The Role Of Current Distribution In Cathodic Protection
lJournal of Research of the Na tional Bureau of StandardsVol. 47, No. I, July 1951Research Paper 2220The Role of Current Distribution in Cathodic ProtectionHomer D. HollerThe paper outlines a procedure for determin ing current d istri bution over an elec trodesurface, as required in cathodic protection or in electroplating whe n the electrode pote ntialbears a known relation to current de nsity; and shows t he relation of current distribution toresistance of current path a.nd co un te r electromotive for ce. The primary curren t di stribution (without polarization) is a lso computed . A m ethod is s uggested for determining theelectrode poten tial-current den sity relation over an exte nsive s urface in a uniform m edium .In a nonuniform m edium, the determ inat ion of current den sity by m cas ureme nt of electrodepote ntial becomes complex. In uch a case t he potential criter ion of cathod ic pro tect ionmust be relied upon.7to be automatically solved. However, let us considerthe typical condition when galvanic corrosion ismost insidious, that is, localized pitting. Then, theanodic area is negligible, and the problem becomesa practical one of obtaining current distributionover the cathodic area, which is approximately thewhole area. In any study of the factors that determine current distribution over an extensive cathodearea, the geometry and dimensions of the metalstructure and its surrounding m edium are determining factors . It is the pmpose of this paper toanalyze the potential-current r elations that controlthis ClllTent distribution, as r elated to ca thodicprotec tion.1. IntroductionThe electrical r equirement for complete cathodicprotection of a metal from corrosion was demonstrated years ago by M ears and Brown [1] .1 Theirwork established a criterion based on the eq ll alization of surface potentials, which is accomplished bypolarizing the cathodic areas of the metal until theirpotentials become equal to the "open-circuit"potential of the anodic areas. As a result, thecurrent leaving the anodic areas, and consequentlythe equivalent rate of corrosion, is r edu ced to zero.The mechanism of the process is based on increasingthe polarization of the cathodic areas by the application of external current to those areas.Let us consider the poten tial 2 relations, when avoltage, E, is applied to a galvanic couple in whichthe potential of the cathodic ftl'ea is ec and t hatof the anodic area is ea. If E is gradually incr easedfrom zero, current I will How first to the cathodicarea when E E o, where Eo is the potential of th ecouple and lies b etween ea and ee. That is,II. Dimensions and Current DistributionIn cathodi c protccLion, we deal with cells of allshapes and sizes. It has b een theoretically demonstrated [2] that the over-all potential-current r elations in a large cell m ay no t b e truly represented bythe results obtained in a model of a very muchsmaller size. This ' is true because the potentialdifferences within a cell, through which current isflowing, consist of two kinds of components. Onecomprises electromotive forces which, for givencurrent densities, are independent of the size of th ecell; and the other includes those potential differencesresulting from currents flowing tlu'ough resistanceswhich, for a given r esistivity, are determined bydimensions. The smaller cell may therefore not bea true electrical model of the larger one for a givencurrent density unless the resistivity of its electrolyteis so adjusted that the resistive components in thetwo cells are equal.If the required adjustment of r esistance is impracticable, t.he potential-current r ela tions found ina small model may not be applicable directly to alarge cell. A procedure for determining these relations by direct measurem ent in the cell thereforeseems desirable . This is particularly true in thecase of electri cal circuits such as those involved inelectrolysis mitigation and cathodic protection ofunderground pipelines where the resistive components may not be realizable on a laboratory scale.Here we have large cathodic areas, and the volumewhereio the current circulating within the couplebefore E is appliedTa resistance of the anodic pathTc resistance of the cathodic path.tOnly when E e a does current b egin flowing tothe initially anodic area, and tlus occurs whenec I crc e a, where I e is the total cathodic current ;and ea becomes equal to E a the open-circuit potential.As the potential relations within a galvanic coupleare such that applied current flows to the cathodicareas as r equired , it may at first appear that there isno problem of current distribution in the applicationof cathodic protection. That is, th e problem seems1Figures in brackets indicate the literature references at the end of this paper.2 Thete rm "potential" used h erein reall y means a poten tial differen ce; and ifa current is flowing, a polarized poten tial is understood.938851- 51- -11--------
