Design charts for impressed current ground beds should be based on the types of an-ode construction adopted by the corrosion engineer for his pipeline system. Typical construction sketches will be shown to illustrate principles involved, but others may be used if found more suitable for specific pipeline conditions.
Figure 7.1illustrates one form of vertical anode installation. The figure includes the essential features only. The carbonaceous backfill surrounding the anode, when well tamped, serves two functions:
• Being of a very low resistivity, it has the effect of increasing the anode size with resulting reduction in resistance to earth, and
• Most of the current is transmitted to the backfill from the anode by direct contact so that the greater part of material consumption should take place at the outer edges of the backfill column.
Since a positive potential (voltage) is impressed on the entire ground bed assembly, it is absolutely essential that all header cable insulation, anode pigtail wire insulation, the connection between anode and pigtail (a manufacturer’s function) and insulation of connections between pigtails and a header cable or cable runs to a test or junction be completely intact and moistureproof. If this is not maintained, current will be discharged through insulation imperfections, causing wires to corrode and sever in a relatively short period of time, thus losing connections to all or part of the ground bed. Connections between header cable and anode pigtail must be of permanent low resistance. This may
INSULATED CONNECTION BETWEEN HEADER CABLE AND ANODE PIGTAIL WIRE
INSULATED CONNECTION WIRE FURNISHED WITH ANODE
ANODE_HIGH SILICON CAST IRON OR GRAPHITE
CARBONACEOUS BACKFILL MATERIAL, WELL TAMPED AUGERED HOLE FOR ANODE AND BACKFILL
8"
1 2
d L
FILL CABLE TRENCH AND TOP OF ANODE AUGER HOLE WITH TAMPED EARTH AFTER COMPLETING
CONNECTIONS
1
L = LENGTH OF SPECIFIED ANODE d = L + 5 FEET (MIN)
INSULATED HEADER CABLE TO POWER SOURCE AND TO OTHER ANODES IN GROUND BED
Figure 7.1 Typical vertical anode installation.
be accomplished by methods such as thermite welding, soldering, or high compression crimp-type connections.
The number of vertical anodes required to attain a required ground bed resistance can be determined by using the typical chart in Figure 7.2. The figure is based on all anodes being along a straight line, the most favorable ground bed configuration in most instances. This chart is for use with the type of anode installation illustrated by Figure 7.1. Similar graphs can be prepared for anode-backfill combinations of other dimensions. Curves on these graphs were developed using the following formulas and procedures.
Total resistance of each anode to earth consists of the resistance of the anode to the carbonaceous backfill plus the resistance to earth of the backfill column itself. Resistance of the anode to backfill is obtained by using the following equation.
Rv= 0.00521ρ
Rv= resistance of vertical anode to earth in (ohms) ρ = resistivity of backfill material (or earth) in (ohm-cm) L= length of anode in (feet)
d = diameter of anode in (feet)
RESISTANCE IN OHMS IN 1000 OHM-CM SOIL
10-FOOT ANODE SPACING 15-FOOT SPACING
Figure 7.2 Typical vertical anode design chart.
Using a value of 50 ohm-cm for the resistivity of the carbonaceous backfill material, resistances are calculated for the backfill column and the anode (7 ft× 8 in and 5 ft × 2 in respectively in this case). The difference between the two figures is the resistance from the anode to the outer edges of the backfill column. For the anode construction shown inFigure 7.1, this was calculated to be 0.106 ohm.
Resistance of several anodes in parallel can be calculated by the following equation:
Rv =0.00521ρ
Rv= resistance of vertical anode to earth in (ohms) ρ = resistivity of backfill material (or earth) in (ohm-cm) L= length of anode in (feet)
d= diameter of anode in (feet) N= number of anodes in parallel S= anode spacing in (feet)
The dimensions of the backfill column (7 ft× 8 in in this case) are used in applying the formula. Curves for 10, 15, 20 and 25-ft anode spacing are included in theFigure 7.2. The
curves do not include the anode internal resistance (anode to backfill). The resistance for any number of anodes in parallel from the curves must be added to the internal resistance of one anode divided by the number of anodes in parallel. The effect of this internal resistance becomes less as the number of anodes is increased.
Curves ofFigure 7.2 are for anodes in 1000-ohm-cm soil. The resistance for the selected number of anodes from the curves varies directly with the resistivity. For ex-ample, if a combination of anodes has a resistance of 0.40 ohm in 1000-ohm-cm soil (as indicated by the curves) but the soil resistivity for design purposes at the installa-tion site selected is 2400 ohm-cm, the ground bed resistance for the same number of anodes is 0.40 × 2400/1000 = 0.96 ohms, plus the internal resistance. For a second ex-ample, assume the soil resistivity for design purposes was 750 ohm-cm, the resistance of the same anode combination would be 0.40 × 750/1000 = 0.30 ohm plus the internal resistance.
