CN112199903B - Numerical simulation method of discrete element nanoparticle plugging shale pores based on multi-parameter - Google Patents

Abstract

The invention discloses a multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles. Grid and wedge grid cells and set the boundary conditions and initial conditions of nanoparticles and fluids, write code to reconstruct the drag force model of nanoparticles in the fluid, calculate the amount of nanoparticles and the total amount of fluid in pores under different well conditions, A parameter model of nanoparticles with different release rates, directions and sizes was established, and real-time parameters such as fluid, nanoparticle velocity and pressure were calculated, and the simulation results were compared through theoretical formula derivation verification and experimental verification. The simulation results using the simulation method of the present invention are closer to the actual situation of horizontal wells and vertical wells, and provide an accurate reference for the actual nanoparticle plugging of shale pores.

Description

Numerical simulation method of discrete element nanoparticle plugging shale pores based on multi-parameter

technical field

The invention relates to the field of unconventional oil and gas exploration and development technology and deep geological drilling, in particular to the plugging of shale pores, in particular to a multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles.

Background technique

Energy is a powerful guarantee for the long-term and stable development of my country's economy. However, with the continuous consumption of fossil energy, the increasing difficulty of development and the increasingly severe environmental protection situation, the development of environmentally friendly large reserves of clean energy has become the focus of global scholars, governments and enterprises. As a kind of unconventional energy with huge reserves, shale gas is an important part of realizing a modern multi-energy system. In 2019, shale gas added 124.7 billion cubic meters of proven geological reserves, which is expected to surpass conventional gas and become the main natural gas in China. source. The maintenance of shale wellbore stability during the exploration and development of shale gas and deep geological drilling is inseparable from drilling and drilling fluids.

The maintenance of shale wellbore stability during the exploration and development of shale gas and deep geological drilling is inseparable from drilling and drilling fluids. Keeping the pressure inside the well higher than the formation pore pressure (but not higher than the fracturing pressure) is a reasonable and safe way of shale gas drilling and deep geological drilling. Under these conditions, water-based drilling fluids inevitably invade shale formations.

To solve the above problems, it is necessary to reduce the degree of drilling fluid invasion as much as possible while maintaining the stability of the wellbore. Adding nanomaterials to plug shale pores is one of the effective methods to enhance wellbore stability. Since the nanomaterials match the shale nanopores on the physical scale, when the nanoparticles migrate deep into the shale pores, the particles accumulate and block the re-invasion of water.

However, the plugging effect of nanoparticle drilling fluid on shale pores is mostly limited to physical experimental data, and there are few reports on the numerical simulation research on nanoparticle plugging of shale pores to maintain wellbore stability. The migration, dynamic accumulation and microscopic plugging mechanisms of nanoparticles in drilling fluids after invading shale pores are not clear.

The problem of experimental data is that of nanoscale physical experiments. Dynamic observation is difficult, costly, and difficult to succeed. Therefore, it is not feasible to fully grasp the microscopic mechanism of nanoparticle plugging through nanophysical experiments under the current conditions.

In addition, the influence of pore complexity, fluid physical properties and pore stress makes the research on the mechanism of nanoparticle plugging of shale pores more complicated and difficult.

At the same time, the particle parameters of the nanoparticle plugging model adopted by the predecessors are relatively single, and only include one particle parameter, that is, the plugging efficiency value calculated from different particle sizes (based on the content disclosed in the existing patent CN104504192B).

At the same time, the previous studies did not include the plugging performance evaluation and model verification brought about by the change of fluid viscosity. The above limitations make it difficult to quickly determine the nanoparticle plugging efficiency and the real-time invasion amount of drilling fluid under different fluid physical properties and diverse particle parameters.

In the actual drilling process of shale gas, there will be two types of vertical wells and horizontal wells. At present, there is no technical method that can simulate the numerical simulation method of nanoparticle plugging under the two well conditions at the same time. Among them, the technical difficulties are how to determine the amount of particles and fluids entering the vertical and horizontal wells, how to set the particle release mode, how to set the viscosity of the fluid filtrate entering the pores, and how to set the diversity of particle parameters.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles. . Further, the nanoparticle drag force model in the nanoparticle-fluid coupled flow model is programmed and reconstructed, and the selection method of the fluid viscosity parameter and the calculation method of the fluid amount and particle amount are determined, so that the results obtained by the simulation method are closer to the actual plugging. Happening.

