Comparison of Resistance to Cathode with Resistance to Ground in the Marine Environment

John Baynham

BEASY Ashurst Lodge

Southampton SO40 7AA United Kingdom

Tim Froome

BEASY Ashurst Lodge

Southampton SO40 7AA United Kingdom

ABSTRACT Anode resistance is a fundamentally important quantity which is used in all CP system design work in the marine environment. Established methods for calculation of anode resistance determine the resistance through the electrolyte between the anode surface and ground (or “remote earth”), and are based on analytical or approximate formulas. Such formulas are generally based on simplified anode geometry, such as long thin cylindrical bars, and may include effects of interference between multiple such bars grouped in fairly simple geometric patterns. Resistance to ground of real anode shapes may be very different from formula-based predictions even for single anodes, and computer-based simulation methods are now available to determine resistance to ground both readily and more accurately. While resistance to ground is a very useful measure of likely anode output, in particular when accurately calculated for groups of nearby anodes such as those mounted on a sled, it is nevertheless the case that resistance to ground may be unrepresentative of performance of the anodes delivering current to the cathodic surfaces of the structure on which they are mounted. This paper investigates resistance through the electrolyte between the anode surfaces and the surfaces of the cathode, using techniques which include polarisation effects on the cathode surfaces, and compares the resulting resistance to cathode with values of resistance to ground which have been determined using formulas and by computer-based simulation. Key words: Anode resistance, formula, simulation, resistance to cathode, interference

INTRODUCTION

Following modern recommended practices generally provides a conservative CP design, although interference between anodes on a single structure, or interference between anodes on adjacent structures can lead to problems, as discussed in earlier papers by the Authors1, 2. When overly conservative designs are not required, or when the degree of conservatism must be understood, there may be a need to use methods which give more precise understanding of effects which influence design. One of the key inputs into practical design methodologies in use today is the anode resistance, which is the resistance through the electrolyte from the surfaces of the anode “to remote earth”, or simply “resistance to ground”, which is the terminology used in for example the paper by Dwight which seems to have been the definitive source of practical formulae to determine such resistance3. Dwight identified two approximate formulae (based on the average potential method) as follows:

An equation which identifies that “resistance of a buried wire of length ‘2L’ and radius ‘a’, no part of which is near the surface of the ground” is:

1

4ln

4 a

L

LR

(1)

An equation which identifies that “resistance to ground of a vertical ground rod of depth ‘L’ and radius ‘a’” (ie the rod extends from the ground surface to depth “L”) is:

1

4ln

2 a

L

LR

(2)

Dwight states that these formulae are accurate to within 1% for a cylinder of the proportions of a ground rod, and he gives examples of ground rods of length 10 feet and diameter ¾ of an inch, for which a/L is 0.003125 (and the inverse L/a is 320) and recommends that if greater accuracy is required then an analytic formula given by Hallen should be used4. In reference 5 the author determined resistance for cylindrical ground rods with a range of L/a from 106 to 1, using the analytic formula by Hallen, the approximate formula shown in equation (2) above, and using boundary element-based simulation and concluded that:

simulation could be applied with confidence to any geometry

the analytic equation predicted values about 0.5% too high at L/a ~ 100 and about 80% too low at L/a =1

the approximate formula predicted values about 1.5% too high at L/a ~ 100, about 2.5% too high at L/a ~10, about 0.1% too high at L/a = 5, but about 54% too low at L/a =1

In the same paper the author showed that for a CP anode well away from the sea surface or any other surface, and of length 2m, height 225mm, and width varying from 265mm to 185mm (ie average width 225mm):

equation 1 under-predicts the anode resistance by about 1%

however if equation 2 above is (mistakenly) used, it over-predicts the anode resistance by nearly 26%

Similar results were shown in reference 1. Since equation 2 above is recommended for application to long slender stand-off anodes in for example reference 6, its use is one possible source of conservatism.