of electrolyte is unlimited . In the application ofcathodic protec tion, the position of the anode,through which the external current is supplied, is ofconsiderable practical importance. It is the purposeof this paper to outline a m ethod tried in the laboratory which might be translated into a field procedurefor determining current distribution. Field experience will then determine whether the laboratoryprocedure is applicable to underground conditions.Theoretical m ethods of computing current attenuation along a conductor of great length frequently neglect the role of counter emf and polarization [3], and consider the resistance as the only controlling factor . On the latter assumption, the currentdensity at different points on the cathode varies inversely as the r esistance of the current paths fromthe anode to the respective points, in accordancewith Ohm's law. However, any counter emf reducesthe current in the same ratio as that of the counteremf to the applied emf at that point. Any increasein counter emf therefore tends to reduce the current at points of higher current density to a greaterdegree than. at points f lower curre t ens.ity .This results m a more umform current dlstnbutlOn,for a given applied voltage, than if r esistance werethe sole current-limi ting factor. For example, ifi l and i2 are the currents flowing to unit areas havingelectrode potentials el and e2, respectively, then [4]A'U IOi2 r2rIwhere I is the total current; and A is the total area,!If I and A can be measured, there is no problem indetermining the apparent current density. However, when the current distribution is not uniform ,the relation of current density to polarization, ifthere is such a relation, may be used to determine iat any point where the cathode potential ec can bem easured. If the potential ec can be measuredwithout including any resistive components, then therelation, ec (j)i, may be used to determine i at anypoint in cells, regardless of dimensions.In order to demonstrate the relation of currentdistribution to polarization and resistance. a test cell,large enough to obtain a convenient current-densitygradient, was used. It consiste of ll: wooden t nk,3 ft by 10 ft by 1 ft deep, entll'ely msulated fromoutside circuits (fig. 1) . A %-in. steel tube extendedthe full length of the tank and a small steel anode , A ,was in one corner, as indicated. The electrolytecovered the tube by several inches. The problemwas to determine the current density at points 1, 2,. . . , 10 inclusive, for a given applied emf, E t .Direct measurement of current density at any pointwas impracticable. However, if the relation ofcathode potential ec to i is known, then i can beeasily determined. In the present case, the currentdensity gradient along only one dimension is ofinterest. For this r eason current density is expressed as current per unit length of tube. Variation in current density around the tube is disregarded.In order to obtain the data for a graph showingthe relation between e, and i, measurement of ec ona given length of tube, on which the apparent current density is assumed to be uniform, is necessaryat different values of I. The obvious method ofobtaining such uniformity is by th e use of a ,Parallelanode. This was accomplished by replacmg thesmall steel anode, A, with a rod equal to the lengthof the tank. Then i I h where l is the length oftube, uniform current distribution b eing assumed.For the determination of " c; a saturated calomeleleetrode was placed on the surface of the tube ateach numerical location. and the potential difference (e,-E s), was m easured , using the circuit infigure 1, where E s is the potential of the calomelelectrode.oe2 ;;;-;U 2 oe '(1);;;-;U Iwhere rl and r2 are the resistances of the paths of thecurrents. For a given metal and environment,oe2oeloeoi 2 oi l o{I} oej oi b ecom es very la.rge as compared with theresistances rand r2, O'/,l j O 2 approaches 1. In electronlfl.t,i np". till's uhenomenon is called "throwing power",;hichO{s a function of oej oi, and the geometry of t hecell and may be expressed in several ways. In cathodicprotection also, a high value, for oej oi, as comparedwith resistance, favors throwmg power and thereforegr eater uniformity in current distribution.In cells of very small dimensions, as in pits andcrevices on th e m etallic surface, th e effective resistances rand r2 may be small; and the value ofoej oi probably greater because of larger ionic concen tration gradients. These conditions favor ahigher throwing pO'wer than over large areas freefrom sharp surface irregularities.IV. Method of MeasurementThis circuit [5J permitted m easurement of thequantities (ec- E s) and (e,-Es Irs), where rs is theresistance between the reference electrode and thecathode surface. For a given current, I , the bridgewas balanced by adjustment of X until momentaryclosing of key [{I, caused no change in the defl ectionof null-indicator G. Since the r esistances in armsDD were equal (each 50,000 ohms), then at balancers X. After balance, the counter emf V wasIII. Determination of Current DistributionIn any study of current distribution, it is essentialthat a m ethod of determining apparent current density at any point be available. When current distribution is uniform,2