The technical scheme of the present invention is as follows:

Numerical simulation method of shale pores plugging with discrete element nanoparticles based on multi-parameter, using CFD-DEM coupling method, including,

Establish a nanoparticle-fluid coupled flow model suitable for horizontal and vertical wells, the nanoparticle-fluid coupled flow model includes a nanoparticle release region, a nanoparticle-fluid coupled flow region and a pore plugging region, a nanoparticle release region and and pore plugging areas are located at the left and right ends of the nanoparticle-fluid coupled flow area, respectively;

Adopt tetrahedral mesh and wedge mesh elements based on implicit time integration and set the boundary conditions and initial conditions of nanoparticles and fluids. In addition, the grid is independently verified;

Write code to reconstruct the drag force model of nanoparticles in fluid; write a program of drag force on particles at the nanoscale, and modify the standard drag equation. Since the particles are nanoparticles, their drag force is different from that of particles with conventional sizes. In order to ensure the rationality of the simulation results, the drag force equation of particles at the nano-scale is programmed and reconstructed;

When _Re < 0.01, the particle drag force _FL is calculated by the Oseen equation;

When Re>1.5×10 ³ , the particle drag force _FL satisfies:

When 250<Re<1.5×10 ³ , the particle drag force _FL satisfies:

When 20<Re<250, the particle drag force _FL satisfies:

When 10<Re<20, the particle drag force _FL satisfies:

When 0.01<Re<10, the particle drag force _FL satisfies:

When Re < 0.01, the particle drag force _FL satisfies:

where μ is the viscosity, m is the particle density, L is the particle diameter, and _Re is the Reynolds number;

According to the different well conditions of horizontal and vertical wells, calculate the amount of particles entering the pores of horizontal and vertical wells, the total amount of fluid and the pore fluidity, establish a parameter model of nanoparticles with different release rates, directions and sizes, and calculate real-time fluid, nanoparticle velocity and pressure parameters;

The simulation results of the plugging efficiency and drilling fluid invasion in the pore plugging area under different well conditions, different fluid viscosities, and different nanoparticle parameters were calculated. The mud cake is formed on the wellbore, and the fluid entering the pores is the drilling fluid filtrate. Based on the viscosity of the drilling fluid filtrate, not the drilling fluid viscosity, the fluid viscosity is determined based on a microfluidic viscometer, because it is a high-performance water-based drilling fluid suitable for shale gas. The filtrate is very small (less than 1mL), which cannot be measured by ordinary viscosity equipment, and requires a specific instrument to measure its viscosity value). Different nanoparticle parameters include particle size, concentration, speed, dispersion, gradation ratio, gravity, rotation, material density, shape and roughness;

The shale pores plugged by nanoparticles in vertical and horizontal wells are evaluated and analyzed by comparing with the simulation results through theoretical formula derivation verification and experimental verification.

Further, when calculating the amount of particles entering the pores of the horizontal and vertical wells, the total amount of fluid and the pore fluidity, the microscopic pictures of the shale pores perpendicular to the bedding plane and parallel to the bedding plane were analyzed by scanning electron microscopy experiments. Based on statistical data, Summarize porosity ratios between layers to determine total fluid and particle ingress for vertical and horizontal wells. At the same time, based on the permeability experiment (liquid measured permeability), the test determines the permeability of the model perpendicular to the bedding plane and parallel to the bedding plane. Based on the reverse verification of the permeability ratio, the pore fluidity in the model is set, and then the final permeability is determined. Two important parameters, the total amount of fluid and the amount of particles entering, provide an accurate calculation basis for subsequent simulations.

Further, when the tetrahedral mesh and wedge mesh elements based on implicit time integration are used and the boundary conditions and initial conditions of nanoparticles and fluid are set, the pore wall is a fixed wall without slip interface, and the collision of nanoparticles is reflective. , the wall reflection coefficients are divided into normal and tangential systems and the normal contact force between collisions between nanoparticles is based on the spring-dashpot model.

