Method and system for analyzing influence of solid-phase particle accumulation on shaft

Abstract

The invention relates to the technical field of shale gas exploitation, and discloses an annular flow field calculation model constructed according to a workover fluid rheological mode. Constructing a solid-phase particle accumulation velocity calculation model according to a seepage mechanics theory; according to solid-phase particle stress analysis, combining the annulus flow field calculation model and the solid-phase particle accumulation velocity calculation model to construct a mud cake dynamic thickness model; establishing a wellbore pressure-bearing plugging analysis model according to multiple pore medium characteristics of the well wall; according to the mud cake dynamic thickness model and the wellbore pressure-bearing plugging analysis model, constructing a model of influence of solid-phase particle accumulation on wellbore boundary conditions; and analyzing the stress of the shaft according to the influence model of the solid-phase particle accumulation on the boundary conditions of the shaft. According to the method, factors such as an annular flow field and solid-phase particle stress are considered, the dynamic permeability and thickness of the solid-phase particle accumulation plugging layer are converted into equivalent pore pressure boundary conditions, and the influence of solid-phase particle accumulation characteristics on pressure-bearing plugging of the shaft is effectively and quantitatively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of shale gas exploitation, and in particular to a method and system for analyzing the influence of solid-phase particle accumulation on a wellbore. Background Art

[0002] The problem of pressure-bearing plugging in complex formations is prominent. Filtrate invasion may cause clay mineral hydration and expansion to cause well collapse. When the invasion pressure is too large, induced cracks may occur, leading to well leakage, resulting in a narrow safety density window for workover fluids in complex formations. As an important factor in stabilizing the well wall, the solid-phase particle accumulation plugging layer can play a key role in isolating the wellbore pressure and preventing the invasion of solid and liquid phases. By optimizing the solid phase and rheological parameters of the workover fluid and constructing a high-quality dynamic filtration plugging layer, the long-term wellbore pressure-bearing plugging effect of the mud cake can be significantly improved. Therefore, it is of great significance to study the dynamic solid-phase particle accumulation characteristics and their influence on the wellbore pressure-bearing plugging effect.

[0003] Although a large number of mud cake characteristic description equations have been established in previous experiments, the effect of solid-phase particle accumulation on wellbore pressure plugging cannot be quantitatively described without analyzing the pore pressure and stress distribution around the wellbore. In order to further quantitatively analyze the effect of solid-phase particle accumulation characteristics on wellbore pressure plugging, domestic and foreign scholars have conducted a series of simulation studies based on the wellbore pressure plugging analysis model. The previous simulation studies on the mechanism of wellbore pressure plugging were mainly based on experimental test results or static mud cake characteristic models, ignoring the influence of wellbore flow field and microscopic forces of solid particles on the dynamic characteristics of the solid particle accumulation plugging layer. Summary of the invention

[0004] The present invention aims to solve at least one of the technical problems in the above-mentioned technology to a certain extent. To this end, the first aspect of the present invention proposes a method for analyzing the influence of solid phase particle accumulation on a wellbore, comprising:

[0005] The calculation model of annular flow field is constructed according to the rheological pattern of workover fluid;

[0006] Construct a solid phase particle accumulation velocity calculation model based on seepage mechanics theory;

[0007] According to the force analysis of solid particles, the mud cake dynamic thickness model is constructed by combining the annular flow field calculation model and the solid particle accumulation velocity calculation model;

[0008] A wellbore pressure plugging analysis model is established based on the multi-porous medium characteristics of the wellbore wall;

[0009] According to the mud cake dynamic thickness model and the wellbore pressure plugging analysis model, a model for the influence of solid phase particle accumulation on wellbore boundary conditions is constructed;

[0010] The stress on the wellbore is analyzed based on the model of the influence of solid phase particle accumulation on the boundary conditions of the wellbore.

[0011] Preferably, when the rheological mode of the workover fluid is a Newtonian fluid mode, the formula corresponding to the annular flow field calculation model includes:

[0012]

[0013]

[0014] Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity.

[0015] Preferably, when the rheological mode of the workover fluid is a Newtonian fluid rheological mode, the formula corresponding to the annular flow field calculation model includes:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity; B and C are integral constants; K and n are the characteristic coefficients of the power-law flow pattern.

[0022] Preferably, the solid phase particle accumulation velocity calculation model corresponds to a formula including:

[0023]

[0024] p=pw|r=Ri-hc

[0025] p=pe|r=Rf

[0026]

[0027] Where r is the radius from the center of the wellbore; p is the pore pressure; p w is the wellbore workover fluid column pressure; R i is the initial radius of the wellbore; h c is the mud cake thickness; p e is the initial pore pressure of the formation; R f is the reservoir radius; μ is the workover fluid viscosity; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; k f is the formation permeability; R e is the formation radius.