adjusted until ther e was no deflection of G.in circuit (1 )r everse order, making a to tal of 20 r eadings. Ther e ults are summarized in figure 2, wher e two graphsr epresent the averages, one for tap wa ter and onefor O.I-per cent N aCl solution. The " breaks" occura t potential levels n ear but slightly below the opencircuit potential of iron in a sa turated solution offerrou s hydroxide. At t,his potential, 0.8 13 vol t,corresponding to a pH of about 9.5, the reactionF epF e 2f r eaches equilibrium, and corrosion ofiron by this process practically ceases [6] . Th e da tain figure 2 were obtained for elec troly tes that wer eundisturbed, except by convec tion, and wer e veryprobably saturated wi th air. An air-free environment is therefore not a requirem ent for obtainingthe air-free potential by ca thodic polarization. Ther eproducibility of the r eadings was better than wasanticipated for iron in a solution initially having anundefined concentra tion of ferrous ions.The protective current, I v, indica ted in th o saltsolution was about 2.4 rna/It and in the tap wa ter ,1.5 rna/ft . Thus, the corrosiven ess in th e morecondu ctiv e salt solution was grea ter than in th e tapwater , though no t in the ratio of the conductivities,which was approximately ten to one. It is appar en ttha t this large differ ence in conductivity had noappar ent effect on the poten tial a t which the breaksin the polarization curves occulTedN ext, th e parallel anode was r eplaeed by th e pointanode A , and for a given v alu e of El and I, eo wasobserved at the number ed points along th e tube.By th e use of th e graphs in figure 2, the correspondingvalues of i wer e then es tima ted for each point. Intable 1 the values of ee and i ar e given, for each poin tof observa tion, in a O.I-percent solution of sodiumchloride for a curren t of 12 rna. Since th e poten tialof the tub e eo, wh en i O, th e differ en ce t.ee ee-eor epresen ts the emf of polariza tion , also given inta ble 1.Then(ee- E s)- 11g (I - In )r s- IDD,and in circuit (2)ubtracting th e equ ation for (2) from that for (1),and since rs X ,(ee- E s) 211gl,where 11gl voltmeter r eading.If k ey K 2 be opened and 11g b e r eadjusted to an ew value 11g2 until G again reads zero , then(ee- E s Ir s) 11g2 , wh ere Y g2 is the voltmeterr eading. This is equivalent to a potrntiometerm easurement. When I r s is negligible, use of thebridge is unnecessary, and (e e-E.) may be observeddirectly as 11g2 , for all practical purposes.The instrumental requirem ents of this circuit arenot stringent. As null indicator G, a Gen eral Electric galvanometer was satisfactory. In the field, aW eston Model 622 voltmeter with zero-center scaleand a r esistance of 200,000 ohms/ v may b e suitableand more convenient. A calibra ted slide-wire rheostat of sufficient curren t-carrying capacity was suitable for balancing the bridge and r eading. Thiscircuit has b een used in preliminary field tes ts but isnot ye t in suitable portable form .v.Potential Criterion of Cathodic ProtectionFor each value of I , th e emf (ee- E ,, ), was measured a t each point in numeri cal order , and also in tbe1000l/950I - 900EDD.JxW:2'(I)0 :!B850.Jl)i:i10 illSTEEL TUBEI23456I7I800uWOODEN TANK'I '" ,8975010d700 ELECTROLYTE-.!1,52,02,53,03,50 .51.0 i MILLIAMPERES -7- FEET ------------- 10FT-------------- ·1F I GUR EaF IGU R E1. Circuit f or measuring polari zation at points ofdifferent current den sities along a steel tube.2.R elation of electrode potenti al to current densityalong a steel tube.A, Tap water; B , O.I-percent NaC! solu tion.3
1. Observed potentials and current densities at differentpoints; calculated resistances and current-density componentsI. BOTABLEeo 715 mv; tA 588 mv; E, 1,170 mv; 1 12 rna.1.70P ointnum berL2 .3456789ID--Ie,Il. e,iE,lrrfe-fA,r-Ae,r(/) --- - -- -- - --- --mvmvmalftOhmsmalftmalf!malfl958928861- 243- 21 3- 1462682943534457624.373.983.3 12.631.54- 1. 37- lo13- 0.76-.48-.24- 0.90-.70-. 40-. 19-. 0795216951695169513511. 230.69.69.69. 87- . 18-. 09- . 09-. 09-. 12-. 05-. 02-.02- . 02774-593. ()()2.852. 552. 151. 30764749746748756- 49-34-3 1-33-411. 050.60. 60. 60.75803-88§Z1.00--lW:::;:0--l.90 .)f-' !(/)::r - . 03- --- --.BO zw.70eO- eA0Cl.VI. Calculation of Resistance of Current Path.60Let us now analyze the relation of current-densityattenuation to the resistance of the current pathsfrom the anode to successive unit lengths of tube.For a given current I , the polarized anode potential eA . Then , since the applied emf E t, and theexternal resistance was negligible,.500FI GU RE23.345678DISTANCE. FEET910II12R elation between emf and ir components of polarization along a steel tube.A, Open-circui t potential of iron, 0.81& volt .1',(2)tion may be expressed as .1ec in millivolts, or as.1eclr in milliamperes. Both indices in table 1 showthat the role of polarization in determining currentdensity distribution diminish es at the lower currentdensities . At th e minimum current density, r esistfl.nce is practically the sole determining factor, asindicated in figure 3.The current-distribution curves for salt water(fig . 