Browsing by Subject "Heat--Convection--Mathematical models"

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Characterizing heterogeneity in low-permeability strata and its control on fluid flow and solute transport by thermalhaline free convection
(2005) Shi, Mingjuan; Sharp, John M.
Studies of salinity-driven free convection across low-permeability strata indicate that permeability heterogeneity is an important factor in controlling solute transport in the system. Heterogeneity exists at different scales in natural geological materials and presents a significant challenge to many aspects of geological science and petroleum studies. The traditional Rayleigh number criterion is overly conservative in predicting thermohaline convection in a heterogeneous system. Heterogeneity effects are investigated with numerical models to study salinity-driven groundwater flow and solute transport through heterogeneous low-permeability units. Monte Carlo stochastic simulations of the permeability fields are applied to model saturated variable-density flow and to examine how the internal structure of the permeability field controls fluid flow and contaminant transport in low-permeability strata. Simulations show that dense plumes take preferential pathways to sink through low-permeability strata; patch analysis using percolation theory shows the threshold permeability for the onset of free convection can be as low as 10-16 m 2 when the mean permeability of the distribution is 10-18 m 2 . The threshold permeability for a percolation cluster decreases with increasing concentration gradient, vertical correlation length, mean permeability, and standard deviation. The connectedness of the relative high permeability zones is important in initiating and controlling plume fingers of free convection. Numerical modeling results also show that free convection occurs more easily and often when there is a sand or sandstone layer on top of the lowpermeability shale layer or below with different boundary conditions. For a fractured low-permeability shale layer, free convection can easily occur along the fracture plane which suggests the inadequacy of two-dimensional fracture model for simulating free convection in parallel-plate discrete fractures. Free convection through hydraulically active tiny fractures can be an important mechanism for flow and solute transport even though these tiny fractures in the shale unit can not be detected by vertical boreholes and flow in most part of the unit is diffusion-dominated.