[0028] Preferably, the mud cake dynamic thickness model is constructed based on the force analysis of solid particles, combined with the annular flow field calculation model and the solid particle accumulation velocity calculation model, including:

[0029] Determine the deposition probability of particles of different sizes based on the force analysis of solid particles;

[0030] Determine the mechanical state of solid particles on the wellbore surface based on the principle of mechanical equilibrium;

[0031] Calculating the probability of solid-phase particles depositing on the well wall surface according to the deposition probability of particles of different sizes and the mechanical state of the solid-phase particles on the well wall surface;

[0032] A mud cake dynamic thickness model is constructed according to the deposition probability of the solid phase particles on the well wall surface.

[0033] Preferably, the calculation formula used to determine the deposition probability of particles of different sizes based on the force analysis of solid phase particles includes:

[0034] The calculation formula for the influence of gravity on solid particles is:

[0035]

[0036] Among them, F g is gravity; ρ s is the solid particle density; g is the gravitational acceleration; D p is the solid phase particle diameter;

[0037] The calculation formula for the influence of buoyancy on solid particles is:

[0038]

[0039] Among them, F b is the buoyancy; ρ l is the workover fluid density;

[0040] The calculation formula for the influence of drag force on solid particles is:

[0041]

[0042]

[0043] Among them, F d is the drag force; w is r=(R i -h c -D p ) / 2 position of the workover fluid velocity; v z and v θ are the annular axial and circumferential velocities, respectively;

[0044] The calculation formula for the influence of lateral lift on solid particles is:

[0045] Fl=3πμDpul

[0046]

[0047] Among them, F l is the lateral lift; u l is the lateral migration velocity; μ is the workover fluid viscosity;

[0048] The calculation formula of the effect of workover fluid column pressure on solid particles is:

[0049] Fp=3πDpupcn

[0050]

[0051]

[0052]

[0053] Among them, F p is the workover fluid column pressure; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; r eff is the effective radius of the particle; a is the permeability variation coefficient; t is the filtration time; ε c is the solid content of the mud cake; where F p The following calculation formula is also satisfied:

[0054] Fn=Fp-Fl

[0055] Ft=Fd+Fb-Fg

[0056] Among them, F n is the resultant normal force; F t is the resultant tangential force.

[0057] Preferably, the deposition probability of the solid phase particles on the well wall surface is calculated based on the deposition probability of the particles of different sizes and the mechanical state of the solid phase particles on the well wall surface, and the calculation formula used includes:

[0058] The calculation formula for the deposition probability of a single solid phase particle is:

[0059]

[0060] Among them, γ(D p ) represents the probability of single solid phase particle deposition, H max H is the maximum protrusion height of the well wall surface that allows solid particles to deposit, max Equal to the solid phase particle radius;

[0061] The calculation formula for the deposition probability of solid particle system is:

[0062]

[0063] Where β is the deposition probability of the solid phase particle system; f(D p ) is the particle probability density function.

[0064] Preferably, when constructing a mud cake dynamic thickness model according to the probability of solid phase particles depositing on the well wall surface, the calculation formula used includes:

[0065]

[0066] Among them, ε s is the solid content of workover fluid.

[0067] Preferably, the establishment of a wellbore pressure-bearing plugging analysis model based on the multi-porous medium characteristics of the wellbore wall includes:

[0068] The porous medium corresponding to the well wall is set to be an overlap of multiple interconnected porous media;

[0069] Determine the constitutive relations and fluid mass conservation relations for each interconnected porous medium;

[0070] According to the constitutive relation of each interconnected porous medium and the fluid mass conservation equation, combined with the ground stress boundary condition, the stress of each interconnected porous medium is determined;

[0071] Superimposing the stresses of interconnected porous media;

[0072] The superimposed stress is transformed from the ground stress coordinate system to the wellbore coordinate system, and the stress relationship of the wellbore coordinate system is used as the wellbore pressure-bearing plugging analysis model.

[0073] Preferably, the constitutive relation of the interconnected porous medium and the corresponding calculation formula include:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] Among them, σ and ε are stress-strain components, i and j represent the directions of stress-strain components; ζ is the change in fluid content; is the equivalent Young's modulus; is the equivalent Poisson’s ratio; is the effective pore pressure coefficient; p is the pore pressure; is the equivalent Biot modulus; is the equivalent bulk modulus; K i is the bulk modulus of porous medium i; N represents the number of interconnected porous media; δ ij is the Kronecker symbol. If i=j, then δ ij =1, otherwise 0; B i is the compressibility coefficient of the interconnected porous medium i; α i is the Biot coefficient of medium i; v i is the Poisson’s ratio of the interconnected porous medium i.

