[0056] , , ;

[0057] in, c is the minor axis of the largest elliptical area; a is the major axis of the largest elliptical area; φ is the azimuth of the spherical coordinate system that represents the spatial position of the bubble, ; is the elevation angle of the spherical coordinate system that represents the spatial position of the bubble, ; b From any point on the bubble surface to xoz The distance of the plane.

[0058] Among them, any point on the bubble surface xoz The distance between the planes is calculated as:

[0059] ;

[0060] ;

[0061] Where, From any point on the bubble surface to xoz Distance of the plane; is Poisson's ratio; is the Young's modulus of rock; is the pressure gradient of the reservoir around the well; and They are the complete elliptic integrals of the first and second kinds respectively; 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 representing the spatial position of the bubble; φ is the azimuth angle of the spherical coordinate system representing the spatial position of the bubble; is the ellipse modulus, , , 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.

[0062] Through this formula, the geometric shape of the entire bubble surface can be numerically simulated using known parameters, thereby obtaining the precise position information of the bubble plane at different positions. The outline of the bubble projected on the three coordinate planes can be seen. Figure 2 、 Figure 3 and Figure 4 ,in =4.4 10 -4 [mm].

[0063] Step 5: Dynamic parameter optimization and process control.

[0064] In the actual well operation process, in order to ensure that the bubbles do not get blocked when passing through the reservoir pore throat, the size of the bubbles must be controlled. The pore throat length and pore throat width of the reservoir are L and W , see the known parameters, calculate and get, satisfy the constraints:

[0065] 2 c ≤0.9 L ;

[0066] 2 ≤0.9 W ;

[0067] When bubbles The projection size on the plane is less than 85% of the pore throat size, and the production of oil and gas wells It meets the requirements and can allow bubbles to pass through the pore throat smoothly, ensuring the efficiency of gas-liquid two-phase transportation and preventing local blockage or reservoir damage caused by excessive bubbles. Further adjustments are made through real-time feedback from field data. q , thereby changing the bubble size c and , in order to achieve the best bubble morphology control effect.

[0068] This method utilizes the principles of linear elastic fracture mechanics, combined with calculations of pressure gradients in the reservoir surrounding the wellbore, to achieve precise control of bubble size and shape. By quantitatively calculating the rock parameters surrounding the wellbore, the pressure gradient, and the distance between the projected area of the bubble during its floating motion and any point on the bubble surface, it improves the transmission efficiency of gas-liquid two-phase flow, enhances the liquid carrying effect, and ensures that the bubbles are of appropriate size as they pass through the pore throats, effectively adjusting the reservoir pressure surrounding the wellbore. Furthermore, this method is applicable to low-permeability reservoirs and complex reservoir environments, providing a scientific basis for optimizing gas injection drive and fracturing schemes in oil and gas development.

[0069] The present invention also provides a system for calculating bubble size in a reservoir around an oil and gas well, comprising:

[0070] The first parameter acquisition module is used to obtain the petrophysical parameters of the reservoir around the well;

[0071] Pressure gradient calculation module, used to calculate the pressure gradient of the reservoir around the well based on rock physical parameters;

[0072] A second parameter acquisition module is used to acquire the major axis and minor axis of the largest elliptical area formed by the bubble projection based on the pressure gradient;

[0073] The bubble size calculation module is used to calculate the distance from any point on the bubble to the plane where the maximum elliptical area is located based on the major and minor axes of the maximum elliptical area and combined with rock physical parameters; calculate the coordinates of any point on the bubble surface based on the major and minor axes of the maximum elliptical area and the distance from any point on the bubble to the plane where the maximum elliptical area is located, and determine the size of the bubble based on the coordinates of any point on the bubble surface.

[0074] The technical advantages of the present invention are as follows:

[0075] 1. Solid theoretical basis.

[0076] The linear elastic fracture mechanics theory is combined with pressure gradient calculation to ensure that the bubble behavior prediction is highly accurate and scientific.

[0077] 2. Improve driving effect.

[0078] By precisely controlling the bubble size, smaller bubbles can enhance momentum transfer between gas and liquid, improve reservoir productivity, and avoid liquid blockage caused by large bubbles.

[0079] 3. The calculation is simple and fast.

[0080] Compared with traditional numerical simulation and field experimental methods, this method has lower computational cost and faster computing speed, and can provide real-time assistance for on-site dynamic control.

[0081] 4. Wide adaptability.

[0082] 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, thereby improving the recovery rate.

[0083] In this example, by combining geological surveys, pressure gradient calculations, bubble shape prediction, and dynamic parameter optimization, precise control of bubble size and shape in the reservoir surrounding the well was achieved. Numerical calculations and field monitoring results demonstrate that this method effectively regulates bubble size, optimizing gas-liquid flow characteristics while ensuring the safety and efficiency of oil and gas well production operations. This provides a reliable technical means for improving reservoir productivity.

