Transport of finite plumes in three-dimensional, heterogeneous, and statistically isotropic aquifers is investigated where the log hydraulic conductivity is characterized by a fractional Gaussian noise (fGn) covariance structure of Hurst coefficient H. Leading-order analytical expressions for velocity autocovariance functions uij, one-particle displacement covariance Xij, and macrodispersivity tensor &agr;ij are derived under ergodic conditions and mean-uniform steady state flow. Nonergodic transport is then discussed for a line source of finite length, either normal or parallel to the mean flow, by evaluating time-dependent ensemble averages of the second spatial moments, Zij≡⟨Aij⟩-Aij(0)=Xij-Rij and the effective dispersivity tensor, &ggr;ij defined as (0.5/&mgr;)(d⟨Aij⟩/dt), where Aij(0) is the initial value of the second spatial moments of a plume Aij, and Rij is the plume centroid covariance. The main finding is that in a fGn log K field the spreading of a solute plume is never ergodic; as H increases, effective dispersivity results differ more from their ergodic counterparts, since a larger H implies the medium is more correlated. The most interesting results are as follows: for a source parallel to flow, &ggr;22 does not decrease below zero at large time but remains strictly positive, in variance with exponential or Gaussian covariance. For a source normal to flow, &ggr;11 reaches a large-time asymptote, whose value depends on H as follows: it decreases with H for a small source, it increases, reaches a peak, and then decreases as H goes from 1/2 to 1 for intermediate and large sources; for H=1,&ggr;11 is zero irrespective of the source size. ¿ 1999 American Geophysical Union