Fracture conductivity evaluation method considering shale hydration

Abstract

The invention constructs a fracture conductivity evaluation method considering shale hydration. The method mainly comprises the following steps: 1, carrying out a triaxial hydration creep mechanics experiment, establishing an elastic-viscoelastic-viscous plastic multi-stage creep constitutive equation based on triaxial experiment data, and analyzing shale elastic and viscous deformation mechanisms; 2, secondly, constructing a shale creep constitutive model by stages according to a stress threshold value, describing a viscoelastic stage by adopting an improved Burgers model, and establishing a viscoplastic strain equation based on an overstress theory; 3, coupling hydration action parameters to correct a shale creep equation, and quantifying the influence of hydration on rock modulus, viscosity coefficient and yield stress; 4, the creep strain and the crack dynamic width are correlated through a mathematical model, and a multi-field coupling relation is established in combination with a permeability evolution rule; and 5, finally constructing a fracture conductivity prediction model when the hydration effect is considered, and realizing fracture conductivity dynamic analysis under the hydration-creep synergistic effect. According to the method, the shale hydration-creep coupling effect is creatively fused into fracture conductivity prediction, and a quantitative tool is provided for shale reservoir long-term productivity evaluation.

Description

Technical Field

[0001] The invention relates to a fracture conductivity evaluation method considering shale hydration, and belongs to the field of oil and gas field development. Technical Background

[0002] Shale gas is an unconventional, clean natural gas resource. In shale gas development, hydraulic fracturing is required to transform the reservoir to produce industrial gas flow, and fracture conductivity is a key factor affecting the stability of shale gas production. Slickwater is often used as the primary fracturing fluid in shale gas volume fracturing. Large amounts of fracturing fluid, when injected into the formation, react physically and chemically with the shale. Research has shown that clay minerals in shale (such as montmorillonite and illite) expand significantly upon contact with water. In particular, surface hydration occurs on the surface of clay particles, generating hydration stress. This hydration causes stress concentration at the crack tip, leading to crack propagation and extension. This expansion and mixing forms a fracture damage zone, disrupting the rock's internal structure. This leads to microstructural damage in the shale, a decrease in the elastic modulus of the rock wall, and increased sensitivity to fracture closure pressure. The loss of conductivity caused by water-rock interaction is a major obstacle to the efficient development of shale gas. Hydration exacerbates viscoplastic deformation of the wall, causing a significant decrease in the width of the hydraulic fracture under closure stress. Analysis of past experimental results on the conductivity of shale fractures found that the conductivity of shale fractures after hydration can drop by up to about 88%. Rock creep is mainly divided into several states, including initial creep, steady-state creep, and accelerated creep. Although some studies have attempted to describe hydration damage through empirical formulas (such as introducing a linear attenuation coefficient), these models are difficult to quantitatively characterize the dynamic coupling relationship between damage variables and creep rate, and lack consideration of three-dimensional heterogeneity. In the existing technology, the creep equation based on the Burgers or Nishihara model can reflect the viscoelastic-plastic behavior of rocks, but does not take the hydration damage variable D into account. T Combined with microscopic characterization methods such as nuclear magnetic resonance T2 spectroscopy, the correlation between shale hydration damage mechanism and macroscopic mechanical response is insufficient.

[0003] Traditional fracture conductivity models are mostly based on purely mechanical constitutive theory. Relatively few fracture conductivity models consider the effects of rock creep, but the key lies in determining parameters such as fracture width and permeability. Hydration also affects rock creep behavior. If the proppant strength is insufficient, it will break. If the formation softening strength is too low, the proppant will become embedded in the fracture surface. These phenomena will cause varying degrees of changes in fracture width, which can lead to significant deviations in fracture conductivity predictions. Calculations in traditional fracture conductivity models often assume a static proportional relationship between fracture width and strain. Even when considering the effects of hydration, clay content is often used as a direct indicator of proppant deformation. These limitations result in significant errors (up to 40% or more) in existing models when predicting long-term fracture conductivity, severely restricting the optimization of fracturing materials and the precise design of reservoir stimulation plans. Summary of the Invention

[0004] To address these issues, the present invention constructs a three-dimensional hydration damage creep equation by coupling the hydration damage variable DT with an improved elastic-viscoelastic-viscoplastic (EVP) theory. This model, for the first time, establishes a multiscale correlation between mineral expansion, microscopic damage, and macroscopic conductivity attenuation. This model not only fills a gap in chemical-mechanical coupling theory but also allows for dynamic parameter correction using in-situ nuclear magnetic resonance data, providing a breakthrough solution for regulating water-rock interactions in shale gas and geothermal engineering.

