Research method for gas cut rule of fractured formation

Abstract

The invention relates to the technical field of fracture gas cut research, and particularly discloses a research method for a gas cut rule of a fractured formation. A reservoir deformation model, a fluid flow model and a fluid-solid cross coupling model are established, a numerical form of a mathematical model is deduced by adopting a finite element method, discrete fractures are constructed by utilizing MATLAB, and finally, the discrete fractures are solved by using commercial software to obtain a fractured formation gas cut rule. By knowing the characteristics and influence factors of gas cut, corresponding measures can be formulated, gas invasion can be reduced, and adverse effects on the drilling process and oil-gas field development can be reduced, by researching the gas cut caused by negative pressure difference drilling, the design and optimization of drilling fluid can be improved, so that the risk of gas invasion into a shaft can be reduced, and by discussing the research result, the development of the gas well can be promoted. And the method has great significance on actual oilfield development.

Description

Technical Field

[0001] The invention relates to the technical field of fracture gas invasion research, and in particular to a method for studying the law of gas invasion in fractured formations. Background Art

[0002] More than 40% of the world's oil and gas reservoirs are naturally fractured reservoirs, and the main oil distribution areas such as the Middle East, North America, South America and Southeast Asia are all naturally fractured reservoirs, and their exploitation process is relatively complicated. In most oil and gas reservoirs, the presence of natural fractures increases the permeability and storage capacity of the reservoir, so the fractures become the main channels for the flow and transportation of formation fluids. Since most natural fractures are in any direction and the fracture apertures are different, discrete fractures have a higher degree of heterogeneity and diversity compared to traditional porous media.

[0003] The drilling safety window for fractured reservoirs is extremely small, especially for carbonate reservoirs, where there is no safety window at all. Therefore, gas invasion or drilling fluid loss is very likely to occur during the drilling process. Commonly used methods for analyzing fractured reservoirs include empirical methods, analytical methods, semi-analytical methods, and numerical simulation methods. Empirical methods generally perform relationship regression on experimental data or field data to obtain models such as linear relationships and exponential relationships, and then perform analysis based on simple mathematical models. Although these methods provide engineers with "rules of thumb" guidance, the analytical accuracy of this method is low. Although some established predictive models can characterize the flow state of reservoir fluids to a certain extent

[32] However, it cannot accurately describe the geomechanical properties of porous media and the influence of rock deformation on gas invasion. Summary of the invention

[0004] In response to the above problems, this research method mainly focuses on the gas invasion problem of fractured reservoirs, comprehensively considers the influence of matrix deformation and fracture aperture change on fluid flow, and establishes a fluid-solid coupling mathematical model of gas invasion in fractured reservoirs.

[0005] The method comprises the following steps:

[0006] Before constructing the mathematical model, the following basic assumptions are made: the reservoir is a uniform, isotropic and elastic continuum; the fluid flow in the reservoir is single-phase flow and conforms to Darcy's law; the reservoir rock is slightly compressible and has a constant compression coefficient; the influence of gravity is ignored; and the fluid flow in the reservoir is isothermal flow.

[0007] The method comprises the following steps:

[0008] S1. Establish reservoir deformation model and fluid flow model;

[0009] For the reservoir deformation model, the Navier equation of the mechanical field during gas invasion obtained from the equilibrium equation of porous media deformation, geometric equation and stress-strain relationship is as follows:

[0010]

[0011] Where G = E / 2 (1 + v) is the shear modulus of the porous elastic material; E and v are the Young's modulus and Poisson's ratio of the porous elastic material, respectively; u ij is the displacement component; a is the Biot coefficient; p is the fluid pressure; f i is the body force component.

[0012] The establishment process of the fluid flow model is as follows:

[0013] The continuity equation in the matrix pores is:

[0014]

[0015] Where ρ g is the gas density under reservoir conditions; is the porosity of the porous medium; v m is the fluid velocity in the matrix pores; q m is the mass of the pore fluid.

[0016] Using Darcy's law to describe the flow rate of the fluid in the porous medium and the continuity equation of the matrix storage behavior into the matrix pores, the governing equation for the flow of the matrix pore fluid can be obtained as follows:

[0017]

[0018] Where k m is the permeability of the matrix pores; μ is the viscosity of the fluid; p is the pressure in the pores; S m is the storage coefficient.