Further, when the tetrahedral mesh and wedge mesh elements based on implicit time integration are used and the boundary conditions and initial conditions of nanoparticles and fluids are set, the mesh fineness is divided based on the randomness of nanoparticle collisions. The tangential contact force of is calculated using the sticking friction coefficient and the sliding friction coefficient,

When v _r ≤ v _glide :

When v _glide ≤ v _r ≤ v _limit :

-μ(v _r )=μ _glide

When v _r > v _limit :

-μ _ratio =(v _r -v _limit )/slope _limit

-μ _ratio = μ _glide / μ _limit

in,

μ _stick is the coefficient of viscous friction;

μ _glide is the sliding friction coefficient;

μ _limit is the high speed limit friction coefficient;

v _glide is the sliding speed, for the low speed state, μ is the quadratic interpolation of μ _stick and μ _glide ;

v _limit is the limiting speed, for high-speed fluid, μ(v _r ) is close to μ _limit ;

The slope _limit is a definite parameter where μ(v _r ) is close to μ _limit .

Further, when establishing the parameter model of nanoparticles with different release rates, directions and sizes, the particle size gradation ratio of nanoparticles is based on the Romm-Ramler classical model. The average particle size of the nanoparticles can be controlled, and the size of the nanoparticles can be adjusted.

Further, when building a parameter model of nanoparticles with different release velocity sizes, directions and sizes, the particle rotation is based on the moving reference frame, and the rotated position and speed of the particles are determined by the new coordinate system under the moving reference frame; the particle cluster model is established, A rectangular coordinate grid is established in the particle collision area, and the length of the grid edge is equivalent to the length of the particle with the largest diameter. This method reduces the amount of calculation sharply and has high calculation efficiency.

Further, when calculating the real-time fluid, nanoparticle velocity and pressure parameters, the particle position and velocity can be calculated through the Runge-Kutta framework. The original ordinary differential equation is regarded as a vector, where the left side is the derivative, and the right side of the equation is an arbitrary function:

The parameters a ₂ -a ₆ , B ₂₁ -b ₆₅ and c ₁ -c ₆ are obtained by Cash and Karp theory.

Furthermore, when calculating the plugging efficiency of the pore plugging area and the simulation results of drilling fluid invasion under different well conditions, different fluid viscosities, and different nanoparticle parameters, the size, concentration, velocity, and density of nanoparticles are set based on the original sphere model.

Further, when calculating the plugging efficiency of the pore plugging area and the simulation results of drilling fluid invasion under different well conditions, different fluid viscosities, and different nanoparticle parameters, the discrete element nanoparticle roughness is determined by the profile arithmetic mean deviation Ra, and the Ra value is determined by TEM experimental measurements of nanoparticles; particle rotation correlates particle roughness and surface friction coefficient.

Further, when calculating the plugging efficiency of the pore plugging area and the simulation results of drilling fluid invasion under different well conditions, different fluid viscosities, and different nanoparticle parameters, the parameters such as nanoparticle gradation ratio, rotation, shape, and roughness are based on the original sphere. Model, Rohm-Ramler model, and moving reference frame model are programmed, and then integrated into the main program of fluid dynamics for calculation.

Compared with the prior art, the present invention provides a multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles. The scheme of the present invention has the following advantages:

(1) In the actual drilling process, there are two types of vertical wells and horizontal wells. The nanoscale discrete element fluid-solid coupling mechanics model established by the present invention can simultaneously simulate nanoparticle plugging under two well conditions.

(2) There are various release modes of nanoparticles, and the average particle size is controllable. For the fluid field and collision field, the mesh fineness and mesh type can be adjusted, and the particle motion capture is more accurate and more in line with the actual situation;

(3) Establish a fluid physical property (viscosity) transformation model, and establish a multi-parameter nanoparticle model, including: particle size, concentration, velocity, dispersion, gradation ratio, gravity, rotation, material density, shape, roughness, almost covering All parameters of the particle, the model has strong applicability.

