CN112199903B - Multi-parameter-based discrete element nanoparticle plugging shale pore numerical simulation method - Google Patents
Multi-parameter-based discrete element nanoparticle plugging shale pore numerical simulation method Download PDFInfo
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Abstract
The invention discloses a numerical simulation method for plugging shale pores by using discrete element nanoparticles based on multiple parameters, which comprises the steps of establishing a nanoparticle-fluid coupling flow model suitable for a horizontal well and a vertical well, adopting tetrahedral mesh and wedge-shaped mesh units based on implicit time integration, setting boundary conditions and initial conditions of nanoparticles and fluid, compiling codes to reconstruct a model of the dragging force of the nanoparticles in the fluid, calculating the nanoparticle amount and the total fluid amount of the pores under different well conditions, establishing nanoparticle parameter models with different release speeds, directions and sizes, calculating parameters such as the speed and the pressure of the fluid and the nanoparticles in real time, and comparing the parameters with simulation results in two modes of derivation verification and experimental verification through theoretical formulas. The simulation result of the simulation method provided by the invention is closer to the actual conditions of a horizontal well and a vertical well, and accurate reference is provided for plugging shale pores by using nanoparticles.
Description
Technical Field
The invention relates to the field of unconventional oil and gas exploration and development technologies and deep geological drilling, in particular to plugging of shale pores, and specifically relates to a numerical simulation method for plugging shale pores by using discrete element nanoparticles based on multiple parameters.
Background
The energy source is a powerful guarantee for the long-term stable development of the economy of China. However, with the continuous consumption of fossil energy, the development difficulty is increasing, the environment protection situation is becoming more severe, and the development of environment-friendly clean energy with large reserves becomes the focus of attention of global scholars and government enterprises. Shale gas is an unconventional energy with huge reserves, is an important ring for realizing a modern multi-energy system, and in 2019, the shale gas is newly added to prove that the geological reserve of 1247 billion cubic meters is hopeful to be a main natural gas source in China beyond the conventional gas. The shale gas is explored and developed, and the shale well wall is maintained to be stable without drilling and drilling fluid in the deep geological drilling process.
The shale gas is explored and developed, and the shale well wall is maintained to be stable without drilling and drilling fluid in the deep geological drilling process. Maintaining the pressure in the well above the pore pressure of the formation (but not above the fracture pressure) is a reasonably safe exploitation mode for shale gas drilling and deep geological drilling. Under such conditions, water-based drilling fluids inevitably invade shale formations.
To solve the above problems, it is desirable to reduce the invasion of drilling fluid as much as possible while maintaining the stability of the borehole wall. Adding the nano material to plug the shale pores is one of effective methods for enhancing the stability of the well wall. Since the nanomaterials are physically matched to the shale nanopores, when the nanoparticles migrate deep into the shale pores, the particles pile up and retard re-invasion of moisture.
However, the plugging effect of the nanoparticle drilling fluid on the shale pores is mostly limited to physical experimental data at present, and a numerical simulation study on the maintenance of the borehole wall stability by plugging the shale pores with the nanoparticles is rarely reported. The migration, dynamic accumulation and micro-plugging mechanisms of the nanoparticles in the drilling fluid after invading the shale pores are not clear.
The experimental data problem is that the nano-scale physical experiment has large difficulty in dynamic observation, high cost and difficulty in success, so that the nano-particle plugging micro mechanism can not be feasible under the current conditions by completely mastering the nano-particle plugging micro mechanism through the nano-scale physical experiment.
In addition, the influence of the porosity, the fluid physical properties and the pore stress makes the mechanism research of the blocking of the shale pores by the nanoparticles more complicated and difficult.
Meanwhile, the nanoparticle plugging model adopted by the predecessor has single particle parameter, and only includes 1 particle parameter, namely the plugging efficiency values calculated by different particle diameters (based on the content disclosed in the prior patent CN 104504192B).
Meanwhile, the research content of the predecessor does not include plugging performance evaluation and model verification brought by the change of the viscosity of the fluid. The above limitations lead to the difficulty in rapidly determining the plugging efficiency of the nanoparticles and the real-time invasion amount of the drilling fluid under different fluid physical characteristics and various particle parameters.
