CN108896588A - A kind of measurement method of porous media microstructure - Google Patents
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Abstract
The invention discloses a kind of measurement methods of porous media microstructure, include the following steps：Determine in different-energy channel range it is corresponding filtering sheet material and thickness, obtain porous media under multiple energy channels data for projection, respectively rebuild the corresponding porous media of each energy channel image, based under multiple energy channels reconstruction image obtain porous media Microstructure characterization；The present invention realizes the function of power spectrum CT using traditional CT, can obtain image of the substance under different-energy channel simultaneously, differences in materials is maximized, realize the material identification of reconstruction image, save the cost；Compensate for the deficiency of single energy image partition method, and the volume fraction ratio of corresponding sill ingredient can be obtained in each voxel, the structural information characterization for realizing the smaller scale of substance, effectively improves the resolution ratio of reconstruction image, so that the differentiation of pore structure becomes apparent from the micro-structure diagram of porous media.
Description
Technical field
The invention belongs to microtexture measurement fields, are related to a kind of measurement method of porous media microstructure.
Background technique
Porous media is widely distributed in the depth of the earth's crust, in shallow-layer, such as the rock of the soil of earth's surface, deep layer, while underground
Petroleum, natural gas and water in rock stratum are a kind of multicomponent systems of complexity in nature porous media, study the micro- of porous media
It sees structure, especially porosity and oil gas in real life is surveyed and exploited significant.It is by mutual in porous media structure
The solid particle and void among particles of connection form, and the complexity of structure, non-homogeneous texture characteristic etc. are all learned both at home and abroad
The extensive research of person.
There are many currently used material microstructure measurement method.One-dimensional measurement often uses load displacement, and two-dimensional measurement is common
Scanning electron microscope and penetrating electrons microscopy, both technologies cannot reflect hole in the distribution shape of three-dimensional space
State.Serial section cutting technique can realize the three dimensional analysis of microstructure, but the shortcomings that technology is to destroy sample, is also easy to produce artifact.
The appearance of CT technology, makes it possible the non-destructive testing of material.Micro- CT system is grown rapidly in recent years, is able to achieve with micron order
Resolution capability nondestructively reproduces the three-dimensional configuration of material internal structure and material, is a kind of novel test and analytical technology.By
In in traditional CT reconstruction process, X-ray attenuation detection imaging is to the weakly absorbing material such as soft tissue being mainly made of light element
The contrast and resolution ratio generated with low atomic number (Z) material is lower, can not differentiate Sample details information.
Subsequent X-ray phase contrast CT imaging technique overcomes the deficiency of traditional CT imaging from mechanism, can be realized pair
The imaging of weakly absorbing material or low Z sample.During Microstructure characterization, traditional image segmentation rebuild based on single energy CT
Microstructure characterization method is lost the small-scale structure information that scale can be parsed lower than CT.In addition, for certain absorbabilities and
The material composition that refractive index information is all closer to can singly descend and be difficult to carry out area to different materials using image partition method
Point.
Summary of the invention
The purpose of the present invention is：A kind of measurement method of porous media microstructure is provided, solution was rebuild in traditional CT
Cheng Zhong, contrast and resolution ratio lower the problem of can not differentiating Sample details information.
In order to solve the above technical problem, the present invention provides a kind of measurement method of porous media microstructure, features
It is, includes the following steps：
S1, component, outer dimension and energy channel range according to test object, it is right in different-energy channel range to determine
The filtering sheet material and thickness answered；
S2, the ray emission end that different filter plates is arranged in CT respectively obtain porous media multiple by filtering
Data for projection under energy channel；
S3, the figure for rebuilding the corresponding porous media of each energy channel respectively according to the data for projection under multiple energy channels
Picture；
S4, porous media Microstructure characterization is obtained based on the reconstruction image under multiple energy channels.
According to the porous media Microstructure characterization that S4 is obtained, the microporosity of porous media can be determined, thus really
The seepage flow situation of stand oil, gas and water in reservoir rocks.
The material of filter plate is aluminium, steel or tantalum.