To quantify the degree of such conservatism, this paper first explores how distance from the sea surface affects resistance to ground for the anode described above, and makes comparison with resistance calculated using equations recommended in DNV and NACE recommended practices6,7. In fact DNV does not suggest use of different formulas (for calculation of anode resistance) based on depth of the anode below the sea-surface, but it does suggest different equations depending on separation distance between the anode and the surface on which it is mounted. This is presumably a recognition of the blocking effect (similar to that of the sea-surface) caused by the structure surface. It appears that NACE does suggest use of a different equation for “deep sea submerged” anodes, but does not seem to give indication of the depth at which the switch from one equation to the next should be made. The NACE recommended practice7 does not mention distance between the anode and the surface on which it is mounted. The investigation therefore refers to “stand-off” distance, and this could be interpreted as distance from the sea surface or distance from a surface on which an anode is mounted. Since in reality anodes deliver current to generally very close structures, it seems likely that resistance through the electrolyte to the close structure will be smaller than the anode resistance to ground, and if so then use of resistance to ground is another source of conservatism. Therefore this paper secondly explores how resistance between an anode and cathode may be determined, and attempts to explain trends observed in the results. Finally we consider interference effects between multiple anodes. In all examples the electrolyte resistivity is taken to be 30 Ohm-cm.

RESULTS Resistance to ground of a typical CP anode positioned at various distances from the sea surface The anode dimensions used to determine resistance to ground are shown in Figure 1. The anode was positioned with its long axis horizontal, and with its 265mm-wide face parallel to the sea surface at various “stand-off” distances (as noted above, here “stand-off” is used to mean distance from the sea-surface).

Figure 1: Dimensions of the anode used to determine effects of distance from the sea-surface

Results are shown in Figures 2 to 4, from which the following observations can be made:

The anode resistance to ground determined according to DNV recommended practices is bigger than the actual resistance (determined using simulation) for distance from the sea surface less than 300mm and greater than about 550mm.

It appears that the DNV recommended practice produces resistance which is non-conservative for stand-off distances from 300 to about 550mm!

Figure 2: Showing variation with stand-off distance of resistance obtained by simulation (blue line) and comparison with equations (1) and (2)

Figure 3: Blue line: variation of anode resistance to ground obtained by simulation with stand-off distance and comparison with resistance calculated using DNV recommended practice

Figure 4: Showing variation of resistance obtained by simulation with stand-off distance and

comparison with resistance calculated using formulas identified by NACE

The over or under-prediction when using the DNV recommended practices is shown in Figure 5:

Note that the step-changes seen in this figure result from a switch from one equation to another, and that it has been assumed that the “flush-mounted” equation should be used for stand-off distances less than 150mm.

The over-prediction is about 36% for a flush mounted anode (zero stand-off distance) and about 20% for an anode at stand-off distance just less than 300mm

There is under-prediction of about 8% at stand-off distance just greater than 300mm

The prediction is right at stand-off distance about 550mm

At stand-off distance 1000mm the over-prediction is about 8%, increasing to about 27% at stand-off distance 50m

Figure 5: Percentage over-prediction of anode resistance to ground determined using DNV

formulas when compared with resistance obtained using simulation. Negative indicates under-prediction. The over-prediction increases to about 27% at stand-off distance 50m.

The over or under-prediction calculated using the formulas mentioned by NACE7 are shown in Figures 6 and 7. Note that as no range of stand-off distance seems to be identified in the NACE recommended practice, the figures show three curves over the entire range of stand-off distances used in the simulation.

All three of the NACE formulas (against which comparison has been made) in fact under-predict at zero stand-off distance, by about 17% for the McCoy formula, by about 26% for the Dwight formula (equation 2 in this paper) for ground rods (equation D1 in reference 7), and by about 43% for the Dwight formula (equation 1 in this paper) for anodes remote from the sea surface (equation D8 in reference 7).

The McCoy formula begins to over-predict resistance at stand-off distance about 180mm, and over-predicts by about 20% at stand-off distance 1000mm, increasing to about 40% at 20m or above. This confirms the advice given in reference 6 that the McCoy formula should be used for flush-mounted anodes.

The Dwight formula for ground rods (equation D1 in reference 7) begins to over-predict at stand-off distance about 550mm, and this increases to about 8% at 1000mm and about 27% at distance 50m.

The Dwight formula for anodes well away from the sea surface (shown as “NACE equ D8” in the figures) under-predicts at all stand-off distances, by about 43% at zero distance, 17% at distance 1000mm, 6% at distance 5m and 2% at distance 50m

Figure 6: Showing percentage over-prediction of anode resistance to ground determined using NACE formulas when compared with resistance obtained using simulation. Negative indicates

under-prediction.

