CN108896588B - Method for measuring microstructure of porous medium - Google Patents

Method for measuring microstructure of porous medium Download PDF

Info

Publication number
CN108896588B
CN108896588B CN201810584258.9A CN201810584258A CN108896588B CN 108896588 B CN108896588 B CN 108896588B CN 201810584258 A CN201810584258 A CN 201810584258A CN 108896588 B CN108896588 B CN 108896588B
Authority
CN
China
Prior art keywords
energy
porous medium
under
microstructure
channels
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810584258.9A
Other languages
Chinese (zh)
Other versions
CN108896588A (en
Inventor
孔慧华
李毅红
潘晋孝
陈平
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
North University of China
Original Assignee
North University of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by North University of China filed Critical North University of China
Priority to CN201810584258.9A priority Critical patent/CN108896588B/en
Publication of CN108896588A publication Critical patent/CN108896588A/en
Application granted granted Critical
Publication of CN108896588B publication Critical patent/CN108896588B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/02—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material
    • G01N23/04—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material and forming images of the material
    • G01N23/046—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material and forming images of the material using tomography, e.g. computed tomography [CT]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00—Investigating materials by wave or particle radiation
    • G01N2223/10—Different kinds of radiation or particles
    • G01N2223/101—Different kinds of radiation or particles electromagnetic radiation
    • G01N2223/1016—X-ray
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00—Investigating materials by wave or particle radiation
    • G01N2223/40—Imaging
    • G01N2223/401—Imaging image processing

Landscapes

  • Health & Medical Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Pulmonology (AREA)
  • Radiology & Medical Imaging (AREA)
  • Analytical Chemistry (AREA)
  • Physics & Mathematics (AREA)
  • Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Analysing Materials By The Use Of Radiation (AREA)
  • Apparatus For Radiation Diagnosis (AREA)

Abstract

The invention discloses a method for measuring a microstructure of a porous medium, which comprises the following steps: determining corresponding filter plate materials and thicknesses in different energy channel ranges, acquiring projection data of the porous medium under a plurality of energy channels, respectively reconstructing an image of the porous medium corresponding to each energy channel, and acquiring microstructure characterization of the porous medium based on the reconstructed images under the plurality of energy channels; the invention realizes the function of energy spectrum CT by utilizing the traditional CT, can simultaneously acquire the images of substances under different energy channels, maximizes the material difference, realizes the substance identification of the reconstructed image and saves the cost; the method makes up the defects of a single-energy image segmentation method, can obtain the volume ratio of corresponding base material components in each voxel, realizes the structural information representation of smaller scales of substances, effectively improves the resolution of a reconstructed image, and makes the pore structure in the microstructure of the porous medium more obvious in distinction.

