cathodic protection systems V. G. DeGiorgi - WIT Press · cathodic protection systems V. G. DeGiorgi ... Cathodic protection systems are designed to ... determined to be sufficient

A review of computational analyses of ship

cathodic protection systems

V. G. DeGiorgi

Mechanics of Materials Branch, Code 6380, Naval Research

, DC20J7J,

Abstract

Computational modeling techniques have long been applied to corrosionproblems. Boundary element techniques are well suited for cathodicprotection systems intended to minimize electrochemical corrosion on theexterior of ship hulls. The performance of these systems is governed byLaPlace's equation and these systems exist in unbounded domains (i.e. theopen sea). This article reviews the work performed in the past decade (1987-present) on boundary element modeling of ship impressed current cathodicprotection systems.

1 Introduction

Corrosion damage has a significant influence on the maintenance of a fleetof ocean vessels, either military or commercial. Corrosion damage is costly infinancial and fleet availability terms. Repairs are costly in time and moneyThere are two primary protection methods in use coatings and cathodicprotection systems. Typically a ship will have both a coating and a cathodicprotection system. Coatings prevent corrosion by isolating the material fromthe electrolyte, i.e. the metal of a ship hull from seawater. Coatings, however,are subject to damage through normal service. The cathodic protectionsystem is a secondary system designed to protect areas where the coating hasbeen breached. Traditionally systems are designed by expertise. A fewsystems have been designed by experimental techniques.

Computational modeling techniques offer immense opportunities foradvancements in cathodic protection system performance. Review articles byMunn [1] and Zamani et al [2] indicate both a level of maturity and neededimprovements in the application of boundary element techniques to cathodic

Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X

830 Boundary Elements

protection systems and corrosion problems in general. In the past decade,significant work has been completed for cathodic protection systems.

The scope of this paper is to review the boundary element workpublished in the past decade which has focused on cathodic protectionsystems for ship hulls. The work can be divided into two categories: designanalyses and case studies. Design analyses deal with general design issuesand analytical development of appropriate boundary element related tools.Case studies use existing techniques to analyze existing systems and compareresults with available experimental data.

2 Electrochemical corrosion and cathodic protection

Corrosion may be chemical, electrochemical or a combination. Cathodicprotection systems are designed to reduce damage associated withelectrochemical corrosion. Electrochemical corrosion occurs when a materialis dissolved into solution by oxidation. Oxidation and reduction reactionsoccur simultaneously but corrosion occurs only at the oxidation site, theanode. The reduction site is the cathode. Electrons are released at the anodeand are attracted by the cathode. This transfer of electrons establishes anelectrical current. The solution containing the material is the electrolyte. Thebasics of the corrosion process are shown schematically in Figure 1.

CATHODE regionReduction reactionAttracts electrons

Typical Reactions:

2H+ + 2e" — +~

4OR-

ELECTROLYTE..,___ . v Source of oxygenANODE region \ Source of hydrogenOxidation reaction 'Site of corrosion/loss of material \ jyjSource of electrons

Figure 1: Schematic of electrochemical corrosion process. Anode and cathodemay be different materials or different locations on the same material.

Electrochemical corrosion is governed by LaPlace's equation:

where O is the electrical potential and k is the conductivity of the electrolyte.LaPlace's equation if valid when there are no polarization gradients in theelectrolyte, the electrolyte is electroneutral and there are no electron sourcesor sinks present. These conditions are met during steady stateelectrochemical corrosion. Boundary element techniques are suitable toanalysis of shipboard cathodic protection systems since only the surface of


Boundary Elements 831

the hull is involved in the electrochemical process and it is appropriate torepresent the electrolyte surrounding the hull, i.e. the open sea, as an infinitevolume. Anodic material can be defined by:

_n

Insulated material is defined by:

Cathodic regions are defined by the polarization response of the material, i.e.the relationship of potential and current density.

