Relación de problemas resueltos de exámenes de la asignatura Matemáticas III para Economistas de la Licenciatura de Economía

Relación de problemas resueltos de exámenes de la asignatura Matemáticas III para Economistas de la Licenciatura de Economía desde febrero de 2001 hasta junio de 2010.

Reutilización de escoria negra de acería como soporte en biofiltros para la eliminación de H2S del biogás.

[EN]Due to the limitations associated with fossil fuels it is necessary to promote energy sources that are renewable as well as eco-friendly, such as biogas generated in anaerobic digesters. The biogas, composed principally of methane and CO2, is the result of the biodegradation of organic matter under anaerobic conditions. Its use as fuel is limited by the presence of minority compounds such as hydrogen sulphide (H2S); therefore, its pre-treatment is necessary. Currently there are various technologies for the removal of H2S from a gas stream, but most of them are based on physic-chemical treatments which have a number of drawbacks as reactive consumption, generation of secondary flows, etc. Biofiltration has been used as an efficient and low cost alternative to conventional purification processes, and excellent results for the degradation of H2S have been obtained. However process can be limited due to the progressive ageing of the support material, along with the loss of nutrients and other specific characteristics necessary for the good development of biomass. The purpose of this project is to develop a mixed support consisting of a mixture of an organic material and an inorganic support for its application in the removal of the H2S from biogas. This support material helps to optimize the characteristics of the bed and extend its lifespan. The development of such material will contribute to the implementation of biofiltration for treating biogas from anaerobic digesters for its use as biofuel. The inorganic material used is electric arc furnace (EAF) black slag, a by-product generated in large quantities in the production of steel in the Basque Country. Although traditionally the slag has been used in civil engineering, its physicochemical characteristics make it suitable for reuse as a filter medium in biofiltration. The main conclusion drawn from the experimental results is that EAF black slag is a suitable co-packing material in organic biofilters treating H2S-polluted gaseous streams. High pollutant removal rates have been achieved during the whole experimental period. The removal capacity recorded in biofilters with less inorganic material was higher than in those with higher slag portion. Nevertheless, all the biofilters have shown a satisfactory response even at high inlet loads (48 g·m-3·h-1), where the RE has not decreased over 82%.

Coste Óptimo para el tratamiento de limpieza de aguas residuales

[ES]El presente trabajo es un estudio sobre un problema de optimización matemático. En él, recabamos información de la Optimización Matemática como tal, y se analizan los modelos de optimización más relevantes, además de plantear y resolver un caso práctico. Primero, distinguiremos dos ramas principales: los métodos clásicos, en donde destacamos las denominadas Optimización Lineal y No Lineal; y los métodos metaheurísticos. Además, clasificaremos y plantearemos los modelos matemáticos en función de la presencia o no de restricciones. En la segunda parte del trabajo, con la finalidad de encuadrar el caso práctico, hablaremos sobre el problema, común a muchas zonas fuertemente industrializadas, de eliminación de las aguas residuales: sus antecedentes, situación actual y nuevas tendencias. Por último, plantearemos un problema práctico en este campo, lo modelizaremos matemáticamente y lo resolveremos con la ayuda de la herramienta Excel Solver. Al final del trabajo, expondremos las conclusiones derivadas del análisis del problema.