A method for drawing a gravity potential function curve of a straight well with a thick reservoir

Abstract

The application discloses a method for drawing a gravity potential function curve of a vertical well with a fixed production rate in a super-thick reservoir, and comprises the following steps: S1, establishing a dimensionless seepage model of the vertical well with the fixed production rate in the super-thick reservoir and considering the gravity factor; S2, obtaining relevant parameters of the dimensionless seepage model of the vertical well with the fixed production rate in the target reservoir, and solving the dimensionless seepage model; and S3, drawing the gravity potential function curve of the vertical well with the fixed production rate in the super-thick reservoir according to the solving result. The application can obtain the dynamic change of the gravity potential function curve considering the gravity influence, can observe the change trend of the formation pressure in the vertical well production process with the gravity influence, and has certain guiding significance for the actual oilfield production.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field exploration and development technology, and in particular to a method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate. Background Technology

[0002] In oilfield production, changes in formation pressure are often one of the most important indicators during development. After a well has been in production for a period of time, understanding the patterns of formation pressure changes can better predict future production conditions and provide guidance for subsequent development.

[0003] In actual production, for very thick reservoirs, during oil well extraction, there is a phenomenon where oil and gas fall back during migration into the wellbore. This phenomenon is considered to be caused by gravity, which acts as a resistance to fluid seepage, and the fluid must overcome this resistance during migration. Therefore, it is urgent to obtain formation pressure variation curves that take gravity into account, in order to provide more accurate guidance for the actual production of this type of reservoir. Summary of the Invention

[0004] To address the aforementioned problems, this invention aims to provide a method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate.

[0005] The technical solution of the present invention is as follows: A method for plotting the gravity potential function curve of a vertical well in a very thick reservoir at a constant production rate includes the following steps: S1: Establish a dimensionless seepage model for fixed-production vertical wells in extremely thick reservoirs, taking gravity factors into account; S2: Obtain the relevant parameters of the dimensionless seepage model for the vertical well fixed production of the target reservoir, and solve the dimensionless seepage model for the vertical well fixed production; S3: Based on the solution results, plot the gravity potential function curve for constant production of vertical wells in thick reservoirs.

[0006] Preferably, in step S1, the dimensionless seepage model for fixed-production vertical well is: (1) (2) Where: G D It is the sum of dimensionless pressure and dimensionless gravity; r D The radius is dimensionless; t D Dimensionless time; P D For dimensionless pressure; g D It is dimensionless gravity.

[0007] Preferably, the dimensionless pressure is calculated using the following formula: (3) In the formula: K is the rock permeability, D; h is the reservoir thickness, m; q is the oil production, m 3 / d; μ is the fluid viscosity, mPa·s; B is the crude oil volume coefficient, dimensionless; P R P represents formation pressure, in MPa; wf The bottom hole pressure is MPa.

[0008] Preferably, the dimensionless gravity is calculated using the following formula: (4) In the formula: ρ is the density of crude oil, g / cm³ 3 g is the acceleration due to gravity, in m / s². 2 ; H is the vertical height from the bottom of the wellbore to the bottom of the reservoir, in meters (m).

[0009] Preferably, the dimensionless radius is calculated using the following formula: (5) In the formula: r is the radial distance, in meters; r w Let be the completion radius of the oil well, in meters (m).

[0010] Preferably, the dimensionless time is calculated using the following formula: (6) In the formula: t is the oil well production time, in hours; c is the rock porosity, a decimal. t The overall compressibility factor is expressed in MPa. -1 .

[0011] Preferably, in step S2, the dimensionless seepage model for the vertical well constant production is solved using Laplace transform and Stefest numerical inversion.

[0012] Preferably, in step S3, when plotting the gravity potential function curve for constant production of a vertical well in a thick reservoir, the horizontal and vertical axes are respectively: (7) (8) In the formula: X is the x-coordinate; C D y is the dimensionless wellbore storage coefficient; Y is the ordinate.

[0013] The beneficial effects of this invention are: This invention can obtain the dynamic changes of the gravitational potential function curve considering the influence of gravity, and can observe the changing trend of formation pressure during the production process of vertical wells under the influence of gravity, which has certain guiding significance for actual oilfield production. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the pressure dynamic curve results for Example 1; Figure 2 This is a schematic diagram of the pressure dynamic curve results for Example 2. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and technical features described in this application can be combined with each other. It should also be pointed out that, unless otherwise indicated, all technical and scientific terms used in this application have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "comprising" or "including" and similar words used in this invention refer to elements or objects preceding the word that encompass the elements or objects listed following the word and their equivalents, without excluding other elements or objects.

