In-Situ RDO PRO Process Optical Dissolved Oxygen Sensor Manual - Manual (Page 19)

6.3.2 Dissolved Oxygen, % Saturation Equations
O
2
%Sat = O
2
Reading/ O
2
100%Sat
Where:
O
2
reading is the mg/L reading from the RDO Sensor.
O
2
100% Sat is the theoretical saturation value in mg/L and is derived as:
O
2
100%Sat = 31.9988
Ч 10 6 Ч ρ [0.20946 × (P – P
wv
)]
× (1 − Θ
o
P)
× S
c
Where:
ρ
is the density of water in g/cm
3
:
ln
ρ = -0.589581 + (326.785/T) − (45,284.1/T 2
)
T is the temperature in Kelvin.
P is the atmospheric pressure in atm.
P
wv
is the partial pressure of water vapor at saturation in atm:
ln P
wv
= 11.8571
− (3,840.70/T) − (216,961/T 2
)
k
o
is Henry’s constant:
ln k
o
= 3.71814 + (5596.17/T) – (1,049,668/T
2
)
T is the temperature in Kelvin.
Molar mass of water: M = 18.0152 g/mole
Θ
o
is the negative of the second pressure coefficient:
Θ
o
= 0.000975 – (1.426
× 10 -5
t) + (6.436
× 10 -8
t
2
)
t is temperature in degrees C.
S
c
is the salinity correction:
ln S
c
= S(B
0
+ B
1
T
s
+ B
2
T
s
2
+ B
3
T
s
3
) + C
0
S
2
B
0
= -6.246090
× 10 -3
B
1
= -7.423444
× 10 -3
B
2
= -1.048635
× 10 -2
B
3
= -7.987907
× 10 -3
C
0
= -4.679983
× 10 -7
T
s
is the scaled temperature:
T
s
= ln [(298.15 – t) / (273.15 + t)]
t is temperature in °C.
S is the salinity in PSU
References:
Benson and Krause, Jr., 1980. The concentration and isotopic fractionation of gases dissolved in
freshwater in equilibrium with the atmosphere. Limnol and Oceanogr, 25(4), 662-671.
k
o
M
Page 19 Modbus Registers