大象传媒

Advisors:听Florin Adrian Radu, Kundan Kumar听and Jan Martin Nordbotten

Short description of project:

Fluid flow phenomena in porous media have always attracted a lot of听attention of scientists and engineers. Attempts to quantify the average听transport in homogeneous media with a simple partial differential听equation with constant coefficients disclosed significant听inconsistencies comparing to experiments. Modern numerical simulations听of porous networks confirmed that those inconsistencies are systematic听and not caused by the observation error. The error appeared as a result听of the, so called, anomalous or non-Fickian transport, which was in听contrast to the normal regime, described by the Fick鈥檚 laws.

The problem has been addressed through the introduction of more complex听and substantial models to describe the phenomena. Although, these new听approaches have resolved the problem of quantification, they have raised听another question for researchers and engineers, how to choose the most听suitable approach and, if it is possible, to parametrize the modeling听choice at all. The models general lack of physical consistency makes it听difficult to distinguish the model parameters. This leaves judging of听suitability to the general accuracy of quantification only, which is听often not the most important criterion. In other words, the model听parameters are typically estimated by fitting the model to the听experimental data, and are often not related to the real properties of听the medium. Therefore, a model is often chosen a priory, based only on听the experience of the researcher.

In this work, we address the problem of model selection by introducing a听new model: the Generalized Continuum Transport model. This model听transforms into existing models at certain limits and, therefore,听constrains the modeling choice through the introduction of the parameter听space. It is shown that the Generalized Continuum Transport model limits听to the advection-dispersion equation, the Continuous Time Random Walk,听the Multi-Rate Mass Transfer and the Multiple-Porosity models, when听corresponding configurations of the parameter space are applied.

The model鈥檚 accuracy is studied by quantifying the breakthrough curves听obtained from a fine scale porous network model demonstrating听significant appearance of anomalous transport phenomena. The results听show that the error of quantification is smaller than the error of the听existing models.

It is discussed that the parameters of the Generalized Continuum听Transport model are related to the physical properties of porous media.听Finally, it is presented that the parameter space of GCT can be听constrained and related to the transport phenomena studied. Hence, the听limits of GCT are controlled by the transport complexity and the desired听accuracy and the modeling choice can be parametrized.

Link to thesis at BORA-UiB:听

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