Dispersion in large scale permeable media
Dispersivity data compiled over many lengths show that values at typical interwell distances are about two to four factors of ten larger than those measured on cores. Such large dispersivities may represent large mixing zones in the reservoir or they may be a result of convective spreading driven by permeability heterogeneity. This dissertation uses the idea of flow reversal (echo tests) to distinguish between convective spreading and dispersive mixing. Spreading is reversible, mixing is not. A zero or small value of echo dispersivity (estimated after flow reversal) implies little or no mixing and convection dominated transport. An echo dispersivity value equal to the transmission value (estimated after forward flow) would imply well mixed transport. A particle tracking code is developed to simulate echo tests for tracer transport in single phase, incompressible flow through three-dimensional, heterogeneous permeable media. Echo dispersivities are estimated for typical heterogeneity realizations and compared with corresponding transmission values at the field scale. The most important observation is that echo dispersivities are significantly larger than core scale values. They also lie on the overall trend of measured dispersivities and corroborate the large echo dispersivities previously inferred from single well tracer test data. This implies that significant mixing occurs in field scale transport. Echo dispersivities increase with permeability heterogeneity (variance and autocorrelation lengths). This is the effect of local (point or pore scale) mixing in the transverse direction, integrated over long and tortuous flow paths. Transport in typical reservoir formations, with significant autocorrelation in permeabilities, is most likely to be in a pre-asymptotic regime and cannot be described by a unique dispersivity value. This is because the Fickian model for dispersion fails to capture the mixing zone growth correctly in this regime. These results highlight the need to develop representative models for dispersion and improve upscaling methodologies.