CN116306186B - Active nanoparticle oil/water interface adsorption-diffusion behavior simulation method and device - Google Patents
Active nanoparticle oil/water interface adsorption-diffusion behavior simulation method and device Download PDFInfo
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Abstract
The invention discloses an active nanoparticle oil/water interface adsorption-diffusion behavior simulation method and device, which relate to the field of petroleum and natural gas exploitation and comprise the following steps: simulating water flooding through a color gradient model in a Boltzmann method, simulating the movement process of active nano particles at a water phase and an oil/water interface through a Langmuir kinematic method, constructing an action relationship between fluid and the active nano particles, realizing coupling between the active nano particles and the fluid, and establishing a mutual influence relationship between the active nano particles and a speed field and an energy field between the fluid; inputting parameters such as radius, main control group, concentration, injection flow rate and the like of the active nano particles into the model, describing the adsorption characteristics of the active nano particles at an oil/water interface, and distinguishing the difference of diffusion characteristics of the active nano particles in an aqueous phase and the oil/water interface. Further guiding the structural performance design and the field use of the active nanoparticle oil displacement material, and promoting the economic and effective and sustainable development of the hypotonic/ultra hypotonic oil reservoir in China.
Description
Technical Field
The invention relates to the field of petroleum and natural gas exploitation, in particular to an active nanoparticle oil/water interface adsorption-diffusion behavior simulation method and device.
Background
The active nano particles have important significance for improving the recovery ratio of low-permeability/ultra-low-permeability oil reservoirs in China, but the oil displacement mechanism of the active nano particles is still unclear at present. The traditional microscopic experiment has the problems of large design difficulty, high experiment cost, unknown mechanism representation and the like, and the numerical simulation is used as a means to establish an active nano particle/oil/water multiphase seepage coupling model, so that the precision and the efficiency are both considered.
The lattice Boltzmann method (lattice Boltzmann method, LBM) is a mesoscale simulation method, has unique advantages in simulating oil-water two-phase flow, and has natural parallelism. The lattice Boltzmann color gradient model allows the surface tension, the density ratio and the viscosity ratio of various fluids at two sides of an interface to be independently controlled, and the contact angle and the wetting behavior of a solid phase to be controlled, so that the lattice Boltzmann color gradient model is more suitable for oil-water two-phase simulation. For particle simulation, langevin kinematics (Langevin dynamics, LD) can characterize the interaction between particles, the effects of thermal fluctuations, and the dynamic behavior of particle and fluid interactions by creating langevin equations.
The device constructs an active nanoparticle/water two-phase simulation method through the two methods, and provides a method guidance for a microscopic mechanism of drag reduction and enhancement of the active nanoparticle in a hypotonic or ultra-hypotonic oil reservoir.
However, the behavior characteristics of active nano particles at oil/water phases, particularly at oil/water interfaces, are still unknown, and the on-site production lacks theoretical guidance and equipment support.
Disclosure of Invention
The first object of the present invention is to provide a method and a device for simulating the adsorption-diffusion behavior of an active nanoparticle oil/water interface, which are used for solving the problem that the characteristic of the adsorption-diffusion behavior of the active nanoparticle oil/water interface is unclear.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an active nanoparticle oil/water interface adsorption-diffusion behavior simulation method comprises the following steps:
step one: simulating water flooding by using a color gradient model in a lattice Boltzmann method, and accurately simulating the water flooding model by accurately describing parameters such as wetting angle, interfacial tension and the like; simulating the motion process of the active nano particles in the water phase and the oil/water interface by using a Langmuir kinematic method, and describing the electrostatic force, van der Waals force, random force and friction force of the active nano particles in the fluid in detail from the force perspective; the acting force of the active nano particles on the fluid is taken as a bridge, the acting relationship between the fluid and the active nano particles is constructed, the coupling between the active nano particles and the fluid is realized, and the interaction relationship between the active nano particles and the velocity field and the energy field between the active nano particles and the fluid is established; the method specifically comprises the following steps:
101 on the basis of a D2Q9 model, establishing a lattice Boltzmann equation (1) based on the D2Q9 model by introducing a color gradient model to realize the simulation of oil/water two phases;
in the method, in the process of the invention,as a particle distribution function, t is the particle movement time, c is the grid movement speed, c=Δx/Δt, Δx is the unit grid length, Δt is the unit time step, τ is the single relaxation time to reach equilibrium, +.>Is the particle velocity direction, f i eq Is a particle equilibrium distribution function;
102, using langevin kinematics, the particle motion simulation is implemented by applying additional force to the tiny particles in the fluid system, and the control equation is:
wherein i is the serial number of the active nano-particles,for active nanoparticle mass, < >>Is aliveThe velocity of the nano-particles,friction force to the active nanoparticle +.>Random forces to which the active nanoparticle is subjected, +.>Respectively represent Van der Waals force between the active nano particles, between the active nano particles and the wall surface, and->Electrostatic force to the active nanoparticle;
103 achieve interaction between the active nanoparticle and the fluid by the universal coupling of lattice Boltzmann-lang, the coupling equation being:
in the method, in the process of the invention,is the total force of the fluid on the active nanoparticle; />Is a friction component; />Is a random component;
step two: on the basis of establishing an effective active nanoparticle water flooding model, describing the adsorption characteristic of the active nanoparticle at an oil/water interface and the influence of the active nanoparticle on the interfacial tension, and distinguishing the difference of the diffusion characteristic of the active nanoparticle in an aqueous phase and an oil/water interface, wherein the specific steps are as follows:
201 by analyzing the force and presence of active nanoparticles at oil/water interfacesThe difference of the water phases realizes the motion depiction of the active nano particles in the oil-water phase and the water phase; by introducing Langmuir adsorption equation and particle adsorption interference coefficient A f Further characterizing its effect on oil/water interfacial tension;
202 analyzing the influence of the oil/water interface on the diffusion of the active nano particles by calculating the difference of the diffusion coefficients of the active nano particles in the horizontal and vertical directions in the water phase and the oil/water interface;
step three: according to the constructed microscopic characterization method of the active nanoparticle oil/water interface adsorption, analyzing main control factors influencing the active nanoparticle oil/water interface adsorption by changing the fluid injection speed, the active nanoparticle injection concentration and the particle size; and constructing an active nanoparticle water flooding parameter design and performance evaluation device, inputting active nanoparticle parameters into the device, and preferably using the active nanoparticles on site.