Extending this analysis, assume that a ground bed installation site has been se-lected where the effective soil resistivity for design purposes has been determined to be 2800 ohm-cm. Assume that the nearest ground bed anode will be 300 ft from the pipeline and that No. 4 copper connecting cable will be used. Also assume that the ground bed is to discharge 20 A at 24 V applied from a rectifier.
Before using the chart, the maximum permissible resistance of the anodes must be determined. This is necessary because, in addition to resistance to earth of the anodes, other considerations must be analyzed to determine the total circuit resistance. These include the following:
• Back voltage between ground bed and pipeline,
• Resistance to earth of the pipeline at the ground bed location, and
• Resistance of cable from the pipeline to power source and from the power source to and along the anodes comprising the ground bed.
The back voltage is that which exists between the anodes and pipeline in opposition to the applied voltage. For ground bed anodes with carbonaceous backfill, this will be, usually, in the order of 2 V. Some areas of unusual soil composition may result in higher back voltages but the 2-V figure is used commonly for design purposes un-less experience in a specific area dictates otherwise. In practice, the back voltage at a working ground bed is determined by measuring the voltage between ground bed and pipeline (across the positive and negative rectifier terminals) immediately after switching the rectifier power OFF. The ground bed will always be positive to the pipeline. If the back voltage is 2 V, it means it will require 2 V of the rectifier source voltage to overcome the back voltage before current can flow through the ground bed.
Resistance to earthof the pipeline depends on the quality of the pipeline coating.
The better the coating, the higher the effective resistances at the ground bed location. In the example being used, if current requirement tests made at (or in the vicinity of) the selected ground bed location had indicated that 20 A of applied current would cause a change in pipeline voltage (1V) of −1.5 V to a remote copper sulfate electrode (CSE), the effective pipeline resistance would be 1.5/20 or 0.075 ohm.
Cable resistanceis the additive resistance of the cable from the pipeline via the power source to the first anode of the ground bed (assuming that the line of ground bed anodes is perpendicular to the pipeline), plus effective resistance of the header cable along the line of anodes or individual anode cables. This effective header cable resistance is less than that of the full length of the ground bed because all current does not flow the full length of the ground bed but is diminished as each anode connected drains off its share of current. Although subject to variations with differences in individual anode resistance and possibly other factors, it is practical to use the resistance of one half of the ground bed header cable resistance as the effective header cable resistance. Table 7.1includes data on resistance of copper conductors in the sizes commonly used in pipeline corrosion engineering work.
With the above discussion in mind, the design of the vertical anode ground bed for the example proposed can be estimated as follows:
• Maximum power source voltage will be 24 minus 2 V back voltage or 22 V.
• For 20 A current output, circuit resistance can not exceed 1.10 ohm. This is determined by using Ohm’s law (Voltage (V) divided by Current (I)= Resistance (R ), 22 V divided by 20 A or 1.10 ohm.)
• Deductions from the circuit resistance must be made for the pipe-to-earth resistance (0.075 ohm in this example), and the resistance of the cable from the rectifier to the first anode. In this example use the resistance of 330 ft of No. 4 cable (300 ft distance given, plus 10% slack) that equals 0.082 ohms. The total resistance is determined by adding the resistance to earth of the anodes plus the effective resistance of the ground bed header cable, a variable, (0.075 + 0.082 = 0.157 ohms). These resistances are deducted from the total circuit resistance allowance (1.10 ohm − 0.157 ohm = 0.94 ohm).
• Make an assumption of the allowance to be made for the header cable resistance. As a first try, assume that the anode resistance alone should be 0.90 ohm.
• Convert the 0.90-ohm anode resistance to a 1000 ohm-cm base to permit using the design chart. Because effective soil resistivity for design purposes for the example is 2800 ohm-cm, the converted resistance is 0.90 × (1000/2800) = 0.321 ohm.
• Using the chart ofFigure 8.2, the indicated number of anodes at 20-ft spacing would be at slightly over 11. For design purposes use 12 anodes. (The number of anodes at other spacing would be determined in similar fashion.)
• Header cable length for 12 anodes would be 11 spaces at 20 ft or 220 ft. Effective resistance would be approximately 110 ft of No. 4 cable or 0.0285 ohm. For design use 0.029 ohm.
• Total anode plus header cable resistance for 12 anodes would then be ((0.308 ohm (from the chart)× (2800/1000)) + internal resistance (0.106/12 = .009) + 0.029 = 0.90 ohm which is within the desired value of 0.94 ohm.
• Following the same procedure for 11 anodes, total resistance would be approximately 0.96 ohm, which is higher than the desired value, indicating that 12 anodes would be the minimum number to be used at the 20-ft spacing.
