Effective equation to assess solute transport in two-lithology reservoirs

Abstract

Understanding solute transport in heterogeneous porous media is a challenging problem due to the degree of complexities coming from the spatial variations of petrophysical properties. The developments of theoretical formulations are powerful tools used to obtain insights regarding the phenomenology involved in the transport process when analyzing large-scale systems. In this context and within the framework of the volume averaging method, in this work we present an effective one-equation model and its validity conditions for the solute transport in heterogeneous reservoirs characterized by two-lithology arrangements. For this purpose, the hypothesis of local mass equilibrium was assumed valid and what follows included the determination of physical constraints supporting such a hypothesis. In a previous work (Aguilar-Madera et al., 2019), the closure problems to calculate the effective coefficients of the two-equation model were presented, and with this base we present here the numerical estimation of the effective velocity vector and the mass dispersion tensor included in the one-equation model. As one application, the numerical solution of the one-equation model was carried out for different lithology arrangements and the breakthrough curves for two permeability ratio scenarios were analyzed. The results confirm that the permeability ratio dramatically impact not only the tracer dispersion but also the arrival time at observation points, which is strongly correlated to the velocity vector field and its spatial deviations. We found that the local mass equilibrium is met more easily in lenticular reservoirs provided that the boundary and initial conditions have no long-term effects. Finally, the dispersion coefficient was compared against reported reservoir field data, finding similarities in the orders of magnitude for certain geologies.