Surrounding rock strain distribution calculation method considering pore pressure effect

Abstract

The invention discloses a surrounding rock strain distribution calculation method considering a pore pressure effect. The method comprises the following steps: S1, establishing a geometric model of a target stratum; s2, acquiring basic parameters of a target stratum; s3, establishing a surrounding rock strain distribution calculation model considering the pore pressure effect; when the model is established, the change of the flow property of formation fluid and the rock physical property under the stress effect is comprehensively considered; and S4, substituting the basic parameters of the target stratum obtained in the step S2 into the calculation model established in the step S3, and calculating to obtain the surrounding rock strain distribution of the target stratum. According to the method, multiple factors such as change of rock permeability under the action of surrounding rock stress, displacement of rock particles in different directions and strain of a rock skeleton in different directions are fully considered, surrounding rock strain distribution which is more practical can be obtained through calculation, and calculation accuracy and reliability are improved.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas exploitation, and in particular to a method for calculating surrounding rock strain distribution taking into account the effect of pore pressure. Background Art

[0002] Shale oil and gas and tight oil and gas are natural gas resources extracted from dense rock formations. Compared with conventional natural gas, their gas production rate is relatively stable and can be mined for a long time. Shale oil and gas and tight oil and gas are mainly distributed in dark mud shale or high-carbon mud shale, and the aggregation mode in mud shale is adsorption or free. my country has relatively abundant shale oil and gas and tight oil and gas resources, but due to the characteristics of low permeability and low porosity of shale oil and gas and tight oil and gas reservoirs, their exploitation requires horizontal well drilling technology and large-scale hydraulic fracturing technology.

[0003] While hydraulic fracturing technology is increasing the production of reservoirs, it will also have a certain impact on the formations in the fracturing area, causing the wellbore walls of adjacent platform wells to collapse and become unstable, which is mainly manifested in two aspects: on the one hand, hydraulic fractures communicate with natural fractures to form a fracture network, making it easier for various fluids to invade the formation along the fracture network, causing water-rock interaction, thereby weakening the rock strength of the formation; on the other hand, artificial fracture areas will be generated after hydraulic fracturing operations, and the expansion of artificial fractures will cause the reservoir strain and pore pressure to be redistributed, which will have a great impact on the drilling construction in the fracturing area. If the drilling construction design in the fracturing area still refers to the data of adjacent wells, it will lead to increased drilling risks. For example, the drilling wells adjacent to the platforms of a shale oil and gas and tight oil and gas field were affected by the fracturing wells, and the actual drilling fluid density was 0.15g / cm higher than that of the wells not affected by fracturing. 3 The above are accompanied by complicated underground conditions such as gas invasion, overflow, and water discharge (fracture fluid contamination). Therefore, there are the following problems in shale oil and gas and tight oil and gas production technology: the impact of hydraulic fracturing on pore pressure will lead to pore pressure redistribution, the mechanism of pore pressure on the strain and deformation of the rock around the well is not clear, and the rationality of the calculation and whether the existing model is suitable for the strain distribution of the surrounding rock after hydraulic fracturing are not considered, which cannot provide an effective reference for the project. Summary of the invention

[0004] Aiming at the technical defect in the prior art that the strain and deformation calculation process of the surrounding rock during the fracturing operation does not take the influence of pore pressure into consideration, the present invention provides a surrounding rock strain distribution calculation method taking the effect of pore pressure into consideration.

[0005] The method for calculating surrounding rock strain distribution considering the effect of pore pressure provided by the present invention comprises the following steps:

[0006] S1. Establish a geometric model of the target formation.

[0007] S2. Obtain the basic parameters of the target formation; the basic parameters include Young's modulus, Poisson's ratio, horizontal maximum principal strain, horizontal minimum principal strain, overburden pressure, formation pressure, formation density, pore fluid density, wellbore liquid column pressure, shale initial porosity, shale initial permeability and wellbore diameter.

