Method for predicting sand production rate and well circumference seepage capacity based on free settlement arch theory

Abstract

The invention belongs to the technical field of oil and gas field development well completion sand prevention, and particularly relates to a sand production rate and well circumference seepage capacity prediction method based on a free settlement arch theory, which comprises the following steps: firstly, testing the particle size distribution of a filling sand control medium selected on site, and obtaining a particle size distribution curve of the filling sand control medium; obtaining a reservoir mud and sand sample, and obtaining a particle size median value of the reservoir mud and sand sample; then establishing a multi-dimensional array for storing particle size distribution on the sand control medium and reservoir interface and distribution characteristics of a Soddy circle; according to a free settlement arch theory, the mud and sand invasion rate and the total amount of the invaded mud and sand in the whole filter layer are calculated, the permeability change of a sand production unit in the mining process is determined, and then quantitative prediction of the sand production rate and the well circumference seepage capacity is achieved. According to the scheme, the mud and sand output rate is calculated based on the particle output behavior in the free settlement arch, generation and track simulation of solid particles are avoided, the mud and sand output behavior under the long-period mining condition can be simulated with few calculation resources, and the method is more suitable for field application.

Description

Technical Field

[0001] The invention belongs to the technical field of well completion and sand control in oil and gas field development, and particularly relates to a quantitative prediction method for sand production rate and well periphery seepage capacity based on free settlement arch theory. Background Art

[0002] Sand production refers to the phenomenon that during the exploitation of oil or gas wells, due to the influence of various factors, the formation structure near the bottom of the well changes, causing mud and sand particles in the formation to fall off and migrate with the fluid or enter the wellbore and pipeline, which will have an extremely adverse impact on the normal production of oil and gas wells. The sand production problem was first discovered in the development of conventional loose sandstone reservoirs, but with the increase of exploitable geological resources, sand production also frequently occurs in the exploitation of various emerging geological energy sources (such as natural gas hydrates, coalbed methane, and underground gas storage). Sand production is currently the most frequent and most widespread engineering geological risk associated with reservoir exploitation.

[0003] In order to formulate reasonable sand control measures and minimize the impact of sand production on oil and gas field development, domestic and foreign scholars have carried out many studies on sand production prediction. The existing numerical simulation methods for sand production prediction can be roughly divided into two categories: continuous medium simulation at the macro scale and discrete medium simulation at the micro scale. The continuous medium numerical simulation method is based on the continuous medium hypothesis, constructs a constitutive model of the reservoir to describe the mechanical response characteristics of the reservoir during the production process, and selects the corresponding failure criteria to determine the critical conditions for reservoir damage and sand production. The continuous medium simulation method can be used for engineering-scale sand production numerical simulation, but it cannot consider the micromechanical behavior of particle migration, nor can it achieve quantitative prediction of the sand production rate in the sand control medium around the well. The mesoscale sand production simulation method is mainly based on the discrete element method, which can simulate the dynamic behavior of skeleton particles during the production process and clarify the sand production mechanism of the reservoir at the pore scale. However, the discrete element method requires the establishment of a physical model for each particle, which often requires a lot of computing resources, and the modeling size and simulation time are very limited.

[0004] In summary, the existing sand production prediction methods for oil and gas wells are difficult to take into account both the quantitative prediction of sand production rate and efficient upscaling application. At present, there is still a lack of a numerical simulation method that can efficiently and quantitatively predict the sand production rate of reservoirs, which is not conducive to the scientific formulation of sand control measures in oil and gas fields. Summary of the invention

[0005] In view of the problems in the existing sand production simulation technology that the finite element method cannot achieve quantitative characterization of the sand production rate and the discrete element method cannot be applied on a scaled basis, the present invention proposes a quantitative prediction method for the sand production rate and the wellbore seepage capacity based on the free settlement arch theory. This method can be applied to calculations under engineering scale and long-term mining conditions, and meets the needs of on-site sand control parameter design and prediction of unblocking timing.

