# Circulation, transport and dispersion of hydrocarbon plumes in the North Brazilian equatorial broadband

H.L. Varona

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H.L. Varona. Circulation, transport and dispersion of hydrocarbon plumes in the North Brazilian equatorial broadband. Physics [physics]. Universidade Federal de Pernambuco, 2018. English. NNT: tel-03521480

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UNIVERSIDADE FEDERAL DE PERNAMBUCO – UFPE
CENTRO DE TECNOLOGIA E GEOCIÊNCIAS
DEPARTAMENTO DE OCEANOGRAFIA
PROGRAMA DE PÓS GRADUAÇÃO EM OCEANOGRAFIA

HUMBERTO LÁZARO VARONA GONZÁLEZ

CIRCULATION, TRANSPORT AND DISPERSION OF HYDROCARBON PLUMES
IN THE NORTH BRAZILIAN EQUATORIAL BROADBAND

RECIFE

2018
CIRCULATION, TRANSPORT AND DISPERSION OF HYDROCARBON PLUMES
IN THE NORTH BRAZILIAN EQUATORIAL BROADBAND

Tese apresentada ao Programa de Pós-graduação
em Oceanografia da Universidade Federal
de Pernambuco como requisito parcial para
obtenção do título de Doutor em Oceanografia.

Área de concentração: Oceanografia Abiótica

Supervisor: Prof. Dr. Moacyr Cunha de
Araújo Filho

Co-supervisor: Profa. Dra. Doris Regina Aires
Veleda

RECIFE
2018
V323c Varona González, Humberto Lázaro.
Circulation, transport and dispersion of hydrocarbon plumes in the north Brazilian equatorial broadband / Humberto Lázaro Varona González. - 2018.
160 folhas, il., gráfs., tabs.

Orientador: Prof. Dr. Moacyr Cunha de Araújo Filho.

Coorientadora: Profa. Dra. Doris Regina Aires Veleda.

Tese (Doutorado) – Universidade Federal de Pernambuco. CTG.
Programa de Pós-Graduação em Oceanografia, 2018.

Inclui Referências, Apêndice e Anexo.

Texto em Inglês.

1. Oceanografia. 2. Modelo ROMS. 3. Modelo GAS_DOCEAN. 4. Pluma do Rio Amazonas. 5. Vazamentos de óleo e gás. 6. Plataforma continental do Brasil. I. Araújo Filho, Moacyr Cunha de. (Orientador). II. Veleda, Doris Regina Aires. (Coorientadora). III. Título.
CIRCULATION, TRANSPORT AND DISPERSION OF HYDROCARBON PLUMES
IN THE NORTH BRAZILIAN EQUATORIAL BROADBAND

Tese apresentada ao Programa de Pós-graduação
em Oceanografia da Universidade Federal
de Pernambuco como requisito parcial para
obtenção do título de Doutor em Oceanografia.

Área de concentração: Oceanografia Abiótica

Trabalho aprovado. Recife, 16 de maio de 2018:

**Prof. Dr. Moacyr Cunha de Araújo Filho**
Orientador/Presidente/Titular Interno –
PPGO/UFPE

**Dra. Carmen Medeiros Limongi**
Titular Interna – PPGO/UFPE

**Dr. Alex Costa da Silva**
Titular Interno – PPGO/UFPE

**Dr. Carlos Esteban Delgado Noriega**
Titular Externo – CEERMA/UFPE

**Dr. Leonardo Vieira Bruto da Costa**
Titular Externo – DOCEAN/UFPE

RECIFE
2018
This Ph. D. thesis is dedicated to:

My beloved parents Ismael Humberto (In Memoriam) and Norka
and to my beloved children Laysun, Humberto Vinlay and Ismael David
## Acknowledgements

* To God for his eternal help and for allowing me to finish this thesis.

* To my supervisor Dr. Moacyr Araújo, for the orientation of this work, for his trust, his help, support and friendship.

* To Dra. Doris Veleda for her good advice, support, supervision and friendship.

* To Dr. Marcus Silva for his constant help, support, supervision and for sharing his knowledge.

