Background
Recently, we focused on a more challenging topic: the coupled mechanism of multi-physical fields in frozen soil surrounding buried hot oil pipeline. Due to the unique nature of frozen soil, i.e. a heat-induced transformation from simple solid to porous media containing liquid water, interactions between different physical fields should be taken into consideration.
We established the governing equations of temperature and water fields for frozen soil and simulated the water-heat coupled phenomenon utilizing the finite volume method based on unstructured grids.
Recently, we focused on a more challenging topic: the coupled mechanism of multi-physical fields in frozen soil surrounding buried hot oil pipeline. Due to the unique nature of frozen soil, i.e. a heat-induced transformation from simple solid to porous media containing liquid water, interactions between different physical fields should be taken into consideration.
We established the governing equations of temperature and water fields for frozen soil and simulated the water-heat coupled phenomenon utilizing the finite volume method based on unstructured grids.
![图片](/uploads/2/5/4/3/25435923/9630201.png?295)
Mathematical Model
The complete description of the whole thermal system includes four main parts as follows:
The complete description of the whole thermal system includes four main parts as follows:
- Part 1: Convective heat transfer of crude oil in pipeline
- Part 2: Heat conduction of wax layer, steel wall and insulation layer
- Part 3: Heat transfer in frozen soil saturated with ice and water
- Part 4: Heat transfer between frozen soil and ambient atmosphere
![图片](/uploads/2/5/4/3/25435923/3838814.png?417)
Numerical Method
- Considering the symmetry of pipeline cross section, take half of the area as the computational domain.
- Generate unstructured quadrilateral grids by the improved Paving method.
- The coupled simulation of water and temperature fields is conducted by utilizing the SIMPLE algorithm for unstructured grids.
- The method of thermal characteristic line is used to calculate the unsteady flow and get the oil temperature distribution along the pipeline.
Results and Conclusions
Based on the mathematical models and numerical method demonstrated above, we conducted coupled simulation for a typical hot crude oil pipeline under different conditions and operating periods. Some general conclusions can be drawn as follows:
Where (a) - Temperature fields obtained by pure heat conduction model (green line) and water-heat coupled model (red line)
(b) - Water content field of frozen soil (red area represents the soil with large water content while the blue area stands for the opposite situation)
(c) - Flow-stream function of water migration
(d) - Distribution of velocity vector of water migration
Based on the mathematical models and numerical method demonstrated above, we conducted coupled simulation for a typical hot crude oil pipeline under different conditions and operating periods. Some general conclusions can be drawn as follows:
- The transport phenomena within frozen soil are determined by the strong coupled interactions between different physical fields and various phases in the porous media.
- The ice in frozen soil absorbs the heat from the pipeline and melts into liquid water which has lower heat conductivity, the whole heat conductivity of soil decreases along with the declined proportion of ice to water. When the ice turns into water, the latent heat of phase change also slows down the heat transfer process in the soil.
- Under the temperature gradients of frozen soil, the unfrozen water would migrate in the porosity of soil and the streamlines of migration diagram distribute denser near the pipeline where there is the largest temperature gradient. It is also worth noting that the magnitude of water migrating velocity is relatively small so the natural convection of unfrozen water in soil has little effect on the ultimate soil temperature field.
Where (a) - Temperature fields obtained by pure heat conduction model (green line) and water-heat coupled model (red line)
(b) - Water content field of frozen soil (red area represents the soil with large water content while the blue area stands for the opposite situation)
(c) - Flow-stream function of water migration
(d) - Distribution of velocity vector of water migration
Future Work
So far, we are still studying on this complex system and the coupled transport phenomena in porous media always excite me to keep moving on. Our main focuses for the future are:
So far, we are still studying on this complex system and the coupled transport phenomena in porous media always excite me to keep moving on. Our main focuses for the future are:
- Study the coupled phenomena between water, temperature and stress fields by combining finite volume method and finite element method
- Carry out lab experiments to characterize structural properties of porous media and to monitor interactions of different phases in dynamic systems
- Develop state-of-the-art computer program to implement 3-D coupled simulation