Description

Method for measuring microstructure of porous medium
Technical Field
The invention belongs to the field of microstructure measurement, and relates to a method for measuring a microstructure of a porous medium.
Background
The porous medium is widely distributed in deep and shallow layers of the earth crust, such as earth on the earth surface, deep rock and the like, meanwhile, oil, natural gas and water in underground rock layers are complex multi-element systems in the porous medium in the nature, and the research on the microstructure of the porous medium, particularly the porosity, has great significance for oil-gas exploration and exploitation in actual life. The porous medium structurally consists of solid particles and gaps among the particles, and the complexity, the non-uniform texture and the like of the structure are widely researched by domestic and foreign scholars.
Many methods for measuring the microstructure of materials are commonly used at present. The one-dimensional measurement is usually carried out on load displacement, the two-dimensional measurement is usually carried out on scanning electron microscope and penetrating electron microscope, and the two techniques cannot reflect the distribution state of pores in a three-dimensional space. The sequential slicing technique allows three-dimensional analysis of microstructures, but has the disadvantage of destroying the sample and creating artifacts. The advent of CT technology has made possible the non-destructive testing of materials. In recent years, micro-CT systems are rapidly developed, can reproduce three-dimensional forms of internal structures and materials of materials in a micro-scale resolution capability without damage, and are novel testing and analyzing technologies. Since in the conventional CT reconstruction process, X-ray attenuation detection imaging produces low contrast and resolution for weakly absorbing materials composed mainly of light elements, such as soft tissue and low atomic number (Z) materials, sample detail information cannot be resolved.
Then, the X-ray phase contrast CT imaging technology overcomes the defects of the traditional CT imaging from the mechanism, and can realize the imaging of weak absorption materials or low-Z samples. In the microstructure characterization process, the traditional image segmentation microstructure characterization method based on single-energy CT reconstruction loses small-scale structure information lower than the resolvable scale of CT. In addition, for some material compositions with relatively close information of absorptivity and refractive index, different materials are difficult to distinguish by using an image segmentation method under single energy.
Disclosure of Invention
The purpose of the invention is: the method for measuring the microstructure of the porous medium is provided, and the problem that the detailed information of a sample cannot be distinguished due to low contrast and resolution in the traditional CT reconstruction process is solved.
In order to solve the technical problem, the invention provides a method for measuring a microstructure of a porous medium, which is characterized by comprising the following steps of:
s1, determining corresponding filter material and thickness in different energy channel ranges according to the components, the external dimensions and the energy channel ranges of the detection object;
s2, respectively arranging different filter plates at the ray emission end of the CT, and obtaining projection data of the porous medium under a plurality of energy channels through filtering;
s3, respectively reconstructing an image of the porous medium corresponding to each energy channel according to the projection data under the plurality of energy channels;
and S4, acquiring microstructure characterization of the porous medium based on the reconstructed images under the multiple energy channels.
According to the microstructure characterization of the porous medium obtained in S4, the micro porosity of the porous medium can be determined, so that the seepage condition of oil, gas and water in the reservoir rock stratum can be determined.
The filter plate is made of aluminum, steel or tantalum.
S3 specifically includes the following steps:
s3.1, establishing a statistical model of the energy spectrum projection data, and determining maximum likelihood functions of all the projection data in one-time scanning;
s3.2, by means of similarity of reconstructed images under different energy channels, firstly combining projection data under different energy channels into wide-energy-spectrum projection data, reconstructing the wide-energy-spectrum projection data through a common reconstruction algorithm to obtain a full-energy channel, namely a wide-energy-spectrum reconstructed image f, using the full-energy channel as a reference object, determining attenuation coefficient distribution of an object to be reconstructed under different energy channels and a correlation coefficient of the wide-energy-spectrum reconstructed image f, and describing the similarity between the images;
and S3.3, respectively reconstructing the attenuation coefficient distribution of the porous medium under each energy channel according to the steps S3.1 and S3.2 to obtain an energy spectrum CT statistical reconstruction algorithm model based on the similarity of energy spectrum images, and respectively reconstructing each energy channel to obtain reconstructed images under a plurality of energy channels.
In S3.1, the statistical model is
Figure BDA0001689092660000031
Wherein: dividing a continuum of energy into M narrow spectra
Figure BDA0001689092660000032
I.e. M energy channels, i denotes the ith X-ray;
Figure BDA0001689092660000033
representing projection data measured on a detector corresponding to the ith ray under the mth energy channel; a ═ aij) Representing a projection matrix; a isijRepresenting the length of the intersection line of the ith ray and the jth voxel;
Figure BDA0001689092660000034
representing the attenuation coefficient distribution of the object to be reconstructed under the mth energy channel;
Figure BDA0001689092660000035
representing the front projection process of the ith detector under the mth energy channel;
