07-BTP v54 Andre Martins

CFD-DEM modeling of the gravel packing operation during horizontal well completions

Modelagem em CFD-DEM da operação de gravel packing na completação de poços horizontais Modelaje en CFD-DEM de la operación de gravel packing durante la terminación de pozos horizontales

André Leibsohn MartinsJoão Vicente Martins de MagalhãesJairo Z. SouzaJoão Américo Aguirre Oliveira Jr.Carlos Eduardo Fontes

AbstractIncreasing oil exploration challenges require the development of new technologies to achieve higher efficiency in oil and gas

extraction, for the lowest possible cost. Numerical simulations of processes facilitate solutions for several industry-faced pro-blems, being able to achieve different virtual try-outs, which offer greater understanding to optimize the process in discussion. With the expressive computer capability development in the simulation field, computational fluid dynamics (CFD) has drawn most attention in recent years. This can computationally easily reproduce complex fluid flow phenomena such as turbulence, reactions, multiphase systems, etc. One of the gaps still taunting modern CFD codes is the incapacity to simulate, in detail, multiphase systems involving granular solids. These are common in many industrial processes, especially in the mining or oil and gas industry. The objective of this study is to develop a new methodology to numerically reproduce granular flows, sourcing a different tool to assist the calculation: the so called Discrete Element Method (DEM), used to perform particles transporta-tion. The methodology adopted was to couple the CFD (Fluid Flow Calculation) and DEM (Particle Tracks Calculation). To assess and validate the proposed approach, the Gravel Packing process of horizontal wells was used as a simulation test. The gravel packing process is widely used by Petrobras to complete deepwater and ultra-deep water wells and a better comprehension could lead to more efficient and economical operations. The first obtained results proved that this approach is very promising, indicating it is possible to work numerically with the complex problem of high solid concentrations. The study’s main results show a validation of the alpha wave height obtained in numerical simulation based on experimental Petrobras data. The results supported the proposed approach suggesting the CFD-DEM coupling may, in the future, be used to aid the design operation of gravel packing in horizontal wells.

keywords: n Discrete Particle Simulation n Computational Fluid Dynamics n Multiphase Flow n Horizontal Gravel Packing

Boletim Técnico da Petrobras, Rio de Janeiro, v. 54, n. 1/2, p. 43-53, abr./ago. 2011 n 43

ResumoO aumento dos desafios na exploração de petróleo requer o desenvolvimento de novas tecnologias para alcançar uma maior

eficiência na extração de petróleo e gás, no menor custo possível. As simulações numéricas de processos reais facilitam as solu-ções para vários problemas enfrentados no setor, sendo capaz de se reproduzir computacionalmente vários fenômenos. Isto ofere-ce uma maior compreensão para aperfeiçoar o processo de gravel packing. Com o desenvolvimento expressivo na capacidade de processamento de dados, experimentada nos últimos anos, pela indústria de computadores, a dinâmica de fluidos computacional (CFD), tem obtido, consequentemente, grandes avanços. Os códigos CFD podem facilmente reproduzir fluxos complexos de fluidos que envolvem fenômenos de: turbulência, reações e sistemas multifásicos. Uma das lacunas ainda existentes nos códigos mo-dernos de CFD é a incapacidade de simular corretamente os sistemas multifásicos envolvendo sólidos granulares. Estes sistemas são comuns em muitos processos industriais, especialmente na indústria de mineração e na de petróleo e gás. O objetivo deste estudo é desenvolver uma nova metodologia para reproduzir numericamente fluxos granulares, utilizando para isto uma abordagem que mescla dois diferentes métodos de modelagem fenomenológica, o baseado nas soluções das equações de Navier-Stokes para o escoamento de fluidos (CFD) e o baseado na solução das equações de Newton para o movimento de partículas (modelo de elementos discretos - DEM). A metodologia adotada foi acoplar as soluções obtidas pelo software de CFD (Cálculo de Fluxo de Fluidos) com as soluções obtidas por um software de DEM (Cálculo da trajetória e choque de Partículas). A completação de poços por gravel packing é amplamente utilizada na Petrobras, principalmente em cenários de águas profundas e ultraprofundas onde temos mais de 270 poços completados desta forma. Os primeiros resultados numéricos obtidos revelaram-se muito promissores, indicando que é possível reproduzir o fenômeno do empacotamento do leito de gravel mesmo nas altas concentrações de sólidos experimentadas, que levam na impossibilidade de se modelar o fenômeno somente utilizando a abordagem CFD. Um dos principais resultados do estudo mostra que é possível validar a altura da onda alfa obtida através de testes experimentais realizados pela Petrobras. Os resultados apoiaram a abordagem proposta sugerindo que o acoplamento CFD-DEM pode, no futuro, ser utilizado com sucesso para reproduzir a operação de gravel packing em poços horizontais.

