Differences in the scale dependence of dispersivity and retardation factors estimated from forced‐gradient and uniform flow tracer tests in three‐dimensional physically and chemically heterogeneous porous media

Abstract

Parameters estimated from forced‐gradient tracer tests are often used to simulate the transport of large contaminant plumes under natural gradients, yet the difference in the flow system and the plume size is important. Recent intermediate‐scale experiments and numerical simulations in two dimensions have suggested that dispersivities from forced‐gradient tracer tests involving a small source may not be adequate to simulate the migration of a large plume under natural‐gradient conditions. The differences in the scale dependence of effective dispersivities Aeff (for conservative and linearly sorbing solutes) and retardation factors Reff due to changes in the flow configuration and source size are investigated here on the basis of numerical simulations in three‐dimensional physically and chemically heterogeneous porous media. It is shown that discrepancies observed in two dimensions due to small‐source size and nonuniform flow conditions are not so dramatic in typical field settings because a small vertical correlation scale permits a tracer source to sample the medium heterogeneity more effectively. We further analyzed the benefit of using multiple injections in tracer tests by evaluating (1) the reduction in dispersivity due to the small‐source size and (2) the uncertainty in dispersivity estimates (coefficient of variation). The distance scales at which Aeff and Reff from single and multiple injection convergent flow tracer tests approach constant values are significantly greater than analogous values for natural gradients. When dispersivities are estimated from convergent flow tracer tests involving multiple injections, asymptotic Aeff values are the same as those obtained from large‐source natural‐gradient tests. In both convergent flows and natural‐gradient systems, in the case of a negative correlation between lnK and lnKd random fields, Reff estimated from temporal moments of breakthrough curves decrease with distance, while Reff estimated from the center of mass velocities of the tracer plumes increase with time, both asymptotically approaching the arithmetic mean of the retardation factor.