Transport in Porous Media 30: 57–73, 1998. 57 © 1998 Kluwer Academic Publishers. Printed in the Netherlands. On the Influence of Pore-Scale Dispersion in Nonergodic Transport in Heterogeneous Formations ALDO FIORI Dipartimento di Scienze dell’Ingegneria Civile, Universit` a di Roma Tre, Roma, Rome, Italy (Received: 30 January 1997; in final form: 30 September 1997) Abstract. Flow of an inert solute in an heterogeneous aquifer is usually considered as dominated by large-scale advection. As a consequence, the pore-scale dispersion, i.e. the pore scale mechanism acting at scales lower than that characteristic of the heterogeneous field, is usually neglected in the computation of global quantities like the solute plume spatial moments. Here the effect of pore- scale dispersion is taken into account in order to find its influence on the longitudinal asymptotic dispersivity D 11 ; we examine both the two-dimensional and the three-dimensional flow cases. In the calculations, we consider the finite size of the solute initial plume, i.e. we analyze both the ergodic and the nonergodic cases. With Pe the P´ eclet number, defined as Pe = Uλ/D, where U,λ,D are the mean fluid velocity, the heterogeneity characteristic length and the pore-scale dispersion coefficient respectively, we show that the infinite P´ eclet approximation is in most cases quite adequate, at least in the range of P´ eclet number usually encountered in practice (Pe > 10 2 ). A noteworthy exception is when the formation log-conductivity field is highly anisotropic. In this case, pore-scale may have a significant impact on D 11 ,especially when the solute plume initial dimensions are not much larger than the heterogeneities’ lengthscale. In all cases, D 11 appears to be more sensitive to the pore-scale dispersive mechanisms under nonergodic conditions, i.e. for plume initial size less than about 10 log-conductivity integral scales. Key words: groundwater, nonergodic transport, dispersion, heterogeneous formations, hydrogeol- ogy. 1. Introduction It is now widely recognized that spreading of solutes in transport through natural porous formations is ruled by the large-scale spatial variability of hydraulic con- ductivity. Experimental and site findings have stimulated in the last decades the development of adequate conceptual models in order to correctly simulate the trans- port mechanism in natural aquifers. The most successful approach is probably the stochastic one (see Dagan (1989) and Gelhar (1993) for an exhaustive review), whose ability to predict the phenomenon has been supported by both field and numerical experiments. In particular, results based on the linear theory has been able to interpret and simulate the outcome of the controlled field experiments which have been car- ried out in recent times (Freyberg, 1986; Garabedian et al., 1991; Adams and Gelhar, 1992). In particular, the gross features or global quantities related to solute plume, like the spatial moments of the concentration field, have been proved to be a quite robust vehicle to predict the basic behavior and spreading of contaminant plumes.