Journal of Nondestructive Evaluation, Vol. 16, No. 3, 1997

Quantitative Characterization of Corrosion Under Insulation P. S. Ong,1 V. Patel,1 and A. Balasubramanyan1 Received September 27, 1995; revised June 27, 1997

A method is described to quantitatively characterize the corrosion status of steel samples under insulation. The method uses backscatter X-rays to obtain a density vs. depth profile of the sample, from which the mass absorption coefficient, density, and thickness of the rust layer are evaluated. From these data, the iron content of the rust layer is computed, and the steel losses are expressed in either wall thickness or in the mass per unit area. Rust with a thickness of less than 1 mm can be detected but not quantified. The upper limit for quantitative expression of steel losses is approximately 6 mm when an X-ray tube operated at 160 KV is used.

KEY WORDS: Backscattered X-rays; X-rays; Nondestructive evaluation (NDE); corrosion under insulation (CUI); radiography.

1. INTRODUCTION

Hence, NDE techniques requiring close contact of the transducer with the sample are unsatisfactory.

The detection and quantitative characterization of corrosion of steel samples under an insulating layer still remains a challenging, and essentially unsolved problem in nondestructive evaluation (NDE). Yet, the corrosion induced damage seriously affects public safety, and has a great economic impact. As a result, an NDE technique which can conveniently be used in the field, and which can quantitatively express the corrosion status of steel structures under insulation, would be highly desirable. Though our original research was motivated by the requirements of the petrochemical industry, where miles of steel piping needs to be inspected for corrosion, the results are equally applicable to any steel structures such as those used in bridges, highways, and the walls of large vessels. The answers to be sought are, first, whether the steel surface is corroded, and second, how much steel is lost due to corrosion. Most steel structures are covered by a thick insulating or protective layer.

1

2. X-RAY TECHNIQUES Two outstanding features of X-rays make their use desirable for the cited applications. These are the large depth of penetration and the unique and well understood interaction of radiation with matter. In conventional applications, X-rays are used in transmission,(1,2) and the wall thickness of a pipe can be found, for example, by obtaining a tangential image of the pipe wall. However, since the X-ray beam has to penetrate the cord of the pipe, such a technique is only suitable for small diameter pipes unless y rays are used. Another shortcoming of the transmission X-ray technique is that the two opposite sides of the sample must be accessible to accommodate the source and detectors. These drawbacks are eliminated when backscattered radiation rather than transmission radiation is used.(3-9) Here the detecting system is at the source side, thus access to the sample is required only from one side. The drawback in such a mode of

University of Houston, EE Department, Houston, Texas 77204-4793.

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136 operation is that the scattered radiation is diffuse (nonimaging) and the intensity is several orders of magnitude lower than that of the incident radiation.

3. SCOPE OF THIS PAPER One of the main purposes of pipe inspection is to rapidly locate areas where corrosion is suspected without removing the insulator, and if such is confirmed, to assess the resulting damage. This type of inspection does not require the surface area to be imaged since corrosion occurs at extended areas. Spot evaluation performed at corrosion-prone locations will suffice, if it can be done in a reasonably short time. When a certain level of corrosion damage is detected, the insulation may be removed to decide whether the pipe section needs to be replaced. The desirable features for such an inspection are that the evaluation be done by a trained technician, the result be quantitative, and the response be easily interpreted. This paper will be limited to the study of the backscatter response of a sample consisting of rust on steel without an insulating layer, and to the development of quantitative techniques for the evaluation of steel losses. The effect of the insulating layer can subsequently be treated as an additional attenuation of the incident and backscattered beam.