* To Claudia Von and Fabiana Leite for his constant help.

* To Marcio das Chagas for his support and help.

* To my mother and children for their love, their patience, their collaboration and support in all stages of this work.

* To Ramón Raudel for providing an initial momentum to this Ph. D.

* To William Artiles for his constant help.

* To Human Resources Program (PRH-47) of the Agência Nacional do Petróleo (ANP) for the concession of PhD scholarships, Financiadora de Estudos e Projetos (FINEP) and Ministério da Ciência, Tecnologia, Inovações e Comunicações (MCTI).

* To Centro de Estudos e Ensaios em Risco e Modelagem Ambiental (CEERMA) and Departamento de Oceanografia (DOCEAN)

* To my friends and my colleagues of CEERMA and DOCEAN: Carlos, Severino, Aubains, Pedro, Christine, Marcio Cintra, Marcio das Chagas, Erasmo, Marisa and Ramilla: for your friendship, help and support.

* To Archie, Macuto and Tan for your constant support.

* To Guillermo Palacios y Javier González for sharing their knowledge with me.

* To Leticia and Edgar for your help and friendship.

* To all those who contributed to the realization of this thesis.
"The Lord is with me; I will not be afraid.
What can mere mortals do to me?
The Lord is with me; He is my helper.
I look in triumph on my enemies.
It is better to take refuge in the Lord than to trust in humans."
(Holy Bible, Psalm 118, 6-8)
ABSTRACT

This Ph. D. thesis focuses on a study of hydrodynamics and oil/gas blowouts in deep water using the Regional Ocean Model System (ROMS) and GAS_DOCEAN models. The first objective was to analyze the potential impact of the Amazon and Pará Rivers on salinity, temperature and hydrodynamics in the Western Tropical North Atlantic between 60.5°-24°W and 5°S-16°N. The ROMS was used to simulate the ocean hydrodynamics with 0.25° horizontal resolution and 32 vertical levels. The sea surface temperature and salinity and the surface current were compared with Simple Ocean Data Assimilation (SODA) and Surface Currents from Diagnostic. Vertical profiles at 8°N, 38°W and 12°N, 38°W are validated with the Prediction Research Moored Array in the Tropical Atlantic. In the ROMS model two experiments are carried out, one taking into account the discharge of freshwater from the Amazon and Pará rivers and the second, without releasing freshwater into the Atlantic ocean. The results of both simulations are compared determining the changes in temperature, salinity and surface currents produced by the influence of the rivers discharge. The Sea Surface Temperature difference between the simulations with river and no-river was about 2°C. The Sea Surface Salinity difference was about 8 psu in the plume area confined to the littoral, with maximum from August to December and 4 psu in the area of the North Equatorial Countercurrent (NECC). The surface current velocities are stronger in the experiment with river (mainly in the NECC area from September to December) and the strongest, close to the coast, in June to August. The experiment with river causes a phase shift in the zonal currents anticipating the strongest velocities in the second semester of the year in 2 months, changing the seasonal cycle. The Mixed Layer Depth and Isothermal Layer Depth (ILD) in the experiment with river is 20 - 50 m shallower over the entire extension of the Amazon plume. The freshwater river discharge perform a fundamental role in the formation of Barrier Layer. The Oceanic Heat Content in the river experiments is smaller than the experiment without rivers, principally as a result of the shifts of the ILD. The second objective focuses on analyzing the behavior of oil/gas plumes from blowouts into deepwater, located at the northern Brazil continental shelf. For this, the result of the hydrodynamics of ROMS model with release freshwater of the Amazon and Pará Rivers into the Atlantic is used. The simulations with the GAS_DOCEAN model were carried out in three points located at 50°W, 5.25°N, 44.5°W, 0.5°N and 42.75°W, 1°S. Previously, the vertical profiles of the temperature and the current speed in these points were validated comparing them with SODA. The time step was adjusted due to the particular oceanographic conditions at each point, in which, the initial velocity tends to zero and the coefficient 0.1 of the original equation was replaced by 0.0250 for 50°W, 5.25°N and 44.5°W, 0.5°N, and 0.0375 for 42.75°W, 1°S. All the plumes behaved as type 3. The seasonal current speed was small from the bottom to the surface, usually not exceeding 0.25 ms⁻¹; the maximum displacement of the plumes from its point of origin was not greater than 1 m. The mean plumes diameter on the surface varied between 54 and 79.7 m and the arrival time to the surface was from 7.25 to 8.05 hours.
**Keywords:** ROMS model. GAS_DOCEAN model. Amazon River plume. Oil/gas blowouts.
Brazil continental shelf.
RESUMO