[0083] Preferably, the fluid mass conservation relation of the interconnected porous medium corresponds to a calculation formula including:

[0084]

[0085]

[0086] Among them, λ is the crossflow coefficient; k is the permeability of the porous medium j; μ is the fluid viscosity.

[0087] Preferably, the calculation formula corresponding to the geostress boundary condition includes:

[0088]

[0089] Among them, σ0 is the stress component of the ground stress in the wellbore coordinate system; r is the radius from the wellbore center; t is the filtration time; p0 represents the initial pore pressure.

[0090] Preferably, the superimposed stress is converted from the geostress coordinate system to the wellbore coordinate system, and the calculation formula used includes:

[0091]

[0092] Among them, σ1 is the vector matrix of geostress in the wellbore coordinate system; σ g is the vector matrix of geostress in the geostress coordinate system; λ1 is the coordinate transformation matrix;

[0093]

[0094] Among them, I w A is the wellbore inclination angle; w is the azimuth.

[0095] Preferably, the model of the influence of solid phase particle accumulation on wellbore boundary conditions and the corresponding calculation formula include:

[0096]

[0097] Among them, P m is the pore pressure at the wellbore wall; P w is the wellbore workover fluid column pressure; k f is the initial permeability of the formation; k c is the mud cake permeability; R e is the formation radius; R i is the initial wellbore radius; h c is the mud cake thickness; p e is the initial pore pressure of the formation.

[0098] Preferably, the analyzing the stress on the wellbore according to the model of the influence of the solid phase particle accumulation on the wellbore boundary conditions includes:

[0099] The influence model of the solid phase particle accumulation on the boundary condition of the wellbore is used as the boundary condition, and the wellbore pressure-bearing plugging analysis model is solved based on the finite element numerical solution method to obtain the stress component of the formation where the wellbore is located.

[0100] Preferably, the analysis method further comprises: based on the stress component of the formation where the wellbore is located, considering the influence of the construction parameters on the wellbore pressure plugging safety density window, calculating the wellbore wall collapse risk and wellbore wall rupture risk; wherein,

[0101] The corresponding calculation formula for the well wall collapse risk is:

[0102]

[0103] The calculation formula for the wellbore rupture risk is:

[0104] P f =max(-σ' min -tensile strength) 0≤θ≤2π

[0105] Among them, P c A positive value of P indicates that the wellbore is at risk of collapse. f A0 is the tangent value of the internal friction angle, D0 is the cohesion, is the average shear stress, S p is the mean effective stress, where

[0106]

[0107]

[0108] Where p represents the pore pressure, the principal stress σ ij The calculation formula is as follows:

[0109]

[0110] A second aspect of the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program / instruction, and when the computer program / instruction is executed by the processor, it is used to implement at least any one of the above methods.

[0111] A third aspect of the present invention provides a readable storage medium, in which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, it is used to implement at least any one of the above methods.

[0112] Compared with the prior art, the present invention has the following beneficial effects:

[0113] In view of the deficiencies in the prior art, the present invention takes into account the influence of factors such as the annular flow field, the interaction force between solid particles and fluid, and the particle size distribution, and converts the dynamic permeability and thickness of the solid-phase particle accumulation plugging layer into equivalent pore pressure boundary conditions, which can effectively and quantitatively analyze the influence of the solid-phase particle accumulation characteristics on the pressure-bearing plugging of the wellbore.

[0114] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description and the accompanying drawings.

[0115] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0117] Figure 1 It is a schematic diagram of the analysis method of the effect of solid phase particle accumulation on the wellbore;

[0118] Figure 2 It is a schematic diagram of the wellbore annulus structure;

[0119] Figure 3 It is a schematic diagram of the force analysis of solid particles;

[0120] Figure 4 It is a schematic diagram of the porous and permeable model;

[0121] Figure 5 It is a curve diagram of the dynamic characteristics of the solid-phase particle accumulation plugging layer;

[0122] Figure 6 It is a curve diagram showing the effect of solid phase particle packing characteristics on pore pressure distribution;

[0123] Figure 7 It is a curve diagram showing the effect of solid phase particle accumulation characteristics on the safe density window of workover fluid;

[0124] Figure 8 is a schematic diagram of an electronic device;

[0125] Fig. 9 A schematic diagram of a readable storage medium. DETAILED DESCRIPTION

[0126] 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.

