Calculation 1. Mean Current Demand Step 1. Determine mean coating breakdown factor alpc ≔ 0.01
blpc ≔ 0.0003
f cm_lpc ≔ alpc + 0.5 blpc ⋅ a fjc ≔ 0.3
t f
Constant associated with line pipe coating (Table A.1)
= 0.015
b fjc ≔ 0.03
f cm_fjc ≔ a fjc + 0.5 b fjc ⋅
t f
Constant associated with field joint coating (Table A.2)
= 0.75
r ≔ 0.033
Ratio of lengths of cutbacks and line pipe coating (Sec.5.6.4)
f cm ≔ f cm_lpc + r ⋅ f cm_fjc = 0.039
Mean coating breakdown factor (Sec.5.2.6)
Step 2. Calculate the total anode mass Ac ≔
⋅ D ⋅ L = 29894.7
2
Steel Surface Area (Sec.5.2.1)
icm ≔ 0.025 ― 2
Mean Current Density (Table 5-1)
I cm ≔ Ac ⋅ f cm ⋅ icm = 29.334
Mean Current Demand (Sec. 5.2.1)
I cm ⋅ t f M ≔ ―― = 6.64 u⋅ε
Total anode net mass (Sec. 5.4.1)
Step 3. Calculate the individual anode mass ta ≔ 61
Anode thickness
Dia ≔ D + 2 tcor + ts = 921.37
Inner diameter
Doa ≔ Dia + 2 ta = 1043.37
Outside diameter
Aa ≔
⎛ ⎝
⋅
⎛ Doa Dia ⎞ ⎞ + − 2 Sg ⋅ La = 1.127 2 2 ⎝ ⎠ ⎠
2
Anoid section area
⎛ Doa Dia ⎞ ⎛ ⎛ Doa Dia ⎞ ⎞ V a ≔ ― − ― ⋅ ― + ― − 2 Sg ⋅ La = 0.06873 2 ⎠⎝ ⎝ 2 2 ⎠ ⎝ 2 ⎠ ma ≔ V a ⋅ ρa = 181.66
Prepared by Kim, Young-tae / P.E.
3
Indivisual anoid volume
Individual anode mass
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Nov.13, 2012 Rev.A
Step 4. Calculate the number of anode and spacing required M N req_m ≔ ― = 33 ma Sreq_m ≔
L N req_m
Reqired Anode Numbers in Mean Condition
= 314
Reqired Anode Spacing in Mean Condition
2. Final Current Demand Step 1. Determine mean coating breakdown factor alpc ≔ 0.01
blpc ≔ 0.0003
Constant associated with line pipe coating (Table A.1)
t f f cf_lpc ≔ alpc + blpc ⋅ ― = 0.019 a fjc ≔ 0.3
b fjc ≔ 0.03
f cf_fjc ≔ a fjc + b fjc ⋅
t f
Constant associated with field joint coating (Table A.2)
= 1.2
r ≔ 0.033
Ratio of lengths of cutbacks and line pipe coating (Sec.5.6.4)
f cf ≔ f cf_lpc + r ⋅ f cf_fjc = 0.059
Mean coating breakdown factor (Sec.5.2.6)
Step 2. Calculate total anode current output to meet final current demand ma ⋅ 1 − u V f ≔ ――― = 0.0137 ρa 값 측 추
V f ＝
약 제
taf ≔
Final anoid volume after consumtion
Doa ≔ 1
건 조
이 풀
3
⎛ Doa Dia ⎞ ⎛ ⎝ 2
Doa ≔
Doa
Aaf ≔
2
−
−
2 ⎠⎝
⋅
⎛ Doa Dia ⎞ ⎝ 2
+
2 ⎠
⎞
− 2 Sg ⋅ La
⎠
Doa = 947.1
Dia 2
= 12.9
⎛
⎛ Doa Dia ⎞ ⎞ ⋅ ― + ― − 2 Sg ⋅ La = 1.069 2 ⎠ ⎝ ⎝ 2 ⎠
0.315 ⋅ ρ Raf ≔ ―― = 0.609 ‾‾ Aaf
Prepared by Kim, Young-tae / P.E.
Final anoid thickness after consumtion
2
Final anode surface per an anode
Final anode resistance
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Nov.13, 2012 Rev.A
∆E ≔ Ec − Ea = 0.35
Driving Voltage (Sec. 5.6.3)
∆E I af ≔ ― = 0.574 Raf
total anode current output per an anode (Sec.5.5.1)
Step 3. Calculate final anode current output I cf ≔ Ac ⋅ f cf ⋅ icm = 43.796
Total final current demand (Sec.5.3.1)
Step 4. Calculate the number of anode and spacing required
⎛ I cf ⎞ N req_f ≔ ceil ― = 77 ⎝ I af ⎠ Sreq_f ≔
L N req_f
Required number of anodes in final condition
= 135.2
Required anode spacing in final condition
3. Check the Attenuation Condition Step 1. Calculate the attenuation length (Sec.5.6.9)
⎛ −2 ⋅ R ⋅ I ⎞ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ⎛ 4 ⋅ Raf 2 ⋅ I cf 2 ⎞ 2 ⋅ ρ Me ⋅ icm ⋅ f cf ⋅ D af cf Latt ≔ ―――― ⋅ ――― + ⎜――― ⎟ + ――――― ⋅ ∆E = 68.25 ρ Me ⋅ D ⋅ f cf ⋅ icm ⎝ L t ⋅ D − t L2 ⎝ ⎠ ⎠ t ⋅ D − t
Step 2. Calculate the spacing for attenucation condtion
⎛ L ⎞ N req_att ≔ ceil ― = 153 ⎝ Latt ⎠ Sreq_att ≔
L N req_att
Required number of anodes by attenuation
= 68
Required anode spacing by attenuation
4. Design the Number and Spacing of Anode N req ≔ max N req_m , N req_f , N req_att = 153
Required number of anodes
Sreq ≔ min Sreq_m , Sreq_f , Sreq_att = 68
Required anode spacing
M final ≔ N req ⋅ ma = 30.6
Total mass of anodes
5. Anode Design Check Total final current demand<=Total final current output
I cf = 43.796
Prepared by Kim, Young-tae / P.E.
Total final current demand
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Nov.13, 2012 Rev.A
I af ⋅ N req = 87.87
Total final current output
Check_1st ≔ ‖ if I cf ≤ I af ⋅ N req| | = “Accept”