Esta tese de doutorado tem como foco o estudo da hidrodinâmica e dos vazamentos de óleo/gás em águas profundas usando os modelos Regional Ocean Model System (ROMS) e GAS_DOCEAN. O primeiro objetivo foi analisar o impacto potencial dos rios Amazonas e Pará sobre a salinidade, temperatura e hidrodinâmica no Atlântico Norte Tropical Ocidental entre 60.5° – 24°W e 5°S – 16°N. O ROMS foi usado para simular a hidrodinâmica do oceano com resolução horizontal de 0.25° e 32 níveis verticais. A temperatura da superfície do mar, a salinidade da superfície do mar e a corrente superficial foram comparadas com os bancos de dados Simple Ocean Data Assimilation (SODA) e Surface Currents from Diagnostic. Os perfis verticais em 8°N, 38°W e 12°N, 38°W foram validados com dados das bóias do projeto Prediction Research Moored Array in the Tropical Atlantic. No modelo ROMS, foram realizados dois experimentos, primeiro considera a descarga de água doce dos rios Amazonas e Pará e o segundo, sem considerar o aporte de água doce no oceano Atlântico. Os resultados de ambas simulações foram comparados determinando as mudanças na temperatura, salinidade e correntes de superfície produzidas pela influência da descarga dos rios. A diferença entre as simulações com rios e sem rios na Temperatura da Superfície do Mar foi de cerca de 2°C, enquanto a diferença da Salinidade da Superfície do Mar foi de cerca de 8 psu na área da pluma confinada à costa, com valores máximos de Agosto a Dezembro e 4 psu na área da Contracorrente Norte Equatorial (NECC). As velocidades de corrente de superfície foram mais fortes no experimento com rios, principalmente na área NECC de Setembro a Dezembro e foram muito mais intensas perto da costa de Junho a Agosto. O experimento com rios provoca um deslocamento de fase nas correntes zonais, antecipando as velocidades mais fortes no segundo semestre do ano aproximidamente em dois meses, alterando o ciclo sazonal. A Profundidade da Camada de Mistura (MLD) e a Profundidade da Camada Isotérmica (ILD) no experimento com rios foram de 20 a 50 m mais rasas sobre toda a extensão da pluma amazônica. A descarga de água doce dos rios desempenha um papel fundamental na formação da Camada de Barreira. O conteúdo de calor oceânico no experimento com rios é menor do que o experimento sem rios, principalmente como resultado dos deslocamentos do ILD. O segundo objetivo concentrou-se na análise do comportamento das plumas produzidas pelos vazamentos de óleo/gás em águas profundas, localizadas na plataforma continental do norte do Brasil. Para isto, utilizou-se o resultado da hidrodinâmica do modelo ROMS com saída de água doce dos rios Amazonas e Pará no Atlântico. As simulações com o modelo GAS_DOCEAN foram realizadas em três pontos localizados em 50°W, 5.25°N, 44.5°W, 0.5°N e 42.75°W, 1°S. Anteriormente, os perfis verticais da temperatura e da velocidade da corrente nesses pontos foram validados comparando-os com SODA. O intervalo de tempo foi ajustado devido às condições oceanográficas particulares em cada ponto, o coeficiente 0.1 da equação original foi substituído por 0.0250 para 50°W, 5.25°N e 44.5°W, 0.5°N e 0.0375 para 42.75°W, 1°S. Todas as plumas comportaram-se como tipo 3. A velocidade de corrente sazonal foi pequena do fundo para a superfície, geralmente não excedendo 0.25 ms⁻¹; o deslocamento máximo das plumas de seu
ponto de origem não foi maior do que 1 m. O diâmetro médio das plumas na superfície variou de 54 a 79.7 m e o tempo de chegada à superfície foi de 7.25 a 8.05 horas.