[0019] The continuity equation inside the crack is:

[0020]

[0021] Where d f is the aperture size of the crack, is the porosity of the fracture; T is the tangential gradient; v f is the flow velocity of the fluid in the fracture; q f is the mass source of the fluid in the fracture.

[0022] Considering the natural fracture as the flow between two plates, the seepage velocity and fracture storage are combined with the continuity equation in the fracture to obtain the control equation of the fluid flow in the natural fracture:

[0023]

[0024] Where S f is the total compression coefficient of saturated fracture.

[0025] S2. Establishing Fluid-Solid Cross-Coupling Model

[0026] The dynamic fluid-solid cross-coupling model mainly analyzes the impact of changes in rock permeability and porosity.

[0027] For the matrix pore permeability k in step S1, m , the calculation formula of matrix permeability can be obtained from the dynamic permeability of the matrix and the specific surface area at different times as shown below:

[0028]

[0029] Where ε v is the volume strain, is the porosity of the reservoir matrix

[0030] The crack aperture d in step 1) f The total length of the crack when deformed is calculated as follows:

[0031] d f =a n +a s +a res

[0032] S3. Use the finite element method to derive the numerical form of the mathematical model In order to solve the unknown variables, the control equation needs to be integrated and simplified to obtain the finite element formula:

[0033] S4. Discrete cracks were constructed using MATLAB and solved using the commercial software COMSOL Multiphysics.

[0034] Beneficial effects of the invention: The discussion of the research results has great significance for actual oil field development.

[0035] 1. Estimation of gas invasion: By understanding the characteristics and influencing factors of gas invasion, appropriate measures can be formulated to reduce gas invasion and reduce the adverse effects on the drilling process and oil and gas field development.

[0036] 2. Drilling fluid design and optimization: By studying the gas invasion caused by negative pressure differential drilling, the design and optimization of drilling fluid can be improved to reduce the risk of gas intrusion into the wellbore. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described below in conjunction with the accompanying drawings.

[0038] Figure 1 The embodiment is a schematic diagram of a single crack;

[0039] Figure 2 Pressure distribution at different times;

[0040] Figure 3 Test points at different distances from the wellbore;

[0041] Figure 4 Pressure variations in fractures at different locations from the wellbore;

[0042] Figure 5 The degree of permeability reduction of fractures at different locations from the wellbore. DETAILED DESCRIPTION

[0043] The following is a geometric model of a single crack (such as Figure 1 The embodiment of the present invention is described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] The specific implementation steps are as follows:

[0045] S1. Establishing reservoir deformation model and fluid flow model

[0046] The mathematical model of porous media deformation includes equilibrium equations, geometric equations and constitutive equations. Based on the poroelasticity theory, the equilibrium equation of reservoir deformation can be defined as:

[0047] σ ij，i +f i =0 (1)

[0048] In the formula, σ ij is the sum of stress components; f i is the volume force component;

[0049] Under the assumption of small deformation, the geometric equation (strain-displacement relationship) can be defined as:

[0050]

[0051] In the formula, ε ij is the strain component; u ij is the displacement component;

[0052] The stress-strain relationship of rock materials obeys the linear poroelastic law. According to the Biot effective stress, it can be obtained:

[0053] σ ij =σ ij -αpδ ij (3)

[0054] In the formula, σ` ij is the effective stress; σ ij is the sum of stress components; a is the Biot coefficient; p is the fluid pressure; δ ij is the Kronecker function;

[0055] Substituting equations (2) and (3) into (1), we can obtain the Navier equation of the mechanical field during gas invasion:

[0056]

[0057] Where, G = E / 2(1+v), G is the shear modulus of the porous elastic material, E and v are the Young's modulus and Poisson's ratio of the porous elastic material, respectively; u ij is the displacement component; a is the Biot coefficient; p, i is the pore pressure; f i is the volume force component;

[0058] For the fluid flow model, the continuity equation in the matrix pores is:

[0059]

[0060] Using Darcy's law to describe the flow rate of fluid in porous media and the matrix storage behavior can be defined as follows:

[0061]

[0062] Substituting formula (6) and (7) in the step into (5), the governing equations for the flow of matrix pore fluid are as follows:

[0063]

[0064] The continuity equation inside the crack is:

[0065]