Ong, Patel, and Balasubramanyan tensity from steel decreases rapidly in the depth dimension. Ideally, the intensity changes at the interfaces can be used to mark the boundaries and hence to evaluate the thickness of the rust layer. In practice, however, these transitions are broadened by a blurring function, referred to as the "point spread function" (PSF). As a result, depth measurements based on transitional boundaries are impractical.(10,11) The PSF has a bell shaped distribution of which the half width is determined by the diameter of the incident beam as well as the size and aspect ratio of the detector collimator. Since this function is the response to a very thin sample it can experimentally be obtained. Figure 3 shows the PSF obtained this way using the experimental conditions of beam and collimator dimensions as shown in Fig. 1. The PSF obtained in this manner can, quite accurately be represented by two polynomials: one for the front end and one for the back end. The close match between the experimental data points and the polynomials (smooth curve) is obvious from Fig. 3. The experimental result in the presence of the PSF can be mathematically obtained by convolving the ideal curve (Fig. 2) with the PSF. The result is the real profile shown in Fig. 4. It will be shown that the ideal curve contains all the information necessary to characterize the rust-onsteel sample. Our task is therefore to reconstruct the ideal curve from the experimental one.

5. THE INTENSITY PROFILE 4. THE BACKSCATTER TECHNIQUE The principle of operation of the backscatter X-ray technique, when applied to a corroded steel sample is illustrated in Fig. 1, which shows a sketch of our experimental set-up. A finely collimated X-ray beam penetrates the sample and the backscattered radiation emerges from a luminous cylinder along the path of the incident beam. The radiation originating from a specific point of this cylinder enters a collimated detector, and as the detector-collimator assembly rotates, it traces the path of the incident X-ray beam. The measured radiation represents a one-dimensional image of the luminous cylinder, and is a density vs. depth profile of the sample. As will be shown in the next section, the response will ideally consist of two exponentially decaying step functions: the first one representing the rust, and the second one the steel. Such an ideal response is shown in Fig. 2. At each boundary, the intensity jumps by a factor which is proportional to the density changes at the interface. Because of the strong photoelectric absorption of both the incident and scattered radiation, the backscatter in-

Referring to Fig 1, the intensity of the backscatter radiation which originates from an elementary volume (voxel) defined by the beam area and a thickness Ax, located at depth x is:

In the above equation, the backscatter intensity is written in boldface to distinguish it from the experimentally measured intensity; I0 is the intensity of the incident beam, Na is Avogadro's number, e is the fraction of the backscatter radiation which is received by the detector, CT is the backscatter cross-section of the material, p its mass density, A the atomic weight, (e~»ixsecei) the attenuation factor of the incident beam after penetrating the sample to depth x, and (e~^s<:c es) the beam attenuation of the backscatter radiation, originating from depth x, after passing the sample on its way to the detector. The linear absorption coefficients of the sample for the incident and scattered beams are (A, and |J,S, respectively, 6, is the angle of incident, and Qs the scatter angle, as defined in Fig. 1. The absorption coefficients are energy

Characterization of Corrosion

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Fig. 1. Sketch of the set-up which was used for the experiments described in the text.

dependent and due to Compton losses, (A, is smaller than M»-

The complexity of the mathematical notation of Eq. (1) can be drastically reduced by substituting experimental values, which will be used throughout this paper, i.e., 6, = Os = 6 = 45° so that the X-ray path length in the sample is x sec 6 = 1.4 x. Furthermore, we will define a value of [i as the "average absorption coefficient," i.e., p. = (l/2)dJ,, + |is). The value of a/A which is 0.27 barn/atom gram at 80 KV for oxygen(12) differs somewhat from that for iron (0.31 barn/atom gram) but

taking into consideration that the weight of rust is predominantly determined by its iron content we will make the assumption here that alA has the same value for rust and iron. Under these assumptions (Eq. 1), when applied to rust with subscript r, can be written as:

where G represents a experimental constant which, for a specific experimental set-up has the same value for rust

Ong, Patel, and Balasubramanyan

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Fig. 2. The ideal density profile according to Eqs. (2) and (3).

as well as for steel. The corresponding equation for steel, where the subscript f(for Fe), will be used, is

The amount of iron converted into rust can be expressed in Wpx or in its equivalent wall thickness.