Significant effort is invested in defining the cathodic section of thepolarization response for engineering materials of interest. Polarizationresponse is material and electrolyte specific and sensitive to a wide range ofenvironmental factors such as temperature, salinity, pH and flow rate.Polarization response is also sensitive to material composition, surface finishand treatment history. In addition, other factors which may influencepolarization response are the initial current applied, the presence ofcalcareous deposits or biological fouling and the formation of films and othercorrosion related products. It has also been observed that testing proceduresinfluence experimental polarization response. Scan rates as well as type oftesting procedures have been shown to produce variations in polarizationresponses. Once an experimental polarization response is generated amathematical representation must be formed for the computationalevaluation. In general, polarization can be represented as linear or nonlineardepending on the material and voltage range. Functional forms can bedetermined from experimental data using standard mathematical techniques.

Cathodic protection systems are designed to take advantage ofelectrochemical corrosion phenomenon to minimize corrosion of a designatedarea. Protection is provided by maintaining the potential on the designatedarea at or above a critical value. There are two types systems: sacrificial andimpressed current.

In sacrificial anode systems, a material is added to the structure which willcorrode in preference to the material to be protected. This material is thesacrificial anode and becomes the source of electrons. The weight of materialrequired is dependent on the relative ease of preferential corrosion and thesurface area to be protected. Sensors may exist to monitor the performanceof the system, but there can be no feedback to adjust system parameters.

Impressed current systems use a power source instead of a differentmaterial to provide a source of electrons. Impressed current systems aretypical for large ships because of the added weight resulting from the addition



of sacrificial anodes. Sensors provide information on potential which is usedto adjust amperage to the anodes. Large impressed current systems mayconsist of multiple subsystems which each contain a power supply, sensorsand anodes. Anodes connected to different subsystems may provide partialprotection to the same geographic region. Even though regions of influencemay overlap, reference cells provide information to only one subsystem.

All of the works cited in this study deal with impressed current cathodicprotection systems. The analysis procedures developed are equally valid forsacrificial systems.

3 Design analyses: analytical solutions

If an initial system design is the goal, sensor and anode locations areamong the unknowns which must be determined. One approach taken in thisphase is to assume a polarization response and to develop algorithms whichcan be used to determine optimum anode current values and placement.Zamani and Chuang [3] determined individual power levels which optimizedprotection by minimizing the difference between potential level at all pointsand the target potential. Solutions procedures were based on proceduresdeveloped for optimum control work on heat transfer problems. In thisinitial work single anode systems are examined. A simple geometry of a tankwith a single anode and cathode was examined but there is no limitation withrespect to geometry for their procedure. An example study of design optionson system performance demonstrates the power and advantages ofcomputational modeling.

Hou and Sun [4,5] further extended use of optimum control procedures todetermine system design parameters. Algorithms are developed to determineboth optimum anode location and anode amperage values. Two types ofproblems were examined: linear control in which the anode location are fixedand anode strengths are unknown and nonlinear control in which the anodelocations and strengths are unknown. Polarization response is defined and isnot a variable in the analysis. Single and dual anode system exampleproblems are presented for tanks containing a single cathode. Exampleproblems using a rectangular tank geometry are presented for both types ofproblems. Anode strength for optimum potential is determined for ashipboard impressed cathodic protection system. Multiple anode locationoptimization is of major importance to system design. Anode strength foroptimum performance is important in determining system requirements andin settling system operating parameters.

Positioning and strength determination for anodes are based on apolarization response for the ship hull material. The determination of theappropriate polarization response for a shipboard system is not a trivialmatter as previously noted. Aoki et al [6] has addressed the issue ofdetermining the polarization response for a ship at sea. The polarizationresponse of the hull is determined based on information obtained from sensorlocations. A inverse problem is defined in which the polarization response is



site in Banks Channel near Wrightsville Beach, NC. Laboratory polarizationresponse curves were used in the analyses. However, polarization responsewas reduced by 50% to account for observed fouling on the anodes on themodel barge. It was* determined that this reduction was necessary for theaccurate prediction of potential distributions and currents for coated and baremetal barges. Potential profiles were determined to be less sensitive topolarization accuracy than current values. In addition it was determined thatrelative trends in potential distributions can be accurately predicted evenwhen current predictions are inaccurate.

