The impact of local diffusion upon mass arrival of a passive solute in transport through three-dimensional highly heterogeneous aquifers

Fluid flow and solute transport take place in a porous formation. The spatial variability of the hydraulic conductivity K has a large impact on the velocity field and advective spreading of solute. The logconductivity Y = ln K is modeled as a stationary random space function, of normal distribution of mean 〈Y 〉 = ln K G and variance View the MathML sourceσY2, and of isotropic autocorrelation of finite integral scale I . The stationary velocity field is of uniform mean U. Transport of an ergodic plume is quantified by the mass arrival (breakthrough curve) at control planes normal to U. First-order solutions in View the MathML sourceσY2, applicable to weak heterogeneity View the MathML sourceσY2⩽1, have been investigated extensively in the past. However, many natural formations are highly heterogeneous View the MathML sourceσY2>1 and the more complex flow and transport problems have been attacked only recently. The present study investigates the impact of local diffusion, quantified by the Peclet number Pe = UI /D , upon the breakthrough curve (BTC), both by numerical simulations and an analytical approach based on the self consistent approximation. The latter is an extension to finite Peclet of a method that we have developed in the past, in which we solved the 3D problem of flow and advective transport by modeling the structure as an ensemble of densely packed spherical inclusions of uniform radius R and independent random Y . Unlike the first-order solution, diffusion has a large impact on the BTC, even for the common values Pe ≫ 1. Two mechanisms associated with finite Pe are identified and quantified: removal of the solute captured by low K blocks (characterized by “slow” flow) and exchange between the fluid flowing past inclusions (i.e. “fast” flow) and their interior. The first mechanism affects primarily the tail of the BTC, while the second one impacts both the peak and the tail. All the parameters of the model View the MathML sourceU,σY2,Pe,I are physically based and depend on the structural and flow characteristics solely.