Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium

Abstract

We present a trajectory‐based technique for calculating solute transport in a porous medium that has several advantages over existing methods. Unlike streamlines, the extended trajectories are influenced by each of the important parameters governing transport, including molecular diffusion and transverse dispersion. The approach is complete and does not require any additional techniques, such as operator splitting or particle tracking, in order to account for the full dispersion tensor. The semianalytic expressions make it clear how the flow field, the concentration distribution, and the dispersion tensor contribute to the velocity field of an injected solute. The equations are valid for an arbitrary porous medium, including those with rapid spatial variations in properties, overcoming limitations faced by previous approaches based upon asymptotic techniques. A test on a layered model with sharp boundaries indicates that the extended trajectories are compatible with the results of a numerical simulator and differ from streamlines. We also describe a new form of the dispersion tensor that incorporates a known asymmetry. The trajectories indicate that the modifications of the dispersion tensor lead to more focused transport within regions of high conductivity. Finally, the trajectories are used to define a semianalytic relationship between solute travel times and variations in solute velocities along a path that may be used for tomographic imaging. In an application to the injection of a radioactive tracer into a Berea sandstone core, monitored using micropositron emission tomographic (micro‐PET) observations, the sensitivities are used to map the spatial variations of permeability within the core.

Subcore Scale Fluid Flow Behavior in a Sandstone With Cataclastic Deformation Bands

“…Many of these studies indicated that sandstones are characterized by subtle small‐scale heterogeneities that actively affect fluid flow. Variations in porosity and permeability affect the fluid velocity field, with high velocities being associated with regions of high porosity and permeability (Bloomfield et al, ; Grathwohl & Kleineidam, ; Vasco et al, ; Zahasky & Benson, ); and for multiphase fluid flow, variations in capillary pressure and relative permeability affect plume migration and residual saturation at both the pore and the field scale (Hingerl et al, ; Krevor et al, ; Krevor et al, ; Li & Benson, ; Perrin & Benson, ; Pini & Benson, ; Saadatpoor et al, ). In particular, Krevor et al () reported that regions presenting high capillary entry pressures (i.e., small pore throats) act as capillary barriers for the nonwetting fluid, leading to an increase in saturation of the latter in the preceding pores.…”

Spatial and Temporal Quantification of Spontaneous Imbibition

“…This increasing end point pressure as the imbibition front approaches the end of the core is likely a combination of capillary heterogeneity and parameterization measurement error. Previous permeability inversion studies using this same core have indicated that the region near the outlet has a slightly lower permeability (Vasco et al, 2018), and therefore likely slightly higher capillary pressure. It is also important to note that capillary pressure end point is sensitive to water relative permeability, total imbibition rate, and water saturation measurement error.…”

An extended trajectory-mechanics approach for calculating the path of a pressure transient: travel-time tomography

“…The trajectory-mechanics approach described in and applied here is very general and can be used to model other hydrological processes such as tracer transport (Vasco et al, 2018a) and multiphase fluid flow. One advantage associated with transient pressure is the rapid propagation of a disturbance in comparison with the velocities associated with fluid transport.…”