Abstract
This paper presents a modification of a classical Godunov-type scheme for the numerical simulation of a two-phase flow in a pipe with a piecewise constant cross-sectional area. This type of flow can occur in wellbores during drilling for oil and gas as well as after well completion. Contrary to classical finite-volume schemes, the numerical scheme proposed in this paper captures the steady-state solution of the system without generating non-physical discontinuities in the numerical solution close to the locations of discontinuities in the cross-section. Moreover, the proposed scheme can be extended to problems with piecewise continuous cross-sectional area. This extension is achieved by discretization of the area along the spatial domain and converting the piecewise continuous area into a piecewise constant area. The proposed scheme reduces to the classical scheme when the cross-sectional area is constant along the spatial domain. For the purpose of computational efficiency, the modification to the classical scheme is only applied at the locations of area variation and the numerical solver reduces to the classical scheme where the cross-sectional area is constant. It is also shown that the proposed scheme can be effectively used to simulate two-phase flows arising from the perturbation of the steady-state solution. The effectiveness of the proposed scheme is shown through illustrative numerical simulations. Finally, it should be noted that the proposed scheme retains the same order of accuracy as the underlying classical scheme.
| Original language | English |
|---|---|
| Pages (from-to) | 796-813 |
| Number of pages | 18 |
| Journal | Journal of Petroleum Science and Engineering |
| Volume | 179 |
| DOIs | |
| Publication status | Published - 1 Aug 2019 |
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Keywords
- Drift Flux Model
- Finite-volume scheme
- Non-conservative PDE
- Two-phase flow
- Variable cross section
- Well-balanced scheme
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A Godunov-type scheme for the drift flux model with variable cross section. / Abbasi, Mohammad (Corresponding author); Naderilordejani, Sajad; Velmurugan, Naveen; Berg, C.; Iapichino, Laura; Schilders, Wil; van de Wouw, Nathan.
In: Journal of Petroleum Science and Engineering, Vol. 179, 01.08.2019, p. 796-813.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - A Godunov-type scheme for the drift flux model with variable cross section
AU - Abbasi, Mohammad
AU - Naderilordejani, Sajad
AU - Velmurugan, Naveen
AU - Berg, C.
AU - Iapichino, Laura
AU - Schilders, Wil
AU - van de Wouw, Nathan
PY - 2019/8/1
Y1 - 2019/8/1
N2 - This paper presents a modification of a classical Godunov-type scheme for the numerical simulation of a two-phase flow in a pipe with a piecewise constant cross-sectional area. This type of flow can occur in wellbores during drilling for oil and gas as well as after well completion. Contrary to classical finite-volume schemes, the numerical scheme proposed in this paper captures the steady-state solution of the system without generating non-physical discontinuities in the numerical solution close to the locations of discontinuities in the cross-section. Moreover, the proposed scheme can be extended to problems with piecewise continuous cross-sectional area. This extension is achieved by discretization of the area along the spatial domain and converting the piecewise continuous area into a piecewise constant area. The proposed scheme reduces to the classical scheme when the cross-sectional area is constant along the spatial domain. For the purpose of computational efficiency, the modification to the classical scheme is only applied at the locations of area variation and the numerical solver reduces to the classical scheme where the cross-sectional area is constant. It is also shown that the proposed scheme can be effectively used to simulate two-phase flows arising from the perturbation of the steady-state solution. The effectiveness of the proposed scheme is shown through illustrative numerical simulations. Finally, it should be noted that the proposed scheme retains the same order of accuracy as the underlying classical scheme.
AB - This paper presents a modification of a classical Godunov-type scheme for the numerical simulation of a two-phase flow in a pipe with a piecewise constant cross-sectional area. This type of flow can occur in wellbores during drilling for oil and gas as well as after well completion. Contrary to classical finite-volume schemes, the numerical scheme proposed in this paper captures the steady-state solution of the system without generating non-physical discontinuities in the numerical solution close to the locations of discontinuities in the cross-section. Moreover, the proposed scheme can be extended to problems with piecewise continuous cross-sectional area. This extension is achieved by discretization of the area along the spatial domain and converting the piecewise continuous area into a piecewise constant area. The proposed scheme reduces to the classical scheme when the cross-sectional area is constant along the spatial domain. For the purpose of computational efficiency, the modification to the classical scheme is only applied at the locations of area variation and the numerical solver reduces to the classical scheme where the cross-sectional area is constant. It is also shown that the proposed scheme can be effectively used to simulate two-phase flows arising from the perturbation of the steady-state solution. The effectiveness of the proposed scheme is shown through illustrative numerical simulations. Finally, it should be noted that the proposed scheme retains the same order of accuracy as the underlying classical scheme.
KW - Drift Flux Model
KW - Finite-volume scheme
KW - Non-conservative PDE
KW - Two-phase flow
KW - Variable cross section
KW - Well-balanced scheme
UR - http://www.scopus.com/inward/record.url?scp=85065438661&partnerID=8YFLogxK
U2 - 10.1016/j.petrol.2019.04.089
DO - 10.1016/j.petrol.2019.04.089
M3 - Article
AN - SCOPUS:85065438661
VL - 179
SP - 796
EP - 813
JO - Journal of Petroleum Science and Engineering
JF - Journal of Petroleum Science and Engineering
SN - 0920-4105
ER -