**Palavras-chave:** Modelo ROMS. Modelo GAS_DOCEAN. Pluma do Rio Amazonas. Vazamentos de oléo e gâs. Plataforma continental do Brasil.
RESUMEN

Esta tesis de doctorado se enfoca en un estudio de la hidrodinámica y de los escapes de pe-
tróleo y gas en aguas profundas usando los modelos Regional Ocean Model System (ROMS)
y GAS_DOCEAN. El primer objetivo fue analizar el impacto potencial que ejercen los ríos
Amazonas y Pará sobre la salinidad, la temperatura y la hidrodinámica en el Atlántico Tropical
Noroccidental entre 60,5°-24°W y 5°S-16°N. El modelo ROMS fue usado para simular la hidro-
dinámica del océano con resolución horizontal de 0,25° y 32 niveles verticales. La temperatura
y la salinidad de la superficial del mar y la corriente superficial validadas comparándolas con
las bases de datos Simple Ocean Data Assimilation (SODA) y el modelo Surface Currents from
Diagnostic. Los perfiles verticales en 8°N, 38°W y 12°N, 38°W son validados com los datos de
las boyas del proyecto Prediction Research Moored Array in the Tropical Atlantic. En el modelo
ROMS fueron realizados dos experimentos, uno que tiene en cuenta la descarga de agua dulce
de los ríos en el océano Atlántico y otro que no considera la descarga de los ríos. Los resultados
de ambas simulaciones son comparadas determinando las variaciones en la temperatura, la
salinidad y las corrientes marinas producida por las descarga de los ríos. Las diferencias entre
las simulaciones con ríos y sin ríos en la temperatura de la superficie del mar fue cerca de 2°C,
mientras que la diferencia de la salinidad de la superficie del mar fue cerca de 8 *psu* en el área de
la pluma confinada a la costa, con valores máximos de Agosto a Diciembre y 4 *psu* en el área de
la Contracorriente Norte Ecuatorial norte (NECC). La corriente superficial es más fuerte cuando
están presentes los ríos, principalmente en el área de la NECC de Septiembre a Diciembre y son
más fuertes cerca de la costa de Junio a Agosto. El experimento con ríos provoca un desfase
en las corrientes zonales, anticipando las velocidades más grande en el segundo semestre del
año en 2 *meses*, alterando el ciclo estacional. La Profundidad de la Capa de Mezcla (MLD) y
la Profundidad de la Capa Isotérmica (ILD) en el experimento con ríos son de 20 a 50 m más
superficiales sobre toda la extensión de la pluma amazónica. La descarga de agua dulce de los
ríos desempeña un papel fundamental en la formación de la Capa de Barrera. El Contenido de
Calor Oceánico en el experimento con ríos es menor que en el experimento sin ríos, principal-
mente como resultado de los desplazamientos de la ILD. El segundo objetivo se concentra en
el análisis del comportamiento de las plumas producidas por los derrames de petróleo/gas en
aguas profundas, localizadas en la plataforma continental norte de Brasil. Para esto, se utilizaron
los resultados de la hidrodinámica del modelo ROMS con la salida de agua dulce de los ríos
Amazonas y Pará hacia el Atlántico. Las simulaciones con el modelo GAS_DOCEAN fueron
realizadas en tres puntos ubicados en 50°W, 5,25°N, 44,5°W, 0,5°N y 42,75°W, 1°S. Previamente
fueron validados los perfiles verticales de la temperatura y la velocidad de la corriente en esos
puntos, comparándolos con SODA. El intervalo de tiempo fue ajustado debido a las condiciones
oceanográficas particulares en cada punto, el coeficiente 0,1 de la ecuación original fue sustituido
por 0,0250 para 50°W, 5,25°N y 44,5°W, 0,5°N y por 0,0375 para 42,75°W, 1°S. El comporta-
miento de todas las plumas fue de tipo 3. La velocidad de la corriente estacional fue pequeña
desde el fondo hasta la superficie, generalmente no excedió de 0,25 $ms^{-1}$; el desplazamiento máximo de las plumas respecto a su origen no fue mayor que 1 m. El diámetro medio de las plumas en la superficie varió de 54 a 79,7 m e el tiempo de llegada a la superficie osciló de 7,25 a 8,05 horas.