[0127] Figure 1 The method for analyzing the influence of solid phase particle accumulation on the wellbore provided by the present invention comprises:

[0128] The calculation model of annular flow field is constructed according to the rheological pattern of workover fluid;

[0129] Construct a solid phase particle accumulation velocity calculation model based on seepage mechanics theory;

[0130] According to the force analysis of solid particles, the mud cake dynamic thickness model is constructed by combining the annular flow field calculation model and the solid particle accumulation velocity calculation model;

[0131] A wellbore pressure plugging analysis model is established based on the multi-porous medium characteristics of the wellbore wall;

[0132] According to the mud cake dynamic thickness model and the wellbore pressure plugging analysis model, a model for the influence of solid phase particle accumulation on wellbore boundary conditions is constructed;

[0133] The stress on the wellbore is analyzed based on the model of the influence of solid phase particle accumulation on the boundary conditions of the wellbore.

[0134] According to an embodiment of the present invention, a method for analyzing the effect of solid phase particle accumulation on a wellbore includes:

[0135] 1. Based on the rheological pattern of workover fluid, the annular flow field calculation model is established.

[0136] During the well repair process, the drill pipe and the wellbore form concentric rings. The well repair fluid is an incompressible fluid. The well repair fluid is a homogeneous solid-liquid suspension system with no slip motion. The solid particles in the well repair fluid accumulate on the well wall surface in the form of mud cakes. With the deposition of solid particles in the well repair fluid, the annular space area gradually decreases. Figure 2 shown.

[0137] (1) When the rheological mode of the workover fluid is the Newtonian fluid mode, the corresponding annular flow pattern is a steady laminar flow, from which the calculation formula of the annular flow field can be obtained:

[0138]

[0139]

[0140] Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity.

[0141] (2) When the rheological mode of the workover fluid is a power-law fluid, the calculation formula for the annular flow field is:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity; B and C are integral constants; K and n are the characteristic coefficients of the power-law flow pattern.

[0148] 2. Establish a calculation model for the solid phase particle deposition and accumulation velocity based on the seepage mechanics theory.

[0149] In order to ensure the wellbore is pressure-bearing and plugged, overbalanced pressure workover is usually used. Therefore, driven by the wellbore pressure, the workover fluid will invade the formation. From the seepage mechanics theory, the relationship between displacement pressure and flow rate can be obtained:

[0150]

[0151] From the void pressure boundary condition, we know that:

[0152] p=p w |r=R i -h c

[0153] p=p e |r=R f

[0154] The analytical solution of the workover fluid invasion velocity can be calculated from the boundary conditions:

[0155]

[0156] Where r is the radius from the center of the wellbore; p is the pore pressure; p w is the wellbore workover fluid column pressure; R i is the initial radius of the wellbore; h c is the mud cake thickness; p e is the initial pore pressure of the formation; R f is the reservoir radius; μ is the workover fluid viscosity; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; k f is the formation permeability; R e is the formation radius.

[0157] 3. Based on the force analysis of particle sedimentation, a mechanical analysis model of solid phase particle accumulation layer is established. Figure 3It is a schematic diagram of the force analysis of solid particles. According to the figure, the solid particles are mainly affected by gravity, buoyancy, drag force, lateral lift and pressure of the workover fluid column.

[0158] The calculation formula for the influence of gravity on solid particles is:

[0159]

[0160] Among them, F g is gravity; ρ s is the solid particle density; g is the gravitational acceleration; D p is the solid phase particle diameter;

[0161] The calculation formula for the influence of buoyancy on solid particles is:

[0162]

[0163] Among them, F b is the buoyancy; ρ l is the workover fluid density;

[0164] The calculation formula for the influence of drag force on solid particles is:

[0165]

[0166]

[0167] Among them, F d is the drag force; w is r=(R i -h c -D p ) / 2 position of the workover fluid velocity; v z and v θ are the annular axial and circumferential velocities, respectively;

[0168] The calculation formula for the influence of lateral lift on solid particles is:

[0169] F l =3πμD p u l

[0170]

[0171] Among them, F l is the lateral lift; u l is the lateral migration velocity; μ is the workover fluid viscosity;

[0172] The calculation formula of the effect of workover fluid column pressure on solid particles is:

[0173] F p =3πD p u p cn

[0174]

[0175]

[0176]

[0177] Among them, F p is the workover fluid column pressure; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; r eff is the effective radius of the particle; a is the permeability variation coefficient; t is the filtration time; ε c is the solid content of the mud cake; where F p The following calculation formula is also satisfied:

[0178] F n =F p -F l

[0179] F t =F d +F b -F g

[0180] Among them, F n is the resultant normal force; F t is the resultant tangential force.

[0181] Fourth, according to the principle of mechanical equilibrium, the mechanical state of solid particles on the well wall surface is analyzed to obtain their deposition probability on the well wall surface.

