Discontinuous pressure approximations for modeling multiphase flow in complex porous media
File(s)
Author(s)
Al Kubaisy, Jumanah Abdulla I
Type
Thesis
Abstract
The control volume finite element (CVFE) method provides a flexible framework for modeling multiphase flow in complex porous media domains. This method employs two meshes—the element mesh and the control volume mesh—to represent the flow field and the transport solution, respectively. In the presence of material heterogeneity, the dual-mesh approach introduces inconsistency due to the control volume construction spanning element boundaries. This inconsistency leads to inaccuracies in the transport solution, which are further exacerbated when encountering sharp material interfaces or discontinuities.
In this thesis, two approaches are developed for addressing the inconsistency challenge exhibited in the CVFE method. First, the hybrid control volume finite element (HyCVFE) method is developed. This approach combines the best features of continuous and discontinuous approximations within a single framework. It applies an efficient, continuous approximation in subdomains with homogeneous or smoothly varying material properties, while exclusively using a discontinuous approximation along subdomain boundaries. The control volumes constructed by this approach are restricted within each subdomain, ensuring accurate transport solutions. The method is validated and demonstrated to outperform other CVFE approximations in the presence of heterogeneity, requiring minimal computational overhead for embedding discontinuities.
The second developed approach is based on a single mesh control volume finite element (SM-CVFE) method. The discretization of the proposed new element pair allows for a one-to-one mapping between the element mesh and control volume mesh. This ensures correct representation of material property between adjacent elements, leading to accurate saturation distributions. The approach is shown to naturally honor geo-statistically mapped material properties. Further extensions to the SM-CVFE framework are described, demonstrating the method's superiority in capturing 3D multiphase flow solutions without exhibiting mesh sensitivity.
In this thesis, two approaches are developed for addressing the inconsistency challenge exhibited in the CVFE method. First, the hybrid control volume finite element (HyCVFE) method is developed. This approach combines the best features of continuous and discontinuous approximations within a single framework. It applies an efficient, continuous approximation in subdomains with homogeneous or smoothly varying material properties, while exclusively using a discontinuous approximation along subdomain boundaries. The control volumes constructed by this approach are restricted within each subdomain, ensuring accurate transport solutions. The method is validated and demonstrated to outperform other CVFE approximations in the presence of heterogeneity, requiring minimal computational overhead for embedding discontinuities.
The second developed approach is based on a single mesh control volume finite element (SM-CVFE) method. The discretization of the proposed new element pair allows for a one-to-one mapping between the element mesh and control volume mesh. This ensures correct representation of material property between adjacent elements, leading to accurate saturation distributions. The approach is shown to naturally honor geo-statistically mapped material properties. Further extensions to the SM-CVFE framework are described, demonstrating the method's superiority in capturing 3D multiphase flow solutions without exhibiting mesh sensitivity.
Version
Open Access
Date Issued
2023-12-10
Date Awarded
01/05/2024
License URL
Advisor
Jackson, Matthew
Salinas, Pablo
Pain, Christopher
Sponsor
Saudi Aramco
Publisher Department
Earth Science & Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)