CN105317433B - Granulation mass microcosmic duct based on level-set function extracting method - Google Patents

Abstract

The present invention provides a kind of granulation mass microcosmic duct based on level set function extracting method, and the method includes: step 1, carries out the structure of background grid；Step 2, in order to obtain the interface of substrate and hole, defines lattice point function to any given lattice point and granule, calculate " lattice point granule " to functional value after, calculate each lattice point level set functional value；Step 3, extracts 0 contour surface of the function field of background grid, can obtain duct geometry；And step 4, the contour surface extracted is carried out smooth treatment to improve the quality of duct geometry further.Should can build offer high accuracy duct geometry for volume mesh in duct by granulation mass microcosmic duct based on level set function extracting method, lay a good foundation for carrying out the numerical prediction of the research of pore scale profit dynamic behavior and high water-cut stage remaining oil micro Distribution based on VOF method.

Description

Granulation mass microcosmic duct based on level-set function extracting method

Technical field

The present invention relates to oil field development technical field, especially relate to a kind of based on level-set letter The granulation mass microcosmic duct extracting method of number.

Background technology

East China oil field generally enters ultra-high water cut stage, and the abnormal distribution of remaining oil is complicated and disperses, Improve recovery ratio difficulty to continue to increase.Numerical reservoir simulation method based on macroscopic view seepage theory can only be from The average characteristics of macro-scale reflection reservoir oil water distribution, and the space of profit in pore scale is divided The prediction of cloth characteristic and morphological character is the most helpless, and in displacement process the interaction of profit with These characteristics are closely related.Pore scale microcosmic based on VOF (volume of fluid) method oozes Flow field simulation method can in accurate description hole the microscopic distribution of remaining oil and its inherent formed Mechanism, it is significant that the further investigation of the method oil reservoir interim to ultra-high water-containing improves recovery ratio. VOF method is computational methods based on grid, and the method needs to extract pore channel, and in passage Build grid.

At present, the construction method of hole geometry is broadly divided into: with construction method (three-dimensional reconstruction), Scanogram method and the construction method of Kernel-based methods.Random structure method refers to by building stochastic process generation (such as, there is the fractal structure similar to target rock core) pore structure of set pattern rule, the method Precision depends on the identification of target core character, and the anisotropy of earth formation is then difficult in the method The rock core built emerges from.Picture construction method is swept by actual rock core is carried out high precision image Retouch, and carry out geometrical reconstruction according to the image of scanning.The contrast of duct and substrate is directly connected to this Method builds the precision of geometry；Meanwhile, the rock core of acquisition is merely capable of reflecting that rock core obtains near position Pore structure, and rock core itself can cause a certain degree of destruction by rock core acquisition process.Based on The construction method of physical process, by granule (the spherical or aspherical) deposition of heap, compression, Diagenetic process is simulated realizing the structure of rock core, and the geometry that the method constructs can truly describe The loose structure on stratum, and there is preferable circulation.This makes the method become research pore scale The important tool of the Micro Numerical Simulation method mid-early stage modeling of flowing and substrate mechanical behavior.

The granulation mass constructed by Process Method contains only the surface grids information of granule or simple Particle geometric shape information (such as: ball heap contains only particle position and radius), and granule and granule Between there is a certain degree of handing-over, directly use these information architecture volume mesh often to there will be grid strange Different, it is impossible to carry out flow simulating in hole.A kind of conventional method is directly to enter the granulation mass of structure Row section scanning, builds digital cores.By the digital cores of structure being carried out after surface grids structure again Construct grid.This method can avoid grid singular problem, but the method utilizes monodrome (0 Or 1) distinguishing substrate and duct, the interface in the substrate built and duct uses ladder approximation, Primary granule smoothness of the surface cannot be embodied so that in the moistening on VOF simulation process mesostroma surface Property cannot accurately embody.A kind of new granulation mass based on level-set function is we have invented for this Microcosmic duct extracting method, solves above technical problem.

Summary of the invention

It is an object of the invention to provide one can provide high accuracy duct several for volume mesh structure in duct Granulation mass microcosmic duct based on the level-set function extracting method of what structure.