Figure BDA0001689092660000036
representing the projection value measured on the detector during blank scanning under the mth energy channel;
Figure BDA0001689092660000037
representing errors in the measured projection data on the ith detector for m energy channels; i is the total number of rays, J is the total number of voxels corresponding to the object to be reconstructed, and M is the total energy channel;
in one scan, the maximum likelihood function of all the measured projection data is:
Figure BDA0001689092660000038
s3.2, the attenuation coefficient distribution of the object to be reconstructed under different energy channels
Figure BDA0001689092660000039
Correlation coefficient with wide-spectrum reconstructed image f
Figure BDA00016890926600000310
Comprises the following steps:
Figure BDA00016890926600000311
where cov represents the covariance of the two images and σ represents the standard deviation of the images.
In S3.3, the maximum likelihood function in S3.1 and the correlation coefficient in S3.2 are both maximized, and a spectrum CT statistical reconstruction algorithm model based on the similarity of the spectrum images is obtained:
Figure BDA0001689092660000041
respectively reconstructing each energy channel to obtain reconstructed images under M energy channels
Figure BDA0001689092660000042
S3.3, by constructing a log-likelihood function
Figure BDA0001689092660000043
Of the proxy function phic(μ；μ(n)) Replacing the original objective function, wherein the proxy function needs to satisfy: the proxy function is monotonously increased to the proxied function; the maximum value of the proxy function is the same as that of the proxied function;
and obtaining the optimal solution of the reconstruction algorithm model by adopting a Newton method
Figure BDA0001689092660000044
Wherein n is the number of iterations;
and the second term in the reconstruction algorithm model obtains its analytic solution by directly deriving it
Figure BDA0001689092660000045
Wherein
Figure BDA0001689092660000046
Is that
Figure BDA0001689092660000047
Is the two-norm of the vector.
S4 specifically includes the following steps:
s4.1, determining attenuation coefficients of the base material under different energy channels;
mixing the base material (alpha)1,α2,…,αK) At different energy channels
Figure BDA0001689092660000048
The attenuation coefficient of the k-th base material is regarded as the attenuation coefficient vector of the base material, and the attenuation coefficient vector of the k-th base material under M energy channels
Figure BDA0001689092660000051
k＝1，2，…，K；
Wherein the content of the first and second substances,
Figure BDA0001689092660000052
is the attenuation coefficient under the mth energy channel;
s4.2, setting
Figure BDA0001689092660000053
Is the volume percentage of various base materials in the j-th voxel, thus
Figure BDA0001689092660000054
And is
Figure BDA0001689092660000055
According to the maximum information entropy principle, combining reconstructed images under M energy channels and attenuation coefficients of base materials under different energy channels, and selecting a solution which is closest to the real distribution from all compatible distributions, namely
Figure BDA0001689092660000056
Thereby obtaining a three-dimensional microstructure characterization model of the porous medium.
The base material is a base material forming a porous medium.
Has the advantages that: the invention realizes the function of energy spectrum CT by utilizing the traditional CT, can simultaneously acquire the images of substances under different energy channels, maximizes the material difference, realizes the substance identification of the reconstructed image and saves the cost; the method mainly utilizes the existing CT system to obtain CT projection image images of the porous medium under different energy channels through effective filtering, then utilizes an energy spectrum CT reconstruction algorithm to obtain an energy spectrum CT reconstruction image, and on the basis, uses voxels as a research object to obtain microstructure representation of the porous medium.
Drawings
FIG. 1 is a schematic view of a conventional CT continuum;
fig. 2 is a narrow spectral diagram of spectral CT.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
The invention discloses a method for measuring a microstructure of a porous medium, which is characterized by comprising the following steps of:
s1, determining corresponding filter material and thickness in different energy channel ranges according to the components, the external dimensions and the energy channel ranges of the detection object;
s2, respectively arranging different filter plates at the ray emission end of the traditional CT, and obtaining projection data of the porous medium under a plurality of energy channels through filtering;
the conventional CT is a CT system based on an energy integration detector, the present invention divides the X-ray of the continuous energy spectrum into non-overlapping energy channels (as shown in fig. 2), and the current energy spectrum CT based on a photon counting detector can directly realize the function, but the price is high and the technology is not mature.
Here projection data sets of a plurality of energy channels are obtained by filtering based on conventional CT. The filter is made of aluminum, steel or tantalum and the like, a wider continuous spectrum is changed into a plurality of narrower energy channels, and then narrow spectrum projection data sets of the energy channels of the object are obtained, so that the traditional CT realizes the function of multi-spectrum imaging.
S3, respectively reconstructing an image of the porous medium corresponding to each energy channel according to the projection data under the plurality of energy channels;
in the energy spectrum filtering process, the photon number (dose) is reduced, and the obtained projection noise level is increased, so that reasonable prior information can be constructed by using statistical iterative reconstruction based on a data physical model and combining the characteristic of spectral CT reconstruction, and an energy spectrum CT statistical reconstruction algorithm model with the prior information is constructed for reconstruction.
The method comprises the following specific steps:
