This thesis focuses on solute transport upscaling. Upscaling of solute transport
is usually required to obtain computationally efficient numerical models in 
many field applications such as, remediation of aquifers, environmental risk 
to groundwater resources or the design of underground repositories of nuclear 
waste. The non-Fickian behavior observed in the field, and manifested by 
peaked concentration profiles with pronounced tailing, has questioned the use 
of the classical advection-dispersion equation to simulate solute transport at 
field scale using numerical models with discretizations that cannot capture 
the field heterogeneity. In this context, we have investigated the use of the 
advection-dispersion equation with mass transfer as a tool for upscaling solute
transport in a general numerical modeling framework.  
  
Solute transport by groundwater is very much affected by the presence of 
high and low water velocity zones, where the contaminant can be channelized 
or stagnant. These contrasting water velocity zones disappear in the upscaled 
model as soon as the scale of discretization is larger that the size of these zones.  
We propose, for the modeling solute transport at large scales, a phenomenological
model based on the concept of memory functions, which are used to represent the 
unresolved processes taking place within each homogenized block in the numerical models.  

We propose a new method to estimate equivalent blocks, for which transport and mass 
transfer parameters have to be provided. The new upscaling technique consists in 
replacing each heterogeneous block by a homogeneous one in which the parameters 
associated to a memory functions are used to represent the unresolved mass exchange
between highly mobile and less mobile zones occurring within the block. 
Flow upscaling is based on the Simple Laplacian with skin, whereas transport 
upscaling is based in the estimation of macrodispersion and mass transfer parameters 
as a result of  the interpretation of the residence time distribution of particles
passing through a given block using fine-scale heterogeneous simulations.  

The methodology proposed is applied in a Monte Carlo framework to model solute transport 
in several two-dimensional synthetic aquifers. The upscaled results are compared to a 
reference Monte Carlo analysis carried out at a smaller scale. The memory functions 
used to model transport at the computational scale are based on the multi-rate mass 
transfer equations. Several formulations of the multi-rate mass transfer model, 
which differ in the type of memory function, were used and compared.  

For the performance of the upscaled models we analyzed the reproduction of the ensemble 
mean behavior of the main features associated with the simulated breakthrough curves (BTCs).
We examined the effect of upscaling on model uncertainty and the spatial distribution of the
solute mass plume. The results showed that an appropriate description of the residence time 
distribution for all blocks of the numerical model provides an upscaled transport model that 
is capable to reproduce the ensemble mean behavior of the BTCs, but has problems in reproducing 
both uncertainty and plume dilution.