CN117113873A - Numerical simulation method and application of multiphase fluid stratum seepage - Google Patents
Numerical simulation method and application of multiphase fluid stratum seepage Download PDFInfo
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Abstract
The application provides a numerical simulation method and application of multiphase fluid stratum seepage, and relates to the technical field of numerical simulation, wherein the method comprises the following steps: s1, acquiring a porosity three-dimensional data body and a permeability three-dimensional data body of a core sample, and constructing a high-precision digital core model; s2, tracking phase interfaces among multiphase fluids through a VOF model, describing the transmission behavior of the multiphase fluids, and establishing a seepage simulation mathematical model; s3, establishing a three-dimensional fluid mechanics model according to the high-precision digital rock core model and the seepage simulation mathematical model, and solving the pressure field of the multiphase fluid according to the three-dimensional fluid mechanics model; wherein, in establishing the seepage simulation mathematical model, the compression coefficient of the multiphase fluid, the mixed viscosity and the mixed density of the mixed fluid are introduced. The application can solve the technical problem that the seepage simulation result of the multiphase fluid stratum in the prior art is far away from the actual seepage situation.
Description
Technical Field
The application relates to the technical field of numerical simulation, in particular to a numerical simulation method and application of multiphase fluid stratum seepage.
Background
In the past multiphase percolation simulation, the classical VOF (Volume of Fluid) method has been widely used. The method is based on the description of the volume fraction of the distribution of the fluid in space, and can effectively simulate the interface behavior of multiphase fluid. However, the conventional VOF method has some limitations, such as relatively difficult handling for complex porous medium structures and heterogeneous media.
In conventional hydrodynamic models, it is often assumed that the liquid and gas are incompressible, i.e. the density remains unchanged. However, this assumption has a certain limitation in some cases, so that the seepage simulation result of the fluid is often far away from the actual seepage situation, which affects the effectiveness of the simulation result, and it is difficult to provide useful data support for projects needing to consider the seepage situation, such as oil gas development, geological engineering, and the like, especially in multiphase fluid seepage simulation.
Disclosure of Invention
The application aims to provide a numerical simulation method and application of multiphase fluid stratum seepage, which are used for solving the technical problem that the multiphase fluid stratum seepage simulation result is far away from the actual seepage situation in the prior art, and can more accurately simulate and describe the interaction, interfacial behavior and dynamic evolution process of multiphase fluid.
It is another object of the present application to provide an application of a numerical simulation method for multiphase fluid formation seepage.
In order to achieve the above object, the present application provides the following technical solutions:
in a first aspect, the present application provides a method for numerical simulation of multiphase fluid formation seepage, comprising:
s1, acquiring a porosity three-dimensional data body and a permeability three-dimensional data body of a core sample, and constructing a high-precision digital core model;
s2, tracking phase interfaces among multiphase fluids through a VOF model, describing the transmission behavior of the multiphase fluids, and establishing a seepage simulation mathematical model;
s3, establishing a three-dimensional fluid mechanics model according to a high-precision digital rock core model and a seepage simulation mathematical model, and solving a pressure field of the multiphase fluid according to the three-dimensional fluid mechanics model;
wherein, the transmission behavior of the multiphase fluid is described in tracking the phase interface between the multiphase fluid through the VOF model, and the compression coefficient of the multiphase fluid, the mixing viscosity and the mixing density of the mixed fluid are introduced in establishing a seepage simulation mathematical model.
Further, in some embodiments of the application, the seepage simulation mathematical model is constructed from multiphase fluid conservation of momentum equations, multiphase fluid conservation of mass equations, and multiphase fluid phase equations.
Further, in some embodiments of the present application, wherein the multiphase fluid mass conservation equation is:
dA is the area of the infinitesimal body, and the unit is m 2 The method comprises the steps of carrying out a first treatment on the surface of the dV is the volume of the primordial volume (dV = dxdydz, x, y, z are three directions of three-dimensional coordinates of the primordial volume), in m 3 The method comprises the steps of carrying out a first treatment on the surface of the m is the mass of the micro-element fluid, and the unit is kg; t is time, and the unit is s; q ogw The unit is kg/s for source and sink phases; v at this time v m Is the speed of the mixed fluid, which is in m/s; ρ m Is the density of the mixed fluid, and the unit is kg/m 3 The expression is as follows:
ρ m ＝S o ρ o +S g ρ g +S w ρ w
wherein S is o 、S g And S is w The saturation of oil, gas and water phases respectively; ρ o 、ρ g 、ρ w Is the density of oil, gas and water three-phase fluid, and the unit is kg/m 3 ；
Further, in some embodiments of the present application, the multiphase fluid momentum conservation equation is:
wherein phi is the porosity of the rock, and the porosity is dimensionless; ρ m The density of the mixed fluid is kg/m3; k is the permeability of the single-phase fluid, and the unit is m 2 ；Is a pressure gradient, and the unit is Pa/m; p is p c The unit is Pa for the pressure of the three-phase capillary; mu (mu) m To mix the viscosity of the fluid, the expression is as follows:
μ m ＝S o μ o +S g μ g +S w μ w
wherein mu o 、μ g 、μ w The viscosity of the oil, gas and water phases is Pa.s respectively;
further, in some embodiments of the application, the multiphase fluid phase equation is:
wherein q o 、q g 、q w Is the source and sink phases of oil, gas and water, and the unit is kg/s.