S3 specifically includes following steps：
S3.1, the statistical model for establishing power spectrum data for projection, in single pass, determine all data for projection greatly seemingly
Right function；
S3.2, by the similitude of the reconstruction image under different-energy channel, first by the projection under different-energy channel
Data are combined into wide power spectrum data for projection, can be rebuild by common algorithm for reconstructing to it, obtain the i.e. wide power spectrum of full energy channel
Reconstruction image f determines attenuation coefficient distribution and the width energy of the object to be reconstructed under different-energy channel as references object
The related coefficient of reconstruction image f is composed, to describe the similitude between image；
S3.3, according to step S3.1 and S3.2, rebuild the porous media attenuation coefficient under each energy channel point respectively
Cloth obtains the power spectrum CT statistics algorithm for reconstructing model based on power spectrum image similarity, rebuilds and obtain respectively to each energy channel
Reconstruction image under multiple energy channels.
In S3.1, statistical model is
Wherein：Continuum is divided into M narrow spectrumsThat is M energy channel, i indicate the
I X-ray；Indicate the projection number measured on the corresponding detector of lower i-th ray of m-th of energy channel
According to；A=(aij) indicate projection matrix；aijIndicate the intersection length of i-th ray and j-th of voxel；Indicate the attenuation coefficient point of object to be reconstructed under m-th of energy channel
Cloth；Indicate the front projection process of i-th of detector under m-th of energy channel；Table
Show the projection value measured on detector when blank scans under m-th of energy channel；It indicates under m energy channel i-th
The error of the data for projection measured on detector；I is ray sum, and J is the corresponding voxel sum of object to be reconstructed, and M is total
Energy channel；
In single pass, the maximum likelihood function of all data for projection measured, i.e.,：
In S3.2, the attenuation coefficient of the object to be reconstructed under different-energy channel is distributedWith wide energy spectrum reconstruction image f
Related coefficientFor：
Wherein, cov indicates the covariance of two images, and σ indicates the standard deviation of image.
In S3.3, making the related coefficient in maximum likelihood function and S3.2 in S3.1 is maximum, is obtained based on power spectrum
The power spectrum CT of image similarity counts algorithm for reconstructing model：
Each energy channel is rebuild respectively and obtains the reconstruction image under M energy channel
In S3.3, by constructing log-likelihood functionProxy function Φc(μ；μ(n)) replace original target
Function, wherein proxy function needs to meet：1. proxy function monotonic increase is in proxied function；2. proxy function and proxied letter
Several maximum values is identical；
And the optimal solution of algorithm for reconstructing model is obtained using Newton method
Wherein n is the number of iterations；
And the Section 2 in algorithm for reconstructing model is by directly obtaining its analytic solutions to its derivation
WhereinIt isMean value image, be vector two norms.
S4 specifically includes following steps：
S4.1, the attenuation coefficient for determining sill under different-energy channel；
By sill (α1,α2,…,αK) in different-energy channelUnder attenuation coefficient regard as
It is the attenuation coefficient vector of the sill, attenuation coefficient vector of the kth kind sill under M energy channel
K=1,2 ..., K；
Wherein,For the attenuation coefficient under m-th of energy channel；
S4.2, it setsIt is the percent by volume that various sills account in j-th of voxel, then
Have
And
By Maximum Entropy Principle Method, in conjunction under M energy channel reconstruction image and different-energy channel under sill
Attenuation coefficient, pick out one closest to the solution being really distributed, i.e., from all compatible distributions
To obtain porous media three-dimensional microstructures characterization model.
The sill is the basic material to form porous media.
Beneficial effect：The present invention realizes the function of power spectrum CT using traditional CT, can obtain substance simultaneously in different-energy
Image under channel, differences in materials is maximized, and realizes the material identification of reconstruction image, save the cost；Mainly utilize existing CT
Then system utilizes power spectrum CT by effectively filtering the CT projected image image for obtaining porous media under different-energy channel
Algorithm for reconstructing obtains power spectrum CT reconstruction image, obtains the microstructure table of hole medium by research object of voxel on this basis
Sign, this method compensate for the deficiency of single energy image partition method, and can obtain corresponding sill in each voxel and (be formed more
The basic material of hole medium) ingredient volume fraction ratio, realize the structural information characterization of the smaller scale of substance (be lower than pixel scale), have
Effect improves the resolution ratio of reconstruction image, so that the differentiation of pore structure becomes apparent from the micro-structure diagram of porous media.
