Dwight's 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

Dwight's 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

Dwight's 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

NACECompanion to the Peabody Book

October 26, 2000Revision 1.1M

NOTICE

For 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).

Modified Dwight's 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

NACECompanion to the Peabody Book

October 26, 2000Revision 1.1M

NOTICE

For 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).

Galvanic Anode Life

Mag Anode Zinc AnodeWeight = 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

Anode¹ Efficiency²Zinc 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 V

Output²(amp-hr/kg)

Consumption Rate²

(kg/amp-hr)

Solution Potential³

(Cu-CuSO4)

NACECompanion to the Peabody Book

October 26, 2000Revision 1.1M

1. Anodes installed in suitable chemical backfill.2. Current efficiency with current density. The shown efficiency, and the resulting consumption rate, are at approximately 30 milliamps/ft² of anode surface. Efficiencies are higher at higher current densities and lower at lower current densities.3. The potentials are solution potentials. When calculating driving potentials, the difference between the protected structure and the anode, allow for anode polarization. Anode polarization is also influenced by current 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 potential may be used.

Rectifier 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 ohms

Deep 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 ohms

Rectifier Efficiency

Meter constant DC Amps = 1.00 A# of revolutions of disk DC Volts = 2.00 VTime in seconds 0.005

410 sec

Efficiency = 27.78%

K =N =T = K =

N =T =

NACECompanion to the Peabody Book

October 26, 2000Revision 1.1M

Impressed Current - # of Anodes Required

Wt = Weight per anode (kg) Wt = 27.2 kgCR = Consumption rate (kg/amp-year) CR = 0.34 kg/A-yrDL = Desired life (years) DL = 20 yrs

Current = Current required (amps) Current = 15.00 AUF = Utilization factor UF = 0.60

# anodes = 7 each

# of Anodes Required Based on Current Discharge

* from anode manufacturer data

Maximum discharge per anode (amps) 2.50 ACurrent required (amps) 15.00 A

# anodes = 6 each

Cable Resistance

Resistance per km 0.833 ohms/km Length in meters (sum of positive and negative cables) 117 m

Cable resistance 0.097 ohms

MD = MD =Current = Current =

NACECompanion to the Peabody Book

October 26, 2000Revision 1.1M