Preferably, the interfacial tension is introduced by a continuous surface force method, the continuous surface tension formula being as follows:
wherein sigma is the interfacial tension,is color gradient, and κ is interface curvature;
after the continuous surface tension is obtained, the external force term phi can be obtained i ，Φ i Can be determined by equation (5):
in the middle ofTo take into account the redefined flow rate after continuous surface force, its value is:
preferably, the formula of the color function is:
in the formula, when a certain lattice point ρ N When the liquid is 1, the liquid is red liquid, when the liquid is-1, the liquid is blue liquid, and when the liquid is-1 and 1, the liquid is red and blue at the same time;
the interface curvature is determined by equation (8);
in which the unit normal vector
Preferably, in step one, the wetting boundary is built by geometric means, the color gradient model introduces the contact angle by special treatment of the upper and lower boundaries by equation (9):
in theta w =tan (pi/2- θ); θ is the contact angle;the direction is a unit normal vector pointing to the wall surface of the fluid, and the direction is dimensionless; />The direction is a unit tangential vector pointing to the wall surface of the fluid, and the direction is dimensionless; the color functions of the upper wall surface and the lower wall surface are determined by the formulas (10) and (11):
in the method, in the process of the invention,is the color function of the upper and lower walls>Is a function of the color of the fluid node immediately adjacent to the upper and lower walls.
Preferably, the amount of friction experienced by the active nanoparticle is proportional to the difference between the velocity of the active nanoparticle and the velocity of the surrounding fluid, as determined by equation (12):
wherein friction coefficient ζ=3ρμ d p ψ, where μ is the fluid viscosity around the active nanoparticle, and if the active nanoparticle is in the aqueous phase, μ is the viscosity of the water taken up by μ, i.e., μ=μ w If at the oil/water interface, a color function ρ needs to be introduced N Viscosity of oil and water mu o Sum mu w Respectively processing d p Is the particle size of the active nano particles, and psi is the shape factor;
wherein the thermal motion of the particles is through a random force termIntroducing, the random force term is obtained by the formula (13):
wherein, alpha, beta epsilon { x, y }; delta is the Croneck function, k B Represents Boltzmann constant, T representsAbsolute temperature of fluid;
the saidDetermined by equation (14):
in the method, in the process of the invention,represents the vector distance between two active nanoparticles, < >>Van der Waals potential energy between two active nano particles is vector distance +.>Is a function of (2);
the saidDetermined by equation (15):
wherein A is cc Is Hamaker constant, d p In order to be the diameter of the active nanoparticle,the vertical distance between the particles and the upper and lower wall surfaces; due to the difference between the aqueous phase and the oil/water interface, when the stress of the active nanoparticle at the oil/water interface is considered, the Hamaker constant needs to be recalculated, and the expression is as follows:
wherein ε w 、ε o 、ε p Dielectric constants of water, oil and active nano particles respectively, n w 、n o 、n p Respectively water, oil and active nano particles, wherein h is the Planck constant; v (v) e Is the adsorption frequency;
the electrostatic force to which the active nanoparticle is subjected is divided into electrostatic forces between particlesElectrostatic force between particle and wall>The calculation formula is as follows:
where κ is the reciprocal of the debye length, Z is the interaction constant, and Z is determined by equation (19):
Z＝64πε o ε(k B T/e) 2 tanh 2 (ze/4k B T) (19)
wherein z is the electrolyte valence, ε 0 Is vacuum dielectric constant, epsilon is water relative dielectric constant;
preferably, the lattice Boltzmann and Langmuir kinematics method is coupled in step 103 to separate the fluid forces exerted on the active nanoparticles into a friction component and a random component:
in the formula (20)Is the total force of the fluid on the active nanoparticle;
to maintain conservation of momentum, pulse density is defined:
particle swarm position, same as before; />Active nanoparticle positions;
and adding the force source item distribution function into an evolution equation of the water phase to finish the coupling of the active nano particles and the fluid.
Preferably, the adsorption capacity of the active nanoparticle in step 201 is determined, that is: the energy change of the active nanoparticles to the left and right of the oil/water interface into the oil/water interface is determined by equation (22):
where Δw represents the energy change, A, B, C is a parameter representing the properties of water, oil, and active nanoparticles, respectively, and less than 0 represents that the process can proceed spontaneously and more than 0 represents that the process cannot proceed spontaneously.
