DETC COMPUTER MODELING OF IMPRESSED CURRENT CATHODIC PROTECTION (ICCP) SYSTEM ANODES

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1 Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009 August 30 - September 2, 2009, San Diego, California, USA DETC COMPUTER MODELING OF IMPRESSED CURRENT CATHODIC PROTECTION (ICCP) SYSTEM ANODES Cristina Peratta CM BEASY Ltd Southampton, SO407AA. UK Andres Peratta CM BEASY Ltd Southampton, SO407AA. UK John Baynham CM BEASY Ltd Southampton, SO407AA. UK Robert Adey CM BEASY Ltd Southampton, SO407AA. UK ABSTRACT Computer modeling is now widely used to predict how effective cathodic protection (CP) systems are at protecting structures and maritime vessels. There are two types of CP systems based on either sacrificial anodes or impressed anodes (ICCP) or some combination of the two types. Impressed anodes are often referred to as active systems as they can respond to changes in the protection requirements as they are connected to some form of control system. Typically in computer models ICCP anodes are controlled by specifying the current they output in response to the potential measured at a reference electrode. In this paper an alternative approach has been investigated where the model also includes the power supply as well as the associated cables etc connecting to the anodes. This enables us to more accurately model situations where any number of anodes are connected to a single power supply, anode/reference electrode (RE) failure scenarios, non symmetric anode layouts, localized damage to coatings and situations where there are significant appendages to the vessel which change the current requirements. The paper will describe the technical approach to the modeling and present examples of modeling of a commercial FPSO vessel. (Floating, Production, Storage and Offloading vessels are used in the Oil & Gas industry typically as part of deepwater developments) The benefits of the proposed approach compared with the conventional approach will be presented and the results critically analyzed. INTRODUCTION The progressive advance of computational resources in the last few decades has made computer modeling of complex CP systems widely available. Nowadays, a computational modeling approach is not only one of the most effective tools for design and optimization of CP systems, but also for failure detection, monitoring, and quality performance assessment as recent advances in numerical methods have allowed the solution of increasingly larger and more complicated structures. There are two types of CP systems based on either sacrificial anodes or impressed anodes (ICCP) or some combination of the two types. Impressed anodes are often referred to as active systems as they can respond to changes in the protection requirements as they are connected to some form of control system. In general, the driving force of ICCP CP systems is the total electric current flowing from individual anodes to the metallic structure under control, which results from the voltage difference provided by the power supply. Typically in computer models ICCP anodes are controlled by specifying the current they output in response to the potential measured at a reference electrode. While this approach is adequate for simple ICCP systems it does not accurately represent the real physics, as when the power supply is supplying multiple anodes the output of individual anodes is a function of the resistance in the cables from the power supply to the anode, the resistance path through the sea water and the electrode kinetics which take place on interface between the metallic surfaces and the sea water. 1 Copyright 2009 by ASME

