Porous medium sand production calculation method under fluid-solid-stress combined action

Abstract

The invention discloses a porous medium sand production calculation method under fluid-solid-stress comprehensive action, which comprises the following steps of: firstly, determining a particle falling critical condition by taking a solid-phase particle as a center, and determining a geometrical relationship and area fractal characterization based on material mechanics and a fractal theory; then, on the basis of a capillary bundle model and a Fourier formula, non-wetting phase fluid flow fractal characterization before and after solid-phase particle blockage under the fluid-solid-stress comprehensive action is obtained; and then combining the Darcy law to obtain the fractal representation of the permeability of the non-wetting phase under the comprehensive action of fluid-solid-stress. And finally, normalizing the permeability of the non-wetting phase, calculating normalized permeability under different displacement pressures, drawing a sand production curve, and determining a sand production critical condition. The method not only can be independently applied to loose, stress-sensitive and multiphase flow reservoirs with complex pore structures and difficulty in obtaining rock cores, but also can be applied to reservoirs under the combined action of the three reservoirs, a traditional sand production experiment is replaced, the prediction precision of the sand production critical condition is improved, and the rock core obtaining and experiment cost is reduced.

Description

Technical Field

[0001] The invention relates to a method for calculating sand production from porous media under the comprehensive action of fluid-solid-stress, and belongs to the technical field of oil and gas field development data analysis. Background Art

[0002] The fluid-solid-stress coupling behavior brings great difficulties to the study of reservoir microstructure, fluid distribution law and fluid seepage capacity. The wettability of the wetting fluid, stress action and the solid particles themselves will affect the microstructure of the porous medium, the flow and distribution of the fluid in the porous medium, thereby changing the solid particle shedding conditions and causing the seepage law of the porous medium to change; considering the combined action of fluid-solid-stress at the same time, the current mathematical model and measurement method cannot well describe the change in the seepage capacity of the porous medium, and also greatly increase the difficulty of experimental operation; how to quickly, efficiently and accurately obtain the critical sanding conditions of porous media under the combined action of fluid-solid-stress, and quickly master the seepage law of porous media under multi-factor conditions is crucial for industries such as oil and gas field development engineering.

[0003] The following concepts are involved in this article: Fractal theory: using fractal and dimension mathematical tools to describe and study objective things, which is closer to the description of the real properties and states of complex systems, and more in line with the diversity and complexity of objective things; Material mechanics: studying the strain, stress, strength, stiffness, stability and the limits of various material destruction produced by various external forces, and analyzing the changes of porous media under stress; Permeability: the ability of rock to allow fluid to pass under a certain pressure difference, which is a parameter that characterizes the ability of soil or rock itself to conduct liquid; Normalization: converting dimensional expressions into dimensionless expressions, eliminating the influence of dimensions and orders of magnitude, simplifying calculations for easy comparison. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating sand production in porous media under the combined action of fluid-solid-stress, so as to solve the problem that the coupling behavior of fluid-solid-strain brings great difficulties to the study of changes in seepage capacity in porous media, and it is difficult to effectively and quickly describe the fluid seepage characteristics.

[0005] To achieve the above object, the present invention provides a method for calculating sand production in porous media under the combined action of fluid-solid-stress, the method comprising the following steps:

[0006] Step 1: Fractal characterization of particle instability blockage area under the combined action of fluid-solid-stress. With the solid phase particle as the center, when the drag force of the gas on the solid phase particle is greater than the maximum static friction between the solid phase particles, it is considered that the critical condition of particle shedding is reached. Based on the tree-like fractal characteristics of material mechanics and porous media, the geometric relationship between the solid phase particle diameter, capillary bundle diameter and liquid film thickness and the particle shedding blockage area A under the combined action of fluid-solid-stress are obtained.bσ Fractal representation, its unit is m 2 ;

[0007] Step 2: Fractal characterization of flow rate under the combined action of fluid-solid-stress. Based on the fractal characterization of particle instability blockage area under the combined action of fluid-solid-stress, the fractal characterization of non-wetting phase fluid flow rate, solid phase particle blockage flow rate and non-wetting phase fluid flow rate after blockage is obtained based on the capillary bundle model, Fourier formula and fractal scaling law.

[0008] The third step: the calculation method of sand production in porous media under the combined action of fluid-solid-stress is based on the fractal characterization of flow rate under the combined action of fluid-solid-stress, combined with Darcy's law and fractal scaling law, to obtain the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress. The normalized permeability fractal characterization of porous media under the combined action of fluid-solid-stress is obtained according to the normalized definition, and the normalized permeability under different displacement pressures is calculated to draw the sand production curve of porous media.