While recognizing that stand-off distances from a structure are not generally greater than about 0.5m if the anode is mounted directly on the structure, the above data does show that application of any formula will result in incorrect prediction under some or other circumstances. Calculation of resistance to ground of an anode at a particular stand-off distance from a structure could readily be determined using simulation, for an anode at any selected depth in the seawater.

The next section shows results of such calculation, and compares with the resistance between an anode and the nearby cathode.

Figure 7: Showing percentage over-prediction of anode resistance to ground determined using NACE formulas when compared with resistance obtained using simulation. Negative indicates

under-prediction.

Resistance of an anode positioned at various distances from the sea surface and from a tank surface The anode (diameter 200mm and length 1.5m) is positioned vertically at various distances below the sea surface and at various separation distances between it and a nearby cylindrical tank (diameter 5m, extending from the sea surface to 20m below the sea surface). A parameter study was performed in which separation was varied from 0.05m to 10m, and distance below the sea-surface was varied from 0.05m to 10m. Three of these configurations are shown in Figure 8.

Figure 8: Three of the configurations used to determine anode resistance.

Anode resistance to ground was found by applying a potential difference between the anode and a boundary a very long way (200km) from the anode. In this case the tank is an insulating surface which forms a barrier to current flowing from the anode to ground (and therefore increasing the anode resistance to ground). Apart from the presence of the barrier (the tank), resistance determined this way is equivalent to resistance to ground calculated by the design formulas. In general this method produces current density which varies with position on the anode surface, for example the current density will be greater at corners or edges of the anode. Resistance to “the local cathode” was found by applying a potential difference between the anode and the tank. In this case all current flows from the anode to the cathode. This resistance through the electrolyte from the anode to the cathode is not the same as “anode resistance to ground” calculated by the design formulas. This method produces current density which varies with position on the surfaces of both the anode and the cathode. Regarding Figure 9, which shows variation of anode resistance to ground with depth of the anode below the sea surface, for anodes at various distances from the tank, it is noted that:

The difference between the curves for “distance 0.05m from tank” and “distance 10m from tank” is a consequence of the greater blocking effect when the anode is close to the tank surface.

Since in this figure the curves for distances 5m and distance 10m from the tank are indistinguishable, it appears from this example that the blocking effect of the tank extends no further than the diameter of the blocking structure.

From the shapes of each curve, it can be seen that the blocking effect of the sea-surface diminishes very rapidly until the anode is about 1m below the surface, and then progressively more slowly at greater depths.

Figure 9: Variation of resistance to ground with distance below the sea surface, for various separations between the anode and the tank.

Figure 10 shows that:

Resistance to cathode increases with distance of the anode from the cathode (simply reflecting the increased distance the current has to flow)

When the anode is close to the tank surface, resistance through the electrolyte to the cathode (ie tank) is hardly affected by depth below the sea surface.

Figure 10: Variation of resistance to the local cathode (ie the tank) with distance below the sea

surface, for various separations between the anode and the tank.

Figure 11 shows how anode resistance (both to ground and to local cathode) varies with separation between the anode and the tank. The pairs of curves (R to ground, and R to cathode, at any depth below the sea surface) converge as separation between the tank and anode increases, until at 10m separation there is little difference between the two resistance values. The pairs of curves (eg red and green) demonstrate that when the anode is moved closer to the tank:

The presence of the tank increases the value of resistance to ground, because the tank acts as a barrier between the anode and remote earth.

By contrast the value of resistance to local cathode becomes smaller, because the path through the electrolyte from the anode to the tank is shorter.

Based on calculated resistance to ground, it would be concluded that an anode 10m from the tank would deliver more current than a flush mounted anode. However, based on resistance to the local cathode, the reverse is true.

Figure 11: Variation of resistance to ground and the local cathode (ie the tank) with separation

between the anode and the tank, for various distances of the anode below the sea surface. Figure 12 shows that as distance increases further:

Resistance to ground changes very little (since the barrier effect reduces as separation increases)

Resistance to cathode increases, and eventually becomes bigger than resistance to ground calculated using the Dwight ground rod formula. The reason for this is that whereas the Dwight formula takes account only of the “constriction effect” near the anode, the resistance to cathode calculation takes account of an additional constriction effect near the cathode. Note that a constriction effect occurs at the anode because at that position flux lines congregate, consequently causing rapid IR drop in that area. When anode to cathode spacing is not great, a constriction effect does not occur at the cathode, because flux lines do not converge close to the cathode. However, when spacing (between anode and cathode) is large enough the flux lines to the local cathode first diverge and then converge again. By contrast, in calculation of resistance to ground the flux lines continuously diverge as the current from the anode flows to “infinity”.