2 Therefore while the total current supplied by the power supply to the anodes is controllable the actual current flowing from individual anodes is dependent upon the effective resistance of individual anodes and therefore is unlikely to be equal to the other anodes except in special circumstances Basics Of Computational Modeling Of Cathodic Protection Systems The main objective of computational modeling applied to the direct simulation of CP systems with ICCP anodes is to obtain quantitative results for levels of protection against corrosion on the structure, while keeping into account the physical configuration of the surrounding environment and design parameters of the system, i.e. anode geometry, type, electrolyte conductivity, etc. Given input data that describes the physical and geometrical properties of the electrolyte anode sizes and locations reference electrode set points and locations condition of any coatings/paints polarization properties of the materials involved The outcome of the simulation is the current densities, overpotentials, and electric potential values at any point in the electrolyte and on the metallic surfaces. Figure 1 illustrates a typical example of conceptual model for simulating a CP system consisting of 4 ICCP anodes protecting a metallic structure. Both the anodes and the metallic structure are immersed in the electrolyte characterized by an electric conductivity k. The electrolyte can have either constant or variable conductivity with space. The anodes may be interconnected by means of a resistive network among them, which is powered by one or more transformer rectifier units (TRU). The TRU provides the electrical power that keeps the CP system operating. I 3 R 3 R 2 I 2 R 1 I 1 I t A 2 A 1 A 3 A 4 TRU METALLIC STRUCTURE ELECTROLYTE Figure 1. Schematic of a typical conceptual model for an ICCP CP system The scenario presented in Figure 1 can be regarded as composed of two coupled problems: the electrolyte and the external circuit. The former involves the electrolyte itself, and all the surfaces surrounding it, including the thin layer on the active electrodes and any other insulating surface bounding the electrolyte, while the latter involves the resistive network composed of discrete electrical components such as resistors, TRU, diodes, shunts, etc. In the problem defined by the external circuit, the TRU maintains a voltage difference Vt between the metallic structure and the anodes circuitry. The total current flowing throughout it (I t ) is consistent with the composition of all the currents flowing to each individual anode (I 1 to I N ) according to Kirchhoff equations for electrical networks. In particular in this scheme: I t = I + I + (1) 1 2 I 3 Problem Formulation The problem formulation for the electrolyte is based on the charge conservation equation in the bulk of the electrolyte under steady state conditions. The mathematical description of the problem is based on the 3D Poisson equation for the electrolyte potential with non-linear boundary conditions imposed by the prescribed polarisation curves on the active electrodes. The physical and mathematical background for the modelling can be taken from references [1, 2]. In the steady state case, the governing equation for the electrolyte becomes: x (2) where ( ( x) ) = 0 = x k ; Ω 1 V e, x 2, x 3 is the 3D gradient operator, and V e (x) is the electric potential in the electrolyte in a point x. The integration domain Ω of this problem is the electrolyte. Numerical Method The numerical approach for solving eq. (2) is based on the Direct Boundary Element Method (BEM) combined with the collocation technique [3]. Basically, following Green s identity, eq (2) for homogeneous conductivity is transformed into its integral formulation (3) which describes the potential at any point x in terms of sources distributed on the boundary Γ of the integration domain: G( x, y) cve ( x) + Ve ( y) dγ( y) n Γ (3) Ve ( y) G( x, y) dγ( y) = 0 n Γ where G(x,y) is the Green s function of Laplace equation, n is the outward unitary normal of the boundary of the integration domain, and c is a constant whose value is 0 if x is outside the 2 Copyright 2009 by ASME

3 integration domain, 1 if interior, and a value 0<c<1 which depends on the local curvature of the boundary if x Γ [3]. Boundary discretisation of eq. (3) combined with collocation technique leads to a algebraic linear system of equations, in which the unknowns are potentials and current densities normal to the boundary evaluated on the boundaries of the electrolyte. In cathodic protection models BEM has important advantages over the more widely used Finite Element Method (FEM) approach. Firstly, the BEM formulation is based on the solution of the leading partial differential operator, thus improving the numerical accuracy in comparison to artificial polynomial approximations. Secondly, the mesh discretisation of the BEM model is required on surfaces only, thus avoiding volume mesh discretisation. This feature helps to decrease the computational burden, especially in complicated geometries. Thirdly, in the standard BEM potential field and potential gradient are treated as independent degrees of freedom and are both involved in the formulation, hence the outcome of the calculation are both potential fields and current densities. In contrast, the outcome of calculations based on a standard FEM is the potential field; then the gradient has to be deduced from the potential result, which adds more inaccuracies to the calculation. Finally, the degrees of freedom are associated with potentials and current densities on the surfaces surrounding the electrolyte, rather than in the bulk of the electrolyte. This is quite appealing for electrochemical corrosion modelling where the electrolyte problem is driven by surface effects in the thin layers developed on the active electrodes. ICCP CONTROL SYSTEM MODELING The representation of ICCP anodes has in the past been achieved by simply applying the anode current as a boundary condition to the surface of the anode. While this technique is perfectly satisfactory for simple ICCP systems which have, for example, a single transformer rectifier unit (TRU) and a single anode (or anode pair arranged perfectly symmetrically), the same cannot be said for simulation of more complex systems. In a situation where there are multiple anodes connected to a single TRU, there is no reason why the current flowing through each anode should be the same. The method used in this paper to provide more realistic representation is to include the ICCP system in the model. The ICCP system is represented mathematically as a circuit including the TRU, distribution cables connecting it to each anode, and the return cable connecting the ship hull to the return of the TRU. The electrical circuit equations are solved to determine current flow and electrical potential throughout the system, taking into account cable resistance, and any additional resistances as appropriate. Current flow from the surfaces of the ICCP anodes into the surrounding electrolyte is described using a polarization curve. As usual, current flowing through the electrolyte is determined by solving the Laplacian equation, using the boundary element method. The entire process is nonlinear, and is solved iteratively. Figure 2: Showing the FPSO and the dielectric shields around the ICCP anodes 3 Copyright 2009 by ASME