Further, in some embodiments of the application, the three-phase capillary pressure p c According to the dominant phase of the multiphase fluid, it is obtained by the following formula:
when the oil phase is the dominant phase, the three-phase capillary pressure p c The method comprises the following steps:
when the gas phase is the dominant phase, the three-phase capillary pressure p c The method comprises the following steps:
when the water phase is the dominant phase, the capillary pressure p is three-phase c The method comprises the following steps:
wherein p is cog 、p cow 、p cwg The capillary pressure of oil gas, oil water and gas water is direct, and the expression is as follows:
wherein sigma og 、σ ow 、σ wg Interfacial tension between oil gas, oil water and gas water respectively, wherein the unit is N/m; θ og 、θ ow 、θ wg The wetting contact angles among oil gas, oil water and gas water are dimensionless; r is the throat radius in m.
Further, in some embodiments of the present application, in step S3,
the pressure field of the multiphase fluid is solved using a fast iterative method or a multiple grid method. Further, in some embodiments of the application, the pressure field solving of the multiphase fluid comprises:
solving a first term in a multiphase fluid mass equation:
wherein C is o 、C g 、C w The compression coefficients of oil, gas and water phases are respectively, and the compression coefficients are dimensionless; t is the current time, t+deltat is the next time, and the units are s;
solving a second term in the multiphase fluid mass equation:
wherein z is c The parameter is dimensionless and is the number of adjacent grids; a is the area of adjacent grids, singlyBit is m 2 I is grid i, j is grid j adjacent to grid i; g m Is conductivity;
the simultaneous multiphase fluid mass equation, a solution formula of a first term and a solution formula of a second term in the multiphase fluid mass equation are obtained:
substituting different parameters of the current time t and the next time t+delta t into the above formula to obtain N above formulas at different times to form a matrix equation A of the above formula t+Δt X t+Δt ＝B t Wherein:
wherein A is t+Δt A sparse matrix of size N X N (N is the number of meshes of the model) related to the hydraulic conductivity of the fluid, X t+Δt And B t Is two vectors of length N, X t+Δt For the pressure field vector of the next moment t+Δt, B t Is a vector related to the pressure field and boundary conditions at the current moment t;
and solving a matrix equation at each moment to obtain the pressure field of the multiphase fluid.
Further, in some embodiments of the present application, the establishing of the high-precision digital core model includes:
acquiring a porosity three-dimensional data volume and a permeability three-dimensional data volume of a core sample by utilizing the core sample and a scanning technology;
establishing a three-dimensional geometric model of the core sample, and assigning the three-dimensional geometric model according to the porosity three-dimensional data volume and the permeability three-dimensional data volume to obtain a high-precision digital core model of the core sample;
wherein the obtaining of the porosity three-dimensional data volume and the permeability three-dimensional data volume comprises the following steps:
s11, obtaining a core sample of a reservoir to be simulated, and obtaining actual porosity phi and actual permeability k of the core sample by using the core sample;
s12, acquiring two-dimensional images of the core sample on different sections by using a scanning technology to acquire two-dimensional image data;
s13, obtaining a three-dimensional data body of the core according to the two-dimensional image data on the sections;
s14, obtaining a porosity conversion coefficient of the core sample according to the relation between the actual porosity phi of the core and the two-dimensional image data; acquiring a permeability conversion coefficient of the core sample according to the relation between the actual permeability k and the actual porosity phi and the two-dimensional image data;
and S15, applying the porosity conversion coefficient and the permeability conversion coefficient, the relation between actual porosity and two-dimensional image data, and the relation between actual permeability and two-dimensional image data to the three-dimensional data body of the core to obtain the three-dimensional data body of the core porosity and the three-dimensional data body of the core permeability.
In a second aspect, the application also provides application of the numerical simulation method of multiphase fluid stratum seepage in the technical fields of oilfield development, underground water management, geological engineering and environmental protection.