Figure 12: View 2 of variation of resistance to ground and the local cathode (ie the tank) with separation between the anode and the tank, for various distances of the anode below the sea

surface.

Effect of electrode kinetics on resistance (to local cathode) of an anode at fixed positioned near a tank In this example, the anode (of diameter 250mm and length 3.0m) is positioned vertically at mid-depth of a nearby cylindrical tank (of diameter 5m, extending from the sea surface to 10m below the sea surface) as shown in Figure 13. Anode resistance to local cathode was in this example determined using a fixed potential on the anode, but applying a polarisation curve (which represents the relationship between potential and current density) to the cathode surface. Use of the polarisation curve results in values of potential which vary with position on the cathode surface, as well as values of current density which vary with position on the cathode surface.

Figure 13: Anode at mid-depth near a tank with coated surface.

The effects of coating of varying quality was investigated by scaling the current density of the polarisation curve, by a factor which is simply the value of the assumed coating breakdown factor (called “bf” from here on). For example if the bf is 1% the current densities were multiplied by factor 0.01. Multiple solutions were obtained, using bf values ranging from 1% to 100%. Resistance to local cathode was calculated using the expression:

V

i

R

1

Where:

δi is current flowing into a small element of area on the cathode surface ΔV is the difference between potential on the small element of area and the anode

and the summation is carried out over the entire surface of the cathode. The path of current flowing from selected points on the anode surface was determined. These “flux-lines” are shown in Figures 14 to 16, from which it can be seen that for 100% breakdown factor (bare steel) the flux-lines go more directly from the anode to the tank, while for smaller breakdown factors the flux-lines extend further away from the anode.

Figure 14: Change of flux-lines as coating breakdown factor (“bf”) decreases: Top left:

bf=100%, bottom right: bf=1%.

Figure 15: Change of flux-lines as coating breakdown factor decreases: Top left: bf=100%,

bottom right: bf=1%.

Figure 16: Change of flux-lines as coating breakdown factor decreases:

Red: bf=100%, Green: bf=1%.

Clearly resistance of the electrolyte between the anode and the cathode is affected by the path followed by the current, a longer path leading to increased resistance. Consider:

It is obvious that if (say) the half of the cathode near to the anode was perfectly coated (so that no current passes into the perfectly coated surface) then the path followed by the current flowing to the remainder of the cathode is longer, so that anode to local cathode resistance is increased.

By extension, a resistive coating which modifies the distribution of current density and potential on the surface of the cathode will also cause the anode to local cathode resistance to increase.

Electrode kinetics (represented by a polarisation curve) similarly modify the distribution of current density and potential on the surface of the cathode, and so also causes the anode to local cathode resistance to increase

This is why in Figure 17 the resistance shown by the green curve at 100% breakdown factor (ie bare metal) is not the same as the resistance (shown by the blue curve) calculated using a fixed potential difference between the anode and the cathode The green curve confirms that for a coated cathode to which a polarisation curve has been applied, a smaller coating breakdown factor- indicating better coating - will lead to bigger resistance.

Figure 17: Anode resistance calculated in various ways. Green line: variation of resistance to

coated cathode with change of coating breakdown factor

The green curve in Figure 17 shows that for this anode and cathode, resistance (determined using a polarisation curve applied to a coated cathode with various breakdown factors) lies in between the resistance to ground calculated using the Dwight equation for an anode remote from the sea surface (equation 1 in this paper) and the resistance to local cathode determined by simulation using fixed potential on the anode and cathode surfaces. The implications of this are that:

Although both of the Dwight equations for resistance to ground (equations 1 and 2 in this paper) over-predict resistance between the anode and the cathode, the equation recommended by

references 6 and 7 (same as equation 2 in this paper) over-predicts by a particularly high amount.

The consequence of such over-prediction of resistance is that anode output will be higher than predicted

The practical consequence is that anode life will be over-estimated – ie the anodes will not last as long as they were intended to do.

The flux-lines shown in Figures 14 to 16 contrast strongly with that obtained during calculation of resistance to ground (Figure 18), but are similar to those obtained during calculation of resistance to local cathode using a fixed potential difference (Figure 19).

