JP6946935B2 - Porosity estimation method and porosity estimation device - Google Patents

Description

The present invention relates to a method and an apparatus for estimating the fine pore ratio, which is the ratio of fine pores in a porous measurement object.

In Patent Document 1 and Non-Patent Documents 1 and 2, a CT cross-sectional image of a sample is imaged using an X-ray CT apparatus. In this CT cross-sectional image, the pixel region having a high CT value (in other words, the density is high) becomes white, and the pixel region having a low CT value (in other words, the density is low) becomes black. Here, the pores existing inside the sample can be grasped based on the CT value of the CT cross-sectional image.

Patent No. 4885311

"Analysis of agglomeration and densification processes in sinter production", Iron and Steel, 1982, No. 7, pp. 1060-1068 "Aeration Structure Analysis of Iron Ore Sintered Ore by X-ray CT", Geological Survey of Japan Monthly Report, Vol. 46, No. 11, pp. 573-594

If the size of the pores contained in the sample is larger than the resolution of the X-ray CT apparatus, the pores can be grasped based on the X-ray CT image of the sample. However, when the size of the pores is smaller than the resolution of the X-ray CT apparatus, it becomes difficult to grasp the pores from the X-ray CT image of the sample.

Further, when a solid and a gas are present in one pixel region of the X-ray CT image, the CT value of this pixel region is determined by the abundance ratio of the solid and the gas, but conventionally, this pixel region is a solid. It is often considered to be included, and it is not known how much gas is present in one pixel region.

The first invention of the present application is a method for estimating the fine pore ratio, which is the ratio of fine pores in a porous measurement object. The fine pores are pores that exist together with the solid portion of the measurement object in one pixel region constituting the X-ray CT image of the measurement object. First, a reference CT value, which is a CT value indicating a minimum value, is specified based on a histogram of CT values in an X-ray CT image including an object to be measured and a gas.

Then, among the plurality of pixel regions constituting the X-ray CT image of the measurement target, the pore ratio corresponding to the solid CT value is set to 0% for the target pixel region showing a CT value larger than the reference CT value, and the gas CT is performed. The pore ratio corresponding to the CT value of each target pixel region is calculated based on a linear function showing the correspondence between the CT value and the pore ratio when the pore ratio corresponding to the value is 100%. The solid CT value is a CT value showing a peak in the histogram of the CT value in the solid X-ray CT image. The gas CT value is a CT value showing a peak in the histogram of the CT value in the X-ray CT image of the gas. Then, a representative value of the porosity in the plurality of target pixel regions is estimated as the fine porosity.

As the solid, a solid reference sample different from the object to be measured can be used. At this time, the solid CT value is specified based on the CT value histogram in the X-ray CT image of the solid reference sample, and the gas CT value is specified based on the CT value histogram in the gas X-ray CT image. Then, the above linear function can be expressed by the following equation (I).

In the above formula (I), ε _XF is the porosity of the target pixel region, CT _X is the CT value of the target pixel region, CT ₁ is the solid CT value, and CT ₀ is the gas CT value.

Here, as a measurement target, a raw material for sintering, a sinter cake or a sinter ore can be used, and a solid reference sample having ^{a true density of 4.74 to 5.74 g / cm 3 can be used.} Further, as the solid reference sample, hematite granules or alloys can be used.

As the gas, a gas existing inside the object to be measured can be used. When the object to be measured is composed of a plurality of chemical components, the linear function can be expressed by the following formula (II).

In the above formula (II), ε _XF is the porosity of the target pixel region, CT _X is the CT value of the target pixel region, and α and β are predetermined coefficients. d _a, based on the mass ratio of each chemical component, an average true density of the weighted average true density of the plurality of chemical components, the density of identifying the solid CT values in the correlation of the density and CT values. Here, as the object to be measured, a raw material for sintering, a sinter cake or a sinter can be used.

On the other hand, it is possible to estimate the crude air porosity, which is the ratio of the crude air pores in the object to be measured. The coarse air pores are pores existing in the entire area of one pixel constituting the X-ray CT image of the object to be measured. Here, in the X-ray CT image of the measurement object, the ratio of the total number of pixels showing the CT value equal to or less than the reference CT value to the total number of all the pixels existing in the area surrounded by the outline of the measurement object is calculated. , Can be calculated as the crude air porosity of the object to be measured. The total value of the crude air porosity and the fine porosity can be estimated as the total porosity of the object to be measured.

The second invention of the present application is an apparatus for estimating the fine pore ratio, which is the ratio of fine pores in a porous measurement object. The calculation unit for estimating the fine porosity identifies a reference CT value, which is a CT value indicating a minimum value, based on a histogram of CT values in an X-ray CT image including a measurement object and a gas.

Further, the calculation unit sets the pore ratio corresponding to the solid CT value to 0% in the target pixel region showing a CT value larger than the reference CT value among the plurality of pixel regions constituting the X-ray CT image of the measurement target. Then, the pore ratio corresponding to the CT value of each target pixel region is calculated based on the linear function showing the correspondence between the CT value and the pore ratio when the pore ratio corresponding to the gas CT value is 100%. The solid CT value is a CT value showing a peak in the histogram of the CT value in the solid X-ray CT image. The gas CT value is a CT value showing a peak in the histogram of the CT value in the X-ray CT image of the gas. Then, the calculation unit estimates the representative value of the porosity in the plurality of target pixel regions as the fine porosity.

According to the present invention, by specifying the reference CT value, it is possible to grasp that the fine pores are present in the target pixel region showing the CT value larger than the reference CT value. For this target pixel region, by paying attention to the correspondence between the CT value and the porosity (linear function), the porosity (that is, the fine porosity for each target pixel region) is calculated based on the CT value of the target pixel region. can do. Then, by calculating the representative value of the fine porosity of all the target pixel regions, the fine porosity of the measurement target can be estimated.

It is a figure which shows the X-ray CT apparatus, arithmetic apparatus and display. It is a figure which shows a plurality of CT images. It is a figure which shows the relationship between density and CT value (peak). It is a figure which shows the size of one pixel area and a pore. It is a figure which shows the size of four pixel regions and pores. It is a figure which shows the histogram of the CT value in Embodiment 1. FIG. It is a figure which shows the relationship between a porosity and a CT value. FIG. 5 is a flowchart showing a process of calculating a fine porosity (representative value) in the first embodiment. It is a flowchart which shows the process of calculating the fine porosity (representative value) in Embodiment 2. It is a figure which shows the histogram of the CT value in Embodiment 2.

(Embodiment 1)
In this embodiment, a CT image of a measurement object is acquired using an X-ray CT (Computed Tomography) device, and the pore ratio of the measurement object (particularly, the fine pore ratio described later) is based on the CT value of the CT image. ) Is estimated.

(X-ray CT device)
FIG. 1 shows a schematic view of an X-ray CT apparatus. The X-ray CT apparatus 10 has an X-ray source 11 and a detector 12, and an object O to be measured is arranged between the X-ray source 11 and the detector 12. The X-rays emitted from the X-ray source 11 pass through the inside of the measurement object O and reach the detector 12.

The detector 12 detects the X-rays that have passed through the object O to be measured, and generates a CT image (digital image) according to the intensity of the X-rays. Specifically, the detector 12 includes a scintillator 12a that converts X-rays into visible light, and a photoelectric conversion element 12b that photoelectrically converts visible light emitted from the scintillator 12a. The photoelectric conversion element 12b has a plurality of pixels, and each pixel outputs a signal (CT value) according to the intensity of X-rays.

When the X-rays emitted from the X-ray source 11 pass through the inside of the measurement object O, the X-rays are attenuated by the measurement object O, and the intensity of the X-rays reaching the detector 12 decreases. Here, the higher the density of the measurement target O and the larger the size of the measurement target O (the size in the direction in which the X-rays pass), the more easily the X-rays are attenuated by the measurement target O, and the detector. The intensity of X-rays reaching 12 tends to decrease.

If the orientation of the measurement object O with respect to the X-ray source 11 is fixed, it is not possible to distinguish whether the X-ray attenuation is due to the size of the measurement object O or the density of the measurement object O. Therefore, as shown by the arrow D1 in FIG. 1, X-ray imaging was performed while rotating the measurement object O to change the direction of the measurement object O with respect to the X-ray source 11, and these X-ray photographs were obtained. By superimposing a plurality of images and performing the reconstruction process, CT images Is (see FIG. 2) including the shape and density of the object O to be measured in a predetermined plane (in the horizontal plane) can be obtained. The process of generating the CT image Is is performed by the arithmetic unit 20 connected to the detector 12.

By performing X-ray photography while changing the position of the measurement object O in the direction (vertical direction) of the arrow D2 shown in FIG. 1 with respect to the X-ray source 11, the position in the vertical direction of the measurement object O can be changed. Multiple different CT images Is are obtained (see FIG. 2). The CT image Is shows an image in the field region of X-ray photography, and the CT image Is includes a solid region S in which the measurement object O exists, a gas region V existing around the solid region S, and the like. A cavity U existing inside the solid region S is included. The arithmetic unit 20 generates three-dimensional information of the measurement object O by stacking a plurality of CT images Is in the vertical direction. The three-dimensional information includes a three-dimensional shape of the outer surface of the measurement object O and a density according to the position in the three-dimensional direction inside the measurement object O. After generating the three-dimensional information of the measurement object O, as shown in FIG. 1, the appearance of the measurement object O is displayed on the display 30 connected to the arithmetic unit 20, or the measurement object is cut at an arbitrary surface. A cross-sectional view of the object O can be displayed.

As for the CT value of the CT image Is, the lower the density of the measurement object O, the lower the CT value, and the higher the density of the measurement object O, the higher the CT value. FIG. 3 shows the relationship (measurement result) between the density and the CT value for CT images of four samples (air, paraffin, aluminum, calcium ferrite and hematite). In the CT image of each sample, since the CT value is obtained for each pixel region constituting the CT image, it can be represented as a histogram showing the frequency for each CT value. Here, the CT value of each sample shown in FIG. 3 is a CT value showing a peak frequency. As can be seen from FIG. 3, the lower the sample density, the smaller the CT value. In other words, the higher the sample density, the higher the CT value. Therefore, the relationship between the density and the CT value can be expressed as a linear function corresponding to the straight line L1 shown in FIG.

The object O to be measured may be a porous material, and for example, a raw material for sintering, a sinter cake or a sintered ore can be used. When a sinter cake or sinter is used as the object O to be measured, the X-ray CT apparatus 10 may include, for example, considering that _{the main component of the sinter cake or sinter is iron oxide (Fe 2} O _3). , "Measurement Technology 2007 (35) Vol. 3, pp. 1-4", high-voltage type X-ray CT apparatus can be used.

When only gas (for example, air) is present in one pixel region of the CT image Is, a CT value corresponding to the density of the gas can be obtained from this pixel region. Further, when only a solid is present in one pixel region of the CT image Is, a CT value corresponding to the density of the solid can be obtained from this pixel region. On the other hand, when gas and solid are present in one pixel region of CT image Is, the CT value of this pixel region is determined by the abundance ratio of gas and solid. It is not possible to ascertain how much gas is present in one pixel region.

In the present embodiment, the pores existing only in a part of one pixel region, in other words, the gas existing together with the solid of the measurement object O in one pixel region (hereinafter referred to as fine pores) is the measurement object. The ratio (referred to as fine porosity) occupied by fine pores in the solid region S (see FIG. 2) of O is calculated (estimated). Here, as the fine pores, as shown in FIG. 4A, there are pores having a size that fits within one pixel region R. Further, even if the pores have a size that does not fit in one pixel region R, as shown in FIG. 4B, when the pores are present over a plurality of pixel regions R (four pixel regions R in FIG. 4B). When focusing on one pixel region R, pores may exist only in a part of the pixel region R. Such pores are also referred to as fine pores in the present embodiment. Hereinafter, a method of calculating the fine porosity in one pixel region R will be described.

(Calculation method of fine porosity in one pixel region R)
The fine pore ratio ε _XF of the object to be measured is a CT value obtained from a CT image of a solid reference sample (solid CT value CT ₁ described later) and a CT value obtained from a CT image of a reference gas (gas CT value described later). It is calculated based on CT _0). Hereinafter, a specific description will be given.

As the solid reference sample, a sample showing a CT value larger than the CT value of the measurement object O is used. For example, hematite granules can be used as the solid reference sample. As hematite grains, the true density is 4.74 to 5.74 [g / cm ³ ] (5.24 ± 0.5 [g / cm ³ ]), and _{the purity of Fe 2} O ₃ is 90% or more. It is preferable to use one having a size equal to or larger than the lower limit of the resolution of the detector 12. Here, even if the size of the hematite granules is too large, it is inconvenient to handle. Therefore, the size of the hematite granules is preferably 50 [mm] or less. More preferably, the true density is 5.14 to 5.34 [g / cm ³ ] (5.24 ± 0.1 [g / cm ³ ]), and _{the purity of Fe 2} O ₃ is 95% or more. , Hematite grains having a size of 10 to 30 [mm] can be used. Specifically, among the obtained natural ores, those whose density, purity and size satisfy the above conditions can be used as a solid reference sample (hematite granules).

On the other hand, an alloy having a density equivalent to that of hematite grains can also be used as a solid reference sample. For example, it was obtained by melting and mixing a metal having a true density of more than 5.24 [g / cm ³ ] and a metal having a true density of ^{less than 5.24 [g / cm 3] and cooling.} The alloy can be used as a solid reference sample. When an alloy is used, it is sufficient that component segregation at a resolution equal to or higher than that of the detector 12 does not occur when the molten metal is cooled. For example, copper (true density 8.9 [g / cm ³ ]) and aluminum (true density 2.7 [g / cm ³ ]) at a weight ratio of about 41:59 (copper: aluminum). The alloy obtained by melting, mixing and quenching can be used as a solid reference sample.

When the solid-state reference sample is photographed using the X-ray CT apparatus 10, a histogram showing the frequency for each CT value is obtained in the region where the solid-state reference sample exists in the CT image Is. In this histogram, the CT value showing the peak frequency is defined as the CT value (referred to as solid CT value) CT ₁ peculiar to the solid-state reference sample.

When the solid-state reference sample is photographed by using the X-ray CT apparatus 10, the solid-state reference sample can be photographed together with the measurement object O, or the measurement object O and the solid-state reference sample can be photographed individually. When the solid reference sample is photographed together with the measurement object O, for example, the solid reference sample can be embedded inside the measurement object O, or the solid reference sample can be attached to the outer surface of the measurement object O.

On the other hand, when the measurement object O and the solid reference sample are photographed individually, it is preferable to make the time interval between the timing of photographing the measurement object O and the timing of photographing the solid reference sample as short as possible. The reason for this is that it is necessary to set the same imaging conditions when acquiring the CT value of the measurement object O and the CT value of the solid-state reference sample. The longer the time interval, the easier it is for the imaging conditions of the X-ray CT apparatus 10 to change, and the change in the imaging conditions may affect the imaging result (CT value) of the X-ray CT apparatus 10.

When a gas is photographed using the X-ray CT apparatus 10, a histogram showing the frequency of each CT value is obtained in the region where the gas exists (gas region V shown in FIG. 2) in the CT image Is. In this histogram, the CT value showing the peak frequency is defined as the CT value (referred to as gas CT value) CT ₀ peculiar to the reference gas. Since the imaging of the X-ray CT apparatus 10 is usually performed in the presence of air, air can be mentioned as the gas.

When the gas is photographed by using the X-ray CT apparatus 10, the gas can be photographed together with the measurement object O, or the measurement object O and the gas can be photographed individually. When the gas is photographed together with the measurement object O, the measurement object O and the gas may be present within the imaging range. Further, since the object O to be measured is a porous body and the cavity U exists inside the object O to be measured, the gas existing in the cavity U can be used as a reference gas. On the other hand, when the measurement target O and the gas are photographed individually, it is preferable to make the time interval between the timing of photographing the measurement object O and the timing of photographing the gas as short as possible. The reason for this is as described above.

FIG. 5 is a histogram showing the frequency of each CT value when the measurement object O, the solid reference sample, and the reference gas are simultaneously photographed using the X-ray CT apparatus 10. Since the measurement object O, the solid reference sample, and the reference gas are simultaneously photographed, in the histogram shown in FIG. 5, the peak corresponding to the measurement object O, the peak corresponding to the solid reference sample, and the reference gas correspond to each other. A peak is appearing.

Comparing the CT values showing peak frequencies for each of the measurement object O, the solid reference sample, and the reference gas, the CT value of the reference gas becomes the smallest due to the difference in density described in FIG. Therefore, among the CT values corresponding to the three peaks shown in FIG. 5, the smallest CT value is the gas CT value CT ₀ . Further, since the CT value of the solid-state reference sample becomes the largest due to the difference in density described in FIG. 3, the largest CT value among the CT values corresponding to the three peaks shown in FIG. 5 is the solid-state CT value CT _1. It becomes.

On the other hand, the CT image also includes pores other than the fine pores. These pores are pores (referred to as coarse air pores) that occupy all of one pixel region. When calculating the fine porosity, it is necessary to distinguish between fine pores and coarse air pores. In the present embodiment, in order to distinguish between the micropores and the coarse air pores, a CT value (referred to as a reference CT value) CT _b indicating a reference indicating a boundary between the coarse air pores and the coarse air pores is specified based on the histogram shown in FIG. ing.

The reference CT value CT _b is a CT value corresponding to the minimum value existing between the peak of the reference gas and the peak of the measurement object O in the histogram shown in FIG. The pixel region R whose CT value is equal to _{or less than the reference CT value CT b} can be regarded as a region where the coarse air pores exist. On the other hand, the _{pixel region R whose CT value is larger than the reference CT value CT b} can be regarded as a region where fine pores exist. In this way, if each pixel region R in the CT image Is is classified into a region where fine pores exist and a region where coarse air pores exist based on _{the reference CT value CT b, as described below,} The fine porosity and the crude air porosity can be calculated individually.

_{The fine porosity ε XF} of the object to be measured O is calculated based on the following equation (1). The following equation (1) shows a straight line L2 shown in FIG. FIG. 6 shows the relationship between the porosity and the CT value in each pixel region R, and the relationship between the porosity and the CT value can be expressed as a linear function.

In the above equation (1), CT ₁ is a solid CT value, CT ₀ is a gas CT value, and CT _X is a CT value for each pixel region R. In the pixel region R showing the solid CT value CT ₁ , the porosity can be considered to be 0%. Further, in the pixel region R showing the gas CT value CT ₀ , the porosity can be considered to be 100%. In a coordinate system with each of the porosity and CT value as the coordinate axis, _{the relationship between the solid CT value CT 1} and the porosity 0% and the relationship between the gas CT value CT ₀ and the porosity 100% are plotted, and these plots are connected. The straight line becomes the straight line L2 shown in FIG.

The solid CT value CT ₁ and the gas CT value CT ₀ are preset in consideration of displaying the CT image in black and white 256 gradations. Therefore, by substituting the CT value CT _X for each pixel region R into the above equation (1), the fine porosity ε _XF for each pixel region R can be calculated. As described above, since fine pores exist in the pixel region R whose CT value is larger than the reference CT value CT _{b, when calculating the fine porosity ε XF , the CT value CT X} shown in the above formula (1) is used. Targets a CT value larger than the reference CT value CT _b.

(Fine porosity of the solid region S of the object O to be measured)
If the fine porosity ε _XF is calculated for each pixel region R, the average value ε _{XF _ave of the fine porosity ε XF} of all the pixel regions R of the solid region S can be calculated. The average value epsilon _XF _ave can be regarded as a fine porosity of the measurement object O solid region S (see FIG. 2) (fine porosity of solids). Mean value epsilon _XF _ave, for example, can be calculated based on the following equation (2).

In the above formula (2), _PF is the total number of pixels in the solid region S. When calculating the total number P _F may be counting the number of CT values of the reference CT value CT _b larger pixel area R than. The molecule on the right side of the above formula (2) is the sum of _{the fine porosity ε XF of all the pixel regions including the fine pores.}

In the present embodiment, is regarded an average value epsilon _XF _ave described above with fine porosity of the solid region S of the measuring object O, is not limited to this, the fine porosity of the solid region S of the measuring object O Any value (representative value) that can specify is sufficient. For example, as a representative value, for all the pixel regions R included in the solid region S, the median value of the range in which _{the fine porosity ε XF of each pixel region R can be taken can be set.}

The flowchart shown in FIG. 7 shows a process of calculating the fine porosity (representative value described above) of the solid region S of the object O to be measured. Hereinafter, a specific description will be given.

In step S101, the measurement object O, the solid reference sample, and the reference gas are photographed using the X-ray CT apparatus 10. As a result, a histogram showing the frequency for each CT value can be obtained for each of the measurement object O, the solid reference sample, and the reference gas. _{In step S102, the solid CT value CT 1} , the gas CT value CT _0, and the reference CT value CT _b are specified based on the histogram obtained in the process of step S101. The method for specifying the solid CT value CT ₁ , the gas CT value CT _0, and the reference CT value CT _b is as described above.

In step S103, for the _{pixel region R whose CT value is larger than the CT value CT b, the CT value CT X} obtained from each pixel region R is substituted into the above equation (1) to obtain fine pores in each pixel region R. Calculate the rate ε _{XF. Here, as the solid CT value CT 1} and the gas CT value CT ₀ represented by the above formula (1), _{the CT values CT 0} and CT ₁ specified in the process of step S102 are used. In step S104, a representative value which is a fine porosity of the solid region S of the measurement object O is calculated based on _{the fine porosity ε XF} of each pixel region R calculated in the process of step S103. For example, it is possible to calculate the average value epsilon _XF _ave based on the equation (2).

(Coarse air porosity)
On the other hand, the crude air porosity ε _XL of the object O to be measured can be calculated based on the following equation (3).

In the above formula (3), epsilon _XL is coarse porosity, the total number of _{P L} is a CT image of Is, CT values present in the contour of the measuring object O is less than the reference CT value CT _b pixel region R ( Number of pixels). _PT is the number (number of pixels) of all the pixel regions R existing in the contour of the measurement object O in the CT image Is. Here, by performing known edge detection on the CT image Is, the contour (outer edge) of the measurement object O included in the CT image Is can be specified. The total number of pixels included in the area (including the contour) surrounded by the contour of the measurement object O is the number of pixels _PT . As shown in FIG. 2, when a cavity (gas region U) exists inside the measurement object O, not only the contour of the measurement object O but also the contour of the cavity is specified by edge detection. Since the contour of this cavity is included in the region surrounded by the contour (outer edge) of the object O to be measured, the number of pixels corresponding to the cavity is included in the number of pixels _PT .

For coarse pores, because all of the one pixel region occupied by the gas, as shown in the equation (3), the number of pixels P _L, by calculating the ratio of P _T, coarse porosity of the measurement object O ε _XL can be calculated. When there are no coarse air holes in the measurement target O, that is, when there is no pixel region R whose CT value is equal to or less than the _{reference CT value CT b in the region surrounded by the contour of the measurement target O.} The crude air porosity ε _XL is 0.

Since the number of pixels P _T can be obtained by specifying the contour of the object O to be measured by edge detection, _{the coarse air porosity ε XL} can _{be obtained by counting the number of pixels P L} based on the above equation (3). Can be calculated. Be calculated measurement target fine porosity of O (typical) epsilon _XF and coarse porosity epsilon _XL, the total value of the fine porosity epsilon _XF and coarse porosity epsilon _XL is the total porosity of the measurement object O ( That is, the porosity of the entire region surrounded by the contour of the object O to be measured). Here, if attention is paid to an arbitrary cross-sectional image of the object O to be measured, the porosity in the cross-sectional image of the object O to be measured can be calculated. Further, if attention is paid to the measurement object O having a three-dimensional shape, the porosity of the measurement object O in the three-dimensional space can be calculated.

(Embodiment 2)
The second embodiment of the present invention will be described. _{In the present embodiment, the fine porosity ε XF} is calculated in consideration of the true densities of a plurality of chemical components constituting the measurement object O. Hereinafter, the differences between the present embodiment and the first embodiment will be mainly described.

First, the proportion of each chemical component contained in the measurement object O is measured and based on this proportion, by weighted average of the true densities of all chemical components, an average true density d _a. Here, the blending ratio of each chemical component of the object to be measured O can be measured by a known chemical analysis. Moreover, the true density of each chemical component may be investigated in advance.

Next, using the X-ray CT apparatus 10, a plurality of substances having different chemical components are photographed. Each substance is composed of a single chemical component, has a known true density, and has a porosity of 0%. The chemical component referred to here is preferably the chemical component contained in the object O to be measured. By photographing a plurality of substances, a histogram showing the frequency for each CT value can be obtained for the CT image of each substance, and the CT value showing the peak frequency can be specified based on this histogram. As a result, for each substance, the relationship between the CT value showing the peak frequency and the true density (known) can be obtained.

By plotting the relationship between the CT values and the true densities of a plurality of substances in a coordinate system with each of the CT values and the true densities as the coordinate axes, an approximate straight line of these plots can be obtained. This approximate straight line is represented by the following equation (4). The following equation (4) corresponds to the straight line L1 shown in FIG.

In the above equation (4), d _X is the true density, and CT _X is the CT value indicating the peak frequency. α and β are coefficients peculiar to the X-ray CT apparatus 10 to be used, α corresponds to the slope of the approximate straight line, and β corresponds to the intercept of the approximate straight line. Coefficients α and β can be determined by photographing a plurality of types of substances having a known density without pores in advance using an X-ray CT apparatus 10 to obtain the CT value, and linearly reverting the correlation between the density and the CT value. .. For example, when Toshiba: TOSCANER-24500twin was used as the X-ray CT apparatus 10 and air and hematite grains were used as the above-mentioned substances, α was 0.0258 and β was −0.697.

On the other hand, the porosity ε can be expressed by the following equation (5) by defining the _{relative density ρ r.}

_{The relative density ρ r} shown in the above formula (5) is a dimensionless number indicating how much the density of any substance is based on the true density. Assuming that the density of the target region of the object O to be measured is the density d _X , the relative density ρ _r is represented by the following equation (6). In the following formula (6), _{d X} is the true density, _{d a} is the average true density.

Considering the above equations (4) to (6), the fine porosity ε _XF of each pixel region R in the CT image of the measurement object O is represented by the following equation (7). The following equation (7) represents the straight line L2 shown in FIG.

According to the equation (7), it can be based on a CT value CT _X and an average true density d _a of each pixel region R, to calculate the fine porosity epsilon _XF in each pixel region. Here, the CT value corresponding to the average true density _{d a} in relation density and CT values shown in Figure 3, CT value when the porosity is 0% (i.e., solid CT value CT ₁₎ become. _{Further, as the CT value CT X} of each pixel region R, as described in the first embodiment, a CT value larger than the _{reference CT value CT b is targeted.}

If the fine porosity ε _XF of each pixel region R is calculated, as described in the first embodiment, the CT value CT _X is larger than the reference CT value CT _b based on _{the fine porosity ε XF} of all the pixel regions R. The representative value can be calculated. This representative value is the fine porosity of the solid region S of the object O to be measured. Further, similarly to Embodiment 1, by calculating a coarse porosity epsilon _XL of the measurement object O, based on the fine porosity epsilon _XF and coarse porosity epsilon _XL, calculates the total porosity of the measurement object O be able to.

The flowchart shown in FIG. 8 shows a process of calculating the total fine porosity (representative value described above) of the object O to be measured. Hereinafter, a specific description will be given.

In step 200, in the X-ray CT apparatus 10 to be used, the coefficients α and β of the above formula (4) representing the relationship between the density and the CT value are determined. The method for determining the coefficients α and β is as described above. In step S201, the blending ratio [% by weight] is measured for the plurality of chemical components contained in the object O to be measured. By examining the true density of each chemical component, it calculates the average true density d _a.

In step S202, the object O to be measured is photographed using the X-ray CT apparatus 10, and the reference CT value CT _b is specified. Since the measurement object O is a porous body and the CT image of the measurement object O usually contains coarse air holes, FIG. 9 is a histogram showing the frequency of each CT value when the measurement object O is photographed. As shown in FIG. 9, a peak corresponding to the gas existing inside the measurement object O (the peak on the left side in FIG. 9) and a peak corresponding to the solid portion (including fine pores) of the measurement object O (FIG. 9). The peak on the right side of the inside) appears. Since there is a minimum value between these peaks, the CT value corresponding to this minimum value is specified as the _{reference CT value CT b.} The CT value indicating the peak corresponding to the gas existing inside the measurement object O is the CT value when the porosity is 100% (that is, the gas CT value CT ₀ ).

In step S203, for the _{pixel region R whose CT value is larger than the reference CT value CT b, the CT value CT X} obtained from each pixel region R is substituted into the above equation (7), so that each pixel region R is fine. The pore ratio ε _XF is calculated. Here, the average true density d _a shown in the equation (7), the average true density d _a calculated in the processing in step S201 is used. In this embodiment, _{in order to calculate the fine porosity ε XF} for each pixel region R, the density and CT are replaced with the _{solid CT value CT 1} and the gas CT value CT ₀ in the first embodiment (the above formula (1)). it is characterized between the values (the above formula (4)) and in that the average is used true density d _a.

In step S204, similarly to step S104 shown in FIG. 7, a representative value which is the total fine porosity of the object O to be measured based on _{the fine porosity ε XF of each pixel region R calculated in the process of step S203.} Is calculated. For example, it is possible to calculate the average value epsilon _XF _ave based on the equation (2).

_{According to the present embodiment, by calculating the fine porosity ε XF in consideration of the average true density da in a} plurality of chemical components constituting the object O to be measured, the fine porosity ε _XF of each chemical component is added to the fine porosity ε XF. The impact can be reflected. For example, the sinter contains other chemical components such as CaO and SiO _{2 in addition to Fe 2} O ₃ , and the mixing ratio of the other chemical components differs depending on the raw material. Therefore, in the calculation of the fine porosity epsilon _XF, by considering other chemical components, it is possible to improve the estimation accuracy of the fine porosity epsilon _XF.

As will be described later in Example 2, the effect of other chemical components on the CT value is much smaller than the effect of pores on the CT value, and therefore the effect of other chemical components on the CT value. Can be ignored, but the estimation accuracy of the _{pore ratio ε XF} can be further improved by considering the influence of other chemical components on the CT value.

Examples 1 and 2 corresponding to the above-described first and second embodiments will be described. Here, the first embodiment corresponds to the first embodiment, and the second embodiment corresponds to the second embodiment.

(Example 1)
In this example, the fine porosity (representative value) ε _XF and the crude air porosity ε _XL were calculated based on the method described in the first embodiment described above. The experimental method will be described below.

Iron ores A to F, limestone, quicklime, return ore and coke shown in Table 1 below were prepared and mixed at the blending ratios shown in Table 1 below. Specifically, it was mixed with a drum mixer for 1 minute. After mixing, 6.8% by mass of water was added to granulate for 4 minutes, and the granulated product (raw material) was charged into a pan. As the pot, a pot made of quartz glass having a diameter of 200 [mm] and a height of 550 [mm] was used. Here, a wool insulating material was placed on the inner wall surface of the pot.

The raw materials were charged into the pot manually. Specifically, a fixed amount of the raw material was dropped toward the pot using a shovel from a position about 10 cm above the top surface of the pot. At this time, the raw material was charged into the pot while randomly changing the drop position of the raw material in the horizontal plane so that the upper surface of the raw material layer charged in the pot was as flat as possible. Further, a flat hematite having a diameter of 20 [mm] was placed in the center of the pan at a position of a height of 300 [mm] in the raw material layer.

Next, using an X-ray CT apparatus 10 (manufactured by Toshiba: TOSCANER-24500twin), a pot in which the raw material was charged was photographed to obtain a CT image Is1 of the raw material layer. Since it took 15 hours to shoot, the opening of the pot was covered with a vinyl sheet in advance to prevent the raw materials from drying out.

Next, the pot for which the imaging was completed was removed from the X-ray CT apparatus 10 and placed in a baking air box, and the raw material was heated and fired under the following conditions.
・ LPG flow rate during heating: 75 [NL / min]
-Flow rate of air during heating: 2300 [NL / min]
-Heating time: 60 [sec]
・ Negative pressure in the air box from heating to the end of firing (constant): 10.8 [kPa]

With the baked sinter cake in the pan, an image was taken with the X-ray CT apparatus 10, and a CT image Is2 was obtained.

A cross-sectional image obtained by reconstructing the CT image Is1 of the raw material layer before firing and the CT image Is2 of the sinter cake after firing with three-dimensional image processing software, and cutting the three-dimensional images of the raw material layer and the sinter cake in the vertical direction. Got The cross-sectional image was black and white 256 gradations (0-255). Further, in the histogram of CT values in the CT image of hematite, the CT value indicating the peak frequency is 232, and in the histogram of the CT values in the CT image of air, the CT value indicating the peak frequency is 30. The brightness of the CT image was adjusted. At this time, when the reference CT value CT _b was specified based on the histogram, the reference CT value CT _b was 90. Therefore, the pixel region R having a CT value of 90 or less is a region where coarse air pores are present, and the pixel region R having a CT value larger than 90 is a region where fine pores are present.

For each of the raw material layer and the sinter cake, the fine porosity ε _{XF for each pixel region R was calculated based on the above formula (1), and the crude air porosity ε XL} was calculated based on the above formula (3). Here, for the fine porosity ε _{XF , the average value ε XF} _ave was calculated based on the above equation (2). In addition, _{the porosity ε TE} was calculated by summing the average values ε _XF _ave of the crude air _{porosity ε XL} and the fine porosity ε _XF. Table 2 below shows the calculation results of the crude air porosity ε _XL , the average value of the fine porosity ε _{XF ε XF} _ave, and the porosity ε _TE.

On the other hand, the apparent volume [g / cm ³ ] and the weight [g] were measured for _{each of the raw material layer and the sinter cake, and the porosity ε TM} was calculated from the apparent volume and the weight. The apparent volume was the volume of the cylinder calculated from the radius of the pot used for baking and the heights of the raw material layer and the sinter cake. The calculation results of this porosity ε _TM are shown in Table 2 below.

As can be seen from Table 2, for the raw material layer, the difference in porosity epsilon _TE and porosity epsilon _TM is 4 [vol%], for the sinter cake, the difference in porosity epsilon _TE and porosity epsilon _TM It was 3 [volume%]. As described above, _{the difference between the porosity ε TE} and the porosity ε _TM was small, and according to this example, the porosity could be estimated accurately based on the CT value.

(Example 2)
_{For the five main chemical components (Fe 2} O ₃ , FeO, CaO, SiO ₂ , Al ₂ O ₃ ) contained in the raw materials used in Example 1, the blending ratio [% by weight] of each chemical component was measured. .. The measurement results are shown in Table 3 below. Table 3 below also shows the true density [g / cm ^{3] of each chemical component.} In addition, Table 3 below also shows _a weighted average value of the true densities of the chemical components (the above-mentioned average true density da) based on the blending ratio of each chemical component.

Regarding the coefficients α and β representing the relationship between the density and the CT value in the X-ray CT apparatus 10 used (the above equation (4)), α was 0.0258 and β was −0.697.

For each material layer and sinter cake, the average true density d _a and CT value CT _X for each pixel region R shown in Table 3 by substituting the above equation (7), fine porosity of each pixel region R epsilon _XF was calculated. Here, the reference CT value CT _b is 90 as described in Example 1. After calculating the fine porosity epsilon _XF for each pixel region R, based on the equation (2) to calculate the average value epsilon _XF _ave.

For each material layer and sinter cake, the average true density _{d a} when calculating the fine porosity epsilon _XF, using the same value ^{(4.8 [g / cm 3]} ). Here, the water of crystallization is contained in the raw material layer, and the water of crystallization decomposes and evaporates when the raw material layer is fired. Therefore, the water of crystallization in the raw material layer can be regarded as pores. Therefore, in the calculation of the average true density d _a, as shown in Table 3, excluding the water of crystallization, which considers only the major chemical components. On the other hand, when the production of sinter cake by firing the raw material layer is proportion of FeO is increased by a few percent by weight, because the impact on the average true density d _a is approximately 0.5%, the proportion of FeO I ignored the rise. In consideration of these points, for each of the raw material layer and sinter cake, the average true density d _a when calculating the fine porosity epsilon _XF, using the same value (4.8 [g / cm 3] ) be able to.

_{The crude air porosity ε XL} was calculated based on the above formula (3), and the pore ratio ε _TE was calculated by summing the average values ε _{XF _ave of the crude air porosity ε XL} and the fine pore ratio ε _XF. Table 4 below shows the calculation results of the crude air porosity ε _XL , the average value of the fine porosity ε _{XF ε XF} _ave, and the porosity ε _TE.

On the other hand, the apparent volume [g / cm ³ ] and the weight [g] were measured for _{each of the raw material layer and the sinter cake, and the porosity ε TM} was calculated from the apparent volume and the weight. The apparent volume was the volume of the cylinder calculated from the radius of the pot used for baking and the heights of the raw material layer and the sinter cake. The calculation results of this porosity ε _TM are shown in Table 4 below.

As can be seen from Table 4, the raw material layer, the difference in porosity epsilon _TE and porosity epsilon _TM is 2 [vol%], for the sinter cake, the difference in porosity epsilon _TE and porosity epsilon _TM It was 1 [volume%]. That is, in this example, _{the difference between the porosity ε TE} and the porosity ε _TM was smaller than that in Example 1, and the estimation accuracy of the porosity based on the CT value could be improved.

(Effect of chemical composition of sinter on CT value)
When estimating the density from the chemical composition of the sinter (measurement object O) without using a solid reference sample and estimating the fine porosity of the sinter based on the correspondence between the density and the CT value, the chemical composition The effect of is on the CT value will be considered below.

In the sinter, CaO is mainly mentioned as a component other than _{Fe 2} O _3. The effect of CaO on the CT value is expressed by the following formula (8).

In the above formula (8), I_CT1 is the degree of influence of CaO on the CT value, ρ_Fe ₂ O ₃ is the true density of Fe ₂ O ₃ [g / cm ³ ], and ρ_CaO is the true density of CaO [g / cm ³ ]. , C_CaO is the CaO content [%]. Since ρ_Fe ₂ O ₃ is 5.2 [g / cm ³ ], ρ_CaO is 3.4 [g / cm ³ ], and C_CaO is usually about 10 [%], the degree of influence I_CT1 is about 3%. It becomes.

On the other hand, the effect of pores on the CT value is expressed by the following formula (9).

In the above formula (9), I_CT2 is the degree of influence of pores on the CT value, ρ_Fe ₂ O ₃ is the true density of Fe ₂ O ₃ [g / cm ³ ], and ρ_gas is the density of pores (gas) [g / cm ³ ], C_air is the abundance rate [%] of pores. ρ_Fe ₂ O ₃ is 5.2 [g / cm ³ ], ρ_gas when the gas is air is 1.3 × 10 ^-3 [g / cm ³ ], and C_gas is usually about 60 [%]. Therefore, the degree of influence I_CT2 is about 60 [%].

As described above, the _{degree of influence I_CT1 of the chemical component (CaO) other than Fe 2} O _{3 on the} CT value in the sinter is much smaller than the degree of influence I_CT2 of the pores of the sinter on the CT value. .. Therefore, even if the influence of other chemical components on the CT value is ignored, the influence on the fine porosity ε _{XF calculated from the CT value CT X} is small, and the estimation accuracy of the _{fine porosity ε XF should be ensured.} Can be done.

10: X-ray CT device, 11: X-ray source, 12: detector, 12a: scintillator,
12b: photoelectric conversion element, 20: arithmetic unit, 30: display, O: object to be measured,
R: 1 pixel, S: solid region (including fine pores), U: cavity existing inside the solid region,
V: Gas region surrounding the solid region, Is: CT image

Claims (6)

A method for estimating the fine porosity, which is the ratio of the gas portion existing together with the solid portion of the measurement object in one pixel region constituting the X-ray CT image of the measurement object in the porous measurement object. And
Based on the histogram of CT values in the X-ray CT image including the object to be measured , the solid reference sample and the gas.
The solid CT value, which is a CT value indicating the frequency peak of the solid reference sample, and the gas CT value, which is a CT value indicating the frequency peak of the gas, are specified, and at the same time.
A reference CT value, which is a CT value indicating a minimum value between the frequency peak of the measurement object and the frequency peak of the gas, is specified.
Among the plurality of pixel regions constituting the X-ray CT images of the measurement object, the target pixel region showing a large CT value than the reference CT value, the porosity corresponding to the solid CT value 0%, the Based on the linear function of the following equation (I) showing the correspondence between the CT value and the pore ratio when the pore ratio corresponding to the gas CT value is 100%, the pore ratio corresponding to the CT value of each target pixel region. Is calculated and
A representative value of the porosity in the plurality of target pixel regions is estimated as the fine porosity.
A method for estimating porosity.

Here, ε _XF is the porosity of the target pixel region, CT _X is the CT value of the target pixel region, CT ₁ is the solid CT value, and CT ₀ is the gas CT value. The porosity estimation method according to claim 1 , wherein the solid reference sample has a true density of 4.74 to 5.74 g / cm ³ and is a hematite grain or an alloy. In a porous measurement object composed of a plurality of chemical components, the ratio of the gas portion existing together with the solid portion of the measurement object in one pixel region constituting the X-ray CT image of the measurement object. A method of estimating a certain fine porosity,
Based on the CT value histogram in the X-ray CT image of the measurement object, a minimum value is shown between the frequency peak of the solid portion of the measurement object and the frequency peak of the gas existing inside the measurement object. Identify the reference CT value, which is the CT value,
Of the plurality of pixel regions constituting the X-ray CT image of the measurement target, the target pixel region showing a CT value larger than the reference CT value is the target pixel region based on the following formula (II). Calculate the pore ratio corresponding to the CT value,
A representative value of the porosity in the plurality of target pixel regions is estimated as the fine porosity.
A method for estimating porosity.

Here, ε _XF is the pore ratio of the target pixel region, CT _X is the CT value of the target pixel region, α and β are predetermined coefficients, and da is the mass ratio of each chemical component. Ru average true density der that the weighted average true density of the plurality of chemical components. The porosity estimation method according to any one of claims 1 to 3, wherein the object to be measured is a raw material for sintering, a sinter cake or a sinter. In the X-ray CT image of the measurement object, the ratio of the total number of pixels showing a CT value equal to or less than the reference CT value to the total number of all pixels existing in the area surrounded by the contour of the measurement object. The pores according to any one of claims 1 to 4 , wherein the measurement object is estimated as a crude air porosity, which is a ratio of crude air pores existing in the entire pixel region. Rate estimation method. The porosity estimation method according to claim 5 , wherein the total value of the crude air porosity and the fine porosity is estimated as the total porosity of the object to be measured.

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