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ABSTRACT
The thermal process during shutdown (a stoppage state of the pipeline), of which the essence is an irregular phase-change process accompanied by natural convection, non-Newtonian behavior, and sometimes turbulence, is a critical problem in crude oil transportation engineering. An accurate calculation of the thermal process during shutdown is more than necessary for the safety of crude oil pipeline; however, it faces some challenges due to the complexity of the phase change. In this study, the phase change of waxy crude oil during the cooling process is divided into four stages, which includes a pure liquid natural convection, solid/liquid dispersion natural convection, coexistence of dispersion system natural convection and porous media natural convection, and pure porous media convection, according to different heat transfer mechanisms on different stages. Based on this division, a general phase-change heat transfer model is proposed for the thermal calculation of waxy crude oil during shutdown. Compared with the previous research, this model appropriately includes the influences of non-Newtonian behavior, phase evolution as well as turbulence. With the proposed model, the temperature drop characteristic of a sample pipeline is analyzed and the influencing factors are investigated.
Nomenclature
| cp | = | specific heat capacity |
| Sij | = | rate-of-deformation tensor |
| Cw | = | WALE constant |
| T | = | temperature |
| d | = | distance to the closest wall |
| Tc | = | reference temperature |
| g | = | gravity acceleration |
| uθ, ur | = | velocity in θ and r directions, respectively |
| gl | = | liquid volume fraction |
| uθ, s, ur, s | = | solid-phase velocity in θ and r directions, respectively |
| gs | = | solid volume fraction |
| k | = | von Kármán constant |
| β | = | coefficient of cubical expansion |
| K | = | consistency coefficient |
| ΔH | = | latent heat |
| Kd | = | permeability |
| Γ | = | diffusion coefficient |
| K0 | = | permeability constant |
| λt | = | eddy diffusion coefficient |
| Ls | = | mixing length for subgrid scales |
| μa | = | apparent viscosity |
| n | = | rheological behavior index |
| μl | = | kinetic viscosity of the liquid phase |
| P | = | pressure |
| μt | = | turbulent viscosity |
| QL | = | latent heat of phase change |
| ρ | = | density |
| r, θ | = | coordinate variables |
| τij | = | shear stress tensor |
| S | = | source term |
| ϕ | = | general dependent variable |
Nomenclature
| cp | = | specific heat capacity |
| Sij | = | rate-of-deformation tensor |
| Cw | = | WALE constant |
| T | = | temperature |
| d | = | distance to the closest wall |
| Tc | = | reference temperature |
| g | = | gravity acceleration |
| uθ, ur | = | velocity in θ and r directions, respectively |
| gl | = | liquid volume fraction |
| uθ, s, ur, s | = | solid-phase velocity in θ and r directions, respectively |
| gs | = | solid volume fraction |
| k | = | von Kármán constant |
| β | = | coefficient of cubical expansion |
| K | = | consistency coefficient |
| ΔH | = | latent heat |
| Kd | = | permeability |
| Γ | = | diffusion coefficient |
| K0 | = | permeability constant |
| λt | = | eddy diffusion coefficient |
| Ls | = | mixing length for subgrid scales |
| μa | = | apparent viscosity |
| n | = | rheological behavior index |
| μl | = | kinetic viscosity of the liquid phase |
| P | = | pressure |
| μt | = | turbulent viscosity |
| QL | = | latent heat of phase change |
| ρ | = | density |
| r, θ | = | coordinate variables |
| τij | = | shear stress tensor |
| S | = | source term |
| ϕ | = | general dependent variable |
