Inversão de funções do plano no plano aplicada ao cálculo de azeótropos

Azeotropia é um fenômeno termodinâmico onde um líquido em ebulição produz um vapor com composição idêntica. Esta situação é um desafio para a Engenharia de Separação, já que os processos de destilação exploram as diferenças entre as volatilidades relativas e, portanto, um azeótropo pode ser uma barreira para a separação. Em misturas binárias, o cálculo da azeotropia é caracterizado por um sistema não-linear do tipo 2 × 2. Um interessante e raro caso é o denominado azeotropia dupla, que pode ser verificado quando este sistema não-linear tem duas soluções, correspondendo a dois azeótropos distintos. Diferentes métodos tem sido utilizados na resolução de problemas desta natureza, como métodos estocásticos de otimização e as técnicas intervalares (do tipo Newton intervalar/bisseção generalizada). Nesta tese apresentamos a formulação do problema de azeotropia dupla e uma nova e robusta abordagem para a resolução dos sistemas não-lineares do tipo 2 × 2, que é a inversão de funções do plano no plano (MALTA; SALDANHA; TOMEI, 1996). No método proposto, as soluções são obtidas através de um conjunto de ações: obtenção de curvas críticas e de pré-imagens de pontos arbritários, inversão da função e por fim, as soluções esperadas para o problema de azeotropia. Esta metodologia foi desenvolvida para resolver sistemas não-lineares do tipo 2 × 2, tendo como objetivo dar uma visão global da função que modela o fenômeno em questão, além, é claro, de gerar as soluções esperadas. Serão apresentados resultados numéricos para o cálculo dos azeótropos no sistema benzeno + hexafluorobenzeno a baixas pressões por este método de inversão. Como ferramentas auxiliares, serão também apresentados aspectos numéricos usando aproximações clássicas, tais como métodos de Newton com técnicas de globalização e o algorítmo de otimização não-linear C-GRASP, para efeito de comparação.

Age and length composition of Columbia Basin chinook, sockeye, and coho salmon at Bonneville Dam in 2001

In 2001, representative samples of adult Columbia Basin chinook (Oncorhynchus tshawytscha), sockeye (O. nerka), and coho salmon (O. kisutch) populations at Bonneville Dam were collected. Fish were trapped, anesthetized, sampled for scales and biological data, revived, and then released adult migrating salmonids. Scales were examined to estimate age composition; the results contributed to an ongoing database for age class structure of Columbia Basin salmon populations. Based on scale analysis of chinook salmon, four-year-old fish (from brood year [BY] 1997) comprised 88% of the spring chinook, 67% of the summer chinook, and 42% of the Bright fall chinook salmon population. Five-year-old fish (BY 1996) comprised 9% of the spring chinook, 14% of the summer chinook, and 9% of the fall chinook salmon population. The sockeye salmon population at Bonneville was predominantly four-year-old fish (81%), with 18% returning as five-year-olds in 2001. The coho salmon population was 96% three-year-old fish (Age 1.1). Length analysis of the 2001 returns indicated that chinook salmon with a stream-type life history are larger (mean length) than the chinook salmon with an ocean-type life history. Trends in mean length over the sampling period for returning 2001 chinook salmon were analyzed. Chinook salmon of age classes 0.2 and 1.3 show a significant increase in mean length over time. Age classes 0.1, 0.3, 0.4, 1.1, 1.2, and 1.4 show no significant change over time. A year class regression over the past 12 years of data was used to predict spring, summer, and Bright fall chinook salmon population sizes for 2002. Based on three-year-old returns, the relationship predicts four-year-old returns of 132,600 (± 46,300, 90% predictive interval [PI]) spring chinook and 44,200 (± 11,700, 90% PI) summer chinook salmon for the 2002 runs. Based on four-year-old returns, the relationship predicts five-year-old returns of 87,800 (± 54,500, 90% PI) spring, 33,500 (± 11,500, 90% PI) summer, and 77,100 (± 25,800, 90% PI) Bright fall chinook salmon for the 2002 runs. The 2002 run size predictions should be used with caution; some of these predictions are well beyond the range of previously observed data.

Age and length composition of Columbia Basin chinook, sockeye, and coho salmon at Bonneville Dam in 2000

In 2000, representative samples of adult Columbia Basin chinook (Oncorhynchus tshawytscha), sockeye (O. nerka), and coho salmon (O. kisutch), populations were collected at Bonneville Dam. Fish were trapped, anesthetized, sampled for scales and biological data, allowed to revive, and then released. Scales were examined to estimate age composition and the results contribute to an ongoing database for age class structure of Columbia Basin salmon populations. Based on scale analysis, four-year-old fish (from brood year (BY) 1996) were estimated to comprise 83% of the spring chinook, 31% of the summer chinook, and 32% of the upriver bright fall chinook salmon population. Five-year-old fish (BY 1995) were estimated to comprise 2% of the spring chinook, 26% of the summer chinook, and 40% of the fall chinook salmon population. Three-year-old fish (BY 1997) were estimated to comprise 14% of the spring chinook, 42% of the summer chinook, and 17% of the fall chinook salmon population. Two-year-olds accounted for approximately 11% of the fall chinook population. The sockeye salmon population sampled at Bonneville was predominantly four-year-old fish (95%), and the coho salmon population was 99.9% three-year-old fish (Age 1.1). Length analysis of the 2000 returns indicated that chinook salmon with a stream-type life history are larger (mean length) than the chinook salmon with an ocean-type life history. Trends in mean length over the sampling period were also analysis for returning 2000 chinook salmon. Fish of age classes 0.2, 1.1, 1.2, and 1.3 have a significant increase in mean length over time. Age classes 0.3 and 0.4 have no significant change over time and age 0.1 chinook salmon had a significant decrease in mean length over time. A year class regression over the past 11 years of data was used to predict spring and summer chinook salmon population sizes for 2001. Based on three-year-old returns, the relationship predicts four-year-old returns of 325,000 (± 111,600, 90% Predictive Interval [PI]) spring chinook and 27,800 (± 29,750, 90% PI) summer chinook salmon. Based on four-year-old returns, the relationship predicts five-year-old returns of 54,300 (± 40,600, 90% PI) spring chinook and 11,000 (± 3,250, 90% PI) summer chinook salmon. The 2001 run size predictions used in this report should be used with caution, these predictions are well beyond the range of previously observed data.