CGiRGS-SGH O? CGFPER 72.35% ’3‘! fiGLETE - $C§FTE§~§E§ ‘é’AfiR: VELSCETY ANS TEMPEEEATBRE E'FFECTS Thais fier fin Dam m“ M. 55. MESHSGAER! STATE UREVE'SRSETY Caries G. [2’3th W58 IIIIIIIIIIIIIIIIIIIIIIIIIIIIII IL 31293 00671 6066 CORROSION OF COPPER TUBES BY ZEOLITE-SOFTENED WATER: VELOCITY AND TEMPERATURE EFFECTS BY Carlo O. Mlcoh A THESIS Submitted to the College of Engineering Michigan State University of Agriculture and Applied Science in Partial.fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1958 < -' J.;vw:v C c." 0' e" 7 Carlo O. Mlcoh ABSTRACT Many water distribution systems consist of copper tubes which, under prevailing conditions, corrode at excessively high rates. The present investigation includes a study of aggressiveness of completely softened water at velocities between 1.5 and 13 ft./sec. and in the temperature range 80° to 200°F. Corrosion data were obtained from a test panel built of Government Type-L phosphor-deoxidized copper tubes. Water of zero hardness, under conditions mentioned above, was madeto flow through this panel continuously for a 500-day period. Corrosion penetration depths were sampled at the end of the run by subdividing the inside tube surface into segments of equal area. The largest penetration value on each segment was measured. Corrosion evaluation methods were investigated on the basis of their capacity to predict the probability of tube wall perforation. The statistical Theory of Extreme Values was chosen. This statistical approach yields one of the following types of information: 1) the probable period within which a perforation may occur in a specified length of tube; and 2) the length of tube necessary for most probable occur- rence of a perforation in a given time. Carlo O. Mlcoh ABSTRACT (CON'T) Data from the test panel furnished information of the second type. "Return period" values appear high in com- parison with aluminum and iron. However, the corrosion mechanism of copper differs from that of aluminum and iron, and the information reported in this thesis is thought to be typical for copper. II ACKNOWLEDGEMENTS The author is greatly indebted to Professors C.F. Gurnham and C.C. DeWitt and wishes to express his thanks for their kind guidance and invaluable help. Sincere thanks are also extended to Professors L.L. Quill and M.F. Obrecht for their continuous inter- est in this investigation. The response of the copper tubing manufacturers was deeply appreciated. Through their organized agency, the Copper and Brass Research Association, an advisory com- mittee was set up. Financial aid, expert guidance and materials for special equipment have been provided. The writer wishes to thank the above Association for making this investigation possible. Thanks are also due to Mr. D.W. Marquardt for ac- quainting the author with some of the applications of the Extreme Value Theory. TABLE OF CONTENTS Acknowledgements Table of Contents Foreword Problem on Campus Mechanisms of Copper Corrosion Methods of Corrosion Evaluation Results and Discussion Summary and Conclusions Appendix A. Evaluation of NDHA Testers B. Design and Operation of the Main Test Panel C. Examples of Curve Fitting and Return Period Calculation Bibliography Tables and Graphs Page II III 13 26 33 36 #3 #5 #9 52 III Copper tubing water distribution systems at Michigan State Universitylmxe corroded at excessively high rates. Replacement of the relatively inaccessible pipe is an ever recurrent expense. A research program aimed at a better understanding of this problem was planned. This thesis covers one of the phases of this program. It deals with the effects on copper tubes of zero-hardness water at velocities from 1.5 ft./sec. to 13.1 ft./sec. and temperatures from 80°F to 200°F. Extreme-value statistics is used toward predicting tube life under above service conditions. PROBLEM ON CAMPUS The period after World War II was one of rapid expan- sion for Michigan State University. Dormitories and other buildings were added. In the period preceding these ad- ditions the number of pipe failures did not constitute a problem. During this build-up and afterwards there oc- curred a sharp increase in the number of leaks. By 1951 the rate of replacements reached alarming proportions, and pipe failures have persisted with unrelenting fre- quency. These corrosion failures occurred with greater fre- quency in some of the new dormitories, the Student Union, Kellogg Center, and other newly built structures. It is of interest to point out that, in the water system in ex- istence before the expansion, the replacement rate remain- ed the same. This state of affairs caused much concern to those in charge of the campus utilities and meetings were held to discuss‘the situation. In the ensuing exchange of views the over-all picture was brought into focus, and means of solving the difficulty were sought. The difference in corrosion resistance between the old and the new part of the water distribution system was ex- plained by some as due to a protective insoluble coating*. According to this theory such a deposit in a pipe, formed during the initial period of operation, greatly prolongs the pipe life. Table 21 shows a typical analysis of untreated well water. Such a water should not be corrosive except for the presence of dissolved oxygen and carbon dioxide. All the hot water on campus is softened. This is done in 63 zeolite softening units of standard commercial designs, distributed about the campus. The practice of ~ water softener regeneration appeared not to be always consistent with the instructions given by softener manu- facturers. It has been said that the presence of calcium and mag- nesium ions in the water has the ability to prevent or re- tard corrosion (1). When these two ions are substituted by sodium ions, as in softened water, corrosiveness increases. Bicarbonate ion (H003) present is in equilibrium, at any temperature, with carbon dioxide and water. The corrosion rates for hot softened waters are in general much higher than for similar cold water (See page A1). The literature (1A,2) gives the carbon dioxide partial pressure and the temperature range of the sodium bicarbonate breakdown interval. * Letter to E. ET-Kinney (May 1, 1952) from J. R. SneIIT From the appearance of corroded tube surfaces it was concluded that water velocity is an important destructive factor. Extensive undercutting of the internal surfaces was always present. It was considered probable that chem- ical and erosive corrosion had taken place simultaneously. Preliminary work with strips and NDHA units showed that tubes carrying cold water presented abundant greenish surface deposits (Tables 11-20). These were probably basic' copper carbonate. On the contrary, very little or no such deposit was found in hot water tubes. In this case the cor- .roded surfaces were bright and clean. All the corrosion took place on the inside surface of the tubes. Conversations with people in the field of corrosion have disclosed the fact that this type of attack was not peculiar to the Michigan State University campus water system. Many other localities had similar corrosion dif- ficulties with like quality water flowing in copper tubes. It was the expressed opinion of water softener manu- facturers that completely softened water (zero hardness) would not produce any corrosion trouble. Another school of thought suggested that proper protection would be se- cured if hardness were kept at 120 ppm. This would allow the formation of a protective film and corrosion immunity would be acquired. MECHANISMS OF COPPER CORROSION water containing oxygen and very little or no carbon dioxide or other cuprisolvent constituents produces on copper surfaces a film.composed mainly of oxide (3). According to Haase and Ulsamer (4) this film never ob- structs the flow in copper tubes as often happens in iron pipes because it is not as bulky as iron corrosion products. They also claim that once the film is com- plete the copper content of the water never exceeds 0.1-0.3 mg/liter; they consider this amount harmless. During the copper tube break-in period, i.e., while the oxide film is being formed, much higher water capper contents are met. This initial period takes only a few weeks for hard waters but a year or more in the case of some soft waters. Disagreements exist