The purpose of the present invention can be achieved by the following technical measures: based on level-set function Grain heap microcosmic duct extracting method, should granulation mass microcosmic duct based on level-set function extraction side Method includes: step 1, carries out the structure of background grid；Step 2, in order to obtain substrate and hole Interface, defines lattice point function to any given lattice point and granule, calculate " lattice point-granule " to After functional value, calculate each lattice point level set functional value；Step 3, extracts the function of background grid 0 contour surface of field, can obtain duct geometry；And step 4, the contour surface extracted is carried out light Sliding process is to improve the quality of duct geometry further.

The purpose of the present invention realizes also by following technical measures:

In step 1, background grid is to cover the uniform cartesian grid lattice structure of granulation mass, grid list Unit is typically square or the cuboid close to square, the size in three directions of grid cell Select relevant with the resolution in required extraction duct.

In step 1, rectangular parallelepiped grid unit in the computing formula of the yardstick in three directions is:

${\mathrm{\δ}}_i=\frac{D_i}{\mathrm{int}\left(\frac{D_i}{\mathrm{\αd}}\right)+1}---\left(1\right)$

Wherein, i is direction index, three direction x of representation space, y, z；D_iExist for zoning Yardstick on i-th direction；D is the yardstick of granule；α is default mesh scale and particle scale Ratio；Int (x) is bracket function, can be yielded less than the maximum integer of x by this function；δ_iFor i The grid cell yardstick in direction；

(i, j, coordinate position k) uses formula below to calculate to background grid lattice point

x_i=x_min+i·δ_x (2)

y_j=y_min+j·δ_y (3)

z_k=z_min+k·δ_z (4)

Wherein, x_min, y_minAnd z_minMinima for tri-directions of zoning x, y and z；I, j, K is grid cell index on tri-directions of x y z.

In step 2, any given lattice point i and granule j is defined as follows lattice point function

Wherein, r_min,i,jFor the minimum distance on lattice point i to granule j surface；For spherical particles, r_min,i,j Employing equation below is asked for

r_min,i,j=| | C_j-p_i|-r_j| (6)

Wherein, C_jFor the centre of sphere of jth spheroid, p_iFor the position coordinates of i-th lattice point, r_iFor spheroid Radius, | x | is for asking for mould or the absolute value of x；And for aspherical particle, need to set up this The surface mesh of grain, and find nearest grid surface by building Octree, then ask for lattice point to net The value in lattice face；By equation (5) calculate " lattice point-granule " to functional value after, use following side Journey calculates each lattice point level set functional value

G_i=min (F_i,0,F_i,1...,F_i,j,...,F_i,N-1) (7)

Wherein, N is the sum placing granule；Lattice point outside for granule, equation (7) calculates Value be on the occasion of；Lattice point in granule, the value that the equation calculates is negative value；Particle surface grid computing goes out Value be then 0；At extra-granular, from particle surface distance more away from the value of lattice point the biggest, at granule Internal from particle surface distance more away from the value of lattice point the least, so that G_iIt is distributed at Spatial continual.

In step 4, to duct being done as follows a little geometrically:

$p_i=\underset{j}{\mathrm{\Σ}}{w}_i\left(r_{\mathrm{ij}}\right)p_j---\left(8\right)$

Wherein, p_iFor the position of duct i-th point geometrically, p_jGeometrically connect with this point for duct The position of point；w_iFor smoothing kernel function, r_ijFor a p_iTo p_jDistance；By the equation (8) Realize the smooth of duct geometry.

