Method for identifying particle migration area of silty sandstone reservoir

Abstract

The invention relates to the technical field of water drive development reservoir particle migration of a silty and fine sandstone reservoir, and provides a method for identifying a particle migration area of the silty and fine sandstone reservoir. Comprising the steps of establishing a particle stress relation equation; carrying out particle stress relation deformation to obtain a particle-started critical flow velocity model; detention and pre-migration corresponding speeds are valued, and a particle starting and detention critical speed chart is formed in combination with a particle starting critical flow velocity model; establishing an oil reservoir seepage mathematical model considering reservoir physical property time variation, determining whether particles in a grid are started or detained by combining a particle starting and detained critical speed chart, and identifying a reservoir particle migration area; by means of physical simulation and numerical simulation methods, geological exploration data and laboratory research results are combined, quantitative analysis and simulation are conducted on the migration and retention process of the deep reservoir particles, factors such as geological characteristics, fluid properties and particle characteristics of the reservoir are comprehensively considered, and accurate prediction of the migration path and the retention area of the particles is achieved.

Description

Technical Field

[0001] This invention relates to the field of reservoir particle migration technology in water-drive development of fine sandstone reservoirs, and proposes a method for identifying particle migration regions in fine sandstone reservoirs. Background Technology

[0002] During waterflooding development of fine sandstone reservoirs, reservoir microparticles are prone to detachment and blockage of well channels and screens, leading to reduced production capacity of production wells. Therefore, identifying microparticle migration zones is of great significance for waterflooding development of fine sandstone reservoirs.

[0003] Currently, most studies on reservoir particle migration focus on near-wellbore or small-scale core particle migration, for example:

[0004] The study can be conducted through indoor experiments on centimeter-scale flat cores, or by using core displacement devices to evaluate flow velocity sensitivity, or by using numerical simulation software to study the particle migration behavior of reservoirs in the near-wellbore area (a 10-meter area centered on the well).

[0005] None of these studies addressed the migration of particles in deep reservoirs (100 meters or more), which provides the material basis for sand production in oil wells. Identifying the migration zones of particles in deep reservoirs is of great significance for controlling sand production in oil wells in fine sandstone reservoirs.

[0006] Chinese invention patent application CN202310000044.3 discloses a method for predicting the scale of sand production in reservoirs during hydrate extraction. This method first establishes a solid particle detachment and transport model. Then, based on the coupling relationship between the thermo-fluid-mechanical-phase change coupling model and the solid particle detachment and transport model, a hydrate extraction sand production model is established. Finally, a site-scale numerical simulation platform for hydrate extraction sand production is established based on the hydrate extraction sand production model. Using this platform, a natural gas hydrate reservoir model for the target area is established based on field geological exploration data. The sand production behavior is quantitatively analyzed based on the calculation results, thus achieving a quantitative prediction of the scale of sand production in reservoirs during hydrate extraction.

[0007] Chinese invention patent CN110390130B discloses a numerical simulation method for sand production in indoor experiments during depressurization mining of hydrate-bearing sediments. This method utilizes the coupling of hydrate reservoir production capacity prediction software and geotechnical mechanics analysis software to establish a macroscopic multi-field coupled model of the thermal-fluid-solid structure of the hydrate-bearing sediment reservoir. Then, a microscopic sand production model is constructed using particle flow discrete element software. The macroscopic multi-field coupled model simulates the depressurization mining process, while simultaneously transferring data such as effective stress, hydrate saturation, and water-gas flow velocity obtained from the simulation as boundary and initial conditions to the microscopic sand production model for dynamic sand production simulation. The beneficial effects of this invention are: Based on the premise of obtaining the reservoir physical and mechanical response laws using the macroscopic multi-field coupled model, the proposed technical solution transfers relevant data to the microscopic sand production model constructed using particle flow discrete element software for dynamic sand production simulation, studying the occurrence and development process of sand production from a microscopic perspective, and clarifying the sand production mechanism and laws.

[0008] Chinese invention patent application CN202210348885.9 discloses a method for monitoring the average sand production rate of oil and gas wells. This method includes: transmitting and receiving ultrasonic signals using an ultrasonic probe in areas prone to pipe perforation accidents; obtaining and recording the remaining pipe wall thickness information based on the principle of ultrasonic pulse reflection; substituting the difference in remaining pipe wall thickness recorded before and after a fixed monitoring time into an erosion and wear equation; and calculating the sand mass flow rate based on the erosion rate determined by the erosion and wear equation. This invention utilizes the erosion and wear equation to calculate the sand production rate, avoiding the influence of single measurement errors and cumulative errors during monitoring. It only requires measuring the pipe wall thickness value within a fixed time period. The circuitry is simple, the processing system is straightforward, the equipment has high reliability, and the implementation is more accurate. It can detect pipe perforation failure in time and allow for timely equipment replacement.

