1

Modelling Impressed Current Cathodic Protection of Storage Tanks

Andres Peratta1, John Baynham

2, Robert Adey

3

1CM BEASY, England, aperatta@beasy.com

2CM BEASY, England, j.baynham@beasy.com

3CM BEASY, England, r.adey@beasy.com

Abstract

This work is focused on the simulation of the type of ICCP system in which a grid of anode

ribbons and distribution bars, buried below the base of a tank, is supplied with power from a

transformer rectifier unit. Current flows from the anode ribbons through the wet sand in

which they are embedded, to the base of the tank, and then back to the TRU.

The ICCP system is represented mathematically as a circuit including the TRU, distribution

cables connecting it to a number of distribution bars, an array of anode ribbons welded to the

distribution bars, and the return cable connecting the tank base to the return of the TRU. The

electrical circuit equations are solved to determine current flow and electrical potential

throughout the grid of anode ribbons and distribution bars. Current flow from the surfaces of

the anode ribbons into the surrounding electrolyte, and from the electrolyte into the surface of

the tank base, is described using polarization curves, which encapsulate the non-linear

relationship between current density and potential difference across the metal / adjacent

electrolyte junction. Current flowing through the electrolyte is determined by solving the

Laplacian equation, using the boundary element method. The entire process is non-linear, and

is solved iteratively.

The results of the mathematical modelling include current density and protection potentials on

all parts of the tank base, as well as power loss, current and potential throughout the circuit.

Using the boundary element method means that potential and current density can be

accurately calculated anywhere inside the sand, so providing information about the potential

at any reference electrode position.

Although modelling a fully functioning system allows assessment of whether or not a

particular ICCP design will work, it is valuable in addition to be able to determine the effects

of damage or degradation of system components. Consideration is made in the paper of the

effects of poor welds and broken connections for a particular ICCP system, with the aims

firstly of determining whether the system can perform properly despite the damage, and

secondly of evaluating effects of remedial modifications to the system. Investigation is made

into the TRU output required to provide some minimum level of protection everywhere on the

tank base, and corresponding reference electrode readings are established. Finally, the paper

compares performance of a number of different ICCP system designs applied to protection of

a tank, and attempts to select the “best” design based on considerations like uniformity of

potential, and greatest degree of over-protection.

Keywords: ICCP; modelling; circuit; tank-base; design

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Introduction

The protection of Tank bottoms with secondary containment membrane is typically

performed with Impressed current cathodic protection (ICCP) systems which may consist of

a linear distributed anode, made of mixed metal oxide activated titanium anode strips (mesh

or ribbon type) connected to titanium current distributors. Mistakes in design are frequent,

including excessive spacing between the anode strips and/or between the current distributors

or insufficient number of feeding connections between the power supply and the current

distributors.

All these factors can have a negative impact upon the performance of the ICCP system

resulting in uneven distribution of the protection potential on the tank base or in the worst

case enhanced corrosion of the tank base. The other important factor is the economic

consequence of over design of the system which can be considerable where many tanks are to

be protected.

The optimal design of a CP system for a particular structure and environmental condition is

not trivial. In the majority of cases, computational modelling is the leading edge technology to

properly address this problem as it can quickly consider many design options and the impact

of different soil or electrolyte conditions. This technology combined with experience and field

data from similar system can be used to determine the optimum design which provides good

protection of the tank while minimising the cost.

The progressive advance of computational resources in the last few decades has made

computer modelling of complex CP systems widely available. Nowadays, a computational

modelling 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 [1-4, 8].

The driving force of an ICCP system is the total electric current flowing from individual

anodes to the metallic structure, 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.

This approach is adequate for ICCP systems where a certain current is impressed in each

distinct individual anode; however this approach cannot be extended to the case when a single

power source is supplying multiple anodes or where the anode is distributed (eg a grid). In

these cases, the output of individual anodes (or parts of the distributed anode) is a function of

the resistance in the cables from the power supply to the anode, the resistance path through

the soil, the resistance in the distributed anode, and the electrode kinetics which take place on

the interface between the metallic surfaces and the soil. Therefore while the total current

supplied by the power supply to the anodes is controllable the actual current flowing from

individual anodes (or parts of a distributed anode) is dependent upon the effective resistance

of those anodes.

While general purpose cathodic protection modelling packages such as BEASY can be used

to model tank bottom ICCP systems the effort required to build the model and define all the

data is relatively time consuming particularly when a number of design options such as the

spacing of the anode grid are to be considered. In this paper a new modelling tool is described

which has been developed specifically for the design and optimisation of tank base ICCP

systems.