Detailed description of the invention
Fig. 1 traditional CT continuous spectrum schematic diagram；
The narrow power spectrum schematic diagram of Fig. 2 power spectrum CT.
Specific embodiment
To keep the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to of the invention
Specific embodiment is described in further detail.
The invention discloses a kind of measurement methods of porous media microstructure, which is characterized in that includes the following steps：
S1, component, outer dimension and energy channel range according to test object, it is right in different-energy channel range to determine
The filtering sheet material and thickness answered；
S2, the ray emission end that different filter plates is arranged in traditional CT respectively obtain porous media by filtering and exist
Data for projection under multiple energy channels；
Traditional CT is the CT system based on energy integral detector, and the X-ray of continuum is divided into not phase by the present invention
The energy channel (as shown in Figure 2) of overlapping can be directly realized by the function currently based on the power spectrum CT of photon counting detector, but
It is expensive and technology is not yet mature.
Here the data for projection collection of multiple energy channels is obtained by filtering based on traditional CT.The material of filter plate be aluminium,
Wider continuous spectrum is become relatively narrow multiple energy channels by steel or tantalum etc., and then multiple energy channels of acquisition object is narrow
Data for projection collection is composed, traditional CT is made to realize the function of multispectral imaging.
S3, the figure for rebuilding the corresponding porous media of each energy channel respectively according to the data for projection under multiple energy channels
Picture；
Since in power spectrum filtering, photon number (dosage) is reduced, obtained projection noise level is increased, therefore,
The characteristics of being rebuild by using the statistics iterative approximation based on Data Physical model in combination with spectrum CT building is reasonable first
Information is tested, the power spectrum CT statistics algorithm for reconstructing model with prior information is constructed and is rebuild.
Specific step is as follows：
S3.1, the statistical model for establishing power spectrum data for projection
Continuum is divided into M narrow spectrumsThat is M energy channel, under each energy channel
Measurement data is influenced by factors such as the scattering of X-ray, the noises of detector so that obtaining data is random, statistical model
For
Wherein：I indicates i-th X-ray；Indicate the corresponding detector of lower i-th ray of m-th of energy channel
On the data for projection that measures；A=(aij) indicate projection matrix；aijIndicate the intersection length of i-th ray and j-th of voxel；Indicate the attenuation coefficient point of object to be reconstructed under m-th of energy channel
Cloth；Indicate the front projection process of i-th of detector under m-th of energy channel；Table
The projection value measured on detector when showing blank scanning (without any object) under m-th of energy channel；Indicate m
The error of the data for projection measured on i-th of detector under energy channel.I is ray sum, and J is the corresponding body of object to be reconstructed
Plain sum, M are total energy channel.
Since each detector cells are independent from each other, therefore the collected data for projection of each detector cellsAlso it is independent from each other, the joint according to mutually indepedent stochastic variable is general
The property of rate distribution is known, in single pass, the likelihood function (joint probability of i.e. all projections of all data for projection measured
Distribution) be：
For convenience of calculation, logarithm is taken simultaneously to above formula both sides and remove constant can be obtained by logarithmic form greatly seemingly
Right function, i.e.,：
S3.2, by the similitude of the reconstruction image under different-energy channel, first by the projection under different-energy channel
Data are combined into wide power spectrum data for projection, can be rebuild by common algorithm for reconstructing to it, obtain the i.e. wide power spectrum of full energy channel
Reconstruction image f is determined under different-energy channel as references objectWith the phase relation of wide energy spectrum reconstruction image f
NumberTo describe the similitude between image：
I.e.