4) were essentially the same as those obtainedin the tap water (fig. 5). For example, cathodicprotection defined as that value of ee, equal to orabove 0.81 3 v , extended approximately to the 4-ftlocation in each elec trolyte; and as shown in (fig. 2),a lower current density was required for protectionin the tap water than in the salt solution.where 1' the resistance of the path of current ifrom anode A to a given unit length of tube. Thatis, 1'1,1'2, . . ., 1'10 are the resistances of the paths ofcurrents i l ,i2 , ., i lO , respectively. Using eq 2,t h e values of l' were computed from the corresponding values of ec and i, where E t I,170 mv, andeA 588 mv. These results ar e also summarized intable 1.VII. PolarizationR earranging eq 2, we obtain. Et - -l'(eC-eA)l',(3)VIII. Location of Reference Electrodewhere i consists of two componen ts in opposition.One, Etl1', with E t constant depends only on 1'; andt h e other (ec-eA)I1', with eA constant, depends on l'and also upon ec. The expression E dr is the primarycurrent distribution representing the current densityt hat would be obtained if there were no counter emf.For example, if t h e cell were entirely fill ed uniformlywith a conductor of the first class, or if it had identical nonpolarizable electrodes, like copper in coppersulphate solution at low current densities, (eC-eA) 0 .Thus Etlr t is th e largest curren t density attainablefor a given valu e of E t and r.If ec eA and ec is nonpolarizable, having a constantvalue eo, then we have a constan t counter emf(eO-eA), as for example, in a lead-acid storagebattery on charge at low current density.If ec eA and ec is polarizable, then we have t hepresent case, where (eC-eA) represents the counteremf in which ec eo .1ec' The amount of polariza-When the tip of the reference electrode was incontact with the steel tube surface, there was asmall r esistan ce 1'8 (fig. 1) b etween the electrode andthe surface, which increased with current density(fig . 6). On a copper t ube, t his resistance wasgreater b y several-fold and may h ave been due toliberated hydrogen, or to a film resulting fromincreased alkalinity at th e surface.When the reference electrode was lo cated 18 in.from the tube surface, th e observed r eadings wereaverages of the true potentials for a range of pointsextending over a considerable length of the tube.For example, in figure 6, t he potential (800 mv)observed at locations 1 and 2, ·w ith the electrode18 in. a way was approximately the average potentialover a 5-ft length as measured with the referen ceelectrode directly on the surface. The significan ceof this observation is that, when the po tential and4
---,---.---,---,---,---,---,---,\\\54f- EU.::;-00lrIII III. t3 Z950'\x0Z.J t B50\1000 t0f-'.J900 t0 f)EW.Jf-Fe (Fe /Fe (OH}z0a. t Zt::wUlaa BOOa::IIIZf-2 w0af-a::a.a0a::::: uIII0fZ.JIIIWIIIIIIlr f-f-in0750.JIIIBOO2aaf-zIIIII:II:700L-.1 2 3 4 5 6 7 B 09::: u75010DISTANCE. FEET4. Cathodic potential ee, C!l1Tent densityi, and pl'imary current distl'ibution E dr along a steel tub e in N aC tsolution.FIGURE700L- 02O.l·Percen t Nael so lu tion ; 1 12 maoF IGUREcunen t-density gradients along th e tube arc st ep ,th e reference electrode mu st be as near as posslblet o the surface in order that th e observed valu eapproach the ' magni tude of ee. at a given po in t. tbest the observed value of ee lS an average potentIalOVCl: an area that increases with the distan ce of thereference electrode from the surface. '1'he purpo eof reducing this distance to a minimum is no t th at ofreducing the effect of resistance, since this can bebalan ced out by the bridge m easurement, but inorder to reduce the observed area to a minimum.Ob viously, if the cathode potential is uniform, therequirement of proximity is unnecessary. A moreremote lo cation may then be used, the distance fromthe surface being greater, in proportion to th e areaof uniformitv.A frequ el t subterfu ge of locating th e referenceelectrode behind th e electrode under investigation,or at some other point of minimum current density,may neither eliminate the ir component in theobserved poten tial nor indicate th e value of e, atthe front surface of th e electrode, which is of mostimportance. The referen ce electrode should therefore b e placed at th e'exact point, wher e the value ofee is required , with the least possible disturban ce ofthe lin es of current flow . This requires a
I, July 1951 Research Paper 2220 The Role of Current Distribution in Cathodic Protection Homer D. Holler The pap er outlines a procedure for det rmining current distri bution over an lectro e surface, as required in cathodic protection or in electroplating when the electrode potential
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