[0006] The present invention is implemented by adopting the following technical scheme: a quantitative prediction method of sand production rate and well perimeter seepage capacity based on free settling arch theory, comprising the following steps:

[0007] Step A: Test the particle size distribution of the filling sand control medium selected on site and obtain its particle size distribution curve; and obtain reservoir mud and sand samples, test the particle size distribution of mud and sand produced by the target reservoir, and obtain its particle size median d 50 ;

[0008] Step B, establishing a multidimensional array for storing the particle size distribution and the distribution characteristics of the Soddy circle on the interface between the sand control medium and the reservoir;

[0009] Step B1: According to the particle size distribution curve of the filling sand control medium obtained in step A, create arrays R[n] and P[n], where R[n] is the particle radius array and P[n] is the distribution probability corresponding to the particle radius in R[n]. Then, establish a filling sand control medium stacking network, assuming that it is a dense stacking, and the pores on the interface of the stacking body are composed of the middle area surrounded by three tangent particles. Assume r 1 、r 2 、r 3 are the radii of the three particles that make up the pore, r s Create a multidimensional array F(x max ,y max ) to store the r in the sand control medium accumulation network 1 、r 2 、r 3 and r s Information, where x max ,y max are the particle coordinates in the horizontal and vertical directions, respectively;

[0010] Step B2, then for variable r 1 、r 2 、r 3 Assign a value and get the corresponding r s Repeat the above operation until the entire filter layer interface multidimensional array F(x max ,y max ) 1 、r 2 、r 3 、r s Assignment; Get four two-dimensional arrays: F(x,y).r 1 、F(x,y).r 2 、F(x,y).r 3 、F(x,y).r sThe particle size at the interface between the sand control medium and the reservoir and the value of the Soddy circle corresponding to it;

[0011] Step C: According to the free settling arch theory, the mud and sand intrusion rate and the total amount of mud and sand intrusion in the entire filter layer are calculated to quantitatively predict the sand discharge rate. Specifically:

[0012] Based on the following free settling arch assumptions, a prediction model suitable for quantitative calculation of sand production rate is established:

[0013] It is assumed that from the moment the particles reach the free settling area, their accelerated motion under the action of fluid drag is uniformly accelerated motion; after a period of acceleration, the particle velocity is considered to be the same as the fluid flow velocity; the plug flow model is used to simplify the through-hole flow field, assuming that there is no particle intrusion at 1 / 2 of the distance near the boundary of the outlet opening, and the particle mass fraction at the remaining positions is the same as the value at the center of the outlet, and the particle outlet velocity is different from the outlet center velocity only at the boundary of the outlet opening;

[0014] (1) Calculate different r s The corresponding mud and sand intrusion rate R in the free settlement arch is stored in the multidimensional array F(x,y).R. The multidimensional array F(x,y).R is expressed as follows:

[0015]

[0016] Where R is the number of mud and sand particles invading per unit time; u exit is the average fluid velocity at the outlet; φ c is the particle mass fraction at the center of the opening, d 50 is the median particle size of the intruding mud and sand, F(x,y).r s Indicates storage of each unit r s A two-dimensional array of values;

[0017] (2) Repeat the operation (1) to obtain the mud and sand intrusion rate of each unit in the entire filter layer, add up their values, and obtain the total number of particles W that invade the filling sand control medium per unit time:

[0018]

[0019] Among them, x max ,y max are the particle coordinates in the vertical and horizontal directions, respectively, i is a variable representing the number of units in the horizontal direction, y j is a variable representing the number of units in the vertical direction.

[0020] Step D: Calculate the permeability change of the sand production unit during the mining process to quantitatively predict the seepage capacity around the well:

[0021] 1) The loose sand production section outside the filling sand control medium is discretized into n sand production units, n = 1, 2, 3..., the sand production unit 1 is connected to the sand control medium, and mud and sand particles are transported into the sand control medium at a speed of W. The deficit caused by this is supplemented by the movable particles in the movable sand production unit 2, and so on;

