Modelagem Matemática e Computacional de fenômenos eletrocinéticos em meios porosos carregados eletricamente

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel, we rewrite the macroscopic model in a one-dimensional version. Finally, using a sequential algorithm, we discretize the macroscopic model via the finite element method, along with the interactive method of Picard for the nonlinear terms. Numerical simulations on transient regime with variable pH in one-dimensional case are obtained, aiming computational modeling of the electroremediation process of clay soils contaminated

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Modelagem analítica e experimental da filtração em meios porosos

Deep bed filtration occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity, etc). A statistical model for filtration in porous media is proposed and analytical solutions for suspended and retained particles are derived. The model, which incorporates particle retention probability, is compared with the classical deep bed filtration model allowing a physical interpretation of the filtration coefficients. Comparison of the obtained analytical solutions for the proposed model with the classical model solutions allows concluding that the larger the particle capture probability, the larger the discrepancy between the proposed and the classical models

Modelagem analítica e experimental da filtração em meios porosos

Deep bed filtration occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity, etc). A statistical model for filtration in porous media is proposed and analytical solutions for suspended and retained particles are derived. The model, which incorporates particle retention probability, is compared with the classical deep bed filtration model allowing a physical interpretation of the filtration coefficients. Comparison of the obtained analytical solutions for the proposed model with the classical model solutions allows concluding that the larger the particle capture probability, the larger the discrepancy between the proposed and the classical models

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Modelagem e previsão da perda de injetividade em poços canhoneados

Waterflooding is a technique largely applied in the oil industry. The injected water displaces oil to the producer wells and avoid reservoir pressure decline. However, suspended particles in the injected water may cause plugging of pore throats causing formation damage (permeability reduction) and injectivity decline during waterflooding. When injectivity decline occurs it is necessary to increase the injection pressure in order to maintain water flow injection. Therefore, a reliable prediction of injectivity decline is essential in waterflooding projects. In this dissertation, a simulator based on the traditional porous medium filtration model (including deep bed filtration and external filter cake formation) was developed and applied to predict injectivity decline in perforated wells (this prediction was made from history data). Experimental modeling and injectivity decline in open-hole wells is also discussed. The injectivity of modeling showed good agreement with field data, which can be used to support plan stimulation injection wells

Modelo Estocástico para bloqueio de poros e redução de permeabilidade

Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

Modelagem e previsão da perda de injetividade em poços canhoneados

Waterflooding is a technique largely applied in the oil industry. The injected water displaces oil to the producer wells and avoid reservoir pressure decline. However, suspended particles in the injected water may cause plugging of pore throats causing formation damage (permeability reduction) and injectivity decline during waterflooding. When injectivity decline occurs it is necessary to increase the injection pressure in order to maintain water flow injection. Therefore, a reliable prediction of injectivity decline is essential in waterflooding projects. In this dissertation, a simulator based on the traditional porous medium filtration model (including deep bed filtration and external filter cake formation) was developed and applied to predict injectivity decline in perforated wells (this prediction was made from history data). Experimental modeling and injectivity decline in open-hole wells is also discussed. The injectivity of modeling showed good agreement with field data, which can be used to support plan stimulation injection wells

Modelo Estocástico para bloqueio de poros e redução de permeabilidade

Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

Simulador de escoamento multifásico em poços de petróleo (SEMPP)

The multiphase flow occurrence in the oil and gas industry is common throughout fluid path, production, transportation and refining. The multiphase flow is defined as flow simultaneously composed of two or more phases with different properties and immiscible. An important computational tool for the design, planning and optimization production systems is multiphase flow simulation in pipelines and porous media, usually made by multiphase flow commercial simulators. The main purpose of the multiphase flow simulators is predicting pressure and temperature at any point at the production system. This work proposes the development of a multiphase flow simulator able to predict the dynamic pressure and temperature gradient in vertical, directional and horizontal wells. The prediction of pressure and temperature profiles was made by numerical integration using marching algorithm with empirical correlations and mechanistic model to predict pressure gradient. The development of this tool involved set of routines implemented through software programming Embarcadero C++ Builder® 2010 version, which allowed the creation of executable file compatible with Microsoft Windows® operating systems. The simulator validation was conduct by computational experiments and comparison the results with the PIPESIM®. In general, the developed simulator achieved excellent results compared with those obtained by PIPESIM and can be used as a tool to assist production systems development

Entendendo as propriedades do arenito Botucatu e sua utilização como meio poroso para estudos envolvendo o deslocamento de fluidos poliméricos

The development of products whose purpose is to promote blockages in high permeability zones as well as to control the hydrate or scale formation also needs some tests in porous media before using the product in the field, where attempts and unavoidable operational errors costs would able to derail any projects. The aim of this study was to analyze and compare the Botucatu and Berea sandstones properties, involving problems related to loss permeability. It was observed that even cores of Berea, without expansible clays in their composition had their permeability reduced, as soon as the salinity of brine reached a lower limit. As expected, the same happened with the Botucatu sandstone samples, however, in this case, the sensitivity to low salinity was more pronounced. In a second phase, the research was focused on the Botucatu Sandstone behavior front of dilute polymer solutions injection, checking the main relationships between the Rock / Fluid interactions, considering the Mobility Reduction, Resistance and Residual Resistance Factors, as well as adsorption/desorption processes of these polymers, and the polymer molecules average size and porous sandstone average size ratio. The results for both phases showed a real feasibility of using the Botucatu sandstone in laboratory tests whose objective is the displacement of fluids through porous media

Simulação de Fluxo no Meio Poroso Utilizando o Fluent

The complexity of the Phenomenon of fluid flow in porous way causes a difficulty in its explicit description. Different in the cases where the flow is given through a pipe, where it is possible to measure the length and diameter of the pipe and to determine their ability to flow as a function of pressure, which is a complicated task in porous way. However, we try to approach clearly the equations used to conjecture the behavior of fluid flow in porous way. We made use of the Gambit to create a fractal geometry with the fluent we give the contour´s conditions we would want to analyze the data. The triangular mesh was created; it makes interactions with the discs of different rays, as barriers putted in the geometry. This work presents the results of a simulation with a flow of viscous fluids (oilliquid). The oil flows in a porous way constructed in 2D. The behavior evaluation of the fluid flow inside the porous way was realized with graphics, images and numerical results used for different datas analysis. The study was aimed in relation at the behavior of permeability (k) for different fractal dimensions. Taking into account the preservation of porosity and increasing the fractal distribution of the discs. The results showed that k decreases when we increase the numbers of discs, although the porosity is the same for all generations of the first simulation, in other words, the permeability decreases when we increase the fractality. Well, there are strong turbulence in the flow each time we increase the number of discs and this hinders the passage of the same to the exit. These results permitted to put in evidence how the permeability (k) is affected in a porous way with obstacles distributed in a diversified form. We also note that k decreases when we increase the pressure variation (P) within geometry. So, in front of the results and the absence of bibliographic subsidies about other theories, the work realized here can possibly by considered the unpublished form to explain and reflect on how the permeability is changed when increasing the fractal dimension in a porous way

Fluxo de fluído através de um meio poroso fractal desordenado. Análise das tensões de cisalhamento e efeito de escala na estimativa das forças viscosas

In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.