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35 NACE INTERNATIONAL: VOL. 56, NO. 4 MATERIALS PERFORMANCE APRIL 2017 where ϕ is the potential. The boundar y conditions related to the electrolyte and the electrodes are presented as Equations (2) through (4): = w w 0 (2) = w i f ( ) c c c (3) = w i f ( ) c a a (4) where ϕ is the potential and ϕ 0 is the given initial constant value of the electrolyte potential; i is the polarized CD of the elec- trodes; and f c (ϕ c ) and f a (ϕ a ) are the nonlin- ear functions describing the relationship between the potential and CD of the anode and cathode, respectively. The platform m o d e l , d e s i g n e d a c c o r d i n g t o L a n's model, 13 and various anode distributions were developed in the software. The vol- ume mesh type used for modeling was a free tetrahedral shape, and the software determined the optimum sacrificial anode arrangement. Materials and Methods Model Construction The physical platform model was made of steel tubes welded together. The jacket had four 60-mm diameter legs, 12 horizon- tal support tubes, and eight vertical cross- support tubes. The ends of all platform legs were sealed using rubber lid caps. Zinc anodes were installed on the platform. The anodes were 60-mm long, 25-mm wide, and 15-mm tall with a weight of 0.25 kg each. The conductivity of seawater in the Persian Gulf and the Caspian Sea was measured as 4.9 and 1.63 S m –1 , respectively. Potentiodynamic Polarization Readings and Boundary Conditions The electrochemical experiments were carried out in natural seawater using a three-electrode corrosion cell kit. The ref- erence electrode was a saturated silver/ silver chloride (Ag/AgCl) electrode; a plati- num wire was applied as th e c ount er electrode; and the working electrodes were carbon steel and zinc specimens mounted in epoxy resin with an exposed surface area of 1·cm 2 . The potentiodynamic curves were drawn at a constant scan rate of 1 · mV s −1 . Each test was repeated three times to con- f irm accuracy. C Ds of th e anodic and cathodic reactions were derived from the polarization curves using the Tafel equa- tions 15 shown in Equations (5) through (8): = × + w i 0.053 10 in Persian Gulf anode 1.139 0.059 anode (5) = × + w i –0.00079 10 in Persian Gulf cathode 0.662 –0.126 cathode (6) = × + w i 0.1271 10 in Caspian Sea anode 1.0773 0.065 anode (7) = × + w i –0.00396 10 in Caspian Sea cathode 0.682 –0.156 cathode (8) Due to the larger exposed area of the cathode (platform) compared to that of the zinc anodes, the steel corrosion potential was set as the initial value for the seawater potential. Its values for the Persian Gulf and Caspian Sea were –0.632 and –0.649 V, respectively. Field Validation of the Model To obtain field potential measurements for three continuous days, the physical platform model was placed in the harbor of Iran's Amir Abad Port in the Caspian Sea. The same procedure was used in the Per- sian Gulf. On the submerged zone of the marine platforms, the formation of calcare- ous scale (an aging effect) under satisfac- tory CP conditions gradually reduced the required protective current. 6 Because of time considerations, only the initial stages of polarization were considered in this study. A saturated Ag/AgCl reference elec- trode and a voltmeter were used to record th e p ot enti al of sel e ct ed sit e s on th e structure. TABLE 1. THE CALCULATED CURRENT OUTPUT OF ANODES AND REQUIRED CP CURRENT IN THE PERSIAN GULF AND CASPIAN SEA Marine Environment Current Output of Anodes (A) Current Demand (A) Persian Gulf 0.60 0.16 Caspian Sea 0.19 0.16 FIGURE 1 Anode positions and potential contour plot (V) for the optimum design in the Persian Gulf.