Heat Transfer In Buried Liquid Pipelines

Dear All,

Today's blog entry relates to heat transfer from liquids flowing in long-distance buried pipelines. When liquids have to be transported at relatively high temperatures, e.g. viscous crudes/products, temperatures and cooling rates can be determined using the following formulae:



where:
T_L = average temperature in cross-section of pipeline at distance L, K
T_s = soil temperature at pipeline depth, K
T_inlet = temperature at pipeline inlet (L = 0), K
U_eff = Effective Heat Transfer Coefficient, W/m²-K
d = pipe internal diameter, m
L = pipeline distance at which T_L is to be measured, m
m = mass flow rate of liquid, kg/s
C_p =Specific Heat Capacity of pipeline contents, J/kg-K

Calculation of U_eff


U_convective
For turbulent flow (Re > 4000)


For Laminar flow (Re < 2300)


where:
U_convective = Convective heat transfer coefficient, W/m²-K
λ_liq = liquid thermal conductivity, W/m-K (for crude oil, λ_liq = 0.13 W/m-K)
u = average liquid velocity, m/s
ρ = liquid density, kg/m³
d = pipe internal diameter, m
C_p = Specific Heat Capacity of pipeline contents, J/kg-K
ν = liquid kinematic viscosity, m²/s
g = acceleration due to gravity = 9.81 m/s²
α = thermal expansion coefficient, 1/K (for crude oil, α = 8*10^-4 K-1)
µ_b = bulk liquid viscosity, Pa.s
μ_w = liquid viscosity at wall temperature, Pa.s
T_b = bulk temperature, K
T_w = inside wall temperature, K

Notes:
1. The inside wall temp. (T_w) is generally assumed 2-3 degrees lower than the bulk temp. (T_b) in laminar flow
2. The bulk liquid viscosity (μ_b) and the liquid viscosity at wall temperature (μ_w) can be assumed same for turbulent flow thus reducing the term (μ_b / μ_w) to 1

Specific Heat Capacity of Crude Oil


where:
C_p = Specific heat capacity at temperature T, J/kg-K
T = Temperature, ⁰C
ρ = crude oil density at temperature T, kg/m³

U_wall


where:
U_wall = steel wall heat transfer coefficient, W/m²-K
λ_steel = thermal conductivity of steel, W/m-K (for Carbon Steel, λsteel = 52 W/m-K)
d_o = outside diameter of the steel pipe, m

d = pipe internal diameter, m
t_wall = wall thickness, m

U_coating (Note: External Coating could be a polyolefin liner or insulation)


where:
U_coating = coating heat transfer coefficient, W/m²-K
d_o = outside diameter of the steel pipe, m
λ_coating = thermal conductivity of coating or insulation, W/m-K
t_coating = coating thickness, m



U_environment (For Buried pipes the environment is soil)





where:
U_environment = heat transfer coefficient to the environment (soil), W/m²-K
λ_soil = thermal conductivity of soil, W/m-K
z = burial depth of the pipe up to the pipe axis, m



I have developed a spreadsheet for temperature drop in a buried crude oil pipeline based on the above methodology. For a set of conditions that I have used and for a pipeline inlet crude oil temperature of 55⁰C, the temperature drops to 48.5⁰C at a distance of 50 km for a 16 inch NPS pipeline based on the above method. The pipeline is also externally coated.

That is all for today's blog entry. Hope to have comments from the knowledgeable members of the forum.

Regards,
Ankur.