**Palabras clave:** Modelo ROMS. Modelo GAS_DOCEAN. Pluma del Rio Amazonas, Derames de petróleo e gas. Plataforma continental de Brasil.
<table>
  <tbody>
    <tr>
      <td>Figure 15 – (a) Monthly distribution of discharge (m<sup>3</sup>s<sup>-1</sup>) of Amazon River (blue lines) and Pará River (black line), from Obidos and Tucuruí gauge stations. (b) Monthly distribution of temperature (°C) of Amazon River (blue line) and Pará River (black line).</td>
      <td>54</td>
    </tr>
    <tr>
      <td>Figure 16 – Working structure of the ROMS model.</td>
      <td>56</td>
    </tr>
    <tr>
      <td>Figure 17 – Theoretical-experimental scheme for displacement of oil and gas plumes used in simulations.</td>
      <td>63</td>
    </tr>
    <tr>
      <td>Figure 18 – Schematic of plume type classification: H<sub>T</sub> is trap height of the first peel and H is reservoir depth.</td>
      <td>67</td>
    </tr>
    <tr>
      <td>Figure 19 – The bathymetry and distribution of the slope in the continental shelf northwest of Brazil. The green rectangle represent the Amazon mouth basin and the magenta rectangle represent Pará-Maranhão-Barreirinhas basin. The oil and gas exploration blocks are represented by black polygons. The location of P1, P2 and P3 is represented by blue points above of exploration blocks where P1, P2 and P3 are placed, block FZA-M-88 (P1), block PAMA-M-337 (P2) and block BAR-M-21 (P3). The coral reef appears in red color.</td>
      <td>68</td>
    </tr>
    <tr>
      <td>Figure 20 – Mean monthly cycle of the difference between SSS (psu) of RRF experiment and SODA dataset.</td>
      <td>72</td>
    </tr>
    <tr>
      <td>Figure 21 – Mean monthly cycle of the difference between SST (°C) of RRF experiment and SODA dataset.</td>
      <td>74</td>
    </tr>
    <tr>
      <td>Figure 22 – Hovmüller diagram of RRF (red dashed lines) and PIRATA buoy (blue solid lines), monthly mean calculated from 2000 to 2015 at 38°W8°N (a) salinity vertical profile (psu) and (b) temperature vertical profile (°C) and at 38°W12°N (c) salinity vertical profile (psu) and (d) temperature vertical profile (°C).</td>
      <td>75</td>
    </tr>
    <tr>
      <td>Figure 23 – Hovmüller diagram of the zonal component in REG2 (a) RRF experiment, (b) SCUD dataset</td>
      <td>76</td>
    </tr>
    <tr>
      <td>Figure 24 – Monthly mean differences between the vertical profile of (a) zonal (m s<sup>-1</sup>) and (b) meridional components (m s<sup>-1</sup>) at 38°W, 8°N, the vertical profile of (c) zonal (m s<sup>-1</sup>) and (d) meridional components (m s<sup>-1</sup>) at 38°W, 12°N.</td>
      <td>77</td>
    </tr>
    <tr>
      <td>Figure 25 – Mean seasonal cycle of difference of SSS between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November).</td>
      <td>78</td>
    </tr>
    <tr>
      <td>Figure 26 – Mean seasonal cycle of difference of SST between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November).</td>
      <td>79</td>
    </tr>
  </tbody>
</table>
Figure 27 – Mean seasonal cycle of difference of surface currents between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November). 80

