A modified version of the slope parameter equation for pipelines that incorporates metallic path resistance is presented. Solutions to this expression are compared to ones based upon a first principles based potential attenuation equation. Agreement between the far field potential projected by each was found to be good for anode spacings less than 10,000 m, but the modified slope parameter equation produced conservative far-field potentials for anode spacing less than 20,000 m.



Because of its strength and relatively low cost, steel is the most widely used structural material for tensile load bearing structures; however, the native reactivity of this material class is sufficiently great that one or more corrosion control measures is generally required. For submerged and buried applications, protection of external surfaces invariably involves coatings combined with cathodic protection (cp). This dual approach is necessary because coatings exhibit defects; and even if this barrier layer can be certified as defect-free at the time of construction, deterioration with time leads to localized exposure of the substrate steel. While cp could, in theory, function as a stand-alone corrosion control method, it is often practical only when employed in conjunction with a coating. In effect, the cp need only provide protection at coating defects. Consequently, current demand is low compared to the bare metal case; and either fewer anodes are required or longer system life results (or both).


Current Design Practice

For space frame (equi-dimensioned) structures in relatively low resistivity electrolytes (offshore petroleum production platforms, for example) protected by galvanic anodes, potential can be assumed constant and metallic path resistance negligible; and design has historically been accomplished in terms of Ohm?s law or,


where Ia is current output of an individual anode, öc and ö a are the closed circuit cathode and anode potentials, respectively, and Ra is resistance of an individual anode. The number of anodes, N, is then determined from the expression,

where ic = cathode current density for polarization (current density demand) and Ac = structure surface area.

For structures in sea water, recommended design protocols (1,2) have for the past two decades been based upon rapid polarization (3-9), which involves application of a relatively high initial current density (io), such that a steady-state structure potential in the range -0.90 to -1.05 VAg/AgCl results, ...within a reasonably short period of time (1). By successive substitution of values for ö c , ö a , and Ra for the initial and final conditions into Equation

1, the corresponding Ia values are determined. Then, sequential substitution of these along with io and if into

Equation 2 yields the corresponding N (No and Nf, respectively). In addition, a third current density, the mean or im, is used to calculate the mean number of anodes, Nm, according to the relationship,



Td = design life,

u = utilization factor,

C = anode current capacity, and

w = weight of a single anode,

in order to ensure that adequate anode mass is present. Ideally, the N that is calculated for each of the three current densities should be the same; however, this is normally not the case; and so the highest of the three is specified. For uncoated structures, this is invariably No. Accordingly, the cp system may be over-designed in terms of im and if. This failure of the design procedure to yield a common number of anodes for each of the three current density criteria arises because the procedure is an algo

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