The results of the mathematical modeling include the usual current density and protection potentials on all parts of the ship hull, but in addition include power loss, current and potential

. In this model, the ICCP anodes are circular with diameter 0.3 meters, positioned in groups of three on a rectangular dielectric shield.

4 The results of the mathematical modeling include the usual current density and protection potentials on all parts of the ship hull, but in addition include power loss, current and potential throughout the circuit. ICCP Control Of An FPSO The FPSO is modeled in its moored position, with mooring chain and various structures on the hull, as shown in Error! Reference source not found.. In this model, the ICCP anodes are circular with diameter 0.3 meters, positioned in groups of three on a rectangular dielectric shield. The surfaces of the anodes are assigned a polarization curve corresponding to a mixed metal oxide surface, which in this case has an open circuit potential of +1400mV (Ag/AgCl/seawater). required in practice. These factors are not important for the purposes of this paper. The as-constructed circuit is shown in Figure 4, where the various steel components are shown on the right hand side of the figure, the 36 anodes are shown on the left hand side in 12 anode groups, the TRU is shown in the middle of the figure, and the resistive connections between them can be seen. It is possible to define either the TRU current output, or the potential difference between the TRU supply and return connections. If the TRU output potential is defined, then clearly nothing will happen until the potential is big enough to overcome the effects of the Mixed Metal Oxide (MMO) polarization curve. In this study the dielectric shield and anodes are positioned slightly off the surface of the hull, to allow easy repositioning of the dielectric shield and / or anodes to take place with minimal effect on the mesh on the hull. This technique is useful when designing the ICCP system, because it allows easy investigation of different anode group positions. The geometry of the anode and the dielectric shield, together with the mesh, can be seen in Figure 3. Figure 4: The ICCP circuit is shown diagrammatically. The lines connecting the components show the resistance of the connections. Figure 4 shows the electrical connections in the model between the anodes (on the left), the TRU (in the center) and the FPSO (on the right). The electrical resistance of the connections between the components is shown next to the connection line. Figure 3: Showing the dielectric shield and ICCP anodes, with the boundary element mesh For this example, we have chosen to use a simplified polarization curve for the hull, which does not include hydrogen evolution sections of the curve. For this reason, the results show over-potential values which would not in reality be reached. Similarly, the total ICCP current used in these examples is somewhat arbitrary, and is probably higher than would be RESULTS The first comparison is between direct application of a current density to the anode surfaces (to represent power supplied to the anode) and the use of a complete circuit model of the ICCP system which includes the TRU and the cables. In this model the ICCP anodes are assumed to be fairly evenly spaced, and the cable resistances are taken to be zero. 4 Copyright 2009 by ASME

AG11 AG5 AG1 AG2 AG4 AG3 AG10 AG9 AG12 AG8 AG7 AG6 Figure 5: Showing location of the anodes groups Case1 Total current supplied to the anodes = 576 Amperes, distributed equally between each of the

Case 2 Total current supplied by the single TRU is 576 Amperes, but now the current is allowed to redistribute itself among the anodes. Contour of over-potential are shown as case 2 in Figure 8.