Preferably, in step 202, the desorption capacity of the active nanoparticle from the interface is determined by Binks' equation for the adsorption energy of the solid particle on the interface:
E＝πr 2 γ(1+cosθ) 2 (23)
wherein r is the radius of the particle, gamma is the interfacial tension, and theta is the contact angle;
adsorption interference coefficient A f (A f The langmuir adsorption equation, corrected for =54.6%), is an interfacial tension-concentration relationship that takes into account the repulsive force of the active nanoparticles and surface non-uniformityEquation, constructing an active nanoparticle oil/water interface unbalanced adsorption equation:
σ(t)＝σ 0 {1+E 0 ln[1-ζ(t)ω(t)]} (24)
wherein omega is the saturation rate of the interfacial active nano-particles,ζ is interfacial adsorption strength, calculated from the following formula:
wherein τ r For the unbalance time of the active nanoparticle system, the value of the index n is related to the individual particle unbalance time τ e The correlation is a time scaling effect at a specific unbalance time. The above equation can thus be written as the equation application result is shown in fig. 3.
Preferably, the mean square displacement is a parameter for measuring the time-dependent change of the position of the active nanoparticle at a certain moment, and the relationship between the mean square displacement and time is as follows:
<Δx(t) 2 >＝2Dt (27)
wherein Δx is the displacement of the active nanoparticle; represents the mean of a plurality of active nanoparticles; d is the diffusion coefficient of the active nano particles;
the mean square displacement of each active nanoparticle is determined by the following formula:
wherein MSD is mean square displacement of a certain active nano particle, N is time interval, N t Is the association time;
calculating diffusion coefficient variation coefficients of different time intervals under the optimal correlation time by the formula (29):
the second object of the present invention is to provide an active nanoparticle oil/water interface adsorption-diffusion behavior simulation device, which is used for solving the problems of lack of theoretical guidance and equipment support for the behavior of active nanoparticles at oil/water phases, particularly at oil/water interfaces, and on-site production.
In order to achieve the above purpose, the technical solution adopted is as follows:
an active nanoparticle oil/water interface adsorption-diffusion behavior simulation device comprises
The oil reservoir parameter updating module is controlled by a grid Boltzmann color gradient model program, and the parameters are specific to a certain layer and comprise parameters such as oil reservoir temperature, oil reservoir pressure, main pore size, pore length, crude oil viscosity, density, components and the like;
the nano fluid parameter updating module is used for simultaneously updating the density, viscosity and interfacial tension of the oil reservoir injection fluid according to the parameters such as the radius, main groups, concentration, injection flow rate and injection position of the active nano particles by a Langmuir dynamics method and calculating Van der Waals force, electrostatic force, friction force and random force between the active nano particles and the fluid and wall surface;
the active nanoparticle/fluid coupling module is used for respectively calculating the motion states of the active nanoparticle and the fluid lattice through the coupling method, coupling the active nanoparticle and the fluid lattice through a force source item distribution function, outputting the motion conditions of the active nanoparticle and an oil/water two-phase (oil/water interface) in real time, returning an input result to the nanofluid parameter updating module, and further calculating the stress conditions of the active nanoparticle and the fluid;
the adsorption judging module judges whether the active nano particles can be adsorbed on an oil-water interface according to the properties of the active nano particles and the oil/water interface, and if so, the active nano particles enter the desorption judging module; if not, entering an active nanoparticle parameter optimization module;
the desorption judging module judges whether the active nano particles can be desorbed from the interface according to the properties of the active nano particles adsorbed on the oil/water interface, and if so, the active nano particles enter the active nano particle parameter optimizing module; if not, entering an oil/water interface tension calculation module;
the oil/water interface tension calculation module calculates the oil/water interface tension in real time according to the adsorption quantity and the property of the oil/water interface active nano particles and the modified Langmuir adsorption equation, and outputs a calculation result;
the diffusion coefficient calculation module is used for describing the distribution condition of the active nano particles in the fluid by solving the diffusion coefficient of the active nano particles at the interface of the water phase and the oil/water, so as to further guide the parameter design of the active nano particles;
and the active nanoparticle parameter optimization and performance evaluation module is used for comprehensively evaluating the action effect of the active nanoparticles in the oil reservoir according to the output results of the oil/water interface tension calculation module and the active nanoparticle diffusion calculation module, further optimizing the performance parameters of the active nanoparticles and inputting the optimized parameters into the nanofluid parameter updating module.
The invention has the beneficial effects that:
the invention builds a lattice Boltzmann-Lang's ten thousand model based on a color gradient model, can truly describe the physical scene of active nanoparticle fluid displacement of reservoir oil, and effectively supplements the still lacking multi-phase flow simulation method of active nanoparticle oil/water under the condition of hypotonic/ultra hypotonic reservoir at home and abroad. The adsorption behavior of the oil/water interface of the active nano particles is analyzed and researched, and the repulsive force among the active nano particles, the surface non-uniformity and the influence of unbalanced adsorption of the active nano particles on the oil/water interface are comprehensively considered. The active nanoparticle diffusion behavior was further analyzed and the residual oil formation mechanism was further explained. And constructing an active nanoparticle parameter optimization and performance evaluation device based on the constructed lattice Boltzmann-Lang multi-phase microscopic simulation of the active nanoparticle/oil/water based on the color gradient model. The method comprises the steps of obtaining the capability of the active nano particles for reducing the interfacial tension of oil/water, the occurrence state of residual oil and the diffusion characteristic by inputting the parameters of the active nano particles and the basic parameters of an oil reservoir, obtaining the optimal parameters of the active nano particles by continuous iterative optimization, and guiding the chemical synthesis of the active nano particles and the use of the active nano particles on site.