M=1,2 ..., M
Wherein f is the high quality graphic that wide range is rebuild, and cov indicates the covariance of two images, and σ indicates the standard of image
Difference；
Due to being in different-energy channelIt scans same object and obtains data for projection, thus it is different
Reconstruction image similitude with higher under energy channel, makes full use of the similitude of interchannel image that can effectively inhibit
Noise improves reconstructed image quality.
S3.3, according to step S3.1 and S3.2, rebuild the porous media attenuation coefficient under each energy channel point respectively
Cloth：
Making the related coefficient in likelihood function and S3.2 in S3.1 is maximum, is obtained based on power spectrum image similarity
Power spectrum CT counts algorithm for reconstructing model：
Above formula can be converted to
Can be used alternating iteration method solution, due to likelihood function be it is nonlinear, institute's above formula be not present analytic solutions,
It can be by constructing log-likelihood functionProxy function Φc(μ；μ(n)), i.e., one form of searching is simple, is easy to
The proxy function of variables separation replaces original objective function, and wherein proxy function needs to meet：1. proxy function monotonic increase
In proxied function；2. proxy function is identical as the maximum value of proxied function.
And optimal solution is obtained using Newton method
Wherein n is the number of iterations.
And the Section 2 in algorithm for reconstructing model can be by directly obtaining its analytic solutions to its derivation
WhereinIt isMean value image, | | | | be vector two norms.
Each energy channel is rebuild respectively and obtains the reconstruction image under M energy channel
S4, porous media Microstructure characterization is obtained based on the reconstruction image under multiple energy channels, it is specific as follows；
S4.1, the attenuation coefficient for determining sill under different-energy channel, the sill are the base to form porous media
Plinth material；Hole also can be used as a kind of sill, attenuation coefficient 0；
By sill (α1,α2,…,αK) in different-energy channelUnder attenuation coefficient regard as
It is the attenuation coefficient vector of the sill, such as attenuation coefficient vector of the kth kind sill under M energy channel
K=1,2 ..., K；
Wherein,For the attenuation coefficient under m-th of energy channel；
Usual attenuation coefficient of the various sills under each energy is known, and it is in an energy channelUnder
Attenuation coefficient be it is unknown, generally obtained by the weighted average under each energy channel.Again since its correctness is direct
The microscopic sdIBM-2+2q.p.approach of material is influenced, in order to more accurately obtain attenuation coefficient of the sill under an energy section, this example passes through depth
Learning method is spent, obtains training data by the repetition test to known materials, and then sill is obtained by training network and is existed
Attenuation coefficient model under each energy channel, to obtain mean attenuation coefficient of the sill under each energy channel.It should
The input of neural network is in the energy channel, and the attenuation coefficient of sill under each energy, output is under the energy channel
The attenuation coefficient of sill.
S4.2, it setsIt is the percent by volume that various sills account in j-th of voxel, then
Have
And
By Maximum Entropy Principle Method, in conjunction under M energy channel reconstruction image and different-energy channel under sill
Attenuation coefficient, pick out one closest to the solution being really distributed, i.e., from all compatible distributions
To obtain porous media three-dimensional microstructures characterization model.
The structural information of small scale in order to obtain, this example is using each voxel as research object, it is believed that different sills with
Certain likelihood ratio (microstructure) is distributed in voxel, in this way will be by every individual lower than the CT small dimensional information that can parse scale
The volume fraction ratio of the sill for including in element embodies.IfIt is that various sills account in j-th of voxel
The percent by volume arrived, then has：
And
ThereforeIt can regard a discrete type probability distribution as.Sill is obtained in voxel
Microstructure, that is, solveAnd
There is unlimited multiple groups solution, most reasonable distribution how is picked out from these compatible distributions and is come, this criteria for selection is exactly most
Big information entropy principle.Discrete type probability distributionComentropy be defined as：
By Maximum Entropy Principle Method, such distribution is selected from all compatible distribution, is under certain constraint conditions
Comentropy is set to reach the distribution of maximum.When entropy being regarded as the most suitable scale of metering uncertainty degree, just substantially
Approved and that maximum distribution of uncertainty degree is selected to be distributed under given constraint as stochastic variable.Because this random point
Cloth be it is the most random, be that subjective ingredient is minimum, uncertain thing made the distribution of maximum estimated.I.e.