as to the maximum.concentration of copper in water that can be tolerated by the human body. Thresh (5) states that l.h mg/liter represents the upper limit. Chase (6) and Howard (7) have investigated the ac- tion on copper and brass of soft ground waters with high carbon dioxide content. In the case of copper pipes the concentration limit mentioned by Thrash is easily reached. Corrosiveness of these waters is much greater toward copper than toward red brass (85% Cu). This latter comp position appears to be optimum for brass from the corro- sion resistance point of view. Yellow brass (60-67% Cu) is destroyed at a much faster rate than red brass by the same type of water. Electrochemically, copper is one of the nobler metals used in commercial tube fabrication. In the electromotive series copper is cathodic with respect to the elements above it, hydrogen included. For this reason the presence of oxidizing agents is necessary for the dissolution of copper. If the corrosion agent has no oxidising proper- ties, cerrosion cannot take place. Carbon dioxide by itself is not able to attack copper, but in water containing oxygen in addition this is easily accomplished. The reaction is usually presented in two steps. Step A: Cu + 02 +Cu0 Step B: 0110 + 002 oCuCO3 Step B is presented in its essential form. Actually it is more complicated and the final product is more or less basic copper carbonate. An interesting fact about this substance is its upper thermal stability limit, which appears to be slightly above luO°F. No definite opinion exists as to the maximum content of dissolved oxygen that could be considered tolerable from the point of view of copper corrosion. Oxygen plays a very important role in the general me- chanism of metal corrosion. Experiments on the so-called "aeration cells” conducted by Evans (8) are illuminating. Aston (9) has shown that currents could be set up be- tween parts of the same iron surface. The presence of rust creates more surface per unit apparent area, in- creasing thus the capacity for subsequent absorption of gases. The existence of electrochemical corrosion because of non-uniform.distribution of oxygen was demonstrated by Evans (10). His "key experiment' was performed with two pieces of iron out out of the same sheet. The two specimens suitably cleaned were placed in a two-compartment cell with N/z [Cl solution as electrolyte. Through one compartment carbon dioxide-free air was bubbled. A current was set up; the aerated electrode being the cathode, the unaerated elec- trode the anode. Other base metals as zinc, lead, and cadmium behave in the same way as iron in this type of experiment. With cop- per, however, the current passes in the opposite direction. Investigations by Evans (11, 12) have shown that the current in the ”abnormal" direction in the case of capper is not due to aeration but to stirring by bubbles passing through the liquid. This same effect may also be pro- duced by stirring the liquid in one compartment by some mechanical means - provided that in both compartments dissolved oxygen is present to an equal extent. On the contrary, if both compartments are equally stirred a "normal" current may be produced by a differ- ence in oxygen concentration. Evans has shown this by an experiment with a divided cell fitted with copper electrodes and containing dilute sulfuric acid in each compartment; both compartments are stirred mechanically while bubbles of oxygen are passed into one side only, the other side being kept comparatively oxygen-free. The current produced is being positive. This shows that cop- per behaves toward aeration basically in the same manner as some less noble metals do. Toward stirring, though, capper responds in a manner that sets it completely apart from the more reactive metals; a current is caused to flow in the direction opposite to that produced by aera- tion. Stirring has apparently the effect of reducing the concentration of copper ions along the surface of the electrode and this shifts the potential in the opposite direction. Zinc and iron produce a relatively large electromotive force by differential aeration, and any effect due to differences in ionic concentrations at the two electrodes does not reverse the direction of the cur- rent. In the case of copper, the e.m.f. set up by differ- ential aeration is, even under favorable conditions, very small. A difference in ionic concentrations at the two electrodes may easily equalize and exceed the aeration current. If one compares the cells: Cu I KCl stirred II KCl unstirred I Cu Cu | KCN 1| KCl | Cu it appears that capper ions are removed from.the electrical double layer by mechanical means in the first case and by chemical means in the second. In the conventional Daniels cell with sulfate ions as one of the electrolytes the noble metal or cathode is cop-' per. When, however, the cyanide ion replaces the sulfate ion in both compartments, it is capper and.not zinc which acts as anode. The formation of the capper-cyanide comp plex maintains the double layer depleted of copper ions to such an extent that the tendency to go into solution is much higher for copper than for mine. This means that the solubility product of the capper-cyanide complex is much smaller than that for the zinc-cyanide complex. 10 The fact that differences in copper ion concentration supersede the effect produced by differences in oxygen con- centration.makes the behavior of copper somewhat different from that of other metals. Iron and zinc, for instance, have anodic areas in inaccessible places and corrode there; with copper the opposite is true. The inaccessible places on a copper surface, unless their immediate environment is totally devoid of oxygen, will not corrode. ‘ It is easy to see how corrosion may be induced by even minute cavities in the inner surfaces of pipes. At these points differential aeration cells are set up (13). Dif- ferential-temperature and differential-stress cells may also be important in initiating corrosion. Later their effects may be obscured by the influence of differential-aeration cells (1h). Under these circumstances marked localized cor- rosion of copper may take place. Electrochemical corrosion is not the only form of de- struction of metal objects. Mechanical action of liquids also produce destructive effects. The latter is classified as erosion. An air jet impinging under the line of immersion of a plate of aluminum bronze in a 6% sulfuric acid solution produced a perforation before any appreciable corrosion occured elsewhere (15). The corrosion was localized at the point of impact of the air jet. The action is not chemical 11 because the solution was more or less saturated with oxygen and under this condition one would expect a uniform attack all over the surface. This suggests that the electro- chemical action produced by inequalities in the velocity of the liquid is reaponsible for this effect. Another example of this mechanism of corrosion is cited by McKay (16), in the case of.Mone1 tie rods used in the construction of wooden pickling tanks. The action of rapidly moving water, considering the different electrochemical behavior of copper as Opposed to other commercial metals, may lead to difficulties in dis- tinguishing between chemical and mechanical actions. When these two effects occur together the situation is classified as corrosion-erosion. At first glance, due to the fact that the attack on capper occurs at the exposed points, one might be led to attribute to the mechanical action a more destructive effect than it usually has. This emphasis on the effects of the mechanical action was followed by Silberrad (1?), Parsons and Cook (18) and Carpenter (19) in their conclu- sions on the deterioration of ship propellers. They con- sidered that it is due mostly to erosion and corrosion, if present, is negligible. The latter is corroborated by the fact (17) that alloys used to fabricate propellers are un- affected chemically by stagnant waters. This destruction, 12 according to these investigators, is caused by "hammer action" due to the collapse of the vortex cavities (vacuum bubbles) against the surface of the blades. Ramsay (20) questions some of the above conclusions by pointing to the fact that if corrosion does exist in certain amounts it would be very difficult to find any evidence of it in the form of corrosion products. Besides, no argument based on the fact that the material in question is unaffected chemically by stagnant water has any bearing on what the behavior of this same material might be toward water in motion (17). An experiment reported by Bengough et a1. (21) is very interesting in this respect, although one might doubt the interpretation of the results. (The experiment deals with the effect of water jets, containing air, on copper and gold surfaces. Although the velocities were less than those commonly reached at the surfaces of prOpellers, it was found that, whereas capper became visibly attacked at the impingement points, gold underwent no change. It is known that gold is softer than copper. 