Figure 18: Flux-lines overlaid on contours of potential, showing the barrier effect of the insulated tank in calculation of resistance to ground

Figure 19: Flux-lines overlaid on contours of potential, showing the effect of the tank in

calculation of resistance to local cathode when using fixed potential on both the anode and cathode surfaces

Figure 17 shows that the resistance to ground -determined taking into account the barrier effect of the insulated tank- is smaller than the resistance to ground calculated using the Dwight equation for a ground rod. This is surprising since the barrier effect of the tank should increase anode resistance to ground. To investigate this apparent anomaly, the calculations were repeated:

Firstly using an anode of the same length (3m) but smaller diameter (10mm) positioned at the same depth as shown in Figure 13. The purpose of this test is to determine the effect of using an anode of dimensions similar to those for which Dwight derived his formulas.

Secondly with the 10mm diameter anode extending down from the sea surface. The additional purpose of this test is to determine whether the apparent anomaly is caused by the “surface effect”.

Table 1 compares the resulting resistances with values calculated using the two Dwight formulas (equations 1 and 2 in this paper). As expected, the barrier effect of the tank causes resistance (obtained with the anode positioned at the sea surface) to be higher than resistance calculated using the appropriate Dwight formula (equation 2 in this paper – the formula for a ground rod). This means that the apparent anomaly is not real, and is a consequence of the inaccuracy of this Dwight formula when applied to anodes positioned below the sea surface (only 3.5m between sea surface and top of anode in this case). These results firstly confirm that equation 2 (recommended in references 6 and 7) does not provide an accurate representation of anode resistance to remote earth if the anode is away from the sea surface, and secondly demonstrate that equation 2 can in fact be non-conservative if there are structures which can act as barriers to current flow from the anode to remote earth.

Method Resistance (Ohms)

Simulation, anode at surface, tank acting as barrier 0.1128

Dwight formula (ground rod) (Equation 2 in this paper) 0.1080

Simulation, anode 3.5m below surface, tank acting as barrier 0.1022

Dwight formula (anode remote from sea surface) (Equation 1 in this paper) 0.0969

Table 1: Resistance to ground of anode of length 3m and diameter 10mm, determined using different methods.

Resistance of an anode positioned inside a tank In this example the anode (of diameter 250mm and length 3.0m) is positioned vertically at mid-depth inside a cylindrical tank (diameter 5m, with internal water depth 10m) as shown in Figure 20.

Figure 20: Geometry of the tank and anode inside the tank

This example was solved firstly using a fixed potential difference and secondly by using a polarisation curve applied to a coated cathode surface with various coating breakdown factors. Resulting resistance is shown in Figure 21 together with “anode resistance to ground” calculated using the two Dwight formulas (equations 1 and 2 in this paper).

As expected Figure 21 shows that for a coated cathode to which a polarisation curve has been applied, a smaller coating breakdown factor- indicating better coating - will lead to bigger resistance.

Figure 21: Anode resistance calculated (a) using fixed potential on anode and cathode (b) with fixed potential on the anode and a polarisation curve applied to the cathode (assumed coated with coating breakdown factor varying from 0.5% to 100%) (c) using the Dwight formula for a

ground rod (equation 2 in this paper) and (d) using the Dwight equation for an anode away from the sea surface(equation 1 in this paper)

As in Figure 17 (which was for an anode outside the tank) the green curve in Figure 21 shows that for this anode and cathode, resistance determined using a polarisation curve (with various breakdown factors) lies in between the resistance calculated using the Dwight equation for an anode remote from the sea surface and the resistance determined by simulation using fixed potential difference between the anode and the cathode. However a significant difference is that for the anode inside the tank (Figure 21) the resistance is much closer to that found using a fixed potential difference, and becomes equal to it at breakdown factor about 50%. This different behaviour is an indication that in this case (anode inside the tank) change of coating breakdown factor does not modify the path followed by the current flowing to the cathode as much as in the example with the anode outside the tank. For example with a long anode inside a long tank the current flow would be purely radial regardless of the coating breakdown factor. It seems logical that for an anode inside a structure, anode resistance to cathode is of greater relevance than anode resistance to ground.

Effect of cathode size on anode resistance to cathode Here the anode used in the previous section (ie diameter 250mm and length 3.0m) is positioned vertically at mid-depth of a nearby cylindrical tank. The tank extends from the sea surface to 10m below the sea surface, but has various diameters. The anode is in all cases separated from the tank by distance 1.0m. A potential difference was applied between the anode and the cathode. Figure 22 shows that the effect of cathode diameter on resistance between the anode and the cathode is to cause the resistance to increase as the cathode size reduces. The increase in this case results from the way the flux-lines are “squeezed together” when the cathode diameter is small – a constriction effect which is well recognized.

