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- 1. NACE Companion to the Peabody Book October 26, 2000 Revision 1.1 Dwights Equation for Single Vertical Anode Resistance to Earth - inches Soil resistivity in ohm-cm 10,000 ohm-cm Rod length in inches 84.0 inches Rod diameter in inches 8.00 inches Resistance of vertical rod in ohms 25.5 ohms Dwights Equation for Single Vertical Anode Resistance to Earth - feet Resistivity of backfill material (or earth) in ohm-cm 10,000 ohm-cm Length of anode in feet 7.0 feet Diameter of anode in feet 0.667 feet Resistance of one vertical anode to earth in ohms 25.5 ohms Dwights Equation for Multiple Vertical Anodes in Parallel - feet Soil resistivity in ohm-cm 10,000 ohm-cm Number of anodes in parallel 10 each Length of anode in feet 7.0 feet Diameter of anode in feet 0.667 feet Anode spacing in feet 10.0 feet Resistance of vertical anodes in parallel to earth in ohms 4.51 ohms NOTICEFor these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill, ascoke, 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 1.1 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 feet Twice depth of anode in feet Diameter of anode in feet 10,000 ohm-cm 7.0 feet 12.0 feet 0.667 feet 22.49 ohms NOTICEFor these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill, ascoke, 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 1.1 Galvanic Anode Life Mag Anode Zinc Anode Weight = 240 lbs Weight = 240 lbs 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 = 3.9 yrs Consumption Solution Output² Rate² Potential³ Anode¹ (amp-hr/lb) (kg/amp-hr) Efficiency² (Cu-CuSO4) Zinc 370 23.7 90% -1.1 V Std. Mg 500 17.4 50% -1.4 to -1.6 V Hi-Pot Mg 500 17.4 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 1.1Rectifier 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 Effective soil resistivity (ohm-cm) 10,000 ohm-cm Anode length (feet) 40 feet Anode diameter (feet) 0.667 feet Resistance to earth of a vertical single anode (ohms) 6.73 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 1.1Impressed Current - # of Anodes Required Wt = Weight per anode (pounds) Wt = 60 lbs CR = Consumption rate (lbs./amp-year) CR = 0.75 lbs/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 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 1000 feet (Mft) 0.254 ohms/Mft Length in feet (sum of positive and negative cables) 384 feet Cable resistance 0.097 ohms

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