palavras-chave: n Simulação de Partículas por discretização do domínio n Dinâmica Computacional de Fluidos n Fluxo Multifásico n Gravel Packing em poços horizontais

ResumenLos crecientes desafíos en la exploración del petróleo, requieren un desarrollo de nuevas tecnologías para lograr una mayor

eficiencia en la extracción del petróleo y del gas con el menor costo posible. Las simulaciones numéricas de procesos reales facilitaron las soluciones a diversos problemas que enfrentan la industria, siendo capaz de reproducir computacionalmente muchos fenómenos. Esto proporciona un mayor conocimiento para mejorar el proceso de gravel packing. Con el desarrollo ex-presivo en la capacidad en el procesamiento de datos, experimentado en los últimos años, en la industria de la computación, la dinámica de fluidos computacional (CFD) haber obtenido por lo tanto los grandes avances. Los códigos CFD pueden reproducir fácilmente los complejos flujos de fluidos que implican fenómenos de: turbulencia, reacciones y sistemas multifásicos. Una de las lagunas que aún existen en los códigos modernos de CFD es la incapacidad para correctamente simular los sistemas multifasicos conteniendo sólidos granulares. Estos sistemas son comunes en muchos procesos industriales, especialmente en la industria minera y en el petróleo y del gas. El objetivo de este estudio es desarrollar una nueva metodología para reproducir numéricamente los flujos granulares, utilizando para esto con un enfoque que combina dos métodos diferentes de modelos fenomenológicos, con base en a las soluciones de las ecuaciones de Navier-Stokes para flujo de fluidos (CFD) y sobre la base de la solución de las ecuaciones de Newton para el movimiento de las partículas (modelo de elementos discretos - DEM). La metodología adoptada fue la de juntar las soluciones obtenidas por el software de CFD (Cálculo de Flujo de Fluidos) con las


44 n Boletim Técnico da Petrobras, Rio de Janeiro, v. 54, n. 1/2, p. 43-53, abr./ago. 2011

IntroductionGravel Packing is today the most frequently applied sand

control technique in the Campos Basin, offshore Brazil. Due to the critical conditions, such as the deep and ultra deep water and low fracture gradients, great precision is required to assure gravel-packing success. Sand production during ex-ploration can sometimes turn the oil extraction unviable. A common problem occurs when the separation equipment is unable to deal with sand flow rates high enough to allow the continuum operation.

The gravel packing process is illustrated in figures 1, 2 and 3. The operation consists of filling the annulus formed between the open reservoir and the screen with particulate material (known as proppant). The particle porous-media for-med acts as a filtering region, permitting only petroleum to flow through the production column. The sand-liquid mixtu-re shown in figure 1 is being injected into the column. In fi-gure 2, the proppant settles in the bottom of the annulus re-gion, due to gravitational effects (alpha wave propagation). The solids are shown filling the top of the annulus in figure 3 (beta wave propagation). The gravel packing column is a tool, which allows the solid-liquid mixture to correctly flow in the annulus. The main components of the process are sho-wn in figure 4.

Due the importance of the gravel packing operation, seve-ral models are available in the oil industry, nevertheless, they are essentially empirical, resulting in imprecise predictions for extrapolated conditions. There are also some mechanistic mo-

Martins et al.

Figure 1 – Proppant injection in Gravel Packing process.

Figura 1 – Injeção de propante no processo de Gravel Packing.