[0009] The above-mentioned method for calculating sand production from porous media under the combined action of fluid-solid-stress, the specific steps of fractal characterization of flow under the combined action of fluid-solid-stress are:

[0010] Step 1: Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: Based on the capillary bundle model and Fourier formula, the fractal characterization of the non-wetting phase fluid flow rate and the solid phase particle blocking flow rate in the porous medium under the combined action of fluid-solid-stress is obtained;

[0011] Step 2: Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: According to the fact that the actual flow rate of non-wetting phase fluid in porous media is the difference between the unblocked flow rate of non-wetting phase fluid in porous media and the blocked flow rate of porous media, the fractal characterization of the actual flow rate of non-wetting phase fluid in porous media under the combined action of fluid-solid-stress is obtained as follows:

[0012] ,

[0013] Where (D cfσ is the fractal dimension of solid particles under stress; D cTσ D is the tortuosity of solid particles under stress; crfσ is the fractal dimension of the movable solid particles under stress; C is the traction coefficient; E is the elastic modulus, Pa; F is the comprehensive shape factor; k is the flow coefficient; L is the length of the porous medium, m; n is the power law index; Q crσ is the non-wetting phase fluid flow rate after the porous medium is blocked, m 3 / s;S wσ is the water saturation of the wetting phase of the porous medium, %; ν is the Poisson's ratio; λcmax0 The maximum diameter of solid particles when stress is 0, m; λ cmin0 The minimum diameter of solid particles when stress is 0, m; κ is the static friction coefficient; κ w Static friction coefficient when the wetting phase exists; σ0 is the initial radial stress, Pa; σ is the stress, Pa; μ is the viscosity of the non-wetting phase fluid, Pa·s; ρ g is the density of the non-wetting phase fluid, kg / m 3 ;v g is the flow rate of the non-wetting phase fluid, m / s; δ σ is the height of the wetting phase fluid covering the solid phase particles, m; Δp is the applied pressure, Pa.

[0014] The above-mentioned method for calculating sand production from porous media under the combined action of fluid-solid-stress, the specific steps of the method for calculating sand production from porous media under the combined action of fluid-solid-stress are as follows:

[0015] The first step: fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress. Based on the fractal characterization of flow under the combined action of fluid-solid-stress, combined with Darcy's law and fractal scaling law, the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress is obtained. The fractal characterization of the non-wetting phase permeability of porous media after blockage under the combined action of fluid-solid-stress is: Where K crσ It is the non-wetting phase permeability of porous media after blockage occurs under the combined action of fluid-solid-stress, and its unit is mD;

[0016] The second step is the fractal characterization of normalized seepage in porous media under the combined action of fluid-solid-stress. Based on the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress, the normalized fractal characterization of seepage in porous media under the combined action of fluid-solid-stress is obtained according to the normalized definition. The fractal characterization of the normalized permeability of porous media under the combined action of fluid-solid-stress is:

[0017] In the formula is the normalized permeability of porous media under the combined action of fluid-solid-stress;

[0018] S303: Calculate the normalized permeability of porous media under the combined effects of fluid-solid-stress at different displacement pressures, draw the sand production curve of porous media, and clarify the critical conditions for sand production of porous media. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is the technical roadmap of the present invention;

[0020] Figure 2 is a comparison diagram of experimental and calculated results under a stress of 3 MPa in an embodiment of the present invention;

[0021] Figure 3 is a graph showing changes in normalized permeability of porous media under different stresses in an embodiment of the present invention;

[0022] Figure 4 It is the normalized permeability variation diagram of porous media with different water saturation;

[0023] Figure 5 It is a graph showing the change in normalized permeability of porous media at different porosities. DETAILED DESCRIPTION

[0024] The present invention will be further described below in conjunction with the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0025] The present invention provides a method for calculating relative permeability of porous media under stress. Figure 1 The technical roadmap of the present invention comprises the following steps:

[0026] Example

[0027] like Figure 1 The technical roadmap of the present invention shown in FIG. 1 is a comparison of the relative permeability curve obtained by the calculation method of the present invention and the method of obtaining the relative permeability curve by the prior art by taking the experimental data of a gas reservoir as an example. Figures 2 to 5 ;

[0028] The same data is processed as follows according to the steps of the method of the present invention:

[0029] Step 1: Fractal characterization of particle instability blockage area under the combined action of fluid-solid-stress. With the solid phase particle as the center, when the drag force of the gas on the solid phase particle is greater than the maximum static friction between the solid phase particles, it is considered that the critical condition of particle shedding is reached. Based on the tree-like fractal characteristics of material mechanics and porous media, the geometric relationship between the solid phase particle diameter, capillary bundle diameter and liquid film thickness and the particle shedding blockage area A under the combined action of fluid-solid-stress are obtained. bσ Fractal representation, its unit is m 2 ;