13 METHODS OF CORROSION EVALUATION A reliable and complete classification of the state of corrosion of a metal Specimen is in general obtained by a two-way approach. One of these approaches is quali- tative and the other is quantitative. Qualitative information is obtained mainly by observ- ing the specimen either with the unaided eye or an appro- priate optical instrument. Quantitative data like pit depth, change in metal properties, etc., are obtained by methods and means which may be specifically adapted for the purpose. In our case, for instance, pit depth deter- minations were made with a suitable micrometerQ/A). The results yielded by these two approaches individ- ually are not only complementary, but in part superimp posed, i.e. quantitative means of investigation may fur- nish some qualitative information and vice-versa. In spite of this, satisfactory reduction of information to a common denominator is difficult. It would be a defi- nite improvement, especially for routine applications, to have one of theabove mentioned approaches suffice where both now appear a necessity. 1h From experience it is known of the difficulty to ob- tain a quantitative reproducibility of the corrosion form and intensity even under rigorously controlled conditions in a laboratory. The main requirement is that the accu- racy of the method of corrosion assessment to be equal to the reproducibility of features. In other words, it would be too much to expect to devise a methodehich would yield information more reliable than that which was fed into it. In some specific cases then, derivation of quali- tative and quantitative results from the same examination should not be excessively difficult. Critical observation of corrosion specimens leads in general to the conclusion that two of their feature as- pects, the horizontal and the vertical ones, are of fun- damental importance. The first concerns itself with the size of the individual sites of attack, which may be clas- sified as "general”, 'semilocalized", and "localized". The second feature considers the intensity or depth of penetration. Our interest is restricted to capper tubing and the probability of its perforation by domestic water of vari- ous compositions flowing through it. Here the importance of pit depth or corrosion penetrations in general is fun- damental. This simplifies the choice of the method of assessing the severity of corrosion. A method which tries 15 to describe the seriousness of corrosion with regard to penetration depth by determining the weight loss of the specimen is not at all indicative of the possibilities of perforation. Considerable relative weight losses may be had in the case of a "general" type of attack with- out any actual perforation of the tube. If failure, on the contrary, is due to a highly localized attack, the overall amount of metal eaten away may be small. With this in view many investigators have suggested a variety of empirical indexes or factors most of which are strong functions of the corrosion penetration. Speller (22) determines a pitting factor by making a ratio between the maximum penetration and the average pene- tration for the same period of time. Copson (23) discusses an analogous approach. He cal- culates a pitting factor by dividing the mean depth of the four deepest points of penetration on the specimen by the mean depth as calculated from.the loss of weight. According to Herzog and Chaudron (2A) the degree of localization of attack may be assessed by comparing the losses of strength or of the electrical conductivity, with the average corrosion penetration as calculated from.the loss of weight. 16 ,The main drawback of these methods is their limited scope, i.e., they do not help draw conclusions useful for comparison with data obtained under different conditions. Other investigators have tried to correlate, always on an empirical basis, the maximum penetration depth with some property or feature of the specimen. It was found that the maximum penetration depth on a corrosion sample is a function of the specimen area. The two ex- pressions which follow show a certain similarity with conclusions drawn from strictly theoretical statistical methods presented later. This, on due reflection, should not appear unusual if we consider the fact that many em- pirical methods are but imperfect statistical techniques. Scott, for example, states (25) that the maximum penetration depth and specimen area relationship assumes the form d I ah (EQ. l) where g_and p_ are constants dependent on the conditions under which corrosion took place and A,is the area of the specimen examined. For very large and very small areas this correlation fails. Logan (26) reports the maximum penetration depth are in some cases better correlated with specimen area as fol- lows dm H . a + b logA (Eq- 2) 17 The nomenclature is identical with that in Equation 1. Logan calls the above expression ”Ewing's equation". ‘Within the area intervals where these two expres- sions are valid they plot as straight lines on log-log and semilog paper respectively. Champion has devised (27) a semiempirical Perforation Factor Method (P.F.) of corrosion classification. He has worked out comparison charts for aluminum (28) to be used in estimating the degree of attack. Vertical and hori- zontal corrosion features have specific charts, each con- taining seven intensity steps or stages ordered in a geometric progression. The stages are numbered from.one to seven and these numbers are called "descriptive numbers% The absolute value of the first term and the ratio of each comparison series is selected on an empirical basis to suit the problem. The basic Champion equation for the Perforation Fac- tor is PeFe .0e2A4'D-Ooll' (Eq0 3) where 5,13 the descriptive number for sites of attack per unit area and Q,the descriptive number for the depth of attack. These numbers appear with coefficients weighted on the basis of the importance of each individual corro- sion feature. Penetration depth is more indicative of perforation, therefore, it requires larger coefficients 18 than the horizontal corrosion features. Champion observes (29) that maximum.penetration depths have widely distributed values for different samples. 'With this in view he assumes a normal statisti- cal distribution to hold for all the pit depths in each individual sample. This is the basis of his Perforation Factor Method. Actually the two extremes of a penetra- tion population distribution, on one side penetrations tending toward infinite depth and on the other side those tending toward zero depth, do not follow the normal dis- tribution law. The way the method is set up, though, this does not represent a problem. In Champion's words (30): "If a certain point on this distribution curve is selected, such that 2.5% of the total number of penetra- tions (2.5% of the area under the curve) exceeds the depth corresponding to that point, then that depth can be used as a Perforation Factor to measure the danger of perfora- tion of the metal by corrosion". The expression for the Perforation Factor is given by Equation 3, which is valid only for that portion of the normal probability curve to the right of the mean (31). The neglecting of a certain percentage of penetrations in the most critical depth region is the really serious shortcoming of the Champion method. Any one of these neg- lected values may be a perforation. 