The application provides a numerical simulation method and application of multiphase fluid stratum seepage, which introduces a compressibility term into a seepage simulation mathematical model established by a VOF model, corrects a traditional fluid mechanics equation, and enables the volume change of fluid in the compression or expansion process to be considered; for example, in high velocity gas flows, the behavior of shock waves, pressure waves and jets can be more accurately simulated in view of the compressibility of the gas; in the liquid ejection problem, the compressibility of the liquid can affect the speed of the jet and the formation process of the spray. Meanwhile, the problem that the density and the viscosity of the multiphase fluid are changed due to different dominant phases is also considered, the mixed viscosity and the mixed density are introduced, a more reliable CFD model is built, and interaction and influence among different components in the multiphase fluid or the mixed fluid can be more accurately captured; the CFD model can more accurately predict the flow characteristics of a fluid such as a velocity field, pressure distribution, vortex structure and the like, so that the accuracy and reliability of a simulation result are improved, and the movement and interaction of the fluid can be more accurately described. Furthermore, introducing the concepts of mixing density and mixing viscosity may also improve modeling of the fluid interface and phase change process. In multiphase fluids, the location and morphology of the fluid interface has an important impact on flow behavior and heat transfer processes. By taking into account the density and viscosity differences of the different components, dynamic changes of the fluid interface and phase change phenomena, such as evaporation and condensation of the gas-liquid interface, formation and rupture of liquid droplets, etc., can be more accurately described.
The numerical simulation method provided by the application can enable the fluid mechanics equation model to describe the behavior and the property of the substance more accurately. This is of great importance for modeling and analysis of complex flows and interactions involving liquids and gases, providing a more reliable numerical modeling tool for a variety of engineering and scientific fields. Meanwhile, the numerical simulation method can improve modeling and prediction capabilities of a traditional CFD model on multiphase fluid or mixed fluid. This has great significance to engineering and scientific research involving complex fluid systems, improving the understanding of multiphase fluid behavior and the ability to optimize designs.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a simulation method of a multiphase fluid seepage process based on VOF.
Detailed Description
The aspects of the present application will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the application are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The inventors propose a numerical simulation method of multiphase fluid stratum seepage in the present application, referring to fig. 1, comprising:
s1, acquiring a porosity three-dimensional data body and a permeability three-dimensional data body of a core sample, and constructing a high-precision digital core model;
s2, tracking phase interfaces among multiphase fluids through a VOF model, describing the transmission behavior of the multiphase fluids, and establishing a seepage simulation mathematical model;
s3, establishing a three-dimensional fluid mechanics model according to a high-precision digital rock core model and a seepage simulation mathematical model, and solving a pressure field of the multiphase fluid according to the three-dimensional fluid mechanics model;
wherein, the transmission behavior of the multiphase fluid is described in tracking the phase interface between the multiphase fluid through the VOF model, and the compression coefficient of the multiphase fluid, the mixing viscosity and the mixing density of the mixed fluid are introduced in establishing a seepage simulation mathematical model.
In the application, the seepage simulation mathematical model is constructed according to a multiphase fluid momentum conservation equation, a multiphase fluid mass conservation equation and a multiphase fluid phase equation.
Wherein, the multiphase fluid mass conservation equation is:
dA is the area of the infinitesimal body, and the unit is m 2 The method comprises the steps of carrying out a first treatment on the surface of the dV is the volume of the primordial volume (dV = dxdydz, x, y, z are three directions of three-dimensional coordinates of the primordial volume), in m 3 The method comprises the steps of carrying out a first treatment on the surface of the m is the mass of the micro-element fluid, and the unit is kg; t is time, and the unit is s; q ogw The unit is kg/s for source and sink phases; v at this time v m Is the speed of the mixed fluid, which is in m/s; ρ m Is the density of the mixed fluid, and the unit is kg/m 3 The expression is as follows:
ρ m ＝S o ρ o +S g ρ g +S w ρ w
wherein S is o 、S g And S is w The saturation of oil, gas and water phases respectively; ρ o 、ρ g 、ρ w Is the density of oil, gas and water three-phase fluid, and the unit is kg/m 3 。
The multiphase fluid momentum conservation equation is:
wherein phi is the porosity of the rock, and the porosity is dimensionless; ρ m The density of the mixed fluid is kg/m3; k is the permeability of the single-phase fluid, and the unit is m 2 ；Is a pressure gradient, and the unit is Pa/m; p is p c The unit is Pa for the pressure of the three-phase capillary; mu (mu) m To mix the viscosity of the fluid, the expression is as follows:
μ m ＝S o μ o +S g μ g +S w μ w
wherein mu o 、μ g 、μ w The viscosity of the oil, gas and water phases is Pa.s.
The speed of the multiphase fluid can be obtained through calculation through a multiphase fluid momentum conservation equation, namely the speed of the multiphase fluid at all grid points can be obtained, namely the speed field of the multiphase fluid can be obtained, and the speed field can be used for calculating other subsequent parameters such as pressure and the like. According to the application, the velocity field of the multiphase fluid is calculated in a three-dimensional hydrodynamic model through a multiphase fluid momentum conservation equation, so that the flow direction of the fluid can be determined, and the flow path of the fluid in a three-dimensional space is solved; in addition, the fluid flow rate can be calculated, flow rate information of the fluid at various points is provided, the motion state of the fluid in the porous medium is known, and future flow behavior of the fluid is further predicted. By analysis of the velocity field, it is also possible to evaluate the dynamic behaviour of the fluid, such as the turbulence of the fluid, whether there is a rotation of the fluid, etc. This helps us to better understand the physical properties of the fluid, as well as the behaviour of the fluid under complex conditions. Velocity field information is also the basis for calculating other important physical quantities, such as kinetic energy, momentum, etc.
