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Mean current Density

A Principal Determinant in Cathodic Protection Design of Offshore Structures, The Mean Current Density
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  CORROSION SCIENCE SECTION 988 C ORROSION  — OCTOBER 2000 0010-9312/00/000195/$5.00+$0.50/0 © 2000, NACE International Submitted for publication June 1999; in revised form, February 2000. Presented as paper no. 627 at CORROSION/99, April 1999,San Antonio, TX  * Center for Marine Materials, Department of Ocean Engineering,Florida Atlantic University, Boca Raton, FL 33431. A Principal Determinant in CathodicProtection Design of Offshore Structures  — The Mean Current Density W.H. Hartt and E. Lemieux*  ABSTRACT The historical development of marine cathodic protection design, along with the recently developed, first-principles- based slope parameter method, is reviewed briefly. It was  projected that the remaining issues that require resolution before cathodic protection design can be optimized are improved methods for representing the slope parameter,anode current capacity, and mean current density. The  present paper focuses on the last of these and, in so doing,evaluates data from a variety of field structures for which such information exists and from laboratory and field test  programs. An analytical model for current density decay with time, as a consequence of calcareous deposit formation, is  presented; and a new method is proposed for specifying mean current density in cathodic protection design of offshore structures.KEY WORDS: analytical model, cathodic protection, design,galvanic anode, mean current density, offshore structures,seawater, slope parameter  INTRODUCTION Cathodic Protection Design Practice  Cathodic protection (CP) design procedures haveevolved historically according to trial and error;Ohm’s law using a single, long-term current density; 1 Ohm’s law and rapid polarization using three designcurrent densities, an initial (i o ), mean, (i m ), and final(i  ƒ  ); 2-3  and the slope parameter method. 4-7  Accordingly, the second and third practices are based upon the equation:  IR  a c a a  = φ φ  –   (1) where I a   is the individual anode current output, φ c  isthe closed circuit cathode potential, φ a   is the closedcircuit anode potential, and R  a   is resistance of anindividual anode.For three-dimensional or space frame typeoffshore structures, anode resistance is normally thedominant component of the total circuit resistance;and so it alone is represented. In most cases, thisparameter is calculated from standard, numericalrelationships that are available in the literature 8-13  based upon anode dimensions and electrolyteresistivity. Figure 1 graphically illustrates the prin-ciple behind this equation and approach.Considering that the net current for protection (I)is the product of the structure current density demand (i c ) and surface area (A  c ), the number of anodes required for protection (N) is determined fromthe relationship:  N i A I c ca  = ×  (2)By earlier practice, 1  CP design was based upon a single time average or mean current density that polarized the structure to the potential required for protection (i.e., to –0.80 V vs silver-silver chloride  CORROSION SCIENCE SECTION 989 C ORROSION  — Vol. 56, No. 10 [Ag-AgCl]), within perhaps several months to 1 year.It was recognized subsequently, however, that application of an initially high current density (rapidpolarization 4,14-18 ) resulted in a lower mean current density and reduced anode mass to provide protec-tion for the design life. Accordingly, present protocolsare based upon three current densities, 2-3  such that i o  and i  ƒ   are substituted successively for i c  in Equa-tions (1) and (2) with the number of anodes corre-sponding to each being determined. However, i m  iscalculated from the mass balance relationship:  N i A T C w  m c = × ××  (3) where T is the time for which protection is achieved,C is anode current capacity, and w is weight of anindividual anode.Invariably, the number of anodes determinedaccording to each of the three calculations is differ-ent with the largest being specified. For uncoatedstructures this is usually i o . Consequently, thesystem is over-designed in terms of the other twocurrent densities. This arises because the procedureis an algorithm rather than being first-principles based. Slope Parameter Approach to CP Design  More recently, the slope parameter approach togalvanic CP system design was developed based upona modification of Equation (1) as: 4-7   φ φ c t c c a  R A i = × ( )  × +  (4) where R  t   is the total circuit resistance. This rela-tionship projects a linear interdependence between  c  and i c , provided R  t  , A  c , and  a   are constant. That this is normally the case has been confirmed by laboratory and field measurements. 