Drawings
FIG. 1 is a flow chart of a method for multi-phase simulation of LB-LD based active nanoparticle oil/water in accordance with the present invention;
FIG. 2 is a schematic diagram of oil-water two phases of coupled nanoparticles of the present invention;
FIG. 3 is a graph of predicted oil/water interfacial tension in accordance with the present invention;
FIG. 4 is a schematic representation of the trajectory tracking of the aqueous phase (a) and the oil/water interface (b) of the nanoparticle of the present invention;
FIG. 5 is a schematic diagram of an active nanoparticle oil/water two-phase flow simulation device of the present invention.
Detailed Description
The present invention will be explained in detail below with reference to the accompanying drawings. The invention provides an active nanoparticle oil/water interface adsorption-diffusion behavior simulation method, and the flow is shown in figure 1. Step one: the water flooding is simulated by using a color gradient model in the Boltzmann method, and the accurate simulation of the water flooding model is realized by accurately describing wetting angle and interfacial tension parameters, wherein the Boltzmann equation is as follows:
in the method, in the process of the invention,as a particle distribution function, t is the particle movement time, c is the grid movement speed, c=Δx/Δt, Δx is the unit grid length, Δt is the unit time step, τ is the single relaxation time to reach equilibrium, +.>Is the particle velocity direction, f i eq Is a particle equilibrium distribution function;
langevin kinematics implements particle motion simulation by applying additional force to tiny particles in a fluid system, and the control equation of the method is:
wherein i is the serial number of the active nano-particles,for active nanoparticle mass, < >>In order to achieve the velocity of the active nanoparticle,friction force to the active nanoparticle +.>Random forces to which the active nanoparticle is subjected, +.>Respectively represent Van der Waals force between the active nano particles, between the active nano particles and the wall surface, and->Electrostatic force to the active nanoparticle;
the interaction between the active nano particles and the fluid is realized through the universal coupling of the lattice Boltzmann-Lang method, and the momentum and energy conservation of the system are realized by calculating the interaction force between the active nano particles and the fluid and considering the interaction effect of the interaction force on the active nano particles and the fluid:
in the method, in the process of the invention,the total acting force of the fluid on the active nano particles is dimensionless; />Is a friction component, dimensionless; />Is a random component.
Interfacial tension is introduced by a continuous surface force method, wherein the interfacial tension of a two-phase fluid is introduced by introducing a color function ρ N Realization of ρ N Is defined as:
in the formula (1), when a certain lattice point ρ N When the liquid is 1, the liquid is red liquid, when the liquid is-1, the liquid is blue liquid, and when the liquid is-1 and 1, the liquid is red and blue at the same time;
the continuous surface tension is determined by equation (2):
where σ is the interfacial tension and,for color gradient, κ is interface curvature obtained by formula (3);
wherein, unit normal vector
After the continuous surface force is obtained, the product can be obtainedExternal force term phi i ，Φ i Can be determined by equation (4):
in the middle ofTo take into account the redefined flow rate after continuous surface force, its value is:
the color gradient model needs to introduce a contact angle through special treatment of upper and lower boundaries, realizes proper wall surface wetting conditions, ensures model stability, constructs a wetting boundary through a geometric method, and introduces the contact angle through a formula (5):
in theta w =tan (pi/2- θ); θ is the contact angle;the direction is a unit normal vector pointing to the wall surface of the fluid, and the direction is dimensionless; />The direction is a unit tangential vector pointing to the wall surface of the fluid, and the direction is dimensionless; the color functions of the upper wall surface and the lower wall surface are determined by the formulas (7) and (8):
in the method, in the process of the invention,is the color function of the upper and lower walls>Is a function of the color of the fluid node immediately adjacent to the upper and lower walls. After the upper wall surface and the lower wall surface are treated by the method, the wettability of oil water and the wall surface can be accurately considered.
The lattice Boltzmann equation of the D2Q9 model is:
in the formula (9)As a particle distribution function, t is the particle movement time, c is the grid movement speed, c=Δx/Δt, Δx is the unit grid length, Δt is the unit time step, τ is the single relaxation time to reach equilibrium, +.>Is the particle velocity direction, f i eq Is a particle equilibrium distribution function.
Establishing a Langmuir kinematic simulation model of the active nano particles, wherein the Langmuir kinematic simulation model realizes particle motion simulation by applying additional acting force to tiny particles in a fluid system, and a control equation of the method is as follows:
in the formula (10), i is the serial number of the active nano-particles,for active nanoparticle mass, < >>For active nanoparticle speed, +.>Friction force to the active nanoparticle +.>Random forces to which the active nanoparticle is subjected, +.>Respectively represent Van der Waals force between the active nano particles, between the active nano particles and the wall surface, and->Electrostatic force to the active nanoparticle;
the amount of friction experienced by the active nanoparticle is proportional to the difference between the velocity of the active nanoparticle and the velocity of the surrounding fluid, as determined by equation (11):
wherein friction coefficient ζ=3ρμ d p ψ, where μ is the fluid viscosity around the active nanoparticle, and if the active nanoparticle is in the aqueous phase, μ is the viscosity of the water taken up by μ, i.e., μ=μ w If at the oil/water interface, a color function ρ needs to be introduced N Viscosity of oil and water mu o Sum mu w Respectively processing d p Is the particle size of the active nano particles, and psi is the shape factor;
random force itemThe thermal motion of the oil-water is introduced and the thermal motion of the particles is shown, and the random force term is obtained by a formula (12):
wherein, alpha, beta epsilon { x, y }; delta is the Croneck function, k B Representing the boltzmann constant, T representing the absolute temperature of the fluid;
van der Waals forces between active nanoparticles are determined by equation (13):
in the method, in the process of the invention,represents the vector distance between two active nanoparticles, < >>Van der Waals potential energy between two active nano particles is vector distance +.>Is a function of (2);
van der Waals forces between the active nanoparticle and the wall are determined by equation (14):
wherein A is cc Is Hamaker constant, d p In order to be the diameter of the active nanoparticle,is the vertical distance between the particles and the upper and lower wall surfaces. Due to the difference between the aqueous phase and the oil/water interface, oil/water is consideredWhen the active nano particles are stressed at the interface, the Hamaker constant needs to be recalculated, and the expression is as follows:
wherein ε w 、ε o 、ε p Dielectric constants of water, oil and active nano particles respectively, n w 、n o 、n p Respectively water, oil and active nano particles, wherein h is the Planck constant; v (v) e Is the adsorption frequency; since the oil is a mixture, the different oil components have different dielectric constants and refractive indices.