Granulation mass microcosmic duct based on level-set function extracting method in the present invention, relates to oil Hide numerical simulation application and oil-gas field development improves oil recovery field.Specifically to granule On the basis of heap builds background grid, application level-set function carries out microcosmic duct to granulation mass and carries Take and carry out smooth treatment, thus obtain high-precision duct geometry, for carrying out hole based on VOF method The numerical prediction of the research of gap yardstick profit dynamic behavior and high water-cut stage remaining oil micro Distribution is established Determine basis.The method lays background grid on the basis of building granulation mass, and to background grid point Definition level-set function, real finally by background grid level set function field is built contour surface Existing substrate and the extracted with high accuracy of duct interface.The present invention combines Micro Numerical Simulation to duct geometry The requirement of precision, it is proposed that granulation mass is being built by a kind of granulation mass microcosmic duct extracting method the method On the basis of background grid, for each background grid grid computing level-set functional value and right The level-set function field generated carries out the extraction of 0 contour surface, finally the contour surface extracted is carried out light Sliding process, thus obtain high-precision duct geometry.To 1mm × 1mm × 1mm and 3mm × 3mm × 3mm The extraction result at interface, granulation mass duct show, context of methods can build for volume mesh in duct and provide Duct geometry in high precision, for carrying out the research of pore scale profit dynamic behavior based on VOF method And the numerical prediction of high water-cut stage remaining oil micro Distribution lays a good foundation.

Accompanying drawing explanation

Fig. 1 is the one of granulation mass microcosmic duct based on the level-set function extracting method of the present invention The flow chart of specific embodiment；

Fig. 2 is the schematic diagram of packed particle shape；

Fig. 3 is the schematic diagram that smooth front 1mm × 1mm × 1mm packed particle duct geometric surface extracts；

Fig. 4 is the schematic diagram that smooth rear 1mm × 1mm × 1mm packed particle duct geometric surface extracts；

Fig. 5 is the schematic diagram of 3mm × 3mm × 3mm packed particle duct geometry；

Fig. 6 is the schematic diagram of 3mm × 3mm × 3mm duct integral grid；

Fig. 7 is the schematic diagram of 3mm × 3mm × 3mm duct local volume mesh details.

Detailed description of the invention

For making the above and other objects, features and advantages of the present invention to become apparent, cited below particularly Go out preferred embodiment, and coordinate institute's accompanying drawings, be described in detail below.

As it is shown in figure 1, the granulation mass microcosmic duct based on level-set function that Fig. 1 is the present invention carries The flow chart of one specific embodiment of access method.

In step 101, build background grid.

First carrying out the structure of background grid, background grid is to cover the uniform cartesian grid of granulation mass Structure, grid cell is typically square or the cuboid close to square.Three of grid cell Selecting of the size in direction is relevant with the resolution in required extraction duct, and such as grid cell is in x side It is δ to yardstick_x, then radius is less than δ_xAnd the duct being perpendicular to x-axis then can be filtered, the most permissible Minimum volume mesh is avoided during the volume mesh subdivision of duct.Therefore, δ_xCan not be too small.Meanwhile, for Ensure extract the precision at interface or prevent from filtering out main duct, δ_xCan not be excessive.When Grain is time scale difference is little in three directions, can using granule circumsphere diameter as particle scale, The yardstick of background grid unit is generally 0.06-0.1 times of particle scale.Three direction chis when granule When degree difference is bigger, then need according to minimum yardstick to determine background grid yardstick.Finally, rectangular The volume mesh unit yardstick in three directions can calculate by formula below

${\mathrm{\δ}}_i=\frac{D_i}{\mathrm{int}\left(\frac{D_i}{\mathrm{\αd}}\right)+1}---\left(1\right)$

Wherein, i is direction index, three direction x of representation space, y, z；D_iExist for zoning Yardstick on i-th direction；D is the yardstick of granule；α is default mesh scale and particle scale Ratio；Int (x) is bracket function, can be yielded less than the maximum integer of x by this function.δ_iFor i The grid cell yardstick in direction.

(i, j, coordinate position k) can calculate background grid lattice point by formula below

x_i=x_min+i·δ_x (2)

y_j=y_min+j·δ_y (3)

z_k=z_min+k·δ_z (4)

Wherein, x_min, y_minAnd z_minMinima for tri-directions of zoning x, y and z.I, j, K is grid cell index on tri-directions of x y z.Flow process enters into step 102.

In step 102, build level-set function.In order to obtain the interface of substrate and hole, right Any given lattice point and granule definition lattice point function, calculate " lattice point-granule " to functional value after, Calculate each lattice point level set functional value.

