A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged—the squeeze pan gap—implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables.A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 mm diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery.It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds.     

Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence Statistics Inside and Over Forest: Influence on Footprint Prediction

Observations of wind statistics within and above a Scots pine forest are comparedwith those predicted from an analytical second-order closure model. The roughnesssublayer (RSL) effects, and the influence of stability on similarity functions, arestudied using observations. The commonly accepted forms of similarity functionsdescribe the influence of diabatic effects above the RSL well. According to earlierstudies they are expected also to apply within the RSL. As an exception, the averagewind speed normalised with friction velocity was found to be invariant with stabilityclose to the canopy top under unstable conditions. Lagrangian stochastic trajectorysimulations were used to evaluate the influence of canopy turbulence profiles onfootprint prediction. The main uncertainty was found to arise from parameterisationof the random forcing term in the Lagrangian velocity equation. The influence ofdiabatic conditions was studied, and it was found that thermal stability affectssignificantly the footprint function above the forest canopy, but significantuncertainty exists because of uncertainties in the formulation of stability functions.     

A Case Study Of An On-Ice Air Flow Over The Arctic Marginal Sea-Ice Zone

A case study of warm air advection over the Arctic marginalsea-ice zone is presented, based on aircraft observations with direct flux measurements carriedout in early spring, 1998. A shallow atmospheric boundary layer (ABL) was observed, which wasgradually cooling with distance downwind of the ice edge. This process was mainly connected with astrong stable stratification and downward turbulent heat fluxes of about 10–20 W m^-2, but wasalso due to radiative cooling. Two mesoscale models, one hydrostatic and the other non-hydrostatic,having different turbulence closures, were applied. Despite these fundamental differences betweenthe models, the results of both agreed well with the observed data. Various closure assumptions had amore crucial influence on the results than the differences between the models.Such an assumption was, for example,the parameterization of the surface roughness for momentum (z₀) and heat (z_T). This stronglyaffected the wind and temperature fields not only close to the surface but also within and abovethe temperature inversion layer. The best results were achieved using a formulation for z₀ that took intoaccount the form drag effect of sea-ice ridges together withz_T = 0.1z₀. The stability within theelevated inversion strongly depended on the minimum eddy diffusivity K_min. A simple ad hocparameterization seems applicable, where K_min is calculated as 0.005 timesthe neutral eddy diffusivity. Although the longwave radiative cooling was largest within the ABL, theapplication of a radiation scheme was less important there than above the ABL. This was related to theinteraction of the turbulent and radiative fluxes. To reproduce the strong inversion, it wasnecessary to use vertical and horizontal resolutions higher than those applied in most regional andlarge-scale atmospheric models.     

Modelling of the OASIS Energy Flux Measurements Using Two Canopy Concepts

Two land surface schemes, SCAM and CSIRO9, were used to model the measured energy fluxes during the OASIS (Observations At Several Interacting Scales) field program. The measurements were taken at six sites along a 100 km rainfall gradient. Two types of simulations were conducted: (1) offline simulations forced with measured atmospheric input data at each of the six sites, and (2) regional simulations with the two land surface schemes coupled to the regional climate model DARLAM.The two land surface schemes employ two different canopy modelling concepts: in SCAM the vegetation is conceptually above the ground surface, while CSIRO9 employs the more commonly used `horizontally tiled' approach in which the vegetation cover is modelled by conceptually placing it beside bare ground. Both schemes utilize the same below-ground components (soil hydrological and thermal models) to reduce the comparison to canopy processes only. However, the ground heat flux, soil evaporation and evapotranspiration are parameterised by the two canopy treatments somewhat differently.Both canopy concepts reproduce the measured energy fluxes. SCAM has a slightly higher root-mean standard error in the model-measurement comparison for the ground heat flux. The mean surface radiative temperature simulated by SCAM is approximately 1K lower than in the CSIRO9 simulations. However, the soil and vegetation temperatures (which contribute to the radiative temperature) varied more in the CSIRO9 simulations. These larger variations are due to the absence of a representation of the aerodynamic interactions between vegetation and ground.     

AN EVALUATION OF SEVERAL TURBULENCE SCHEMES FOR THE PREDICTION OF MEAN AND TURBULENT FIELDS IN COMPLEX TERRAIN

A prognostic three-dimensional mesoscale model has been developed andused in one- and two-dimensional modes to evaluate ten local turbulenceclosure schemes. The schemes ranged from first-order to the two-equationprognostic schemes. Predictions by the models were compared for aone-dimensional convective boundary layer using mixed layer scaling andmeasurements to interpret the results. Two-dimensional simulations were alsoperformed for a sea-breeze flow and for flow over a hill. The results showedthat for all of the models considered, minor differences were produced in themean meteorological fields and in the vertical scalar fluxes, but majordifferences were apparent in the velocity variances and dissipation rate.Predicted tracer concentrations were very sensitive to the turbulence modelformulation for dispersion from a point source in the convective boundarylayer, particularly for the prediction of maximum concentrations. Predictedtracer concentrations from a surface volume source for the two-dimensionalsimulations were similar for all models, although the degree of mixing in themorning growth period produced some differences. Generally, good results forthe mean meteorological fields can be obtained with first-order schemes, evenif they underpredict the magnitude of turbulence in the convective boundarylayer, and reasonable tracer concentrations can also be obtained with thesemodels provided near-source effects are not important. The two-equationprognostic models performed best for the prediction of turbulence in theconvective boundary layer.     