The multiphase fluid phase equation is:
wherein q o 、q g 、q w Is the source and sink phases of oil, gas and water, and has the unit of kg/S, S o 、S g And S is w The saturation of the oil phase, the gas phase and the water phase respectively; ρ o 、ρ g 、ρ w Density of oil phase, gas phase and water phase fluid respectively, kg/m 3 ；v o 、v g 、v w The speeds of the oil phase fluid, the gas phase fluid and the water phase fluid are m/s respectively.
The specific establishment process is as follows:
and establishing a three-dimensional geometric model of the rock sample, wherein the three-dimensional geometric model of the rock sample is divided into a plurality of grid cells by a grid method, each grid cell is 1 micro-element body, and the three-dimensional coordinates of the micro-element bodies can be expressed as (x, y, z).
Thus when the fluid is a single phase fluid, the rock has the following expression during seepage according to newtonian second law:
wherein F is pres 、F grav 、F visc 、F cap The fluid elements are respectively subjected to the net force, gravity, viscous force and interfacial force (capillary pressure P c Generated) with pressure as the motive force, viscous force, inertial force as the resistive force, and gravity and interfacial force as both motive force and resistive force, all in N. Single phase fluid has no interfacial force, F c =0, m is the mass of the microbody fluid in kg; a is acceleration, and the unit is m/s2.
Taking the x-direction as an example, wherein the fluid element is subjected to a net force F of surrounding fluid pres Can be expressed as the following formula:
wherein p is pressure in Pa; dA is the area of the infinitesimal body, and the unit is m 2 The method comprises the steps of carrying out a first treatment on the surface of the dV is the volume of the primordial volume (dV = dxdydz) in m 3 The method comprises the steps of carrying out a first treatment on the surface of the The gravitational term of the fluid is ignored.
At this time, the viscous force is used as resistance, and the unit is N; viscous forces (F) visc ) Can be expressed as the following formula:
mu is the viscosity of the single-phase fluid and is expressed in Pa.s; k (k) x Absolute permeability in the x-direction in m 2 ；v x The velocity of Darcy seepage in the x direction is m/s; a, a x Acceleration in the x direction in m/s 2 。
For the three directions x, y, z, one can express the following formula:
v is Darcy seepage velocity, and the unit is m/s; a acceleration in m/s 2 。
Wherein the pressure gradient isCan be expressed by the following formula:
for equation (5), the three terms dxdydz are reduced on both sides, which can be further deduced as:
wherein the method comprises the steps ofThe unit is m/s for Darcy seepage velocity; but->The unit is m/s for the true seepage velocity; wherein the two have the following speed relationship:
wherein, the true seepage velocitySubstance derivative of->Can be expressed as:
a continuity equation is introduced, the expression of which is as follows:
both sides of the above equation multiply the velocity simultaneously
The simultaneous equations (7), (9) and (11) can be obtained:
in rock, the conservation of momentum equation for single-phase fluids (Ledda P G, siconolfi L, viola F, et al support of von Ka rm n vortex streets past porous rectangular cylinders [ J ]. Physical Review Fluids,2018,3 (10)) is as follows:
wherein phi is the porosity of the rock, and the porosity is dimensionless; ρ is the density of the single-phase fluid in kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the Mu is the viscosity of the single-phase fluid, and is expressed in Pa.s; k is the permeability of the single-phase fluid, and the unit is m 2 。
For multiphase fluid, in the seepage process in rock, the flux of the physical quantity flowing into the control surface of the micro-element body is equal to the increase of the fluid mass in unit time of the micro-element body, the flowing direction is positive, the flowing direction is negative, and the formula of the increase of the oil, gas and water mass in unit time is obtained, namely a multiphase fluid mass conservation equation is as follows:
wherein q ogw The unit is kg/s for source and sink phases; v at this time v m Is the speed of the mixed fluid, which is in m/s; ρ m Is the density of the mixed fluid, and the unit is kg/m 3 The expression is as follows:
ρ m ＝S o ρ o +S g ρ g +S w ρ w (15)
for multiphase momentum conservation equation of oil, gas and water three-phase fluid, capillary pressure P needs to be considered c Is effective in (1); meanwhile, since there are differences in density and viscosity between different components of the multiphase fluid or the mixed fluid, in order to more accurately simulate and predict the behaviors of these complex fluid systems, concepts of mixed density and mixed viscosity are introduced, and in combination with a single-phase fluid momentum conservation equation (13), the momentum conservation equation of the multiphase fluid is as follows:
μ w to mix the viscosity of the fluid, the expression is as follows:
|μ m ＝S o μ o +S g μ g +S w μ w (17)
wherein mu o 、μ g 、μ w The viscosity of the oil, gas and water phases is Pa.s. For capillary pressure P c If the oil phase is dominant, then the three-phase capillary pressure at this time can be expressed as:
if the gas phase is dominant, then the three-phase capillary pressure can be expressed as:
if the water phase is dominant, then the three-phase capillary pressure can be expressed as:
p cog 、p cow 、p cwg the capillary pressure of oil gas, oil water and gas water is direct, and the expression is as follows:
σ og 、σ ow 、σ wg interfacial tension between oil gas, oil water and gas water respectively, wherein the unit is N/m; θ og 、θ ow 、θ wg The wetting contact angles among oil gas, oil water and gas water are dimensionless; r is the throat radius in m.