Figure 28 – Comparison of zonal component between RRF and NRF simulations in REG1, area defined in figure 12. The black arrow represents the phase shift of the zonal component of the current. 81

Figure 29 – Mean seasonal cycle of difference in MLD (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November). 82

Figure 30 – Mean seasonal cycle of difference in ILD (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November). 83

Figure 31 – Mean seasonal cycle of difference in BLT (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November). The nodes of the grid where the thickness of the layer is less than 10% of the maximum depth (ILD or MLD) are shown with value 0 and in white color. 84

Figure 32 – Mean seasonal cycle of difference in OHC(J m⁻²) integrated from Z<sub>REF</sub> to ILD. Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November). 85

Figure 33 – (a) Temperature and (b) current speed vertical profiles in DJF (December- January-February) and JJA (June-July-August) periods for SODA and ROMS at point P1. 87

Figure 34 – ROMS output of mean seasonal cycle of the currents measured (a) between the surface and 100 m depth; and (b) between 1000 and 1200 m depth during the winter (DJF-December, January, February), spring (MAM-March, April, May), summer (JJA-June, July, August), and fall (SON-September, October, November). The centers of the red circle represent the positions of the simulation points P1, P2 and P3. 88
Figure 35 – Oil/gas plumes evolution in the middle of each month (simulation day 15) at P1. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south. 90

Figure 36 – Oil/gas plumes evolution in the middle of each month (simulation day 15) at P2. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south. 92

Figure 37 – Oil/gas plumes evolution in the middle of each month (simulation day 15) at P3. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south. 93

Figure 38 – Vertical profiles of the current speed (a) at P1 (March) and P3 (November) and (b) at P1 (September) and P3 (May and July). 94

Figure 39 – Outline of the logical sequence of oceanic processes due to the effect of the Amazon and Pará rivers in WTNA 98
LIST OF TABLES

<table><tr><td>Table 1</td><td>U<sub>N</sub> intervals for plume classification</td><td>67</td></tr><tr><td>Table 2</td><td>Parameterization of GAS_DOCEAN</td><td>67</td></tr><tr><td>Table 3</td><td>Comparison between the SSS RRF and SODA in REG2, area defined in figure 12. In the first rows mean value ± standard deviation and in the second rows minimum – maximum.</td><td>73</td></tr><tr><td>Table 4</td><td>Monthly radius and displacement of oil/gas plumes at points P1, P2 and P3</td><td>91</td></tr></table>
List of abbreviations and acronyms