Table 7.1 Resistance of Copper Conductors
Resistance of Stranded Copper Conductors in Ohms per Foot Times 10−3at 25◦C1
1 1
INSULATED HEADER CABLE TO POWER SOURCE AND OTHER ANODES IN GROUND BED
INSULATED CONNECTION BETWEEN CABLE AND
ANODE PIGTAIL WIRE TAMPED EARTH FILL
2 2
L
L = LENGTH OF SPECIFIED ANODE
Figure 7.3 Typical horizontal anode installation.
Another important consideration in selecting the number of anodes is desired anode life. This is discussed in detail in the Chapters 8 and 9 on ground bed materials. If the minimum number of anodes that will give a satisfactory low ground bed resistance will not result in adequate life, the number of anodes would have to be increased accordingly.
Although, as a general principle, vertical ground bed anodes are preferable to horizontal anodes, it may be necessary to use horizontal construction because of unfavorable soil conditions at depths reached by vertical anodes. A typical method of installing horizontal anodes is shown inFigure 7.3.
Figure 7.4includes design charts that may be used for determining the resistance of horizontal anodes in parallel. These charts are based on the type of construction shown inFigure 7.3with all anodes placed along a straight line.
The same general procedure is followed in determining the resistance from the anode to the outer edges of the backfill as was used inFigure 7.2except that the applicable formula (also derived from H. B. Dwight equations) is the following:
Rh = 0.00521ρ
Rh = resistance of horizontal anode to earth in (ohms) ρ = resistivity of backfill material (or earth) in (ohm-cm) L= length of anode in (feet)
d= diameter of anode in (feet) S= twice depth of anode in (feet)
15-FOOT ANODE SPACING 20-FOOT SPACING 25-FOOT SPACING
(CENTERLINE TO CENTERLINE)
0 5 10 15 20 25 30
NUMBER OF ANODES 3.0
2.0
1.00.9 0.80.7 0.6 0.5 0.4 0.3
0.2
0.1
RESISTANCE IN OHMS IN 1000 OHM-CM SOIL
Figure 7.4 Typical horizontal anode bed design chart.
Using this procedure, the resistance in 1000 ohm-cm soil of one horizontal anode installed per Figure 7.3 is approximately 2.22 ohms (including 0.136 ohm internal resistance).
No specific formula applicable to horizontal anodes in parallel is known. The curves of Figure 7.4were obtained by dividing the resistance of 1 anode (excluding internal resistance) by the number of anodes in parallel and applying paralleling factors obtained from the curves ofFigure 7.2. To the values obtained from the curves must be added an amount equal to the internal resistance of 1 anode divided by the number of anodes in parallel. To allow for the reduced distance between nearest portions of horizontal anodes at a given spacing compared to that for vertical anodes at the same spacing, paralleling factors for 15 ft horizontal anode spacing were taken from the curve for 10 ft vertical anode spacing, and so forth. This is not at all rigorous but will serve as a reasonable guide.
As an example, the paralleling factor for 20 vertical anodes at 15-ft spacing (from Figure 7.2) is 0.218 ohm. The resistance of one anode calculated from Eq 3 is 2.56 ohm.
Paralleling factor= 0.218/(2.56/20) = 1.70. Using this factor for 20 horizontal anodes at 20 ft spacing, the parallel resistance would be 2.08 ohm (resistance of one horizontal anode excluding internal resistance) divided by 20 and multiplied by the factor.
(2.08/20) × 1.70 = 0.177 ohm (seeFigure 7.4).
Another approach to horizontal ground bed construction involves the use of a con-tinuous strip of carbonaceous backfill with anodes located at intervals within the strip.
Construction would be similar to that shown inFigure 7.3except that the carbonaceous
0 100 200 300 400 500 600 GROUND BED LENGTH IN FEET
2.0
1.0 0.9 0.8 0.7 0.6 0.5
0.4
0.3
0.2
0.1
RESISTANCE IN OHMS IN 1000 OHM-CM SOIL
15-FOOT SPACING
Figure 7.5 Typical design for continuous horizontal anode.
backfill layer is continuous throughout the length of the ground bed. Figure 7.5is a design curve for determining the resistance of a continuous horizontal ground bed with anodes on 15-ft centers with the carbonaceous backfill strip starting 5 ft before the end of the first anode and ending 5 ft after the end of the last anode.
The curve inFigure 7.5is based on the formula for a horizontal anode given earlier plus an allowance for longitudinal resistance of the carbonaceous backfill. This curve is based on carbonaceous backfill having 50-ohm-cm resistivity, a conservative value because a good quality backfill, well tamped, should have less than this amount. In using this curve, as with the other design charts, effective soil resistivity must be known with reasonable accuracy.