The main objectives of this work are to show that simulation during the design stage of a

tank-base ICCP system can be of considerable benefit to the designer, that simulation results

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can assist in initial set-up of a system, and that simulation can be used to investigate the fault-

tolerance of a design, its ability to perform adequately despite occurrence of faults, and the

effects of any planned remedial actions.

The modelling approach is based on the fundamental equations of electro-neutrality for the

electrolyte, surface distribution of polarization in the active electrodes in contact with the

electrolyte as prescribed by the governing electrochemistry, as well as Ohm’s law and charge

conservation equation for the electrical network interconnecting power supply units, anodes,

discrete resistors, etc in the external circuit.

The modelling approach is based on the boundary element method (as described in [1]). The

simulation considers non linear polarization curves and three dimensional potential and

current flow distributions throughout the electrolyte.

The remainder of this paper includes:

• A description of the mathematical techniques used

• Description of software facilities required to make an effective tool for Designers

• Some details of the GUI system used to generate models and results shown in this

paper

• Sections showing application of the methodology:

o to compare performance of several ICCP system designs

o to investigate suitable choice of set point for a selected ICCP system, with

correlation to potentials on the tank base

o to investigate the fault-tolerance of an ICCP system

o to investigate the impact of remedial actions planned to mitigate the effects of

component failure

• Discussion of the results

• Some conclusions

Basics Of Computational Modelling Of Cathodic Protection Systems

This work is focused on the direct simulation of CP systems with ICCP anodes. The main

objective of the simulation is to obtain quantitative results for levels of protection against

corrosion on the structure by considering the physical configuration of the surrounding

environment and design parameters of the system, i.e. anode geometry, type, electrolyte

conductivity, etc.

In general the input data for a model of a CP system consists of the following:

• physical and geometrical properties of the electrolyte

• anode geometry (sizes and locations)

• reference electrode set points and locations

• condition of any coatings/paints

• polarization properties of the materials involved as active electrodes

The outcomes of the simulation are the current densities and protection-potentials on the

metallic surfaces, electric potential and gradient values at any point in the electrolyte, and

voltage and current in the components of the circuit.

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Figure 1 illustrates a typical example of a 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 conductivity or conductivity which varies with position.

The anodes may be interconnected by means of a resistive network, which is powered by one

or more transformer rectifier units (TRU). The TRU provides the electrical power that keeps

the CP system operating.

A3A4

A2

A1

STRUCTURE

METALLIC

R2

R3

R1

It

TRU

ELECTROLYTE

I1

I2

I3

Figure 1: Schematic of a typical conceptual model for an ICCP 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 through it

(It) is consistent with the composition of all the currents flowing to each individual anode (I1

to IN) according to the Kirchhoff equations for electrical networks. In particular in this

scheme:

321 IIIIt ++= (1)

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 description of the problem is based on the 3D Poisson equation for the electrolyte

potential with non-linear boundary conditions imposed by the prescribed polarization curves

on the active electrodes. The physical and mathematical background for the modelling can be

taken from references [5,6].

In the steady state case, the governing equation for the electrolyte becomes:

( ) 0)( =∇−⋅∇ xeVk ; Ω∈x (2)

where ( )321 ,, xxx ∂∂∂∂∂∂=∇ is the 3D gradient operator, and Ve(x) is the electric potential

in the electrolyte at point x with respect to remote earth. The integration domain Ω of this

problem is the electrolyte.

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Numerical Method

The numerical approach for solving eq. (2) is based on the Direct Boundary Element Method

(BEM) combined with the collocation technique [7].

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:

0)()(

),( )()(),(

)( =Γ∂

∂−Γ

∂

∂+ ∫∫

ΓΓ

yy

yxyyyx

x dn

VGdV

n

GcV e

ee (3)

where G(x,y) is the Green’s function of the Laplace equation, n is the outward unit normal to

the boundary of the integration domain, and c is a constant whose value is 0 if x is outside the

integration domain, 1 if interior, and a value 0<c<1 which depends on the local curvature of

the boundary if Γ∈x [7].

Boundary discretisation of eq. (3) combined with the collocation technique leads to an

algebraic linear system of equations, in which the unknowns are potentials and current

densities normal to the boundary evaluated on the surfaces 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 outcomes 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; the gradient has to be determined

by differentiation of the potential, a process which inevitably adds more inaccuracies to the

solution.

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.

The boundary conditions applied to surfaces of the electrolyte in contact with active

electrodes consist of polarization curves, of the form:

)(ˆ

Vfn

Vkj e

n ∆=∂

∂−= , (4)

which relate the normal current density flowing to throughout the surface (nj ) to the potential

drop across the interface metal/electrolyte (me VVV −=∆ ), where Vm is the potential in the

metal with respect to remote earth.