s3.1, establishing a statistical model of energy spectrum projection data
Dividing a continuum of energy into M narrow spectra
Figure BDA0001689092660000061
That is, the measured data under each energy channel is influenced by the scattering of X-ray, the noise of detector, etc. to make the obtained data random, and its statistical model is
Figure BDA0001689092660000071
Wherein: i represents the ith X-ray;
Figure BDA0001689092660000072
representing projection data measured on a detector corresponding to the ith ray under the mth energy channel; a ═ aij) Representing a projection matrix; a isijRepresenting the length of the intersection line of the ith ray and the jth voxel;
Figure BDA0001689092660000073
representing the attenuation coefficient distribution of the object to be reconstructed under the mth energy channel;
Figure BDA0001689092660000074
representing the front projection process of the ith detector under the mth energy channel;
Figure BDA0001689092660000075
represents the projection value measured on the detector during the blank scan (without any object) under the mth energy channel;
Figure BDA0001689092660000076
representing the error of the measured projection data on the i-th detector for the m energy channels. I is the total number of rays, J is the total number of voxels corresponding to the object to be reconstructed, and M is the total energy channel.
Because each detector unit is independent, the projection data collected by each detector unit
Figure BDA0001689092660000077
Also independent of each other, the likelihood function of all the projection data measured in one scan (i.e. the joint probability distribution of all the projections) is, according to the nature of the joint probability distribution of the random variables independent of each other:
Figure BDA0001689092660000078
for the convenience of calculation, the logarithm is taken at both sides of the above formula and the constant is removed to obtain the maximum likelihood function in the form of a logarithm, that is:
Figure BDA0001689092660000079
s3.2, through the similarity of the reconstructed images under different energy channels, firstly combining the projection data under different energy channels into wide-energy-spectrum projection data, reconstructing the wide-energy-spectrum projection data through a common reconstruction algorithm to obtain a full-energy-channel wide-energy-spectrum reconstructed image f, and determining the full-energy-channel wide-energy-spectrum reconstructed image f as a reference object
Figure BDA0001689092660000081
Correlation coefficient with wide-spectrum reconstructed image f
Figure BDA0001689092660000082
To describe the similarity between images:
namely, it is
Figure BDA0001689092660000083
m＝1,2,…,M
Where f is the high quality image of the wide spectral reconstruction, cov denotes the covariance of the two images, and σ denotes the standard deviation of the images;
due to the fact that the energy channels are different
Figure BDA0001689092660000084
The same object is scanned to obtain projection data, so reconstructed images under different energy channels have higher similarity, the similarity of the images among the channels is fully utilized, noise can be effectively inhibited, and the quality of the reconstructed images is improved.
S3.3, respectively reconstructing the attenuation coefficient distribution of the porous medium under each energy channel according to the steps S3.1 and S3.2:
and (3) maximizing the likelihood function in the S3.1 and the correlation coefficient in the S3.2 to obtain a spectrum CT statistical reconstruction algorithm model based on the similarity of the spectrum images:
Figure BDA0001689092660000085
can convert the above formula into
Figure BDA0001689092660000086
The solution can be realized by using an alternative iteration method, and since the likelihood function is nonlinear, the above formula has no analytic solution, and the log likelihood function can be realized by constructing the log likelihood function
Figure BDA0001689092660000087
Of the proxy function phic(μ；μ(n)) I.e. to find a simple formAnd replacing the original target function by the proxy function which is easy to separate variables, wherein the proxy function needs to meet the following requirements: the proxy function is monotonously increased to the proxied function; ② the maximum value of the proxy function is the same as the maximum value of the proxied function.
And obtaining the optimal solution by adopting a Newton method
Figure BDA0001689092660000091
Where n is the number of iterations.
And the second term in the reconstruction algorithm model can obtain the analytic solution thereof by directly deriving the second term
Figure BDA0001689092660000092
Wherein
Figure BDA0001689092660000093
Is that
Figure BDA0001689092660000094
The average image of (1), where | | is a two-norm of the vector.
Respectively reconstructing each energy channel to obtain reconstructed images under M energy channels
Figure BDA0001689092660000095
S4, acquiring microstructure characterization of the porous medium based on the reconstructed images under the multiple energy channels, specifically as follows;
s4.1, determining attenuation coefficients of a base material under different energy channels, wherein the base material is a base material for forming a porous medium; the pores may also be a base material with an attenuation coefficient of 0;
mixing the base material (alpha)1,α2,…,αK) At different energy channels
Figure BDA0001689092660000096
The lower attenuation coefficient is considered to beAttenuation coefficient vector of the base material, e.g. of kth base material under M energy channels
Figure BDA0001689092660000097
k＝1，2，…，K；
Wherein the content of the first and second substances,
Figure BDA0001689092660000098
is the attenuation coefficient under the mth energy channel;
the attenuation coefficient of various base materials at each energy is generally known and it is in one energy channel
Figure BDA0001689092660000101