Real ship system data is limited. Another source of data for comparisonis physical scale modeling, an experimentally based technique for design andevaluation of cathodic protection systems [9]. In physical scale modeling thegeometry of ship hulls are exactly reproduced but at a reduced scale. Theelectrolyte conductivity is also scaled by the same factor. Twocomputational models have been completed for direct comparison withexperimental results: a U S Navy destroyer [10-12] and aircraft carrier [13].Coating damage is modeled as discrete damage locations defined by assigningmetal polarization response to selected elements along the ship hulls.Damage locations correspond to cathodic areas defined on the experimentalmodels. Two damage patterns have been analyzed: 2.8% and 15% of the hullsurface area defined as bare metal. Static and dynamic flow polarizationresponse curves were used to represent these test conditions. Extensiveanalyses were completed for single power supply systems and 2 subsystem6 and 7 anode systems [10-12]. It was determined that a high degree of meshrefinement was required to obtain accurate current results. The mesh used forthe destroyer analyses is shown in Figure 2. The aircraft carrier mesh has asimilar degree of refinement.

Figure 2: Boundary element mesh for U S Navy destroyer. Mesh refinementdetermined to be sufficient for current and potential calculation accuracy.



the unknown and is determined through an series of boundary elementanalyses. The error between sensor measured values and calculated values atthe sensor locations is minimized. Once the polarization response of thesystem is determined, anode strengths required to maintain target potentiallevels are readily calculated. In addition, the authors demonstrated the abilityto locate a single damaged area location due to variations in sensor readings attwo points in time. This discrete damage is determined by changes in sensorreadings. This is in addition to the general degradation of coating integritywhich would affect the polarization response at any point in time.

Aoki et al [6] have provided a means for determining polarizationresponse for an existing system which incorporates material interactions,coating damage, geometric effects, electrolyte composition and otherenvironmental affects. Factors which make determining an appropriatepolarization response difficult are included in the response determined by theinverse method. This is of major importance to the evaluation of existingsystems. Changing polarization response with service conditions and time inservice can be calculated. System parameters can then be determined basedon the actual service conditions.

4 Case studies: comparison with experimental data

Case studies are computational models which have emphasized comparisonwith experimental or shipboard data. These studies have resulted in increasedunderstanding of the factors which must be carefully detailed in order toaccurate predict system response.

Zamani et al completed an analysis of a Canadian Navy destroyer andexisting impressed current cathodic protection system [7]. An academicdevelopment boundary element code was used in the analysis. The propellerand rudder where not modeled as discrete surfaces but as an equivalentcathodic area defined on the ship hull. This eliminates any geometricinteractions between the rudder, propeller and hull.. At the time of theanalysis, the sensitivity of computational analysis to these factors wasunknown. The hull surface was defined as a perfect coating with theexception of the equivalent cathodic area. There was not provision forcoating damage. Laboratory obtained values of linear polarization responsewere used for the equivalent cathodic area. Potential profiles were calculatedfor defined anode strengths. These values were compared with measuredvalues taken from the actual frigate when at dock. Even with the modelingsimplification potential values have a maximum relative error of 6% whencompared to ship data. No comparison was made for current values.

In an effort to determine the sensitivity of the modeling process toenvironmental and spatial factors, a combined experimental andcomputational modeling project was completed by Hack [8]. A flat bottomrectangular barge was designed, built and modeled. The barge wasinstrumented so that potential profiles could be compared withcomputational results. The barge was maintained in natural seawater at a test



Analyses were completed for textbook values of polarization response,standard small sample laboratory specimen generated polarization responsesand large scale open seawater plate generated polarization responses. Theaccuracy of polarization response was shown to be critical to accuracy ofcomputational results as was noted in contemporary work by Hack [8].Polarization data which most closely matched model conditions resulted incomputational results which most closely matched model results. Calculatedpotential was less sensitive to polarization accuracy than current values.

The destroyer ship hull model has been used for parametric studies whichexamine modeling small amounts of coating damage by scaling polarizationresponse [11] and system performance for ranges of electrolyte conductivitypossible during service [12]. These are numerical studies which utilizeboundary element capabilities to determine system sensitivities.