[0005] The present invention provides a technical solution to solve the above technical problems: a method for evaluating fracture conductivity taking into account shale hydration, comprising the following steps:

[0006] Step S10: conducting a triaxial hydration creep experiment, and calculating the axial strain and radial strain caused by the increase in axial stress based on the deep shale reservoir data and the axial stress applied by the triaxial compression experiment;

[0007] Step S20: when the applied stress is lower than the yield strength, a viscoelastic creep equation is established based on the improved Burgers model;

[0008] Step S30: when the applied stress is higher than the yield strength, a linear relationship between the viscoplastic strain rate and the super-yield stress is established;

[0009] Step S40: establishing a total creep strain equation based on elasticity-viscoelasticity-viscoplasticity theory;

[0010] Step S50 considers the influence of hydration on rock creep deformation and establishes a modified rock creep equation considering hydration;

[0011] Step S60 considers the effect of hydration on the crack width and establishes a relationship between creep strain and crack width;

[0012] Step S70 considers the effect of hydration on permeability and establishes a relationship between the creep equation and permeability;

[0013] Step S80 establishes a calculation formula for the flow conductivity taking into account the influence of hydration according to the flow conductivity calculation formula.

[0014] Hydration creep triaxial mechanical experiments were conducted. In triaxial creep compression experiments, a linear elastic stress-strain relationship can be established by applying axial stress (σ1) and confining pressure (σ2 = σ3). When the confining pressure is constant, the axial strain Δε1 and radial strain Δε2 caused by the axial stress increment Δσ1 follow the generalized Hooke's law, calculated as follows:

[0015] Where E is the elastic modulus and ν is the Poisson's ratio.

[0016] Viscoelastic behavior is manifested as time-dependent delayed deformation, which can be observed by constant load creep tests. s (σ<σ s ), the strain gradually increases with time and tends to a steady state. Based on the improved Burgers model, the viscoelastic creep equation can be expressed as:

[0017] Where E0 is the instantaneous elastic modulus, E1 is the viscoelastic modulus, and η1 is the viscosity coefficient.

[0018] When t→∞, the exponential term approaches zero and the steady-state strain is:

[0019]

[0020] In step S30, when the applied stress exceeds the yield stress (σ>σ s ), the rock enters the accelerated creep stage, at which time the viscoplastic strain rate is linearly related to the super yield stress, and the calculation formula is:

[0021]

[0022] In the formula, η2 is the viscoplastic coefficient, which reflects the material's ability to resist plastic flow. The smaller its value, the more significant the trend of accelerated failure.

[0023] Table 1 Creep parameter range parameter Physical meaning Typical value range unit E elastic modulus 15～50 GPa υ Poisson's ratio 0.15～0.3 dimensionless <![CDATA[E0]]> Instantaneous elastic modulus <h2 style=";text-align:left;direction:ltr"><![CDATA[0.8E <h2 style=";text-align:left;direction:ltr"> e <h2 style=";text-align:left;direction:ltr"> ~1.2E<h2 style=";text-align:left;direction:ltr"> e <h2 style=";text-align:left;direction:ltr"> ]]><h2 style=";text-align:left;direction:ltr"> GPa <![CDATA[E1]]> Viscoelastic modulus <![CDATA[0.2E e ~0.5E e ]]> GPa <![CDATA[η1]]> Viscosity coefficient <![CDATA[1×10 12 ~1×10 14 ]]> mPa·s <![CDATA[η2]]> Viscoplastic coefficient <![CDATA[1×10 15 ~1×10 17 ]]> Pa·s

[0024] Based on the elastic-viscoelastic-viscoplastic (EVP) theory, the total creep strain is:

[0025]

[0026] Where E0 is the elastic modulus, E1 is the viscoelastic modulus, η1 is the viscosity coefficient, and η2 is the viscoplastic coefficient.

[0027] Calculate the T2 spectrum integral area using the following formula:

[0028] S≈∫F S n(t,T2)dT2

[0029] F s is the geometric shape factor, and S is the integrated area of the NMR T2 spectrum.

[0030] According to the basic principle of strain equivalence hypothesis, the transverse relaxation time T2 spectrum of nuclear magnetic resonance is used to characterize the hydration damage variable D. T , reflecting the weakening effect of hydration on the rock microstructure. The calculation formula is:

[0031]

[0032] The hydration damage variable D T Substituting this into the equation, we obtain the one-dimensional viscoelastic-plastic damage creep equation considering hydration damage:

[0033]

[0034] The three-dimensional viscoelastic-plastic hydration damage creep equation considering initial hydration damage can be extended to a three-dimensional equation:

[0035]

[0036] Wherein, G0 is the shear elastic modulus corresponding to E0, G1 is the shear viscoelastic modulus corresponding to E1, K is the bulk modulus, F is the rock yield function, and F0 is the initial reference value of the rock yield function.

[0037] Assume that the crack width ω is proportional to the material strain ε, that is:

[0038] w(t)=w0(1-ε(t))

[0039] Substitute the one-dimensional creep equation into the crack width formula:

[0040]

[0041] The connectivity of microcracks is an important factor affecting the evolution of permeability. Under the accelerated state of the creep process, the connectivity of microcracks will eventually form mesoscopic cracks, providing fluid channels for seepage. According to the Hagen-Poiseuille law, the volume flow rate in porous media is given by the following equation:

[0042]

[0043] Where A s is the cross-sectional area of the specimen

[0044] The permeability of porous media can be expressed as:

[0045]

[0046] The permeability k is the additional permeability due to the connectivity of microcracks. Therefore, the true permeability of the porous medium should be:

[0047]

[0048] The evolution of the cross-sectional area of the equivalent small tube can be given by the following formula:

[0049] πR 4 =n(3ε m -ε(t))A s

[0050] Where n is the coefficient related to the connectivity of microcracks, ε m Volumetric strain.