[0030] Step 2: Fractal characterization of flow rate under the combined action of fluid-solid-stress. Based on the fractal characterization of particle instability blockage area under the combined action of fluid-solid-stress, the fractal characterization of non-wetting phase fluid flow rate, solid phase particle blockage flow rate and non-wetting phase fluid flow rate after blockage is obtained based on the capillary bundle model, Fourier formula and fractal scaling law under the combined action of fluid-solid-stress:

[0031] (1) Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: Based on the capillary bundle model and Fourier formula, the fractal characterization of non-wetting phase fluid flow rate and solid phase particle blocking flow rate under the combined action of fluid-solid-stress is obtained;

[0032] (2) Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: Based on the fact that the non-wetting phase flow velocity of a porous medium is the difference between the free-flowing flow velocity of the porous medium and the blocked flow velocity of the porous medium, the fractal characterization of the non-wetting phase fluid flow rate after blockage under the combined action of fluid-solid-stress is obtained.

[0033] Step 3: The calculation method of sand production in porous media under the combined action of fluid-solid-stress is based on the fractal characterization of flow under the combined action of fluid-solid-stress, combined with Darcy's law and fractal scale law, to obtain the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress. The fractal characterization of the normalized permeability of porous media under the combined action of fluid-solid-stress obtained by normalization definition is used to calculate the normalized permeability under different displacement pressures and draw the sand production curve of porous media:

[0034] (1) Fractal characterization steps of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress.

[0035] -Fractal characterization of flow rate under the combined action of solid-stress, combining Darcy's law and fractal scaling law to obtain the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of flow-solid-stress;

[0036] (2) A fractal characterization step of normalized seepage flow in porous media under the combined action of fluid-solid-stress, based on the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress, and according to the normalization definition, a fractal characterization of normalized seepage flow in porous media under the combined action of fluid-solid-stress is obtained;

[0037] (3) Calculate the normalized permeability of porous media under the combined effects of fluid-solid-stress at different displacement pressures, draw the sand production curve of porous media, and clarify the critical conditions for sand production of porous media.

[0038] According to this method, the critical conditions for particle shedding are first determined with solid particles as the center, and the geometric relationship between diameters and the fractal representation of the area are determined based on material mechanics and the tree-like fractal characteristics of porous media; then, based on the capillary bundle model, Fourier formula and fractal scaling law, the fractal representations of the non-wetting phase fluid flow rate, solid phase particle blockage flow rate and non-wetting phase fluid flow rate after blockage under the combined action of fluid-solid-stress are obtained; then, combined with Darcy's law and fractal scaling law, the fractal representation of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress is obtained; finally, the non-wetting phase fluid permeability is normalized, the normalized permeability under different displacement pressures is calculated, the sand production curve of porous media is drawn, and the critical conditions for sand production of porous media are determined. Figure 2 is a comparison chart of the experimental and calculated results under a stress of 3 MPa in an embodiment of the present invention, Figure 3 is a graph showing changes in normalized permeability of porous media under different stresses in an embodiment of the present invention, Figure 4 is the normalized permeability variation diagram of porous media with different water saturation. Figure 5 It is a graph showing the change in normalized permeability of porous media at different porosities. From the comparison, it can be seen that the scheme proposed by the present invention is highly consistent with the experimental results and can be used to predict the critical conditions for actual sand production in oil and gas fields.

[0039] Compared with the prior art, the present invention has the following beneficial effects: (1) the flow law of fluid in porous media is more in line with the actual situation by comprehensively considering the combined effects of fluid, solid and stress; (2) the physical meaning of parameters is clear and there are no empirical constants, and the critical conditions for sand production in porous media are more accurate.