6. THE EXPERIMENTAL PROFILE where a = e <2 8 '**' represents the rust attenuation. The constant G which appears in Eqs. (2) and (3) can be eliminated when intensity ratios are taken. In doing so, the following two basic equations are obtained:

Assuming that rust consists of oxygen and iron only, the steel content of rust can be found using the well-known relation

where W and (/ - W) are the weight fractions of iron and oxygen, respectively, and u.* is the mass absorption coefficient. Hence,

Experimental density profiles were obtained with a set-up which was designed to accommodate a cut section of a typical insulated pipe. A sketch of this set-up is given in Fig. 1 showing the important features and dimensions. The structure was mounted on the baseplate of the prototype "COMSCAN" unit,(7) on loan to the University of Houston by Philips Electronic Instruments, Inc. All experiments were performed on this equipment with an X-ray slit of 1 mm width and 2 mm length. The X-ray tube, which has a spot size of 1.5 mm, was operated at 160 KV and a current of 10 mA. A single scintillation detector was mounted on an arm which can be rotated around a point 200 mm away from the nominal sample location. The collimator slit width and aspect ratio were made adjustable to obtain a maximum intensity with an acceptable PSF. The rotation of the detector arm was controlled by a stepping motor. A pointer, mounted to the detector arm at its center of rotation moves across a mm scale, and its position was used to determine the sample depth location. The output of the scintillation detector was recorded on a strip chart recorder with the time axis calibrated to show the

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Fig. 3. Experimental point spread function (dots) which has been approximated by two polynomials (solid curve). Obtained with the set-up shown in Fig. 1, using an X-ray tube operated at 160 KV.

Fig. 4. This graph was obtained by convolving the curve shown in Fig. 2 with that shown in Fig. 3.

sample depth in mm. Backscatter intensities were read from these charts at 0.1-mm intervals and entered into a computer. Figure 7 shows the data points of density

profiles obtained from of a flat piece of rust mounted in close contact on a flat steel surface. The size of the rust samples was large enough to assure that the scat-

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Fig. 5. The linear absorption coefficient (I sec & = 1.4 n in mm-1 vs. the front half width FW as defined by Fig. 4.

tered beam passed through the rust on its way to the detector.

7. THE CHARACTERISTIC PARAMETERS In earlier discussions we have shown how the critical parameters to obtain the iron loss can be derived from the ideal profile depicted in Fig 2. We will now show that these parameters can also be derived from the experimental profiles shown in Fig. 7. Theoretically, it would be possible to obtain the ideal curve from the experimental one by a inverse convolution process.(13) Such a deconvolution process requires a computer with a large storage capacity, and is also very time consuming. It is therefore not suitable for practical applications. Moreover, a complete deconvolution operation is not necessary since all we need to derive from the experimental curve are the values of |i,, pr, and xr. To do so we will first study how the convolution process modifies the ideal density profile. A computer is used to convolve an exponentially decaying step function, i.e., exp (-ujc) with the experimental PSF. Both functions are normalized to give a unity amplitude, and adjusted to start at a point x = 0, for various values of (0.. The results show that the convolution process transforms the step function into a asymmetrical bell shaped function, as shown in

Fig. 4.(14) The half width at the front part (FW) depends on the value of p.. The half width value at the rear end depends on p., and also on the rust thickness. The peak value, originally of unit magnitude, is increased by a factor P, and its location is shifted by a distance A*. The factor P depends on the value of (a, and the density p, while the shift Ax depends only slightly on u. These results are represented by Figs. 5 and 6. An important finding is that the parameter |j. can readily be derived from the front half width by using Fig. 5. Once the value of [l is found, the peak multiplication factor P can be derived from Fig. 6. After studying a large number of experimental profiles, it was found that the jump ratio, which in the case the theoretical curve was evaluated by use of Eq. (4) cannot accurately be determined from the experimental profile because the back slope of the rust overlaps the front slope of the steel. On the other hand, we found that it is more practical to start with finding the value of [ir from the front half width using the curve of Fig. 5. This is followed by finding the value of Pr for rust from Fig. 6. The corresponding value Pf for iron can be evaluated from Fig. 6 using a known value of (j^ According to Eq. (5), the ratio of the rust peak and the iron peak is equal to the density ratio of the rust peak and the iron peak is equal to the density ratio multiplied by the attenuation, e-2.8 frr. Since the peak shifts are only slightly dependent on

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Characterization of Corrosion

Fig. 6. The intensity increase P as discussed in the text vs. ^sec 0 in mm - l . Compare with Fig. 5.