Figura 1 – Inyección del proppant en el proceso de Gravel Packing.

soluciones obtenidas por un software de DEM (Cálculo de la trayectoria y choque de Partículas). La terminación de pozos con gravel packing se utiliza ampliamente en Petrobras, especialmente en situaciones de aguas profundas y ultra-profundas donde tenemos más de 270 pozos terminados de esta manera. Los primeros resultados numéricos fueron muy prometedores, lo que indica que es posible reproducir el fenómeno de embalaje en el lecho de gravel misma en las altas concentraciones de sólidos de la experiencia, lo que es imposible modelar el fenómeno sólo utilizando el enfoque de CFD. Uno de los principales resultados del estudio muestran que es posible validar la altura de la onda alfa obtenido por medio de pruebas experimentales realizadas por Petrobras. Los resultados apoyan el enfoque propuesto sugiriendo que el acoplamiento de CFD-DEM en el futuro pueda ser utilizado con éxito para reproducir el operación de gravel packing en pozos horizontales.

palabras-clave: n Simulación de partículas por desratización del dominio n Dinámica Computacional de Fluidos n Flujo multifásico n Gravel Packing en pozos horizontales

dels, but those models are unable to describe operational de-tails, such as alpha wave height and conditions where the pre-mature screen out occurs. The premature screen out occurs when the beta wave of the gravel packing process forms befo-re filing the entire open-hole region.

Seeking a better process understanding and obtain a pa-rameter to adjust the Petrobras Mechanistic Model, Petro-bras Research Center (Cenpes) and ESSS have developed a CFD-DEM model to numerically reproduce the multiphase flow in the gravel packing operation. The approach couples computational fluid dynamics and the discrete element me-thod. This new methodology allows the solid flow details to be evaluated, such as particle-particle interaction and parti-


cle-fluid interaction. The study’s goal is to forecast the solid bed height under different operational conditions. These data can be compared with experimental data provided by Petro-bras engineers, to validate the approach. The methodology steps are listed below.

MethodologyThe study’s objective is to reproduce the gravel packing

process, to obtain data to facilitate the design of the practi-cal operation.

However, multiphase flow modeling poses a lot of chal-lenges. Some examples:•granular solids flowing under different regimes. The

presence of a high solid volume fraction and stagnated solid flow is very problematic for numerical simulations;•the size of the problem. The gravel packing process is

applied in large well sections, which is not feasible in numerical simulations using CFD;•the total number of particles is very high, turning com-

putational simulation very expensive. Therefore, a simplified case has been studied, requiring

less computational effort, but without losing quality in the fi-nal results.

GeometryThe gravel packing process scheme is illustrated in figure

5. In this case study, the analysis is in the contraction region (rat-hole/open-hole transition). The 3D simulation is not fea-sible, due the high number of particles. A 2D domain is pro-posed, as shown in figure 6.

Computational MeshThe computational mesh results from the geometry dis-

cretization. Its goal is to divide the domain into small ele-ments, where the conservation equations will be applied to obtain the flow profiles.

To obtain an optimal discretization, a hexahedral mesh was generated into the geometry. In the hexahedral mesh, the dis-crete elements were aligned with the flow, in order to facilita-

Figure 3 – Beta wave displacement.

Figura 3 – Desloca-mento da onda Beta.

Figura 3 – Despla-zamiento de la onda Beta.

Figure 4 – Gravel Packing components.

Figura 4 – Componen-tes do Gravel Packing.

Figura 4 – Compo-nentes de la Gravel Packing.

Figure 2 – Alpha wave displacement.

Figura 2 – Desloca-mento da onda Alfa.

Figura 2 – Desplaza-miento de la onda Alfa.



te the solution convergence. Some images of the generated computational mesh for the gravel packing simulation are sho-wn in figure 7. The final mesh had 24.000 elements.

Physical set upThe proposed problem was set up according to the ope-

rational data provided by Petrobras. In a CFD-DEM approach, the results are obtained through two simultaneous software calculations: Fluent, from Ansys Inc (CFD Side); and EDEM, from DEM Solutions (DEM Side).

The fluid flow is solved through mass and momentum balances. The momentum balance equation (Navier-Stokes equation) is shown in equation 1.

(1)

Figure 5 – Gravel Packing scheme.

Figure 5 – Esquema de Gravel Packing.

Figura 5 – Esquema de la Gravel Packing.

Figura 6 –Simplified geometry in CFD simulations. Figure 6 – Geometria simplificada em simulações de CFD. Figura 6 – Geometría simplificada en simulaciones de CFD.

Figure 7 – Computatio-nal mesh.

Figura 7 – Malha Computacional.

Figura 7 – Malla computacional.