The electrostatic force to which the active nanoparticle is subjected is divided into electrostatic forces between particlesElectrostatic force between particle and wall>The calculation formula is as follows:
where κ is the reciprocal of the debye length, Z is the interaction constant, and Z is determined by equation (18):
Z＝64πε o ε(k B T/e) 2 tanh 2 (ze/4k B T) (18)
wherein z is the electrolyte valence, ε 0 For vacuum dielectric constant, ε is the relative dielectric constant of water.
The movement process of the active nano particles in the water phase and the oil/water interface is simulated by using the Langmuir kinematic method, and the detailed description is drawn from the aspect of forceElectrostatic forces, van der waals forces, random forces, and frictional forces to which the active nanoparticle is subjected in a fluid; the acting force of the active nano particles on the fluid is taken as a bridge, the acting relationship between the fluid and the active nano particles is constructed, the coupling between the active nano particles and the fluid is realized, and the interaction relationship between the active nano particles and the velocity field and the energy field between the active nano particles and the fluid is established; the lattice Boltzmann and Langmuir kinematics method is coupled to separate the fluid forces exerted on the active nanoparticles into friction and random components:
in the formula (19)The total acting force of the fluid on the active nano particles is dimensionless; />Is a friction component, dimensionless; />Is a random component;
to maintain conservation of momentum, pulse density is defined:
particle swarm position, same as before; />Active nanoparticle positions;
and adding the force source item distribution function into an evolution equation of the water phase to finish the coupling of the active nano particles and the fluid.
Step two: on the basis of establishing an effective active nanoparticle water flooding model, parameters such as the radius of the active nanoparticle, a main control group, concentration, injection flow rate and the like are input into the model, the adsorption characteristic of the active nanoparticle at an oil/water interface is described, the influence of the active nanoparticle on the tension of the oil/water interface is further described by introducing a Langmuir adsorption equation and a particle adsorption interference coefficient Af, and the difference of the diffusion characteristic of the active nanoparticle in an aqueous phase and an oil/water interface is resolved.
Judging the adsorption capacity of the active nano particles, namely: the energy change of the active nanoparticles to the left and right of the oil/water interface into the oil/water interface is determined by equation (22):
where Δw represents the energy change, A, B, C is a parameter representing the properties of water, oil, and active nanoparticles, respectively, and less than 0 represents that the process can proceed spontaneously and more than 0 represents that the process cannot proceed spontaneously. From the above formula, when the nature of the active nanoparticle is between that of the aqueous phase and the oil phase, i.e. amphiphilic active nanoparticle,and->All negative, the active nanoparticle will spontaneously enter the oil/water interface.
Judging the desorption capacity of the active nano particles from the interface, and determining by using a Binks' adsorption energy formula for putting forward solid particles on the interface:
E＝πr 2 γ(1+cosθ) 2 (23)
wherein r is the radius of the particle, gamma is the interfacial tension, and θ is the contact angle. For the active nanoparticle, the adsorption energy is a very large energy, taking the active nanoparticle with radius r of 20nm as an example, assuming that the oil/water interfacial tension γ is 40mN/m and the contact angle θ is 90 °, the adsorption energy is about 12222KT, so that the active nanoparticle adsorbed at the oil/water interface is difficult to detach from the interface.
Adsorption interference coefficient A f (A f =54.6%) the modified langmuir adsorption equation is an interfacial tension-concentration relationship equation that takes into account the repulsive force of the active nanoparticles and surface non-uniformity. In practical situations, the collision between the active nano particles and the oil/water interface belongs to inelastic collision, the active nano particles do not immediately enter the interface when approaching to the oil/water interface, a slow buffering process is needed, then the buffer process reaches an equilibrium state, and the time of the buffering process is defined as the unbalanced adsorption time tau of the oil/water interface of the active nano particles e . An active nanoparticle oil/water interface unbalanced adsorption equation is constructed.
σ(t)＝σ 0 {1+E 0 ln[1-ζ(t)ω(t)]} (24)
Wherein omega is the saturation rate of the interfacial active nano-particles,ζ is interfacial adsorption strength, calculated from the following formula:
wherein τ r For the unbalance time of the active nanoparticle system, the value of the index n is related to the individual particle unbalance time τ e The correlation is a time scaling effect at a specific unbalance time. The above equation can thus be written as the equation application result is shown in fig. 3.