19 The limiting factor of Champion's method lies in as- suming the existence of only one type of penetration depth distribution for values below that of the Perforation Factor. Likewise he fails in that he neglects altogether penetration depths above the Perforation Factor Value. (Fig. 1). Below the Perforation Factor value the penetration depth distribution may be of many different types other than normal. Above the Perforation Factor value all dis- tribution types behave similarly in their approach to- ward the same asymptotic limit (Fig. 2). Until all the possible asymptotic distributions are accounted for, any corrosion evaluation method is seriously limited in its application. The limitations of the Champion Perforation Factor Method appear to be completely missing in the statistical approach afforded by the Statistical Theory of Extreme Values. This Theory provides a firm basis without limit- ing assumptions and is applicable to the data obtained from any closed or limited system (32). Gumbel among others has contributed considerably to the theory and especially to the application of Extreme Value Theory to specific problems. In his own words (33) "an extreme value is essentially an ordered or ranked sample value, i.e., a sample of g observations or values 20 (x1, x2, x3,...xi...xn) is arranged in ascending or de- scending order of magnitude so that the subscript i_in- dicates the order or rank. In the case of a succession of samples taken from the same pOpulation , interest may be centered about a single value (the maximum value) of Ithe many values in each such sample. The question is now which is the type of distribution that may be ex- pected to apply to a series of these extreme values (one from each sample, as said before)". What follows is a brief introduction into the Extreme Value Theory. , In the specific case of a corroded specimen let the probability of a penetration as deep or deeper than a certain value xlbe 1 - F(x), where F(x) is the prob- ability of a penetration being shallower than x. The derivative of F(x), F'(x) - f(x) is the probability density function.* * Lower case letters indicate frequency distribution or probability density functions; capital letters indi- cate probability distributions or cumulative frequency distributions. Probability is an area and as such has the dimensions of an area. 21 The probability that x_be the depth not exceeded by g_random penetrations in Fn(xn) or the product of g in- dependent probabilities.* This new probability we shall indicate as<§n(xn). Its probability density function shall be gun) . nFn‘l (xn). f(xn). If the form of the distribution and g were known the exact extreme value distribution could in theory be derived. The procedure is complex and laborious increas- ing in difficulty with the increase of a, In another approach recourse can be made to an asymp- totic distribution of extreme values. For a wide variety of population distributions the same asymptotic distri- bution applies. The limit of the latter is approached as g_becomes infinitely large but it is also applicable to moderate g_values due to a rapid convergence. According to the theory of extreme values (3A) the distributions of maximum penetration depths fall into three types: 1 - Exponential Type 2 - Cauchy Type 3 - Truncated.or'Limited Type * The expressions above containing the subscri t.‘c g are for a finite number n of penetrations. imilar expressions but without She subscript are going to be used later. These are limits for n-u-oo 22 In the first type penetrations of any depth are pos- sible but the probability of having one as deep or deeper than a certain (large) value decreases exponentially with depth. If F(x) is the probability that agy‘ggg penetra- pigg is shallower 'than 5, then the above statement may be expressed as follows: 1 - F(x) -->—Ce'kx as x-v-oo (Eq. 1+) The probability that 9gg_maximum penetration be as deep or deeper than x is: l -<§(x) +1 - exp [-exp (-y)] as x-p-oo (Eq. 5) where y - a(x - u) is the so called reduced variate (3h). Equation 5 is valid for a number of types of penetra-I tion depth population distributions. Among these are the normal, log-normal, chi-square, and logistic distributions. The constants g,and u_have specific meanings and their values may be calculated. To perform this, knowledge of the individual penetration depth distribution is neces- sary; that is sometimes laborious to obtain. 'If then the population distribution is not known, but may safely be assumed to be one of the above types, and at the same time a sample of the maximum penetration depth population is known, it is easy to obtain g,and u; by plotting the extreme values at hand in an appropriate manner e 23 The reduced variate 1,13 plotted as ordinate and the observed variate x_as abscissa on arithametic graph paper. From the expression y - a(x.- u) it is easy to see that maximum penetration depth data plot as straight lines in the limit, i.e., if they were to follow exactly a distri- bution of the exponential type no scattering would occur. The reduced variate is obtained from the cumulative frequency <§(x). Actually the latter is not known ex- cept in the form of estimates which are made from the samples of maximum penetration depth. The expression used for estimating is ( )as i where i,is the I)“ :11 rank subscript (page 20) and n_is the total number of extreme depths measured. The expression (F(x) . exp [-exp (-y)] (Eq. 6) truly valid in this form only for x - a), may be assumed sufficiently exact, for all practical purposes, for rather small values of 5. From Equation 6 y - 1n 1 firm If we want to plot cumulative frequencies as ordi- nates directly, a special graph paper with abscissae on a normal scale and ordinates on a mat. log - nat. log scale makes the task much simpler. The values of <§(x1) always fall between 0 and 1, limits that are never reached. 'With this fact in mind 2h any amount of data can be plotted on a normal size sheet of graph paper. Following a reasoning identical to that underlying the formulation of the expression P . 1 (Eq. 7) n a similar formula is obtained using the cumulative fre- quency é (x) . 1- I 1 Ee8 on) W) (q) In Equation 7, P is the probability that any one of the unrelated g_events takes place and is calculated from a known value of p. In Equation 8, l - @(x) is the probability that one of the maxima is equal to or exceeds certain value x, This probability is, by analogy, set equal to the inverse of T(x), the number of independent extreme events necessary to fulfill the above requirements. This number T(x) is the so called ”return period” and is calculated from.the cumulative frequency corresponding to a specific value of x, In our particular case corrosion specimens are made or assumed to be of definite and constant size. When 5, corresponds to the tube wall thickness a very important information about the probability of perforation is ob- tained. T(x) is the number of these specimens, corre- sponding to a total area and indirectly tube length, to have the probability of just one penetration, in the 25 average, equaling or exceeding the tube wall thickness. While in the exponential type of distribution the probability of having penetrations as deep or deeper than §_approached in the limit Ce'kx , in the Cauchy type dis- tribution the probability tends toward Cx'k ( C and K:>l, for x-p-oo). Also in this type of distribution penetra- tions of any depth are possible. The same type of prob- ability paper mentioned before may be used. The only difference is that the logarithm of penetration depth versus cumulative frequency will plot, in the limit,.as a straight line. In the third or truncated type of distribution a certain penetration depth is approached and never ex- ceeded. For obvious reasons this type never applied in our case. ,0. 