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The thermal neutron absorption cross section is one of important parameters in geophysical interpretation procedures. It is measured in the Institute of Nuclear Physics using the pulsed neutron technique. In such experiments the bulk density of the sample, the material heterogeneity, and the porosity, influence the neutron decay constant which is the basic result of pulsed neutron experiments. Homogeneity of a medium consisting of two components may be affected by the grain size being too large, by a possible segregation of the rock material, and by a non-uniform saturation with the fluid.

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The absorption cross section which is used in geophysical interpretations is expressed in capture units: S _a [c.u.] where 1 c.u. = 10^-3 cm^-1. What does it means ? It means that the value of this parameter is valid only for a given density of the medium. This is seen from the formula which defines the linear macroscopic absorption cross section of the complex medium. In most cases the absorption cross section for rocks is known from measurements on samples. If the result of any kind of experiments is the linear absorption cross section S _a , the density of the sample has also to be reported. In the opposite case the S _a value is useless.

The above statement is especially important when bulk materials are considered. The explanation of variation of the bulk density is presented here.

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Let us consider an isometric medium, i.e. grains being small spheres of identical diameters, made of the same homogeneous material of the solid material density r ₀ . The following two extreme cases of an arrangement of the spheres exist.

a) Simple cubic metastable arrangement in which each sphere contacts with 6 neighbors. The pores created in this way are regular concave octahedrons. Then the porosity of the medium is maximal, which involves the minimum bulk density r _min = 0.5236 r ₀ .

b) Compact arrangement in which each sphere is tangential to 12 neighbors and the pores have shapes of regular concave octahedrons and tetrahedrons. The resulting porosity is minimal, which involves the maximum bulk density r _max = 0.7405 r ₀ .

The linear absorption cross section in such cases changes proportionally to the bulk density.

The conclusion from the presented discussion is, that it is better if the mass absorption cross section is the primary result of the measurement. This requirement is fulfilled in the method of the absorption cross section measurement elaborated and used in the Institute of Nuclear Physics in Kraków.

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The method uses the pulsed neutron generator. The mass absorption cross section of a given rock material is determined from the time decay of thermal neutrons after the neutron burst. The mass absorption cross section of the rock material investigated is the primary result of the measurement which is independent of the material density. The rock material is crushed before the measurement. The density of the solid material can be measured using different equipments and methods. We have a possibility to measure the density, first, during the preparation of the rock sample for the measurement (comparable to the water pycnometer method) and, second, using the helium pycnometer.

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The cross sections [c.u./(g cm^-3)] obtained in our laboratory and the corresponding S _a [c.u.] values calculated using two different densities of the material (from two different methods) are presented in the table.

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In conclusion: the absorption cross section for a homogeneous bulk material has to be reported as:

either the mass absorption cross section [c.u./(g cm^-3)]

or the linear absorption cross section S _a [c.u.] necessarily with the material density r [g cm^-1].

HETEROGENEITY OF THE MATERIAL

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Whole consideration up till now and the basic formula for calculation of the S _a is valid under the assumption that the material investigated is homogeneous. In practice, especially for environmental materials, they are rare cases. The effective thermal neutron absorption cross section of a heterogeneous mixture can differ significantly from that of a homogeneous mixture made of the same components. The material heterogeneity for neutrons can be considered as regular grains of a highly absorbing material in a low absorbing matrix or as irregular layers of strong absorption, bubbles of the air, etc.

The simplest model of the grain heterogeneity is a two-medium system (low/high absorbers) of different sizes of grains.

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Such models have been made in our Institute for test experiments. There are three models of Plexiglass-silver cylinders. The total mass of silver is the same in each sample but the sizes of silver grains are different. The absorption cross section has been measured by Czubek’s method for each model. The results are shown in the figure (Transparency 8).

The simplest estimate of the influence of the absorbing centers can be made by utilizing the results of a theory given by Umiastowski et al. (Nucl. Instr. Meth. 141, 347, 1977) for g rays. The effective absorption cross section is calculated as a function of the absorption cross section of a highly and weakly absorbing components, its mass contribution and the dimensionless size of the grain. This function and the comparison between theory and experimental results are shown in the Transparency.

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The results clearly show that the effect of the change of the absorption cross section for the heterogeneous mixture really appears. The observed effect is stronger than anticipated by Umiastowski’s theory. It is obvious because the g ray transport differs significantly from the thermal neutrons transport. The research is continued by our group.

From the examples shown it results that it is important to have a homogeneous sample in pulsed neutron experiments. In any kind of pulsed neutron experiment the time decay constant is measured. The responses from the detector situated at the bottom or on the top of the container can be different if the sample is heterogeneous. The two-detector system is applied in our Laboratory observes such an effect.

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The experimental set-up is fully symmetrical. If the material is distributed as in the figure, the neutron absorption in the upper and lower parts is different. If the signals from the top and bottom detector are the same, we assume that the sample is homogeneous. The two-detector system is used routinely in our Lab in the absorption cross section measurements for rock materials.

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The neutron decay constants measured with the top and bottom detectors in a large experimental series of rock samples are shown in the figure. These results confirm that the samples have been homogeneous and the macroscopic absorption cross section is measured correctly.

Conclusions

The pulsed neutron experiments, when the thermal neutron decay is registered and interpreted, are dependent on the bulk density, the porosity and the grain size of the material investigated. The measured decay constants are the base of different absorption cross section measurement methods, like Czubek’s method, the variable buckling method, etc. Preparation of samples for the experiments has to be done with a high attention:

• The density of the bulk material has to be carefully measured and reported with the S _a results.
• The grain size has to be taken into account if the experiments are made on crushed rock material.
• The absorption cross section measured on samples is treated as the material parameter of the homogeneous medium.

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That parameter is used later for the interpretation of the well-logging neutron tool response. It has to be taken into account that the medium surrounding the borehole can be heterogeneous. The neutron tool is sensitive to the effective absorption cross section of that real medium not to the ideal homogeneous material. The consideration presented above can be important in this case.

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