In the actual drilling process of shale gas, two modes of a vertical well and a horizontal well exist, and no technical method can be used for simulating the nanoparticle blocking numerical simulation method under two well conditions at the same time. The technical difficulties are how to determine the amount of particles and fluid entering the vertical well and the horizontal well, how to set the particle release mode, how to set the viscosity of the fluid filtrate entering the pores, how to set the particle parameter diversity, and the like.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the numerical simulation method for the shale pore plugging by the discrete element nanoparticles based on multiple parameters is provided, and the nanoparticle-fluid coupling flow model can be suitable for the pore plugging simulation of horizontal wells and vertical wells. Further, a nanoparticle drag force model in the nanoparticle-fluid coupling flow model is reconstructed in a programming mode, and a selection method of fluid viscosity parameters and a calculation mode of fluid quantity and particle quantity are determined, so that the result obtained by a simulation method is closer to the actual blocking condition.
The technical scheme of the invention is as follows:
a numerical simulation method for plugging shale pores by using discrete element nano particles based on multiple parameters adopts a CFD-DEM coupling method, comprises the following steps,
establishing a nanoparticle-fluid coupling flow model suitable for a horizontal well and a vertical well, wherein the nanoparticle-fluid coupling flow model comprises a nanoparticle release area, a nanoparticle-fluid coupling flow area and a pore blocking area, and the nanoparticle release area and the pore blocking area are respectively positioned at the left end and the right end of the nanoparticle-fluid coupling flow area;
using tetrahedral mesh and wedge mesh units based on implicit time integration and setting boundary conditions and initial conditions of nanoparticles and fluid, wherein the main bodies of the nanoparticles and the fluid are tetrahedral mesh, the boundaries are wedge mesh, and the meshes are subjected to independence verification;
writing codes to reconstruct a model of the drag force of the nanoparticles in the fluid; and (4) writing a dragging force program of the particles under the nanoscale, and modifying a standard resistance equation. Because the particles are nanoparticles, the dragging force of the nanoparticles is different from that of the particles with the conventional size, and in order to ensure the rationality of the simulation result, a particle dragging force equation under the nanoscale is programmed and reconstructed;
when R ise<0.01, particle drag force FLCalculating by an Oseen equation;
when Re > 1.5X 103While, the particle drag force FLSatisfies the following conditions:
when Re is more than 250 and less than 1.5X 103While, the particle drag force FLSatisfies the following conditions:
when 20 < Re < 250, the particle drag force FLSatisfies the following conditions:
particle drag force F when 10 < Re < 20LSatisfies the following conditions:
when Re is more than 0.01 and less than 10, the particle dragging force FLSatisfies the following conditions:
when Re < 0.01, particle drag force FLSatisfies the following conditions:
where μ is viscosity, m particle density, L particle diameter, ReIs the Reynolds number;
aiming at different well conditions of a horizontal well and a vertical well, calculating the particle quantity, the total fluid quantity and the pore circulation degree entering pores of the horizontal well and the vertical well, establishing nanoparticle parameter models with different release speeds, directions and sizes, and calculating real-time fluid and nanoparticle speeds and pressure parameters;
calculating the plugging efficiency of a pore plugging area and the drilling fluid invasion simulation result under different well conditions, different fluid viscosities and different nanoparticle parameters, wherein the fluid viscosity is the viscosity of a high-performance water-based drilling fluid filtrate suitable for a shale gas well (as mud cakes are generated on a well wall, the fluid entering pores is drilling fluid filtrate, the fluid viscosity is determined based on a trace fluid viscosity instrument instead of the drilling fluid viscosity because the high-performance water-based drilling fluid filtrate suitable for shale gas is very little (less than 1mL), common viscosity equipment cannot measure the viscosity and a specific instrument is needed to measure the viscosity), and the different nanoparticle parameters comprise the particle size, the concentration, the speed, the dispersion, the grading proportion, the gravity, the rotation, the material density, the shape and the roughness;
and comparing two modes of theoretical formula derivation verification and experimental verification with the simulation result, and evaluating and analyzing the shale pores of the vertical well and the horizontal well blocked by the nanoparticles.
