Heat loss¶
Three types of heatlosses in the pipeline are considered, in accordance to the NEN-EN 13941+A1. These are heat loss through:
Tube wall
Subsoil
Though neighboring pipeline
Visualized schematically, these are heat losses/fluxes as follows:
If we write it in a set of equations (which can be formulated as constraints), we get the following equation for the temperature loss inside a pipe from its in- to its outport:
In which the heat loss \(Q_{loss}\) is equal to:
In which:
\(L\): Length of pipeline [m]
\(T_h\): Temperature in hot (feed) pipeline [K]
\(T_c\): Temperature in cold (return) pipeline [K]
\(T_g\): Temperature at ground temperature [K]
The values for \(U_1\) and \(U_2\) follow from the following set of equations:
In which:
\(R_g\): Subsoil heat resistance [mK/W]
\(R_{iso}\): Insulation heat resistance [mK/W]
\(R_m\): Heat resistance due to neighboring pipeline [mK/W]
As the description above shows, \(U_1\) and \(U_2\) are constant values based on type, placement en dimensions of the pipelines.
For the MILP formulation of HeatMixin
, the hot and cold temperature lines are fixed.
The heat loss of a pipe in the MILP formulation is therefore not dependent on the flow rate.
For the NLP formulation of QTHMixin
, the temperature of a pipe is the average of its in- and outgoing temperatures.
This means that the heat loss is dependent on flow rate.