The function f, usually containing exponential factors of V∆ as prescribed by Butler-Volmer

type equations, is in general non-linear and considered as an assembly of linear functions. The

data points coming from potentiodynamic measurements are interpolated with piecewise

linear functions. For example, the function between two consecutive data points i and i + 1 is

approximated by iiin Vbaj ∆+= , where a and b change from interval to interval, hence the

BEM equation can be locally linearised as follows:

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( ) )(-k )()()( )()()( yyyyyyx ∫∫∫∫ΓΓΓΓ

Γ−=Γ

+

∂

∂+Γ+Γ

∂

∂+

ppnpnp

GdVbadVGkbn

GdGjkdV

n

GcV miieinee

(5)

where pΓ is the part of the electrolyte boundary with polarizing boundary conditions, where

npΓ is the rest, such that npp Γ∩Γ=Γ , and 0=Γ∩Γ npp . Eq. (5) is valid only within the range

of currents and potentials between data points i and i+1, if the solution to this equation falls

outside this interval, a new set of constants has to be defined and the same equation will have

to be solved again. This is done in an iterative way, until the solution of eq.(5) is consistent

with the definition of the polarization curve.

Use of simulation for CP system Design

In almost all cases of engineering applications the high level of complexity of the input data

requires the assistance of specialised computational resources, which basically consist of a

Graphical User Interface, perhaps combined with CAD, a database system, and a suite of

visualisation tools. Although sometimes considered as peripheral to the main simulation tool,

these computational resources are not only essential for facilitating the interaction between

the user and the simulation tool, but also necessary for conducting effective engineering

analysis. This is especially true in both the pre-processing stage for defining the problem

inputs, and the post-processing stage for analysing the results obtained.

The Tank CP Design software has a dedicated user interface which enables the key features of

the design to be easily defined. Parameters such as the tank diameter, anode spacing, power

supply characteristics and distribution grid etc can be easily defined. The software then

automatically generates the computational model required to predict the performance of the

CP system thus providing a quick and easy to use tool which can be used by engineers who do

not need to be experts in modelling.

Some details of the user interface

The system allows choice of unit system and reference electrode, as shown in Figure 2.

Because designs are generally based on selection from ranges of available components, the

details of which are known before the design process starts, the user interface provides a

database which can be modified to include components favoured by the Designer. For

example details of a specific type of anode ribbon or ribbon material may be defined and

stored in the database using forms as shown in Figure 3, so that for subsequent design work

the ribbon type and material can be selected from the range of stored types. Similarly other

design details, such as the depth of the anode grid below the tank base, can be defined using

forms and/or selected from the tree data-structure, as shown in Figure 4. The power supply

can be defined as a specific output voltage or current, or maximum values can be defined, and

the TRU output will be automatically adjusted by the system to try to achieve some required

potential at a selected reference electrode. The selected numbers of anode and distribution

bars are displayed as shown in Figure 5, which also shows definition of a reference electrode.

Each power supply cable is defined by identifying cable length, resistance per metre,

connection position on a distribution bar, and any additional resistance at either end of the

cable, as shown in Figure 6.

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Figure 2: Tree based selection and display, in this case of the units to be used for the design

Figure 3: Definition of new anode ribbon data

Figure 4: Data entry using forms, or selecting from database using the tree structure

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Figure 5: Defining a reference electrode, and showing display of anode and distribution bars

Figure 6: Defining supply and return cabling

Comparisons of different Tank CP system Designs

Four different CP designs are compared in this section. In all cases the tank diameter is 40.5

metres, with sand depth 0.9 metres below the tank base, and with the anode grid at 0.4 metres

below the tank base. In this comparison a fixed TRU output of 17.5 volts has been used.

Power supply cables and power return cable have resistance 0.001 Ohms/m (corresponding to

16mm2 copper cable), and have various lengths ranging from 7 to about 35 metres. The

selected anodes are 6.35mm by 0.635mm MMO coated titanium ribbons, and the distribution

bars are uncoated titanium, 12.7mm by 1.0mm. The sand has resistivity 200 Ohm-m. The tank

base is bare steel. There are 36 anode ribbons, spaced 1.1m apart. The anode ribbons and the

distribution bars terminate 100mm radially away from the circumference of the tank. The

same polarization curves are used throughout. The curve for the tank base shows potential -

587mV at zero current density.

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The differences between the four designs are as follows:

• Design 1 has 3 distribution bars and 3 supply cables connected as shown in Figure 7.