[0008] S3. Establish a calculation model for surrounding rock strain distribution that takes into account the effect of pore pressure. When establishing the calculation model, comprehensively consider the flow properties of formation fluids under stress and the changes in rock physical properties. The calculation model is as follows:

[0009]

[0010] Where: is the porosity; C w is the fluid compressibility coefficient, MPa -1 ;p p is the pore pressure of shale formation, MPa; t is time, s; C s is the rock skeleton compression coefficient, MPa -1 ; μ is fluid viscosity, mPa·s; K is permeability, μm 2 ;p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; H is the pressure gradient, m; ε V is the rock skeleton strain.

[0011] The permeability K is calculated by the following formula:

[0012]

[0013] Where: is the initial porosity; K0 is the initial permeability, μm 2 ; K m is the bulk compression modulus of the skeleton, MPa; Δp p is the change in pore pressure, MPa.

[0014] The rock skeleton strain ε V Calculated by the following formula:

[0015]

[0016] Where: u, v, w are the displacements of rock skeleton particles in the x, y, and z directions; G is the shear modulus, MPa; m is the Poisson's ratio; F x is the strain of rock skeleton particles in the x direction; F y is the strain of rock skeleton particles in the y direction; F z is the strain sum of rock skeleton particles in the z direction.

[0017] The strain and F of rock skeleton particles in the x, y, and z directions x 、F y 、F z The calculation formula is as follows:

[0018]

[0019] F x =F z cosθ

[0020] F y =F z sinθ

[0021] Where: R is the borehole radius, m; r is the distance from the borehole center, m; θ is the wellbore angle, rad; σ r is radial strain, MPa; σ H is the maximum horizontal strain, MPa; σ h is the minimum horizontal strain, MPa; x, y are the positions of the particles.

[0022] S4. Substituting the basic parameters of the target formation obtained in step S2 into the calculation model established in step S3, the surrounding rock strain distribution of the target formation is calculated.

[0023] Compared with the prior art, the present invention is beneficial in that:

[0024] The method of the present invention takes into account the influence of pore pressure on the strain distribution of surrounding rocks, specifically considering multiple factors such as the change in rock permeability under the action of surrounding rock stress, the displacement of rock particles in different directions, the strain of rock skeleton in different directions, etc., which can enable the calculation to obtain a surrounding rock strain distribution that is more in line with the actual situation, improve the accuracy and reliability of the calculation, and provide technical support for oil and gas development.

[0025] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 4 is a comparison curve diagram of the circumferential stress distribution of the wellbore of the embodiment.

[0027] Figure 2 This is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 30 MPa in the embodiment.

[0028] Figure 3 This is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 35 MPa in the embodiment.

[0029] Figure 4 This is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 40 MPa in the embodiment.

[0030] Figure 5 This is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 45 MPa in the embodiment. DETAILED DESCRIPTION

[0031] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0032] In the method of the present invention, step S3 is to establish a surrounding rock strain distribution calculation model taking into account the effect of pore pressure, and the specific process is as follows:

[0033] First, the formation fluid exists in the pores and matrix of the rock around the well. During the fluid seepage process, the fluid pressure generated will cause the rock skeleton to deform, causing the skeleton particles to move at a certain speed. The absolute speed of fluid movement can be expressed as:

[0034]

[0035] Where: is the absolute velocity of the fluid, m / s; is the relative velocity of the fluid, m / s; is the relative velocity of rock mass skeleton particles, m / s;

[0036] The relative velocity of rock mass skeleton particles can be expressed as:

[0037]

[0038] Where: u, v, w are the displacements of rock skeleton particles in the x, y, z directions, m; t is time, s.

[0039] The velocity of a single-phase fluid can be obtained according to Darcy's law:

[0040]

[0041] Where: is the porosity, dimensionless; μ is the fluid viscosity, mPa·s; K is the permeability, μm 2 ;p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; g is the acceleration due to gravity, m / s 2 ; H is the pressure gradient, m.

[0042] According to the law of conservation of mass, the change in the mass of the fluid in the microelement per unit time is equal to the mass difference between the fluid flowing in and out of the microelement. Therefore, the continuity equation of the pore fluid can be obtained as follows:

[0043]

[0044] Substituting equations (2) and (3) into equation (4), we can obtain the continuity equation of pore fluid:

[0045]

[0046] Where: ε V is the rock skeleton strain, dimensionless.

[0047] Similarly, the continuity equation of the skeleton is:

[0048]

[0049] Where: s is the rock mass skeleton density, g / cm 3 .