Martins et al.


This equation is the traditional momentum equation, where εf denotes the fluid volume fraction. S is the source term (the particle influence on the fluid flow will take place in this term).

On each particle, a force balance is applied (all the for-ces acting on the particle: contact, body forces, drag, etc.). Therefore, DEM will basically solve two equations, which tra-ck the particle inside the domain: equation 2 for translational movement and equation 3 for rotational movement.

(2)

(3)

During the calculation, a coupling module promotes the interaction between the phases. This coupling is made throu-gh the additional sources terms in the fluid equations, ex-changing momentum with the particles via drag forces.

The coupling module also returns the solid and fluid volu-me fraction, through the average number of particles inside each fluid computational cell.

The assumptions made in these CFD-DEM simulations are described below:

CFD Side•symmetry condition;•constant properties (specific mass, viscosity;

temperature);•turbulent flow regime (k-ε model);•boundary Conditions; · Inlet: Prescribed velocity; · Outlet: Prescribed pressure; · Walls: No slip condition;•Ansys Fluent software.

DEM Side•periodic condition;•constant particle shape (no particle deformation);•spherical particle, with just one particle diameter;•non-slip between particle and geometry;•constant particle generation rate ;•DEM Solutions EDEM software.

The boundary condition application is shown in figure 8.

Figure 8 – Simulation boundary conditions. Figura 8 – Condições de contorno das simulações. Figura 8 – Simulación de condiciones del contorno.



Different cases have been simulated, evaluating the ope-rational conditions influence in the rat-hole solid bed height. The simulated operational conditions are listed below:

Case 1•particle diameter: 630 μm;•particle density: 2,71;•flow rate: 6 BPM.

Case 2•particle diameter: 630 μm;•particle density: 2,71;•flow Rate: 7 BPM.



Figure 9 – Simulated flow profile. Figura 9 – Perfil do fluxo simulado. Figura 9 – Perfil del flujo simulado.

ResultsThe CFD-DEM results supply detailed information about the

fluid and solid flow in the domain. Velocity profiles, volume frac-tion, pressure and turbulence are easily obtained with numerical simulations. The CFD analysis of this study is concentrated in the velocity profiles and solid volume fraction profiles, due the inte-rest to evaluate different flow regimes and the solid bed height.

The case 1 flow profile snapshots are shown in figure 9. It is possible to identify the bed growing until the fluid flow rea-ches a critical velocity. At this point, the fluid velocity is suffi-ciently high to guarantee no solids sedimentation. The same behavior is observed in the other simulated cases.

This stable situation occurs due the drop in pressure equi-librium between the fluid flowing above the solid bed and the fluid flowing into the wash-pipes. The simulation results show that when solid particles start settling on the top of the screen, the fluid velocity into the annular region formed be-tween the wash-pipes and screens increases.

To evaluate the bed height in the simulations, five mo-nitor positions were marked in the rat-hole, according to fi-

Martins et al.


gure 10. These five monitors record the bed height time- evolution as shown in figure 11. The total stability was not reached in all the rat-hole channel, but at points 1 and 2, the bed height was stabile after 25 seconds. Therefore, the bed height was evaluated as at these points.

The simulated bed height was compared with experimen-tal data provided by Petrobras. The tests were performed in a real-diameter physical simulator, assuring the similarity with a practical gravel packing displacement operation.

The tests were carried out at Halliburton’s base in Macaé city. In order to visualize the solids flow, three acrylic windo-ws were made in the simulator, as well as to watch the alpha and beta wave displacement and to measure bed heights and velocity. The equipment used in these tests is illustrated in figures 12 and 13.

Experimental

DataSimulation

DataError

Case 1 85% 84,74% -0,30%

Case 2 84% 82,5% -1,78%

Case 3 80% 79,61% -0,49%

Case 4 79% 81,82% +3,57%

Table 1 – Simulated bed height.

Tabela 1 – Altura do leito simulado.

Tabla 1 – Altura del lecho camada simulada.

Figure 12 – Experi-mental plant - Acrylic Window.

Figura 12 – Planta experimental - Janela de acrílico.

Figura 12 – Planta experimental - Ventana de acrílico.

Figure 13 – Experimen-tal plant.

Figura 13 – Planta experimental.

Figura 13 – Planta experimental.