[0182] The calculation formula for the deposition probability of a single solid phase particle is:

[0183]

[0184] Among them, γ(D p ) represents the probability of single solid phase particle deposition, H max H is the maximum protrusion height of the well wall surface that allows solid particles to deposit, max Equal to the solid phase particle radius;

[0185] The calculation formula for the deposition probability of solid particle system is:

[0186]

[0187] Where β is the deposition probability of the solid phase particle system; f(D p ) is the particle probability density function. The probability density function models of different particle size distributions are shown in Table 1.

[0188] Table 1

[0189]

[0190] 5. Combining the above annular flow field calculation model with the solid phase particle accumulation velocity calculation model, according to the conservation of solid phase mass, the mud cake dynamic thickness model is obtained, and the expression equation is:

[0191]

[0192] Among them, ε s is the solid content of workover fluid.

[0193] 6. Considering the characteristics of multiple porous media, a pressure-bearing plugging analysis model for inclined wells is established.

[0194] The N-pore / N-permeable fluid-saturated porous medium K is assumed to be a superposition of N interconnected porous media K1-KN, as Figure 4 When N-pore / N-permeable fluid-saturated porous media are subjected to stress or pressure disturbance, each porous medium and its associated porosity have independent pressure and stress fields. These media have independent elastic and poroelastic mechanical properties.

[0195] (1) The constitutive equation for the relationship between stress and strain of the above medium is:

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204] Among them, σ and ε are stress-strain components, i and j represent the directions of stress-strain components; ζ is the change in fluid content; is the equivalent Young's modulus; is the equivalent Poisson’s ratio; is the effective pore pressure coefficient; p is the pore pressure; is the equivalent Biot modulus; is the equivalent bulk modulus; K iis the bulk modulus of porous medium i; N represents the number of interconnected porous media; δ ij is the Kronecker symbol. If i=j, then δ ij =1, otherwise 0; B i is the compressibility coefficient of the interconnected porous medium i; α i is the Biot coefficient of medium i; v i is the Poisson’s ratio of the interconnected porous medium i.

[0205] (2) The corresponding calculation formula for the above medium fluid mass conservation relationship includes:

[0206]

[0207]

[0208] Among them, λ is the crossflow coefficient; k is the permeability of the porous medium j; μ is the fluid viscosity.

[0209] (3) Based on the ground stress boundary condition, the influence of the inclined well on the pressure plugging of the wellbore is reflected. The boundary condition at infinity in the above-mentioned medium ground stress boundary condition is:

[0210]

[0211] Among them, σ0 is the stress component of the ground stress in the wellbore coordinate system; r is the radius from the wellbore center; t is the filtration time.

[0212] According to some embodiments of the present invention, the superimposed stress is converted from the geostress coordinate system to the wellbore coordinate system, and the calculation formula used includes:

[0213]

[0214] Among them, σ1 is the vector matrix of geostress in the wellbore coordinate system; σ g is the vector matrix of geostress in the geostress coordinate system; λ1 is the coordinate transformation matrix;

[0215]

[0216] Among them, I w A is the wellbore inclination angle; w is the azimuth.

[0217] 7. Based on the prediction results of the dynamic accumulation characteristics of solid particles (see step 8 below for details), the seepage mechanics theory is used to establish an equivalent calculation model for the influence of solid particle accumulation on the boundary conditions of the wellbore. According to Darcy's law, the calculation formula for the pore pressure at the wellbore wall is:

[0218]

[0219] Among them, P m is the pore pressure at the wellbore wall; P w is the wellbore workover fluid column pressure; k f is the initial permeability of the formation; k c is the mud cake permeability; R e is the formation radius; R i is the initial wellbore radius; h c is the mud cake thickness; p e is the initial pore pressure of the formation.

[0220] 8. Use the fourth-order Runge-Kutta method to calculate the numerical solution of the characteristics of the dynamic accumulation of solid particles. This step is based on the solution of step 5. The fourth-order Runge-Kutta method can be simplified to the partial differential equation expression of the solid particle accumulation thickness:

[0221]

[0222] h(t0)=h0

[0223] The numerical calculation method expression is:

[0224]

[0225]

[0226] k1=Δf(t i ,h i )

[0227]

[0228]

[0229] k4=Δf(t i +Δ,h i +k3)

[0230] In the formula, Δ is the calculation step size, t max and t min They are the maximum and minimum values ​​of the calculation duration respectively.

[0231] 9. Use the finite element numerical solution method to calculate the stress on the formation. Use the iterative method to solve the finite element equations, use the numerical value of the previous time step to calculate the initial stiffness matrix of the current time step, and solve the nonlinear equations. In any time step of the numerical process, use the initial conditions to calculate the stiffness matrix, solve the linear equations, and obtain the new displacement and pore pressure fields. Then, use the new displacement and pore pressure parameters to calculate the stiffness matrix, and solve the displacement field and pore pressure field of the next iteration until the error between two adjacent iterations is less than the specified value, and the displacement and pore pressure distribution at that moment can be obtained.