[0009] Chinese invention patent CN108612519B relates to a method and device for monitoring sand production in oil and gas wells. This method falls under the field of online sand production monitoring technology for oil and gas wells, specifically involving a method and device for monitoring sand production in oil and gas wells. The method includes: acquiring impact signals within a preset area using a focused ultrasonic phased array transducer; performing spatial beamguide processing on the impact signals to obtain the main area where sand particles impact the pipe wall; picking up the ultrasonic signals from the main area where sand particles impact the pipe wall and performing spatial, frequency, and time domain filtering to obtain the sand production signal. This invention can achieve three-dimensional joint filtering in the spatial, frequency, and time domains to reduce noise, extract effective sand production signals, and improve the accuracy of sand production monitoring.

[0010] In the Chinese invention patent with authorization number CN111594101B, there is a method for predicting the sand production deficit profile outside the vertical well casing and constructing a high-saturation gravel backfill. The method includes the following steps: (1) Calculating the longitudinal sand production deficit index: First, based on the density logging and sonic transit time logging data of the production layer, the rock density strength index and the rock sonic transit time intensity index are calculated respectively; then, the longitudinal sand production deficit index is calculated by weighted average of the rock density strength index and the rock sonic transit time intensity index, and the distribution of the longitudinal sand production deficit index of the production layer outside the vertical well casing is obtained; (2) Calculating the average equivalent deficit radius: First, based on the density logging and sonic transit time logging data of the production layer, the rock density strength index and the rock sonic transit time intensity index are calculated respectively; then, the longitudinal sand production deficit index is calculated by weighted average of the rock density strength index and the rock sonic transit time intensity index, and the distribution of the longitudinal sand production deficit index of the production layer outside the vertical well casing is obtained; Historical data, including production years, average output, and average sand content, are used to estimate the cumulative sand production volume of the vertical well, i.e., the sand production deficit volume; then, the average equivalent deficit radius of the overall production layer of the vertical well is calculated based on the sand production deficit volume; (3) Draw a longitudinal sand production deficit profile: First, combine the longitudinal sand production deficit index distribution obtained in step (1) and the average equivalent deficit radius obtained in step (2) to calculate the equivalent deficit radius at the depth point of the production layer of the vertical well, and then draw a distribution map of the sand production deficit radius along the longitudinal direction based on the calculated data, i.e., a longitudinal sand production deficit profile, where the formula for calculating the equivalent deficit radius at the depth point of the production layer of the vertical well is given.

[0011] None of the above-mentioned existing technologies have been able to identify the deep particulate migration regions of reservoirs. Summary of the Invention

[0012] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for identifying particle migration zones in fine sandstone reservoirs. Firstly, based on force analysis and assuming particle torque balance, a critical velocity model for particle initiation is established. This model, combined with previous research, establishes a boundary map between critical velocities for particle initiation and retention. Secondly, by incorporating a reservoir seepage mathematical model that considers the time-varying properties of reservoir materials, a method for identifying particle migration zones in fine sandstone reservoirs is formed. Finally, using a specific oil reservoir as an example, reservoir migration zones are identified to obtain the distribution of sand-producing areas in the actual reservoir. This provides strong support for improving production and efficiency in water-drive development of fine sandstone reservoirs.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A method for identifying particle migration zones in fine-grained sandstone reservoirs includes the following steps:

[0015] S1. Establish the equations relating the forces acting on the particles;

[0016] S2. Deform the force relationship of the particles to obtain the critical flow velocity model for particle initiation;

[0017] S3. Take the corresponding velocity values ​​for retention and pre-transport, and combine them with the critical velocity model for particle initiation to form a critical velocity chart for particle initiation and retention.

[0018] S4. Establish a reservoir seepage mathematical model that considers the time-varying nature of reservoir properties, and then combine it with the critical velocity chart of particle initiation and retention to determine whether particles in the grid are initiated or retained, and identify the reservoir particle migration area.

[0019] Furthermore, the force relationship equation for the particles is established based on the force analysis of the particles in the reservoir, taking particle detachment as a condition, and includes:

[0020] Based on the requirement that torque balance must be satisfied when particles detach:

[0021] F e L d +F g L d -F p L d =F a L n (1)

[0022] Among them, F e For electrostatic attraction, N; F g For gravity, N; F p For particle buoyancy, N; F a The drag force of a fluid on a particle, N; L n With L d Let m be the lever arm of the horizontal force and the lever arm of the vertical force, respectively.

[0023] Furthermore, the deformation of the force relationship of the particles is achieved by combining the expressions for electrostatic adsorption force, gravity, buoyancy, and drag force to transform the equation of the force relationship of the particles.

[0024] Furthermore, the calculation expressions for the electrostatic adsorption force Fe, gravity Fg, buoyancy Fp, and the drag force Fa of the fluid on the particles are as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, V is the total electric potential energy, VLVA is the van der Waals gravitational potential energy, VDKR is the double-layer repulsive potential energy, VBR is the Born repulsive potential energy, h is the interparticle distance in μm, rs is the particle size in μm, and Δρ is the solid-liquid density difference in kg / m³. 3; χ is the fluid lift coefficient; g is the gravitational acceleration, 10 m / s²; μ is the fluid viscosity, in mPa·s; ω is the fluid traction constant; R-hc is the effective flow radius, in μm; Vs is the critical velocity, in cm / s.