The comparison between simulated and experimental data is presented in table 1. The difference between simu-lated and experimental data is also shown in the table. The good agreement between simulation and experimental bed height results can be observed. These results show the CFD- DEM approach is able to supply operational data for gravel- packing process design.

The CFD-DEM methodology can also determine the fluid velocity profile and the flow regimes found in the granular system. A common velocity profile in the rat-hole is illustra-ted in the figure 14.

The higher velocity region is the zone where there are no particles, and the fluid flow is at the critical velocity. At the

Figure 10 – Analysis positions to evaluate the bed height.

Figura 10 – Pontos de análise da altura do leito.

Figura 10 – Puntos de análisis de la altura del lecho.

Figure 11 – Bed height time-evolution - Case 1.

Figura 11 – Evolução temporal do leito- Caso 1.

Figura 11 – Evolución temporal del lecho - Caso 1.



stagnated solid bed, the fluid experiences the flow resistan-ce into the porous bed, therefore velocities in those regions are very small. Between the stagnated bed and high veloci-ty regions, there is a flow transition regime, where some par-ticles move due the fluid drag, but the velocity is not so high as the critical velocity. At the bottom, the velocity profile flo-wing in the wash-pipe can be seen.

Conclusions and next stepsIn general, the CFD-DEM methodology showed consistent

results. The gravel packing process characteristics were repro-duced successfully through the numerical simulations.

Figure 14 – Velocity profile into the Rat hole - Case 1.

Figura 14 – Perfil de velocidade no Rat hole - Caso 1.

Figura 14 – Perfil de la velocidad en el Rat hole - Caso 1.

The combination between critical velocity and bed stability supplied an alpha wave bed height that showed strong agree-ment with the experimental tests. The CFD-DEM approach is able to reproduce the phenomena that govern the horizontal solid fluid flow.

The CFD-DEM approach is a promising way to test diffe-rent operating conditions, evaluating bed height and also con-ditions where the premature screen-out occurs. The study’s main goal is to forecast the operational limits of the gravel-pa-cking process, avoiding problems during practical operations.

The project’s next steps are to simulate more realistic ca-ses, making the virtual experiment even closer to reality. To achieve this, some challenges must be overcome:

• increase the number of particles inside the domain;• work with the real geometry (3D case);• drastic increse in computational effort

(needs parallel computing).

By fine tuning the CFD-DEM simulation methodology, the-se CAE softwares (Fluent + EDEM) will become a practical design tool for such cases.

n n n

Referências Bibliográficas

n ANSYS. Fluent User Guide. Canonsburg: Ansys, 2008.

n DEM SOLUTIONS. EDEM Fluent Coupling Mode Guide. Edinburgh: Dem Solutions, 2009.

n MAGALHÃES, J. V M. Estudos para o Deslocamento do Gravel Pack em Poços Horizontais Extensos em Cenários de Óleos Pesados. In: ENCON-TRO NACIONAL DE HIDRÁULICA DE PERFURAÇÃO E COMPLETAÇÃO DE

POÇOS DE PETRÓLEO E GÁS – ENAHPE, 2006, Pedra Azul, Domingos Mar-tins, ES, 2006. Anais... Manguinhos, ES: Faculdade do Centro Leste, 2006.

n MARTINS, MAGALHÃES, J. V. M.; MARTINS, A. L.; CALDERON, A.; CHAGAS, C. M. A Mechanistic Model for Horizontal Gravel Pack Displa-cement. In: SPE EUROPEAN FORMATION DAMAGE CONFERENCE, 2003, Netherlands. Proceedings… Richardson: Society of Petroleum Engineers, 2003. Paper n. 82247-MS.

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André Leibsohn Martins é consultor sênior na Tecnologia de En-genharia de Poço do Cenpes. Começou na Petrobras em 1986 e coordenou diversos projetos envolvendo perfuração, completação e hidráulica de cimentação de poços. É formado em Engenharia Química pela Universidade Federal do Rio de Janeiro (UFRJ). Mes-tre em Engenharia de Petróleo pela Universidade Estadual de Cam-pinas (Unicamp).