4-7,19  For space frame type structures with multiple galvanicanodes:  R  R N t a  ≅  (5) with the product R  t    ×  A  c  being defined as the slopeparameter (S) such that:  S R A N a c = ×  (6)Substitution of the latter expression into Equation (3)then yields:  R w  i T SC a m × = × ×  (7)Upon defining an appropriate value for S, all termson the right side are known from the design choices;and so the process is reduced to determination of theoptimum combination of R  a   and w. This may beaccomplished in terms of anodes of standard dimen-sions or, perhaps more effectively, by specifying anelongated anode or dualnodes. 20  Thus, if anoderesistance is represented in terms of Dwight’smodified equation:  R L L r  a   = ×        ρπ 241ln –   (8) where   is electrolyte resistivity, L is anode length,and r is equivalent anode radius, then the left side of Equation (7) becomes:  R w  r L r  × = × ′ × ×  ρ ρ ν 2 241ln –   (9) where  ′  is anode density and  ν  is volume fraction of the anode that is galvanic metal as opposed to core. The required number of anodes then can becalculated from Equations (3) or (6).Hartt, et al., projected that the slope parameter- based design approach yields a 32% reduction inanode mass in the case of typically sized structurescompared to design 5  according to present recom-mended practice. 2-3  This arises because Equation (7)is first-principles-based and incorporates i m  and i o ,the former explicitly and the latter implicitly via theslope parameter. As such, design can be optimized interms of both parameters instead of just one. Analternative view is that, of the two terms on the left side of Equation (7), R  a   determines i o  while w relatesto i m . FIGURE 1. Schematic of a polarization diagram and parameters relevant to galvanic anode cathodic protection system design.  CORROSION SCIENCE SECTION 990 C ORROSION  — OCTOBER 2000 (1) i maint   is defined as the value for i c  at an exposure time of interest.In these cases, this was the time at which CP surveys on theindividual structures were performed. Subsequently, these twoterms, i maint   and i c , are used interchangeably as the i required tomaintain a particular φ . (2) Most of the data in Figure 2 represent values read from graphicalplots of the various authors rather than actual data per se. (3) UNS numbers are listed in Metals and Alloys in the Unified Numbering System  , published by the Society of AutomotiveEngineers (SAE) and cosponsored by ASTM. REMAINING CRITICAL ISSUES  With the advent of the first-principles-basedslope parameter approach to CP design, the remain-ing issue that requires resolution before CP systemscan be better designed is development of improvedprocedures for specifying the parameters on the right side of Equation (7), namely i m , S, and C, where thefirst two relate to polarization characteristics of thestructure and the third to galvanic anode perfor-mance. Of interest in the present paper is the designchoice for i m , since recommended practices 2-3  list thisparameter as 55 mA/m 2  to 80 mA/m 2  for near surface subtropical regions, while significantly lower maintenance current densities (i maint  )—3.4 mA/m 2 and 8.8 mA/m 2  for two Gulf of Mexico structures(ages 19 years and 22 years, respectively) 19  and5.4 mA/m 2  to 34.4 mA/m 2  for 15 Arabian Gulf structures (ages 13 years to 26 years) 21  —have beenreported. (1)  Since anode mass to achieve a particular design is directly proportional to i m , significant cost savings potentially can result if, indeed, designaccording to a reduced i m  can be justified. RESULTS AND DISCUSSION Field Data   As the initial step in developing an empiricalmean current density model, existing literature data  were synthesized. Thus, Figure 2 reports i maint   vs timedata that have been extracted from the literature for  various offshore structures. These include informa-tion from structures exposed to different oceans andrepresent shallow and deep and tropical/temperateand northern latitude locations. (2)  In most cases, theindividual data sets correspond to either a givenstructure overall, a given elevation on a structure, or a test panel or leg wrap on a structure. Exceptionsare references 19 and 22—for which the data to7,008 h (292 days) are from one structure 22  and thesingle data points at 166,440 h and 192,720 h(19 years and 22 years, respectively) are from twoothers 19  —and reference 21 where each data point isfor a separate structure. The general trend, for thedata collectively and for individual structures,consists of an initial period during which i maint   wasroughly constant followed by decay according to a power law relationship (linear on log-log coordinates).Note, however, that the early time, constant i maint  period is not apparent in some cases, and slope of the individual data sets differs. Also, i maint   decayedcontinuously with time, albeit at a progressively reduced rate, such that there is no indication of a true steady-state value being ultimately achieved. The overall scatter is such that at any given timei maint   varied by ~ 1 order of magnitude. This probably reflects variations in factors such as temperature, wave action, water velocity, water chemistry, andCP system design and the effect of these uponcalcareous deposit formation kinetics and properties.Data for the shallow water of the Gulf of Mexico,South Atlantic, and Arabian Gulf exposures subse-quently are referred to as “warm” water results andthose for the remainder as “cold” water ones. Al-though these two data sets are within the same rangein the short term (10 h to 10 4  h), i maint   at greater times for most of the warm water locations falls below those for the cold. Presumably, this is a consequence of the greater tendency for calcareousdeposit formation under the former type exposure(warm water) compared to the latter. 