26 RESULTS AND DISCUSSION Main Test Panel penetration depths were evaluated to determine the influence of water velocity and temperature on the corrosion of cOpper tubes. Average penetration depths (d ) obtained from random measurements were correlated as ave functions of water velocity and temperature. The extreme value theory was applied to the maximum penetration depths (dmax) calculated. Return periods T(x) for selected cases) were calculated. Except for occasional brief inepections to check on corrosion progress the panel was in Operatknlcontinuously between June, 1955 and November, 1956. The corrosion test lasted 500 days. After the panel was finally disassembled each tube sec- tion was cut in half and the inlet portion saved. The other half was cut in two lengthwise portions, with one piece sent out for evaluation by others and the other piece retained at Michigan State for examination. On these last tube portions maximum and average penetration measurements were performed. The partitioning into samples of the overall pit pOpula- tion, within each tube portion, was done by subdividing the latter into segments without cutting. Measurements were 62/4 . carried out on samples one square inch in areaA This was done with the Ames 212 micrometer of the B.C.Ames Company 27 of Waltham, Iassachusetts. The sensitivity of this instru- ment was of the order of 0.0001 inch. .These data appear in Tables 1 through A. They actually represent the residual minimum wall thickness (tfinal) or the average residual wall thickness (x). The segments are designated with capital letters in alphabetical order in the direction Opposite to that of water flow. By examining these data a trend in the tfinal and x values is evident as the temperature and velocity are increasing. To make this trend evident by graphical means the following was done. First, the i values groups with the same temperature and tube diameter were averaged again and the grand averages R obtained (Tables 1 - A). The latter was then used to com— pute the average penetration depths (d ave) from: ave z tinitial - x (Eq.9) These calculated values are presented in Table 9. d It may be mentioned here that in a similar way the maximum penetration depths (dmax) for each segment were obtained from: dmax = tinitial ' tfinal These last values will be used later in connection (Eq.10) with the extreme value theory. Since the actual initial wall thickness (t . ) at final the points of penetration were not known either the nominal or some average wall thickness had to be used. Table 9 pre- sents values for these two types of tfinal' The nominal 28 wall thickness was preferred because in all instances positive depth penetration values were obtained. Finally, the davevalues were plotted first against temperature (water velocity as parameter) and then against velocity (temperature as parameter) - Figures 3 and A. Disregarding the few points that are out of trend the two graphs show an increase in aggressivity with increase in temperature and velocity. If the velocity is low (up to about 2 ft./sec.) temperatures almost up to the boiling point (200°F) do not contribute appreciably to soft water aggressiveness. The same low aggressivity is encountered if the parameters are reversed. With water at ambient temper- ature, velocities up to 13 ft./sec. do not impart any appreciable aggressiveness. Simultaneous increase in velocity and temperature worsen the picture considerably. A combination of high velocities and high temperatures creates the worst corrosive conditions. All the above conclusions and important additional ones may be drawn from results obtained by applying the extreme value theory to the maximum penetration data. The values of dmax calculataiwith Equation 10 appear in Tables 5 through 8. The maximum penetrations ranked in increasing order are tabulated together with thé corresponding estimated cumu- lative frequencies<¥(xi) and reduced variates - y. 29 These data were plotted on ordinary graph paper with maximum penetration depths as abscissae and the reduced variates as ordinates (Figures 5 - 9). Each figure re- presents a Specific tube diameter with water temperature as the variable parameter. The best straight lines through the data ware fitted mathematically (See page R5) and their equations determined. Equations for tubes of 3/8", 1/2" and 3/R" diameter were calculated and are listed in Table 10. The lack of local initial wall thicknesses is eSpecially felt in the dma values for l" and 1-1/4" diameter tubes. x Small wall thickness differences produce large relative errors in the dmax calculated. For this reason the line equations of these two diameters would not be very reliable and were not calculated. The Spread of the dmax values in each case is small and thus steep lines were obtained. With this type of data it would be of little use to make an attempt at assessing which of the two extreme value distributions apply: The Cauchy or the eXponential type. For ease of treatment of data the exponential type of distribution was assumed. The straight line equations at hand make it easy to calculate the return periods. The reduced variate for dmax equal to the tube wall thickness is first determined. From this <§(x) is calculated with Equation 6, then Equation 8 is used to obtain T(x). 30 For large values of dmaxand consequently y the approxi- mate eXpression T(x) = ey (Eq. 11) yields sufficiently accurate values of the return period to forego the use of the exact but longer and tedious method. Even for return periods of the order of 50 the discrepancy is only about 1%. I Two sample calculations of T(x) by both methods (See page A6) Show the excellent approximation obtained. The examples chosen represent the two lowest return period values. Their meaning is as follows: A section of 3/8" dia- meter tube 1.67 miles long with water 170°F (zero hardness) flowing through it would; in the average, have one per- foration within a 500 day period; with 200°F water flowing through a 1/2" diameter tube a 0.379 mile section would, in the average, have one perforation within the same period of time. All other cases calculated (Table 10) show higher values. One instance (80°F water, 1/2" diameter tube) has an infinite return period, i.e.,no perforation would occur within 500 days under these conditions in any finite length of tube. This situation might at first cast some doubts on the reliability of our data. Even so, the applicability of the correlation method is not in doubt. Corrosion of c0pper, just as of any other metal, is a phenomenon that may be treated statistically; and the maximum penetration depth pOpulation follows a dis- 31 tribution of either the exponential or the Cauchy type. The only problem is to take a sample..in_ such a way that itbe as representative of the pOpulation as the experimental con- ditions will permit. Although in our case straight lines fit the data rather well a disturbing fact is present: The Spread of dmax values is almost in all instances small with con- sequent unusually high return periods. The experience is, with similar application of the extreme values theory to aluminum tubes (35) and iron pipes (36), that d spreads max are much greater. At first then we might conclude that our measurements are not sufficiently representative of the maximum penetration depth pOpulation. 0n the other hand, it may be typical of this kind of c0pper corrosion that the Spread be smaller than for other metals. In this case nothing could be helped. The only im- provement could be obtained by taking advantage of one of the prOperties of the correlation methods. An increase in the segment size would make it more sure for the values of the penetration maxima to fall well within the tail of the eXperimental function. How far this segment increase should be carried to get more representative data it is impossible to say. The statistical method does not give us this infor- mation. It only states that as the sample approximates the pOpulation more closely, its depth versus frequency curve -kx .— tends toward Ce or Cx k reSpectively for the eXponential 32 type or Cauchy type distribution. It would not be sur- prizing that panel sections longer than those in the Main Test Panel should be used. The Main Test Panel eXperiment was not set up to fur- nish data that might be used toward obtaining the other type of return period mentioned before, i.e., predicting the probable period of time within which a perforation may occur in a Specified length of tube. The investigation of the probability of c0pper tube perforation is evidently made more difficult by the cor- rosion mechanism of this metal, where penetration depths advance on a more or less uniform front. The second type of return period would yield very useful complementary information on c0pper tube life. 33 SUMMARY AND CONCLUSIONS 1. The methods of correlating corrosion data have been critically reviewed. 