<table><tr><td>ADM</td><td>Advection-diffusion model</td></tr><tr><td>AGRIF</td><td>Adaptive Grid Refinement in Fortran</td></tr><tr><td>AM</td><td>Adjoint Model</td></tr><tr><td>AMIP</td><td>Atmospheric Model Intercomparison Project</td></tr><tr><td>APDRC/IPRC</td><td>Asia Pacific Data Research Center/International Pacific Research Center.</td></tr><tr><td>AVHRR</td><td>Advanced Very High Resolution Radiometer</td></tr><tr><td>AVISO</td><td>Archiving Validation and Interpretation of Satellite Data in Oceanography.</td></tr><tr><td>BC</td><td>Brazil Current</td></tr><tr><td>BL</td><td>Barrier Layer</td></tr><tr><td>BLT</td><td>Barrier Layer Thickness</td></tr><tr><td>CALTECH</td><td>California Institute of Technology (CIT)</td></tr><tr><td>CFL</td><td>Courant - Friedrichs - Lewy</td></tr><tr><td>CNRS</td><td>Centre National de la Recherche Scientifique.</td></tr><tr><td>COADS</td><td>Comprehensive Ocean-Atmosphere Data Set</td></tr><tr><td>CONAE</td><td>Comisión Nacional de Actividades Espaciales. Argentina</td></tr><tr><td>DHN</td><td>Diretoria de Hidrografia e Navegação.</td></tr><tr><td>DOE</td><td>U. S. Department of Energy</td></tr><tr><td>ECMWF</td><td>European Centre for Medium-Range Weather Forecasts</td></tr><tr><td>ESA</td><td>European Space Agency</td></tr><tr><td>ESMF</td><td>Earth System Modeling Framework</td></tr><tr><td>GD</td><td>Gabinete do Diretor</td></tr></table>
<table>
   <tr>
    <td>GEBCO</td>
    <td>General Bathymetric Charts of the Oceans</td>
   </tr>
   <tr>
    <td>GES DISC</td>
    <td>Goddard Earth Sciences Data Information Services Center</td>
   </tr>
   <tr>
    <td>GPCC</td>
    <td>Global Precipitation Climatology Centre</td>
   </tr>
   <tr>
    <td>GST</td>
    <td>Generalized Stability Theory</td>
   </tr>
   <tr>
    <td>IFREMER</td>
    <td>Institut Français de Recherche pour L'exploitation de la Mer.</td>
   </tr>
   <tr>
    <td>IHO</td>
    <td>International Hydrographic Organization</td>
   </tr>
   <tr>
    <td>ILD</td>
    <td>Isothermal Layer Depth</td>
   </tr>
   <tr>
    <td>IOM</td>
    <td>Inverse Ocean Modeling</td>
   </tr>
   <tr>
    <td>INPE</td>
    <td>Instituto Nacional de Pesquisas Espaciais</td>
   </tr>
   <tr>
    <td>IPRC</td>
    <td>International Pacific Research Center</td>
   </tr>
   <tr>
    <td>IRD</td>
    <td>Institut de Recherche pour le Développement</td>
   </tr>
   <tr>
    <td>JPL</td>
    <td>Jet Propulsion Laboratory</td>
   </tr>
   <tr>
    <td>KPP</td>
    <td>K - Profile Parameterization</td>
   </tr>
   <tr>
    <td>MIRAS</td>
    <td>Microwave Imaging Radiometer using Aperture Synthesis</td>
   </tr>
   <tr>
    <td>MLD</td>
    <td>Mixed Layer Depth</td>
   </tr>
   <tr>
    <td>NASA</td>
    <td>National Aeronautics and Space Administration</td>
   </tr>
   <tr>
    <td>NBC</td>
    <td>North Brazil Current</td>
   </tr>
   <tr>
    <td>NCAR</td>
    <td>National Center for Atmospheric Research</td>
   </tr>
   <tr>
    <td>NCEI (formally NGDC)</td>
    <td>National Centers for Enviromental Information</td>
   </tr>
   <tr>
    <td>NCEP</td>
    <td>National Centers for Environmental Prediction</td>
   </tr>
   <tr>
    <td>NEC</td>
    <td>North Equatorial Current</td>
   </tr>
   <tr>
    <td>NECC</td>
    <td>North Equatorial Counter Current</td>
   </tr>
   <tr>
    <td>NERSC</td>
    <td>Nansen Environmental and Remote Sensing Center</td>
   </tr>
   <tr>
    <td>NESDIS</td>
    <td>National Environmental Satellite, Data and Information Service</td>
   </tr>
   <tr>
    <td>NGDC</td>
    <td>National Geophysical Data Center</td>
   </tr>
   <tr>
    <td>NLM</td>
    <td>Non-Linear model</td>
   </tr>
  </table>
<table>
   <tr>
    <td>NOAA</td>
    <td>National Oceanic and Atmospheric Administration</td>
   </tr>
   <tr>
    <td>OHC</td>
    <td>Oceanic Heat Content</td>
   </tr>
   <tr>
    <td>OI</td>
    <td>Optimum Interpolation</td>
   </tr>
   <tr>
    <td>OML</td>
    <td>Oceanic Mixed Layer</td>
   </tr>
   <tr>
    <td>OSCAR</td>
    <td>Ocean Surface Analyses - Real time</td>
   </tr>
   <tr>
    <td>PDM</td>
    <td>Plume dynamics model</td>
   </tr>
   <tr>
    <td>PIRATA</td>
    <td>Prediction Research Moored Array in the Tropical Atlantic.</td>
   </tr>
   <tr>
    <td>PO.DAAC</td>
    <td>Physical Oceanography Distributed Active Archive Center</td>
   </tr>
   <tr>
    <td>QuikSCAT</td>
    <td>Quick Scatterometer.</td>
   </tr>
   <tr>
    <td>ROMS</td>
    <td>Regional Ocean Modeling System</td>
   </tr>
   <tr>
    <td>RPM</td>
    <td>RePresenter tangent linear Model</td>
   </tr>
   <tr>
    <td>SCRUM</td>
    <td>S-Coordinate Rutgers University Model</td>
   </tr>
   <tr>
    <td>SCUD</td>
    <td>Surface CCurrents from Diagnostic model</td>
   </tr>
   <tr>
    <td>SEC</td>
    <td>South Equatorial Current</td>
   </tr>
   <tr>
    <td>SID</td>
    <td>Serviço de Informação e Documentação</td>
   </tr>
   <tr>
    <td>SMOS</td>
    <td>Soil Moisture and Ocean Salinity</td>
   </tr>
   <tr>
    <td>SODA</td>
    <td>Simple Ocean Data Assimilation</td>
   </tr>
   <tr>
    <td>SSH</td>
    <td>Sea Surface Height</td>
   </tr>
   <tr>
    <td>SSS</td>
    <td>Sea Surface Salinity</td>
   </tr>
   <tr>
    <td>SST</td>
    <td>Sea Surface Temperature</td>
   </tr>
   <tr>
    <td>TLM</td>
    <td>Tangent Linear Model</td>
   </tr>
   <tr>
    <td>UCLA</td>
    <td>University of California, Los Angeles</td>
   </tr>
   <tr>
    <td>WOA</td>
    <td>World Ocean Atlas</td>
   </tr>
   <tr>
    <td>WTNA</td>
    <td>Western Tropical North Atlantic</td>
   </tr>
  </table>
List of symbols

