Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Conhecimento disciplinar: (im)possibilidades do discurso sobre a problemática ambiental

This essay presents the environmental crisis as a result of the capitalist society's way of life. It adopts three "ecological registers" that compose the human being: the environment, the social relationships and the subjectivity, as it is understood by Félix Guattari. Studies about concepts as discourse, discipline, knowledge, truth and power developed by Michel Foucault were used to think of the possibilities of the discourse about the environmental problems considering how knowledge is produced in modernity. From this theoretical reference, it presents some views about how transversality is adopted by the MEC (Ministry of Education and Sports) and points some of its impossibilities. Finally, it offers a purpose to think about some possibilities for environmental education from Deleuze and Guattari's concepts such as State and war machine.Este ensaio apresenta a crise ambiental como um resultado do modo de vida da sociedade capitalista, que abrange os três "registros ecológicos" que constituem o ser humano: o do ambiente, o social eo da subjetividade, tal como é entendido por Félix Guattari. Realiza uma reflexão acerca das possibilidades do discurso sobre a problemática ambiental no contexto da produção do conhecimento na modernidade, a partir dos conceitos de discurso, disciplina, saber, verdade e poder desenvolvidos por Michel Foucault. Diante desses referenciais, apresenta algumas observações sobre a transversalidade do tema meio ambiente na educação, tal como foi adotada pelo MEC, indicando algumas impossibilidades dessa proposta. Por fim, propõe o conceito de Estado e máquina de guerra de Deleuze e Guattari para pensar algumas possibilidades para a educação ambiental

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

Comprehensive Analysis of Acid Stimulation in Carbonates

Most wells in conventional carbonate reservoirs are stimulated with acid, either by acid fracturing or by matrix acidizing. Both methods can result in effective stimulation in carbonate reservoirs, but currently there is no published scientific criterion for selecting one technique or the other. The objectives of this study are to define ways to estimate the well performance that can be obtained from each of these treatments, and finally to define a decision criterion to select the best acid stimulation technique for a given scenario. Improvements in the modeling of both matrix acidizing and acid fracturing are proposed in this study. A new upscaled global model of wormhole propagation is proposed, based on experimental results and simulations using the Two-Scale Continuum Model. The proposed model represents experiments in different scales and field treatments. The wormhole propagation in anisotropic formations and in limited entry completions was also studied, and new analytical equations to calculate the post-acidizing skin factor for these cases were presented. In terms of acid fracturing modeling, a productivity model was developed for acid fractures, coupled to an in-house acid fracturing simulator. A leak-off model accounting for efficient wormholing was also developed, improving the prediction of high leak-off observed in acid fracturing treatments. Comparing the predicted productivity of matrix acidized and acid fractured wells, this study proposes a criterion for selection of the acid stimulation technique that results in the most productive well, for a given scenario and volume of acid. For all scenarios studied, there is a cutoff permeability above which a matrix acidized well is more productive than an acid fractured well. The value of this cutoff permeability, however, changes significantly for different scenarios. For example, in shallower reservoirs with small horizontal stresses, the cutoff permeability is much higher than in deeper reservoirs subject to high horizontal stresses. For hard rocks, the cutoff permeability is higher than for softer rocks. Concise analytical decision criteria were proposed to select the best acid stimulation method for both vertical and horizontal wells

The formulation of hypotheses in mathematical modelling activities

Background: the formulation of hypotheses in mathematical modeling activities, although it has been pointed out as one of the specificities of this kind of activities, it is still little discussed by the research in the area of mathematical modeling. Purpose: in this paper we look for influences on mathematical modeling activities arising from the formulation of hypotheses. Design: our statements are based on a theoretical framework about wittgenstein's philosophy and previous studies related to hypotheses’ formulation as well as an empirical research. Scenario and participants: modeling activities were performed by groups of students from different degrees. Data collection: in modeling classes, data were collected through audio and video recordings. The students also delivered the written records they produced. Findings: the findings indicate three categories for the formulation of hypotheses: hypotheses are formulated based on the students' view of the situation; hypotheses are based on students' experiences; hypotheses influence students' choices at different stages of the activity's development. Conclusion: the research concludes that the hypotheses determine the idealized situation, guide the mathematization and direct the students' actions in the development of the activity. In wittgenstein's philosophical perspective, hypotheses are a way of perceiving reality and new experiences can lead to other formulations