[0017] This invention provides a method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate, comprising the following steps: S1: Establish a dimensionless seepage model for constant production of vertical wells in extremely thick reservoirs, taking gravity into account. The dimensionless seepage model for constant production of vertical wells is as follows: (1) (2) Where: G D It is the sum of dimensionless pressure and dimensionless gravity; r D The radius is dimensionless; t D Dimensionless time; P D For dimensionless pressure; g D It is dimensionless gravity.

[0018] In one specific embodiment, the dimensionless pressure is calculated using the following formula: (3) In the formula: K is the rock permeability, D; h is the reservoir thickness, m; q is the oil production, m 3 / d; μ is the fluid viscosity, mPa·s; B is the crude oil volume coefficient, dimensionless; PR P represents formation pressure, in MPa; wf The bottom hole pressure is MPa.

[0019] The dimensionless gravity is calculated using the following formula: (4) In the formula: ρ is the density of crude oil, g / cm³ 3 g is the acceleration due to gravity, in m / s². 2 ; H is the vertical height from the bottom of the wellbore to the bottom of the reservoir, in meters (m).

[0020] The dimensionless radius is calculated using the following formula: (5) In the formula: r is the radial distance, in meters; r w Let be the completion radius of the oil well, in meters (m).

[0021] The dimensionless time is calculated using the following formula: (6) In the formula: t is the oil well production time, in hours; c is the rock porosity, a decimal. t The overall compressibility factor is expressed in MPa. -1 .

[0022] S2: Obtain the relevant parameters of the dimensionless seepage model for the vertical well fixed production of the target reservoir, and solve the dimensionless seepage model for the vertical well fixed production; In one specific embodiment, the dimensionless seepage model for constant production in vertical wells is solved using Laplace transform and Stefest numerical inversion. Specifically: First, initial conditions, inner boundary conditions, and outer boundary conditions are established for the dimensionless seepage model of the vertical well constant production. The initial conditions are as follows: (9) The inner boundary conditions are as follows: (10) The outer boundary condition is an infinite outer boundary, a closed outer boundary, or a constant pressure outer boundary, which are respectively: (11) (12) (13) Then, mathematical methods such as Laplace transform and Stefest numerical inversion are used to solve it, and the result is: (14) (15) (16) (17) (18) (19) In the formula: , , These are dimensionless semi-analytical solutions considering gravity under the conditions of an infinite outer boundary, a closed outer boundary, and a isobaric outer boundary, respectively; G' D The reduced gravity coefficients are dimensionless; K0, K1, I0, and I1 are all Bessel functions; u is the Laplace operator; r eD Dimensionless drain radius; Δp is the production pressure differential; r e Let be the radius of the outer boundary of the oil well, in meters (m).

[0023] It should be noted that the above solution method is only a preferred solution method. Those skilled in the art, based on the known dimensionless seepage model of vertical well constant production, can combine other mathematical methods in the prior art to obtain the solution of the model.

[0024] S3: Based on the solution results, plot the gravity potential function curve for constant production of vertical wells in thick reservoirs.

[0025] In a specific embodiment, when plotting the gravity potential function curve for a fixed production rate of a vertical well in a very thick reservoir, the horizontal and vertical axes are respectively: (7) (8) In the formula: X is the x-coordinate; C D y is the dimensionless wellbore storage coefficient; Y is the ordinate.

[0026] In one specific embodiment, MATLAB was used to plot the gravity potential function curve for constant production of the vertical well in the thick reservoir.

[0027] Example 1 Taking well X1 in block X as an example, the pressure dynamic curve of well X1 is obtained by using the gravity potential function curve plotting method for fixed-production vertical wells in thick reservoirs described in this invention. In this embodiment, the permeability of well X1 is k = 5.6 mD, and the porosity is... = 0.02, comprehensive elastic compressibility coefficient c t = 2.3×10 -4 MPa -1The reservoir thickness is h = 55 m, the vertical height from the bottom of the wellbore to the bottom of the reservoir is ΔH = 42 m, and the daily gas production per well is q = 38 × 10⁻⁶ m. 4 m 3 / d, skin factor S = 1.3, wellbore reservoir factor Cs = 0.08 MPa / m 3 oil well completion radius r w = 0.078 m, fluid density ρ = 0.89 g / cm³ 3 The fluid viscosity μ = 7.8 mPa·s, and the fluid oil saturation s o = 0.19, production pressure differential Δp = 4.5 MPa. The dimensionless wellbore reservoir coefficient C of well X1 is calculated. D = 0.83, the sum of dimensionless pressure and gravity G D = 0.05. Based on the above data, using an infinitely large outer boundary as the boundary condition, the dynamic pressure curve of well X1 is plotted as follows. Figure 1 As shown.