[0030] Furthermore, the deformation of the force relationship of the particles includes:

[0031] Substituting equations (2) to (5) into equation (1), we obtain the critical velocity model for particle initiation:

[0032]

[0033] Furthermore, the velocity corresponding to the retention and pre-transport is 0.5 times the critical velocity for particle initiation.

[0034] Furthermore, step S3 specifically includes:

[0035] Based on different particle sizes, the reservoir parameters are assigned values, and the reservoir parameters are substituted into equation (6) to obtain the critical velocity chart for particle initiation and retention; the reservoir parameters include fluid traction constant, fluid lift coefficient, fluid viscosity, fluid density, effective pore flow radius, particle size, particle density and g-gravity acceleration.

[0036] Furthermore, the establishment of the reservoir seepage mathematical model includes: conducting waterflooding experiments under different water cut conditions using a waterflooding experimental device with loose sandstone cores, recording the displacement pressure and production rate at different times, and obtaining the permeability under different water cut conditions by applying Darcy's formula; then dividing the permeability under different water cut conditions by the reservoir permeability when the water cut is zero to obtain the permeability increase factor, and finally plotting the relationship between the permeability increase factor and the water cut change. Simultaneously, the flow control equations for the oil and water phases are established based on seepage theory.

[0037]

[0038]

[0039] In the formula, k is the reservoir permeability, μm2; k ro With k rw S represents the relative permeability of the oil phase and the water phase, dimensionless; w With S o B represents water saturation and oil saturation, dimensionless. w With B o The volume coefficients of water and crude oil are dimensionless; μ w With μ o Water viscosity and crude oil viscosity, mPa·s; φ is porosity, decimal; p w With p oThe pressures of the water phase and oil phase are 105 Pa; ρ w With ρ o For the densities of water and crude oil, g / cm3; q w With q o t represents the outflow velocity of the water phase per unit volume and the outflow velocity of the oil phase per unit volume, in cm / s; g represents the simulation time, in s; g represents the gravitational acceleration, in g / s²; and D represents the reservoir depth, in cm.

[0040] Normalization conditions:

[0041] S o +S w =1 (9)

[0042] Auxiliary equation:

[0043] p c =p o -p w (10)

[0044] In the formula, p c Capillary pressure, 105 Pa;

[0045] The relative permeability curves in equations (22) and (23) are calculated as follows:

[0046]

[0047]

[0048] In the formula, k rwi The relative permeability under residual oil saturation conditions, s wc With s or , respectively, represent the bound water saturation and residual oil saturation, and m and n represent the oil phase index and water phase index, respectively.

[0049] Furthermore, step S4 also includes solving for the pressure and saturation of each grid based on the reservoir seepage mathematical model, and then calculating the fluid velocity within the grid.

[0050] Furthermore, the pressure solution includes: transforming and adding equations (7) and (8), combining them with the capillary force equation (10), and eliminating water saturation and oil saturation to obtain the pressure equation;

[0051] The saturation solution includes: substituting the pressure to be solved into the discrete equation to solve for the water saturation; and obtaining the saturation solution equation based on equation (13) and the discrete three-dimensional space.

[0052] The beneficial effects of this invention are as follows:

[0053] This invention uses physical and numerical simulation methods, combined with geological exploration data and laboratory research results, to quantitatively analyze and simulate the migration and retention process of deep particles in reservoirs. It establishes a complete mathematical model that comprehensively considers factors such as reservoir geological characteristics, fluid properties, and particle characteristics, thereby achieving accurate prediction of particle migration paths and retention areas. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the force analysis of microparticles on a rock skeleton provided by the present invention;

[0055] Figure 2 This is a graph showing the critical velocities for particle initiation and retention provided by the present invention;

[0056] Figure 3 This is a graph showing the relationship between the increase in permeability and water cut in water-driven reservoirs provided by this invention;

[0057] Figure 4 This invention provides the identification results of the activation, retention, and non-activation areas of 58 microparticles.

[0058] Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0059] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0060] Example 1:

[0061] Please see Figures 1-5 A method for identifying particle migration zones in fine sandstone reservoirs, comprising:

[0062] Step 1: Based on the force analysis of particles in the reservoir, and taking particle detachment as a condition, establish the force relationship equation of the particles.

[0063] Step two: By combining the expressions for electrostatic adsorption force, gravity, buoyancy and drag force, the force relationship of the particles is deformed to obtain the critical flow velocity model for particle initiation.

[0064] Step 3: Based on Zhang Xiuliang's understanding in his 2011 master's thesis "Research on Sand Production Prediction Technology" that "the velocity corresponding to retention and pre-transport is 0.4-0.6 times the critical velocity for particle initiation", this invention takes the velocity corresponding to retention and pre-transport as 0.5 times the critical velocity for particle initiation; combined with the critical velocity model for particle initiation, a critical velocity chart for particle initiation and retention is formed.