Figure 22: Variation with tank diameter of resistance to local cathode

Effects of interference between anodes on resistance to local cathode This example uses 22 anodes (of diameter 200mm and length 1.5m) positioned on the outer surfaces of a cylindrical tank (diameter 5m, extending from the sea surface to 20m below the sea surface). In one case the anodes are well-separated (shown on the left in Figure 23), and in another the anodes are grouped together on one quadrant of the tank (shown on the right in Figure 23). The resistance to cathode was determined using a fixed potential applied to the anode surface and a different fixed potential applied to the cathode surface. Resulting contours of current density are shown in Figure 23. Resistance of an individual anode was determined by dividing the applied potential difference by the current flowing from the anode.

Figure 23: Two layouts of 22 anodes, Left: anodes well-spaced, Right: Anodes clustered

together

With well-spaced anodes:

Resistance of the anodes on the side of the tank was almost the same at 0.0527 Ohms for all anodes

Resistance of the two anodes on the bottom of the tank was 0.0524 Ohms

Resistance of all anodes (in parallel) to the tank was 0.00239 Ohms With anodes clustered in one quadrant there was some very slight variation for the bottom two rows of anode, but in general terms:

Resistance of the anodes on the side of the tank was 0.0546 Ohms for those on the edge of each group of 4

Resistance of the anodes on the side of the tank was 0.0564 Ohms for those at the middle of each group of 4

Resistance of the two anodes on the bottom of the tank was 0.0585 Ohms

Resistance of all anodes (in parallel) to the tank was 0.00253 Ohms

Thus the resistance to cathode method shows that as a result of interference between anodes, output of the design with anode clustered in one quadrant will be reduced by about 6% compared with the design with well-spaced anodes.

CONCLUSIONS

Firstly this paper has shown that anode resistance to ground, calculated using the recommended formulas and practices, is in some cases too high and in other cases too low. The practical implications of this could (depending on circumstance) include either:

Lower anode output than expected (and hence more positive protection potentials)

Or higher anode output than expected (and hence reduced anode life)

Secondly the paper has shown that whereas resistance calculated using the recommended formulas is a constant that is determined using only anode dimensions and electrolyte resistivity, anode resistance to ground determined using simulation can take into account:

Depth of the anode below the sea surface

Barrier effects caused by other structures

Interference between anodes Thirdly this paper has discussed the concept of anode resistance to cathode, determined either using fixed potential difference or using polarisation curves, and has gone on to show that whereas anode resistance to ground (whether calculated using formulas or by simulation) is based only on size and position of the anode(s), resistance to cathode also takes into account geometry of the cathode and position of the anode(s) relative to the cathode. This paper has sought to raise awareness that, as a result of advances in simulation technology:

alternative methods of calculating anode resistance have become available

these alternative methods may be useful when designing a CP system

these simulation methods may be more accurate than previous methods.

REFERENCES 1. T. Froome, J. Baynham, “Assessing Interference Between Sacrificial Anodes on Anode Sleds”, NACE 2013 [Orlando, Florida], paper number 2344. 2. J.Baynham, T.Froome, “Interference between sacrificial CP systems in the marine environment”, NACE 2016 [Vancouver, Canada], paper number 7797. 3. H.B. Dwight, “Calculation of Resistances to Ground,” Electrical Engineering, December 1936: p. 1319. 4. E. Hallen, “Losung zweir Potentialprobleme der Elektrostatik” Arkiv fur Matematik, Astronomi och Fysik, v 21A, No 22, 1929 Stockholm. 5. J. Baynham, “Mathematical Modelling of Cathodic Protection Anode Currents - comparison with classical equations, and the impact of interference effects for anode sleds”, presented at the Marine Corosion Forum meeting in October 2012., held at Lloyd’s Register, London. 6. DNV-RP-B401 (October 2010), “Recommended Practice DNV-RP-B401, Cathodic Protection Design”. 7. NACE Standard RP0176-2003, “Standard Recommended Practice, Corrosion Control of Steel Fixed Offshore Structures Associated with Petroleum Production”. ISBN 1-57590-170-6, NACE International