SEIDEL and KLIMA: CRITERIA FOR ELECTRICAL HARVESTING 



separation distance, the configuration of the 

 electrode in the array is the principal factor in 

 determining the resistance value, as would be the 

 case with small balls or cables for electrodes. For 

 our situation, the size of the electrodes and 

 separation distance are equally important. Since 

 the load resistance of the array in seawater is 

 extremely low, the resistance value used to calcu- 

 late power requirements becomes extremely 

 important. A small error in the resistance could 

 result in a large miscalculation of the necessary 

 power requirements. For this reason we took great 

 care in computing resistance accurately. Resis- 

 tance measurements for this situation can be 

 calculated by two methods referred to as Kreutzer 

 and empirical technique. Kreutzer developed a 

 formula for calculating spread resistance for one 

 electrode: 



R. 



Ko a +Tx 0.02) 



(4) 



where Rs = 



T 



A 



= spread resistance of one electrode, 



including field fringing 

 = a constant at a specific salinity 

 = temperature in centigrade 

 = area, square meters. 



(C. Kreutzer, pers. commun.) The constant K^, 

 varies with different salinity values and must be 

 recalculated for each new salinity. It can be ob- 

 tained by solving fori^,, in Equation (4) which re- 

 quires knowledge of resistance, surface area, and 

 temperature. Once the value of /Co is determined 

 for a specific salinity. Equation (4) can be used to 

 calculate Rs for varying electrode surface areas. 

 Because the value of K^, varies with different 

 salinity and is difficult to determine since in situ 

 resistance measurements are required, we 

 decided to establish an empirical ratio which com- 

 pares the theoretical calculated resistance from 

 Equation (3) to an actual measured electrode 

 resistance. The calculated resistance according to 

 Equation (3), using the 2 x 2 x 4 m electrodes 

 of one test was: 



0.189x4 

 R = = 0.189ohm 



with a salinity of 32.9%o and a temperature of 

 28.7°C (p = 0.189 ohm-m). The measured resis- 



tance was actually 0.039 ohm. An index of dif- 

 ference between the calculated and measured 

 resistance provides a ratio of 4.85. The ratio of 

 calculated to measured resistance ranged from 

 4.85 to 5.2 throughout the study period, with the 

 measured resistance of the electrode array vary- 

 ing from 0.035 to 0.04 ohm. Hence, a midrange 

 value of 5.0 seems the most practical and resis- 

 tance value one-fifth of the Equation (3) calculated 

 value is used to compute total spread resistance 

 as shown in the following equation: 



Rt = 



PL 

 5A 



(5) 



where R, 



= total spread resistance including 

 both electrodes. 



As a cross-check to Equation (5) we also computed 

 the spread resistance from Equation (4) using a 

 value of K „ derived from the sample test. The 

 measured resistance of the electrode array in sea- 

 water was 0.039 ohm. Since each electrode con- 

 tributes one-half the resistance, the spread resis- 

 tance for Equation (4) is 0.0195 ohm. In addi- 

 tion, since both sides of each electrode in our 

 tests were exposed, the surface area for 

 the equation is twice that of one side. Using 

 these values, K^ is determined to be: 



0.0195 = 



K^a + 28.7 X 0.02) 



\| 2(2)2 

 where Ko = 0.035 ohm-m. 



For a 5 X 5 X 10 m electrode array using 

 Equations (4) and (5), the following load resis- 

 tances are determined at 28.7°C and 32.9 'oo: 



Equation (4) 



0.189 X 10 

 Ri = = 0.01512 ohm, 



5(5)2 



Equation (5) 



0.035(1 + 28.7x0.02) 



ii<j 



where R t 

 Rt 



n] 2(5)2 



0.00779, 



2Rs = 2(0.00779) = 0.01558, 

 2i?, since Rs is the resistance of 

 one electrode. 



665 