The attenuation coefficients of the lower are unknown and are typically obtained by weighted averaging of the lower energy channels. In order to more accurately obtain the attenuation coefficient of the base material under an energy section, the method obtains training data through repeated tests on known materials by a deep learning method, and further obtains an attenuation coefficient model of the base material under each energy channel through a training network, so that the average attenuation coefficient of the base material under each energy channel is obtained. The input of the neural network is the attenuation coefficient of the base material under each energy in the energy channel, and the output is the attenuation coefficient of the base material under the energy channel.
S4.2, setting
Figure BDA0001689092660000102
Is the volume percentage of various base materials in the j-th voxel, thus
Figure BDA0001689092660000103
And is
Figure BDA0001689092660000104
Press maximum messageThe entropy principle combines reconstructed images under M energy channels and attenuation coefficients of base materials under different energy channels, and selects a solution which is closest to the real distribution from all compatible distributions, namely
Figure BDA0001689092660000105
Thereby obtaining a three-dimensional microstructure characterization model of the porous medium.
In order to obtain the small-scale structural information, each voxel is considered as a research object in the present example, and different basis materials are considered to be distributed in the voxels with a certain probability ratio (microstructure), so that the small-scale information below the CT resolvable scale is represented by the volume ratio of the basis materials contained in each voxel. Is provided with
Figure BDA0001689092660000106
The volume percentage of various base materials in the jth voxel is as follows:
Figure BDA0001689092660000107
and is
Figure BDA0001689092660000108
Thus, it is possible to provide
Figure BDA0001689092660000109
Can be viewed as a discrete probability distribution. To obtain the microstructure of the base material in the voxel, i.e. to solve
Figure BDA00016890926600001010
While
Figure BDA00016890926600001011
There are infinite groups of solutions, and how to select the most reasonable distribution from these compatible distributions is the maximum entropy principle. Discrete probability distribution
Figure BDA00016890926600001012
Information entropy definition ofComprises the following steps:
Figure BDA0001689092660000111
according to the principle of maximum information entropy, such distributions are selected from all compatible distributions, which are distributions that maximize the information entropy under certain constraints. When considering entropy as the most appropriate scale for measuring uncertainty, it has been generally accepted to select as the random variable distribution, under given constraints, the one with the greatest degree of uncertainty. Because this random distribution is the most random, the distribution that has the least subjective component and the greatest estimate of uncertainty. Namely, it is
Figure BDA0001689092660000112
Considering that the microstructure of the base material is the same under different energy channels, the m-th energy channel
Figure BDA0001689092660000113
For the jth voxel
Figure BDA0001689092660000114
m＝1,2,…,M
Wherein
Figure BDA0001689092660000115
Is at the m-th energy channel
Figure BDA0001689092660000116
The attenuation coefficient of the next j-th voxel is obtained by S3.
The formula is used as a constraint condition for solving the maximum entropy, and then a constrained maximum entropy microstructure reconstruction model is obtained
m＝1,2,…,M
The method is an optimization problem with constraint conditions, and is solved by using a Lagrange multiplier method to order
Figure BDA0001689092660000117
And introducing a Lagrange multiplier lambda0，λ1，…,λMTo obtain a Lagrangian function
Figure BDA0001689092660000118
The volume percentage of the base material in the jth voxel can be obtained by the method of partial derivation
Figure BDA0001689092660000119
The microstructure of J voxels is obtained, and the microstructure of the whole porous medium can be obtained by applying the same method to each voxel, wherein J is 1,2, … and J.
In the microstructure characterization process, the traditional image segmentation microstructure characterization method based on the single-energy CT reconstruction loses small-scale structure information lower than the CT resolvable scale. In addition, when attenuation coefficient information of base materials existing in a sample under the condition of single energy of X-rays is relatively close, the distribution of different base materials is difficult to distinguish by using an image segmentation method under the condition of single energy. The step can effectively acquire the small-scale structural information of the porous medium with the analyzable scale lower than the CT.
And S5, according to the microstructure characterization of the porous medium obtained in the S4, the microporosity of the porous medium can be determined, so that the seepage condition of oil, gas and water in the reservoir rock stratum is determined.
Because fluid resources such as oil, gas, groundwater and the like are stored in the porous medium of the storage rock, and the micro-pore structure of the rock is a main factor for controlling seepage of the oil, the gas and the water in the storage rock stratum, the micro-pore structure of the porous medium can be obtained by obtaining the micro-structure of the porous medium, and the micro-pore structure plays a great role in the seepage rheology field.
According to the method, narrow spectrum projection data of the porous medium under a plurality of different energy channels are obtained through filtering based on the traditional CT, a three-dimensional reconstruction image corresponding to the porous medium under each channel is reconstructed by utilizing a statistical iteration energy spectrum CT reconstruction algorithm based on similarity constraint, then a voxel is taken as a research object, a maximum entropy model based on energy spectrum data constraint is solved to obtain the volume ratio of a base material in the unit voxel, small-scale information is effectively expressed, and therefore the representation of the three-dimensional microstructure of the porous medium is obtained.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (9)