[0066] In equations (5) to (9), ρ g is the gas density under reservoir conditions; is the porosity of the porous medium; v m is the fluid velocity in the matrix pores; q m is the mass of pore fluid; k m is the permeability of matrix pores; μ is the viscosity of the fluid; p is the fluid pressure; ▽ p is the pressure gradient; S m is the storage coefficient; df is the crack aperture, is the porosity of the fracture; T is the tangential gradient; v f is the flow velocity of the fluid in the fracture; q f is the mass source of the fluid in the fracture; considering the natural fracture as the flow between two plates, its seepage velocity and fracture storage behavior can be defined as:

[0067]

[0068] Substituting formula (10) (11) into formula (9) we can obtain the governing equations for the fluid flow in natural fractures:

[0069]

[0070] In formulas (10) to (12), v f is the flow velocity of the fluid in the fracture; k f is the fracture permeability; μ is the viscosity of the fluid; d f is the crack aperture; p is the fluid pressure; ▽ p is the pressure gradient; ρ g is the gas density under reservoir conditions; is the porosity of the fracture; S f is the total compression coefficient of saturated fracture; T is the tangential gradient; q f is the mass source of the fluid in the fracture.

[0071] S2. Establishing Fluid-Solid Cross-Coupling Model

[0072] Assuming that the surface area of ​​the rock particles remains constant, the total volume change of the rock is equal to the change in pore volume. The specific surface area at different times can be expressed as:

[0073]

[0074] In formulas (13) and (14), V b is the volume of the rock; V s is the change in rock volume, ε v is the volume strain;

[0075] The calculation formula of matrix permeability can be obtained by combining equations (13) and (14):

[0076]

[0077] In the formula, k m is the permeability of matrix pores; k m0 is the initial permeability; ε v is the volume strain; is the initial porosity;

[0078] The total pore size when the crack is deformed is:

[0079]

[0080] Where a n 、a s is the normal deformation, shear deformation, and a of the crack res The size of the residual aperture, is the effective expansion angle.

[0081] S3. Use the finite element method to derive the numerical form of the mathematical model

[0082] In order to solve the unknown variables, the control equation needs to be integrated and simplified to obtain the finite element formula:

[0083]

[0084] S4. Discrete cracks were constructed using MATLAB and solved using the commercial software COMSOL Multiphysics.

[0085] Embodiment 1:

[0086] Assuming that the geometry of a fracture is known, the fracture is parallel to the x-axis and intersects the wellbore. The established geometric model is as follows: Figure 1 Some parameters used in the simulation are shown in Table 1.

[0087] Table 1

[0088] Parameter name Numeric Reservoir area 8m×8m Reservoir thickness 8m Initial formation pressure 24MPa Bottom hole pressure 20MPa Fluid Viscosity <![CDATA[4.74×10 -5 Step]]> Fluid compressibility <![CDATA[4×10 -4 MPa -1 ]]> Pore ​​compressibility <![CDATA[7.5×10 -4 MPa -1 <!-- 5 -->]]> Crack compression coefficient <![CDATA[7.5×10 -3 MPa -1 ]]> Matrix porosity 0.07 Fracture porosity 0.0001 Rock Poisson's ratio 0.25 Initial crack width 0.5mm Biot coefficient 0.6

[0089] The outer boundary is a non-flowing boundary, and the inner boundary wellbore is set to a fixed pressure. Some of the formulas used are as follows:

[0090]

[0091]

[0092] The commercial software COMSOL Multiphysics was used to solve the problem. Figure 2 The pressure distribution at different times is shown, and it can be seen that the pressure inside the crack decreases rapidly along the length of the crack. Figure 3 There are 8 test points at different distances from the wellbore.

[0093] After drilling into the cracks, Figure 4It can be seen that the pressure in the cracks near the wellbore will decrease instantaneously and approach the pressure at the bottom of the well, while the pressure in the cracks far away from the wellbore will decrease but change slowly, and the pressure difference between the cracks and the bottom of the well will also increase. The law of change of permeability in the cracks can be inferred based on the effective stress and the cubic law combined with the change of pressure, that is, the closer to the wellbore, the greater the decrease in permeability of the cracks. The obtained law is also consistent with the results obtained by simulation. Figure 5 Match.

[0094] The present invention establishes a mathematical model to simulate and explore the characteristics of fluid flow and rock deformation in fractures when drilling encounters fractures. The pressure in the fracture will drop rapidly and approach the bottom hole pressure, and the effective stress will increase due to the decrease in formation pressure, thereby reducing the permeability of the fracture.