23  Results fromthe 15 different Arabian Gulf structures 21  and twoGulf of Mexico structures 19  are of particular interest  because of the otherwise general unavailability of truly long-term data. Laboratory and Field Test Data  Recent emphasis in laboratory experimentationpertaining to marine cathodic protection has been ona procedure in which a steel specimen is electrically connected to a galvanic anode through an appropri-ately sized resistor, and  c  and i c  are monitored as a function of exposure time. 4-6  Equation (4), then,facilitates a direct comparison between data fromsuch specimens and those from actual structures.In the present research, results of previouslaboratory experiments of the type described werereevaluated and compared with the data from full-size structures (Figure 2). As an example, Figure 3shows i c  vs time data for four 51-mm high by 25-mmdiameter structural steel (UNS K12037) (3)  cylinders with a 600-grit surface finish that were coupled to a symmetrically positioned aluminum anode ringthrough a resistor of the indicated size and exposedto natural seawater at ambient laboratory tempera-ture. In each case, the data trend parallels that inFigure 2 in that i c  was initially constant with time but subsequently decayed according to a power law relationship with no indication of a steady-state value ever being reached. The initial i c  varied in- versely with size of the external resistance, and thetime at which i c  began to decay was greater thehigher this resistance. As a second example, Figure 4 shows i c  vs timeplot for three 200-mm 2  structural steel plate (UNSG10200) specimens also coupled to a galvanicaluminum anode through an external resistor andexposed at a deep water Gulf of Mexico site for   CORROSION SCIENCE SECTION 991 C ORROSION  — Vol. 56, No. 10 Smith, et al., 30  and Hugus and Hartt  31  previously have applied this expression to analyze i c  decay trends for cathodically polarized steel specimens indefined flow fields. In the present analysis, it wasassumed that calcareous deposits formed and i c decayed according to the following sequentialsteps 31 : —Precipitation of a thin, magnesium-richdeposit within the first several minutes of expo-sure, accompanied by a corresponding decreasein i c  (the data in Figures 2 through 4 are thought to have resulted subsequent to this film havingformed). —A period of constant i c  corresponding to thetime required for calcium-rich deposits, either ascalcite or aragonite, to nucleate and begin to grow. Accordingly, the break in the i c  vs time trend, wherethis occurred (Figures 3 and 4), is thought to corre-spond to the onset of calcium carbonate (CaCO 3 )precipitation. FIGURE 3. Current density vs time data for four laboratory specimens, each with a different slope parameter. FIGURE 4. Current density vs time plots for three specimens exposed at a deep water Gulf of Mexico site. ≈  400 days. 29  The trend here is somewhat different from that in Figures 2 and 3 in that the initial data are not constant with time but conform to a sloping,albeit shallow, straight line (log-log coordinates);the break to a more steep i c  decay occurred moreabruptly; and a threshold current density is appar-ent. Figure 5 shows the data for the S = 0.70 Ω -m 2 specimen in linear coordinates, thus allowing occur-rence of an apparent threshold to be viewed moredefinitively. Also shown in Figures 3 and 4 are theupper and lower data bounds from Figure 2, thusindicating a general correspondence between thelaboratory/test panel results and data from actualstructures.Clearly, however, the long-term current demandfor an offshore structure is not revealed adequately from laboratory or even field test data of the dura-tions addressed here. Analytical Model   An attempt was made to evaluate empirically thecurrent density vs time trends in Figures 2 through4. This was based upon the expression: 30-31   i D n F c x Sht p L   = × × ×+  (10) where i L   is the limiting current density for oxygenconcentration polarization, D is the diffusion coeffi-cient for oxygen, n and F have their normal mean-ings, c is the bulk oxygen concentration, x is a dimensional parameter related to the flow, Sh is theSherwood number (0.03[Re] 0.8   ×  [Sc] 0.33 , where Re isthe Reynold’s number and Sc the Schmidt number),t is the calcareous deposit thickness, and p is theporosity constant for the calcareous deposits(unitless). FIGURE 2. Current density vs time plot for offshore structures in various ocean locations. Solid symbols are for warm water and open and linear ones are for cold/deep water locations.
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