2. The sc0pe of Champion's correlation method was found too limited. The method was not applicable for comparative representation of perforation data. 3. A general statistical approach known as the "Extreme Value Theory" has been applied to the problem of the pres- entation of comparative corrosion data. A. This statistical approach is capable of predicting: a. The probable period within which a perforation may occur in a Specified length of tube; and b. The length of tube necessary for most probable occurence of a perforation in a given time. 5. Information under Ab was obtained from our data for a time period of 500 days. Some doubt exists that our maxi- mum penetration data may not be representative of their population distribution. 6. Advantages of using larger sample segments and con— sequently larger Main Test Panel tube section sizes have been discussed. Considering the different corrosion mecha- nisms of c0pper as compared to that of other metals infor- mation as indicated under Ra was thought to be necessary. 3A 7. Qualitative preliminary corrosion information was ob- tained with standard NDHA testers. 8. The Main Test Panel construction and Operation is de- scribed. APPENDIX 35 36 A. EVALUATION OF THE NATIONAL DISTRICT HEATING ASSOCIATION TESTERS Preliminary information on corrosion rates at different points of Michigan State campus water system was obtained from a number of National District Heating Association testers. An NDHA tester consists of a stainless steel frame shaped to support the actual corrosion sample. The latter is represented by a chain of three Springs of metal or metals to be tested. Micarta plugs serve as interconnectors and insulators. The stainless steel frame is fastened by means of a screw to the flat bottom of a l-inch pipe plug. All the dimensions and most of the procedures for performing the test are standardized (ASTM Designation D 935-A8T). Be- fore the assembly of the tester the coils are individually weighed. The coil surfaces must be bright and clean. The device is applicable to testing waters which are relatively free of suSpended materials. The minimum recommended test period is 30 days or that period of time in which cOils lose 10% of their initial weight. The testers have to be installed in Specially prepared locations, preferably in bends. The elbow is replaced by a tee and the tester inserted through the run of the tee so that it points in the direction of flow. 37 In our particular case the type and the temperature of the water were determinant in the choice of the locations. The action of raw and cold water versus hot and partially softened water (120 ppm hardness) was compared. Also by choosing c0pper and mild steel as coil materials, their corrosion resistance was investigated. Neither temperature recorders nor flow rate measuring devices were installed. All the "hot" location temperatures were between lh0° and 180°F. This temperature interval contains at least part of the basic c0pper carbonate decomposition range. The "hot" locations were installed, whenever possible, in the hot water circulating line just before the centrifugal pump inlet. The testers were left in residence for an adequately long period of time (one group for 86 days and another for 135 days on the average). After removal from the corroding environment they were carefully inspected and observations recorded. The subsequent step consisted in the quantitative evaluation of the corrosion rates. For this purpose the coils were cleaned thoroughly of all the corrosion products. A dip into a dilute acid solution containing an inhibitor eliminates the last traces of the corrosion products with- out dissolving any detectable amounts of base metal. Wash- ing in distilled water and drying completes the procedure. Corrosion rates are expressed either in terms of weight loss or in terms of penetration depth. The most commonly 38 employed units are: mg/(sq.dm. x 2h hr.day) abbreviated into (mdd), in the first case; and inches/year - (ipY) or mils/year in the second. The penetration in inches/year may be calculated from: D wi-w2 2T _ W1 Wlw2 (Eq.12) ipy = where: D is initial wire diameter, (inches), T is eXposure time (years), W1 is initial weight of wire (grams), W2 is final weight of wire (grams). The relationship between corrosion rates (mdd) and pen- etration rates (ipy) is based on the following equation: d 1000 ipy = where d is density of metal in g/cu.cm. For c0pper d = 8.9 and for mild steel d a 7.8. The two following formulas are used in Tables 11 through 19. COpper: mdd a 6.21 (mils/year) Steel: mdd = 5.47 (mils/year) The experiment consisted of two runs of 19 NDHA testers each. The period of residence for the individual samples is shown in Table 20. The numbers in the 500 series desig- nate samples of the first run, those in the 700 series be- long to the second run. While the samples of the second group were in their locations, hydrated lime treatment was started on an intermittent basis. It should be noted though 39 that this treatment had begun three weeks to one month be- fore the samples were taken out for evaluation. While the second series samples were in place forced circulation in the"hot" locations was intermittent. Data in Tables 11 through 19 columns A, B and C pertain to coils starting with the one further away from the l-inch plug. In both runs the metals used were c0pper and mild steel (SAE 1010). The capital C in front of the corrosion rate values indicate a c0pper coil. Comparing the data in Tables 11 through 19 it is evident that penetration rates for c0pper in some locations are many times higher than those for steel. The ratios of the pens; tration rates for c0pper vs. those for steel (the latter taken as l) is revealing. Tester Ratio Tester Ratio Health Service 558 25 715 6-7 Union 559 15 725 - Campbell Hall 556 25 718 25 Agriculture 55h 6-10 713 2-3 Samples for both Kellogg Center runs were destroyed while the experiment was in course. The indication is that water velocity in this particular case was well above the allowed limit for the testers. There is a considerable drOp in c0pper penetration rates from correSponding samples of Run No. l to those of Run NOe 2e AO Tester Ratio Tester Ratio Union 559 15.3 725 2.h Health Service 558 17.65 715 10.24 Agriculture 554 10.65 713 6.5 Ag. Enginnering 558 0.001 726 0.001 Agricultural Engineering then shows practically no penetration rate. Samples for both this location and the Judging Pavilion were covered with a dark reddish-brown deposit of dusty appearance, which easily rubbed off ex— posing a bright metal surface. All the locations with water temperatures above 140°F. presented high penetration ratios. This fact is not apparent in cold water locations, although some of them Show higher penetration rates for c0pper than for steel. Union Tester 5A7 - Ratio 2 Health Service Tester 561 - Ratio 2 Penetration rates higher for c0pper than steel in many samples of Run No. l were not apparent in Run No. 2. In the latter case penetration rates for steel were often greater than those for c0pper. Tester Ratio Tester Ratio Shaw Hall (cold) 543 1 716 0.25 Shaw Hall (hot) ' 549 0.7 720 0.143- -0.17 In the latter case both runs presented same COpper penetration rates. Al Tester Ratio Tester Ratio Demonstration 555 0.6 707 0.167 Hall (cold) Demonstration 5A6 0.33h 71R 0.167 Hall (hot) Union (cold) 5A7 2 717 1 Health 561 2-3 721 0.3Ah- Service (cold) -0.l67 Discussion of NDHA Data A general decrease in aggressiveness of the hot as well as cold water from the period of the first to that of the second run was noticed. No definite proof may be had about the cause of this change. It might be due to a difference in water composition or discontinuation of the forced circulation. Other factors, unacounted for, might very well be a substantial cause of this change in behavior. The higher penetration rates in the first run for 00p- per as compared to steel were not apparent in the second run. The data indicate that hot water as used on the Michi- gan State University campus is more aggressive than the cold and raw water. In the set-up as vast and complex as the one used, it is difficult to maintain determinate steady conditions with regard to water composition, temperature and velocity to such a degree that reliable eXperimental results can be ob- tained in connection with c0pper corrosion. 