In view of the microstructure of sill under different-energy channel is identical, therefore in m-th of energy channelTo
For j voxel
M=1,2 ..., M
WhereinIt is in m-th of energy channelThe attenuation coefficient of lower j-th of voxel, is obtained by S3.
Using this formula as the constraint condition for solving maximum entropy, then obtain having constrained maximum entropy microstructure reconstruction mould
Type
M=1,2 ..., M
This is the optimization problem of a with constraint conditions, is solved using lagrange's method of multipliers to it, is enabled
And introduce Lagrange multiplier λ0, λ1..., λM, obtain Lagrangian
Pass through the percent by volume for asking the available sill of method of local derviation to account in j-th of voxelTo obtain the microstructure of j voxel, identical method acts on j=1 on each voxel,
2 ..., J, so that it may obtain the microstructure of entire porous media.
During Microstructure characterization, traditional image segmentation Microstructure characterization method rebuild based on single energy CT is lost
The small-scale structure information of scale can be parsed lower than CT.In addition, when the decaying in sample there are sill under X-ray list energy
When coefficient information is closer to, it can singly descend to would become hard to distinguish using image partition method the distribution of different substrate materials material.The step can
The small-scale structure information of scale can be parsed effectively to obtain porous media lower than CT.
S5, the porous media Microstructure characterization obtained according to S4, can determine the microporosity of porous media, thus
Determine oil, seepage flow situation of the gas and water in reservoir rocks.
Because the fluid resources such as oil, gas, underground water are all preserved in the porous media for preserving rock, and the microcosmic hole of rock
Gap structure is the principal element of control oil, gas and water seepage flow in reservoir rocks, therefore acquires the microstructure of porous media
The micropore structure of porous media can be obtained, and to play great role in seepage flow Neo-Confucianism field.
The present invention is directed to a certain porous media, obtains porous media by filtering based on traditional CT and leads in multiple and different energy
Narrow spectrum data for projection under road reconstructs porous media using the statistics iteration power spectrum CT algorithm for reconstructing based on similarity constraint and exists
Corresponding three-dimensional reconstruction figure under each channel, then using voxel as research object, by solving based on gamma-spectrometric data constraint most
Big entropy model obtains the volume fraction ratio of sill in unit voxel, so that small dimensional information effectively indicates, to obtain porous media
The characterization of three-dimensional microstructures.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations
Also it should be regarded as protection scope of the present invention.
Claims (10)
1. a kind of measurement method of porous media microstructure, which is characterized in that include the following steps：
S1, component, outer dimension and energy channel range according to test object, determine corresponding in different-energy channel range
Filter sheet material and thickness；
S2, the ray emission end that different filter plates is arranged in CT respectively obtain porous media in multiple energy by filtering
Data for projection under channel；
S3, the image for rebuilding the corresponding porous media of each energy channel respectively according to the data for projection under multiple energy channels；
S4, porous media Microstructure characterization is obtained based on the reconstruction image under multiple energy channels.
2. a kind of measurement method of porous media microstructure as described in claim 1, it is characterised in that：It is obtained according to S4
Porous media Microstructure characterization can determine the microporosity of porous media, so that it is determined that oil, gas and water are in reservoir rocks
In seepage flow situation.
3. a kind of measurement method of porous media microstructure as described in claim 1, it is characterised in that：The material of filter plate
For aluminium, steel or tantalum.
4. a kind of measurement method of porous media microstructure as described in claim 1, it is characterised in that：S3 specifically include with
Lower step：
S3.1, the statistical model for establishing power spectrum data for projection determine the maximum likelihood letter of all data for projection in single pass
Number；
S3.2, by the similitude of the reconstruction image under different-energy channel, first by the data for projection under different-energy channel
It is combined into wide power spectrum data for projection, it can be rebuild by common algorithm for reconstructing, the i.e. wide energy spectrum reconstruction of full energy channel is obtained
Image f determines attenuation coefficient distribution and the width power spectrum weight of the object to be reconstructed under different-energy channel as references object
The related coefficient of image f is built, to describe the similitude between image；
S3.3, according to step S3.1 and S3.2, rebuild attenuation coefficient distribution of the porous media under each energy channel respectively, obtain
Algorithm for reconstructing model is counted to the power spectrum CT based on power spectrum image similarity, each energy channel is rebuild respectively and obtains multiple energy
Measure the reconstruction image under channel.
