Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Study of mineral dust entrainment in the planetary boundary layer by lidar depolarisation technique

Measurements on 27 June 2011 were performed over the Southern Iberian Peninsula at Granada EARLINET station, using active and passive remote sensing and airborne and surface in-situ data in order to study the entrainment processes between aerosols in the free troposphere and those in the planetary boundary layer (PBL). To this aim the temporal evolution of the lidar depolarisation, backscatter-related Angström exponent and potential temperature profiles were used in combination with the PBL contribution to the aerosol optical depth (AOD). Our results show that the mineral dust entrainment in the PBL was caused by the convective processes which ‘trapped’ the lofted mineral dust layer, distributing the mineral dust particles within the PBL. The temporal evolution of ground-based in-situ data evidenced the impact of this process at surface level. Finally, the amount of mineral dust in the atmospheric column available to be dispersed into the PBL was estimated by means of POLIPHON (Polarizing Lidar Photometer Networking). The dust mass concentration derived from POLIPHON was compared with the coarse-mode mass concentration retrieved with airborne in-situ measurements. Comparison shows differences below 50 µg/m³ (30% relative difference) indicating a relative good agreement between both techniques.