42 For this reason it is suggested that a number of test panels be built presenting geometrical and dynamic simi- larities with actual water distribution systems. The pipe material and water composition would be set for each indi- vidual panel and the influence of water temperature and velocity would be studied. 43 B. DESIGN AND OPERATION OF THE MAIN TEST PANEL Designers of the Main Test Panel assumed that corrosion in the Michigan State University water system is a result of the interaction of a number of variables such as tube material, composition of the water used, water temperature, and water velocity. It was decided to use a Specific tube material and water composition and study the influence on corrosion of the remaining above variables. The Test Panel consisted of six trains Of phOSphor de- oxidized OOpper tubes (Government Type L) in series. Each train included 1-1/4, 1, 3/4, 1/2 and 3/8-in. diameter tube sections in lengths equivalent to 60 pipe diameters, con— nected by soldered reducer—unions. The 3/8-in. end of each train was connected by 3/A-in. COpper tube to a heater and this one in turn to the begin- ning of the next train. Each heater exit was provided with a thermoregulator bulb which controled its separately trapped steam valve. Thermometers in thermowells allowed observation of the Operating temperature, and manual adjust- ment of steam admission was made when necessary. Each heater maintained a 30°F. temperature rise per train, with an over-all temperature increase from 50 to #4 200°F. Water of practically zero hardness was flowing at a rate of 6 g.p.m. and the path was upward from the larger to the smaller tubes, down to the heater, and thence to the bottom of the succeeding train. Flow rates were determined by weighing the effluent water. The calculated water velocities and individual tube lengths for each section are presented in the following table. Nominal Diameter 1-1/1." 1" 3/t" 1/2" 3/8" Velocity, ft./sec. 1.5 2.3 3.9 8.1 13.1 Section Length 6' 5' h' 3' 2' Seven samplfiugoutlets were provided: One each at the beginning and the end of the panel and between trains. The panel was built on two levels. The upper level contained the pipe trains with their return lines. The lower level contained the heaters and all the regulating instruments. The trains were disassembled a certain number of times during its period of Operation. These inspections were made to check the progress of corrosion. 45 C. EXAMPLES OF CURVE FITTING AND RETURN PERIOD CALCULATION The equation of a straight line is usually expressed in the form Y = a + bX . In order to obtain the expression that fits best the individual groups of data the Specific coefficients a and b,have to be determined. The following system of two simultaneous equations with their coeffici- ents in terms of the data at hand and g_and b_as unknowns may be used for this purpose (37). aN - b(Z.‘.X) =ZY (Eq. 11.) aZX - bZX2 =ZIXY (Eq. 15) where ZX - the sum of all the independent variates 25X2- the sum of all the squares of the independent variates ZY - the sum of all the reduced variates EEXY - the sum of the products of each independent variate and its corresponding reduced variate. N - total number of data points used in con- structing the curve The unknowns obtained from Equations lb and 15 are a JYZle- ZX ZXY- b , NZXX -ZXZYA Nzx‘ — (22x)7 NZX‘ - (ZX)‘ 46 First Case 3/8" and 170°F x y x2 xy 0.018 -0.665 0.000324 -0.0ll970 0.018 -0.223 0.000324 -0.004014 0.019 -0.l65 0.000361 0.003135 0.019 0.582 0.000361 0.011058 0.020 1.092 0.000400 0.021840 0.021 1.852 0.000441 0.038892 0.115 = Zx 2.803 =Zy 0.002211 =2x2 0.058941 SEXY 0.013225 = (Zx)2; 0.322345 =Z’ny ; N = 6 b = 763.439 e = -14.165 y = -14.165 - 763.439 x For x = 0.035 y = 12.560 ; T(x) = eY= 284930 (Phi) = eXpE-eXp(-y)] = l 1 782.976 a 1.000003509 e (x) a 0.999996491 ; 1 - chic) -_. 0.000003509 1 1 1 - @(x) 0.000003509 T(x) a = 284916 Segment (sample) area = 1 sq. in. 0.430" inside diameter; 0.1125 sq.ft./ft. of tube T(x) = 284930 ; 28u930/(2)(144) . 991 sq. ft. CorreSponding to 8810 ft. or 1.67 mi. of tube 47 Second Case 1/2" and 200°F Zx = 0.096 Zy = 3.824 2x2: 0.001184 ny = 0.058275 (2102: 0.009216 iny = 0.367104 N = 8 a = -4.167 b = 387.094 y = —4.167 - 387.09h x For x = 0.040 y = 11.317 ; T(x) = eye 82208 1.00001216 cphc) = 1 = 1 099998784 inéhn; e 1 - Xqu'fitflUOwP 80°F x .0327 .0327 .0326 .0329 .0334 .0320 .0327 tfin .031 .032 .030 .032 .030 .030 80°F .0385 .0383 .0383 .0383 .0383 .0384 .0388 .0386 .0384 * See tfin .038 .038 .038 .038 .038 .038 .038 .038 Table 2 for Table 1 * Tube Diameter 3/8" 140°F 110°F x .0276 .0284 .0293 .0297 .0301 .0306 .0293 tfin .025 .025 .027 .027 .028 .028 x .0235 .0244 .0234 .0240 .0253 .0239 .0241 tfin .021 .023 .022 .022 .021 .022 Tube Diameter 1/2" 110°F x .0344 .0346 .0374 .0343 .0350 .0348 .0341 .0343 .0348 tfin .031 .033 .032 .033 .034 .034 .033 .033 140°F x .0338 .0336 .0342 .0334 .0339 .0337 .0349 .0333 .0338 tfin .029 .031 .031 .030 .030 .029 .031 .031 nomenclature. l70°F .0207 .0169 .0209 .0179 .0181 .0203 .0191 tfin .017 .014 .016 .015 .016 .017 l70°F .0270 .0267 .0269 .0263 .0274 .0264 .0260 .0260 .0266 tfin .023 .023 .021 .021 .022 .021 .023 .020 53 200°F x .0206 .0220 .0208 .0199 .0204 .0217 .0209 tfin .015 .014 .015 .014 .016 .015 200°F .0357 .0366 .0365 .0358 .0350 .0340 .0358 .0360 .0350 tfin .029 .030 .029 .028 .023 .028 .029 .028 HNQHIEQ'EIFJUQCDp XII 54 Table 2 Tube Diameter 3/4" 80°F 110°F 140°F l70°F 200°F x ti‘in X trin x tfin X tfin x .0438 .042 .0410 .040 .0395 .037 .0370 .034 .0394 .0442 .042 .0408 .040 .0393 .037 .0382 .036 .0372 .0441 .042 .0413 .039 .0387 .036 .0381 .036 .0350 .0448 .043 .0409 .040 .0384 .036 .0385 .037 .0370 .0443 .044 .0403 .038 .0387 .037 .0381 .036 .0348 .0440 .042 .0396 .038 .0391 .037 .0387 .035 .0360 .0445 .043 .0401 .039 .0389 .037 .0382 .037 .0364 .0441 .043 .0401 .039 .0388 .036 .0390 .037 .0370 .0443 .043 .0401 .038 .0381 .037 .0379 .035 .0352 .0443 .043 .0398 .038 .0387 .036 .0382 .035 .0360 .0445 .043 .0395 .038 .0396 .035 .0382 .037 .0358 .0444 .043 .0402 .038 .0388 .036 .0376 .035 .0354 .0442 .0403 .0388 .0381 .0362 Nomenclature for Tables 1 through 4. Minimum residual wall thickness - tfin Average of 5 to 10 random residual wall thicknesses per sample - 2 Grand averages (constant velocity and temperature) for individual 2 groups - i All these dimensions are in inches. tfin .036 .036 .034 .034 .033 .033 .033 .036 .034 .034 .034 .034 WSWOZZHKQHEQWWUOUJP Kn 80°F x .0457 .0458 .0457 .0456 .0461 .0454 .0457 .0460 .0455 .0457 .0456 .0453 .0460 .0456 .0460 .0464 .0458 .0459 .0457 tfin .044 .044 .045 .045 .044 .044 .044 .045 .044 .044 .044 .044 .044 .044 .044 .045 .044 .044 *See Table Table 3 * Tube Diameter 1" 140°F 110°F x .0463 .0467 .0467 .0466 .0469 .0459 .0468 .0466 .0467 .0468 .0466 .0468 .0466 .0463 .0464 .0463 .0466 .0463 .0465 tfin .045 .046 .046 .046 .046 .045 .046 .045 .046 .046 .045 .045 .045 .045 .045 .045 .046 .046 x .0446 .0449 .0451 .0448 .0442 .0442 .0444 .0437 .0438 .0444 .0440 .0440 .0448 .0445 .0438 .0447 .0447 .0449 .0444 2 for nomenclature. trin .043 .043 .044 .043 .043 .043 .043 .043 .042 .043 .042 .043 .044 .043 .043 .043 .043 .043 170°F x .0472 .0468 .0468 .0470 .0458 .0460 .0446 .0452 .0442 .0450 .0448 .0446 .0438 .0442 .0440 .0446 .0444 .0442 .0452 tfin .046 .045 .046 .045 .044 .044 .043 .044 .043 .044 .043 .044 .043 .043 .043 .044 .044 .043 55 200°F x .0482 .0482 .0480 .0476 .0468 .0470 .0470 .0472 .0474 .0472 .0474 .0474 .0476 .0474 .0476 .0472 .0472 .0474 .0484 ti‘in .048 .047 .047 .047 .045 .046 .046 .046 .047 .046 .047 .047 .047 .047 .047 .047 .047 .047 HmFUtOWOZZHNhP-IZBQWFJUOCUP C: Kn Tube Diameter 1-1/4" tfin i .0538 .0526 .0522 .0526 .0530 .0526 .0526 .0532 .0528 .0532 .0530 .0530 .0528 .0526 .0522 .0528 .0532 .0526 .0526 .0524 .0528 Table 2 for .0530. Table 4 * 110°F tfin .053 .052 .050 .052 .051 .050 .051 .051 .051 .050 .051 .050 .052 .050 .051 .052 .050 .051 .050 .050 .051 140°F x .0544 .0544 .0538 .0536 .0544 .0544 .0550 .0540 .0536 .0538 .0538 .0536 .0538 .0542 .0540 .0538 .0540 .0540 .0540 .0536 .0538 .0540 tfin .053 .054 .053 .053 .053 .053 .054 .053 .053 .053 .053 .053 .053 .053 .053 .053 .052 .053 .053 .052 .053 nomenclature. 