The mixing density refers to the overall average density taking into account the density difference between the different components, and the mixing viscosity refers to the overall average viscosity taking into account the viscosity difference between the different components.
While multiphase systems such as multiphase fluids also need to consider the Phase equation, i.e., the continuous equation (mass conservation equation for each Phase), to solve for the volume fraction of each component (lagere e B, zaleski S, bond i.e., formulation of Viscous Fingering in Rectangular Porous Media with Lateral Injection and Two-and Three-Phase Flows [ J ]. Transport in Porous Media,2016,113 (3)). The expression of the phase equation is as follows:
q o 、q g 、q w is the source and sink phases of oil, gas and water, and the unit is kg/s.
And the multiphase seepage flow mathematical model can be obtained by combining the multiphase seepage flow conservation equation, the multiphase seepage flow conservation equation and the multiphase seepage flow phase equation.
Then solving a multiphase seepage mathematical model based on a digital core model of the core sample to obtain a core sample indoor seepage simulation result of multiphase seepage, wherein the solving comprises solving of a pressure field, and the specific solving process comprises the following steps:
for the first term of formula (14),
wherein C is o 、C g 、C w The compression coefficients of oil, gas and water phases are respectively, and the compression coefficients are dimensionless; this term can be further reduced to:
wherein t is the current time, t+Δt is the next time, and the units are s. For the acquisition formula(14) To obtain the second item of (2)The phase-separated seepage equation of oil, gas and water can be obtained by further differentiating the phase-separated seepage equation based on the formula (20), so as to calculate the saturation of each phase of fluid in the grid:
wherein A is the area, and the unit is m 2 ；S o t 、S g t 、S w t Respectively the saturation of oil, gas and water at the current moment, S o t +Δt 、S g t+Δt 、S w t+Δt The saturation of the oil, gas and water three phases at the next moment is dimensionless; ρ o t 、ρ g t 、ρ w t The density of the oil, gas and water phases at the current moment, ρ o t+Δt 、ρ g t+Δt 、ρ w t+Δt The density unit of the oil, gas and water three phases at the next moment is kg/m 3 ；q o t 、q g t 、q w t Is the source and sink phases of oil, gas and water, and the unit is kg/s; v o t+Δt 、v g t+Δt 、v w t+Δt The speed of the oil, gas and water at the next moment is m/s respectively; phi t+Δt The porosity is dimensionless for the porosity at the next moment.
The differential discretization of equation (16) can be expressed as follows:
both sides are multiplied by
Can be obtained by solving the formula
Equation (27) can be derived based on equation (26):
therefore, conductivity G m Can be expressed as:
based on equation (27), the second term of equation (14) may be expressed as,
wherein z is c The parameter is dimensionless and is the number of adjacent grids; a is the area of adjacent grids, and the unit is m 2 。
Simultaneous equation (14), equation (22), equation (29) can be obtained:
the term transfer can be obtained:
all grids can substitute different parameters of the current time t and the next time t+delta t into a formula (31), so that an equation set consisting of N equations similar to the formula can be obtained. According to the subscript of the equation set, the equation set can be arranged into a matrix form, namely A t+Δt X t+Δt ＝B t ：
Wherein A is t+Δt A sparse matrix of size N X N (N is the number of meshes of the model) related to the hydraulic conductivity of the fluid, X t+Δt And B t Is two vectors of length N, X t+Δt For the pressure field vector of the next moment t+Δt, B t And solving the matrix equation for vectors related to the pressure field at the current moment t and the boundary condition to obtain the pressure field of the fluid in the model at the next moment.
In the fluid mechanics (CFD) model solving process, the CFD solving process is improved, and a more accurate and stable discretization method is adopted to calculate the velocity field, for example, a high-order precision format or grid self-adaption technology is used to reduce the numerical dissipation and diffusion and improve the resolution precision of the velocity field. This helps to more accurately capture details of the fluid flow and the vortex structure. Particularly, when the propagation problem of fluid in a complex porous medium is solved, the high-order precision format and grid self-adaptive technology has extremely high self-adaptability to the selection of space discretization and time integration step length, can be automatically adjusted according to the complexity and flow characteristics of fluid flow, further dynamically adjusts grids and time step length, and realizes the acceleration convergence and the improvement of solving stability.