[0232] The formulas used in the above finite element numerical solution method include:

[0233]

[0234]

[0235]

[0236]

[0237] Where u is displacement, p is pore pressure, N u and N p are the shape functions of the displacement field and pore pressure field, respectively. and are the node displacement and node pressure respectively, K, A and S are the coefficient matrices of parameters respectively, and f is the external load matrix.

[0238] 10. Analyze the influence of solid phase particle characteristics, workover fluid rheological characteristics and construction parameters on the safe density window of wellbore pressure plugging. In order to further analyze the influence of filtration time on the wellbore strengthening effect, the influence of filter cake on the safe density window of workover fluid is analyzed using the rock strength failure criterion. The judgment expression of collapse and rupture state is as follows:

[0239] The calculation formula corresponding to the wellbore collapse risk is:

[0240]

[0241] The calculation formula corresponding to the wellbore rupture risk is:

[0242] P f =max(-σ' min -tensile strength) 0≤θ≤2π

[0243] Among them, P c A positive value of P indicates that the wellbore is at risk of collapse. f A0 is the tangent value of the internal friction angle, D0 is the cohesion, is the average shear stress, S p is the mean effective stress, where

[0244]

[0245]

[0246] In the formula, the calculation formula of principal stress is as follows, and the three roots of the following formula are the principal stresses.

[0247]

[0248] It should be noted here that, since there is a quadratic function relationship between the collapse pressure judgment value and the workover fluid density, the minimum collapse potential energy value should be obtained before calculating the critical collapse pressure. The fracture pressure judgment value and the workover fluid density satisfy a monotonic function relationship, so the dichotomy method can be used to directly calculate the critical fracture pressure.

[0249] Figure 5 The curve diagram of the dynamic characteristics of the solid-phase particle accumulation plugging layer given in the embodiment, the horizontal axis represents the filtration time, the left vertical axis represents the thickness of the solid-phase particle accumulation plugging layer, that is, the mud cake thickness, and the right vertical axis represents the permeability of the solid-phase particle accumulation plugging layer. It can be seen from the figure that with the increase of the filtration time, the mud cake thickness increases logarithmically. In a short period of time, affected by the instantaneous filtration, the mud cake thickness increases rapidly; in the later stage of filtration, affected by the mud cake permeability, the invasion speed of the well repair fluid solid particles gradually decreases, so the growth rate of the mud cake thickness gradually slows down. The dynamic function of mud cake thickness and permeability over time is substituted into the fluid-solid coupling wellbore pressure plugging analysis model in the form of an interpolation function, and the influence of the dynamic characteristics of the mud cake on the pore pressure distribution and the safe density window of the well repair fluid can be calculated.

[0250] Figure 6 This is a curve diagram of the effect of solid phase particle accumulation characteristics on pore pressure distribution. The horizontal axis represents the radial distance ratio, the vertical axis represents the effect of solid phase particle accumulation characteristics on pore pressure, and t represents the filtration time. It can be seen from the figure that under the plugging effect of the mud cake, the pore pressure near the wellbore wall has decreased significantly. With the increase of filtration time, the formation pore pressure gradually decreases. Affected by the logarithmic growth of mud cake thickness, the reduction of pore pressure gradually slows down.

[0251] Traditional theory holds that, under the condition of fixed mud cake thickness, the pore pressure transmission caused by filtration time is not conducive to wellbore pressure plugging. Therefore, its prediction of the safe density window of workover fluid is relatively conservative, ignoring the impact of changes in the dynamic characteristics of the mud cake. Figure 7 The curve diagram of the effect of solid phase particle accumulation characteristics on the safe density window of workover fluid, in which the horizontal axis represents the well inclination angle, the vertical axis represents the equivalent drilling fluid density of the safe density window, the dotted line represents the fracture pressure, the solid line represents the collapse pressure, and t represents the filtration time. It can be seen from the figure that with the increase of filtration time, the safe density window of workover fluid gradually increases, and the change amplitude of the fracture pressure is greater than the collapse pressure. This shows that the dynamic plugging process of mud cake is conducive to the pressure plugging of wellbore, and can achieve the effect of increasing the formation fracture pressure by slowing down the pressure transmission of workover fluid.

[0252] Figure 8A schematic diagram of an electronic device provided in an embodiment, the electronic device includes a memory and a processor, the memory stores a computer program / instruction, and when the computer program / instruction is executed by the processor, it is used to implement at least any one of the above-mentioned methods for analyzing the impact of solid phase particle accumulation on the wellbore. According to other embodiments of the present invention, the memory of the electronic device is also used to store the above-mentioned various calculation models.