[0040] Finally, it should be noted that as described above, the embodiments of this article are only used to illustrate the technical method and do not impose any form of limitation on the present invention. Although the present invention is described in detail with reference to the above embodiments, ordinary technicians in this field should understand that any modification or equivalent substitution in accordance with the technical essence of the present invention without departing from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for calculating sand production in porous media under the combined action of fluid-solid-stress, characterized in that: The method comprises the following steps: S100: Fractal characterization step of particle shedding blockage area under the combined action of fluid-solid-stress. With the solid phase particle as the center, when the drag force of the gas on the solid phase particle is greater than the maximum static friction between the solid phase particles, it is considered that the critical condition of particle shedding is reached. Based on the tree-like fractal characteristics of material mechanics and porous media, the geometric relationship between the solid phase particle diameter, capillary bundle diameter and liquid film thickness and the particle shedding blockage area A under the combined action of fluid-solid-stress are obtained. bσ Fractal representation, its unit is m 2 ; S200: flow fractal characterization step under the combined action of fluid-solid-stress. On the basis of the fractal characterization of particle shedding blockage area under the combined action of fluid-solid-stress, based on the capillary bundle model, Fourier formula and fractal scaling law, the fractal characterization of non-wetting phase fluid flow, solid phase particle blockage flow and non-wetting phase fluid flow after blockage under the combined action of fluid-solid-stress is obtained; S300: Steps of the method for calculating sand production in porous media under the combined action of fluid-solid-stress. Based on the fractal characterization of flow rate under the combined action of fluid-solid-stress, combined with Darcy's law and fractal scaling law, the fractal characterization of the non-wetting phase permeability of porous media before and after blockage under the combined action of fluid-solid-stress is obtained. According to the fractal characterization of the normalized permeability of porous media under the combined action of fluid-solid-stress obtained by normalization definition, the normalized permeability under different displacement pressures is calculated, and the sand production curve of porous media is drawn.

2. The method for calculating sand production from porous media under the combined effects of fluid-solid-stress according to claim 1, characterized in that: The steps of fractal characterization of flow rate under the combined action of fluid-solid-stress in S200 are as follows: S201: Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: Based on the capillary bundle model and Fourier formula, the fractal characterization of the non-wetting phase fluid free flow rate and the solid phase particle blocking flow rate in porous media under the combined action of fluid-solid-stress is obtained; S202: Fractal characterization of non-wetting phase fluid flow rate under the combined action of fluid-solid-stress: According to the fact that the actual flow rate of non-wetting phase fluid in porous media is the difference between the unblocked flow rate of non-wetting phase fluid in porous media and the blocked flow rate of porous media, the fractal characterization of the actual flow rate of non-wetting phase fluid in porous media under the combined action of fluid-solid-stress is obtained as follows: ， Where (D cfσ is the fractal dimension of solid particles under stress; D cTσ D is the tortuosity of solid particles under stress; crfσ is the fractal dimension of the movable solid particles under stress; C is the traction coefficient; E is the elastic modulus, Pa; F is the comprehensive shape factor; k is the flow coefficient; L is the length of the porous medium, m; n is the power law index; Q crσ is the non-wetting phase fluid flow rate after the porous medium is blocked, m 3 / s;S wσ is the water saturation of the wetting phase of the porous medium, %; v is the Poisson's ratio; λ cmax0 The maximum diameter of solid particles when stress is 0, m; λ cmin0 The minimum diameter of solid particles when stress is 0, m; κ is the static friction coefficient; κ w Static friction coefficient when the wetting phase exists; σ0 is the initial radial stress, Pa; σ is the stress, Pa; μ is the viscosity of the non-wetting phase fluid, Pa·s; ρ g is the density of the non-wetting phase fluid, kg / m 3 ;v g is the flow rate of the non-wetting phase fluid, m / s; δ σ is the height of the wetting phase fluid covering the solid phase particles, m; Δp is the applied pressure, Pa.

3. The method for calculating sand production from porous media under the combined effects of fluid-solid-stress according to claim 1, characterized in that: The steps of the porous medium sand production calculation method under the combined action of fluid-solid-stress in S300 are as follows: S301: The fractal characterization step of the non-wetting phase permeability of porous media before and after clogging under the combined action of fluid-solid-stress is based on the fractal characterization of flow under the combined action of fluid-solid-stress, combined with Darcy's law and fractal scaling law, to obtain the fractal characterization of the non-wetting phase permeability of porous media before and after clogging under the combined action of fluid-solid-stress, wherein the fractal characterization of the non-wetting phase permeability of porous media after clogging under the combined action of fluid-solid-stress is: In the formula Kcr σ is the non-wetting phase permeability of the porous medium after blockage occurs under the combined action of fluid-solid-stress, and its unit is mD; S302: A fractal characterization step of normalized seepage flow in porous media under the combined action of fluid-solid-stress, based on the fractal characterization of the non-wetting phase permeability of porous media before and after clogging under the combined action of fluid-solid-stress, a fractal characterization of normalized seepage flow in porous media under the combined action of fluid-solid-stress is obtained according to the normalization definition, wherein the fractal characterization of the normalized permeability of porous media under the combined action of fluid-solid-stress is: In the formula is the normalized permeability of porous media under the combined action of fluid-solid-stress; S303: Calculate the normalized permeability of porous media under the combined effects of fluid-solid-stress at different displacement pressures, draw the sand production curve of porous media, and clarify the critical conditions for sand production of porous media.

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