[0084] The above-described embodiments are only preferred specific implementation methods 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 any technician familiar with the field within the technical scope disclosed in the present invention fall within the protection scope of the present invention.

Claims

1. A method for calculating bubble size in a reservoir around an oil and gas well, characterized in that: The steps include: Obtaining petrophysical parameters of the reservoir around the well; Calculate the pressure gradient of the reservoir around the well based on rock physical parameters; Based on the pressure gradient, obtaining the major axis and minor axis of the largest elliptical area formed by the bubble projection; The distance from any point on the bubble to the plane containing the largest elliptical area is calculated based on the major and minor axes of the largest elliptical area and combined with rock physical parameters. The coordinates of any point on the bubble surface are calculated based on the major and minor axes of the largest elliptical area and the distance from any point on the bubble to the plane containing the largest elliptical area. The size of the bubble is determined based on the coordinates of any point on the bubble surface. The pressure gradient of the reservoir around the well is specifically expressed by the following formula: Where q is the production of oil and gas wells, unit is m 3 / day;D k is the effective permeability, in m 2 ; μ is the fluid viscosity, unit is Pa·s; h is the formation depth, unit is m; r0 is the distance from the reservoir around the well to the wellbore wall, unit is m; The major axis of the largest elliptical area formed by the bubble projection is obtained by the following formula: Where K Icrit is the critical value of stress intensity factor; k 2 is the ellipse modulus, k0 is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection, k0 = c / a, with a value range of [0.85, 0.95], a is the major axis of the largest elliptical area; c is the minor axis of the largest elliptical area; E(k) and K(k) are the first kind complete elliptic integral and the second kind complete elliptic integral, respectively; σ0 is the pressure gradient of the reservoir around the well; The distance from any point of the bubble to the plane where the maximum elliptical area is located is calculated based on the major axis and minor axis of the maximum elliptical area and combined with rock physical parameters, specifically using the following formula: Where b(r, θ) is the distance from any point on the bubble surface to the xoz plane; v is the Poisson's ratio; E is the Young's modulus of the rock; σ0 is the pressure gradient of the reservoir around the well; E(k) and K(k) are the complete elliptic integral of the first kind and the complete elliptic integral of the second kind, respectively; k0 is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection; θ is the elevation angle of the spherical coordinate system that represents the spatial position of the bubble; k is the azimuth of the spherical coordinate system that represents the spatial position of the bubble; 2 is the ellipse modulus, k0=c / a, with a value range of [0.85, 0.95]; 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.

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

3. A system for calculating bubble size in the reservoir around an oil and gas well, characterized in that: include: The first parameter acquisition module is used to obtain the petrophysical parameters of the reservoir around the well; Pressure gradient calculation module, used to calculate the pressure gradient of the reservoir around the well based on rock physical parameters; A second parameter acquisition module is used to acquire the major axis and minor axis of the largest 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 on the bubble to the plane where the largest elliptical area is located based on the major and minor axes of the largest elliptical area and combined with rock physical parameters; calculate the coordinates of any point on the bubble surface based on the major and minor axes of the largest elliptical area and the distance from any point on the bubble to the plane where the largest elliptical area is located; and determine the size of the bubble based on the coordinates of any point on the bubble surface; The pressure gradient of the reservoir around the well is specifically expressed by the following formula: Where q is the production of oil and gas wells, unit is m 3 / day;D k is the effective permeability, in m 2 ; μ is the fluid viscosity, unit is Pa·s; h is the formation depth, unit is m; r0 is the distance from the reservoir around the well to the wellbore wall, unit is m; The major axis of the largest elliptical area formed by the bubble projection is obtained by the following formula: Where K Icrit is the critical value of stress intensity factor; k 2 is the ellipse modulus, k0 is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection, k0 = c / a, with a value range of [0.85, 0.95], a is the major axis of the largest elliptical area; c is the minor axis of the largest elliptical area; E(k) and K(k) are the first kind complete elliptic integral and the second kind complete elliptic integral, respectively; σ0 is the pressure gradient of the reservoir around the well; The distance from any point of the bubble to the plane where the maximum elliptical area is located is calculated based on the major axis and minor axis of the maximum elliptical area and combined with rock physical parameters, specifically using the following formula: Where b(r, θ) is the distance from any point on the bubble surface to the xoz plane; v is the Poisson's ratio; E is the Young's modulus of the rock; σ0 is the pressure gradient of the reservoir around the well; E(k) and K(k) are the complete elliptic integral of the first kind and the complete elliptic integral of the second kind, respectively; k0 is the ratio parameter of the major axis to the minor axis of the elliptical area formed by the bubble projection; θ is the elevation angle of the spherical coordinate system that represents the spatial position of the bubble; k is the azimuth of the spherical coordinate system that represents the spatial position of the bubble; 2 is the ellipse modulus, k0=c / a, with a value range of [0.85, 0.95]; 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.

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