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ABSTRACT
Since the temperature drop of waxy crude oil after a shutdown determines whether the pipeline is able to restart successfully or not, it is necessary to calculate the temperature drop and clarify the characteristic of the thermal process of waxy crude oil pipeline after the shutdown. However, the relevant techniques proposed in the previous researches for this calculation are not accurate enough, due to the complex phase change, non-Newtonian behavior of the fluid, and the transition of different heat transfer mechanisms involved within the physical problem. Therefore, in a companion piece to this paper, a general and accurate mathematical model was proposed for the phase-change heat transfer of waxy crude oil. In this paper, the mathematical model of the waxy crude oil pipeline system after its shutdown is established, based on the phase-change heat transfer model proposed in the companion piece, and the numerical procedure is established for the calculation of the model. With the proposed techniques, the thermal process of the shutdown of waxy crude oil is investigated in detail, and the temperature drop characteristic is clarified on the level of heat transfer mechanism. The research will provide theoretical support for the establishment of shutdown scheme and thermal preservation method for waxy crude pipeline.
Nomenclature
| = | filtered variables | |
| cp | = | specific heat capacity |
| Cw | = | WALE constant |
| g | = | gravity acceleration |
| gl | = | liquid volume fraction |
| gs | = | solid volume fraction |
| k | = | von Kármán constant |
| K | = | consistency coefficient |
| Kd | = | permeability |
| K0 | = | permeability constant |
| Ls | = | mixing length for sub-grid scales |
| n | = | rheological behavior index |
| P | = | pressure |
| QL | = | latent heat of phase change |
| r, θ | = | coordinate variables |
| S | = | source term |
| Sij | = | rate-of-deformation tensor |
| T | = | temperature |
| Tc | = | reference temperature |
| uθ, ur | = | velocity in θ and r direction, respectively |
| uθ, s, ur, s | = | solid-phase velocity in θ direction and r direction, respectively |
| β | = | coefficient of cubical expansion |
| ΔH | = | latent heat |
| Γ | = | diffusion coefficient |
| λt | = | eddy diffusion coefficient |
| μa | = | apparent viscosity |
| μl | = | kinetic viscosity of the liquid phase |
| μt | = | turbulent viscosity |
| ρ | = | density |
| τij | = | shear stress tensor |
| ϕ | = | general dependent variable |
| Subscripts | = | |
| ins | = | insulation |
| l | = | liquid |
| s | = | solid |
Nomenclature
| = | filtered variables | |
| cp | = | specific heat capacity |
| Cw | = | WALE constant |
| g | = | gravity acceleration |
| gl | = | liquid volume fraction |
| gs | = | solid volume fraction |
| k | = | von Kármán constant |
| K | = | consistency coefficient |
| Kd | = | permeability |
| K0 | = | permeability constant |
| Ls | = | mixing length for sub-grid scales |
| n | = | rheological behavior index |
| P | = | pressure |
| QL | = | latent heat of phase change |
| r, θ | = | coordinate variables |
| S | = | source term |
| Sij | = | rate-of-deformation tensor |
| T | = | temperature |
| Tc | = | reference temperature |
| uθ, ur | = | velocity in θ and r direction, respectively |
| uθ, s, ur, s | = | solid-phase velocity in θ direction and r direction, respectively |
| β | = | coefficient of cubical expansion |
| ΔH | = | latent heat |
| Γ | = | diffusion coefficient |
| λt | = | eddy diffusion coefficient |
| μa | = | apparent viscosity |
| μl | = | kinetic viscosity of the liquid phase |
| μt | = | turbulent viscosity |
| ρ | = | density |
| τij | = | shear stress tensor |
| ϕ | = | general dependent variable |
| Subscripts | = | |
| ins | = | insulation |
| l | = | liquid |
| s | = | solid |