1. A method for measuring the microstructure of a porous medium is characterized by comprising the following steps:
s1, determining corresponding filter material and thickness in different energy channel ranges according to the components, the external dimensions and the energy channel ranges of the detection object;
s2, respectively arranging different filter plates at the ray emission end of the CT, and obtaining projection data of the porous medium under a plurality of energy channels through filtering;
s3, respectively reconstructing an image of the porous medium corresponding to each energy channel according to the projection data under the plurality of energy channels, specifically comprising the following steps:
s3.1, establishing a statistical model of the energy spectrum projection data, and determining maximum likelihood functions of all the projection data in one-time scanning;
the statistical model is:
Figure FDA0002602957060000011
wherein: dividing a continuum of energy into M narrow spectra
Figure FDA0002602957060000012
I.e. M energy channels, i denotes the ith X-ray;
Figure FDA0002602957060000013
representing projection data measured on a detector corresponding to the ith ray under the mth energy channel; a ═ aij) Representing a projection matrix; a isijRepresenting the length of the intersection line of the ith ray and the jth voxel;
Figure FDA0002602957060000014
representing the attenuation coefficient distribution of the object to be reconstructed under the mth energy channel;
Figure FDA0002602957060000015
representing the forward projection process of the ith detector at the mth energy channel,
Figure FDA0002602957060000016
representing the attenuation coefficient of the jth voxel under the mth energy channel;
Figure FDA0002602957060000017
representing the projection value measured on the detector during blank scanning under the mth energy channel;
Figure FDA0002602957060000018
representing errors in the measured projection data on the ith detector for m energy channels; i is the total number of rays, J is the total number of voxels corresponding to the object to be reconstructed, and M is the total energy channel;
s3.2, by means of similarity of reconstructed images under different energy channels, firstly combining projection data under different energy channels into wide-energy-spectrum projection data, reconstructing the wide-energy-spectrum projection data through a common reconstruction algorithm to obtain a full-energy channel, namely a wide-energy-spectrum reconstructed image f, using the full-energy channel as a reference object, determining attenuation coefficient distribution of an object to be reconstructed under different energy channels and a correlation coefficient of the wide-energy-spectrum reconstructed image f, and describing the similarity between the images;
s3.3, respectively reconstructing the attenuation coefficient distribution of the porous medium under each energy channel according to the steps S3.1 and S3.2 to obtain an energy spectrum CT statistical reconstruction algorithm model based on the similarity of energy spectrum images, and respectively reconstructing each energy channel to obtain reconstructed images under a plurality of energy channels;
and S4, acquiring microstructure characterization of the porous medium based on the reconstructed images under the multiple energy channels.
2. A method of measuring the microstructure of a porous medium as recited in claim 1, wherein: according to the microstructure characterization of the porous medium obtained in S4, the micro porosity of the porous medium can be determined, so that the seepage condition of oil, gas and water in the reservoir rock stratum can be determined.
3. A method of measuring the microstructure of a porous medium as recited in claim 1, wherein: the filter plate is made of aluminum, steel or tantalum.
4. A method of measuring the microstructure of a porous medium as recited in claim 1, wherein: in S3.1, in one scan, the log-form maximum likelihood function of all the measured projection data is:
Figure FDA0002602957060000021
Figure FDA0002602957060000022
as a function of the likelihood of all measured projection data.
5. The method of claim 4, wherein the step of measuring the microstructure of the porous medium comprises: s3.2, the attenuation coefficient distribution of the object to be reconstructed under different energy channels
Figure FDA0002602957060000023
With a wide energy spectrum reconstructionCorrelation coefficient of image f
Figure FDA0002602957060000024
Comprises the following steps:
Figure FDA0002602957060000025
where cov represents the covariance of the two images and σ represents the standard deviation of the images.
6. The method of claim 5, wherein the step of measuring the microstructure of the porous medium comprises: in S3.3, the maximum likelihood function in S3.1 and the correlation coefficient in S3.2 are both maximized, and a spectrum CT statistical reconstruction algorithm model based on the similarity of the spectrum images is obtained:
Figure FDA0002602957060000031
respectively reconstructing each energy channel to obtain reconstructed images under M energy channels
Figure FDA0002602957060000032
7. The method of claim 6, wherein the step of measuring the microstructure of the porous medium comprises: in the step S3.3, the first step,
by constructing a log-form maximum likelihood function
Figure FDA0002602957060000033
Proxy function of
Figure FDA0002602957060000034
Replacing the original objective function, wherein the proxy function needs to satisfy: the proxy function is monotonously increased to the proxied function; the maximum value of the proxy function is the same as that of the proxied function;
and obtaining the optimal solution of the reconstruction algorithm model by adopting a Newton method
Figure FDA0002602957060000035
Wherein n is the number of iterations;
and the second term in the reconstruction algorithm model obtains its analytic solution by directly deriving it
Figure FDA0002602957060000036
Wherein
Figure FDA0002602957060000037
Is that
Figure FDA0002602957060000038
The average image of (1), where | | is a two-norm of the vector.
8. A method of measuring the microstructure of a porous medium as claimed in any one of claims 4 to 7, wherein: s4 specifically includes the following steps:
s4.1, determining attenuation coefficients of the base material under different energy channels;
mixing the base material (alpha)1,α2,…,αK) At different energy channels
Figure FDA0002602957060000041
The attenuation coefficient of the k-th base material is regarded as the attenuation coefficient vector of the base material, and the attenuation coefficient vector of the k-th base material under M energy channels
Figure FDA0002602957060000042
Wherein the content of the first and second substances,
Figure FDA0002602957060000043
is the attenuation coefficient under the mth energy channel;
s4.2, setting
Figure FDA0002602957060000044
Is the volume percentage of various base materials in the j-th voxel, thus
Figure FDA0002602957060000045
And is
Figure FDA0002602957060000046
According to the maximum information entropy principle, combining reconstructed images under M energy channels and attenuation coefficients of base materials under different energy channels, and selecting a solution which is closest to the real distribution from all compatible distributions, namely
Figure FDA0002602957060000047
Thereby obtaining a three-dimensional microstructure characterization model of the porous medium.
9. A method of measuring the microstructure of a porous medium as recited in claim 8, wherein: the base material is a base material forming a porous medium.
CN201810584258.9A 2018-06-08 2018-06-08 Method for measuring microstructure of porous medium Active CN108896588B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810584258.9A CN108896588B (en) 2018-06-08 2018-06-08 Method for measuring microstructure of porous medium