Meanwhile, in the pressure field solving process, in order to accelerate the convergence rate of the pressure field and improve the solving stability, a rapid iteration method or a multiple grid method is introduced, so that the iteration times can be reduced, the solving efficiency of the pressure field can be improved, and the solving efficiency and the calculated amount of the pressure field can be improved.
The fast iteration method (Fast Iterative Method) in the application refers to a method capable of accelerating the iteration convergence speed. Such methods mainly utilize some properties of the equation or introduce preconditions to improve traditional iterative methods (such as jacobian or gaussian-seidel methods) so that after each iteration, the improvement of the solution is more significant, thereby speeding up the convergence. The fast iterative method is of many kinds, including conjugate gradient method, GMRES method, BICGSTAB method, etc.
Multiple grid method:
the multi-grid Method in the application refers to a Method for efficiently solving a large-scale linear equation set obtained by discretizing a partial differential equation. The method mainly uses the information on different scales by iterating on different grid scales, thereby achieving faster convergence speed. The multiple grid method mainly comprises two steps: a smoothing step and a correction step. The smoothing step is mainly to iterate locally on the current grid scale to eliminate high-frequency errors; the correction step is to transfer the problem to a coarser grid scale, further iterate, and eliminate the low-frequency error. The two steps are alternately executed, so that the multiple grid method can obtain good convergence effect in a few iteration times.
Meanwhile, a high-precision digital core model is introduced in the solving process so as to cope with the problem of complex boundary conditions or flow phenomena, so that the characteristics of fluid flow can be better simulated, and the accuracy of a simulation result is improved. Meanwhile, the extended multiphase seepage model can track the phase interface among fluids through a VOF volume fraction equation to describe the transmission behaviors of oil, gas and water phases, so that interface tracking and interaction description between phases are realized, and the behavior of a liquid-gas interface in a porous medium can be more accurately simulated. In addition, the simulation method provided by the application also has multi-scale simulation capability, can be used for processing seepage problems of different scales, and provides more comprehensive simulation and analysis.
The construction of the high-precision digital core model of the core sample comprises the following steps:
s11, obtaining a core sample of a reservoir to be simulated, and obtaining actual porosity phi and actual permeability k of the core sample by using the core sample;
s12, acquiring two-dimensional images of the core sample on different sections by using a scanning technology to acquire two-dimensional image data;
s13, obtaining a three-dimensional data body of the core according to the two-dimensional image data on the sections;
s14, obtaining a porosity conversion coefficient of the core sample according to the relation between the actual porosity phi of the core and the two-dimensional image data; acquiring a permeability conversion coefficient of the core sample according to the relation between the actual permeability k and the actual porosity phi and the two-dimensional image data;
s15, applying the porosity conversion coefficient and the permeability conversion coefficient, the relation between actual porosity and two-dimensional image data, and the relation between actual permeability and two-dimensional image data to the three-dimensional data body of the core to obtain the three-dimensional data body of the core porosity and the three-dimensional data body of the core permeability;
and S16, establishing a three-dimensional geometric model of the core sample, and assigning the three-dimensional geometric model according to the three-dimensional data volume of the core porosity and the three-dimensional data volume of the core permeability to obtain a high-precision digital core model of the core sample.
The core sample is subjected to oil washing and salt washing and is dried at a certain temperature, such as 80 ℃. The scanning technology can be any one of nuclear magnetic resonance scanning technology or CT scanning technology, and the core sample is subjected to section scanning after being saturated with formation water. When the core sample is scanned, the section position and the section number can be adjusted according to the precision of an instrument adopted during scanning, and the section number can be properly increased if the precision is high; the number of cross sections can be reduced appropriately with low accuracy. Wherein the obtained two-dimensional image data includes image data, i.e. pixel volume data of the image, and section coordinates, i.e. slice position coordinates. The obtained two-dimensional image data can be saved as TXT text so as to facilitate subsequent data processing.
When the scanning technique is a nuclear magnetic resonance scanning technique, the actual porosity phi is related to two-dimensional image data by phi=alpha MRI ×V MRI The method comprises the steps of carrying out a first treatment on the surface of the Wherein V is MRI Is image data, alpha MRI Is a conversion coefficient; relationship of the actual permeability k to the actual porosity phi, two-dimensional image data: k=β MRI ×V MRI 2 ×φ；β MRI Is a conversion coefficient; wherein V is MRI Scan data V for each scan area i of the rock sample MRIi Average value of (2).
When the scanning technique is a CT scanning technique, the actual porosity phi is related to two-dimensional image data as phi = alpha CT ×1/V CT The method comprises the steps of carrying out a first treatment on the surface of the Wherein V is CT Is image data, alpha CT Is a conversion coefficient; relationship of the actual permeability k to the actual porosity phi, two-dimensional image data: k=β CT ×(1/V CT 2 )×φ；β CT Is a conversion coefficient; wherein V is CT Scan data V for each scan area i of the rock sample CTi Average value of (2).