• Design 2 has 4 distribution bars and 4 supply cables connected as shown in Figure 8.

• Design 3 has 4 distribution bars and 6 supply cables connected as shown in Figure 9.

• Design 4 has 4 distribution bars and 6 supply cables connected as shown in Figure 10.

Results of Comparisons of Tank CP system design

Each of figures Figure 7 to Figure 10 shows on the left the distribution of metal voltage on the

anode/distribution bar grid, and shows on the right the distribution of protection potential on

the surface of the tank base.

Table 1 shows these ranges of voltage in the anode/distribution bar grid, and of protection

potential on the tank base.

Figure 7: Design 1 has 3 distribution bars, and 3 supply cables attached near mid-length of the distribution bars

Figure 8: Design 2 has 4 distribution bars, and 4 supply cables attached near mid-length of the distribution bars

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Figure 9: Design 3 has 4 distribution bars, and 6 supply cables. Cables to the outer two distribution bars are attached near mid-length of the bars. Cables to the two inner distribution bars are attached roughly the "one-third" positions along the bars

Figure 10: Design 4 has 4 distribution bars, and 6 supply cables. Cables to the outer two distribution bars are attached near mid-length of the bars. Cables to the two inner distribution bars are attached at 20% of the distance from the ends

Case Max voltage in

anode grid

(volts)

Min voltage in

anode grid

(volts)

Most negative

potential on tank

base (mV)

Most positive

potential on tank

base (mV)

Design 1 16.4 10.9 -914 -643

Design 2 16.6 12.2 -943 -643

Design 3 16.7 14.2 -989 -654

Design 4 16.8 15.3 -945 -661

Table 1: Showing extremes of voltage in the anode/distribution bar grid, and of protection potential on the tank base, for Designs 1 to 4

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Correlation between Reference Electrode Reading and Potential on the Tank Base

In this section, the “best” design from the previous section (ie Design 4, undamaged – see

“discussion”) is used to investigate the correlation between the observed reference electrode

potential and the potential on the tank base. The reference electrode is positioned at the centre

of, and 100 mm below the tank base. The TRU output is varied from 10 volts to 30 volts.

Table 2 shows the TRU output voltage, and the corresponding potential at the reference

electrode, most positive potential occurring on the tank base, most negative potential

occurring on the tank base, and the magnitude of the vertical electric field at the position of

the reference electrode. The relationship between RE potential and extremes of potential on

the tank base is shown graphically in Figure 11, which also shows (horizontal blue dashed

line) the potential corresponding to a 100mV shift. The vertical magenta dashed line marks

the RE potential at which all parts of the tank base have a 100mV or better potential shift.

TRU output

voltage (volts)

RE potential

(mV)

Most positive

potential on the

tank base (mV)

Most negative

potential on the

tank base (mV)

Vertical electric

field at the RE

(V/m)

10 -1105 -625 -758 4.99

12.5 -1263 -637 -822 6.53

17.5 -1638 -661 -945 9.57

30 -2456 -723 -1198 17.25

Table 2: Correlation between RE potential and tank base potential, for different TRU outputs, for undamaged CP system "Design 4"

Figure 11: Correlation between RE potential and extremes of potential on the tank base, showing RE potential which corresponds to at least a 100mV shift on the tank base

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Investigation into the effects of a poor weld

The effects of a poor weld are investigated for Design 4, with TRU output fixed at 17.5 volts.

The poor weld is represented by introducing a resistance of 0.5 Ohms between the supply

cable and the distribution bar to which it connects at the position shown in Figure 12.

Table 3 shows corresponding ranges of voltage in the anode grid and potential on the tank

base.

Figure 12: Design 4, this time with a poor weld with resistance 0.5 Ohms joining the cable to the distribution bar at the position indicated by the black arrow.

Case Max voltage in

anode grid

(volts)

Min voltage in

anode grid

(volts)

Most negative

potential on tank

base (mV)

Most positive

potential on tank

base (mV)

Design 4 (bad

weld)

16.8 14.5 -944 -657

Table 3: Showing extremes of voltage in the anode/distribution bar grid, and of protection potential on the tank base, for Design 4 with a bad weld

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Investigation to determine effects of remedial actions planned to mitigate the effects of a

broken connection

In this section we investigate firstly the effect of a complete break in the connection between

a supply cable and the distribution bar (at the same position as in the previous section.

Secondly we investigate the effect of adding a 0.5 Ohm resistance in series with the supply

cables attached to the two central distribution bars on the side away from the broken

connection. This is an example of possible remedial action, and the aim here is to demonstrate

the investigation.