The mean square displacement is a parameter for measuring the time-dependent change relation of the position of the active nano particle at a certain moment, and the relation of the mean square displacement and the time is as follows:
<Δx(t) 2 >＝2Dt (27)
wherein Δx is the displacement of the active nanoparticle; represents the mean of a plurality of active nanoparticles; d is the diffusion coefficient of the active nano particles;
first, the trajectory curve of each active nanoparticle at the oil/water interface is traced by the above method, as shown in fig. 4, and the tracing time length N is recorded, and the mean square displacement of each active nanoparticle is determined by the following formula: the mean square displacement of each active nanoparticle is determined by the following formula:
wherein MSD is mean square displacement of a certain active nano particle, N is time interval, N t Is the association time;
calculating diffusion coefficient variation coefficients of different time intervals under the optimal correlation time by the formula (29):
divide it into N s ＝N/N t Obtaining N by solving the mean square displacement of each section of small track curve at different time intervals according to the section of small track curve (29) t -1 mean square displacement, averaging the mean square displacements calculated under the same time interval of different small track curves to obtain a correlation time N t Is set of N t -1 mean square shift and the corresponding diffusion coefficient is derived from equation (27). And selecting different association time to obtain a plurality of groups of diffusion coefficients, wherein the association time is optimal when the diffusion coefficients are distributed in positive bias. And calculating diffusion coefficient variation coefficients of different time intervals under the optimal correlation time according to the following formula, selecting the time interval when the variation coefficient is minimum, and taking the average value of the diffusion coefficients under the time interval as the diffusion coefficient of the active nano particles under the system.
The diffusion coefficient of the active nano particles at the water phase and the oil/water interface, which are solved according to the method, is analyzed to analyze the concentration distribution of the active nano particles in the system, and further guide the parameter design of the active nano particles.
Based on the same inventive concept, the embodiment of the invention also provides an active nanoparticle oil-water interface adsorption-diffusion behavior simulation device, the structure of which is shown in fig. 5, comprising:
and an oil reservoir parameter updating module: and inputting specific parameters of the oil reservoir according to the field implementation environment. The parameters are specific to a certain layer, and include parameters such as oil reservoir temperature, oil reservoir pressure, main pore size, pore length, crude oil viscosity, density, components and the like. The module is mainly controlled by a lattice Boltzmann color gradient model program;
a nanofluid parameter updating module: and updating parameters such as radius, main groups, concentration, injection flow rate, injection position and the like of the active nano particles, and updating density, viscosity and interfacial tension of the injected fluid of the oil reservoir. Further, van der Waals force, electrostatic force, friction force and random force between the active nano particles, the fluid and the wall surface are calculated. The module is controlled mainly by the langevin kinematics method.
Active nanoparticle/fluid coupling module: the module calculates the motion state of the active nano particles and the fluid lattice respectively through the coupling method, couples the active nano particles and the fluid lattice through a force source item distribution function, and outputs the motion condition of the active nano particles and oil/water two phases (oil/water interfaces) in real time. And returning the input result to the nanofluid parameter updating module to further calculate the stress conditions of the active nano particles and the fluid.
And an adsorption judging module: judging whether the active nano particles can be adsorbed on an oil-water interface or not according to the properties of the active nano particles and the oil/water interface, if so, entering a desorption judging module; and if not, entering an active nanoparticle parameter optimization module.
And a desorption judging module: judging whether the active nano particles can be desorbed from the interface according to the properties of the active nano particles adsorbed on the oil/water interface, and if so, entering an active nano particle parameter optimization module; and if not, entering an oil/water interface tension calculation module.
Oil/water interfacial tension calculation module: and calculating the interfacial tension of the oil/water in real time according to the adsorption quantity and the property of the oil/water interfacial active nano particles and the modified Langmuir adsorption equation, and outputting a calculation result.
And a diffusion coefficient calculation module: the module is mainly used for solving the diffusion coefficient of the active nano particles at the water phase and the oil/water interface, describing the distribution condition of the active nano particles in the fluid, and further guiding the parameter design of the active nano particles.
Active nanoparticle parameter optimization and performance evaluation module: and comprehensively evaluating the action effect of the active nano particles in the oil reservoir according to the output results of the oil/water interface tension calculation module and the active nano particle diffusion calculation module, further optimizing the performance parameters of the active nano particles, and inputting the optimized parameters into the nano fluid parameter updating module.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (10)
1. An active nanoparticle oil/water interface adsorption-diffusion behavior simulation method is characterized by comprising the following steps:
step one: simulating water flooding by using a color gradient model in a lattice Boltzmann method, and accurately simulating the water flooding model by accurately describing parameters such as wetting angle, interfacial tension and the like; simulating the motion process of the active nano particles in the water phase and the oil/water interface by using a Langmuir kinematic method, and describing the electrostatic force, van der Waals force, random force and friction force of the active nano particles in the fluid in detail from the force perspective; the acting force of the active nano particles on the fluid is taken as a bridge, the acting relationship between the fluid and the active nano particles is constructed, the coupling between the active nano particles and the fluid is realized, and the interaction relationship between the active nano particles and the velocity field and the energy field between the active nano particles and the fluid is established; the method specifically comprises the following steps:
101 on the basis of a D2Q9 model, establishing a lattice Boltzmann equation (1) based on the D2Q9 model by introducing a color gradient model to realize the simulation of oil/water two phases;
