Transactions on Modelling and Simulation vol 18, 1997 WIT Press, ISSN X

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1 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 corrosion problems. Boundary element techniques are well suited for cathodic protection systems intended to minimize electrochemical corrosion on the exterior of ship hulls. The performance of these systems is governed by LaPlace's equation and these systems exist in unbounded domains (i.e. the open sea). This article reviews the work performed in the past decade (1987- present) on boundary element modeling of ship impressed current cathodic protection systems. 1 Introduction Corrosion damage has a significant influence on the maintenance of a fleet of ocean vessels, either military or commercial. Corrosion damage is costly in financial and fleet availability terms. Repairs are costly in time and money There are two primary protection methods in use coatings and cathodic protection systems. Typically a ship will have both a coating and a cathodic protection system. Coatings prevent corrosion by isolating the material from the electrolyte, i.e. the metal of a ship hull from seawater. Coatings, however, are subject to damage through normal service. The cathodic protection system is a secondary system designed to protect areas where the coating has been breached. Traditionally systems are designed by expertise. A few systems have been designed by experimental techniques. Computational modeling techniques offer immense opportunities for advancements in cathodic protection system performance. Review articles by Munn [1] and Zamani et al [2] indicate both a level of maturity and needed improvements in the application of boundary element techniques to cathodic

2 830 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 work published in the past decade which has focused on cathodic protection systems for ship hulls. The work can be divided into two categories: design analyses and case studies. Design analyses deal with general design issues and analytical development of appropriate boundary element related tools. Case studies use existing techniques to analyze existing systems and compare results with available experimental data. 2 Electrochemical corrosion and cathodic protection Corrosion may be chemical, electrochemical or a combination. Cathodic protection systems are designed to reduce damage associated with electrochemical corrosion. Electrochemical corrosion occurs when a material is dissolved into solution by oxidation. Oxidation and reduction reactions occur simultaneously but corrosion occurs only at the oxidation site, the anode. The reduction site is the cathode. Electrons are released at the anode and are attracted by the cathode. This transfer of electrons establishes an electrical current. The solution containing the material is the electrolyte. The basics of the corrosion process are shown schematically in Figure 1. CATHODE region Reduction reaction Attracts electrons Typical Reactions: 2H+ + 2e" +~ 4OR- ELECTROLYTE..,. v Source of oxygen ANODE region \ Source of hydrogen Oxidation reaction ' Site of corrosion/loss of material \ jyj Source of electrons Figure 1: Schematic of electrochemical corrosion process. Anode and cathode may 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 the electrolyte, the electrolyte is electroneutral and there are no electron sources or sinks present. These conditions are met during steady state electrochemical corrosion. Boundary element techniques are suitable to analysis of shipboard cathodic protection systems since only the surface of

3 Boundary Elements 831 the hull is involved in the electrochemical process and it is appropriate to represent the electrolyte surrounding the hull, i.e. the open sea, as an infinite volume. 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 the polarization response for engineering materials of interest. Polarization response is material and electrolyte specific and sensitive to a wide range of environmental factors such as temperature, salinity, ph and flow rate. Polarization response is also sensitive to material composition, surface finish and treatment history. In addition, other factors which may influence polarization response are the initial current applied, the presence of calcareous deposits or biological fouling and the formation of films and other corrosion related products. It has also been observed that testing procedures influence experimental polarization response. Scan rates as well as type of testing procedures have been shown to produce variations in polarization responses. Once an experimental polarization response is generated a mathematical representation must be formed for the computational evaluation. In general, polarization can be represented as linear or nonlinear depending on the material and voltage range. Functional forms can be determined from experimental data using standard mathematical techniques. Cathodic protection systems are designed to take advantage of electrochemical corrosion phenomenon to minimize corrosion of a designated area. Protection is provided by maintaining the potential on the designated area at or above a critical value. There are two types systems: sacrificial and impressed current. In sacrificial anode systems, a material is added to the structure which will corrode in preference to the material to be protected. This material is the sacrificial anode and becomes the source of electrons. The weight of material required is dependent on the relative ease of preferential corrosion and the surface area to be protected. Sensors may exist to monitor the performance of the system, but there can be no feedback to adjust system parameters. Impressed current systems use a power source instead of a different material to provide a source of electrons. Impressed current systems are typical for large ships because of the added weight resulting from the addition