An analysis of U S Navy aircraft carrier was performed to verifyguidelines established by the multiple stages of the destroyer analysis [13].Complexity is increased by the analysis of the carrier s 3 subsystem 17 anodesystem. Experimental results indicate that there is a strong degree ofinteraction between the systems. This observation was verified during theiterative solution procedure. Representative comparisons between physicalscale and computational results are shown in Figure 3. The success of thisanalysis indicates that guidelines can be established which allow for creationof models which accurately predict performance.

I iS1.5-

Figure 3: Dynamic flow and minimum damage conditions. Measurementstaken at a depth of 10 feet. A frame is a unit distance along the length of thehull.

Finally, a proposed design methodology which utilizes computationalmethods and physical scale modeling has been presented [14]. Thisprocedure would use computational methods to determine a best systemdesign. This design would then be generated as a physical scale model. Finalmodifications of anode and sensor placement would be determined from theexperimental procedure. The advantages of both design systems would becombined to determine an optimal system. The primary advantage for use of



the experimental procedure for final design is the independence from anassumed polarization response.

While not applied to a ship hull, work on stray currents in electrochemicalsystems by Trevelyan and Hack [15] is applicable to ship systems. Astandard boundary element formulation was modified to include an secondaryelectrical source, a astray current. Examples are presented for pipingsystems but the numerical formulation is applicable to ship cathodicprotection systems. Stray current is an important issue when a ship isbrought into the vicinity of another operating cathodic system such as mayexist on a companion ship or on a dock.

5 Summary

A considerable amount of computational modeling work on ship cathodicprotection systems based on the boundary element techniques has beencompleted in the past decade (1987-present). Optimum design and casestudies have firmly established the capabilities of boundary elementapproach. Results which are critical to the application of this technology toship system design are:

(1) Development of an algorithm to determine optimumanode location.(2) Development of an algorithm to determine optimumanode amperage values.(3) Development of an procedure to determine in situpolarization response of a ship hull.(4) Successful comparison of computational and experimentaldata for real ship geometries.

Each achievement must be considered with the following in mind:(1) The accuracy of computational results depends on theaccuracy of the polarization response for the serviceconditions.(2) Even an inappropriate polarization response can be used todetermine trends in system performance.

The ability to computationally determine optimum anode locationprovides a basis, other than designer expertise, for the design of new cathodicprotection. This provides a rational analytical approach to the design of newsystems. Systems can be designed to optimum protection levels even withless than accurate polarization response.

Determination of optimum amperage to anodes to maintain protectionlevels is of interest but is not as significant as the ability to define optimumanode placement. This is primarily due to the uncertainty of polarizationresponse. A less than accurate polarization response will have a significantaffect on calculated current values.

At the present time, inspection is the only means available for assessingdamage to a coating. The ability to calculate the polarization response for thehull, which would include undamaged and damaged sections of coating, during



service is an important breakthrough. Damage assessment and healthmonitoring protocols can be developed based on this approach. The sensorpopulation on existing systems is probably too sparse for useful informationto be obtained. However, addition of sensors in strategic locations would be alow cost method to provide real time coating health monitoring.

Comparison of computational and experimental results is essential to thetransitioning of this technology to the design community. The ability toaccurately reproduce experimental results is critical to the acceptance of anycomputational procedure. Use of physical scale model and otherexperimental data is important because of the scarcity of real ship data.

Cathodic protection systems respond to their environment with a highlevel of synergism. Computational models which have been verified bycomparison with experimental results are good tools for expanding the basicunderstanding of system interactions. Computational parameteric studieswhich isolate individual system characteristics can provide invaluableinformation to the designer.

In closing, the use of boundary elements for design and evaluation ofcathodic protection system has greatly matured during the past decade. Onechallenges for the future would be the adaptation of design algorithms, whichhave been demonstrated for relatively simple systems, to existing shipsystems consisting of multiple subsystems. In addition, furtherdemonstration of analysis capabilities through design studies on different hullgeometries will provide additional evidence of the accuracy and advantages ofusing computational methods for the design and evaluation of ship cathodicprotection systems.