[0022] The target reservoir is discretized into three parts: the sand-producing section of the reservoir, the free settling zone FFZ, and the sand retaining medium; the sand-producing section of the reservoir is discretized into i stratigraphic units, and the skeleton sand liquefaction constitutive equation is used to calculate the stripped sand volume Vsf(i) in the unit. It is assumed that the free sand forms a loose accumulation in the pore space of the stratigraphic sand unit, and the particle start threshold velocity u is used. fc Determine whether the stripped sand forms movable sand that can be carried and transported by reservoir fluid;

[0023] 2) Calculate the critical velocity of particle start-up in the particle accumulation body and determine whether the particle start-up threshold velocity is reached; if the start-up velocity is reached, the particles migrate to the pore space of the previous unit or the free settling zone FFZ; if the start-up velocity is not reached, the particles do not migrate with the fluid, the permeability and porosity of the current sand-producing unit remain unchanged, and the porosity of the previous sand-producing unit increases;

[0024] Particle start threshold speed u fc The derivation process is as follows: Assume that the particle body in the model is composed of spherical free sand particles of equal diameter, and the stacking angle is θ; the restart of the particle starts from the particle at the front edge of the stack; and assume that the injected fluid is a pure liquid phase; Under the above assumptions, the particle force analysis is carried out, and the threshold speed u of the particle start is derived according to the particle force analysis diagram fc :

[0025]

[0026] Where: θ is the stacking angle of the dispersed particles; ε is the porosity of the particle stack; k is the permeability of the particle stack; μ is the viscosity of the reservoir fluid; F g is the combined force of particle buoyancy and gravity, F f The friction force exerted by other particles;

[0027] 3) By calculating the permeability change, the seepage capacity around the well can be predicted;

[0028] Calculate the volume of particles entering the sand control medium from the sand production unit per unit time:

[0029]

[0030] The total number of movable sand in the sand production unit is:

[0031]

[0032] In the formula, i max To achieve the maximum number of units for the particle start threshold speed, when V p Greater than V stotal When , it means that all the movable sand in the sand production unit has been produced and the sand production stops;

[0033] According to the law of mass conservation, the increase in porosity ε caused by particle stripping in the sand unit is calculated:

[0034]

[0035] In the formula, ε 0 is the initial porosity of the reservoir; V element is the total volume of the sand production unit;

[0036] The permeability increase caused by the porosity increase is calculated according to the Kozeny-Carman formula:

[0037]

[0038] Where: KC is the Kozeny-Carman constant; S b is the specific surface area of ​​the particle accumulation.

[0039] Compared with the prior art, the advantages and positive effects of the present invention are:

[0040] This scheme quantitatively predicts the sand production rate and seepage capacity based on the Soddy circle and free settling arch theory. It can be solved based on the finite difference method to efficiently solve the mud and sand production rate and the evolution of the wellbore seepage characteristics of loose sandstone reservoirs, natural gas hydrate reservoirs and other sand-prone reservoirs. It can also be coupled with other solvers based on the finite element method. Compared with other technical solutions based on discrete elements, the mud and sand production rate is calculated based on the particle production behavior in the free settling arch, which avoids the generation and trajectory simulation of physical particles. It can use less computing resources to simulate the mud and sand production behavior under long-term mining conditions, and is more suitable for field applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of a Soddy circle formed by inscribing three circles in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the Soddy circle size distribution on the sand control medium interface of an embodiment of the present invention;

[0043] Figure 3 This is a flow chart for calculating the permeability change of the sand production unit according to an embodiment of the present invention;

[0044] Figure 4Schematic diagram of the relationship between the distribution of sand production units and particle transfer in an embodiment of the present invention;

[0045] Figure 5 This is a force analysis diagram of loose particles in a reservoir according to an embodiment of the present invention;

[0046] Figure 6 This is a schematic diagram of the variation of the permeability of the sand production unit of the reservoir over time according to an embodiment of the present invention;

[0047] Figure 7 It is a schematic diagram of the dynamic permeability distribution law of the reservoir sand production unit according to an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention can also be implemented in other ways different from those described herein, and therefore, the present invention is not limited to the specific embodiments disclosed below.

[0049] The present embodiment discloses a method for quantitatively predicting the sand production rate and the seepage capacity around the well based on the free settling arch theory, which is suitable for predicting the mud and sand production in the sand control medium after sand control operations in various reservoirs, and can be applied to predicting the blockage degree of the sand control medium and the permeability recovery of the sand production section around the well. The present embodiment is described in detail below.