[0051] Substituting the above formula into the actual permeability calculation equation of porous media, the permeability model of shale creep process within the unit cross-sectional area of porous media is:

[0052]

[0053] Substituting permeability and fracture width into the definition of conductivity:

[0054] C(t)=k(t)·w(t)

[0055] Finally, the conductivity expression under hydration damage is obtained:

[0056] BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Method flow chart

[0058] Figure 2 Schematic diagram of the fractal derivative creep model based on damage mechanism

[0059] Figure 3 This is the result of the nuclear magnetic resonance T2 peak spectrum experiment of shale hydration experiment

[0060] Figure 4 This is the experimental curve of the effect of hydration on creep strain

[0061] Figure 5 This is the experimental curve of the effect of hydration on creep rate

[0062] Figure 6This is the prediction diagram of conductivity considering creep.

Claims

1. A method for evaluating fracture conductivity considering shale hydration, comprising the following steps: Step S10: conducting a triaxial hydration creep experiment, and calculating the axial strain and radial strain caused by the increase in axial stress based on the shale reservoir data and the axial stress applied by the triaxial compression experiment; Step S20: when the applied stress is lower than the yield strength, a viscoelastic creep equation is established based on the improved Burgers model; Step S30: when the applied stress is higher than the yield strength, a linear relationship between the viscoplastic strain rate and the super-yield stress is established; Step S40: establishing a total creep strain equation based on elasticity-viscoelasticity-viscoplasticity theory; Step S50 considers the influence of hydration on rock creep deformation and establishes a modified rock creep equation considering hydration; Step S60 considers the effect of hydration on the crack width and establishes a relationship between creep strain and crack width; Step S70 considers the effect of hydration on permeability and establishes a relationship between the creep equation and permeability; Step S80 constructs a shale fracture conductivity prediction model considering hydration, and establishes a calculation equation for shale fracture conductivity under the influence of hydration based on the conductivity calculation formula to evaluate fracture conductivity.

2. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein the calculation formula in step S10 is: Where E is the elastic modulus and ν is the Poisson's ratio.

3. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that when the applied stress is lower than the yield strength, the calculation formula in step S20 is: Where E0 is the instantaneous elastic modulus, E1 is the viscoelastic modulus, and η1 is the viscosity coefficient.

4. The fracture conductivity evaluation method considering shale hydration according to claim 1, further comprising: when the applied stress is lower than the yield strength and when t→∞, the exponential term approaches zero, and the calculation formula for the steady-state strain in step S20 is: Viscoplastic parameters and accelerated creep mechanisms.

5. The fracture conductivity evaluation method considering shale hydration according to claim 1, further comprising: when the applied stress is higher than the yield strength, the calculation formula in step S30 is: Where η2 is the viscoplastic coefficient, which reflects the material's ability to resist plastic flow. The smaller its value, the more significant the trend of accelerated failure.

6. According to the fracture conductivity evaluation method considering shale hydration according to claim 1, the creep parameter ranges of deep shale are shown in the following table; Table 1 Shale creep parameter range 7. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the calculation formula in step S40 is: Where E0 is the elastic modulus, E1 is the viscoelastic modulus, η1 is the viscosity coefficient, and η2 is the viscoplastic coefficient.

8. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the hydration damage variable calculation formula in step S50 is: Where F s is the geometric shape factor, and S is the integral area of the NMR T2 spectrum. T0 is the T2 spectrum integral area of the initial state (undamaged); S T2 is the integrated area of the T2 spectrum after hydration damage.

9. The fracture conductivity evaluation method considering shale hydration according to claim 1, further comprising the following technical solution: the modified rock creep equation considering hydration in step S50 is calculated as:

10. The fracture conductivity evaluation method considering shale hydration according to claim 1, further comprising the following technical solution: the modified three-dimensional rock creep equation considering hydration in step S50 is calculated as: in, G0 is the shear elastic modulus corresponding to E0, G1 is the shear viscoelastic modulus corresponding to E1, K is the bulk modulus, F is the rock yield function, and F0 is the initial reference value of the rock yield function.

11. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the relationship between the creep equation and the fracture width in step S60 is: w(t)=w0(1-ε(t)) (10) Where w0 is the initial slit width.

12. The fracture conductivity evaluation method considering shale hydration according to claim 1, further comprising the following technical solution: the fracture width calculation equation considering hydration in step S60 is:

13. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the permeability calculation equation considering hydration in step S70 is: Where A s is the cross-sectional area of the specimen k0 is the initial permeability.

14. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the relationship between the creep equation and the permeability in step S70 is: Where n is the coefficient related to the connectivity of microcracks, ε m is the volume strain.

15. The fracture conductivity evaluation method considering shale hydration according to claim 1, wherein a further technical solution is that the calculation formula in step S80 is: C(t)=k(t)·w(t) (17)

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