And further, when the amount of particles entering pores of the horizontal well and the vertical well, the total amount of fluid and the porosity are calculated, analyzing shale pore microscopic pictures vertical to a bedding surface and parallel to the bedding surface through a scanning electron microscope experiment, and summarizing the porosity ratio between layers based on statistical data so as to determine the total amount of fluid and the entering amount of particles of the vertical well and the horizontal well. Meanwhile, based on a permeability experiment (liquid permeability measurement), the permeability of the model perpendicular to the bedding surface and the permeability parallel to the bedding surface are determined through testing, the porosity in the model is set through reverse verification based on the permeability ratio, the final fluid total amount and the final particle entering amount are further determined, and an accurate calculation basis is provided for subsequent simulation.
Further, when a tetrahedral grid and a wedge-shaped grid unit based on implicit time integration are adopted and boundary conditions and initial conditions of the nano particles and the fluid are set, the pore wall surface is a fixed wall surface without a sliding interface, the nano particle collision has reflectivity, and the wall surface reflection coefficient is divided into normal contact force between normal and tangential nano particle collision and is based on a spring-dashpot model.
Further, when tetrahedral mesh and wedge-shaped mesh units based on implicit time integration are adopted and boundary conditions and initial conditions of nanoparticles and fluid are set, mesh fineness is divided based on nanoparticle collision randomness, tangential contact force between nanoparticle collisions is calculated using an adhesive friction coefficient and a sliding friction coefficient,
when v isr≤vglideWhen the method is used:
when v isglide≤vr≤vlimitThe method comprises the following steps:
-μ(vr)＝μglide
when v isr＞vlimitThe method comprises the following steps:
-μratio＝(vr-vlimit)/slopelimit
-μratio＝μglide/μlimit
wherein,
μstickis a coefficient of viscous friction;
μglideis the coefficient of sliding friction;
μlimithigh speed limiting coefficient of friction;
vglideis the sliding velocity, for low velocity states, μ is μstickAnd muglideThe second interpolation of (2);
vlimitto limit the velocity, for high velocity fluids, μ (v)r) Approach to mulimit；
slopelimitIs mu (v)r) Approach to mulimitThe determination parameter of (1).
Further, when the parameter models of the nanoparticles with different release speeds, directions and sizes are established, the particle size grading ratio of the nanoparticles is based on a Rohm-Lamehler classical model, the nanoparticles with different particle sizes are established in a nanoparticle release area, the average particle size of the nanoparticles is controllable, and the size number of the nanoparticles is adjustable.
Further, when a nanoparticle parameter model with different release speeds, directions and sizes is established, particle rotation is based on a moving reference frame, and the position and the speed of the particle after rotation are determined by a new coordinate system under the moving reference frame; and establishing a particle cluster model, and establishing a rectangular coordinate grid in a particle collision area, wherein the edge length of the grid is equivalent to the length of the particle with the largest diameter.
Further, when calculating the real-time fluid, nanoparticle velocity and pressure parameters, the particle position and velocity can be calculated by the Runge-Kutta framework, the original ordinary differential equation is considered as a vector, where the left is the derivative and the right is an arbitrary function:
wherein the parameter a2～a6，B21～b65And c1～c6Obtained by Cash and Karp theory.
Further, when calculating the plugging efficiency of the pore plugging area under different well conditions, different fluid viscosities, different nanoparticle parameters and the drilling fluid invasion simulation result, the nanoparticle size, concentration, velocity, density settings are based on the original spherical model.
Further, when calculating the plugging efficiency of a pore plugging area under different well conditions, different fluid viscosities and different nanoparticle parameters and the simulation result of the drilling fluid invasion amount, the roughness of the discrete element nanoparticles is determined by the arithmetic mean deviation Ra of the profile, and the Ra value is measured by a TEM experiment of the nanoparticles; particle rotation correlates to particle roughness and surface friction coefficient.
Further, when calculating the plugging efficiency of the pore plugging area under different well conditions, different fluid viscosities and different nanoparticle parameters and the drilling fluid invasion simulation result, the parameters such as nanoparticle grade proportion, rotation, shape and roughness are compiled based on an original sphere model, a rum-lamb model and a mobile reference frame model, and then are incorporated into a fluid dynamics main program for calculation.