Os “mundos da matemática” em atividades de modelagem matemática

As argumentações pautadas nos interesses e objetivos de alunos e professores durante o desenvolvimento de atividades de modelagem matemática foram sistematizadas em Kaiser e Sriraman (2006) por meio de perspectivas para a Modelagem Matemática na Educação Matemática. Considerando o propósito do nosso trabalho de investigar a modelagem matemática como prática favorável ao desenvolvimento do pensamento matemático de alunos, pautamos nossas discussões na perspectiva cognitivista para a modelagem matemática. Para abordar o pensamento matemático utilizamos os pressupostos teóricos de Dreyfus (2002) sobre o pensamento matemático de estudantes, e as caracterizações de Tall (2004) para diferentes “Mundos da Matemática”. As análises empreendidas se realizam a partir do desenvolvimento de atividades de modelagem por estudantes de um curso de Licenciatura em Matemática e expressam reflexões e considerações sobre o pensamento matemático dos alunos e os processos cognitivos que mobilizaram e apontam indícios do trânsito dos alunos pelos três mundos da matemática durante o desenvolvimento destas atividades. Os resultados obtidos a partir dessa análise indicam o potencial de atividades de modelagem matemática como desencadeadoras de processos de pensamento matemático caracterizados por Dreyfus (2002) e Tall (2004)

Efeito de fontes de cálcio na firmeza do tomate.

O objetivo deste trabalho foi avaliar a firmeza do tomate em função da pulverização com fontes de cálcio. O experimento foi conduzido em casa de vegetação no período de janeiro a maio de 2011. O delineamento experimental utilizado foi blocos casualizados com quatro repetições e sete tratamentos (pulverização com fontes de Ca+ solúveis ou dispersíveis em água). Foi avaliada a firmeza de frutos em duas épocas de colheita. Observou-se que os tratamentos avaliados não influenciaram a firmeza do tomate

Os três mundos da matemática e atividades de modelagem matemática nos anos iniciais

A formação matemática dos sujeitos é foco de estudos no meio acadêmico desde a inserção das crianças na escola até sua saída já na fase adulta. Nesse contexto, o desenvolvimento de atividades de modelagem matemática com alunos dos primeiros anos de escolaridade é objeto de estudo deste artigo. A modelagem é abordada como alternativa pedagógica para o ensino de matemática, por meio dessa alternativa são analisados os registros em áudio, vídeo, bem como registros escritos de três atividades desenvolvidas por alunos no âmbito do quarto ano do primário. Para analisar os dados coletados e inferir sobre a formação matemática dos sujeitos utilizamos o quadro teórico dos Três Mundos da Matemática de David Tall que caracteriza ‘estágios’ de desenvolvimento cognitivo, diferenciados por meio das representações, modos de operação e da atribuição de significados aos objetos matemáticos. Nos orientamos pelas questões: ‘quais mundos da matemática são evidenciados no trabalho dos alunos dos primeiros anos de escolaridade?’ e, nesse sentido, ‘é possível que dizer que atividades de modelagem matemática auxiliam na formação matemática dos alunos dos primeiros anos de escolaridade?’. As considerações finais versam sobre a potencialidade da modelagem matemática nos primeiros anos de escolaridade, evidenciando os modos de representar os objetos matemáticos

Modelagem e educação infantil: percepções e ações dos professores

Este artigo tem por objetivo investigar percepções e ações manifestadas por professores da educação infantil no desenvolvimento de atividades de modelagem matemática, em particular, ao aprender sobre modelagem matemática. Dados coletados no desenvolvimento de uma oficina formativa com cinco professores balizam o processo analítico por meio de registros escritos no desenvolvimento de atividades, respostas à questionários e relatórios reflexivos. Amparados na abordagem metodológica da Análise de Conteúdo, a discussão de resultados indica que o grupo de professores, a partir de suas vivências e considerando a familiarização com a modelagem matemática, manifestam percepções e ações ao aprender sobre modelagem matemática, tais como: reconhecer a modelagem matemática como alternativa para o ensino; conhecer aspectos teóricos sobre modelagem matemática; identificar as características da modelagem matemática; reconhecer e identificar as fases e procedimentos por meio do desenvolvimento de uma atividade de modelagem matemática; possibilitar o ensino de matemática de maneira lúdica na Educação Infantil; planejar atividades de modelagem matemática para implementação na sala de aula da Educação Infantil