4 832 Boundary Elements of sacrificial anodes. Sensors provide information on potential which is used to adjust amperage to the anodes. Large impressed current systems may consist of multiple subsystems which each contain a power supply, sensors and anodes. Anodes connected to different subsystems may provide partial protection to the same geographic region. Even though regions of influence may overlap, reference cells provide information to only one subsystem. All of the works cited in this study deal with impressed current cathodic protection systems. The analysis procedures developed are equally valid for sacrificial systems. 3 Design analyses: analytical solutions If an initial system design is the goal, sensor and anode locations are among the unknowns which must be determined. One approach taken in this phase is to assume a polarization response and to develop algorithms which can be used to determine optimum anode current values and placement. Zamani and Chuang [3] determined individual power levels which optimized protection by minimizing the difference between potential level at all points and the target potential. Solutions procedures were based on procedures developed for optimum control work on heat transfer problems. In this initial work single anode systems are examined. A simple geometry of a tank with a single anode and cathode was examined but there is no limitation with respect to geometry for their procedure. An example study of design options on system performance demonstrates the power and advantages of computational modeling. Hou and Sun [4,5] further extended use of optimum control procedures to determine system design parameters. Algorithms are developed to determine both optimum anode location and anode amperage values. Two types of problems were examined: linear control in which the anode location are fixed and anode strengths are unknown and nonlinear control in which the anode locations and strengths are unknown. Polarization response is defined and is not a variable in the analysis. Single and dual anode system example problems are presented for tanks containing a single cathode. Example problems using a rectangular tank geometry are presented for both types of problems. Anode strength for optimum potential is determined for a shipboard impressed cathodic protection system. Multiple anode location optimization is of major importance to system design. Anode strength for optimum performance is important in determining system requirements and in settling system operating parameters. Positioning and strength determination for anodes are based on a polarization response for the ship hull material. The determination of the appropriate polarization response for a shipboard system is not a trivial matter as previously noted. Aoki et al [6] has addressed the issue of determining the polarization response for a ship at sea. The polarization response of the hull is determined based on information obtained from sensor locations. A inverse problem is defined in which the polarization response is

5 Boundary Elements 833 site in Banks Channel near Wrightsville Beach, NC. Laboratory polarization response curves were used in the analyses. However, polarization response was reduced by 50% to account for observed fouling on the anodes on the model barge. It was* determined that this reduction was necessary for the accurate prediction of potential distributions and currents for coated and bare metal barges. Potential profiles were determined to be less sensitive to polarization accuracy than current values. In addition it was determined that relative trends in potential distributions can be accurately predicted even when current predictions are inaccurate. Real ship system data is limited. Another source of data for comparison is physical scale modeling, an experimentally based technique for design and evaluation of cathodic protection systems [9]. In physical scale modeling the geometry of ship hulls are exactly reproduced but at a reduced scale. The electrolyte conductivity is also scaled by the same factor. Two computational models have been completed for direct comparison with experimental results: a U S Navy destroyer [10-12] and aircraft carrier [13]. Coating damage is modeled as discrete damage locations defined by assigning metal polarization response to selected elements along the ship hulls. Damage locations correspond to cathodic areas defined on the experimental models. Two damage patterns have been analyzed: 2.8% and 15% of the hull surface area defined as bare metal. Static and dynamic flow polarization response curves were used to represent these test conditions. Extensive analyses were completed for single power supply systems and 2 subsystem 6 and 7 anode systems [10-12]. It was determined that a high degree of mesh refinement was required to obtain accurate current results. The mesh used for the destroyer analyses is shown in Figure 2. The aircraft carrier mesh has a similar degree of refinement. Figure 2: Boundary element mesh for U S Navy destroyer. Mesh refinement determined to be sufficient for current and potential calculation accuracy.