Wherein the image data, i.e. the pixel volume data, may be any one of rock density or gray scale or pixel number. Since the gray scale or the number of pixels of an image can be used to represent the magnitude of the rock density, the relative rock density is directly represented in the present application by the gray scale or the number of pixels.
Since the scanned data volume is difficult to fall within the range of convenient processing, in the step S3, before the three-dimensional data volume of the core is obtained from the two-dimensional image data on the plurality of sections, the two-dimensional image data is roughened and/or interpolated. For example, when the number of nodes in a data volume reaches tens or even hundreds of millions, the two-dimensional data image is coarsened. Wherein, after the coarsening treatment, the grid number of the two-dimensional image data is not lower than 100 ten thousand and not higher than 300 ten thousand; and when the number of nodes of the two-dimensional image data is less than 100 ten thousand, interpolation processing is performed on the two-dimensional image data, and the gray values of the unknown pixels are generated by using the gray values of the known adjacent pixels (or the three color values in the rgb image) so as to reproduce the image with higher resolution from the original image.
Wherein the actual porosity phi and the actual permeability k are the actual porosity phi and the actual permeability k of any slice of the core sample scanned by the scanning technology; or alternatively; the actual porosity phi and the actual permeability k are the actual porosity and the actual permeability obtained by testing the whole core sample.
In some embodiments, the interpolation algorithm comprises a tri-linear interpolation algorithm or a kriging interpolation algorithm.
In some embodiments, when the scanning technique is a CT scanning technique, in step S11, the core sample is subjected to oil washing, salt washing and drying treatment and the actual porosity Φ and the actual permeability k are measured, and the length and diameter of the rock sample are measured;
when the scanning technology is a nuclear magnetic resonance scanning technology, the core sample is subjected to oil washing, salt washing and drying treatment, then saturated formation water treatment is carried out, and the actual porosity phi and the actual permeability k as well as the length and the diameter of the rock sample are measured.
In summary, the compressibility of liquid and gas is introduced, the mixed density and the mixed viscosity are considered, a multiphase seepage mathematical model is built, and meanwhile, the most commonly used projection method in the traditional CFD model solving process is improved in the solving process, so that the CFD model can describe the behaviors and properties of the liquid and the gas more accurately, the accuracy and the reliability of a simulation result are improved, and a powerful tool is provided for engineering design and scientific research.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features can be replaced equivalently; such modifications and substitutions do not depart from the spirit of the application.
Claims (10)
1. A method for numerical simulation of multiphase fluid formation seepage, comprising:
s1, acquiring a porosity three-dimensional data body and a permeability three-dimensional data body of a core sample, and constructing a high-precision digital core model;
s2, tracking phase interfaces among multiphase fluids through a VOF model, describing the transmission behavior of the multiphase fluids, and establishing a seepage simulation mathematical model;
s3, establishing a three-dimensional fluid mechanics model according to a high-precision digital rock core model and a seepage simulation mathematical model, and solving a pressure field of the multiphase fluid according to the three-dimensional fluid mechanics model;
wherein, the transmission behavior of the multiphase fluid is described in tracking the phase interface between the multiphase fluid through the VOF model, and the compression coefficient of the multiphase fluid, the mixing viscosity and the mixing density of the mixed fluid are introduced in establishing a seepage simulation mathematical model.
2. A method of numerical simulation of multiphase fluid formation seepage according to claim 1, wherein the seepage simulation mathematical model is constructed from multiphase fluid conservation of momentum equations, multiphase fluid conservation of mass equations, and multiphase fluid phase equations.
3. A method of numerical modeling multiphase fluid formation seepage as claimed in claim 2, wherein the multiphase fluid mass conservation equation is:
wherein A is the area of the micro-element body, m 2 The method comprises the steps of carrying out a first treatment on the surface of the dV is the volume of the primordial volume (dV = dxdydz, x, y, z are three directions of three-dimensional coordinates of the primordial volume), m 3 The method comprises the steps of carrying out a first treatment on the surface of the m is the mass of the micro-element fluid and kg; t is time, s; q ogw Kg/s as source sink phase; v m For mixingVelocity of fluid, m/s; ρ m To mix the density of the fluid, kg/m 3 The expression is as follows:
ρ m ＝S o ρ o +S g ρ g +S w ρ w
wherein S is o 、S g And S is w The saturation of the oil phase, the gas phase and the water phase respectively; ρ o 、ρ g 、ρ w Density of oil phase, gas phase and water phase fluid respectively, kg/m 3 。
4. A method of numerical modeling multiphase fluid formation seepage as defined in claim 2, wherein the multiphase fluid momentum conservation equation is:
wherein phi is the porosity of the rock, and the porosity is dimensionless; ρ m To mix the density of the fluid, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the k is the permeability of the single-phase fluid, m 2 ；Is the pressure gradient, pa/m; p is p c The capillary pressure Pa is three-phase capillary pressure; l is the length, m; let denote a gradient operation; mu (mu) m To mix the viscosity of the fluid, the expression is as follows:
μ m ＝S o μ o +S g μ g +S w μ w
wherein mu o 、μ g 、μ w The viscosity of the oil, gas and water phases is Pa.s respectively; s is S o 、S g And S is w The saturation of the oil phase, the gas phase and the water phase respectively.