[0095] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0096] The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.

Claims

1. A method for studying the gas invasion law of fractured formations, characterized in that: The research method comprises the following steps: S1. Establishing reservoir deformation model and fluid flow model The mathematical model of porous media deformation includes equilibrium equations, geometric equations and constitutive equations. Based on the poroelasticity theory, the equilibrium equation of reservoir deformation can be defined as: s ij，i +f i =0 (1) In the formula, σ ij is the sum of stress components; f i is the volume force component; Under the assumption of small deformation, the geometric equation (strain-displacement relationship) can be defined as: In the formula, ε ij is the strain component; u ij is the displacement component; The stress-strain relationship of rock materials obeys the linear poroelastic law. According to the Biot effective stress, it can be obtained: In the formula, is the effective stress; σ ij is the sum of stress components; a is the Biot coefficient; p is the fluid pressure; δ ij is the Kronecker function; Substituting equations (2) and (3) into (1), we can obtain the Navier equation of the mechanical field during gas invasion: Where, G = E / 2(1+v), G is the shear modulus of the porous elastic material, E and v are the Young's modulus and Poisson's ratio of the porous elastic material, respectively; u ij is the displacement component; a is the Biot coefficient; p, i is the pore pressure; f i is the volume force component; For the fluid flow model, the continuity equation in the matrix pores is: Using Darcy's law to describe the flow rate of fluid in porous media and the matrix storage behavior can be defined as follows: Substituting formula (6) and (7) in the step into (5), the governing equations for the flow of matrix pore fluid are as follows: The continuity equation inside the crack is: In equations (5) to (9), ρ g is the gas density under reservoir conditions; is the porosity of the porous medium; v m is the fluid velocity in the matrix pores; q m is the mass of pore fluid; k m is the permeability of matrix pores; μ is the viscosity of the fluid; p is the fluid pressure; is the pressure gradient; S m is the storage coefficient; d f is the crack aperture, is the porosity of the fracture; is the tangential gradient; v f is the flow velocity of the fluid in the fracture; q f is the mass source of the fluid in the fracture; considering the natural fracture as the flow between two plates, its seepage velocity and fracture storage behavior can be defined as: Substituting formula (10) (11) into formula (9) we can obtain the governing equations for the fluid flow in natural fractures: In formulas (10) to (12), v f is the flow velocity of the fluid in the fracture; k f is the fracture permeability; μ is the viscosity of the fluid; d f is the crack aperture; p is the fluid pressure; is the pressure gradient; ρ g is the gas density under reservoir conditions; is the porosity of the fracture; S f is the total compression coefficient of saturated fracture; is the tangential gradient; q f is the mass source of the fluid in the fracture; S2. Establishing Fluid-Solid Cross-Coupling Model Assuming that the surface area of ​​the rock particles remains constant and the total volume change of the rock is equal to the change in the pore volume, the specific surface area at different times can be expressed as: In formulas (13) and (14), V b is the volume of the rock; V s is the change in rock volume, ε v is the volume strain; The calculation formula of matrix permeability can be obtained by combining equations (13) and (14): In the formula, k m is the permeability of matrix pores; k m0 is the initial permeability; ε v is the volume strain; is the initial porosity; The total pore size when the crack is deformed is: Where a n 、a s is the normal deformation, shear deformation, and a of the crack res The size of the residual aperture, is the effective expansion angle; S3. Use the finite element method to derive the numerical form of the mathematical model In order to solve the unknown variables, the control equation needs to be integrated and simplified to obtain the finite element formula: S4. Discrete fractures were constructed using MATLAB and solved using commercial software.

2. The method for studying gas invasion law of fractured formations according to claim 1, characterized in that: Before constructing the step S1 reservoir deformation model and fluid flow model, the following basic assumptions are made: the reservoir is a uniform, isotropic and elastic continuum; the fluid flow in the reservoir is a single-phase flow and conforms to Darcy's law, the reservoir rock is slightly compressible and has a constant compression coefficient, the influence of gravity is ignored, and the fluid flow in the reservoir is isothermal.

3. The method for studying gas invasion law of fractured formations according to claim 1, characterized in that: The commercial software used in step S4 is COMSOL Multiphysics.

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