5 AG11 AG5 AG1 AG2 AG4 AG3 AG10 AG9 AG12 AG8 AG7 AG6 Figure 5: Showing location of the anodes groups Case1 Total current supplied to the anodes = 576 Amperes, distributed equally between each of the anodes. Contours of over-potential are shown as case 1 in Figure 8. Case 2 Total current supplied by the single TRU is 576 Amperes, but now the current is allowed to redistribute itself among the anodes. Contour of over-potential are shown as case 2 in Figure 8. It can be seen that there is very little difference in the distributions of potential in these two cases. However, when the output of the individual anodes is determined, it is found that whereas in Case 1 each anode delivers 16 Amps, by contrast in Case 2 the anode current ranges from 15 Amps to 16.5 Amps. This difference can be explained by the unsymmetrical distribution of the anodes and the area of metal to be protected. Case 3 In this case, the resistances of the supply cables are taken into account in the representation of the ICCP circuit, assuming that the connections are represented by a single cable supplying each of the three anodes in an anode group. The equivalent cable cross-sectional area is taken to be 100mm**2, and the cable resistance computed to be 1.935*10-4 Ohms/metre length. The cable lengths and corresponding resistances are shown in Table 1 and Figure 5 show the location of each anode group ( AG in the table). Anode group Cable length between anodes and supply [m] AG AG AG AG AG Cable resistance (Ohms) AG AG AG AG AG AG AG Table 1: Showing cable lengths and corresponding resistance When these cable resistances are included in the model, it is found the over-potential distribution is more significantly affected, with correspondingly bigger differences in the current delivered by individual anodes, which now range from 14.3 Amps to 17.4 Amps. Contours of over-potential near the bow of the vessel are shown in Figure 6 for this case, and are compared in the figure with over-potentials for case 1 (note the colour scale used in Figure 6 is not the same as in other figures). Figure 6: Comparison of potential vs Ag/Ag/Cl electrode for Case 1 (all anodes delivering 16 Amps) and Case 3 (ICCP circuit with cable resistances taken into account) 5 Copyright 2009 by ASME

The variation of the current delivered by each anode for cases 1 to 3 are shown in Figure 7, where anodes 1 to 3 are in anode group 1, anodes 2 to 6 are in anode group 2, and so on.

6 The variation of the current delivered by each anode for cases 1 to 3 are shown in Figure 7, where anodes 1 to 3 are in anode group 1, anodes 2 to 6 are in anode group 2, and so on. The effects of modeling the ICCP circuit are more clearly demonstrated in this figure Each anode same current ICCP circuit, with cable resistance ICCP circuit, but NO cable resistance In this case no attempt was made to balance the resistances of the connections between the TRU and the anodes. If this was done the differences would not be so large. Current [Amps] Case 4 In this case, the response of the two different approaches to the presence of an area of damage is assessed. The damage is on the starboard side, on the forward half of the vessel, and is represented as an area of bare metal 670 m**2 in extent. Contours of over-potential with each anode delivering 16 Amps are shown in Figure 9, in which the area of damage can be identified on the forward starboard side of the vessel (top right of the figure) as an area where contour colours are not shown because the over-potential has become more positive than the maximum of the scale, which is -800mV. Contours of overpotential for the case in which the ICCP circuit is modeled are very similar Anode Number Figure 7: Shows the variation of the individual anode currents for the case with no cable resistance and WITH cable resistance. As a reference the current on each anode is plotted when the current is uniformly distributed. (16mA each anode) The variation of current delivered by each anode when considering the ICCP circuit is modeled, is shown in Figure 10 for the cases with and without an area of damage. Figure 8: Comparison of over-potential for cases 1 and 2 (Case 1 has 16Amps delivered from each of the 36 anodes; case 2 has representation of the ICCP circuit with no cable resistance) 6 Copyright 2009 by ASME

Figure 9: Potential vs Ag/Ag/Cl/seawater, with total ICCP current 576 Amps, evenly distributed between the 36 ICCP anodes (ie 16 Amps each) ICCP circuit with cable resistance, damage ICCP circuit,

Total TRU current 579 Amps, with ICCP circuit modeled (anode current varies from 17.5 Amps to 20.6 Amps) 17.5 ICCP circuit with cable resistance Each anode same current (19.2Amps) 17 22.