[0065] Step 4: Based on the relationship between reservoir properties and water cut, establish a reservoir seepage mathematical model that considers the time-varying nature of reservoir properties. Solve the model to obtain the pressure and saturation of each grid, and then calculate the fluid velocity within the grid. Combined with the critical velocity chart for particle initiation and retention, determine whether particles in the grid are initiated or retained, and identify the reservoir particle migration region.

[0066] Step 5: The established method for identifying the migration zones of fine sandstone reservoir particles is applied to actual blocks, and the reliability of the method is verified by comparing the actual results with the understanding gained from mining practice.

[0067] Example 2:

[0068] A method for identifying particle migration zones in fine-grained sandstone reservoirs, comprising:

[0069] In step one, based on the force analysis of particles in the reservoir, and taking particle detachment as a condition, the specific process of establishing the force relationship equation for particles is as follows:

[0070] The stress analysis of the particles on the rock skeleton is shown in Figure 1 Based on the requirement that torque balance must be satisfied when particles detach:

[0071] F e L d +F g L d -F p L d =F a L n (1)

[0072] Among them, F e For electrostatic attraction, N; F g For gravity, N; F p For particle buoyancy, N; F a The drag force of a fluid on a particle, N; L n With L d Let m be the lever arm of the horizontal force and the lever arm of the vertical force, respectively.

[0073] In step two, by combining the expressions for electrostatic adsorption force, gravity, buoyancy, and drag force, the force relationship equation of the particles (equation (1)) is transformed to obtain the critical flow velocity model for particle initiation. The specific process is as follows:

[0074] Based on theoretical mechanics and fluid mechanics, the calculation expressions for electrostatic adsorption force Fe, gravity Fg, buoyancy Fp, and the drag force Fa of the fluid on the particle are as follows:

[0075]

[0076]

[0077]

[0078]

[0079] In the formula, V is the total electric potential energy, VLVA is the van der Waals gravitational potential energy, VDKR is the double-layer repulsive potential energy, VBR is the Born repulsive potential energy, h is the interparticle distance in μm, rs is the particle size in μm, and Δρ is the solid-liquid density difference in kg / m³. 3 ; χ is the fluid lift coefficient; g is the gravitational acceleration, 10 m / s²; μ is the fluid viscosity, in mPa·s; ω is the fluid traction constant; R-hc is the effective flow radius, in μm; Vs is the critical velocity, in cm / s.

[0080] Substituting equations (2) to (5) into equation (1), we obtain the critical velocity model for particle initiation:

[0081]

[0082] In step three, based on Zhang Xiuliang's understanding in his 2011 master's thesis "Research on Sand Production Prediction Technology" that "the corresponding velocities of retention and pre-transport are 0.4-0.6 times the critical velocity for particle initiation," this invention takes the corresponding velocities of retention and pre-transport as 0.5 times the critical velocity for particle initiation; then, combined with the critical velocity model for particle initiation, a graph of critical velocities for particle initiation and retention is formed. The specific process is as follows:

[0083] When the reservoir parameters are: fluid traction constant is 40; fluid lift coefficient is 1190; fluid viscosity is 0.5 mPa·s; fluid density is 1000 kg / m³; effective pore flow radius is 100 μm; particle size is 50-400 μm; particle density is 1700 kg / m³; and gravitational acceleration is 10 m / s², and these parameters are substituted into equation (6) according to different particle size values, the critical velocity charts for particle initiation and retention can be obtained, see [reference needed]. Figure 2 .

[0084] In step four, based on the relationship between reservoir properties and water cut, a reservoir seepage mathematical model considering the time-varying nature of reservoir properties is established. Solving this model yields the pressure and saturation of each grid cell, allowing for the calculation of fluid velocity within the grid. Then, combined with a critical velocity chart for particle initiation and retention, it determines whether particles within the grid are initiated or retained, identifying reservoir particle migration regions. The specific process is as follows:

[0085] Waterflooding experiments were conducted using a waterflooding experimental setup with loose sandstone cores under different water cut conditions. Displacement pressure and production volume were recorded at different times. The permeability under different water cut conditions was obtained using Darcy's formula. The permeability under different water cut conditions was then divided by the reservoir permeability at zero water cut to obtain the permeability increase factor. Finally, a graph showing the relationship between the permeability increase factor and water cut change was plotted. Figure 3 Meanwhile, based on seepage theory, the flow control equations for the oil phase and the water phase are established as follows:

[0086]

[0087]

[0088] In the formula, k is the reservoir permeability, μm2; k ro With k rw S represents the relative permeability of the oil phase and the water phase, dimensionless; w With S o B represents water saturation and oil saturation, dimensionless. w With B o The volume coefficients of water and crude oil are dimensionless; μ w With μ o Water viscosity and crude oil viscosity, mPa·s; φ is porosity, decimal; p w With p o The pressures of the water phase and oil phase are 105 Pa; ρ w With ρ o For the densities of water and crude oil, g / cm3; q w With q o t represents the outflow velocity of the water phase per unit volume and the outflow velocity of the oil phase per unit volume, in cm / s; g represents the simulation time, in s; g represents the gravitational acceleration, in g / s²; and D represents the reservoir depth, in cm.

