# US 2014/0192953 A1 · Method for determination of spatial distribution and concentration of contrast components in a porous and/or heterogeneous sample

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- Number: US 2014/0192953 A1
- Document ID: US20140192953A1
- Status: Published application
- Kind: A1
- Application number: 14/119,661
- Filed: 2011-05-31
- Published: 2014-07-10
- Earliest claimed: 2011-05-31
- Assignees: Schlumberger Technology Corporation
- Inventors: Valery Vasilievich Shako; Nikita Ilyich Ryzhikov; Dmitry Nikolaevich Mikhailov
- Web page: https://patentgrep.com/patent/US20140192953A1

## CPC

- G01N 23/046: using tomography, e.g. computed tomography [CT]
- G01N 2223/419: computed tomograph
- G01N 2223/616: earth materials
- G01N 2223/646: flaws, defects
- G01N 2223/649: porosity
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

A method for determination of a spatial distribution and concentration of contrast components in a porous sample comprises the steps of scanning a sample with X-ray and obtaining a computer tomographic image of the sample. Then an area of interest inside the obtained computer tomographic image is selected and a first cross-section of the computer tomographic image is defined. Spatial distribution and concentration of contrast components inside the area of interest are determined by analyzing histograms of grayness distribution in the cross-sections of the computer tomographic image starting with the reference cross-section.

## Claims

### Claim 1

A method for determination of spatial distribution and concentration of contrast components in a porous or/and heterogeneous sample comprising the following steps:
scanning the sample with X-ray,
obtaining a computer tomographic image of the sample,
defining an area of interest inside the obtained computer tomographic image,
defining a reference cross-section of the obtained computer tomographic image,
obtaining histograms of grayness distribution in the cross-sections of the computer tomographic image,
determining spatial distribution and concentration of contrast components along the sample by analyzing histograms of grayness distribution in the cross-sections of the computer tomographic image starting with a histogram of grayness distribution in the reference cross-section.

### Claim 2 (depends on 1)

A method of claim 1 wherein a step of analyzing histograms of grayness distribution in the cross-sections of the computer tomographic image comprises the following:
defining the number of the components as the number of peaks on the histogram of grayness distribution inside the area of interest of the reference cross-section,
approximating the histogram Ii1(z) of grayness distribution for each component inside the reference cross-section by normal distribution (Gaussian function):
I
i
1

(
z
)
=
A
i
1

exp

[
-
(
z
-
B
i
1
C
i
1
)
2
]
wherein
i is an index of a component;
I is “intensity” (total number of pixels) of grayness z;
Ai1, Bi1, Ci1 are adjustable parameters corresponding to the reference cross-section;
upper index “1” corresponds to the reference cross-section,
crudely estimating adjustable parameters for all components from the histogram of grayness distribution inside the area of interest of the reference cross-section,
accurately estimating adjustable parameters for the components by minimization of module of difference between the histogram of grayness distribution inside the area of interest of the reference cross-section and sum of normal distributions corresponding to individual components
∑
j
=
1
M

[
H
1

(
z
j
)
-
∑
i
=
1
N

A
i
1

exp

(
-
(
z
j
-
B
i
1
C
i
1
)
2
)
]
→
0
wherein
j is index of grayscale;
M is total number of grayscales;
N is total number of different components,
using obtained parameters of Gaussians Ai1, Bi1, Ci1 as initial parameters for minimization of module of difference between the histogram of grayness distribution and it's approximation by sum of normal distributions for the next cross-section of the computer tomographic image,
applying previous step to all cross-sections inside the area of interest of the computer tomographic image,
defining the fraction of the individual components inside each cross
section k by integration of individual Gaussians:
a
i
k
=
∫
A
i
k

exp

[
-
(
z
-
B
i
k
C
i
k
)
2
]


z
,
wherein k=1 . . . K is the number of cross-section.

### Claim 3 (depends on 1)

The method of claim 1 wherein a step of analyzing grayness distribution in the cross-section of the computer tomographic image comprises the following:
selecting the sub-areas inside the area of interest on the reference cross-section, each containing only one individual component,
obtaining histograms of grayness distribution of the individual components,
normalizing all histograms by their area,
transforming the histograms of all individual components to general scale,
approximating the histogram of the area of interest on the reference cross-section by sum of histograms of individual components with the weight coefficients, corresponding to the areas occupied by the individual components on this cross-section of the computer tomographic image,
defining weight coefficients by minimization of module of difference between the histogram of the area of interest on the reference cross-section and sum of histograms of individual components:
[
∑
j
=
1
M

(

A
j
1
-
b
1

B
j
1

c
1

C
j
1
-
…

)
]
→
0
wherein
Aj1, Bj1, Cj1, . . . are vectors of values of histograms,
b1, c1, . . . are weight coefficients;
j is index of grayscale;
M is total number of grayscales;
applying previous step to all cross-sections inside the area of interest of computer tomographic image.

### Claim 4 (depends on 3)

Method of claim 3 wherein the sub-areas containing individual components are expanded.