Modelling Carbon Dioxide Depressurization with Different Two-Phase Models

Abstract

Carbon capture and storage (CCS) has emerged as a cornerstone technology for mitigating climate change, as highlighted by the Intergovernmental Panel on Climate Change (IPCC) and International Energy Agency (IEA). A key component of CCS involves the safe and efficient transport of CO2 between capture sites and storage facilities, often over long distances. Pipelines can be an attractive mode of transport, with CO2 typically maintained in a liquid or supercritical state to optimize density and viscosity. However, rapid depressurization events, whether due to intentional releases or accidental pipeline ruptures, lead to complex two-phase flow dynamics. Accurately modelling these phenomena is critical to designing pipelines that are both safe and cost-effective.
This thesis investigates various one-dimensional, unsteady, compressible two-phase flow models to simulate CO2 depressurization scenarios in pipelines. All models are implemented using a finite volume method and discretization is done with the HLLC approximate Riemann solver, enabling the resolution of shocks and dis- continuities. Thermodynamic properties are computed using equations of state (EOS), with a focus on the Span-Wagner (SW) EOS, to capture the CO2 unique phase behaviour under high-pressure conditions. The models are validated against existing experimental data from SINTEF’s depressurization facility, which provided high-resolution measurements of pressure and temperature during rapid phase transitions.
Three different models are initially looked at: DF3, DF4, and TF5. Key findings demonstrate that while the DF3 model provides accurate predictions of pressure variations over time, it underestimates the initial pres- sure drop by up to 20 [bar]. In contrast, the DF4 model, through the manual adjustment of the mass transfer term (Γ) using the relaxation parameter ,θ , more accurately captures the initial transient behaviour, aligning closely with experimental data. Both models ultimately converge to approximately the same state after 20 [ms], with no more than 4 [bar] difference between the models.
Temperature predictions, however, pose a greater challenge. The DF3 model exhibits a spurious downward temperature spike immediately following pipeline rupture, while the DF4 model predicts an even greater initial temperature drop, neither of which align with experimental observations. The delayed cooling effect observed in experiments is not captured by either model, highlighting limitations in the energy equation and the need for additional source terms to account for temperature drop delays.
Limitations of the models include challenges in simulating temperature variations near the critical point and an inability to accurately model delayed temperature effects for both the DF3 and DF4 models. Recommendations for future work include developing a generalized mass transfer model, incorporating implicit numerical schemes for stability near critical conditions. Furthermore, the TF5 model shows promise for improving temperature predictions over longer timescales.