Compared with the prior art, the invention provides a numerical simulation method for plugging shale pores by using discrete element nanoparticles based on multiple parameters. The scheme of the invention has the following advantages:
(1) in the actual drilling process, a vertical well and a horizontal well exist, and the nano-scale discrete element fluid-solid coupling mechanical model established by the invention can simultaneously simulate the nano-particle plugging under two well conditions.
(2) The nano particles have various release modes and controllable average particle size, the mesh fineness and the mesh type can be regulated and controlled aiming at a fluid field and a collision field, and the particle motion capture is more accurate and more accordant with the actual situation;
(3) establishing a fluid physical property (viscosity) transformation mode and establishing a multi-parameter nanoparticle model, wherein the method comprises the following steps: the particle size, concentration, speed, dispersion, grading proportion, gravity, rotation, material density, shape and roughness almost cover all parameters of the particles, and the model has strong applicability.
(4) Aiming at different well conditions of a horizontal well and a vertical well, shale pore microscopic pictures vertical to a bedding surface and parallel to the bedding surface are analyzed through a scanning electron microscope experiment, based on statistical data, the porosity ratio between the bedding surfaces is summarized, so that the total fluid amount and the particle entering amount of the vertical well and the horizontal well are determined, and then the set porosity (namely the tortuosity of a bent pipeline) is determined through a liquid permeability test.
Drawings
FIG. 1 is a schematic view of a particle collision model;
FIG. 2 is a schematic diagram of horizontal and vertical well nanopore fluid-solid coupling models;
FIG. 3 is a schematic diagram of the combination of a nanoporous fluid-solid coupled wedge-shaped mesh and a tetrahedral mesh;
FIG. 4 is a schematic diagram of a grid independence validation result;
FIG. 5 is a cloud of horizontal and vertical well nanoparticle plugging dynamic packing calculations;
FIG. 6 is a graph of pressure drop data comparing simulated data to data calculated by the Kozeny-Carman theoretical equation;
FIG. 7 is a graphical representation comparing experimental data to simulated data at different particle concentrations.
Detailed Description
The invention will be further described with reference to the accompanying drawings, but the scope of the invention is not limited to the following.
A numerical simulation method for plugging shale pores by using discrete element nanoparticles based on multiple parameters is matched with software such as ANSYS Fluent and EDEM (enhanced dynamic simulation), and comprises the following steps:
s1, writing a dragging force program of the particles under the nanoscale, and modifying a standard dragging force equation. Because the particles are nanoparticles, the dragging force of the nanoparticles is different from that of the particles under the conventional size, and in order to ensure the rationality of a simulation result, a nanoparticle dragging force equation is programmed and reconstructed based on a viscous flow Oseen equation under a small Reynolds number, an experimental data fitting formula of Pruppacher-Steinberger, a sphere laminar flow calculation equation of Dennis and Walker, and a sphere resistance coefficient formula of different sizes proposed by Goin and Lawrence;
to ensure rationality, a standard particle drag curve is not used directly, but a modified version of the drag curve is used based on screening and validation of data available for spherical particles, the rationale for modifying the drag force formula is as follows:
where μ is viscosity, m particle density, L particle diameter, ReIs the reynolds number.
By customizing the programming function for Re<0.01, and experiments prove that the Oseen result is more reliable. The particle collision model is shown in figure 1.
When Re > 1.5X 103And then, based on a Beard empirical formula, a particle dragging force formula is obtained through derivation:
when Re is more than 250 and less than 1.5X 103And then, the formula of the particle dragging force is obtained through derivation:
when 20 < Re < 250, the particle drag force formula is derived as:
when Re is more than 10 and less than 20, the particle drag force formula is derived from two groups of specific data of Pruppacher and Steinberger as follows:
when Re is more than 0.01 and less than 10, based on experimental data, the formula of the particle dragging force is derived as follows:
when Re is less than 0.01, based on experimental data, the formula of the particle dragging force is derived as follows:
based on the nanoparticle drag force equation described above, the fluid-solid coupling model assumes that the pore fluid is continuous and described by the local Navier-Stoke equation. From the conservation of mass equation and the conservation of momentum equation, the fluid is calculated by the following equation:
where p 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, p is the static pressure,
is the tensor of the stress(s),
and
is the physical force of gravitation and external force.
