Heat transport is completely analogous to mass transport. Hence, heat can be simulated as a species in GoldSim. Note, however, that GoldSim treats all species in terms of mass. In order to simulate heat transport, therefore, you will need to enter data which reference heat (e.g., calories) as if it were mass (e.g., grams). The easiest way to do this is to assume, for the purpose of data entry and calculations, that 1 gram is equivalent to 1 calorie. At the end of your calculations, you can then multiply results by 1 cal/g so that they display in the proper units.
When simulating heat, the following points should be noted:
•The molecular diffusivity must be replaced by the thermal diffusivity (typically denoted as κ). The thermal diffusivity is computed as follows:
κ = K/(ρ cp)
where:
|
κ |
= thermal diffusivity [m2/sec]; |
|
K |
= thermal conductivity [cal/(sec m °C)] |
|
ρ |
= density [kg/m3]; and |
|
cp |
= specific heat [cal/(kg °C)]. |
•To convert computed “heat concentrations” in a fluid (in cal/m3) to temperature, it is necessary to divide the “heat concentration” by the product ρ cp.
•To convert computed “heat concentrations” in a solid (in cal/kg) to temperature, it is necessary to divide the “heat concentration” by cp.
•Partition coefficients between media for heat can be computed by assuming that at equilibrium, the temperature in all media is the same. The partition coefficient (which simply represents the ratio of concentrations) between solid A and fluid B is then:
KAB = cp,A / (cp,B ρB)
where:
|
KAB |
= partition coefficient between solid A and fluid B [m3/kg]; |
|
ρB |
= density of fluid B [kg/m3]; |
|
cp,A |
= specific heat of solid A [cal/(kg °C)]; and |
|
cp,B |
= specific heat of fluid B [cal/(kg °C)]. |
Similarly, the partition coefficient between fluid C and fluid B is:
KCB = (cp,C ρC) / (cp,B ρB)
where:
|
KCB |
= partition coefficient between fluid C and fluid B [m3/m3]; |
|
ρC |
= density of fluid C [kg/m3]; and |
|
cp,C |
= specific heat of fluid C [cal/(kg °C)]. |
•Note that the species heat could be produced by a reaction:
A + B ⇒ 2C + n HEAT
where n is the number of calories of heat produced per mole of A reacted.
If you also had to simulate heat conduction through a solid (e.g., conduction through the wall of pipeline), you could do so as follows:
•Give the solid (e.g., representing the pipeline material) an arbitrarily small fictitious porosity value.
•Define the tortuosity for the solid in such a way that it produces the correct heat flow (since in GoldSim, all of the transport is through the fluid phase):