and for another sphere (specimen CWL-6) at a 

 simulated depth of 3,760 feet it was: 



0.32 logj^T - 0.01 



(3) 



where T is time (days). 



Figure 13 shows a comparison between D'Arcy's 

 equation, Equation 1, using K^ = 0.13 x 10" ft/sec 

 and the empirical equations, Equations 2 and 3. Data 

 from the ocean spheres are shown to be bracketed by 

 the D'Arcy and empirical semi-log relations. D'Arcy's 



relation assumes a constant rate of permeability, 

 whereas the extrapolation of the empirical semi-log 

 relation assumes a decreasing rate with time. It is not 

 apparent at this time which approach defines the 

 permeability behavior of the concrete spheres. 

 Additional data from inspections are required. 



Sphere 8 was found intact but sitting on the 

 seafloor after 43 1 days. A total seawater intake of 

 15.3 cu ft or more was required to overcome the 

 positive buoyancy of the sphere. This quantity of sea- 

 water was three to four times that of the other 



5.0 





1 1 1 



1 1 1 1 1 1 1 1 



1 1 1 1 1 1 1 1 III 



1 1 1 1 



^ 









D'Arcy's Equation, Eq 1 / 





3 



"a. 4.0 



a 









Ocean 



Depth (ft) / 



_ 





Symbol 



Sphere 



3,760 — v.^ / / 





a 





o 



• 



uncoated 

 coated 



2,520 —n/\„^^/ / 





i 



1 3.0 



- 



3 



half-coated 



Same sphere inspected twice 



Ji 



- 



i 









1 1 





"o 









/ A 





c 2.0 



5 





Emp 



irical Semi-Log Relations 

 Depth (ft) 



/ / .o 



/ / y r\ 





1.0 



- 



\ 



— 3,760 (Eq 3) 

 r 2,520 (Eq 2) 



/45^ 



- 



n 





1 PT 



1 1 1 1 \f^^^^\ 1 



1 1 1 1 III « 1 \ m\ 



MM 



Time, T (days) 



Figure 13. Comparison of ocean sphere permeability data with the D'Arcy equation and the 

 empirical semi-log relations as given in Reference 8. 



16 



