Tratamiento de lixiviados de residuos de origen urbano mediante MBR

Se ha utilizado una planta de tratamiento a escala laboratorio consiste en un biorreactor de membrana (MBR). Esta planta está compuesta por un reactor biológico de 25 L de capacidad. Se utilizó una membrana plana de micro filtración marca Kubota de polietileno clorado, tamaño de poro 0,1 μm y área de filtración 0.116 m2. Se utilizaron como condiciones de operación: tiempo de residencia hidráulico 3 días, caudal de permeado 0.35 L/h y LMH 3 L/m2h. Se ha podido comprobar que es posible adaptar una población microbiológica a las particulares características químicas del lixiviado procedente de la planta y tratar estos lixiviados en un reactor biológico de membrana sumergida operando en condiciones habituales de sólidos en suspensión en el reactor entre 8-12 g/L durante un periodo de 6 meses. El proceso utilizado permite reducir la materia orgánica (97% DBO5 y 40% DQO) presente en estas corrientes residuales, agotando prácticamente toda la materia biodegradable. Respecto a los contenidos de nutrientes, el tratamiento MBR ensayado permite reducir de 35-40% el nitrógeno total, 45-50% el nitrógeno amoniacal y un 65-70% el fósforo total. Los sólidos en suspensión se han reducido en el efluente tratado en más de un 99%.

Influence of sludge retention time on filtration performance and biomass characteristics in a hollow fiber membrane bioreactor

In this study, the filtration process and the biomass characteristics in a laboratory-scale submerged membrane bioreactor (MBR) equipped with a hollow fiber (HF) microfiltration membrane were studied at different solid retention times (SRT). The MBR was fed by synthetic wastewater and the organic loading rate (OLR) was 0.5, 0.2, 0.1, and 0.08 kg COD kg VSS−1 d−1 for 10, 30, 60, and 90 days of SRT, respectively. The hydraulic retention time was 8.4 h and the permeate flux was 6 L m−2 h−1(LMH). Data analysis confirmed that at all the studied SRTs, the HF-MBR operated very good obtaining of high quality permeates. Chemical Oxygen Demand (COD) removal efficiencies were higher than 95%. The best filtration performance was reached at SRT of 30 d. On the other hand, the respirometric analysis showed that biomass was more active and there was more biomass production at low SRTs. The concentration of soluble extracellular polymeric substances (EPS) decreased with increasing SRT. A decrease of soluble EPS caused a decrease of membrane fouling rate, decreasing the frequency of chemical cleanings. The floc size decreased with SRT increasing. At high SRTs, there was more friction among particles due to the increase of the cellular density and the flocs broke decreasing their size.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.