Sea-Bird Electronics SBE 45 MicroTSG, Руководство пользователя

Страница: 110 / 143

DISCUSSION OF PRESSURE CORRECTION
Conductivity cells do not measure the specific conductance (the desired property), but rather the conductance of a
specific geometry of water. The ratio of the cell’s length to its cross-sectional area ( cell constant ) is used to relate the
measured conductance to specific conductance. Under pressure, the conductivity cell’s length and diameter are
reduced, leading to a lower indicated conductivity. The magnitude of the effect is not insignificant, reaching
0.0028 S/m at 6800 dbars.
The compressibility of the borosilicate glass used in the conductivity cell (and all other homogeneous, noncrystalline
materials) can be characterized by E (Young’s modulus) and
ν (Poisson’s ratio). For the Sea-Bird conductivity cell,
E = 9.1 x 10
6
psi, ν = 0.2, and the ratio of indicated conductivity divided by true conductivity is:
1 + s
where s = (CPcor) (p)
Typical value for CPcor is - 9.57 x 10
-8
for pressure in decibars or - 6.60x 10
-8
for pressure in psi
Note:
This equation and the mathematical derivations below deal only with the pressure correction term, and do not
address the temperature correction term.
MATHEMATICAL DERIVATION OF PRESSURE CORRECTION
For a cube under hydrostatic load:
Δ L / L = s = -p (1 - 2 ν ) / E
where
•
p is the hydrostatic pressure
•
E is Young’s modulus
•
ν is Poisson’s ratio
•
Δ L / L and s are strain (change in length per unit length)
Since this relationship is linear in the forces and displacements, the relationship for strain also applies for the length,
radius, and wall thickness of a cylinder.
To compute the effect on conductivity, note that R
0
= ρ L / A , where R
0
is resistance of the material at 0 pressure,
ρ is volume resistivity, L is length, and A is cross-sectional area. For the conductivity cell A = π r
2
, where r is the
cell radius. Under pressure, the new length is L (1 + s ) and the new radius is r (1 + s ). If R
p
is the cell resistance
under pressure:
R
p
= ρ L (1 + s ) / ( π r
2
[1 + s ]
2
) = ρ L / π r
2
(1 + s ) = R
0
/ (1 + s )
Since conductivity is 1/R:
C
p
= C
0
(1 + s ) and C
0
= C
p
/ (1 + s ) = C
p
/ (1 + [Cpcor] [p])
where
•
C
0
is conductivity at 0 pressure
•
C
p
is conductivity measured at pressure
A less rigorous determination may be made using the material’s bulk modulus. For small displacements in a cube:
Δ V / V = 3 Δ L / L = -3p (1 - 2 ν ) / E or Δ V/V = -p / K
where
•
Δ V / V is the change in volume per volume or volume strain
•
K is the bulk modulus. K is related to E and ν by K = E / 3 (1 - 2 ν ).
In this case,
Δ L / L = -p / 3K.
107