[0050] The method for predicting sand production rate and seepage capacity of the present invention comprises the following steps:

[0051] Step 1: Obtain the basic physical parameters required for numerical simulation based on the actual situation on site, including:

[0052] 1) The particle size distribution of the filling sand control medium (gravel, ceramsite, coated sand, etc.) selected on site is tested to obtain its particle size distribution curve. In this embodiment, the particle size of the filling sand control medium selected is 20-40 mesh;

[0053] 2) Obtain reservoir mud and sand samples, test the particle size distribution of mud and sand produced by the target reservoir, and obtain its median particle size d 50 .

[0054] Step 2: Establish a multidimensional array to store the particle size distribution and the distribution characteristics of the Soddy circle at the interface between the sand control medium and the reservoir, including:

[0055] 1) According to the particle size distribution curve of the filling sand control medium obtained in step 1, create arrays R[n] and P[n], where array R[n] is the particle radius array, unit m; P[n] is the distribution probability corresponding to the particle radius in R[n], dimensionless, and then establish a filling sand control medium stacking network to create a multidimensional array F(xmax ,y max ) is used to store the information in the sand control medium accumulation network, where x max ,y max They are the particle coordinates in the horizontal and vertical directions, respectively. In this embodiment, x max 65, y max is 130;

[0056] According to the particle size curve of the filling sand control medium, the radius of the three particles in each unit grid and the radius of the Soddy circle formed by them are constructed and stored. Assuming that the filling sand control medium accumulation body is densely packed, the pores on the accumulation body interface are composed of the middle area surrounded by the three tangent particles. max ,y max ) allocates storage for the following variables: r 1 、r 2 、r 3 、r s space, where r 1 、r 2 、r 3 are the radii of the three particles that make up the pores, in m; r s The radius of the inner Soddy circle formed by the three particles inscribed in each other, in meters;

[0057] 2) is the variable r 1 、r 2 、r 3 Assignment: First, according to the measured radius value R[n] of the sand control medium and its corresponding probability array P[n], three particle sizes are randomly generated and assigned to r 1 、r 2 、r 3 . Then according to Figure 1 According to the Soddy circle calculation formula, the corresponding r s Specifically, we can select the radius value in R[n] according to the probability in the probability array P[n] and assign it to r 1 ; Repeat the selection twice, and use the same method to select r 2 、r 3 Assignment; apply the assigned r 1 、r 2 、r 3 , substitute into the following formula to calculate the corresponding r s value:

[0058]

[0059] 3) Repeat the above operation to complete the entire filter layer interface array F(x max ,y max )1 、r 2 、r 3 、r s Assignment; Get four two-dimensional arrays: F(x,y).r 1 、F(x,y).r 2 、F(x,y).r 3 、F(x,y).r s The particle size at the interface between the sand control medium and the reservoir and the value of the Soddy circle corresponding to it, where F(x,y).r s The value of Figure 2 as shown in .

[0060] Step 3: Calculate the mud and sand intrusion rate and the total amount of mud and sand intrusion in the entire filter layer according to the free settlement arch model. Specifically:

[0061] 1) Based on the following free settling arch hypothesis, a prediction model suitable for quantitative calculation of sand discharge rate is established: from the moment the particles reach the free settling area, their accelerated motion under the action of fluid drag can be regarded as uniform accelerated motion; after a period of acceleration, the particle velocity can be considered to be the same as the fluid velocity; the plug flow model is used to simplify the through-hole flow field, that is, it is assumed that there is no particle intrusion at 1 / 2 of the distance from the outlet opening boundary, and the particle mass fraction at the remaining positions is the same as the value at the outlet center; the particle outlet velocity is significantly different from the outlet center velocity only at the outlet opening boundary;

[0062] 2) Calculate different r s The corresponding mud and sand intrusion rate R in the free settlement arch is stored in the multidimensional array space F(x,y).R:

[0063]

[0064] In the above formula, R is the number of mud and sand particles invading per unit time, unit is s -1 ;u exit is the average fluid velocity at the outlet, in m / s; d 50 is the median particle size of the intruding mud and sand, m; φ c is the particle mass fraction at the center of the opening, dimensionless, and its calculation formula is as follows:

[0065]

[0066] In the above formula, φ j is the critical blockage experimental constant and is dimensionless.