In order to obtain the interface of substrate and hole, any given lattice point i and granule j is defined as follows lattice Point function

Wherein, r_min,i,jFor the minimum distance on lattice point i to granule j surface.For spherical particles, r_min,i,j Employing equation below is asked for

r_min,i,j=| | C_j-p_i|-r_j| (6)

Wherein, C_jFor the centre of sphere of jth spheroid, p_iFor the position coordinates of i-th lattice point, r_iFor spheroid Radius, | x | is for asking for mould or the absolute value of x.And for aspherical particle, need to set up this The surface mesh of grain, and find nearest grid surface by building Octree, then ask for lattice point to net The value in lattice face.By equation (5) calculate " lattice point-granule " to functional value after, use following side Journey calculates each lattice point level set functional value

G_i=min (F_i,0,F_i,1...,F_i,j,...,F_i,N-1) (7)

Wherein, N is the sum placing granule.Lattice point outside for granule, equation (7) calculates Value be on the occasion of；Lattice point in granule, the value that the equation calculates is negative value；Particle surface grid computing goes out Value be then 0.At extra-granular, from particle surface distance more away from the value of lattice point the biggest, at granule Internal from particle surface distance more away from the value of lattice point the least, so that G_iIt is distributed at Spatial continual.Stream Journey enters into step 103.

In step 103, extract duct geometry.Extract 0 contour surface of the function field of background grid, i.e. Duct geometry can be obtained.

Equation (7) is that each lattice point constructs a level set functional value, the lattice values in duct For just, intramatrical lattice values is negative, and the lattice values on duct and substrate interface is 0.This level The absolute value of set value is the lattice point distance to interface, duct.Therefore, duct to be obtained geometry, only need 0 contour surface of the function field of background grid to be extracted.Given grid and the extraction of lattice point function field etc. The technology relative maturity in value face, and have some programs increased income directly to use.Flow process enters into step Rapid 104.

In step 104, duct geometric smoothness processes.

In order to improve the quality of duct geometry further, the contour surface to extracting is needed to carry out smooth place Reason.To duct being done as follows a little geometrically:

$p_i=\underset{j}{\mathrm{\Σ}}{w}_i\left(r_{\mathrm{ij}}\right)p_j---\left(8\right)$

Wherein, p_iFor the position of duct i-th point geometrically, p_jGeometrically connect with this point for duct The position of point.w_iFor smoothing kernel function, r_ijFor a p_iTo p_jDistance.Permissible by above-mentioned equation Realize the smooth of duct geometry.

In application one embodiment of the invention, in order to verify feasibility and the effectiveness of the present invention, choosing Take the granule shown in Fig. 2 to pile up.In order to make problem reduction, do not carry out accumulation horizon compression and The diagenesis of granule processes, and this has no effect on the checking of this method.This granule is used to carry out 1mm × 1mm × 1mm and 3mm × 3mm × 3mm region is piled up.

Fig. 3 and Fig. 4 give use this method to the granulation mass mesostroma of 1mm × 1mm × 1mm and The extraction result of duct interface.Fig. 3 is the result not carrying out smooth treatment.It can be seen that Context of methods remains the original geometry form of granule, geometric jacquard patterning unit surface ladder approximation does not occur.So And, at the granule interface with granule, there are " sawtooth ".Boundary after smooth treatment Face is as shown in Figure 4.It can be seen that after smooth treatment, " sawtooth " shape of interface interface Disappearing, integral surface mesh quality is also obviously improved, and base established by the volume mesh structure for the later stage Plinth.

In order to verify that the granulation mass mesostroma duct in bigger zoning is joined by this method further The feasibility of interface extraction and effectiveness, use the granule shown in Fig. 2 to carry out 3mm × 3mm × 3mm region has carried out particle packing, and uses this method boundary to substrate duct Face is extracted, and result is as shown in Figure 5.From this figure, it can be seen that particle surface approximate exact, Intersection is smooth.Illustrate that in this method extraction to duct in granulation mass and substrate interface be feasible And it is effective.