6 834 Boundary Elements the unknown and is determined through an series of boundary element analyses. The error between sensor measured values and calculated values at the sensor locations is minimized. Once the polarization response of the system is determined, anode strengths required to maintain target potential levels are readily calculated. In addition, the authors demonstrated the ability to locate a single damaged area location due to variations in sensor readings at two points in time. This discrete damage is determined by changes in sensor readings. This is in addition to the general degradation of coating integrity which would affect the polarization response at any point in time. Aoki et al [6] have provided a means for determining polarization response for an existing system which incorporates material interactions, coating damage, geometric effects, electrolyte composition and other environmental affects. Factors which make determining an appropriate polarization response difficult are included in the response determined by the inverse method. This is of major importance to the evaluation of existing systems. Changing polarization response with service conditions and time in service can be calculated. System parameters can then be determined based on the actual service conditions. 4 Case studies: comparison with experimental data Case studies are computational models which have emphasized comparison with experimental or shipboard data. These studies have resulted in increased understanding of the factors which must be carefully detailed in order to accurate predict system response. Zamani et al completed an analysis of a Canadian Navy destroyer and existing impressed current cathodic protection system [7]. An academic development boundary element code was used in the analysis. The propeller and rudder where not modeled as discrete surfaces but as an equivalent cathodic area defined on the ship hull. This eliminates any geometric interactions between the rudder, propeller and hull.. At the time of the analysis, the sensitivity of computational analysis to these factors was unknown. The hull surface was defined as a perfect coating with the exception of the equivalent cathodic area. There was not provision for coating damage. Laboratory obtained values of linear polarization response were used for the equivalent cathodic area. Potential profiles were calculated for defined anode strengths. These values were compared with measured values taken from the actual frigate when at dock. Even with the modeling simplification potential values have a maximum relative error of 6% when compared to ship data. No comparison was made for current values. In an effort to determine the sensitivity of the modeling process to environmental and spatial factors, a combined experimental and computational modeling project was completed by Hack [8]. A flat bottom rectangular barge was designed, built and modeled. The barge was instrumented so that potential profiles could be compared with computational results. The barge was maintained in natural seawater at a test

7 Boundary Elements 835 Analyses were completed for textbook values of polarization response, standard small sample laboratory specimen generated polarization responses and large scale open seawater plate generated polarization responses. The accuracy of polarization response was shown to be critical to accuracy of computational results as was noted in contemporary work by Hack [8]. Polarization data which most closely matched model conditions resulted in computational results which most closely matched model results. Calculated potential was less sensitive to polarization accuracy than current values. The destroyer ship hull model has been used for parametric studies which examine modeling small amounts of coating damage by scaling polarization response [11] and system performance for ranges of electrolyte conductivity possible during service [12]. These are numerical studies which utilize boundary element capabilities to determine system sensitivities. An analysis of U S Navy aircraft carrier was performed to verify guidelines established by the multiple stages of the destroyer analysis [13]. Complexity is increased by the analysis of the carrier s 3 subsystem 17 anode system. Experimental results indicate that there is a strong degree of interaction between the systems. This observation was verified during the iterative solution procedure. Representative comparisons between physical scale and computational results are shown in Figure 3. The success of this analysis indicates that guidelines can be established which allow for creation of models which accurately predict performance. I S1.5-i Figure 3: Dynamic flow and minimum damage conditions. Measurements taken at a depth of 10 feet. A frame is a unit distance along the length of the hull. Finally, a proposed design methodology which utilizes computational methods and physical scale modeling has been presented [14]. This procedure would use computational methods to determine a best system design. This design would then be generated as a physical scale model. Final modifications of anode and sensor placement would be determined from the experimental procedure. The advantages of both design systems would be combined to determine an optimal system. The primary advantage for use of

8 836 Boundary Elements the experimental procedure for final design is the independence from an assumed polarization response. While not applied to a ship hull, work on stray currents in electrochemical systems by Trevelyan and Hack [15] is applicable to ship systems. A standard boundary element formulation was modified to include an secondary electrical source, a astray current. Examples are presented for piping systems but the numerical formulation is applicable to ship cathodic protection systems. Stray current is an important issue when a ship is brought into the vicinity of another operating cathodic system such as may exist on a companion ship or on a dock. 5 Summary A considerable amount of computational modeling work on ship cathodic protection systems based on the boundary element techniques has been completed in the past decade (1987-present). Optimum design and case studies have firmly established the capabilities of boundary element approach. Results which are critical to the application of this technology to ship system design are: (1) Development of an algorithm to determine optimum anode location. (2) Development of an algorithm to determine optimum anode amperage values. (3) Development of an procedure to determine in situ polarization response of a ship hull. (4) Successful comparison of computational and experimental data for real ship geometries. Each achievement must be considered with the following in mind: (1) The accuracy of computational results depends on the accuracy of the polarization response for the service conditions. (2) Even an inappropriate polarization response can be used to determine trends in system performance. The ability to computationally determine optimum anode location provides a basis, other than designer expertise, for the design of new cathodic protection. This provides a rational analytical approach to the design of new systems. Systems can be designed to optimum protection levels even with less than accurate polarization response. Determination of optimum amperage to anodes to maintain protection levels is of interest but is not as significant as the ability to define optimum anode placement. This is primarily due to the uncertainty of polarization response. A less than accurate polarization response will have a significant affect on calculated current values. At the present time, inspection is the only means available for assessing damage to a coating. The ability to calculate the polarization response for the hull, which would include undamaged and damaged sections of coating, during