[0067] 3) Repeat the operation in 2) and calculate the mud and sand invasion rate at each opening of the entire filter layer F(x,y) according to the prediction model in equations (2)-(4); sum the mud and sand invasion rate per unit time of the entire storage sand control medium and the reservoir interface, read the mud and sand invasion rate R of each unit in F(x,y), add their values, and obtain the total number of particles W invading the filling sand control medium per unit time:

[0068]

[0069] Step 4: Follow Figure 3 The process in Figure 1 calculates the permeability change of the sand production unit during mining, which includes the following steps:

[0070] 1) The loose sand production section outside the filling sand control medium is discretized into n sand production units. Sand production unit 1 is connected to the sand control medium, and mud and sand particles are transported into the sand control medium at a speed of W. The deficit caused by this is supplemented by the movable particles in the movable sand production unit 2, and so on. If the flow velocity state in the sand production unit x does not reach the critical flow velocity for particle startup, the deficit of the previous unit cannot be supplemented. At this time, the particles in the sand production unit x do not move, and the permeability and porosity remain unchanged.

[0071] In this embodiment, the target reservoir is discretized and divided into three parts: the sand production section of the reservoir, the free falling zone (FFZ) and the sand retaining medium. Figure 4 As shown in . Assuming that when the far-field particles migrate with the reservoir fluid to the area between the sand retaining medium and the formation, the velocity gradient generated by the sudden expansion of the pores is retained at the interface to form an FFZ. The particles in the FFZ are all dispersed, and there is no cementation between the particles. The formation particles entering the FFZ move only under the action of their main driving force (fluid drag). The sand invasion velocity on the interface between the sand retaining medium and the formation is obtained by the particle pore velocity model based on step 3. The sand production section of the reservoir is discretized into i formation units, and the skeleton sand liquefaction constitutive equation is used to calculate the volume of stripped sand in the unit, that is, Figure 4 Vsf(i) in the equation; Assuming that the free sand forms a loose accumulation in the pore space of the formation sand unit, the particle starting threshold velocity u fc Determine whether the stripped sand forms movable sand that can be carried and transported by reservoir fluid. The liquefied sand in the x1 unit is the source of the intruding sand particles in the FFZ, and the liquefied sand in the subsequent unit is also driven by the liquid flow to supplement the previous unit.

[0072] 2) Calculate the critical velocity of particles in the particle accumulation body: particle starting threshold velocity u fcThe derivation of needs to make the following assumptions: the particles in the model are piled up by spherical free sand particles of equal diameter, and the stacking angle is θ; the restart of the particles starts from the particles at the front edge of the pile, and the collapse process of the pile when the particles start is not considered; it is assumed that the injected fluid is pure liquid phase, and the starting force of the solid phase particles mainly comes from the drag force of the liquid phase; under the premise of the above assumptions, the particle force analysis is carried out. According to the particle force analysis diagram ( Figure 5 ), derive the threshold speed u for particle activation fc :

[0073]

[0074] Where: θ is the stacking angle of the bulk particles; ε is the porosity of the particle stack; k is the permeability of the particle stack, m 2 ; μ is the viscosity of the reservoir produced fluid, Pa·s;

[0075] F g is the combined force of particle buoyancy and gravity, N, and its calculation formula is as follows:

[0076]

[0077] Where: p and ρ f are the densities of particles and fluid, kg / m 3 ;

[0078] F f is the friction force exerted by other particles, N, which is calculated as follows:

[0079]

[0080] Where: m is the average mass of particles, kg; h is the thickness of sand control medium, m.