[0089] Normalization conditions:

[0090] S o +S w =1 (9)

[0091] Auxiliary equation:

[0092] p c =p o -p w (10)

[0093] In the formula, p c Capillary pressure, 105 Pa;

[0094] The relative permeability curves in equations (22) and (23) are calculated as follows:

[0095]

[0096]

[0097] In the formula, k rwi The relative permeability under residual oil saturation conditions, s wc With s or , respectively, represent the bound water saturation and residual oil saturation, and m and n represent the oil phase index and water phase index, respectively.

[0098] Equations (7) to (12) are three-dimensional oil-water two-phase flow mathematical models. The time-varying influence of reservoir properties is realized by correcting the reservoir permeability at each time step (the correction method is to calculate the water cut of each grid at each time step and look up the water cut value). Figure 3 To obtain the permeability increase factor of each grid at each time point, multiply it by the permeability at the initial time point to obtain the permeability of each grid at each time point, and establish a reservoir seepage mathematical model considering the time-varying reservoir properties. The water saturation and pressure of each grid are obtained by numerical solution of the discrete model. The pressure solution process is as follows: Equations (7) and (8) are transformed and added together. Combined with the capillary force equation (Equation (10)), the water saturation and oil saturation are eliminated to obtain the pressure equation, as follows:

[0099]

[0100] In the formula,

[0101] After discretizing the 3D reservoir, the number of grid cells in each direction (X, Y, Z) are M, N, and L, respectively. For the grid cell numbered (1, 1, 1), the discretization equation is:

[0102]

[0103] For the grid numbered (M, 1, 1), the discrete equations are:

[0104]

[0105] For the grid numbered (1, N, 1), there is a discrete equation:

[0106]

[0107] For the grid numbered (1, 1, L), the discrete equations are:

[0108]

[0109] For a grid numbered (M, 1, L), the discrete equations are:

[0110]

[0111] For a grid numbered (M, N, L), the discrete equations are:

[0112] (19)

[0114] For a grid numbered (M, N, 1), the discrete equations are:

[0115]

[0116] For a grid numbered (1, N, L), there is a discrete equation:

[0117]

[0118] For the grid numbered (ii, 1, 1), where ii takes values ​​from 2 to M-1, the discrete equation is:

[0119]

[0120] For a grid numbered (1, jj, 1), where jj takes values ​​from 2 to N-1, there is a discrete equation:

[0121]

[0122] For a grid numbered (1, 1, kk), where kk takes values ​​from 2 to L-1, the discrete equation is:

[0123]

[0124] For a grid numbered (ii1, 1, L), where ii1 takes values ​​from 2 to M-1, the discrete equation is:

[0125]

[0126] For a grid numbered (M, jj1, L), where jj1 takes values ​​from 2 to N-1, the discrete equation is:

[0127]

[0128] For a grid numbered (M, 1, kk1), where kk1 takes values ​​from 2 to L-1, the discrete equation is:

[0129]

[0130] For a grid numbered (ii1, N, 1), where ii2 takes values ​​from 2 to M-1, the discrete equation is:

[0131]

[0132] For a grid numbered (M, jj2, 1), where ii2 takes values ​​from 2 to N-1, the discrete equation is:

[0133]

[0134] For a grid numbered (M, N, kk2), where kk2 takes values ​​from 2 to L-1, the discrete equation is:

[0135]

[0136]

[0137] For a grid numbered (ii3, N, L), where ii3 takes values ​​from 2 to M-1, the discrete equation is:

[0138]

[0139] For a grid numbered (1, jj3, L), where jj3 takes values ​​from 2 to N-1, the discrete equation is:

[0140]

[0141] For a grid numbered (1, N, kk3), where kk3 takes values ​​from 2 to L-1, the discrete equation is:

[0142]

[0143] The discrete equations for the other grids are (i takes values ​​from 2 to M-1, j takes values ​​from 2 to N-1, and k takes values ​​from 2 to L-1).

[0144]

[0145] In equations (14) and (34) above, the superscript indicates the time and the subscript indicates the grid coordinate.

[0146] Combining (14) and (34), we can obtain the matrix of the water phase pressure equation. Solving the matrix by elimination method can obtain the water phase pressure. Combining it with equation (10), we can obtain the oil phase pressure.