The trajectories of the discrete phase particles are integrated by the equilibrium forces written on the particles in the lagrange reference system. This balancing force equates the particle inertia to the force acting on the particle. Re is defined as:
here, FDIs an additional acceleration (force/unit mass) term,
is the resistance per unit mass of the particle, ppIs a granuleThe density of the particles is such that,
is the velocity of the fluid phase and,
is the particle velocity, μ is the molecular viscosity of the fluid, ρ is the fluid density, dpIs the particle diameter.
The wiener stokes equation contains virtual mass forces, the first of which is the "virtual mass" force, which is the force that accelerates the fluid around the particle.
Wherein, CvmIs 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 are not important, as are the liquid/solid particles in the gas stream.
When a fluid has a certain temperature, small particles suspended in the fluid with a temperature gradient are subjected to a force in the opposite direction to the gradient, a phenomenon known as thermophoresis.
Wherein D isT,PThe thermophoretic coefficient.
Meanwhile, for submicron particles, the influence of brownian motion may optionally be included in the additional force term. The component of the brownian force is modeled as a gaussian white noise process with spectral strength:
for sub-micron particles, the influence of brownian motion may optionally be included in the additional force term. The component of the Brownian force is modeled as a Gaussian white noise process with a spectral strength of
Sn,ij＝S0δij (14)
Wherein, deltaijCloneckerThe function of the delta, and S0The derivation formula is:
wherein T is the absolute temperature of the fluid, v is the kinematic viscosity, Cc is the Canning correction, kBBoltzmann constant.
S2, developing tetrahedral grid and wedge-shaped grid units based on implicit time integration, and setting boundary conditions and initial conditions of fluid and nano particles; the pore wall surface is a fixed wall surface without a slip interface (figure 2), particle collision has reflectivity, and the wall surface reflection coefficient is divided into a normal coefficient and a tangential coefficient. 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 and sliding friction coefficients; the mesh of the model is divided into structured mesh and unstructured mesh (fig. 3), and the mesh fineness is divided based on the particle collision randomness; tetrahedral meshes are body meshes, primarily used for fluid flow and particle migration, and wedge meshes are used as boundary meshes to more accurately distinguish boundary layer contacts and collisions. In addition, grid independence calculation is performed to ensure accurate and effective capture of particle motion characteristics by grid division (fig. 4).
Under the conditions of horizontal wells and vertical wells, the gravity direction is vertical to the shale bedding surface, so that the influence of the fluid on the shale pores is different. Firstly, analyzing shale pore microscopic pictures vertical to a bedding surface and parallel to the bedding surface based on a scanning electron microscope experiment, and summarizing the porosity ratio between the bedding surfaces based on statistical data, thereby determining the total fluid amount and the particle entering amount of a vertical well and a horizontal well. In addition, based on permeability experiments, the permeability of the model perpendicular to the bedding plane and the permeability parallel to the bedding plane are determined through testing, and the porosity circulation degree in the model is set through reverse verification based on the permeability ratio. Based on the above experiments and parameters, the particle dynamic stacking number under different well conditions is calculated through the particle drag force formula in S1 and the mesh setting suitable for the model.
The particle packing model, trajectory equations, and any ancillary equations describing the heat or mass transfer of the 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 from the following equation:
a includes accelerations due to all other factors except resistance.
For implicit and trapezoidal schemes, the position of the new particle is always computed by the trapezoidal discretization:
the particle position and velocity can be calculated by the Runge-Kutta framework, and the original ordinary differential equation can be regarded as a vector, where the derivative is on the left and an arbitrary function is on the right.
Wherein the parameter a2～a6，B21～b65And c1～c6Derived from the Cash and Karp theories, the above calculation scheme provides an embedded error control that will shut down when the "accuracy control" is not enabled. For a motion reference system, the integration is performed in the motion system, and the particle force accounts for the force extra term in the motion equation, thus taking into account the system rotation. At the same time, using mechanisms that can be used for precision control, trajectory integration will be completed accurately in time.