[0081] 3) The volume of particles entering the sand control medium from the sand production unit per unit time is:

[0082]

[0083] The total number of movable sand in the sand production unit is:

[0084]

[0085] In the formula, i max To achieve the maximum number of units for the particle start threshold speed, when V p Greater than V stotal When , it means that all the movable sand in the sand production unit has been produced and the sand production stops;

[0086] According to the law of mass conservation, the increase in porosity ε caused by particle stripping in the sand unit is calculated, and its value is calculated by the following formula:

[0087]

[0088] In the formula, ε 0 is the initial porosity of the reservoir; V element is the total volume of the sand production unit, m 3 ;

[0089] The permeability increase caused by the porosity increase is calculated according to the Kozeny-Carman formula:

[0090]

[0091] Where: KC is the Kozeny-Carman constant; S b is the specific surface area of ​​the particle accumulation, m -1 .

[0092] The calculation method proposed in this application can be used to obtain the overall evolution law and distribution characteristics of the permeability of the sand-producing section of the reservoir during oil well production. Figure 6 The figure shows the variation of the permeability of the sand-producing unit of the reservoir obtained by this method over time. Figure 7 The permeability distribution diagram of the sand production unit of the reservoir obtained by using this method is shown in FIG.

[0093] The above description is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the technical content disclosed above to change or modify it into an equivalent embodiment with equivalent changes and apply it to other fields. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting sand production rate and wellbore seepage capacity based on free settlement arch theory, characterized in that: The following steps are involved: Step A: Test the particle size distribution of the filling sand control medium selected on site and obtain its particle size distribution curve; and obtain reservoir mud and sand samples, test the particle size distribution of mud and sand produced by the target reservoir, and obtain its particle size median d 50 ; Step B, establishing a multidimensional array to store the particle size distribution and the distribution characteristics of the Soddy circle on the interface between the sand control medium and the reservoir; Step B1: According to the particle size distribution curve of the filling sand control medium obtained in step A, create arrays R[n] and P[n], where R[n] is the particle radius array and P[n] is the distribution probability corresponding to the particle radius in R[n]. Then, establish a filling sand control medium stacking network, assuming that it is a dense stacking, and the pores on the interface of the stacking body are composed of the middle area surrounded by three tangent particles. Let r1, r2, and r3 be the radii of the three particles that make up the pores, respectively, and r s Create a multidimensional array F(x max ,y max ) to store r1, r2, r3 and r s Information, where x max ,y max are the particle coordinates in the horizontal and vertical directions, respectively; Step B2: Assign values ​​to variables r1, r2, and r3, and obtain the corresponding r s Repeat the above operation until the entire filter layer interface multidimensional array F(x max ,y max ) in r1, r2, r3, r s Assignment; Get four two-dimensional arrays: F(x,y).r1, F(x,y).r2, F(x,y).r3, F(x,y).r s The particle size at the interface between the sand control medium and the reservoir and the value of the Soddy circle corresponding to it; Step C, according to the free settling arch theory, the mud and sand intrusion rate and the total amount of intruded mud and sand in the entire filter layer are calculated to achieve quantitative prediction of the sand discharge rate; Step D: Calculate the permeability change of the sand production unit during the mining process to quantitatively predict the seepage capacity around the well.

2. The method for predicting sand production rate and wellbore seepage capacity based on free settling arch theory according to claim 1, characterized in that: In step B2, when assigning values ​​to variables r1, r2, and r3, firstly, three particle sizes are randomly generated according to the measured radius value R[n] of the sand control medium and its corresponding probability array P[n], and the values ​​are assigned to r1, r2, and r3, and the corresponding r is calculated. s value:

3. The method for predicting sand production rate and wellbore seepage capacity based on free settling arch theory according to claim 1, characterized in that: In step C, a prediction model suitable for quantitative calculation of sand production rate is established based on the following free settling arch hypothesis: It is assumed that from the moment the particles reach the free settling area, their accelerated motion under the action of fluid drag is uniformly accelerated motion; after a period of acceleration, the particle velocity is considered to be the same as the fluid flow velocity; the plug flow model is used to simplify the through-hole flow field, assuming that there is no particle intrusion at 1 / 2 of the distance near the boundary of the outlet opening, and the particle mass fraction at the remaining positions is the same as the value at the center of the outlet, and the particle outlet velocity is different from the outlet center velocity only at the boundary of the outlet opening; (1) Calculate different r s The corresponding mud and sand intrusion rate R in the free settlement arch is stored in the multidimensional array F(x,y).R. The multidimensional array F(x,y).R is expressed as follows: Where R is the number of mud and sand particles invading per unit time; u exit is the average fluid velocity at the outlet; φ c is the particle mass fraction at the center of the opening, d 50 is the median particle size of the intruding mud and sand, F(x,y).r s Indicates storage of each unit r s A two-dimensional array of values; (2) Repeat the operation (1) to obtain the mud and sand intrusion rate of each unit in the entire filter layer, add up their values, and obtain the total number of particles W that invade the filling sand control medium per unit time: Among them, x max ,y max are the particle coordinates in the vertical and horizontal directions, respectively, i is a variable representing the number of units in the horizontal direction, y j is a variable representing the number of units in the vertical direction.

4. The method for predicting sand production rate and wellbore perimeter seepage capacity based on free settling arch theory according to claim 1, characterized in that: In step D, the following method is used to calculate the permeability change of the sand production unit during the mining process: 1) The loose sand production section outside the filling sand control medium is discretized into n sand production units, n = 1, 2, 3..., the sand production unit 1 is connected to the sand control medium, and mud and sand particles are transported into the sand control medium at a speed of W. The deficit caused by this is supplemented by the movable particles in the movable sand production unit 2, and so on; 2) Calculate the critical velocity of particle start-up in the particle accumulation body and determine whether the particle start-up threshold velocity is reached; If the start-up velocity is reached, the particles migrate to the pore space of the previous unit or the free settling zone FFZ. If the start-up velocity is not reached, the particles do not migrate with the fluid, the permeability and porosity of the current sand-producing unit remain unchanged, and the porosity of the previous sand-producing unit increases. By calculating the permeability change, the seepage capacity around the well can be predicted.

5. The method for predicting sand production rate and wellbore perimeter seepage capacity based on free settling arch theory according to claim 4, characterized in that: In step D, the target reservoir is discretized and divided into three parts: the sand-producing section of the reservoir, the free settling zone FFZ and the sand retaining medium; the sand-producing section of the reservoir is discretized into i formation units, and the liquefaction constitutive equation of skeleton sand is used to calculate the volume of stripped sand Vsf(i) in the unit. It is assumed that the free sand forms a loose accumulation in the pore space of the formation sand unit, and the particle start threshold velocity u is used. fc Determine whether the stripped sand forms movable sand that can be carried and transported by reservoir fluid; Among them, the particle starting threshold speed u fc The derivation process is as follows: Assume that the particle body in the model is composed of spherical free sand particles of equal diameter, and the stacking angle is θ; the restart of the particle starts from the particle at the front edge of the stack; and assume that the injected fluid is a pure liquid phase; Under the above assumptions, the particle force analysis is carried out, and the threshold speed u of the particle start is derived according to the particle force analysis diagram fc : Where: θ is the stacking angle of the dispersed particles; ε is the porosity of the particle stack; k is the permeability of the particle stack; μ is the viscosity of the reservoir fluid; F g is the combined force of particle buoyancy and gravity, F f The friction force exerted by other particles.

6. The method for predicting sand production rate and wellbore perimeter seepage capacity based on free settling arch theory according to claim 5, characterized in that: In the step D, the permeability around the well is characterized by the change in permeability, specifically: Calculate the volume of particles entering the sand control medium from the sand production unit per unit time: The total number of movable sand in the sand production unit is: In the formula, i max To achieve the maximum number of units for the particle start threshold speed, when V p Greater than V stotal When , it means that all the movable sand in the sand production unit has been produced and the sand production stops; According to the law of mass conservation, the increase in porosity ε caused by particle stripping in the sand unit is calculated: Where ε0 is the initial porosity of the reservoir; V element is the total volume of the sand production unit; The permeability increase caused by the porosity increase is calculated according to the Kozeny-Carman formula: Where: KC is the Kozeny-Carman constant; S b is the specific surface area of ​​the particle accumulation.

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