(4) According to the different well conditions of horizontal wells and vertical wells, the microscopic pictures of shale pores perpendicular to the bedding plane and parallel to the bedding plane are firstly analyzed by scanning electron microscopy experiments. Based on statistical data, the porosity ratio between layers is summarized. Thereby, the total amount of fluid and the amount of particles entering the vertical well and the horizontal well are determined, and then the set pore fluidity (that is, the tortuosity of the bent pipe) is determined by the liquid permeability experiment. Compared with the existing random set bending Pores are more accurate, because it is easy to flow parallel to the bedding, and difficult to flow perpendicular to the bedding, so the setting of the pore fluidity has an important impact on the accuracy of the simulation results.

Description of drawings

Figure 1 is a schematic diagram of a particle collision model;

Figure 2 is a schematic diagram of the nanopore fluid-structure coupling model of horizontal and vertical wells;

Figure 3 is a schematic diagram of the combination of a nanopore fluid-structure coupled wedge mesh and a tetrahedral mesh;

Fig. 4 is the schematic diagram of grid independence verification result;

Fig. 5 is a cloud map of the dynamic stacking calculation for the plugging of nanoparticles in horizontal and vertical wells;

Figure 6 is a schematic diagram showing the comparison of the pressure drop data between the simulated data and the data calculated by the Kozeny-Carman theoretical equation;

Figure 7 is a schematic diagram of the comparison between experimental data and simulated data at different particle concentrations.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following.

Based on the multi-parameter discrete element nanoparticle plugging shale pore numerical simulation method, the simulation is carried out with ANSYS Fluent, EDEM and other software, including the following steps:

S1. Write a program for the drag force on particles at the nanoscale, and modify the standard drag force equation. Since the particles are nanoparticles, the drag force they experience is different from that of particles with conventional sizes. In order to ensure the rationality of the simulation results, the Pruppacher-Steinberger experimental data fitting is based on the Oseen equation of viscous flow at a small Reynolds number. Formula, Dennis and Walker's sphere laminar flow calculation equation, and Goin and Lawrence's formula for drag coefficient of spheres with different sizes, programming and reconstructing the drag force equation of nanoparticles;

In order to ensure rationality, the standard particle drag curve is not directly used, but the modified version of the drag curve is used based on the screening and verification of the available data of spherical particles. The following is the basic principle of modifying the drag force formula:

where μ is the viscosity, m is the particle density, L is the particle diameter, and _Re is the Reynolds number.

With a custom programming function, for _Re < 0.01, the Oseen results are more reliable experimentally verified. The particle collision model is shown in Figure 1.

When Re>1.5×10 ³ , based on Beard’s empirical formula, the particle drag force formula is derived as:

When 250＜Re＜1.5×10 ³ , the formula of particle drag force is derived as:

When 20<Re<250, the formula of particle drag force is derived as:

When 10<Re<20, the formula of particle drag force is derived from two sets of specific data of Pruppacher and Steinberger:

When 0.01＜Re＜10, based on the experimental data, the formula of particle drag force is derived as:

When Re < 0.01, based on the experimental data, the formula of particle drag force is derived as:

Based on the above nanoparticle drag force equation, the fluid-structure interaction model assumes that the pore fluid is continuous and is described by the local Navier-Stoke equation. According to the conservation of mass and momentum equations, the fluid is calculated by the following equations:

是流体的速度，S是从分散的第二相添加到连续相的质量，ρ是静压，

是应力张量，

和

是引力体力和外力。Here, ρ is the density of the fluid,

is the velocity of the fluid, S is the mass added to the continuous phase from the dispersed second phase, ρ is the static pressure,

is the stress tensor,

and

gravitational force and external force.

Integrate the trajectories of discrete-phase particles by means of equilibrium forces written on the particles in the Lagrangian frame of reference. This balancing force equates particle inertia with the force acting on the particle. Re is defined as:

是单位颗粒质量的阻力，ρ_p是颗粒的密度，

是流体相速度，

是颗粒速度，μ是流体的分子粘度，ρ是流体密度，d_p是颗粒直径。Here, F _D is the additional acceleration (force/unit mass) term,

is the resistance per unit particle mass, ρ _p is the particle density,

is the fluid phase velocity,

is the particle velocity, μ is the molecular viscosity of the fluid, ρ is the fluid density, and d _p is the particle diameter.