The above calculation method may not be accurate in cases where there are large steps of particle motion and where the particles are not in hydrodynamic equilibrium with the continuous flow. Implicit and trapezoidal numerical schemes are combined with automatic tracking of the particles, most of the changes of the force acting on the particles are considered, and the method has high adaptability.
The discrete element method is based on the Cundall and Strack theory, which explains the forces generated by particle collisions. Other forces to which the particles are subjected
And (6) determining. The collision force of the particles is determined by the morphology of the particles, and the degree of deformation depends on the particleThe overlap between them.
The particle friction is based on the friction-collision method, whereas the law of friction-collision is based on the coulomb friction equation,
wherein, mu is a friction coefficient,
refers to a force normal to the surface. The direction of the frictional force is opposite to the relative tangential movement and may or may not impede the relative tangential movement, depending on: the magnitude of the tangential momentum and the magnitude of other tangential forces (e.g., the tangential components due to gravity and drag).
The friction coefficient is a function of the magnitude of the relative tangential velocity based on different velocity criteria:
when v isr≤vglideThe method comprises the following steps:
when v isglide≤vr≤vlimitThe method comprises the following steps:
-μ(vr)＝μglide (31)
when v isr＞vlimitThe method comprises the following steps:
-μratio＝(vr-vlimit)/slopelimit (32)
-μratio＝μglide/μlimit (33)
wherein,
μstickis a coefficient of viscous friction;
μglideis the coefficient of sliding friction;
μlimithigh speed limiting coefficient of friction;
vglideis the sliding velocity, mu is mu for the low velocity regimestickAnd muglideThe quadratic interpolation of (2);
vlimitto limit the velocity, for high velocity fluids, μ (v)r) Approach to mulimit；
slopelimitIs mu (v)r) Approach to mulimitThe determination parameter of (2).
The particle, wall and fluid basis parameters in the model are shown in table 2:
TABLE 2 particle, wall and fluid basis parameters
S3, establishing particle parameter models with different release speeds, directions and sizes, and calculating real-time fluid, particle speed and pressure parameters; the particle size and size are calculated based on the formula in S2, but the nanoparticles rotate during the movement of the fluid, so the direction is not determined, and the influence of the particle rotation on the particle migration is determined based on the following Cartesian rotation coordinate system; and establishing a particle cluster model, establishing a rectangular coordinate grid (wherein the length of the edge of the grid is equivalent to the length of the particle with the largest diameter) in a particle collision area, evaluating the position, the size and the direction of a collision particle cluster, and reducing half of calculated amount of the model.
Additional force item
But also forces on the particles due to the rotation of the reference frame. When modeling the moving frame, particle rotational forces are generated. For a rotation defined around the z-axis, the forces on the particle in the cartesian x and y directions can be written as
Wherein the particle and fluid velocities in the Cartesian y-direction are u, respectivelyp,yAnd uyAnd the particle and fluid velocities in the Cartesian x-direction are u, respectivelyp,xAnd ux。
S4, taking the viscosity of the filtrate of the drilling fluid as the fluid viscosity, and calculating the influence of the parameters (particle size, concentration, speed, dispersion, grading proportion, gravity, rotation, material density, shape and roughness) of the nanoparticles on the plugging efficiency of the shale pores under different fluid viscosities; first, particles are released from an initial position, the diameters of the released particles are different, the diameters of the particles are randomly divided into 10 or more, and the average diameter of the particles can be set. When particles enter the pore channel along with the fluid, the particles move forwards along with the fluid, then the particles are released continuously, when the particles in the pores gradually increase, the particles collide with each other, and the particles can also collide with the wall surface. Each step of particle movement, including speed, trajectory and pressure, is recorded by the system, as is wall pressure. When the plugging calculation is finished, the particle motion trajectory and the velocity thereof can be reproduced by using image post-processing software. As can be seen from fig. 5, since the particle release area is above the circular aperture, most of the particles hit the outlet cylinder, which is shown in the cloud above the outlet cylinder in red. But the outlet size is smaller than the inlet size, so that the particles rebound and collide with the particles behind, and then move towards the outlet direction together, and the outlet begins to be blocked along with the increase of the particles. The real-time movement track, speed and particle accumulation condition of the particles can be calculated and visualized in three dimensions through a model.