[0253] Fig. 9 A schematic diagram of a readable storage medium provided in an embodiment, wherein the readable storage medium stores a computer program / instruction, wherein when the computer program / instruction is executed by a processor, the computer program / instruction is used for at least any one of the above methods. According to other embodiments of the present invention, the readable storage medium is also used to store the above-mentioned various computing models.

[0254] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for analyzing the effect of solid phase particle accumulation on a wellbore, characterized in that: include: The calculation model of annular flow field is constructed according to the rheological pattern of workover fluid; Construct a solid phase particle accumulation velocity calculation model based on seepage mechanics theory; According to the force analysis of solid particles, the mud cake dynamic thickness model is constructed by combining the annular flow field calculation model and the solid particle accumulation velocity calculation model; A wellbore pressure plugging analysis model is established based on the multi-porous medium characteristics of the wellbore wall; According to the mud cake dynamic thickness model and the wellbore pressure plugging analysis model, a model for the influence of solid phase particle accumulation on wellbore boundary conditions is constructed; The stress on the wellbore is analyzed based on the model of the influence of solid phase particle accumulation on the boundary conditions of the wellbore.

2. The method according to claim 1, characterized in that When the rheological mode of the workover fluid is a Newtonian fluid mode, the formula corresponding to the annular flow field calculation model includes: Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity.

3. The method according to claim 1, characterized in that When the rheological mode of the workover fluid is a Newtonian fluid rheological mode, the formula corresponding to the annular flow field calculation model includes: Among them, v θ is the annular circumferential velocity; Ω is the drill pipe rotation speed; R i is the initial radius of the wellbore; h c is the thickness of the mud cake; r is the radius from the center of the wellbore; R s is the drill pipe radius; v z is the annular axial velocity; p b is the annular axial pressure gradient; μ is the workover fluid viscosity; B and C are integral constants; K and n are the characteristic coefficients of the power-law flow pattern.

4. The method according to claim 1, characterized in that The solid phase particle accumulation velocity calculation model and the corresponding formula include: p=p w |r=R i -h c p=p e |r=R f Where r is the radius from the center of the wellbore; p is the pore pressure; p w is the wellbore workover fluid column pressure; R i is the initial radius of the wellbore; h c is the mud cake thickness; p e is the initial pore pressure of the formation; R f is the reservoir radius; μ is the workover fluid viscosity; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; k f is the formation permeability; R e is the formation radius.

5. The method according to any one of claims 2 to 4 is characterized in that: According to the analysis of the force on solid particles, the mud cake dynamic thickness model is constructed by combining the annular flow field calculation model and the solid particle accumulation velocity calculation model, including: Determine the deposition probability of particles of different sizes based on the force analysis of solid particles; Determine the mechanical state of solid particles on the wellbore surface based on the principle of mechanical equilibrium; Calculating the probability of solid-phase particles depositing on the well wall surface according to the deposition probability of particles of different sizes and the mechanical state of the solid-phase particles on the well wall surface; A mud cake dynamic thickness model is constructed according to the deposition probability of the solid phase particles on the well wall surface.

6. The method according to claim 5, characterized in that The calculation formula used to determine the deposition probability of particles of different sizes based on the force analysis of solid phase particles includes: The calculation formula for the influence of gravity on solid particles is: Among them, F g is gravity; ρ s is the solid particle density; g is the gravitational acceleration; D p is the solid phase particle diameter; The calculation formula for the influence of buoyancy on solid particles is: Among them, F b is the buoyancy; ρ l is the workover fluid density; The calculation formula for the influence of drag force on solid particles is: Among them, F d is the drag force; w is r=(R i -h c -D p ) / 2 position of the workover fluid velocity; v z and v θ are the annular axial and circumferential velocities, respectively; The calculation formula for the influence of lateral lift on solid particles is: F l =3πμD p u l Among them, F l is the lateral lift; u l is the lateral migration velocity; μ is the workover fluid viscosity; The calculation formula of the effect of workover fluid column pressure on solid particles is: F p =3πD p u p c n Among them, F p is the workover fluid column pressure; u p is the invasion velocity of workover fluid; k c is the mud cake permeability; r eff is the effective radius of the particle; a is the permeability variation coefficient; t is the filtration time; ε c is the solid content of the mud cake; where F p The following calculation formula is also satisfied: Fn=Fp-Fl Ft=Fd+Fb-Fg Among them, F n is the resultant normal force; F t is the resultant tangential force.

7. The method according to claim 6, characterized in that The deposition probability of the solid phase particles on the well wall surface is calculated according to the deposition probability of the particles of different sizes and the mechanical state of the solid phase particles on the well wall surface, and the calculation formula used includes: The calculation formula for the deposition probability of a single solid phase particle is: Among them, γ(D p ) represents the probability of single solid phase particle deposition, H max H is the maximum protrusion height of the well wall surface that allows solid particles to deposit, max Equal to the solid phase particle radius; The calculation formula for the deposition probability of solid particle system is: Where β is the deposition probability of the solid phase particle system; f(D p ) is the particle probability density function.

