Publication Date


Document Type


Committee Members

David Dominic (Committee Member), Mark Goltz (Committee Member), Ramya Ramanathan (Committee Member), Robert Ritzi (Advisor)

Degree Name

Master of Science (MS)


The general principle of maximum entropy can be used to guide the construction of flow and transport models parameters when are uncertain. The principle states that the model which maximizes the entropy should be chosen so that the full multiplicity or uncertainty is represented in the model outcomes.

In models for flow and transport through georeservoirs, the principle would commonly be applicable to the uncertainty in the model outcome for the time of travel through the system, in order to represent the full range of multiplicity in the distribution of residence times. Importantly, the model which maximizes the entropy in the distribution of mass residence times may not be the model which has maximum entropy in the spatial distribution of parameters. Simulations that represent geologic structure have reduced entropy in the spatial distribution of strata, and consequently the spatial distribution of permeability, as compared to independent random simulations. Though geologic structure reduces spatial entropy in the parameter field, it can lead to maximum entropy in the model outcomes. The maximum entropy principle should be applied at the relevant decision point (particle residence times) and not at some intermediate point (model parameterization).

Geologic structure will have a large impact on increasing the entropy in the distribution of residence times when it manifests as preferential flow pathways through the system via connected high-permeability sediments. At certain volume fractions, the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly under-represent the entropy in model outcomes. The results underscore the importance of characterizing the proportions and three-dimensional structure of high-permeability units in models for mass transport.

Page Count


Department or Program

Department of Earth and Environmental Sciences

Year Degree Awarded