in the method, in the process of the invention,as a particle distribution function, t is the particle movement time, c is the grid movement speed, c=Δx/Δt, Δx is the unit grid length, Δt is the unit time step, τ is the single relaxation time to reach equilibrium, +.>Is the particle velocity direction, f i eq Is a particle equilibrium distribution function;
102, using langevin kinematics, the particle motion simulation is implemented by applying additional force to the tiny particles in the fluid system, and the control equation is:
wherein i is the serial number of the active nano-particles,for active nanoparticle mass, < >>For active nanoparticle speed, +.>Friction force to the active nanoparticle +.>Random forces to which the active nanoparticle is subjected, +.>Respectively represent Van der Waals force between the active nano particles, between the active nano particles and the wall surface, and->Electrostatic force to the active nanoparticle;
103 achieve interaction between the active nanoparticle and the fluid by the universal coupling of lattice Boltzmann-lang, the coupling equation being:
in the method, in the process of the invention,is the total force of the fluid on the active nanoparticle; />Is a friction component; />Is a random component;
step two: on the basis of establishing an effective active nanoparticle water flooding model, describing the adsorption characteristic of the active nanoparticle at an oil/water interface and the influence of the active nanoparticle on the interfacial tension, and distinguishing the difference of the diffusion characteristic of the active nanoparticle in an aqueous phase and an oil/water interface, wherein the specific steps are as follows:
201, by analyzing the difference between the stress of the active nano particles at an oil/water interface and the difference between the stress of the active nano particles in an aqueous phase, the motion depiction of the active nano particles in an oil-water phase and an oil-water phase is realized; by introducing Langmuir adsorption equation and particle adsorption interference coefficient A f Further characterizing its effect on oil/water interfacial tension;
202 analyzing the influence of the oil/water interface on the diffusion of the active nano particles by calculating the difference of the diffusion coefficients of the active nano particles in the horizontal and vertical directions in the water phase and the oil/water interface;
step three: according to the constructed microscopic characterization method of the active nanoparticle oil/water interface adsorption, analyzing main control factors influencing the active nanoparticle oil/water interface adsorption by changing the fluid injection speed, the active nanoparticle injection concentration and the particle size; and constructing an active nanoparticle water flooding parameter design and performance evaluation device, inputting active nanoparticle parameters into the device, and preferably using the active nanoparticles on site.
2. The method for simulating the adsorption-diffusion behavior of an active nanoparticle oil/water interface according to claim 1, wherein the interfacial tension is introduced by a continuous surface force method in the first step, and the continuous surface force is expressed as follows:
wherein sigma is interfacial tension, rho N is color gradient, and kappa is interfacial curvature;
after the continuous surface force is obtained, the external force term phi can be obtained i ，Φ i Can be determined by equation (5):
in the middle ofTo take into account the redefined flow rate after continuous surface force, its value is:
3. the method for simulating adsorption-diffusion behavior of an active nanoparticle oil/water interface according to claim 2, wherein the color function is formulated as:
in the formula, when a certain lattice point ρ N When the liquid is 1, the liquid is red liquid, when the liquid is-1, the liquid is blue liquid, and when the liquid is-1 and 1, the liquid is red and blue at the same time;
the interface curvature is determined by equation (8);
in which the unit normal vector
4. The method for simulating the adsorption-diffusion behavior of an active nanoparticle oil/water interface according to claim 1, wherein in the first step, a wetting boundary is constructed by a geometric method, and a color gradient model introduces a contact angle by special treatment of upper and lower boundaries through formula (9):
in theta w =tan (pi/2- θ); θ is the contact angle;is a unit normal vector directed to the wall of the fluid; />Is a unit tangential vector directed to the wall surface of the fluid; the color functions of the upper wall surface and the lower wall surface are determined by the formulas (10) and (11):
in the method, in the process of the invention,is the color function of the upper and lower walls>Is a function of the color of the fluid node immediately adjacent to the upper and lower walls.
5. A method of modeling the adsorption-diffusion behavior of an active nanoparticle oil/water interface according to claim 1, wherein the amount of friction experienced by the active nanoparticle is proportional to the difference between the velocity of the active nanoparticle and the velocity of the surrounding fluid, as determined by equation (12):
wherein friction coefficient ζ=3ρμ d p ψ, where μ is the fluid viscosity around the active nanoparticle, and if the active nanoparticle is in the aqueous phase, μ is the viscosity of the water taken up by μ, i.e., μ=μ w If at the oil/water interface, a color function ρ needs to be introduced N Viscosity of oil and water mu o Sum mu w Respectively processing d p Is the particle size of the active nano particles, and psi is the shape factor;
wherein the thermal motion of the particles is through a random force termIntroducing, the random force term is obtained by the formula (13):
wherein, alpha, beta epsilon { x, y }; delta is the Croneck function, k B Representing the boltzmann constant, T representing the absolute temperature of the fluid;
the saidDetermined by equation (14):
in the method, in the process of the invention,represents the vector distance between two active nanoparticles, < >>Van der Waals potential energy between two active nano particles is vector distance +.>Is a function of (2);
the saidDetermined by equation (15):
wherein A is cc Is Hamaker constant, d p In order to be the diameter of the active nanoparticle,the vertical distance between the particles and the upper and lower wall surfaces; due to the difference between the aqueous phase and the oil/water interface, when the stress of the active nanoparticle at the oil/water interface is considered, the Hamaker constant needs to be recalculated, and the expression is as follows:
wherein ε w 、ε o 、ε p Dielectric constants of water, oil and active nano particles respectively, n w 、n o 、n p Respectively water, oil and active nano particles, wherein h is the Planck constant; v (v) e Is the adsorption frequency;
the electrostatic force to which the active nanoparticle is subjected is divided into electrostatic forces between particlesElectrostatic force between particle and wall>The calculation formula is as follows:
where κ is the reciprocal of the debye length, Z is the interaction constant, and Z is determined by equation (19):
Z＝64πε o ε(k B T/e) 2 tanh 2 (ze/4k B T) (19)
wherein z is the electrolyte valence, ε 0 For vacuum dielectric constant, ε is the relative dielectric constant of water.