André Leibsohn Martins

Centro de Pesquisas da Petrobras (Cenpes)Gerência de Interação Rocha-Fluido e-mail: [email protected]

Autores

João Vicente Martins de Magalhães é engenheiro químico, graduado pela Universidade Federal Fluminense (UFF), em 2001, especializado em engenharia de petróleo pela Pontifícia Universi-dade Católica do Rio de Janeiro (PUC-Rio), em 2003. Ingressou na Petrobras em 2001, inicialmente como estagiário, no setor de Tecnologia em Engenharia de Poço (TEP), do Centro de Pes-quisas da Petrobras (Cenpes). Em 2002 passou a ser contratado no mesmo setor para iniciar o desenvolvimento do simulador de deslocamento de gravel pack para poços horizontais (SimGPH). Desde então, desenvolve o software e realiza diversas análises relacionadas à hidráulica de deslocamento do gravel pack. Em 2006 participou do curso de formação de Engenheiros de Petró-leo da Petrobras (CEP-2006) realizado na Universidade Petrobras (UP - Salvador). Em 2008 obteve grau de Mestre em Engenha-ria de Petróleo, pelo Departamento de Engenharia Mecânica da PUC. Trabalha com análise de hidráulica de perfuração e comple-tação e no desenvolvimento de diversos softwares para aplica-ção na engenharia de poço.

João Vicente Martins de Magalhães

Centro de Pesquisas da Petrobras (Cenpes)Gerência de Interação Rocha-Fluido e-mail: [email protected]

Jairo Zago de Souza graduou-se em Engenharia Química pela Universidade Federal de Santa Catarina (2007) e mestrado em Engenharia Química pela Universidade Federal de Santa Catarina na área de Desenvolvimento de Processos Químicos e Tecnológi-cos (2010). Desde 2007, atua como engenheiro de CAE na em-presa Engineering Simulation and Scientific Software Ltda., onde realiza trabalho de consultoria em Fluidodinâmica Computacional para Indústria de Processos Químicos e Indústria Mecânica. Tem experiência na área de simulação numérica de processos e equi-pamentos industriais, com ênfase para a Indústria de Petróleo. Tem atuado junto a Petrobras em simulações numéricas utilizando CFD com foco em escoamentos multifásicos envolvendo líquidos e sólidos, visando o desenvolvimento de processos para perfura-ção e completação de poços de petróleo.

Jairo Zago de Souza

ESSS – Engineering Simulation and Scientific Software e-mail: [email protected]



Carlos Eduardo Fontes formou-se em 1994 pela Escola de Quí-mica da UFRJ, possui mestrado (1997) e doutorado (2002) em Engenharia Química pelo Programa de Engenharia Química/ Co-ppe, pela Universidade Federal do Rio de Janeiro. Durante cinco anos trabalhou na empresa de Engenharia Chemtech, atuando como engenheiro sênior e como líder de Projetos da Divisão de Projetos Especiais, atuando em áreas como Engenharia Básica, Controle Estatístico de Processos, Simulação de Processos, Flui-dodinâmica Computacional (CFD), Análise de Risco e Estudos de Segurança. Atualmente é gerente técnico do Setor de Serviços da empresa ESSS, sendo responsável pelos trabalhos nas áreas de CAE (CFD e FEA) e de desenvolvimento de software científi-co. Tem experiência e interesse na área de simulações fluidodi-nâmicas (CFD), com ênfase em escoamentos reativos e multifá-sicos. Outras áreas de interesse são a aplicação de simulações fluidodinâmicas em análise de risco e o desenvolvimento de no-vos processos nas áreas de óleo/gás/álcool.

João Américo Aguirre Oliveira Junior graduou-se engenheiro mecânico pela Universidade Federal do Rio Grande do Sul (UFR-GS), em 2003. Obteve o título de Mestre em Engenharia Mecâ-nica em 2006 também pela UFRGS com foco em modelagem e simulação de grandes escalas (LES) de escoamentos turbulen-tos. Trabalha na ESSS desde 2006 e, a partir de 2009 desempe-nha a atividade de coordenador de serviços na área de Dinâmica dos Fluidos Computacional. Atua desde 2006 na simulação nu-mérica de escoamentos da indústria do petróleo, coordenando um grupo de engenheiros da ESSS dedicado ao estudo da mo-delagem de problemas ligados à área de exploração e produção.

Carlos Eduardo Fontes


João Américo Aguirre Oliveira Junior


Martins et al.


07-BTP v54 Andre Martins

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