Macrodispersion by Point-Like Source Flows in Randomly Heterogeneous Porous Media |
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Authors: | Gerardo Severino |
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Institution: | 1.Division of Water Resources Management,University of Naples Federico II,Portici,Italy;2.Department of Mechanical and Aerospace Engineering (MAE),University of California,San Diego,USA |
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Abstract: | A pulse of a passive tracer is injected in a porous medium via a point-like source. The hydraulic conductivity K is regarded as a stationary isotropic random space function, and we model macrodispersion in the resulting migrating plume
by means of the second-order radial spatial moment X
rr
. Unlike previous results, here X
rr
is analytically computed in a fairly general manner. It is shown that close to the source macrodispersion is enhanced by
the large local velocities, whereas in the far field it drastically reduces since flow there behaves like a mean uniform one.
In particular, it is demonstrated that X
rr
is bounded between X
∞ corresponding to the short-range (far field), and X
0 pertaining to the long-range (near-field) correlation in the conductivity field. Although our analytical results rely on
the assumption of isotropic medium, they enable one to grasp in a simple manner the main features of macrodispersion mechanism,
therefore providing explicit physical insights. Finally, the proposed model has potential toward the characterization of the
spatial variability of K as well as testing more general numerical codes. |
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Keywords: | |
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