5. a kind of measurement method of porous media microstructure as claimed in claim 4, it is characterised in that：In S3.1, statistics
Model is
Wherein：Continuum is divided into M narrow spectrumsThat is M energy channel, i indicate that i-th X is penetrated
Line；Indicate the data for projection measured on the corresponding detector of lower i-th ray of m-th of energy channel；A=(aij) indicate to throw
Shadow matrix；aijIndicate the intersection length of i-th ray and j-th of voxel；
Indicate the attenuation coefficient distribution of object to be reconstructed under m-th of energy channel；Indicate m-th of energy
Measure the front projection process of i-th of detector under channel；It indicates when blank scans under m-th of energy channel on detector
The projection value measured；Indicate the error of the data for projection measured on i-th of detector under m energy channel；I is to penetrate
Line sum, J are the corresponding voxel sum of object to be reconstructed, and M is total energy channel；
In single pass, the maximum likelihood function of all data for projection measured, i.e.,：
6. a kind of measurement method of porous media microstructure as claimed in claim 5, it is characterised in that：It is different in S3.2
The attenuation coefficient of object to be reconstructed under energy channel is distributedWith the related coefficient of wide energy spectrum reconstruction image fFor：
Wherein, cov indicates the covariance of two images, and σ indicates the standard deviation of image.
7. a kind of measurement method of porous media microstructure as claimed in claim 6, it is characterised in that：In S3.3, make
The related coefficient in maximum likelihood function and S3.2 in S3.1 is maximum, obtains the power spectrum CT based on power spectrum image similarity
Count algorithm for reconstructing model：
Each energy channel is rebuild respectively and obtains the reconstruction image under M energy channel
8. a kind of measurement method of porous media microstructure as claimed in claim 7, it is characterised in that：In S3.3,
By constructing log-likelihood functionProxy function Φc(μ；μ(n)) replace original objective function, wherein generation
Reason function needs to meet：1. proxy function monotonic increase is in proxied function；2. the maximum value of proxy function and proxied function
It is identical；
And the optimal solution of algorithm for reconstructing model is obtained using Newton method
Wherein n is the number of iterations；
And the Section 2 in algorithm for reconstructing model is by directly obtaining its analytic solutions to its derivation
Wherein It isThe mean value image of f, | | | | it is two norms of vector.
9. such as a kind of described in any item measurement methods of porous media microstructure of claim 5~8, it is characterised in that：S4
Specifically include following steps：
S4.1, the attenuation coefficient for determining sill under different-energy channel；
By sill (α1,α2,…,αK) in different-energy channelUnder attenuation coefficient regard this as
The attenuation coefficient vector of sill, attenuation coefficient vector of the kth kind sill under M energy channel
Wherein,For the attenuation coefficient under m-th of energy channel；
S4.2, it setsIt is the percent by volume that various sills account in j-th of voxel, then has
And
By Maximum Entropy Principle Method, in conjunction with declining for the reconstruction image under M energy channel and sill under different-energy channel
Subtract coefficient, picks out one closest to the solution being really distributed, i.e., from all compatible distributionFrom
And obtain porous media three-dimensional microstructures characterization model.
10. a kind of measurement method of porous media microstructure as claimed in claim 9, it is characterised in that：The sill
For the basic material for forming porous media.
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| CN111521624A (en) * | 2019-05-03 | 2020-08-11 | 伟博泰有限公司 | Method and device for X-ray inspection of products, in particular food products |
| CN114063138A (en) * | 2021-11-16 | 2022-02-18 | 武汉联影生命科学仪器有限公司 | Method and device for determining effective energy of scanning imaging system and scanning imaging system |
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