the density and absorption coefficients of the samples, the distance between the peak locations in the experimental graph is essentially equal to the actual rust thickness. The derived value of xr can be multiplied by \nr to determine the rust attenuation. Equations (4) and (5) can be modified in a manner which is valid for the experimental profile:

where the values of |J.r and xr are derived from the experimental profile. From the above discussion it is clear that the ideal profile shown in Fig. 2 can be reconstructed using the values of [ir, xr Pf, and Pr obtained from the experimental profile. Since the factor P was the increase of the peak value from unity, due to the convolution operation, the amplitude of the rust peak in Fig. 2 is equal to If (at rust peak) divided by Pr. To test the validity of the procedure, the ideal profile so constructed is convolved with the PSF and compared to the experimental curve, from which the characteristic parameters were derived. Any discrepancies between the computer reconstructed and the experimental profile will indicate a flaw in the operating assumption, or in the evaluation

of the parameters. Several profiles have been subjected to this test, and the results obtained on four representative samples are shown in Fig. 7.(14) It shows that the match is reasonably good. A marked discrepancy has always been found at the front toes of the curves, and a miss-match in the region between the two peaks. We feel that the first mentioned discrepancy is caused by the presence of very soft radiation which participates in the formation of the toe. The second is caused by beam hardening and inhomogeneity of the rust sample. In the examples shown, a beam hardening correction in [i, has been applied so that the discrepancy is mainly due to the inhomogeneity of the sample.(14) At this stage, the shape of the function between the two peaks is not relevant for the evaluation of the iron content of rust.

8. THE EFFECT OF BEAM HARDENING Two aspects of the use of continuous radiation need further consideration. The first one is the change in the mass absorption coefficient u*/ as the depth x of the sample changes, while the second is the fact that the mass absorption coefficient of oxygen is only available at specific photon energies.(12) To study beam hardening for continuous radiation we performed a set of experiments to evaluate the mass absorption coefficients of steel samples as the sample thickness increased. The set

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Fig. 7. Experimental and reconstructed density profiles of rust on steel for various values of rust thicknesses: (a) 1.62 mm, (b) 2.2 mm, (c) 3.0 mm, and (d) 4.3 mm.

up used for these experiments is essentially the same as shown in Fig. 1 with the exception that a fixed detector was used, aimed at the intercepting point of the X-ray beam and a steel scatter. The samples, consisting of layers of steel sheets were mounted in front of the scatterer. They were cut to a specific area from a single sheet of rolled steel, and weighed to determine the mass per unit area px. To minimize the cross-talk, a 2.5-mm layer of low density foam was inserted between the sample and the scatterer. The intensity received by the detector can be expressed as

where Iso denotes the intensity in the absence of any sample, |a/p the average mass absorption coefficient, px the mass per unit area, while the factor 2.8 accounts for the increase of the X-ray path within the sample, as was discussed earlier in the derivation of Eq. (4). The results

of these measurements are shown in Fig. 8 and the mass absorption coefficient will be

The mass absorption coefficient |i* as expressed in Eq. (11) is valid for monochromatic radiation. In the case where continuous radiation is used, it is more realistic to use the "differential mass absorption" coefficient, which is obtained by taking the derivative of the ratio of Eq. (11). Denoting this differential mass absorption coefficient with the symbol d\i*,

The values of d[i*, derived from Fig. 8 are shown in Fig. 9 for steel.

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Characterization of Corrosion

Fig. 8. Backscatter intensity response of steel as represented by Eq. (11). The data points were obtained from a 3rd order curve fit.

Fig. 9. Differential mass absorption coefficient d[i* for steel in cnvVg, vs. the mass per unit area px in g/cm2, derived from the curve in Fig. 8 by using Eq. (12).

Values of the mass absorption coefficient of oxygen n*, can be found in Ref. 12 for various values of photon energies. In order to find a practical way of using these data for continuous radiation, a graph of

H* vs. \\f, as shown in Fig. 10, was made. From this graph, a table of values can be prepared so that the value of u,* can be found when \if is known from the experimental profile.

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Fig. 10. Plot of the mass absorption coefficient of oxygen vs. that of iron from Ref. 12.