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810584258.9A CN108896588B (en) 2018-06-08 2018-06-08 Method for measuring microstructure of porous medium

Publications (2)

Publication Number Publication Date
CN108896588A CN108896588A (en) 2018-11-27
CN108896588B true CN108896588B (en) 2020-11-20

Family

ID=64344270

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810584258.9A Active CN108896588B (en) 2018-06-08 2018-06-08 Method for measuring microstructure of porous medium

Country Status (1)

Country Link
CN (1) CN108896588B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE102019111567A1 (en) * 2019-05-03 2020-11-05 Wipotec Gmbh Method and device for X-ray inspection of products, in particular food
CN114063138B (en) * 2021-11-16 2023-07-25 武汉联影生命科学仪器有限公司 Method and equipment for measuring effective energy of scanning imaging system and scanning imaging system

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH11218486A (en) * 1998-01-30 1999-08-10 Seitai Hikarijoho Kenkyusho:Kk Optical ct method
CN101308102A (en) * 2008-07-16 2008-11-19 中北大学 Computer tomography scanned imagery apparatus and method
CN103900931A (en) * 2012-12-26 2014-07-02 首都师范大学 Multi-energy-spectrum CT imaging method and imaging system
CN104346820A (en) * 2013-07-26 2015-02-11 清华大学 X-ray dual-energy CT reconstruction method
CN104408758A (en) * 2014-11-12 2015-03-11 南方医科大学 Low-dose processing method of energy spectrum CT image
CN104422704A (en) * 2013-08-21 2015-03-18 同方威视技术股份有限公司 Method of decomposing energy spectrum information of X-ray energy spectrum CT and corresponding reconstruction method
CN106659449A (en) * 2014-08-13 2017-05-10 皇家飞利浦有限公司 Quantitative dark-field imaging in tomography
EP3178558A3 (en) * 2007-07-13 2017-10-25 Handylab, Inc. Intergrated apparatus for performing nucleic acid extraction and diagnostic testing on multiple biological samples
WO2016161022A8 (en) * 2015-03-30 2017-11-16 Accelerate Diagnostics, Inc. Instrument and system for rapid microorganism identification and antimicrobial agent susceptibility testing