9 Boundary Elements 837 service is an important breakthrough. Damage assessment and health monitoring protocols can be developed based on this approach. The sensor population on existing systems is probably too sparse for useful information to be obtained. However, addition of sensors in strategic locations would be a low cost method to provide real time coating health monitoring. Comparison of computational and experimental results is essential to the transitioning of this technology to the design community. The ability to accurately reproduce experimental results is critical to the acceptance of any computational procedure. Use of physical scale model and other experimental data is important because of the scarcity of real ship data. Cathodic protection systems respond to their environment with a high level of synergism. Computational models which have been verified by comparison with experimental results are good tools for expanding the basic understanding of system interactions. Computational parameteric studies which isolate individual system characteristics can provide invaluable information to the designer. In closing, the use of boundary elements for design and evaluation of cathodic protection system has greatly matured during the past decade. One challenges for the future would be the adaptation of design algorithms, which have been demonstrated for relatively simple systems, to existing ship systems consisting of multiple subsystems. In addition, further demonstration of analysis capabilities through design studies on different hull geometries will provide additional evidence of the accuracy and advantages of using computational methods for the design and evaluation of ship cathodic protection systems. 6 References 1. Zamani, N. G, Porter, J. F. and Mufti, A. A., "A Survey of Computational Efforts in the Field of Corrosion Engineering " Int. J. of Numerical Methods in Engrg., Vol. 23, (1986). 2. Munn, R. S., "A Review of the Development of Computational Corrosion Analysis for Spatial Corrosion Modeling Through It's Maturity in the Mid 's," Computer Modeling in Corrosion, ASTM STP 1154, American Society Testing and Materials, (1991). 3. Zamani, N. G. and Chuang, J. M, "Optimal Control of Current in a Cathodic Protection System: A Numerical Investigation," Optimal Control y^/. af%/m;f/k%&, Vol. 8, (1987). 4. Hou, L S. and Sun, W, "Numerical Methods for Optimal Control of Impressed Cathodic Protection Systems," Int. J. of Numerical Methods in ##rg., Vol. 37, (1994). 5. Hou, L. S. and Sun, W, "Optimal Positioning of Anodes for Cathodic Protection," SIAM J. Control and Optimization, Vol. 34, No. 3, (1996). 6. Aoki, S., Amaya, K. and Gouka, K., "Optimal cathodic protection of ship/' Boundary Element Technology XI, R. C. Ertekin, C A. Brebbia, M.

10 838 Boundary Elements TanakaandR. Shaw (eds.), Computational Mechanics Publications, (1996). 7. Hack, H P., "Verification of the Boundary Element Modeling Technique for 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 Physical Scale Modeling with Shipboard Trials," Corrosion 90, Paper 370, National Association 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 Service Conditions," Boundary Element Technology VII, C. A. Brebbia and M. S. Ingber (eds.), Computational Mechanics Publications, (1992). 10. DeGiorgi, V. G, Kee, A. and Thomas, E. D, "Characterization accuracy in modeling of corrosion systems," Boundary Element XV, Vol. 1, C. A Brebbia and J. J. Rencis (eds.), Computational Mechanics Publications, (1993). 11. DeGiorgi, V. G and Hamilton, C P., "Coating integrity effects on impressed current cathodic protection system parameters," Boundary Elements XVII, C A. Brebbia, S. Kim, T. A. Osswald and H Power (eds.), (1995). 12. DeGiorgi, V. G, "Influence of Seawater Composition on Corrosion Prevention System Parameters," Boundary Element Technology XII, J. J. Frankel, C A. Brebbia and M. A. H. Aliabadi (eds.), Computational Mechanics Publications, (1997). 13. DeGiorgi, V G, Thomas, E. D, Lucas, K. E. and Kee, A., "Verification of scale effects of modeling of shipboard impressed current cathodic protection systems," Computers and Structures, in press (1997). 14. DeGiorgi, V. G, Thomas, E. D. and Lucas, K. E., "A Combined Design Methodology for Impressed Current Cathodic Protection Systems," Boundary Element Technology XI, R. C Ertekin, C. A. Brebbia, M. Tanaka and R Shaw (eds.), Computational Mechanics Publications, (1996). 15. Trevelyan, J and Hack, H P., "Analysis of stray current corrosion problems using the boundary element method," Boundary Element Technology IX, C A. Brebbia and A. J. Kassab (eds.), Computational Mechanics Publications, (1994)