Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

Assessment of a UASB reactor for the removal of sulfate from acid mine water

A bench-scale Upflow Anaerobic Sludge Blanket (UASB) reactor was used to study the treatment of acid mine drainage through the biological reduction of sulfate. The reactor was fed with acid mine drainage collected at the Osamu Utsumi uranium mine (Caldas, MG, Brazil) and supplemented with ethanol as an external carbon source. Anaerobic granular sludge originating from a reactor treating poultry slaughterhouse wastewater was used as the inoculum. The reactor's performance was studied according to variations in the chemical oxygen demand (COD)/SO42- ratio, influent dilution and liquid-phase recirculation. The digestion of a dilution of the acid mine drainage resulted in a 46.3% removal of the sulfate and an increase in the effluent pH (COD/SO42- = 0.67). An increase in the COD/SO42- ratio to 1.0 resulted in an 85.6% sulfate reduction. The reduction of sulfate through complete oxidation of the ethanol was the predominant path in the reactor, although the removal of COD was not greater than 68% in any of the operational stages. The replenishment of the liquid phase with tap water positively affected the reactor, whereas the recirculation of treated effluent caused disequilibrium and decreased efficiency. (C) 2012 Elsevier Ltd. All rights reserved.