7 Figure 9: Potential vs Ag/Ag/Cl/seawater, with total ICCP current 576 Amps, evenly distributed between the 36 ICCP anodes (ie 16 Amps each) ICCP circuit with cable resistance, damage ICCP circuit, with cable resistance Each anode same current, damage Each anode same current Figure 11: Over-potential with 2 anode groups not functioning. Total TRU current 579 Amps, with ICCP circuit modeled (anode current varies from 17.5 Amps to 20.6 Amps) 17.5 ICCP circuit with cable resistance Each anode same current (19.2Amps) ICCP circuit, with cable resistance and all the anodes 16.5 Current [Amps] Current [Amps] Anode Number 15 Figure 10: Shows the variation of individual anode current for the cases with and without cable resistance and with and without an area of damage. Total ICCP current is 576 Amps. As a reference the current on each anode is plotted when the current is uniformly distributed (16mA each anode) Case 5 Finally, in this case we determine the effect of a break of the cables supplying the two anode groups on the underside of the vessel near the bow. In this case, it is assumed the total current remains the same. Contours of over-potential are shown in Figure 11 and for the case where the ICCP circuit is modeled. There is not much difference in over-potential, between the cases considering uniform current distribution along the 30 remaining anodes with19.2 Amps each and the over-potential resulted when modeling the ICCP circuit with cable resistance. However, the current in the latter case has redistributed among the anodes, with anode current varying from 17.5 Amps to 20.6 Amps, as can be seen in Figure 12. The comparison for the case with all the anodes working has been included in the Figure as well Anode Number Figure 12: Variation of anode current when modeling the ICCP circuit with cable resistance with two not functioning anodes (1) and when all the anodes are working (2). Total ICCP current is 576 Amps. As a reference the current on each anode is plotted for the case of uniform distribution of current ( 19.2mA each anode) Finally, Table 2 shows the results for the potential at the reference electrode using the different approaches modeled for the case with an area of damage (case 4) and the case with two non functioning anodes (case5). ICCP system with cable resistance Uniform distribution of current among anodes CASE mv mv CASE mV mv Table 2 Potential at the reference electrode. (Located mid way along the ship) 7 Copyright 2009 by ASME

8 CONCLUSIONS With the new modeling capability reported here, a user is able to use the details of the ICCP circuit to determine: the output from each individual ICCP anode the potential predicted at the reference electrodes the effects of cabling resistance the way in which coating damage or component failure causes redistribution between the various anodes of the total current The results indicate for the case considered there is no major changes in the protection potential generated on the vessel but the output of individual anodes varies significantly which may impact the design of the anode and the scope of dielectric shields etc. The methodology of representing the anodes using potential control can produce significant differences in the potential measured at the reference electrode compared with anodes where the current is controlled. In this study no attempt has been made to model the control system and the set points at the reference electrodes. Its inclusion in the model may cause additional differences in the results, in particular the individual anode currents. A further benefit of the new approach based on potential control of the anode may become apparent when the vessel coatings degrade and more current is required. In particular changes may be required to the ICCP control system to ensure adequate protection. REFERENCES [1] Robert A. Adey and Seyyed Niku. Computer Modelling of Galvanic Corrosion, in Galvanic Corrosion. Harvey P. Hack, editor. ASTM Committee G-1 on Corrosion of Metals. ASTM International, 1988 [2] Pierre R. Roberge. Corrosion Engineering Principles and Practice. Mc Graw Hill. NY, Chicago, SF, Lisbon, London, Madrid, Toronto, [3] C. A. Brebbia, J.F.C. Telles and L.C. Wrobel. Boundary Element Techniques Theory and Applications in Engineering. Springer-Verlag. Berlin, Heidelberg, NY, Tokyo [4] R Adey, J Baynham, R Jacob, Prediction of interactions between FPSO and subsea cathodic protection systems. NACE Corrosion Conference. New Orleans. USA Copyright 2009 by ASME

Modelling Impressed Current Cathodic Protection of Storage Tanks

Modelling Impressed Current Cathodic Protection of Storage Tanks Andres Peratta 1, John Baynham 2, Robert Adey 3 1 CM BEASY, England, aperatta@beasy.com 2 CM BEASY, England, j.baynham@beasy.com 3 CM BEASY,