6 References

1. Zamani, N. G, Porter, J. F. and Mufti, A. A., "A Survey ofComputational Efforts in the Field of Corrosion Engineering " Int. J. ofNumerical Methods in Engrg., Vol. 23, 1295-1311 (1986).2. Munn, R. S., "A Review of the Development of Computational CorrosionAnalysis for Spatial Corrosion Modeling Through It's Maturity in the Mid-1980 's," Computer Modeling in Corrosion, ASTM STP 1154, AmericanSociety Testing and Materials, 215-228 (1991).3. Zamani, N. G. and Chuang, J. M , "Optimal Control of Current in aCathodic Protection System: A Numerical Investigation," Optimal Controly /. af%/M;f/K%&, Vol. 8, 339-350 (1987).4. Hou, L S. and Sun, W, "Numerical Methods for Optimal Control ofImpressed Cathodic Protection Systems," Int. J. of Numerical Methods in##rg., Vol. 37, 2779-2796 (1994).5. Hou, L. S. and Sun, W, "Optimal Positioning of Anodes for CathodicProtection," SIAM J. Control and Optimization, Vol. 34, No. 3, 855-873(1996).6. Aoki, S., Amaya, K. and Gouka, K., "Optimal cathodic protection ofship/' Boundary Element Technology XI, R. C. Ertekin, C A. Brebbia, M.



TanakaandR. Shaw (eds.), Computational Mechanics Publications, 345-356(1996).7. Hack, H P., "Verification of the Boundary Element Modeling Techniquefor Cathodic Protection of Large Ship Structures," CARDIVNSWC-TR-61-93/02, Carderock Division NSWC Report, Dec. (1993).8. Thomas, E. D , Lucas, K. E. and Parks, A R, "Verification of PhysicalScale Modeling with Shipboard Trials," Corrosion 90, Paper 370, NationalAssociation of Corrosion Engineers (1990).9. DeGiorgi, V. G. Lucas, K. E, Thomas, E D and Shimko, M. J.,"Boundary Element Evaluation of ICCP Systems Under Simulated ServiceConditions," Boundary Element Technology VII, C. A. Brebbia and M. S.Ingber (eds.), Computational Mechanics Publications, 405-422 (1992).10. DeGiorgi, V. G, Kee, A. and Thomas, E. D , "Characterization accuracyin modeling of corrosion systems," Boundary Element XV, Vol. 1, C. ABrebbia and J. J. Rencis (eds.), Computational Mechanics Publications, 679-694 (1993).11. DeGiorgi, V. G and Hamilton, C P., "Coating integrity effects onimpressed current cathodic protection system parameters," BoundaryElements XVII, C A. Brebbia, S. Kim, T. A. Osswald and H Power (eds.),395-403 (1995).12. DeGiorgi, V. G, "Influence of Seawater Composition on CorrosionPrevention System Parameters," Boundary Element Technology XII, J. J.Frankel, C A. Brebbia and M. A. H. Aliabadi (eds.), ComputationalMechanics Publications, 475-583 (1997).13. DeGiorgi, V G, Thomas, E. D, Lucas, K. E. and Kee, A., "Verificationof scale effects of modeling of shipboard impressed current cathodicprotection systems," Computers and Structures, in press (1997).14. DeGiorgi, V. G, Thomas, E. D. and Lucas, K. E., "A Combined DesignMethodology for Impressed Current Cathodic Protection Systems,"Boundary Element Technology XI, R. C Ertekin, C. A. Brebbia, M. Tanakaand R Shaw (eds.), Computational Mechanics Publications, 335-345 (1996).15. Trevelyan, J and Hack, H P., "Analysis of stray current corrosionproblems using the boundary element method," Boundary ElementTechnology IX, C A. Brebbia and A. J. Kassab (eds.), ComputationalMechanics Publications, 347-356 (1994)


Documents

cathodic protection systems V. G. DeGiorgi - WIT Press · cathodic protection systems V. G. DeGiorgi ... Cathodic protection systems are designed to ... determined to be sufficient