The Venus-Stokes equations contain virtual mass forces, the first of which is the "virtual mass" force, which is the force that accelerates the fluid around the particle.

where _Cvm is the virtual mass force factor.

When the density of the fluid is much lower than the density of the particles, the virtual mass and pressure gradient forces do not matter, as is the case with liquid/solid particles in a gas flow.

When a fluid has a certain temperature, small particles suspended in a fluid with a temperature gradient are subjected to forces in the opposite direction to the gradient, a phenomenon known as thermophoresis.

where D _T,P is the thermophoretic coefficient.

Meanwhile, for submicron particles, the effect of Brownian motion can optionally be included in the additional force term. The components of Brownian force are modeled as Gaussian white noise processes with spectral intensities:

For submicron particles, the effect of Brownian motion can optionally be included in the additional force term. The component of Brownian force is modeled as a Gaussian white noise process with a spectral intensity of

S _n,ij =S ₀ δ _ij (14)

Among them, δ _ij Kronecker delta function, and the derivation formula of S ₀ is:

where T is the absolute temperature of the fluid, v is the kinematic viscosity, Cc is the Cunningham correction, and k _B is the Boltzmann constant.

S2. Develop tetrahedral meshes and wedge meshes based on implicit time integration, set fluid and nanoparticle boundary conditions and initial conditions; pore walls are fixed walls with no slip interface (Fig. 2), and particle collisions have reflections The wall reflection coefficient is divided into normal and tangential coefficients. The normal contact force between particle collisions is based on the spring-dashpot model, while the tangential contact force between particle collisions is calculated using the sticking friction coefficient and the sliding friction coefficient; the mesh of the model is divided into structured mesh and unstructured mesh grid (Fig. 3), the mesh fineness is divided based on the randomness of particle collision; the tetrahedral mesh is the main mesh, mainly used for fluid flow and particle migration, and the wedge mesh is used as the boundary mesh to distinguish more accurately Boundary layer contact and collision. In addition, the mesh independence calculation is performed to ensure that the meshing is accurate and effective to capture the particle motion characteristics (Fig. 4).

In horizontal and vertical wells, the direction of gravity is perpendicular to the shale bedding plane, so fluids have different effects on shale pores. First, the microscopic pictures of shale pores perpendicular to the bedding plane and parallel to the bedding plane are analyzed based on SEM experiments, and the porosity ratio between layers is summarized based on statistical data, so as to determine the total fluid volume and particle size of vertical wells and horizontal wells amount of entry. In addition, based on permeability experiments, the test determines the permeability of the model perpendicular to the bedding plane and parallel to the bedding plane, and based on the reverse verification of the permeability ratio, the pore fluidity in the model is set. Based on the above experiments and parameters, the particle drag force formula in S1 and the grid settings suitable for this model are used to calculate the dynamic accumulation of particles under different well conditions.

Particle packing models, trajectory equations, and any auxiliary equations describing the transfer of heat or mass by particles are implemented by stepwise integration over discrete time steps. The velocity of the particle at each point on the trajectory, and its trajectory can be calculated by the following equation:

aIncludes acceleration due to all factors other than drag.

For implicit and trapezoidal schemes, the positions of new particles are always computed by trapezoidal discretization:

The particle position and velocity can be calculated through the Runge-Kutta framework. The original ordinary differential equation can be regarded as a vector, where the left side is the derivative and the right side of the equation is an arbitrary function.

Among them, the parameters a ₂ ~ a ₆ , B ₂₁ ~ b ₆₅ and c ₁ ~ c ₆ are obtained by Cash and Karp theory, the above calculation scheme provides an embedded error control, when the "accuracy control" is not enabled, the control will close. For the kinematic reference frame, the integration is performed in the kinematic frame, and the particle force takes into account the additional term of the force in the equation of motion, thus accounting for the system rotation. At the same time, using mechanisms available for precision control, trajectory integration will be done in a timely and accurate manner.

The above calculation method may be inaccurate when there are large steps in particle motion and when the particle is not in hydrodynamic equilibrium with the continuous flow. The implicit and trapezoidal numerical schemes are combined with automatic particle tracking, which takes into account most of the changes in the forces acting on the particles and has strong adaptability.