5. A method of numerical modeling multiphase fluid formation seepage as defined in claim 2, wherein the multiphase fluid phase equation is:
wherein q o 、q g 、q w Is the source and sink phases of oil, gas and water, kg/s; s is S o 、S g And S is w The saturation of the oil phase, the gas phase and the water phase respectively; ρ o 、ρ g 、ρ w Density of oil phase, gas phase and water phase fluid respectively, kg/m 3 ；v o 、v g 、v w The speeds of the oil phase fluid, the gas phase fluid and the water phase fluid are m/s respectively.
6. A method of numerical simulation of multiphase fluid formation seepage according to claim 4, wherein the three phase capillary pressure p c According to the dominant phase of the multiphase fluid, it is obtained by the following formula:
when the oil phase is the dominant phase, the three-phase capillary pressure p c The method comprises the following steps:
when the gas phase is the dominant phase, the three-phase capillary pressure p c The method comprises the following steps:
when the water phase is the dominant phase, the capillary pressure p is three-phase c The method comprises the following steps:
wherein p is cog 、p cow 、p cwg The capillary pressure of oil gas, oil water and gas water is direct, and the expression is as follows:
wherein sigma og 、σ ow 、σ wg Interfacial tension between oil gas, oil water and gas water respectively, wherein the unit is N/m; θ og 、θ ow 、θ wg The wetting contact angles among oil gas, oil water and gas water are dimensionless; r is the throat radius in m.
7. A method for numerical simulation of formation seepage of a multiphase fluid according to claim 1, wherein in step S3, the pressure field of the multiphase fluid is solved using a fast iterative method or a multiple grid method.
8. A method of numerical simulation of formation seepage of a multiphase fluid according to any one of claims 1 to 7, wherein the solving of the pressure field of the multiphase fluid comprises:
solving a first term in a multiphase fluid mass equation:
wherein C is o 、C g 、C w The compression coefficients of oil, gas and water phases are respectively, and the compression coefficients are dimensionless; t is the current time, t+deltat is the next time, and the units are s;
solving a second term in the multiphase fluid mass equation:
wherein z is c The parameter is dimensionless and is the number of adjacent grids; a is the area of the grid, and the unit is m 2 I is grid i, j is grid j adjacent to grid i; g m Is conductivity;
the simultaneous multiphase fluid mass equation, a solution formula of a first term and a solution formula of a second term in the multiphase fluid mass equation are obtained:
substituting different parameters of the current time t and the next time t+delta t into the above formula to obtain N above formulas at different times to form a matrix equation A of the above formula t+Δt X t+Δt ＝B t Wherein:
wherein A is t+Δt A sparse matrix of size N X N (N is the number of meshes of the model) related to the hydraulic conductivity of the fluid, X t +Δt And B t Is two vectors of length N, X t+Δt For the pressure field vector of the next moment t+Δt, B t Is a vector related to the pressure field and boundary conditions at the current moment t;
and solving a matrix equation at each moment to obtain the pressure field of the multiphase fluid.
9. The method for numerical simulation of multiphase fluid formation seepage according to claim 1, wherein the establishing of the high-precision digital core model comprises:
acquiring a porosity three-dimensional data volume and a permeability three-dimensional data volume of a core sample by utilizing the core sample and a scanning technology;
establishing a three-dimensional geometric model of the core sample, and assigning the three-dimensional geometric model according to the porosity three-dimensional data volume and the permeability three-dimensional data volume to obtain a high-precision digital core model of the core sample;
wherein the obtaining of the porosity three-dimensional data volume and the permeability three-dimensional data volume comprises the following steps:
s11, obtaining a core sample of a reservoir to be simulated, and obtaining actual porosity phi and actual permeability k of the core sample by using the core sample;
s12, acquiring two-dimensional images of the core sample on different sections by using a scanning technology to acquire two-dimensional image data;
s13, obtaining a three-dimensional data body of the core according to the two-dimensional image data on the sections;
s14, obtaining a porosity conversion coefficient of the core sample according to the relation between the actual porosity phi of the core and the two-dimensional image data; acquiring a permeability conversion coefficient of the core sample according to the relation between the actual permeability k and the actual porosity phi and the two-dimensional image data;
and S15, applying the porosity conversion coefficient and the permeability conversion coefficient, the relation between actual porosity and two-dimensional image data, and the relation between actual permeability and two-dimensional image data to the three-dimensional data body of the core to obtain the three-dimensional data body of the core porosity and the three-dimensional data body of the core permeability.
10. The numerical simulation method of multiphase fluid stratum seepage is applied to the technical fields of oilfield development, underground water management, geological engineering and environmental protection.
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