Modelling Impressed Current Cathodic Protection of Storage Tanks

Transcription

1 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, 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 1

2 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 2

3 can assist in initial set-up of a system, and that simulation can be used to investigate the faulttolerance 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. 3

4 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. R 3 A 3 A 4 I 3 R 2 A 2 I 2 R 1 METALLIC STRUCTURE I 1 A 1 I t TRU ELECTROLYTE 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: Problem Formulation I t = I + (1) 1 + I2 I3 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: ( ( x) ) = 0 k ; x Ω (2) V e 1 2, 3 is the 3D gradient operator, and V e (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. where = ( x, x x ) 4

5 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: G( x, y) Ve ( y) cv ( x) + V ( y) dγ( y) (, ) Γ( ) = 0 G x y d y (3) e e n n Γ Γ 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 x Γ [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: j n Ve = k = f ( V ), (4) nˆ which relate the normal current density flowing to throughout the surface ( j n ) to the potential drop across the interface metal/electrolyte ( V = V e Vm ), where V m 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 jn = ai + bi Vi, where a and b change from interval to interval, hence the BEM equation can be locally linearised as follows: 5

6 G G cv ( x) + V ( y) dγ( y) + k Gj dγ( y) + + kbg V ( y) dγ( y) = -k ( a bv ) GdΓ( y) (5) e e n i e i i m n n Γnp Γnp Γp where Γp is the part of the electrolyte boundary with polarizing boundary conditions, where Γnp is the rest, such that Γ = Γp Γnp, and Γp Γnp = 0. 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. Γp 6

7 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 7

8 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 Ohms/m (corresponding to 16mm 2 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. 8

9 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 9

10 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) Design Design Design Design Most positive potential on tank base (mv) 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 10

11 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 (mv) potential Most positive potential on the tank base (mv) Most negative potential on the tank base (mv) Vertical electric field at the RE (V/m) 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 11

12 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 Design 4 (bad weld) 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) 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 12

13 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. 13

14 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 14

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. References [1] Andres B Peratta, John M W Baynham, and Robert A. Adey. A Computational Approach for Assessing Coating Performance in Cathodically Protected Transmission Pipelines. CORROSION 2009, Paper 6595 Atlanta, Georgia. NACE International [2] D. P. Riemer and M. E. Orazem, Modelling Coating Flaws with Non-Linear Polarization Curves for Long Pipelines, in Corrosion and Cathodic Protection Modelling and Simulation, Volume 12 of Advances in Boundary Elements, R. A. Adey, editor, WIT press, Southampton, 2005, [3] R.A. Adey, J. Baynham. Design and optimization of cathodic protection systems using computer simulation. CORROSION 2000, Paper 723. Houston, Texas. NACE International, [4] Andres B Peratta, John M W Baynham, and Robert A. Adey. Advances In Cathodic Protection Modelling of Deep Well Casings In Multi-Layered Media. CORROSION 2009, Paper 6555 Atlanta, Georgia. NACE International [5] 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 [6] Pierre R. Roberge. Corrosion Engineering. Principles and Practice. McGraw-Hill (2008) [7] C.A. Brebbia, J.C.F. Telles and L.C. Wrobel. Boundary Element Techniques Theory and Application in Engineering. Springer Verlag Berlin, Heidelberg NY, Tokyo [8] Robert A.Adey, John Baynham, and Robin Jacob. Prediction of Interactions between FPSO and Subsea Cathodic Protection Systems. Corrosion 2008, Paper 08546, NACE International