决定。粒子碰撞力由颗粒的形态决定，变形的程度取决于颗粒之间的重叠。The discrete element method is based on the theory of Cundall and Strack, which explains the forces created by particle collisions. Other forces on the particles are due to

Decide. The particle collision force is determined by the shape of the particles, and the degree of deformation depends on the overlap between the particles.

Particle friction is based on the frictional collision method, which is based on the Coulomb friction equation,

是指与表面垂直的力。摩擦力的方向与相对切向运动相反，并且可能会或可能不会阻止相对切向运动，具体取决于以下内容：切向动量的大小和其他切向力的大小(例如，重力和阻力产生的切向分量)。where μ is the coefficient of friction,

is the force normal to the surface. The frictional force is in the opposite direction of relative tangential motion and may or may not prevent relative tangential motion, depending on the magnitude of the tangential momentum and the magnitude of other tangential forces (e.g., due to gravity and drag) tangential component).

The coefficient of friction is a function of relative tangential velocity magnitude based on different velocity criteria:

When v _r ≤ v _glide :

When v _glide ≤ v _r ≤ v _limit :

-μ(v _r )=μ _glide (31)

When v _r > v _limit :

-μ _ratio = (v _r -v _limit )/slope _limit (32)

-μ _ratio = μ _glide / μ _limit (33)

in,

μ _stick is the coefficient of viscous friction;

μ _glide is the sliding friction coefficient;

μ _limit is the high speed limit friction coefficient;

v _glide is the sliding speed, for the low speed state, μ is the quadratic interpolation of μ _stick and μ _glide ;

v _limit is the limiting speed, for high-speed fluid, μ(v _r ) is close to μ _limit ;

The slope _limit is a definite parameter where μ(v _r ) is close to μ _limit .

The basic parameters of particle, wall and fluid in the model are shown in Table 2:

Table 2 Particle, Wall and Fluid Basic Parameters

S3. Establish particle parameter models with different release velocity sizes, directions and sizes, and calculate real-time fluid, particle velocity and pressure parameters; particle size and size are calculated based on the formula in S2, but nanoparticles will rotate during fluid motion , so the direction has not yet been determined, determine the effect of particle rotation on particle migration based on the following Cartesian rotating coordinate system; establish a particle cluster model, and establish a rectangular coordinate grid in the particle collision area (where the grid edge length and diameter are the largest. The particle lengths are equivalent), evaluate the position, size and direction of the colliding particle clusters, and reduce the calculation amount of the model by half.

还包括由于参考系的旋转而产生的对粒子的力。当对移动框架建模时，产生颗粒旋转力。对于围绕z轴定义的旋转，笛卡尔x和y方向上的粒子上的力可以写为additional force term

Also includes the force on the particle due to the rotation of the reference frame. When modeling a moving frame, particle rotational forces are generated. For a rotation defined around the z-axis, the forces on the particles in the Cartesian x and y directions can be written as

where the particle and fluid velocities in the Cartesian y-direction are up _,y and _uy , respectively, and the particle and fluid velocities in the Cartesian _x -direction are up _,x , and ux, respectively.

S4. Take the viscosity of the drilling fluid filtrate as the fluid viscosity, and calculate the nanoparticle parameters (particle size, concentration, velocity, dispersion, gradation ratio, gravity, rotation, material density, shape, roughness) under different fluid viscosities. The influence of the plugging efficiency of rock pores; first, the particles are released from the initial position, and the released particles have different diameters. The particle diameters are randomly divided into 10 types or more, and the average particle diameter can be set. When the particles enter the pores with the fluid, the particles move forward with the fluid, and then the particles continue to be released. When the particles in the pores gradually increase, the particles will collide with each other, and the particles may also collide with the wall. Every step of the particle movement, including the movement speed, movement trajectory and pressure will be recorded by the system, and the wall pressure will also be recorded. When the occlusion calculation is complete, the particle motion trajectory and its velocity can be reproduced using image post-processing software. It can be seen from Figure 5 that since the particle release area is above the circular channel, most of the particles collide above the outlet cylinder, and the cloud map shows that the top of the outlet cylinder is red. But at this time, the size of the outlet is smaller than that of the inlet, and the particles rebound, and then collide with the particles behind, so as to move toward the outlet together. As the particles continue to increase, the outlet begins to be blocked. The real-time movement trajectory, velocity and particle accumulation status of particles can be calculated and visualized in 3D through the model.

