Don Kulasiri Bücher

Focusing on stochastic calculus, this research monograph addresses the critical issue of predicting dispersivity from hydraulic conductivity covariance in porous media. It emphasizes the significance of this problem for applications like tracer analysis and enhanced recovery via gas injection. The book offers a comprehensive mathematical model and effective numerical methods, beginning with an overview of dispersion coefficient scale dependence. It also reviews relevant stochastic calculus topics and details a generalized solute transport model applicable across scales, avoiding Fickian assumptions.

The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.