[0050] By superimposing equation (5) and equation (6), we can obtain the continuity equation of the porous medium as a whole:

[0051]

[0052] When the temperature effect is not considered, the density of the pore fluid is related to the pore pressure as follows:

[0053]

[0054] Where: ρ0 is the initial fluid density, g / cm 3 ; p0 is the initial fluid pressure, MPa; p p is the pore pressure of shale formation, MPa; C w is the fluid compressibility coefficient, MPa -1 .

[0055] The fluid density and pore pressure vary with time, so taking the partial derivative with respect to time yields:

[0056]

[0057] Similarly, the state equation of the rock mass skeleton particles can be expressed as:

[0058]

[0059] Where: C s is the rock skeleton compression coefficient, MPa -1 .

[0060] Substituting equations (9) and (10) into equation (7), we can obtain the calculation model of surrounding rock strain distribution considering the pore pressure effect:

[0061]

[0062] In a specific embodiment, when pore pressure is not applied, the shale formation and the wellbore are mainly affected by the maximum horizontal principal stress, the minimum horizontal principal stress and the drilling fluid column pressure. The combined effect of these forces will form a stress concentration phenomenon around the wellbore. Since the wellbore is symmetrical, this example takes 1 / 4 of the wellbore as an example. The geometric model selects a square with a side length of 5m as the wellbore surrounding rock, and intercepts a 1 / 4 circle with a radius of about 0.15m at the corner of the square as the wellbore radius. The formation mechanics parameters of the reservoir are based on the basic parameters of a shale oil and gas and tight oil and gas work area in southern Sichuan before fracturing. Therefore, in order to balance the formation pressure, the wellbore fluid column pressure is set to 26MPa, and the basic parameters set by the numerical model are shown in Table 1.

[0063] Table 1. Basic parameters of numerical model settings

[0064] Parameter name Numeric Parameter name Numeric Young's modulus of formation (GPa) 30 <![CDATA[Formation density (kg / m 3 )]]> 2450 Poisson's ratio 0.3 <![CDATA[Pore fluid density (kg / m 3 )]]> 1000 Maximum horizontal principal strain (MPa) 45 Wellbore liquid column pressure (MPa) 26 Horizontal minimum principal strain (MPa) 35 Initial porosity of shale (%) 5 Overburden pressure (MPa) 40 <![CDATA[Initial shale permeability (μm 2 )]]> <![CDATA[1×10 -5 ]]> Formation pressure (MPa) 25 Wellbore diameter (mm) 311.2

[0065] The circumferential conversion formula and theoretical calculation formula are given below. The accuracy of this model can be verified by comparing the calculation results.

[0066] σ θ =σ x sin 2 θ+σ y cos 2 θ-τ xy sin(2θ) (12)

[0067] σ θ =(σ H +σ h )-2(σ H -σ h )cos(2θ) (13)

[0068] Where: θ is the circumferential stress, MPa; θ is the wellbore angle, rad; σ x , σ y is the normal stress component in the x and y directions, MPa; τ xy is the shear stress component, MPa.

[0069] According to the basic parameters in Table 1, the model after ground stress equilibrium is solved, and the curve of circumferential stress changing with wellbore angle is obtained, as shown in Figure 1As shown in the figure, the prescribed stress value is: tension is positive and pressure is negative. It can be seen from the figure that the ground stress produces pressure on the wellbore, and the circumferential stress shows a periodic change with the increase of the wellbore angle. The numerical solution of the circumferential stress is consistent with the analytical solution, which proves that the calculation results of the surrounding rock strain distribution calculation model established by the present invention are relatively accurate.

[0070] In another embodiment, the surrounding rock strain is calculated by the surrounding rock strain distribution calculation method considering the pore pressure effect of the present invention. In this embodiment, since the wellbore is symmetrical, this example selects 1 / 4 of the wellbore as an example. The geometric model selects a square with a side length of 5m as the surrounding rock of the wellbore, and intercepts a 1 / 4 circle with a radius of about 0.15m at the corner of the square as the wellbore radius. The formation mechanics parameters of the reservoir are based on the basic parameters of a shale oil and gas and tight oil and gas work area in southern Sichuan before fracturing. The pore pressure of the shale formation is set to 25MPa. Therefore, in order to balance the formation pressure, the wellbore liquid column pressure is set to 26MPa. The basic parameters set by the numerical model are shown in Table 2.

