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- 1. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1M Dwights Equation for Single Vertical Anode Resistance to Earth - millimeters Soil resistivity in ohm-cm 10,000 ohm-cm Rod length in mm 2134 mm Rod diameter in mm 203 mm Resistance of vertical rod in ohms 25.6 ohms Dwights Equation for Single Vertical Anode Resistance to Earth - meters Resistivity of backfill material (or earth) in ohm-cm 10,000 ohm-cm Length of anode in meters 2.13 m Diameter of anode in meters 0.203 m Resistance of one vertical anode to earth in ohms 25.6 ohms Dwights Equation for Multiple Vertical Anodes in Parallel - meters Soil resistivity in ohm-cm 10,000 ohm-cm Number of anodes in parallel 10 each Length of anode in meters 2.13 m Diameter of anode in meters 0.203 m Anode spacing in meters 3.0 m Resistance of vertical anodes in parallel to earth in ohms 4.52 ohms NOTICEFor these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill, as coke, d is taken as the diameter of the coke and L as the length of the backfill provided it does not extend too much greater than the length of the anode (about 1.5 times the coke diameter).
- 2. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1M Modified Dwights Equation for Multiple Anodes Installed Horizontally Resistance, in ohms, of horizontal anode to earth Resistivity, in ohm-cm, of backfill material (or earth) Length of anode in meters Twice depth of anode in meters Diameter of anode in meters 10,000 ohm-cm 2.13 m 3.7 m 0.203 m 22.52 ohms NOTICEFor these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill, as coke, d is taken as the diameter of the coke and L as the length of the backfill provided it does not extend too much greater than the length of the anode (about 1.5 times the coke diameter).
- 3. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1M Galvanic Anode Life Mag Anode Zinc Anode Weight = 109 kg Weight = 30 kg Efficiency = 0.50 Efficiency = 0.90Utilization Factor = 0.85 Utilization Factor = 0.85 Current = 2.0 A Current = 2.0 A Mg Life = 5.9 yrs Zn Life = 1.1 yrs Consumption Solution Output² Rate² Potential³ Anode¹ (amp-hr/kg) (kg/amp-hr) Efficiency² (Cu-CuSO4) Zinc 815 10.8 90% -1.1 V Std. Mg 1100 7.9 50% -1.4 to -1.6 V Hi-Pot Mg 1100 7.9 50% -1.7 to -1.8 V1. Anodes installed in suitable chemical backfill.2. Current efficiency with current density. The shown efficiency, and the resulting consumption rate, areat approximately 30 milliamps/ft² of anode surface. Efficiencies are higher at higher current densities andlower at lower current densities.3. The potentials are solution potentials. When calculating driving potentials, the difference between theprotected structure and the anode, allow for anode polarization. Anode polarization is also influenced bycurrent density at the anode surface. For magnesium polarization allow for 0.1 V anodic polarization.Zinc in a proper backfill is not usually subject to significant anodic polarization and the solution potentialmay be used.
- 4. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1MRectifier Total Circuit Resistance Ground bed resistance (ohms) 3.08 ohms Cable resistance (ohms) 0.097 ohms Pipeline/structure to earth resistance (ohms) 7.53 ohms Total circuit resistance (ohms) 10.71 ohmsDeep Anode Ground Bed Resistance - meters Effective soil resistivity (ohm-cm) 10,000 ohm-cm Anode length (meters) 12 m Anode diameter (meters) 0.203 m Resistance to earth of a vertical single anode (ohms) 6.74 ohmsRectifier Efficiency K = Meter constant DC Amps = 1.00 A N = # of revolutions of disk DC Volts = 2.00 V T = Time in seconds K= 0.01 N= 4 T= 10 sec Efficiency = 27.78%
- 5. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1MImpressed Current - # of Anodes Required Wt = Weight per anode (kg) Wt = 27.2 kg CR = Consumption rate (kg/amp-year) CR = 0.34 kg/A-yr DL = Desired life (years) DL = 20 yrs Current = Current required (amps) Current = 15.00 A UF = Utilization factor UF = 0.60 # anodes = 7 each# of Anodes Required Based on Current Discharge * from anode manufacturer data MD = Maximum discharge per anode (amps) MD = 2.50 A Current = Current required (amps) Current = 15.00 A # anodes = 6 eachCable Resistance Resistance per km 0.833 ohms/km Length in meters (sum of positive and negative cables) 117 m Cable resistance 0.097 ohms

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