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2885394A4 (en) * 2012-08-17 2016-04-20 Univ Central Florida Res Found Methods, systems and compositions for functional in vitro cellular models of mammalian systems

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH11218486A (en) * 1998-01-30 1999-08-10 Seitai Hikarijoho Kenkyusho:Kk Optical ct method
EP3178558A3 (en) * 2007-07-13 2017-10-25 Handylab, Inc. Intergrated apparatus for performing nucleic acid extraction and diagnostic testing on multiple biological samples
CN101308102A (en) * 2008-07-16 2008-11-19 中北大学 Computer tomography scanned imagery apparatus and method
CN103900931A (en) * 2012-12-26 2014-07-02 首都师范大学 Multi-energy-spectrum CT imaging method and imaging system
CN104346820A (en) * 2013-07-26 2015-02-11 清华大学 X-ray dual-energy CT reconstruction method
CN104422704A (en) * 2013-08-21 2015-03-18 同方威视技术股份有限公司 Method of decomposing energy spectrum information of X-ray energy spectrum CT and corresponding reconstruction method
CN106659449A (en) * 2014-08-13 2017-05-10 皇家飞利浦有限公司 Quantitative dark-field imaging in tomography
CN104408758A (en) * 2014-11-12 2015-03-11 南方医科大学 Low-dose processing method of energy spectrum CT image
WO2016161022A8 (en) * 2015-03-30 2017-11-16 Accelerate Diagnostics, Inc. Instrument and system for rapid microorganism identification and antimicrobial agent susceptibility testing

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Evaluation of an Analytic Reconstruction Method as a Platform for Spectral Cone-beam beam CT;Huihua Kong 等;《IEEE Access Practical Innovations Open Solutions》;20180328;全文 *
基于能谱匹配先验的多谱CT成像方法;黄甜甜;《光谱学与光谱分析》;20170228;第37卷(第2期);第503-507页 *

Also Published As

Publication number Publication date
CN108896588A (en) 2018-11-27

Similar Documents

Publication Publication Date Title
Taud et al. Porosity estimation method by X-ray computed tomography
Costanza‐Robinson et al. Representative elementary volume estimation for porosity, moisture saturation, and air‐water interfacial areas in unsaturated porous media: Data quality implications
Willson et al. Quantification of grain, pore, and fluid microstructure of unsaturated sand from X-ray computed tomography images
CN108896588B (en) Method for measuring microstructure of porous medium
Teles et al. Rock porosity quantification by dual-energy X-ray computed microtomography
AU2012264597A1 (en) An X-ray tomography device
EP2715325A1 (en) An x-ray tomography device
Borges et al. Computed tomography to estimate the representative elementary area for soil porosity measurements
US20220028127A1 (en) Energy weighting of photon counts for conventional imaging
Hendrickx et al. Distribution of moisture in reconstructed oil paintings on canvas during absorption and drying: A neutron radiography and NMR study
Japelj et al. Simulating MOS science on the ELT: Lyα forest tomography
Kato et al. Evaluation of porosity and its variation in porous materials using microfocus x-ray computed tomography considering the partial volume effect
Chen et al. A synchrotron-based local computed tomography combined with data-constrained modelling approach for quantitative analysis of anthracite coal microstructure
CN113075731B (en) Deep reservoir continuity wellbore digital modeling method and device
Lofi et al. SCOPIX–digital processing of X-ray images for the enhancement of sedimentary structures in undisturbed core slabs
Wildenschild et al. Using synchrotron‐based X‐ray microtomography and functional contrast agents in environmental applications
Chaves et al. Low-and high-resolution X-ray tomography helping on petrophysics and flow-behavior modeling
Claes et al. The application of computed tomography for characterizing the pore structure of building materials
Triolo et al. Combined application of X-ray and neutron imaging techniques to wood materials
Mendoza et al. Statistical methods to enable practical on-site tomographic imaging of whole-core samples
Coles et al. Characterization of reservoir core using computed microtomography
Schembre-McCabe et al. A framework to validate digital rock technology
Bolshakov et al. Investigation of the pore space structure by a scanning electron microscope using the computer program collector
Sinigaglia et al. MIGHTEE-H i: H i galaxy properties in the large-scale structure environment at z∼ 0.37 from a stacking experiment
Fernandes et al. Porosity and pore size distribution determination of tumblagooda formation sandstone by X-Ray Microtomography

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant