Double Wall Technique pipelines' inspection using gamma rays
V. Dorobantu
Physics Department, "Politehnica" University,
Timisoara, Romania,
Corresponding Author Contact: Email: wdorobantzu@zappmobile.ro
Abstract
Gamma rays emitted by Ir^{192} make up a polychromatic radiation, and this polychromatic nature involves thickness dependence of the linear attenuation coefficient  µ  . An expression for µ is obtained and verified for Ir^{192} gamma rays absorption in steel.
1. Introduction
Inspecting pipelines, for possible defects, with gamma rays became a current procedure. Usually, there are two methods: double wall technique ( DWT ) and tangential technique ( TT ). The first one (DWT) requires knowledge of the linear attenuation coefficient of the gamma rays, in order to have a good estimation of the defect's dimension. Ir^{192} polychromatic gamma rays supply an appropriate tool for this goal, especially when one does not know where is the defect in a pipeline with a variable thickness, due to pipelines' ageing.
2. Theoretical background
Ir^{192} nucleus, with half life of 74 days, has the main gamma deexcitation rays in the range of 300  613 keV, and taking into account their relative intensities, an average of 330 keV results. The fact that we can have an average of deexcitation gamma energy does not mean that Ir^{192} behaves as a monochromatic radiation source, the real behavior is that of a polychromatic source and, because of it, the thickness dependence of the linear attenuation coefficient must be considered. As it was shown in previous paper [1], the linear absorption coefficient of electromagnetic waves depends on energy, and if that electromagnetic wave is a polychromatic one, on traversed material thickness as well. As a result, for the linear attenuation coefficient of gamma rays emitted by Ir^{192} nucleus, we can write:
 (1) 
where f(x) is a function depending on thickness of the traversed material, and
 (2) 
µ_{i}( E_{i} ) being the attenuation coefficient for the gamma ray of energy E_{i} , with weight w_{i} and a  coefficient depending on the geometrical arrangement. Using Ir^{192} gamma rays, we can consider that the main effect of radiation's interaction with matter is Compton effect. In this case we may use the Klein  Nishina [2] total scattering cross section per electron  s .
 (3) 
where e  electron's charge, m  electron's mass, c  light speed in vacuum and a E / 511 , with E  energy of the gamma ray ( keV ) and 511 keV is the electron's rest energy .
 (4) 
with n  the number of electrons per cubic centimeter of the material traversed by gamma rays.
According to [1], the second term, f(x), in the expression (1), can be approximated by a simpler expression, namely:
 (5) 
So, we shall look for an expression like this:
 (6) 
{a} and b, will be found from experimental data.
3. Geometrical arrangement
The essential of the Double Wall Technique (DWT) consists in taking one image of a pipeline, the gamma ray source being outside the pipe. The most unfavorable case is when we have to checkup a pipeline in use, and, having isolation, we do not know anything about the outer and inner diameters. The experimental setup is like this one:
Fig.1

PS  is the gamma ray point source; ES  extended source with horizontal size  s; R  outer radius of the pipe; r  inner radius of the pipeline, d_{2}/2 = AC = outer radius measured on film when we have extended source; d_{1}/2 = BC = inner radius measured on film when we have extended source; f_{2}/2 = CE = outer radius measured on film when we have point source; f_{2}/2 = CD = inner radius measured on film when we have point source; t  wall thickness; g  isolation thickness and f  source to film distance. From geometrical considerations, we can find t , R and r.
 (7) 
 (8) 
 (9) 
So, one shut is needed to get information about pipeline. Particularly, when we have no isolation we will take, in the above formulae, g = 0, and if gamma source is a point source, s = 0 obviously, d_{1} and d_{2} becoming f_{1}, respectively f_{2}. Another shut, or even two, are needed to find out where the defect is, and what are its dimensions.
Here is an example of how to deal with a defect placed in the upper side of the pipe:
Fig.2

d  the horizontal size of the defect; x  the vertical size of the defect, or the defect's depth; d'  defect's dimension measured on film. Other notations have the same meaning as in Fig.1. Again, using Geometry, we will get:
 (10) 
To notice that the above expression for d is valid in both cases: d > s and d < s, respectively. If the defect is placed on the bottom of the pipe, the horizontal dimension is just that measured on film. In the case, we do not know if the defect is on upper side or on the bottom side, another shut is needed moving the source left or right, regarding its position in Fig.2, the measured size being changed. Also, I have to mention that the depth of the defect (due to erosion or corrosion) can be determined if we know the absorption coefficient of Ir^{192} gamma rays.
4. Results
One testing pipeline (made of steel) has been used, having outer diameters of 6 inches (168.3 mm) and wall thickness of 14 mm, with outer and inner holes, of different diameters and depths, made onto steps of different thicknesses and amounting to 56 "experimental points" of study. I have used an Ir^{192} gamma ray source, with an activity of 14 Ci placed at 70 cm from a D7 Agfa film, and a noncollimated (wide) beam. Measuring blackening densities on defect (D_{1}) and near it (D_{2}) [1], and knowing the defect size  Dx , we can find, fitting the experimental data, {a} and b, assuming that the attenuation coefficient  µ has the form given by (6).
 (11) 
The result is:  (12) 
This time, measuring blackening densities and knowing the linear absorption coefficient µ, one can calculate the defect's dimension. Here is (Fig.3) what is obtained:
Fig.3

In Fig.3, we have a graph of real values of defects, versus real values  red line, and calculated defects' values (using formula (12)) versus real ones  blue line. The errors are well within 6 %. Using formulae (2), (3), (4) and comparing with (12), the coefficient a = 0.63.
5. Conclusions
The main result of this paper is the expression of the linear attenuation coefficient of Ir^{192} gamma rays, as a function of the traversed material thickness and energy of the gamma rays, expression obtained for the first time, and which is consistent with what we have found in the previous papers [1],[3].
References
 V. Dorobantu, "X rays linear attenuation coefficient in steel. I. Thickness dependence", NDT.net Dec 2004, Vol 9, No 12. http://www.ndt.net/article/v9n12/dorobant/dorobant.htm
 Emilio Segré, " Nuclei and Particles", W.B. Benjamin, Inc., New York,1965
 V. Dorobantu, "X rays linear attenuation coefficient in steel", to appear in Journal of Optoelectronics and Advanced Materials, April, 2005