[0147] Saturation Calculation Process: The water saturation is calculated using an explicit method, that is, when solving for saturation, the pressure to be solved is substituted into the discrete equation to directly solve for the water saturation. Based on equation (13), combined with the discrete three-dimensional space, the saturation calculation equation can be obtained as follows:

[0148] For the grid numbered (1, 1, 1), the discrete equation is:

[0149]

[0150] For the grid numbered (M, 1, 1), the discrete equations are:

[0151]

[0152] For the grid numbered (1, N, 1), there is a discrete equation:

[0153]

[0154] For the grid numbered (1, 1, L), the discrete equations are:

[0155]

[0156] For a grid numbered (M, 1, L), the discrete equations are:

[0157]

[0158] For a grid numbered (M, N, L), the discrete equations are:

[0159]

[0160] For a grid numbered (M, N, 1), the discrete equations are:

[0161]

[0162] For a grid numbered (1, N, L), there is a discrete equation:

[0163]

[0164] For the grid numbered (ii, 1, 1), where ii takes values ​​from 2 to M-1, the discrete equation is:

[0165]

[0166] For a grid numbered (1, jj, 1), where jj takes values ​​from 2 to N-1, there is a discrete equation:

[0167]

[0168] For a grid numbered (1, 1, kk), where kk takes values ​​from 2 to L-1, the discrete equation is:

[0169]

[0170] For a grid numbered (ii1, 1, L), where ii1 takes values ​​from 2 to M-1, the discrete equation is:

[0171]

[0172] For a grid numbered (M, jj1, L), where jj1 takes values ​​from 2 to N-1, the discrete equation is:

[0173]

[0174] For a grid numbered (M, 1, kk1), where kk1 takes values ​​from 2 to L-1, the discrete equation is:

[0175]

[0176] For a grid numbered (ii2, N, 1), where ii2 takes values ​​from 2 to M-1, the discrete equation is:

[0177]

[0178] For a grid numbered (M, jj2, 1), where ii2 takes values ​​from 2 to N-1, the discrete equation is:

[0179]

[0180] For a grid numbered (M, N, kk2), where kk2 takes values ​​from 2 to L-1, the discrete equation is:

[0181]

[0182] For a grid numbered (ii3, N, L), where ii3 takes values ​​from 2 to M-1, the discrete equation is:

[0183]

[0184] For a grid numbered (1, jj3, L), where jj3 takes values ​​from 2 to N-1, the discrete equation is:

[0185]

[0186] For a grid numbered (1, N, kk3), where kk3 takes values ​​from 2 to L-1, the discrete equation is:

[0187]

[0188] The discrete equations for the other grids are (i takes values ​​from 2 to M-1, j takes values ​​from 2 to N-1, and k takes values ​​from 2 to L-1).

[0189]

[0190] Combining equations (35) to (55), the water saturation of each grid can be obtained. Then, combining the saturation normalization condition, the oil saturation of each grid can be obtained. Next, according to equation (56), the fluid velocity within each grid can be obtained, combined with the particle initiation and retention critical velocity chart (…). Figure 2 This determines whether particles within the grid are activated or retained, thereby identifying reservoir particle migration zones.

[0191]

[0192] In the formula, Δp and L grid These represent the pressure difference between two grids and the distance between the grid centers, respectively, in units of 10⁵ Pa and cm. grid , respectively, represent the fluid velocity within the grid, in cm / s.

[0193] Example 3:

[0194] A method for identifying particle migration zones in fine-grained sandstone reservoirs further includes step five: applying the established method to an actual block, comparing the actual results with mine practice, and verifying the reliability of the method. The specific process is as follows:

[0195] Taking the Lin 58 block of Shengli Oilfield as an example, this study identifies microparticle migration zones. The Lin 58 block in Shengli Oilfield has numerous small fault blocks, mostly reverse-roof type fault-block reservoirs. The largest fault block area is approximately 1.5 km², the smallest is approximately 0.02 km², and the average area is approximately 0.45 km². The permeability ranges from 80 to 2800 mD, the surface crude oil viscosity is 350-584 mPa·s, and the subsurface crude oil viscosity is 20-90 mPa·s. Analysis of the reservoir rock grain size composition shows that the reservoir particle size ranges from 50 μm to 400 μm, with a median of 120 μm. For the Lin 58 block of Shengli Oilfield, microparticle migration zones are identified, determining the microparticle migration zones, retention zones, and unactivated zones. (See...) Figure 4 .

[0196] Example 4:

[0197] Please refer to the instruction manual appendix. Figures 1-4 A method for identifying particle migration zones in fine sandstone reservoirs, comprising:

[0198] Step 1: Based on the force analysis of particles in the reservoir ( Figure 1 It can be seen that the forces acting on reservoir particles include: electrostatic adsorption force Fe, gravity Fg, buoyancy force Fp exerted by the fluid on the particles, and drag force Fa exerted by the fluid flow on the particles. Based on the torque balance at the time of particle initiation, the force relationship equation at the time of particle initiation can be obtained. e L d +F g L d -Fp L d =F a L n (Equation (1)).

[0199] Step 2: Based on theoretical mechanics and fluid mechanics, we can obtain the calculation expressions for electrostatic adsorption force Fe, gravity Fg, buoyancy Fp, and the drag force Fa of the fluid on the particle (equations (2) to (5)). Equation (1) can be simplified, and thus the critical flow velocity model for particle initiation can be obtained by transforming the equation.