8. The method according to claim 7, characterized in that When constructing a mud cake dynamic thickness model based on the probability of solid phase particles depositing on the wellbore surface, the calculation formula used includes: Among them, ε s is the solid content of workover fluid.

9. The method according to claim 8, characterized in that The wellbore pressure-bearing plugging analysis model is established according to the multiple porous media characteristics of the wellbore wall, including: The porous medium corresponding to the well wall is set to be an overlap of multiple interconnected porous media; Determine the constitutive relations and fluid mass conservation relations for each interconnected porous medium; According to the constitutive relation of each interconnected porous medium and the fluid mass conservation equation, combined with the ground stress boundary condition, the stress of each interconnected porous medium is determined; Superimposing the stresses of interconnected porous media; The superimposed stress is transformed from the ground stress coordinate system to the wellbore coordinate system, and the stress relationship of the wellbore coordinate system is used as the wellbore pressure-bearing plugging analysis model.

10. The method according to claim 9, characterized in that The constitutive relation of the interconnected porous medium and the corresponding calculation formula include: Among them, σ and ε are stress-strain components, i and j represent the directions of stress-strain components; ζ is the change in fluid content; is the equivalent Young's modulus; is the equivalent Poisson’s ratio; is the effective pore pressure coefficient; p is the pore pressure; is the equivalent Biot modulus; is the equivalent bulk modulus; K i is the bulk modulus of porous medium i; N represents the number of interconnected porous media; δ ij is the Kronecker symbol. If i=j, then δ ij =1, otherwise 0; B i is the compressibility coefficient of the interconnected porous medium i; α i is the Biot coefficient of medium i; v i is the Poisson’s ratio of the interconnected porous medium i.

11. The method according to claim 9, characterized in that The fluid mass conservation relation of the interconnected porous medium and the corresponding calculation formula include: Among them, λ is the crossflow coefficient; k is the permeability of the porous medium j; μ is the fluid viscosity.

12. The method according to claim 9, characterized in that The calculation formula corresponding to the ground stress boundary condition includes: Among them, σ0 is the stress component of the ground stress in the wellbore coordinate system; r is the radius from the wellbore center; t is the filtration time; p0 represents the initial pore pressure.

13. The method according to claim 9, characterized in that The superimposed stress is transformed from the ground stress coordinate system to the wellbore coordinate system, and the calculation formula used includes: Among them, σ1 is the vector matrix of geostress in the wellbore coordinate system; σ g is the vector matrix of geostress in the geostress coordinate system; λ1 is the coordinate transformation matrix; Among them, I w A is the wellbore inclination angle; w is the azimuth.

14. The method according to claim 13, characterized in that The model of the influence of solid phase particle accumulation on wellbore boundary conditions and the corresponding calculation formula include: Among them, P m is the pore pressure at the wellbore wall; P w is the wellbore workover fluid column pressure; k f is the initial permeability of the formation; k c is the mud cake permeability; R e is the formation radius; R i is the initial wellbore radius; h c is the mud cake thickness; p e is the initial pore pressure of the formation.

15. The method according to claim 14, characterized in that The analyzing the stress of the wellbore according to the model of the influence of the solid phase particle accumulation on the wellbore boundary conditions includes: The influence model of the solid phase particle accumulation on the boundary condition of the wellbore is used as the boundary condition, and the wellbore pressure-bearing plugging analysis model is solved based on the finite element numerical solution method to obtain the stress component of the formation where the wellbore is located.

16. The method according to claim 15, characterized in that Also includes: Based on the stress component of the formation where the wellbore is located, the influence of the construction parameters on the safe density window of wellbore pressure plugging is considered, and the risk of wellbore wall collapse and wellbore wall rupture is calculated; wherein, The corresponding calculation formula for the well wall collapse risk is: The calculation formula for the wellbore rupture risk is: P f =max(-σ' min -tensile strength) 0≤θ≤2π Among them, P c A positive value of P indicates that the wellbore is at risk of collapse. f A0 is the tangent value of the internal friction angle, D0 is the cohesion, is the average shear stress, S p is the mean effective stress, where Where p is the pore pressure, and the principal stress σ is ij The calculation formula is as follows:

17. An electronic device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a computer program / instruction, and when the computer program / instruction is executed by the processor, it is used to implement at least any one of the methods described in claims 1-16.

18. A readable storage medium, characterized in that: A computer program / instruction is stored, and when the computer program / instruction is executed by a processor, it is used to implement at least any one of the methods described in claims 1-16.

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