9. LIMITATION The above described technique can only be applied when the density profile shows two distinct peaks, one for the rust and one for the steel. When the rust layer is very thin, only one peak appears since the rust peak merges into the steel peak. When the rust layer is too thick, the steel peak becomes so small that it can not be distinguished from the background noise. The front half width of a very thin rust layer is, however, larger than that of pure iron so that the presence or absence of rust may still be detectable, although no quantitative conclusions can be made about its thickness. The minimum value of rust which can so be detected is determined by the half width of the PSF, and the precision at which the front width at half maximum can be determined. Statistical errors in the evaluation of the latter give rise to an uncertainly in the linear absorption coefficient value derived from Fig. 5. This affects the minimum detectability of rust at the surface. A very thick rust layer is characterized by a broad tail which extends into the location of the iron peak. The statistical variation of this tail adds a "background noise" to the iron peak and will affect its detectability. Experiments were conducted to establish these limits and some of the results(15) are shown in Fig. lla and b. Figure lla shows the case where the rust thickness varies between 1.2 and 2.2 mm. Figure l1b shows the profiles for rust thicknesses between 3

and 6.3 mm. Note that the depth scale in the graphs for the two ranges of rust thickness are different. The results shown indicate that the rust and iron peaks start to merge at a rust thickness of around 1 mm. This is an experimental, rather than a theoretical derived value. At this thickness, the "valley" between the peaks is statistically undistinguishable from the background noise. The maximum value of the rust thickness is similarly determined by statistical errors. At a rust thickness of about 6 mm, the steel peak intensity becomes less that the "three sigma" value of the background due to the rust tail. The experimental upper and lower limits can be extended by narrowing the width of the PSF, the use of a higher tube voltage, and a lowering of the inherent background noise.

10. CONCLUSIONS We have developed a technique to quantitatively characterize steel losses due to corrosion of steel sample under insulation by using the continuous radiation of an X-ray tube operated at 160 KV. The range of rust thicknesses which can be quantitatively evaluated is between 1 mm and 6 mm. The steel losses can be expressed in either wall thickness or in mass per unit area. A computer convolution technique was used to test the method

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Characterization of Corrosion

Fig. 11. Density profiles of rust on steel, using various values of rust thicknesses as indicated in the insets in (a) and (b).

for flaws, and the results showed that the flaws do not seriously affect the precision of the technique.

ACKNOWLEDGMENTS The work described here was made possible by the following grants: Advance technology program of the

State of Texas, Energy laboratory of the University of Houston. Exxon Research and Engineering Company, and Exxon Education Foundation. The authors wish to express their gratitude to Dr. J. Kosanetszky, Philips Industrial X-ray, Hamburg Germany for loaning us the prototype COMSCAN instrument, which was used to perform the experiments described in this paper.

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Ong, Patel, and Balasubramanyan 7. G. Harding, H. Strecker, and R. Tischler, X-ray imaging with Compton-scatter radiation, Philips Technol. Rev. 41(46) (1983/84). 8. G. Harding and R. Tischler, Dual energy Compton scatter tomography, Phys. Med. Biol. 31:477-489 (1986). 9. B. Bridge, A theoretical feasibility study of the use of Compton backscatter gamma-ray tomography (CBGT) for underwater offshore NDT, Brit. J. Nondestr. Testing (Nov. 1985). 10. A. Viswanth, A Study of a Thickness Probe for Steel Using Backscattered X-Rays, MS thesis, UH (1991). 11. P. S. Ong, Material Losses in Steel Pipes Under Insulation, Technical Report for EXXON, University of Houston (1991). 12. J. H. Hubbell, Photon Cross Sections, Attenuation Coefficients and Energy Absorption Coefficients from 10 KeV to 100 GeV, NSRDS-NBS 29 (1969). 13. Qiu Feng, W. L. Anderson, and P. S. Ong, Deconvolution of Xray backscatter diffraction data for NDE, in Review of Progress in Quantitative NDE (University of California at San Diego, La Jolla, July 19-24, 1992). 14. A. Balasubramanyan, Quantitative Evaluation of Corrosion by Analysis of Backscattered X-Ray Data, MS thesis, UH (1994). 15. V. Patel, Nondestructive Evaluation of Material Loss due to Corrosion Using Backscatter X-Ray Technique, MS thesis, UH (1993).