[0200] Step 3: Substitute the reservoir parameters and fluid parameters (fluid traction constant is 40; fluid lift coefficient is 1190; fluid viscosity is 0.5 mPa·s; fluid density is 1000 kg / m3; effective pore flow radius is 100 μm; particle size is 50-400 μm; particle density is 1700 kg / m3; gravitational acceleration is 10 m / s2) into the critical velocity model for particle initiation (Equation (6)) to obtain the critical velocity for particle initiation in the reservoir. Combined with the research results of predecessors (Zhang Xiuliang's understanding in his master's thesis "Research on Sand Production Prediction Technology" in 2011 that "the velocity corresponding to retention and pre-migration is 0.4-0.6 times the critical velocity for particle initiation" (in this invention, the velocity corresponding to retention and pre-migration is 0.5 times the critical velocity for particle initiation)), the critical velocity for particle retention can be obtained, thus forming a graph of particle initiation limit and retention critical velocity ( Figure 2 ).from Figure 2 It can be seen that as the particle size increases, both the critical velocity limits for initiation and retention increase, and the increasing trend is initially steep, then becomes gentler. The critical velocity limit for initiation is greater than the critical velocity limit for retention.

[0201] Step four involves conducting waterflooding experiments under different water cut conditions, recording the displacement pressure and production rate at different times. The permeability under different water cut conditions can be obtained using Darcy's formula. Then, the permeability under different water cut conditions is divided by the reservoir permeability when the water cut is zero to obtain the permeability increase factor. Finally, a graph showing the relationship between the permeability increase factor and the change in water cut is plotted. Figure 3 Meanwhile, based on seepage theory, the flow control equations for the oil phase and the water phase are established as follows:

[0202]

[0203]

[0204] In the formula, k is the reservoir permeability, μm2; k ro With k rw S represents the relative permeability of the oil phase and the water phase, dimensionless; w With S oB represents water saturation and oil saturation, dimensionless. w With B o The volume coefficients of water and crude oil are dimensionless; μ w With μ o Water viscosity and crude oil viscosity, mPa·s; φ is porosity, decimal; p w With p o The pressures of the water phase and oil phase are 105 Pa; ρ w With ρ o For the densities of water and crude oil, g / cm3; q w With q o t represents the outflow velocity of the water phase per unit volume and the outflow velocity of the oil phase per unit volume, in cm / s; g represents the simulation time, in s; g represents the gravitational acceleration, in g / s²; and D represents the reservoir depth, in cm.

[0205] Normalization conditions:

[0206] S o +S w =1 (16)

[0207] Auxiliary equation:

[0208] p c =p o -p w (17)

[0209] In the formula, p c Capillary pressure, 105 Pa;

[0210] The relative permeability curves in equations (22) and (23) are calculated as follows:

[0211]

[0212]

[0213] In the formula, k rwi The relative permeability under residual oil saturation conditions, s wc With s or , respectively, represent the bound water saturation and residual oil saturation, and m and n represent the oil phase index and water phase index, respectively.

[0214] The time-varying influence of reservoir properties is realized by correcting the reservoir permeability at each time step (the correction method is to calculate the water cut of each grid at each time step and look up the water cut value). Figure 3 The permeability increase factor for each grid at each time step is obtained, and multiplied by the initial permeability to obtain the permeability for each grid at each time step. A mathematical model of reservoir seepage considering time-varying reservoir properties is then established. The water saturation and pressure of each grid are obtained through numerical solution of the discrete model, and then the equation is applied... Obtain the fluid velocity within each grid, combined with the critical velocity chart for particle initiation and retention. Figure 2 This determines whether particles within the grid are activated or retained, thereby identifying reservoir particle migration zones.

[0215] Step 5: Taking the Lin 58 block of Shengli Oilfield as an example, we will conduct reservoir microparticle migration zone identification. Based on the reservoir properties, particle size, and microparticle initiation and retention critical velocity charts of the Lin 58 block, we can conclude that: for 120μm microparticles, when the fluid velocity is less than 0.0033cm / s, the microparticles are not initiated; when the fluid velocity is greater than 0.0033cm / s and less than 0.0066cm / s, the microparticles are in a retention state; and when the fluid velocity is greater than 0.0066cm / s, the microparticles are in an initiated state.

[0216] The results of reservoir particle migration region identification are shown in Figure 4 .from Figure 4 It can be seen that oil wells L58-X204 and L58-CP41 are currently in the particulate initiation zone and require sand control operations; oil wells L58-14, L58-6, and L58-X491 are in the particulate retention zone and should be closely monitored to determine whether sand control is necessary. Figure 3 The sand-producing wells shown are consistent with the current sand-producing situation in Block 58 of Shengli Oilfield (severe sand production in wells L58-X204 and L58-CP41), verifying the reliability of the patented method.