[0028] Example 2 Taking well X2 in block X as an example, the pressure dynamic curve of well X1 is obtained by using the gravity potential function curve plotting method for fixed-production vertical wells in thick reservoirs described in this invention. In this embodiment, the permeability k of well X2 is 7.1 mD, and the porosity is... = 0.05, comprehensive elastic compression coefficient c t = 2.5×10 -4 MPa -1 The reservoir thickness is h = 75 m, the vertical height from the bottom of the wellbore to the bottom of the reservoir is ΔH = 50 m, and the daily gas production per well is q = 51 × 10⁻⁶ m. 4 m 3 / d, skin factor S = 1.28, wellbore reservoir factor Cs = 0.08 MPa / m 3 oil well completion radius r w = 0.082 m, fluid density ρ = 0.79 g / cm³ 3 The fluid viscosity μ = 6.9 mPa·s, and the fluid oil saturation s o = 0.23, production pressure differential Δp = 5.1 MPa. The dimensionless wellbore reservoir coefficient C of well X1 is calculated. D = 0.2, the sum of dimensionless pressure and gravity G D = 0.03. Based on the above data, using an infinitely large outer boundary as the boundary condition, the dynamic pressure curve of well X2 is plotted as follows. Figure 2 As shown.

[0029] from Figure 1 and Figure 2 It is clear that the formation pressure changes are caused by gravity falling back during the migration of oil and gas into the wellbore.

[0030] In summary, this invention can obtain information on formation pressure variations considering the influence of gravity. Compared with existing technologies, this invention represents a significant advancement.

[0031] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate, characterized in that, Includes the following steps: S1: Establish a dimensionless seepage model for constant production in vertical wells of extremely thick reservoirs, taking gravity into account; the dimensionless seepage model for constant production in vertical wells is as follows: （1） （2） In the formula: G D It is the sum of dimensionless pressure and dimensionless gravity; r D The radius is dimensionless; t D Dimensionless time; P D For dimensionless pressure; g D It is dimensionless gravity; The dimensionless pressure is calculated using the following formula: （3） In the formula: K is the rock permeability, D; h is the reservoir thickness, m; q is the oil production, m 3 / d; μ is the fluid viscosity, mPa·s; B is the crude oil volume coefficient, dimensionless; P R P represents formation pressure, in MPa; wf The bottom hole flowing pressure is in MPa. The dimensionless gravity is calculated using the following formula: （4） In the formula: ρ is the density of crude oil, g / cm³ 3 g is the acceleration due to gravity, in m / s². 2 ; H is the vertical height from the bottom of the wellbore to the bottom of the reservoir, in meters (m). S2: Obtain the relevant parameters of the dimensionless seepage model for the vertical well fixed production of the target reservoir, and solve the dimensionless seepage model for the vertical well fixed production; S3: Based on the solution results, plot the gravity potential function curve for constant production in a vertical well of a very thick reservoir; when plotting the gravity potential function curve for constant production in a vertical well of a very thick reservoir, the horizontal and vertical axes are respectively: （7） （8） In the formula: X is the x-coordinate; C D y is the dimensionless wellbore storage coefficient; Y is the ordinate.

2. The method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate according to claim 1, characterized in that, The dimensionless radius is calculated using the following formula: （5） In the formula: r is the radial distance, in meters; r w Let be the completion radius of the oil well, in meters (m).

3. The method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate according to claim 1, characterized in that, The dimensionless time is calculated using the following formula: （6） In the formula: t is the oil well production time, in hours; c represents rock porosity, a decimal. t The overall compressibility factor is expressed in MPa. -1 ;r w Let be the completion radius of the oil well, in meters (m).

4. The method for plotting the gravity potential function curve of a vertical well in a thick reservoir at a constant production rate according to claim 1, characterized in that, In step S2, the dimensionless seepage model for the vertical well constant production is solved using Laplace transform and Stefest numerical inversion.

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