S5, the simulation result is subjected to deduction verification and experimental verification through a theoretical formula, so that the accuracy and the applicability of the model are improved, and finally evaluation and analysis are performed on the pore of the shale blocked by the nano particles;
and a theoretical verification part: the flow rate of the particles was 0.1mm/s and the viscosity, μ, was 8.9X 10-4Pa · s. The exit pressure loss was monitored by setting the model and particle concentration and was 53.4Pa for the same particle packing thickness when the average plug porosity was 0.5 according to the Kozeny-Carman formula. During the simulation calculation, a pressure loss of 52.28Pa was monitored. Releasing particles with different concentrations and sizes, and monitoring the pressure loss of an outlet when the plugging porosity is different, wherein the calculated pressure loss is consistent with the simulated pressure loss (figure 6) as a result;
experimental verification section: the model is consistent with the Kozeny-Carman formula in the calculation of pressure loss of solid particle packing, and the reliability of the model is proved. Comparing the ' water-based drilling fluid +10 wt% NPs ' VS water-based drilling fluid, ' water-based drilling fluid +5 wt% NPs ' VS water-based drilling fluid, ' water-based drilling fluid +10 wt% NPs ' VS water-based drilling fluid +5 wt% NPs ', and obtaining the influence results of the solution without the nano-particles and the solution containing the nano-particles but with different concentrations on the plugging efficiency. Comparing the experimental data with the simulated data, the data difference was less than 2% (fig. 7).
Claims (10)
1. A numerical simulation method for plugging shale pores by using discrete element nanoparticles based on multiple parameters is characterized by comprising the following steps: the CFD-DEM coupling method is adopted, including,
establishing a nanoparticle-fluid coupling flow model suitable for a horizontal well and a vertical well, wherein the nanoparticle-fluid coupling flow model comprises a nanoparticle release area, a nanoparticle-fluid coupling flow area and a pore blocking area, and the nanoparticle release area and the pore blocking area are respectively positioned at the left end and the right end of the nanoparticle-fluid coupling flow area;
writing code reconstructs the model of the drag force of the nanoparticles in the fluid as follows:
when R ise<0.01, particle drag force FLCalculating by an Oseen equation;
when Re > 1.5X 103While, the particle drag force FLSatisfies the following conditions:
when Re is more than 250 and less than 1.5X 103While, the particle drag force FLSatisfies the following conditions:
particle drag force F when 20 < Re < 250LSatisfies the following conditions:
particle drag force F when 10 < Re < 20LSatisfies the following conditions:
when Re is more than 0.01 and less than 10, the particle dragging force FLSatisfies the following conditions:
when Re < 0.01, particle drag force FLSatisfies the following conditions:
where μ is viscosity, m particle density, L particle diameter, ReIs the Reynolds number;
using tetrahedral mesh and wedge mesh units based on implicit time integration and setting boundary conditions and initial conditions of the nanoparticles and the fluid, wherein the main bodies of the nanoparticles and the fluid are tetrahedral mesh, and the boundaries are wedge mesh;
aiming at different well conditions of a horizontal well and a vertical well, calculating the particle quantity, the total fluid quantity and the pore circulation degree entering pores of the horizontal well and the vertical well, establishing nanoparticle parameter models with different release speeds, directions and sizes, and calculating real-time fluid and nanoparticle speeds and pressure parameters;
calculating the plugging efficiency of a pore plugging area and the drilling fluid invasion simulation result under different well conditions, different fluid viscosities and different nanoparticle parameters, wherein the fluid viscosity is the viscosity of a water-based drilling fluid filtrate suitable for a shale gas well, and the different nanoparticle parameters comprise particle size, concentration, speed, dispersion, grading proportion, gravity, rotation, material density, shape and roughness;
and comparing two modes of theoretical formula derivation verification and experimental verification with the simulation result, and evaluating and analyzing the shale pores of the vertical well and the horizontal well blocked by the nanoparticles.
2. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the particle amount, the fluid total amount and the pore circulation degree entering pores of the horizontal well and the vertical well are calculated, shale pore microscopic pictures perpendicular to a bedding surface and parallel to the bedding surface are analyzed through a scanning electron microscope experiment, the porosity ratio between the bedding surfaces is summarized based on statistical data, so that the fluid total amount and the particle entering amount of the vertical well and the horizontal well are determined, the permeability of the model perpendicular to the bedding surface and the permeability of the model parallel to the bedding surface are determined through testing based on a permeability experiment, and the pore circulation degree in the model is set through reverse verification based on the permeability ratio.
3. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the tetrahedral mesh and the wedge-shaped mesh unit based on implicit time integration are adopted and the boundary condition and the initial condition of the nano particles and the fluid are set, the pore wall surface is a fixed wall surface without a sliding interface, the nano particle collision has reflectivity, and the wall surface reflection coefficient is divided into a normal contact force between a normal direction and a tangential system nano particle collision and is based on a spring-dashpot model.
4. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when tetrahedral mesh and wedge-shaped mesh units based on implicit time integration are adopted and boundary conditions and initial conditions of nanoparticles and fluid are set, the mesh fineness is divided based on the nanoparticle collision randomness, the tangential contact force between nanoparticle collisions is calculated by using the sticking friction coefficient and the sliding friction coefficient,
when v isr≤vglideThe method comprises the following steps:
when v isglide≤vr≤vlimitThe method comprises the following steps:
-μ(vr)＝μglide
when v isr＞vlimitThe method comprises the following steps:
-μratio＝(vr-vlimit)/slopelimit
-μratio＝μglide/μlimit
wherein,
μstickis the coefficient of viscous friction;
μglideis a coefficient of sliding friction;
μlimithigh speed limiting coefficient of friction;
vglideis the sliding velocity, mu is mu for the low velocity regimestickAnd muglideThe second interpolation of (2);
vlimitto limit the speed, forHigh velocity fluid, mu (v)r) Approach to mulimit；
slopelimitIs mu (v)r) Approach to mulimitThe determination parameter of (1).
5. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the nanoparticle parameter models with different release speed, direction and size are established, the nanoparticle size fraction ratio is based on the Rohm-Lamehler classical model, and nanoparticles with different particle size are established in the nanoparticle release region.
6. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when a nanoparticle parameter model with different release speed sizes, directions and sizes is established, particle rotation is based on a moving reference frame, and the position and the speed of the particle after rotation are determined by a new coordinate system under the moving reference frame; and establishing a particle cluster model, and establishing a rectangular coordinate grid in a particle collision area, wherein the edge length of the grid is equivalent to the length of the particle with the largest diameter.
7. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when calculating the real-time fluid, nanoparticle velocity and pressure parameters, the particle position and velocity can be calculated by the Runge-Kutta framework, the original ordinary differential equation is considered as a vector, where the left side is the derivative and the right side is an arbitrary function:
wherein, the parameter a2～a6，B21～b65And c1～c6Obtained by Cash and Karp theory.
8. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the plugging efficiency of the pore plugging area and the drilling fluid invasion simulation result under different well conditions, different fluid viscosities and different nanoparticle parameters are calculated, the nanoparticle size, concentration, speed and density settings are based on the original spherical model.
9. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the plugging efficiency of a pore plugging area and the simulation result of the drilling fluid invasion amount under different well conditions, different fluid viscosities and different nanoparticle parameters are calculated, the roughness of the discrete element nanoparticles is determined by the arithmetic mean deviation Ra of the profile, and the Ra value is measured by a TEM experiment of the nanoparticles.
10. The numerical simulation method for plugging shale pores based on multi-parameter discrete element nano particles according to claim 1, wherein the numerical simulation method comprises the following steps: when the plugging efficiency of a pore plugging area and the drilling fluid invasion simulation result under different well conditions, different fluid viscosities and different nanoparticle parameters are calculated, the nanoparticle grade proportion, the rotation, the shape and the roughness are compiled based on an original sphere model, a Rohm-Lameller model and a moving reference frame model, and then are incorporated into a fluid dynamics main program for calculation.
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