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An analytical and computational model for non-reactive solute transport inperiodic heterogeneous media with arbitrary non-uniform flow and dispersionfields within the unit cell of length {\epsilon} is described. The model lumpsthe effect of non-uniform flow and dispersion into an effective advectionvelocity Ve and an effective dispersion coefficient De. It is shown that bothVe and De are scale-dependent (dependent on the length scale of the microscopicheterogeneity, {\epsilon}), dependent on the P\'eclet number Pe, and on adimensionless parameter {\alpha} that represents the effects of microscopicheterogeneity. The parameter {\alpha}, confined to the range of [-0.5, 0.5] forthe numerical example presented, depends on the flow direction and non-uniformflow and dispersion fields. Effective advection velocity Ve and dispersioncoefficient De can be derived for any given flow and dispersion fields, and{\epsilon}. Homogenized solutions describing the macroscopic variations can beobtained from the effective model. Solutions with sub-unit-cell accuracy can beconstructed by homogenized solutions and its spatial derivatives. A numericalimplementation of the model compared with direct numerical solutions using afine grid, demonstrated that the new method was in good agreement with directsolutions, but with significant computational savings.

Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields