TRANSIENT BEHAVIOR OF TWO PHASE FLOW(AIR-WATER) IN HORIZONTAL PIPELINES WITH MULTIPLE LEAKS

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1 TRANSIENT BEHAVIOR OF TWO PHASE FLOW(AIR-WATER) IN HORIZONTAL PIPELINES WITH MULTIPLE LEAKS J. W. S. Costa (1), P. H. C. de Melo (1), F. O. Freire (1), A. G. B. de Lima (2), C. H. Sodré (1),W.G. Vieira (1) (1) Universidade Federal de Alagoas, Maceió- Alagoas-Brazil. (2) Universidade Federal de Campina Grande: Campina Grande-Paraíba-Brazil 1. Introduction The use of pipes for transporting fluids, especially liquids, is an old practice of mankind. There are reports that the Chinese used bamboo, the Aztecs and Egyptians used ceramic and the Greeks and Romans used lead for making your pipes (SOUZA, 2009). Actually, this transport is the most used worldwide for transporting fluids, particularly for gases, if used for long-distance it offers safe operation, efficiency and economic viability compared to other ways of transportation, such as rail, road or sea (SOUSA, 2007; Bezerra, 2008; AGUIAR, 2010; TAVARES, 2012). Even with advance of new materials, the most significant problem created by this type of transportation is due to leaks. For this reason, techniques that reduce the problem has arisen. According Colombaroli (2009), the main leak detection methods are: acoustic, infrared, negative pressure waves, mass balance, change in pressure or flow and modeling. Computer simulation technique intended to complement the theoretical and experimental analyzes and helps to have a better understanding of the process during the leak through the studies of the fluid flow profiles variables. Pressure falls, the velocity profile across the tube changes. Leak detection becomes important not only for the loss of fluid through the pipe, but also by the environmental disaster( Gulf of Mexico in April 2010). Recent research in industry oil in Brazil estimated that the cost of a leak was approximately R $ 150, per cubic meter leaked (BARBOSA, 2012). Leaks mostly occurs by corrosion, showing that companies do not have a proper maintenance, (Azevedo, 2009), and the crude oil is the product that more leaks. This study aims to evaluate the fluid dynamics of two-phase flow( water-air) in pipelines during the leak through computer analysis. The variable behavior of the process variables such as pressure, volume fraction and velocity of fluids were evaluated, and how these parameters are affected by the leak..2. Experimental- The simulation and computational modeling of processes are represented by the use of energy and mass transport equations, that predict the behavior of phenomena such as fluid flowing in pipes.the geometry of the object studied is a horizontal tube with dimensions of 20 m in length, 10 cm in radius. The tube contains two holes in the top surface from 8 and 12 m of the entrance, each hole having a radius of 2.5 cm. From the pipe geometry the mesh was constructed. The technique chosen was block construction because gives the user the opportunity to refine certain location of the object separately, in this case the region of the leak that concentrate a larger 12 m number of elements in this area, Image 1. 8 m This region generates greater influence in the variables than the others. Several meshes were used with different numbers of elements and then the comparisons between the results obtained by them after the mathematical simulation were made Image 1- Mesh construction with 2 holes(8m and 12 m) and the mesh chosen was with elements that takes 22 minutes of Time Processing. The interfacial transfer model of particles is assumed when one phase is continuous and the other phase is dispersed or poly-dispersed. The surface area per unit volume is calculated assuming that the phases are present as particles which can take various forms, for example, spherical (Andrade, 2014).

2 For a description of the interface between the phases was used the particle model that treats the surface area density, A αβ, as Eq. 1 represented by the equation 1. In this case thw water is the continus pahse and the air is disperse phase. In cases studied only the drag force was considered, which may be generically represented by equation 2. Eq. 2 The turbulent pattern flow has influences in the mass transport, movement and energy due to irregularity of the flux lines, because have a higher level of mixture. This characteristic of flow pattern implies in speed and temperature fluctuations. The turbulence models are the equations to predict the effects caused by the turbulence of the fluid (ANDRADE, 2014). The κ-ε turbulence model was used to describe the turbulence of the flow, where κ is the turbulent kinetic energy and ε is the effective turbulent dissipation. The equation of the conservation movement, now being represented by equations 3 and 4 which are modeled separately and solved for the turbulent length and time scale. f t f U f C1G C2 Eq. 3 t k fk t f Uk k f G t k 3. Results and Discussion- Operating Conditions: Fluids: Water and Air; Temperature: 25 ºC; fluid: Incompressible, Three-dimensional and Isothermal; Turbulence Equation: k-ε ;Input Condition: speed of 3.8 m / s; Two cases were studied: Case 1 In the first case it was simulated two-phase flow of water and air in a duct in the presence of one leak, at 8m from the entrance. Case 2. The second case study is the flow of water and air in a tube having two leaks, at 8 m and 12 m from the entrance. In both cases, the holes are located in the upper region of the tube, have the same geometry, mesh and the same boundary conditions. The variables analyzed in this work are the pressure, velocity and volume fraction. The analysis times are taken at 1, and 45 sec for the case 1; and 1, and 53 s to the case 2. Data were obtained drawing up a line at the top of the tube (Figure 14), a region where there are greater variations also being the region of interest. Then, thousand points were taken and then built the graphs for the analysis of results. As might be expected, it is clear, the air tends to go to the upper region, because its density is less than that of water. Due to this fact, the presence of a leak at the top tends to decrease the amount of air flowing in the duct in a larger proportion than that of water, so its volume fraction will decrease. The presence of a leak in the upper region has a cumulative effect, then when there are two holes, the air fraction will decreases even further. These facts can be observed in Image 2 and 3. Eq. 4 Image 2- Volumetric fraction of water in case 1 (left) and in case 2 (right) 1s

3 Image 3-Volumetric fraction of water in case 1 (left) in 45s and case 2 (right) 53 sec. Evaluating, the speed of the fluid flowing through the system for both cases 1 and 2. As the superficial velocity of a fluid is dependent of its volume fraction, it is expected that the fluid has higher surface speed where it has a higher volume fraction. Thus, as the Images 4 at 1s and 5 at 53 s show, the superficial velocities of the water are greater near the holes, where the water has its major volume fraction. These results are consistent with the analysis of volume fraction. Image 4- Superficial velocity of water in case 1 (left) and in case 2 (right) 1 s. Image 5-Superficial velocity of water in case 1 (left) at 45 in the case 2 (right) 53 sec. Image 6 and 7 show the Pressure along the tube in case 1 (left) in case 2 (right) at 1s, and 53s. As the

4 tube is not at higher pressure. The existence of a leak is characterized by slight pressure drop. The pressure drops and recovers from the lower level landing at other stage different from the instant without leak in which the system pressure again stabilize. is the pressure fluctuation due to leakage over time. This can be perceived through the curves presented in Figure 36, where you can see features like these fluctuations. Pressure along the tube in case 1 (left) and in case 2 (right) 1 s. Pressure along the tube in case 1 (left) in 45s and case 2 (right) in 53s. 4. Conclusions -For the analysis of simulated cases in this study the pressure, surface speed and volume fraction profiles were evaluated. It was observed that a higher proportion of air was lost due to the holes, so it is possible to assume that the volume fraction of water would tend to drive the pipe outlet near the hole. As expected, the regions with higher pressures are located in the regions of higher water concentrations. The surface water velocity profiles are directly related to the volume fraction of the component. As the volume fraction of the water tends to one near the region of the leak, the system behaves similarly to the single-phase flow of water. This study was for the case that the leak is very small, about 5% of the nominal flow. 5. References AGUIAR, F. G. Utilização de Redes Neurais Artificiais para Detecção de Padrões de Vazamentos em Oleodutos p. Dissertação (Mestrado em Engenharia Mecânica) - Universidade de São Paulo, Escola de Engenharia de São Carlos, São Paulo, ANDRADE, T. H. F. Introdução à Escoamento Multifásico.Notas de Aula UNIVERSIDADE FEDERAL DE ALAGOAS, Alagoas. 2014;

5 AZEVEDO, F. M. Proposta de Algoritmo para Detecção de Vazamentos em Oleodutos Utilizando Análise Frequencial de Sinais de Pressão f. Dissertação (Mestrado em Engenharia Elétrica) - Universidade Federal do Rio Grande do Norte, Centro de Tecnologia, Natal, RN, 2009; BARBOSA, L. M. C. Escoamento não-isotérmico de óleo pesado, água e gás em duto vertical com vazamento. 91f. Dissertação ( Mestrado em Engenharia Química) UNIVERSIDADE FEDERAL DE CAMPINA GRANDE, Campina Grande. 2012; BEZERRA, B. A. F. Detecção de vazamentos em tubulações de gás pelo método de transitório de pressão utilizando CLP e sensores f. Monografia. (Especialização em Engenharia de Instrumentação) Universidade Federal de Pernambuco, Recife, PE, 2008; CARDOSO, L. C. Petróleo: do Poço ao Posto. Rio de Janeiro: Qualitymann Ed., 2005, 84 p. COLOMBAROLI, P. L. S. Sistema de Detecção de Vazamento em Dutos de Petróleo. 8f. PRH16- ANP/MCT UNIVERSIDADE FEDERAL DE ITAJUBÁ. 2009; SOUSA, E. O. Detecção de vazamento em tubulações através de método acústico e da analise de transientes de pressão f. Dissertação ( Engenharia Química) UNIVERSIDADE ESTADUAL DE CAMPINAS, São Paulo. 2007; SOUZA, R. G. S. Escoamento Bifásico Líquido-Gás: Previsão de Gradientes de Pressão com a Correlação de Lockhart& Martinelli e Fluidodinâmica Computacional f. Projeto Final de Curso UNIVERSIDADE FEDERAL DO RIO DE JANEIRO, Rio de Janeiro. 2009; TAVARES, D. P. S. de A., Escoamento Trifásico Não-Isotérmico em Oleodutos Horizontais com Vazamentos: Modelagem e Simulação f. Dissertação UNIVERSIDADE FEDERAL DE CAMPINA GRANDE, Paraíba. 2012; Nomenclature Latin A αβ - Density interfacial area C 1 - Constant turbulence model k-ε C 2 - Constant turbulence model k-ε c µ - empirical constant of turbulence model k-ε c α - empirical constant of turbulence modelk-ε C D - Coefficient of drag d β - Mean diameter of the beta particle f α - Volumetric fraction of alpha phase f β - Volumetric fraction of beta phase G α - turbulent kinetic energy generation within the alpha phase k α - turbulent kinetic energy for alpha phase M α - interfacial forces acting in the alpha phase S Mα - time supply due to external body strength S MSα - specific mass Source t - Time U α - Vector speed alpha phase U β - Vector speed beta phase Grec α, β Phases α, β ε α - turbulent kinetic energy dissipation rate of alpha phase ρ α - density of the alpha phase ρ αβ - mixture density µ - dynamic viscosity µ α - Dynamic viscosity of the alpha phase µ tα - turbulent viscosity σ k - Constant turbulence modelk-ε σ ε - Constant turbulence modelk-ε - nabla operator - Partial derivative with time