In order to the geometry feasibility at later stage volume mesh subdivision of extraction is described, to the boundary shown in Fig. 5 Face geometry uses cut-cell mesh generation technology to carry out net to (removing dead band) in negotiable duct Lattice subdivision.Fig. 6 and Fig. 7 gives integral grid and volume mesh local detail in duct.From volume mesh From the point of view of local detail, the smooth mesh quality that can be obviously improved of inner surfaces of pores, simultaneously granule with Grain junction grid is preferable.

Claims (2)

1. granulation mass microcosmic duct based on level-set function extracting method, it is characterised in that should be based on The granulation mass microcosmic duct extracting method of level-set function includes:

Step 1, carries out the structure of background grid；

Step 2, in order to obtain the interface of substrate and hole, defines lattice point letter to any given lattice point and granule Number, calculate " lattice point-granule " to functional value after, calculate each lattice point level-set functional value；

Step 3, extracts 0 contour surface of the function field of background grid, can obtain duct geometry；And

Step 4, carries out smooth treatment to improve the quality of duct geometry further to the contour surface extracted；

In step 1, background grid is to cover the uniform cartesian grid lattice structure of granulation mass, and grid cell is usual It is square or the cuboid close to square, the selection of the size in three directions of grid cell and required The resolution extracting duct is relevant；Rectangular parallelepiped grid unit in the computing formula of the yardstick in three directions is:

${\mathrm{\δ}}_i=\frac{D_i}{\mathrm{int}\left(\frac{D_i}{\mathrm{\α}d}\right)+1}---\left(1\right)$

Wherein, i is direction index, three direction x of representation space, y, z；D_iFor zoning in i-th direction On yardstick；D is the yardstick of granule；α is the ratio of default mesh scale and particle scale；Int is to round Function, can obtain clipping the maximum integer of fractional part by this function；δ_iGrid cell chi for i direction Degree；

(i, j, coordinate position k) uses formula below to calculate to background grid lattice point

x_i=x_min+i·δ_x (2)

y_j=y_min+j·δ_y (3)

z_k=z_min+k·δ_z (4)

Wherein, x_min, y_minAnd z_minMinima for tri-directions of zoning x, y and z；I, j, k are grid cell Index on tri-directions of xyz；

In step 2, any given lattice point i and granule j is defined as follows lattice point function

Wherein, r_min,i,jFor the minimum distance on lattice point i to granule j surface；For spherical particles, r_min,i,jUse as follows Formula is asked for

r_min,i,j=| | C_j-p_i|-r_j| (6)

Wherein, C_jFor the centre of sphere of jth spheroid, p_iFor the position coordinates of i-th lattice point, r_jFor the radius of spheroid, | x | For asking for mould or the absolute value of x, x is | | the acute pyogenic infection of finger tip of formula in symbol；And for aspherical particle, need to build The surface mesh of this granule vertical, and find nearest grid surface by building Octree, then ask for lattice point to net The value in lattice face；By equation (5) calculate " lattice point-granule " to functional value after, use following Equation for Calculating every Individual lattice point level-set functional value

G_i=min (F_i,0,F_i,1...,F_i,j,...,F_i,N-1) (7)

Wherein, N is the sum placing granule；Lattice point outside for granule, the value that (7) equation calculates on the occasion of；? Intragranular lattice point, the value that the equation calculates is negative value；The value that particle surface grid computing goes out is then 0；Outside granule Portion, from particle surface distance more away from the value of lattice point the biggest, inside granule from particle surface distance more away from lattice point Value the least, so that G_iIt is distributed at Spatial continual.

Granulation mass microcosmic duct based on level-set function the most according to claim 1 extracting method, It is characterized in that, in step 4, to duct being done as follows a little geometrically:

$p_i=\underset{j}{\Σ}{w}_i\left(r_{ij}\right)p_j---\left(8\right)$

Wherein, p_iFor the position of duct i-th point geometrically, p_jPosition for the point that duct geometrically connects with this point Put；w_iFor smoothing kernel function, r_ijFor a p_iTo p_jDistance；Duct geometry is realized by the equation (8) Smooth.