6. A method of simulating the adsorption-diffusion behavior of an active nanoparticle oil/water interface according to claim 1, wherein the lattice Boltzmann and langevin kinematics are coupled in step 103 to separate the fluid forces exerted on the active nanoparticle into a friction component and a random component:
in the formula (20)Is the total force of the fluid on the active nanoparticle;
to maintain conservation of momentum, pulse density is defined:
particle swarm position, same as before; />Active nanoparticle positions;
and adding the force source item distribution function into an evolution equation of the water phase to finish the coupling of the active nano particles and the fluid.
7. The method for simulating adsorption-diffusion behavior of an oil/water interface of an active nanoparticle according to claim 1, wherein in step 201, the adsorption capacity of the active nanoparticle is determined by: the energy change of the active nanoparticles to the left and right of the oil/water interface into the oil/water interface is determined by equation (22):
where Δw represents the energy change, A, B, C is a parameter representing the properties of water, oil, and active nanoparticles, respectively, and less than 0 represents that the process can proceed spontaneously and more than 0 represents that the process cannot proceed spontaneously.
8. The method for simulating the adsorption-diffusion behavior of an oil/water interface of an active nanoparticle according to claim 1, wherein in step 202, the desorption capacity of the active nanoparticle from the interface is determined by Binks's proposed adsorption energy formula of solid particles on the interface:
E＝πr 2 γ(1+cosθ) 2 (23)
wherein r is the radius of the particle, gamma is the interfacial tension, and θ is the contact angle.
Adsorption interference coefficient A f (A f =54.6%) modified langmuir adsorption equation is an interfacial tension-concentration relationship equation taking into account the repulsive force and surface non-uniformity of the active nanoparticles, constructing an active nanoparticle oil/water interface unbalanced adsorption equation:
σ(t)＝σ 0 {1+E 0 ln[1-ζ(t)ω(t)]} (24)
wherein omega is the saturation rate of the interfacial active nano-particles,ζ is interfacial adsorption strength, calculated from the following formula:
wherein τ r For the unbalance time of the active nanoparticle system, the value of the index n is related to the individual particle unbalance time τ e The correlation is a time scaling effect at a specific unbalance time. The above equation can thus be written as the equation application result is shown in fig. 3.
9. The method for simulating the adsorption-diffusion behavior of an oil/water interface of an active nanoparticle according to claim 1, wherein the mean square displacement is a parameter for measuring the time-dependent change of the position of the active nanoparticle at a certain moment, and the time-dependent change of the position of the active nanoparticle is as follows:
<Δx(t) 2 >＝2Dt (27)
wherein Δx is the displacement of the active nanoparticle; represents the mean of a plurality of active nanoparticles; d is the diffusion coefficient of the active nano particles;
the mean square displacement of each active nanoparticle is determined by the following formula:
wherein MSD is mean square displacement of a certain active nano particle, N is time interval, N t Is the association time;
calculating diffusion coefficient variation coefficients of different time intervals under the optimal correlation time by the formula (29):
10. an active nanoparticle oil/water interface adsorption-diffusion behavior simulation device is characterized by comprising
The oil reservoir parameter updating module is controlled by a grid Boltzmann color gradient model program, and the parameters are specific to a certain layer and comprise parameters such as oil reservoir temperature, oil reservoir pressure, main pore size, pore length, crude oil viscosity, density, components and the like;
the nano fluid parameter updating module is used for simultaneously updating the density, viscosity and interfacial tension of the oil reservoir injection fluid according to parameters such as the radius, main groups, concentration, injection flow rate and injection position of the active nano particles by a Langmuir dynamics method and calculating Van der Waals force, electrostatic force, friction force and random force between the active nano particles and the fluid and wall surface;
the active nanoparticle/fluid coupling module is used for respectively calculating the motion states of the active nanoparticle and the fluid lattice through the coupling method, coupling the active nanoparticle and the fluid lattice through a force source item distribution function, outputting the motion conditions of the active nanoparticle and an oil/water two-phase (oil/water interface) in real time, returning an input result to the nanofluid parameter updating module, and further calculating the stress conditions of the active nanoparticle and the fluid;
the adsorption judging module judges whether the active nano particles can be adsorbed on an oil-water interface according to the properties of the active nano particles and the oil/water interface, and if so, the active nano particles enter the desorption judging module; if not, entering an active nanoparticle parameter optimization module;
the desorption judging module is used for judging whether the active nano particles can be desorbed from the interface according to the properties of the active nano particles adsorbed on the oil/water interface, and if so, the active nano particles enter the active nano particle parameter optimizing module; if not, entering an oil/water interface tension calculation module;
the oil/water interface tension calculation module calculates the oil/water interface tension in real time according to the adsorption quantity and the property of the oil/water interface active nano particles and a modified Langmuir adsorption equation, and outputs a calculation result;
the diffusion coefficient calculation module is used for solving the diffusion coefficient of the active nano particles at the water phase and the oil/water interface, describing the distribution condition of the active nano particles in the fluid and further guiding the parameter design of the active nano particles;
and the active nanoparticle parameter optimization and performance evaluation module is used for comprehensively evaluating the action effect of the active nanoparticles in the oil reservoir according to the output results of the oil/water interface tension calculation module and the active nanoparticle diffusion calculation module, further optimizing the performance parameters of the active nanoparticles and inputting the optimized parameters into the nanofluid parameter updating module.
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