S5. The simulation results are verified by theoretical formula derivation and experimental verification to increase the accuracy and applicability of the model, and finally evaluate and analyze the shale pores plugged by nanoparticles;

Theoretical verification part: the particle flow rate is 0.1 mm/s, and the viscosity μ is 8.9×10 ^-4 Pa·s. Set the model and particle concentration, and monitor the outlet pressure loss. According to the Kozeny–Carman formula, when the average plugging porosity is 0.5 and the same particle stacking thickness is reached, the pressure loss is 53.4Pa. During the simulation calculation, the monitored pressure loss was 52.28Pa. Particles of different concentrations and sizes are released, and the plugging porosity is different. When the same accumulation thickness is reached, the pressure loss at the outlet is monitored, and the results show that the calculated pressure loss is consistent with the simulated pressure loss (Fig. 6);

Experiment verification part: The model and the Kozeny–Carman formula are consistent in the calculation of the pressure loss of solid particle accumulation, which proves the reliability of the model. Comparison of "water-based drilling fluid + 10wt% NPs" VS water-based drilling fluid, "water-based drilling fluid + 5wt% NPs" VS water-based drilling fluid, "water-based drilling fluid + 10wt% NPs" VS "water-based drilling fluid + 5wt% NPs”, and obtained the results of the effect of the solution without nanoparticles and solutions containing nanoparticles but with different concentrations on the plugging efficiency. Comparing the experimental data with the simulated calculation data, the data gap is less than 2% (Fig. 7).

Claims (10)

1. based on the multi-parameter discrete element nanoparticle plugging shale pore numerical simulation method, it is characterized in that: adopt the CFD-DEM coupling method, including, Establish a nanoparticle-fluid coupled flow model suitable for horizontal and vertical wells, the nanoparticle-fluid coupled flow model includes a nanoparticle release region, a nanoparticle-fluid coupled flow region and a pore plugging region, a nanoparticle release region and The pore blocking areas are located at the left and right ends of the nanoparticle-fluid coupled flow area, respectively; Write code to reconstruct the drag force model of nanoparticles in the fluid as follows: When _Re < 0.01, the particle drag force _FL is calculated by the Oseen equation; When Re>1.5×10 ³ , the particle drag force _FL satisfies:

When 250<Re<1.5×10 ³ , the particle drag force _FL satisfies:

When 20<Re<250, the particle drag force _FL satisfies:

When 10<Re<20, the particle drag force _FL satisfies:

When 0.01<Re<10, the particle drag force _FL satisfies:

When Re < 0.01, the particle drag force _FL satisfies:

where μ is the viscosity, m is the particle density, L is the particle diameter, and _Re is the Reynolds number; Adopt tetrahedral mesh and wedge mesh elements based on implicit time integration and set the boundary conditions and initial conditions of nanoparticles and fluid, wherein the main body of nanoparticles and fluid adopts tetrahedral mesh, and the boundary adopts wedge mesh; According to the different well conditions of horizontal and vertical wells, calculate the amount of particles entering the pores of horizontal and vertical wells, the total amount of fluid and the pore fluidity, establish a parameter model of nanoparticles with different release rates, directions and sizes, and calculate real-time fluid, nanoparticle velocity and pressure parameters; Calculate the plugging efficiency and drilling fluid intrusion simulation results in the pore plugging area under different well conditions, different fluid viscosities, and different nanoparticle parameters. Parameters include particle size, concentration, velocity, dispersion, gradation ratio, gravity, rotation, material density, shape and roughness; The shale pores plugged by nanoparticles in vertical and horizontal wells are evaluated and analyzed by comparing with the simulation results through theoretical formula derivation verification and experimental verification. 2. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles according to claim 1, characterized in that: when calculating the amount of particles entering the pores of horizontal wells and vertical wells, the total amount of fluid and the pore fluidity , through SEM experiments to analyze the microscopic pictures of shale pores perpendicular to the bedding plane and parallel to the bedding plane, based on the statistical data, summarize the porosity ratio between the layers, so as to determine the total amount of fluid and particle entry in vertical and horizontal wells Based on the permeability experiment, the test determines the permeability of the model perpendicular to the bedding plane and parallel to the bedding plane, and based on the reverse verification of the permeability ratio, the pore fluidity in the model is set. 3. The numerical simulation method for plugging shale pores with discrete element nanoparticles based on multi-parameter according to claim 1, characterized in that: adopting tetrahedral grid and wedge grid elements based on implicit time integration and setting nanometer When the boundary conditions and initial conditions of particles and fluids are used, the pore wall is a fixed wall with no slip interface, the collision of nanoparticles is reflective, and the wall reflection coefficient is divided into normal and tangential normal contact force between collisions of nanoparticles Based on the spring-dashpot model. 4. The numerical simulation method for plugging shale pores with discrete element nanoparticles based on multi-parameters according to claim 1, characterized in that: adopting tetrahedral grid and wedge grid elements based on implicit time integration and setting nanometer When the boundary conditions and initial conditions of particles and fluids are used, the mesh fineness is divided based on the randomness of nanoparticle collisions, and the tangential contact force between nanoparticle collisions is calculated using the adhesive friction coefficient and the sliding friction coefficient, When v _r ≤ v _glide :

