Estimation of True Dispersivity in Field Scale Permeable Media

Abstract

Abstract Simulation studies (Solano et al.1; Stalkup2) show that oil recovery for enriched gas drives depends on the amount of dispersion in reservoir media. But the true value of dispersion, expressed as dispersivity, at the field scale, is unknown. This work investigates three types of dispersion in permeable media to obtain realistic estimates of dispersive mixing at the field scale. The dispersivity from single-well tracer tests (SWTT), also known as echo dispersivity, is the dispersivity that is unaffected by fluid flow direction. Layering in permeable media tends to increase the observed dispersivity in well-to-well tracer tests, also known as transmission dispersivity, but leaves the echo dispersivity unaffected. A collection of SWTT data is analyzed to estimate echo dispersivity at the SWTT scale. The estimated echo dispersivities closely match a published trend with length scale in dispersivities obtained from groundwater tracer tests. This unexpected result—it was thought that transmission dispersivity should be greater than echo dispersivity—is analyzed with numerical simulation. A third type of dispersive mixing is local dispersivity, or the mixing observed at a point as tracer flows past it. Numerical simulation results show that the local dispersivity is always less than the transmission dispersivity and greater than the echo dispersivity limits. It is closer to one limit or the other depending on the amount and type of heterogeneity, the autocorrelation structure of the medium's permeability, and the lateral (vertical) permeability. The agreement between the SWTT echo dispersivities and the field trend suggests that the field data are measuring local dispersivities. All dispersivities appear to grow with length.