Multiresolution Flux Decomposition

Geophysical variables are orthogonally decomposed by averaging timeseries using different averaging lengths, referred to as a (Haar)multiresolution decomposition. This simple and economic decomposition isassociated with cospectra that formally satisfy Reynolds averaging rules foreach averaging length. The multiresolution decomposition provides a naturalestimate of the random error in estimating a mean turbulent flux. The Fourierand multiresolution decompositions are compared using aircraft data fromBOREAS.     

Rapid cooling and exhumation of eclogitic rocks from the Great Caucasus, Russia

Diffusion modelling of growth-zoned garnet is used in combination with standard geothermometric and geobarometric techniques to estimate cooling and denudation rates from the mafic eclogites of the Red Cliff area, Great Caucasus, Russia. Euhedral garnet porphyroblasts exhibit different degrees of prograde growth zoning depending on the size of the grain (100 μm to several mm in diameter). Zoning patterns are mainly expressed in terms of Fe–Mg exchange, with 100*Mg/(Mg+Fe) increasing from 18–20 to 33–37 from core to rim. Geothermobarometry yields conditions of 680±40 °C and a minimum of 1.6±0.2 GPa and of 660±40 °C and 0.8±0.2 GPa for the high-pressure and retrograde stages of equilibration, respectively. A temperature of 600±40 °C has been recorded for the late-stage metamorphic overprint in the mica schists surrounding the eclogites. Relaxation of garnet zoning profiles was modelled for three different hypothetical P–T –t trajectories, all with an initial temperature of 680 °C and a pressure change of 0.8 GPa. The first two trajectories involve decompression associated with regular cooling down to 660 °C (near isothermal) and 600 °C. The third path is a two-step trajectory comprising near-isobaric cooling down to 600 °C followed by isothermal decompression to 0.8 GPa. These P–T trajectories cover as wide a range of pressure and temperature changes endured by the rocks as possible, thus representing extreme cases for calculating cooling and exhumation rates. Calculations indicate that the zoning pattern of the smallest garnet (i.e. garnet for which the zoning is most easily eliminated during post-growth processes) along the different paths can be preserved for the following average exhumation and cooling rates: path 1, 143 mm a^?1 and 102 °C Ma^?1; path 2, 60 mm a^?1 and 171 °C Ma^?1; path 3, 11–30 mm a^?1 and 200–400 °C Ma^?1. These results are discussed in light of theoretical P–T–t paths extracted from thermal models of regions of thickened crust, and from analogue models of accretionary wedge and continental lithosphere subduction.     

Sustainable management of a coastal lagoonal system (Ria Formosa, Portugal): An ecological model for extensive aquaculture

The Ria Formosa lies in southern Portugal, extending for about 55 km. It is a true barrier island system, comprising mainland, backbarrier lagoons, inlet deltas, barrier islands, barrier platforms and shoreface. Of the Ria Formosa system, which covers a total area of 163 km², 20 km² are occupied by salinas and aquaculture ponds. The main water reservoir of thesalinas and the extensive aquaculture ponds behave like small lagoons where there are one or more openings to a tidal channel. These small lagoons have the advantage of being easy to study and to model. An ecological model was developed to estimate the potential production of the gilthead seabream in the Ria Formosa, in an extensive aquaculture regime. This model was based on information concerning chemical and physical factors (forcing functions) and secondary production estimates from four sites in the Ria Formosa with different environmental conditions, where extensive aquaculture is practised. Published information on optimal growth parameters of the gilthead was used to build the model, which was based on some assumptions concerning the detrimental effect of an excessive increase of salinity and other environmental factors both on gilthead growth (one state variable) and on prey production (divided into two state variables), which is essentially benthic macrofauna. Reservoirs with low water renewal undergo large environmental fluctuations. The growth of gilthead or other fish can be difficult, not only because of the adverse environmental conditions but also because of the low secondary production. The maximum yield of fish is predicted to be less than 6 g m⁻². In reservoirs where the water exchanges on almost every tide, the maximum yield of gilthead can be in excess of 22–25 g m⁻². Nevertheless, the high productivity of these sites in terms of secondary production of benthos and fish, as well as primary production, can lead to oxygen depletion during the night or at day-break. An attempt to further improve fish production by fertilisation or by adding food could provoke a rapid deterioration of the water quality and endanger all production.     

Modelling the Venice Lagoon

In this paper, an overview is given on the modelling activities at the National Research Council in Venice (ISDGM-CNR) concerning the Venice Lagoon. A short history of former modelling efforts is given. A finite element hydrodynamic model is presented that has been created especially for the Venice Lagoon. This model has been applied to various situations. Residual currents have been computed for one year. A specific storm surge event has been simulated with spatially varying real winds. A transport diffusion model has been applied to model the impact of a treatment plant on the central lagoon. And a sub-basin has been modeled with a high resolution grid.