When v _glide ≤ v _r ≤ v _limit : -μ(v _r )=μ _glide When v _r > v _limit : -μ _ratio =(v _r -v _limit )/slope _limit -μ _ratio = μ _glide / μ _limit

in, μ _stick is the coefficient of viscous friction; μ _glide is the sliding friction coefficient; μ _limit is the high speed limit friction coefficient; v _glide is the sliding speed, for the low speed state, μ is the quadratic interpolation of μ _stick and μ _glide ; v _limit is the limiting speed, for high-speed fluid, μ(v _r ) is close to μ _limit ; The slope _limit is a definite parameter where μ(v _r ) is close to μ _limit . 5. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles, characterized in that: when establishing a nanoparticle parameter model with different release velocity sizes, directions and sizes, the nanoparticles The particle size gradation ratio is based on the classic Roehm-Ramler model, and nanoparticles with different particle sizes are established in the nanoparticle release area. 6. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles, characterized in that: when establishing a nanoparticle parameter model with different release velocity sizes, directions and sizes, the particles rotate Based on the moving reference frame, the rotated position and velocity of the particles are determined in the new coordinate system under the moving reference frame; a particle cluster model is established, and a rectangular coordinate grid is established in the particle collision area, where the length of the grid edge is equivalent to the length of the particle with the largest diameter . 7. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles, characterized in that: when calculating real-time fluid, nanoparticle velocity and pressure parameters, particle position and velocity can be calculated by Runge -Kutta framework for calculation, the original ordinary differential equation is regarded as a vector, where the left side is the derivative, and the right side of the equation is an arbitrary function:

Among them, parameters a ₂ -a ₆ , B ₂₁ -b ₆₅ and c ₁ -c ₆ are obtained by Cash and Karp theory. 8. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles according to claim 1, characterized in that: calculating the sealing of pore plugging areas under different well conditions, different fluid viscosities, and different nanoparticle parameters When simulating the plugging efficiency and drilling fluid intrusion, the nanoparticle size, concentration, velocity, and density settings are based on the original sphere model. 9. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles according to claim 1, characterized in that: calculating the sealing of pore plugging areas under different well conditions, different fluid viscosities, and different nanoparticle parameters When simulating the plugging efficiency and drilling fluid intrusion, the discrete element nanoparticle roughness was determined by the arithmetic mean deviation Ra of the profile, and the Ra value was measured by the TEM experiment of the nanoparticle. 10. The multi-parameter-based numerical simulation method for plugging shale pores with discrete element nanoparticles according to claim 1, characterized in that: calculating the sealing effect of the pore plugging area under different well conditions, different fluid viscosities, and different nanoparticle parameters. When simulating results of plugging efficiency and drilling fluid intrusion, the nanoparticle gradation ratio, rotation, shape, and roughness were programmed based on the original sphere model, the Romm-Ramler model, and the moving reference frame model, and then incorporated into the fluid dynamics master model. program to calculate.

Images