[0217] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for identifying particle migration zones in fine sandstone reservoirs, characterized in that, Includes the following steps: S1. Establish the equations relating the forces acting on the particles; S2. Deform the force relationship of the particles to obtain the critical flow velocity model for particle initiation; S3. Take the corresponding velocity values ​​for retention and pre-transport, and combine them with the critical velocity model for particle initiation to form a critical velocity chart for particle initiation and retention. S4. Establish a reservoir seepage mathematical model that considers the time-varying nature of reservoir properties, and then combine it with the critical velocity chart of particle initiation and retention to determine whether particles in the grid are initiated or retained, and identify the reservoir particle migration area.

2. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 1, characterized in that, The force relationship equation for the particles is established based on the force analysis of particles in the reservoir, taking particle detachment as a condition, and includes: Based on the requirement that torque balance must be satisfied when particles detach: F e L d +F g L d -F p L d =F a L n (1) Among them, F e For electrostatic attraction, N; F g For gravity, N; F p For particle buoyancy, N; F a The drag force of a fluid on a particle, N; L n With L d Let m be the lever arm of the horizontal force and the lever arm of the vertical force, respectively.

3. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 2, characterized in that, The deformation of the force relationship of the particles is achieved by combining the expressions for electrostatic adsorption force, gravity, buoyancy and drag force to transform the equation of the force relationship of the particles.

4. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 3, characterized in that, The calculation expressions for the electrostatic adsorption force Fe, gravity Fg, buoyancy Fp, and the drag force Fa of the fluid on the particles are as follows: In the formula, V is the total electric potential energy, VLVA is the van der Waals gravitational potential energy, VDKR is the double electric layer repulsive potential energy, VBR is the Born repulsive potential energy, h is the interparticle spacing in μm, and rs is the particle size in μm. Δρ is the density difference between solid and liquid, in kg / m³. 3 ; χ is the fluid lift coefficient; g is the gravitational acceleration, 10 m / s²; μ is the fluid viscosity, in mPa·s; ω is the fluid traction constant; R-hc is the effective flow radius, in μm; Vs is the critical velocity, in cm / s.

5. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 4, characterized in that, The deformation of the force relationship of the particles includes: Substituting equations (2) to (5) into equation (1), we obtain the critical velocity model for particle initiation:

6. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 5, characterized in that, The velocity corresponding to the retention and pre-transport is 0.5 times the critical velocity for particle initiation.

7. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 6, characterized in that, Step S3 specifically includes: Based on different particle sizes, the reservoir parameters are assigned values, and the reservoir parameters are substituted into equation (6) to obtain the critical velocity chart for particle initiation and retention; the reservoir parameters include fluid traction constant, fluid lift coefficient, fluid viscosity, fluid density, effective pore flow radius, particle size, particle density and g-gravity acceleration.

8. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 7, characterized in that, The establishment of the reservoir seepage mathematical model includes: conducting water-drive oil production experiments under different water cut conditions using a water-drive experimental device with loose sandstone cores, recording the displacement pressure and production rate at different times, and obtaining the permeability under different water cut conditions by applying Darcy's formula; then dividing the permeability under different water cut conditions by the reservoir permeability when the water cut is zero to obtain the permeability increase factor, and finally plotting the relationship between the permeability increase factor and the water cut change. Simultaneously, the flow control equations for the oil and water phases are established based on seepage theory. In the formula, k is the reservoir permeability, μm2; k ro With k rw S represents the relative permeability of the oil phase and the water phase, dimensionless; w With S o B represents water saturation and oil saturation, dimensionless. w With B o The volume coefficients of water and crude oil are dimensionless; μ w With μ o Water viscosity and crude oil viscosity, mPa·s; φ is porosity, decimal; p w With p o The pressures of the water phase and oil phase are 105 Pa; ρ w With ρ o For the densities of water and crude oil, g / cm3; q w With q o t represents the outflow velocity of the water phase per unit volume and the outflow velocity of the oil phase per unit volume, in cm / s; g represents the simulation time, in s; g represents the gravitational acceleration, in g / s²; and D represents the reservoir depth, in cm. Normalization conditions: S o +S w =1 (9) Auxiliary equation: p c =p o -p w (10) In the formula, p c Capillary pressure, 105 Pa; The relative permeability curves in equations (22) and (23) are calculated as follows: In the formula, k rwi The relative permeability under residual oil saturation conditions, s wc With s or , respectively, represent the bound water saturation and residual oil saturation, and m and n represent the oil phase index and water phase index, respectively.

9. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 8, characterized in that, Step S4 further includes solving the pressure and saturation of each grid according to the reservoir seepage mathematical model, and then calculating the fluid velocity within the grid.

10. The method for identifying particle migration regions in fine sandstone reservoirs according to claim 9, characterized in that, The pressure solution includes: transforming and adding equations (7) and (8), combining them with capillary force equation (10), and eliminating water saturation and oil saturation to obtain the pressure equation; The saturation solution includes: substituting the pressure to be solved into the discrete equation to solve for the water saturation; and obtaining the saturation solution equation based on equation (13) and the discrete three-dimensional space.

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