Implementation and Validation of Gravity Effects in a Pore-Network Solver

Table of Contents

1 Introduction

2 Pore network solver with gravity

2.1 Physical displacement mechanism

2.2 Local capillary pressure pc i(sw i) (Lee et al. [2009])

2.3 Gravity affected flow rate between pore bodies

2.4 Mathematical Equations and algorithm

2.4.1 Assumptions

2.4.2 Boundary Conditions

2.4.3 Governing equations

2.4.4 Pressure Field Solver

2.4.5 Time-step Calculation

2.4.6 Algorithm

3 Validation and code development

3.1 Test Case 1 - Macroscale pore column (single phase)

3.2 Test Case 2 - Microscale pore column (single phase & low interfacial tensions)

3.3 Test Case 3 - Microscale pore column (single phase & high interfacial tensions)

3.4 Test Case 4 - Macroscale pore column (multiphase)

3.5 Test Case 5 - Microscale pore column (multiphase & low interfacial tension)

3.6 Test Case 6 - Microscale pore column (multiphase & high interfacial tension)

3.7 Test Case 7 & 8 - Microscale pore column with injection of less dense fluid

3.8 Test Case 9 - 2D-Pore field with equal sized pore bodies (low interfacial tension)

3.9 Test Case 10 - 2D-Pore field with equal sized pore bodies (high interfacial tension)

3.10 Test Case 11 - 2D-Pore field with poly sized pore bodies (low interfacial tensions)

3.11 Test Case 12 - 2D-Pore field with poly sized pore bodies (high interfacial tensions)

4 Parameter study on fluid displacement

4.1 Drainage Phase-diagram for immiscible displacement after Lenormand et al. [1988]

4.2 Influence of Interfacial Tension

4.3 Influence of the viscosity ratio

4.4 Influence of inlet pressure and injection rate

4.4.1 Displacement evolution

4.4.2 Influence of flow rate variations

5 Simulation of the CCS-Showcase

5.1 Experimental setup

5.2 Pore network modeling of CCS-Showcase

5.2.1 HYPON-model after Acharya et al.

5.2.2 Assumptions for the pore network

5.2.3 Generation of the pore network

5.3 Simulation of the experiments

5.3.1 Physical properties of injected fluids

5.3.2 Ethyl acetate with a flow rate of 150 ml/min and 2mm glass beads

5.3.3 Heptane with a flow rate of 150 ml/min and 2mm glass beads

5.3.4 Comparison of ethyl acetate and heptane

5.4 Simulation of a High Pressure Showcase

6 Conclusion

7 Outlook

Research Objectives & Topics

This thesis aims to enhance a pore-scale network solver by implementing gravity effects to better simulate and analyze fluid displacement in porous media, specifically regarding carbon dioxide capture and storage (CCS) applications. The research focuses on validating this modified solver against experimental data from a scaled-down porous media showcase.

• Implementation of gravity effects in pore-network solvers.
• Validation of the numerical model through various test cases.
• Analysis of influencing factors such as density, viscosity ratio, and interfacial tension.
• Predictive simulation of fluid migration in a glass-bead packed CCS showcase.
• Comparison of simulation results with experimental fluid injection data.

Excerpt from the Book

Summary of Chapters

1 Introduction: Provides the historical and environmental context of carbon dioxide capture and storage (CCS) and outlines the motivation for the study.

2 Pore network solver with gravity: Details the theoretical framework, the modified pressure solver incorporating gravity, and the governing mathematical equations.

3 Validation and code development: Describes the series of numerical test cases used to verify the correct implementation of gravity and the physical accuracy of the solver.

4 Parameter study on fluid displacement: Analyzes the impact of various physical properties like density, viscosity, and flow rates on the fluid migration patterns.

5 Simulation of the CCS-Showcase: Applies the validated model to simulate the experimental CCS showcase, comparing the results with actual laboratory injections of ethyl acetate and heptane.

6 Conclusion: Summarizes the findings regarding gravity implementation and the solver's predictive capabilities for fluid displacement.

7 Outlook: Proposes future improvements, such as including imbibition mechanisms and utilizing supercomputing for 3D simulations.

Keywords

Pore-network solver, Gravity effects, Fluid displacement, Porous media, Carbon Capture and Storage (CCS), CCS-Showcase, Multiphase flow, Capillary pressure, Viscosity ratio, HYPON model, Numerical validation, Drainage, Immiscible displacement, Fluid migration, Hydrostatic pressure.

Frequently Asked Questions

What is the core subject of this thesis?

The thesis focuses on simulating fluid displacement in porous media for CCS applications, specifically by improving a pore-network solver to account for gravity effects.

What are the key thematic areas covered?

The study covers the development of numerical solvers, validation through test cases, comprehensive parameter studies on fluid properties, and practical application to a laboratory CCS showcase model.

What is the primary goal of the research?

The goal is to implement and validate gravity effects within an existing pore-network solver to improve the prediction of fluid migration in porous structures during carbon dioxide storage.

Which scientific method is utilized?

The research uses a pore-scale network model combined with numerical pressure solvers (in GFortran/Fortran 90) and MATLAB for network generation and result visualization.

What is addressed in the main part of the work?

The main part encompasses the mathematical derivation of the gravity-weighted solver, validation steps, extensive parameter investigations, and the final simulation of ethyl acetate and heptane injection in a CCS showcase.

Which keywords characterize the work?

Key terms include pore-network solver, gravity effects, porous media, fluid displacement, CCS-Showcase, multiphase flow, and numerical validation.

How does gravity affect the fluid flow in the model?

Gravity is incorporated as a direction-dependent force added to the flow rate calculations between pore bodies, which influences the pressure distribution and the driving force of the nonwetting fluid.

Why are ethyl acetate and heptane used in the study?

These substances are used to investigate fluid displacement patterns that serve as a proxy for the spreading behavior of supercritical CO2 in experimental conditions.