[0071] Table 2 Basic parameters of numerical model settings

[0072] Parameter name Numeric Parameter name Numeric Young's modulus of formation (GPa) 310 <![CDATA[Formation density (kg / m 3 )]]> 2450 Poisson's ratio 0.29 <![CDATA[Pore fluid density (kg / m 3 )]]> 1000 Maximum horizontal principal strain (MPa) 44 Wellbore liquid column pressure (MPa) 26 Horizontal minimum principal strain (MPa) 32 Initial porosity of shale (%) 5 Overburden pressure (MPa) 41 <![CDATA[Initial shale permeability (μm 2 )]]> <![CDATA[5×10 -5 ]]> Formation pressure (MPa) 25 Wellbore diameter (mm) 333..4

[0073] Substituting the basic parameters in Table 2 into the calculation model for surrounding rock strain distribution considering the pore pressure effect, the surrounding rock strain distribution results obtained by calculation are as follows: Figure 2-5 shown. Figure 2-5 They are the wellbore strain distribution diagrams under the conditions of simulated formation pore pressure of 30MPa, 35MPa, 40MPa and 45MPa.

[0074] In summary, the method of the present invention can more accurately and reasonably calculate the surrounding rock strain distribution under the action of pore pressure by comprehensively considering the effect of pore pressure on the strain and deformation of the surrounding rock, ensure the exploitation of shale oil and gas and tight oil and gas, and provide an effective reference for the surrounding rock strain distribution under the action of pore pressure on site.

[0075] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating surrounding rock strain distribution considering pore pressure, characterized in that: The following steps are involved: S1. Establishing a geometric model of the target stratum; S2. Obtaining basic parameters of the target formation; S3. Establish a calculation model for surrounding rock strain distribution considering the effect of pore pressure; the calculation model is as follows: Where: is the porosity; C w is the fluid compressibility coefficient, MPa -1 ;p p is the pore pressure of shale formation, MPa; t is time, s; C s is the rock skeleton compression coefficient, MPa -1 ; μ is fluid viscosity, mPa·s; K is permeability, μm 2 ;p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; H is the pressure gradient, m; ε V is the rock skeleton strain; S4. Substituting the basic parameters of the target formation obtained in step S2 into the calculation model established in step S3, the surrounding rock strain distribution of the target formation is calculated.

2. The method for calculating surrounding rock strain distribution considering pore pressure effect according to claim 1, characterized in that: In step S2, basic parameters of the target formation are obtained, including Young's modulus, Poisson's ratio, horizontal maximum principal strain, horizontal minimum principal strain, overburden pressure, formation pressure, formation density, pore fluid density, wellbore fluid column pressure, shale initial porosity, shale initial permeability and wellbore diameter.

3. The method for calculating surrounding rock strain distribution considering pore pressure effect according to claim 1, characterized in that: The permeability K is calculated by the following formula: Where: is the initial porosity; K0 is the initial permeability, μm 2 ; K m is the bulk compression modulus of the skeleton, MPa; Δp p is the change in pore pressure, MPa.

4. The method for calculating surrounding rock strain distribution considering pore pressure effect according to claim 1, characterized in that: The rock skeleton strain ε V Calculated by the following formula: Where: u, v, w are the displacements of rock skeleton particles in the x, y, and z directions; G is the shear modulus, MPa; m is the Poisson's ratio; F x is the strain of rock skeleton particles in the x direction; F y is the strain of rock skeleton particles in the y direction; F z is the strain sum of rock skeleton particles in the z direction.

5. The method for calculating surrounding rock strain distribution considering pore pressure effect according to claim 4, characterized in that: The strain and F of rock skeleton particles in the x, y, and z directions x 、F y 、F z The calculation formula is as follows: F x =F z cosθ F y =F z sinθ Where: R is the borehole radius, m; r is the distance from the borehole center, m; θ is the wellbore angle, rad; σ r is the radial strain, MPa; σ H is the maximum horizontal strain, MPa; σ h is the minimum horizontal strain, MPa; x, y are the positions of the particles.

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