user manual

Appendix E Data tables
Page E.5
E.2. Equations used to derive data tables
Density/temperature relationship
The density/temperature relationship is:
where:
t
ρ = density at line temperature t°C (kg/m
3
)
15
ρ = density at base temperature 15°C (kg/m
3
)
t
Δ = t°C -15°C (i.e. t - base temperature)
15
α = tangent thermal expansion coefficient per °C at base temperature 15°C
Tangent thermal expansion coefficient
The tangent thermal expansion coefficient differs for each of the major groups of hydrocarbons. It is obtained
from the equation:
Product compressibility
The definition of compressibility used to develop the table in Section 1 of the IP Petroleum measurement Manual
is the isothermal secant compressibility, defined by the equation:
T
21
21
0
PP
VV
V
1
»
¼
º
«
¬
ª
−
∂−∂
−=β
Where:
β
= isothermal secant compressibility at temperature T
0
V
= volume of liquid at atmospheric pressure
1
V∂ = change in volume from
0
V to
1
V
2
V∂ = change in volume from
0
V to
2
V
1
V&
2
V = volumes at pressures
1
P and
2
P , respectively
1
P &
2
P
= gauge pressure readings (Bar)
()
[]
t15t1515t
8.01exp Δα+Δα−ρ=ρ
2
15
1510
15
KK
ρ
ρ+
=α
Where
0
K and
1
K are API factors which are obtained from the table:
Product
Density Range
(kg/m
3
)
0
K
1
K
Crude Oil 771 - 981 613.97226 0.00000
Gasolines 654 - 779 346.42278 0.43884
Kerosines 779 - 839 594.54180 0.00000
Fuel Oils 839 - 1075 186.96960 0.48618