170°F x .0542 .0542 .0534 .0534 .0540 .0538 .0542 .0538 .0542 .0526 .0532 .0528 .0532 .0528 .0530 .0530 .0522 .0532 .0532 .0532 .0534 .0534 tfin .052 .052 .053 .052 .053 .052 .053 .052 .053 .051 .051 .051 .052 .051 .052 .052 .051 .052 .051 .052 .052 56 200°F x .0532 .0532 .0530 .0530 .0532 .0528 .0526 .0526 .0530 .0532 .0530 .0526 .0536 .0530 .0530 .0530 .0528 .0528 .0528 .0534 .0530 .0529 tfin. .052 .052 .052 .051 .052 .051 .051 .052 .052 .052 .052 .052 .051 .052 .052 .052 .052 .052 .052 ~053 .052 0.143 0.286 0.428 0.572 0.714 0.857 §< Average of 10 readings on new tubing. Nominal 3/8" 0.035 1/2" 0.040 3/4" 0.045 1" 0.050 1—1/4" 0.055 initial in inches Average* Tolerance 0.033 0.039 0.039 0.044 0.043 0.049 0.047 0.054 0.055 0.059 61 0.0141 0.0041 0.0088 0.0026 0.0021 62 Table 10 Optimum Line Equation Fitted Through Individual Group Data and loglO T(x) x Temp. y log10 T(x) 0.035 80°F y= - 2.935 - 816.58 x 25.645 11.13748 110°F ya - 4.749 - 625.89 x 17.157 7.45119 140°F y= -l4.13 - 1088.82 x 23.979 10.41394 170°F ya -14.l6 - 763.44 x 12.560 5.45474 200°F y= -21.895 - 1108.88 x 16.916 7.34653 0.040 80°F 00 110°F y: - 6.051 - 916.364x 30.604 13.29115 140°F Ya - 9.284 - 1001.273x 30.767 13.36194 170°F y: -13.625 - 772.737x 17.284 7.50635 200°F y= - 4.167 - 387.094x 11.317 4.91491 0.045 80°F y= - 2.279 - 1204.650x 51.929 22.55248 110°F y= - 5.799 - 1008.879x . 39.600 17.19806 140°F y: -11.549 - 1404.525x 51.655 22.43348 170°F y= - 7.294 - 850.986x 31.000 13.46313 200°F y= - 5.917 - 597.596x 20.975 9.10933 Nomenclature. x = dmax identical to the nominal tube wall thickness. y - the reduced variate T(x) - return period 63 Table 11 * Corrosion Rates for NDHA Test Samples NDHA No. Temp. A B 0 556 174°F. wl 1.6001 2.2955 1.6009 w2 1.5513 0.8388 1.5651 wl-w2 0.0488 1.4467 0.0358 mils/y 0.99 C-18.4 0.726 mdd 5.41 c-114.0 3.97 718 W1 1.5722 2.2553 1.5764 W2 1.5520 1.3470 1.5530 wl-w2 0.0202 0.9083 0.0234 mils/y 0.635 0—17.75 0.736 mdd 3.47 0-110.0 4.02 559 wl 1.5841 2.2952 1.5960 w2 1.5036 1.0545 1.5045 41-w2 0.0805 1.2407 0.0915 mils/y 1.595 C-15.3 1.815 mdd 8.72 C-94.9 9.92 725 wl 2.3390 2.2571 2.2455 W2 2.2169 2.1334 2.1312 wl-w2 0.1221 0.1237 0.1143 mils/y 0-2.395 0—2.42 0-2.23 mdd 0-14.85 0—15.0 C-13.8 * See Table 19 for Nomenclature. Corrosion Rates for NDHA Test Samples (cont.) NDHA No. Temp. 547 Cold 717 Cold 561 Gold 721 Cold * See Table 19. Table 12 * W W Wi-W2 mils/y mdd W1'w2 mils/y mdd W1 W2 mils/y mdd A 2.2936 2.1384 0.1552 C-1.9l5 C-11.85 1.5601 1.4603 0.0998 3.135 17.15 1.5974 1.5537 0.0437 0.886 4.85 1.5596 1.5022 0.0574 1.805 9.86 for Nomenclature. B 1.5986 1.5487 0.0499 0.99 5.41 2.2488 2.1067 0.1421 C-2.78 C-l7.2 2.2854 2.0946 0.1908 C-2.4 cC-14.9 2.2384 2.2107 0.0277 C-0.506 C-3.ll4 64 C 2.2946 2.1175 0.1771 C-2.195 C-13.6 1.5682 1.5062 0.0620 1.95 10.66 1.6054 1.5462 0.0592 1.202 6.57 1.5644 1.4433 0.1211 3.81 20.85 Corrosion Rates for NDHA Test Samples (cont.) NDHA No. Temp. 558 150°F 715 15008 554 150°F 713 150°F * See Table 19 Table 13 * w1 w2 W1"W2 mils/y mdd mils/y mdd W1 W2 Wl-W2 mils/y mdd w1 W2 w1'W2 mils/y mdd A 1.5902 1.5533 0.0369 0.748 4.09 1.5730 1.5231 0.0499 1.568 8.56 1.60 1.5111 0.0889 1.804 9.86 2.2680 1.8857 0.3823 C-7.47 C-46.3 for Nomenclature. B 2.2962 0.8978 1.3984 C-17.65 C-109.5 2.2365 1.7126 0.5230 C-10.24 C-63.6 2.2917 1.4486 0.8431 C‘66el 1.5576 1.5138 0.0438 1.375 7.52 65 C 1.6027 1.5673 0.0354 0.719 3.93 1.5687 1.5150 0.0528 1.650 9.05 1.5557 0.0500 1.015 5.55 2.2832 2.0496 0.2336 C-4.565 C-28.3 Corrosion Rates for NDHA Test Samples (cont.) NDHA No. 557 722 551 719 * See Table 19 Temp. 150°F 150°F 150°F 150°F Table 14 * W1 1 N2 1'1 432 mils/y mdd mils/y mdd W1"W2 mils/y mdd W1 W2 Wl-W2 mils/y mdd A 1.5946 1.5393 0.0553 1.105 6.04 1.5663 1.4872 0.0791 2.485 13.65 2.2903 2.0622 0.2281 C-2.77l C-17.15 1.5577 1.3891 0.1686 5.3 29.0 for Nomenclature. B 2.2850 1.9652 0.3198 C-4.04 C-25.0 2.2338 1.9093 0.3245 C-6.35 C-39.3 1.6015 1.5407 0.0608 1.187 6.49 2.2287 2.1378 0.0909 C-1.777 C-11.0 66 C 1.6034 1.5520 0.0514 1.043 5.7 1.5718 1.4905 0.0813 2.552 13.96 2.2831 2.0250 0.2581 C-3.12 C-l9.35 1.5647 1.4917 0.0730 2.29 12.52 Corrosion Rates for NDHA Test Samples (cont.) NDHA N0. 542 723 543 716 Temp. 148°F 148°F cold cold Table 15 * W W2 Wl-W2 mils/y mdd W1 Nl-N2 mils/y mdd W mils/y mdd W1 W2 Wl—W2 mils/y mdd A 2.2929 2.1995 0.0944 C-l.167 C-7.23 1.5710 1.3980 0.1730 5.44 29.75 2.2924 2.1711 0.1213 C-l.462 C-9.07 1.5651 1.4220 0.1431 4.49 24.55 * See Table 19 for Nomenclature. B 1.5981 1.4356 0.1625 3.25 17.76 2.2433 2.1150 0.1283 C-2.506 C—15.55 1.5990 1.5146 0.0844 1.635 8.94 2.2855 2.2230 0.0625 C-1.222 C-7.58 67 0 2.2954 2.2090 0.0864 C-1.068 C-6.61 1.5659 1.3961 0.1698 5.32 29.1 2.2778 2.1214 0.1564 C-l.886 C-11.7 1.5660 1.4071 0.1589 4.99 27.2 Corrosion Rates for NDHA Test Samples (cont.) NDHA No. Temp. 549 150°F 720 . 150°F 546 140°F 714 140°F * See Table 19 Table 16 * EV]- w2 T _r N1 N2 mils/y mdd W Wl-W2 mils/y mdd w1‘W2 mils/y mdd A 2.2966 2.2364 0.0602 C-0.726 C-4.5 1.5730 1.3358 0.2372 7.45 40.7 2.2900 2.1714 0.1186 C-1.44 C-8.93 2.2492 2.1897 0.0595 C-1.161 C-7.2 for Nomenclature. B 1.6009 1.5522 0.0487 0.944 5.16 2.2414 2.1832 0.0582 C-1.138 C-7.05 1.6045 1.4176 0.1869 3.652 19.4 1.5724 1.3546 0.2178 6.84 37.4 68 C 2.2866 2.2326 0.0540 C-0.65l C-4.03 1.5717 1.3614 0.2103 6.61 36.2 2.2894 2.1790 0.1104 C-1.34 C-8.31 2.3485 2.2900 0.0585 C-l.l44 C-7.l Corrosion Rates for NDHA Test Samples (cont.) NDHA No. 555 707 545 709 Temp. Cold Cold Cold Cold Table 17 * W Wl-W2 mils/y mdd 171 -‘N2 mils/y mdd W -W 1 2 mils/y mdd A 1.6051 1.5134 0.0917 1.79 9.78 2.2342 2.2000 0.0342 C-0.666 C-4.13 2.2915 2.1877 0.1038 C-l.242 C-7.7l 2.2486 2.1930 0.0556 C-1.085 C-6.73 * See Table 19 for Nomenclature. B 2.3007 2.2032 0.0975 C-l.184 C-7.35 1.5696 1.4110 0.1586 4.98 27.3 1.6016 1.4773 2.4 13.12 1.5662 1.4850. 0.0812 2.55 13.95 69 C 1.6006 1.5016 0.0990 1.932 10.57 2.2410 2.1977 0.0433 C-0.845 C-Sezll' 2.2860 2.1846 0.1014 C-l.215 C-7.54 2.2493 2.1965 0.0528 C-1.033 C-6.41 Corrosion Rates for NDHA Test Samples (cont.) NDHA NO. 565 724 548 726 Temp. 150°F 150°F 177°F 177°F * See Table 19 Table 18 * W1 W2 wl’wz mils/y mdd W Wl-Nz mils/y mdd W -W mils/y mdd W1 w2 Wl-WZ mils/y mdd A 2.3030 2.1433 0.1597 C-1.915 C-ll.86 1.5606 1.4790 0.0816 2.56 14.0 2.2965 2.2940 0.0025 C-0.03 C-0.186 2.2911 2.2902 0.0009 C-0.0018 B 2.2932 2.1502 0.1430 C-1.713 C-10.72 2.2367 2.1154 0.1213 0-2.331 C-l4.45 1.5934 1.0657 0.5277 10.15 55.5 2.2943 0.0012 0-0.01115 0-0.0155 for Nomenclature. 70 0 2.2967 2.1411 0.1556 C-l.862 C-11.55 1.5782 1.4892 0.0890 2.795 15.3 2.2834 2.2778 0.0056 C-0.0664 C-0.412 2.2261 2.2228 0.0033 C-0.0628 C-0.389 71 Table 19 Corrosion Rates for NDHA Test Samples (cont.) NDHA No. Temp. A B c 550 150°F wl 2.2914 1.5775 2.2992 W2 1.9692 1.4892 2.0705 Wl-W2 0.3222 0.0883 0.2287 mils/y c-a.1 1.805 0-2.91 mdd C-25.4 9.86 C-l8.05 708 150°F W1 2.2455 1.5614 2.2360 W2 1.9855 1.4335 2.1060 Wl-W2 0.2600 0.1279 0.1300 mils/y C-5.08 4.02 c-2.51 mdd c-31.5 22.0 c-15.55 Nomenclature for Tables 11 trough 19. Initial weight of wire - W1 (grams) Final weight of wire - W2 (grams) Penetration rate - Mils/year Corrosion rate - mg/(sq. dm. x 24 hr. day) or mdd Note: The capital C in front of the corrosion and pen- etration rate values indicate a COpper coil. 72 Table 20 NDHA Testers Location List Location Run No. 1 Run No. 2 Tester Days Tester Days Shaw Hall (cold) 543 139 716 86 Shaw Hall (hot) 549. 139 720 86 Demonstration Hall (hot) 546 138 714 86 Demonstration Hall (cold) 555 138 707 86 Plant science Greenhouse (hot) 565 140 724 86 Plant Science Greenhouse (cold) 545 140 709 86 Union (hot) 559 136 725 86 Union (cold) 547 136 717 86 Health Service (cold) 561 133 721 86 Health Service (hot) 558 133 715 86 Agricultural Engineering (hot) 548 140 726 86 Judging Pavilion (hot) 542 136 723 86 Permanent Apartments (hot) - - 710 86 Married Housing (hot) 550 132 708 86 Kellogg Center (hot) - - - - Snyder Hall (hot) 551 138 719 86 Agriculture (hot) 554 133 713 86 Gilchrist (hot) 557 133 722 86 Campbell Hall (hot) 556 133 718 86 73 Table 21 Typical Raw Water Analysis - South Reservoir (March 31, 1952) Dissolved Oxygen 4.66 ppm Carbon Dioxide 40 ppm pH 7.15 Alkalinity 323 ppm (as H003) .Total Hardness 310 ppm (as CaC03) Silicates 8 ppm (as Si02) Chlorides 16 ppm I III,- oll‘ 1101 I1 I - a- - 1 I -.-I .1 1 1 . 1 1 1. 1.- 1. 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