The investigation is based on Design 4, with TRU output fixed at 17.5 volts.

The effect on distribution of voltage in the anode grid is shown in Figure 13, and the effect on

distribution of potential on the tank base is shown in Figure 14.

Figure 13: Effect of the remedial action on voltage in the anode grid. On the left is voltage with the broken connection, and on the right voltages after remedial action has been taken.

Figure 14: Effect of the remedial action on potentials on the tank base. On the left are potentials with the broken connection, and on the right potentials after remedial action has been taken.

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Discussion

From Table 1 is can be seen that design 1 (Figure 7) shows the biggest voltage drop (5.5

volts) in the anode/distribution bar grid, while design 4 shows the smallest (1.5 volts).

The slight asymmetry in the results (visible for example in Figure 7) is caused partly by the

attachment of the supply cables at the position of the anode bar adjacent to the centre-line of

the tank (ie not exactly on the centre-line), and partly by differences in the lengths and

therefore resistances of the supply cables.

Design 1 also shows the most positive potential on the tank base, and a 271mV range of

potentials on the tank base.

Adding a fourth distribution bar (and cable) makes design 2 perform better than design 1, with

a reduced voltage drop in the anode grid (now 4.4 volts), although the most positive potential

remains the same at -643mV, and the range of potentials on the tank base is now increased to

300mV.

Using 6 power supply cables in design 3 further improves the results, with a voltage drop of

2.5 volts in the anode grid, and a most positive potential of -654mV on the tank base,

although the range of potentials on the tank base has increased to 335mV, showing that

protection is less uniform.

Moving the attachment positions of the cables on the two central distribution bars from the

“one third positions” used in design 3 to the “20% positions” has made design 4 perform

better still, with the voltage drop in the anode grid now down to 1.5 volts, a most positive

potential on the tank base of -661mV, and a range of potentials on the tank base of 284mV.

Clearly design 4 performs best of the cases studied, showing the most uniform potential

distribution both on the anode grid and on the tank base.

Each of figures Figure 7 to Figure 10 shows that the most positive potential on the tank base

occurs near the circumference, generally in between distribution bars. Design 1 in particular

shows an extreme spread (of poor protection) towards the centre of the tank, demonstrating

that connecting a single supply cable to a long distribution bar does not give good

performance for this situation at least.

The correlation between RE potential and tank base potential shown in Figure 11 and Table 2

is revealing, since it shows that to achieve a 100mV potential shift on all parts of the tank

base requires a set point of about -1970mV, and at this setting the most negative potential on

the tank base is about -1050mV. The sensitivity of the RE potential to position is clearly seen

from the magnitude of the vertical electric field at the position of the RE, which is about 12.5

volts per metre at a set point of -1970mV. Thus a vertical positioning error of 25mm would

require a change of the set point by around 313 mV.

Although not demonstrated in this paper, a further application during set-up of an ICCP

system with suspect RE positioning is to compare simulation results for measured TRU

output with measured RE potential, and to estimate distance of the RE from the tank base

using the simulation results for electric field.

Unfortunately, components do fail in practice. Effective planning of remedial actions to

minimize the impact of a failure requires informed and quantitative understanding not just of

the consequences the failure, but also of the effects of the planned remedial action.

The results for design 4 with a bad weld (at the attachment of one of the supply cables to a

central distribution bar) as expected show an increased potential drop of 2.3 volts in the anode

grid, although this is still better than any of the other undamaged designs! The effect of the

15

bad weld can be clearly seen both in the voltage distribution in the anode grid shown on the

left hand side of Figure 12, and (less clearly) in the potential distribution on the tank base on

the right of the same figure.

The broken connection causes potentials which are not very different from the potentials

shown in Figure 12, which were for the case where the connection weld had a resistance of

0.5 Ohms. As can be seen from Figure 13 and Figure 14, the “remedial action” has a very

significant impact on voltages in the anode grid as well as on the distribution of potential on

the tank base. Results such as these can be used to optimize the corrective actions, with a

view to achieving as uniform a protection as possible for the damaged system.

Conclusions

It has been shown that the simulation of tank-base ICCP systems provides results which allow

the system design to be critically assessed, both from the point of view of as-built

performance, and from the point of view of damage tolerance and planning of remedial

action.

The application of information, gained by simulation, to initial set up of the ICCP system and

selection of an appropriate set point has been demonstrated,

It has been shown that the simulation can be performed by any CP designer, who does not

need to acquire expert skills at using the software.

The benefits of this type of simulation as part of the ICCP system design process are obvious.

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