u, v, w Components of the velocity vector v.

$T(u, v, w, t)$ Potential temperature.

$S(u, v, w, t)$ Total salinity.

$\rho_o + \rho(x, y, z, t)$ Total Density.

$\phi(x, y, z, t)$ Dynamic pressure.

$P$ Total pressure.

$f$ Parameter of Coriolis.

$g$ Gravity acceleration.

$K_M(x, y, z, t)$ Eddy Vertical Viscosity.

$K_H(x, y, z, t)$ Eddy vertical diffusivity.

$D_u, D_v, D_T, D_S$ Terms of viscosity and horizontal diffusivity.

$F_u, F_v, F_T, F_S$ Forcing terms.

$t$ Time.

$h(x, y)$ Depth.

$\zeta(x, y, t)$ Surface elevation.

$\tau_s^x, \tau_s^y$ Surface wind force.

$\tau_b^x, \tau_b^y$ Bottom Forcing.

$E$ Evaporation.

$P_r$ Precipitation.

$Q_T$ Surface heat flow.

$T_{ref}$ Surface reference temperature.
$\gamma_1$ Linear forcing coefficients of the bottom.

$\gamma_2$ Quadratic coefficients of the bottom forcing.

$Q_T$ Strong surface temperature function.

$F_c$ Compressibility factor

$P$ Ambient pressure

$V$ Gas volume

$n$ Number of gas moles

$R = 8.314 \text{ Pa} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$ Universal gas constant

$T$ Ambient temperature

$h_s$ Phase separation height

$d$ particle diameter

$d_c$ critical diameter

$\nu$ Viscosity of seawater

$\rho_d$ Density of the drop

$\rho_w$ Seawater density

$h$ Depth of control volume

$V$ Total velocity

$\Delta t$ Time step

$b_0$ Ratio of initial control-volume

$V_0$ Initial blowout velocity

$M_0$ Momentum excess in the control-volume (gas + oil)

$U_0$ Velocity of the mixture oil + gas

$U_A$ Velocity of the currents in the ocean

$n$ Number of moles of consumed gas

$K^*$ Rate of diffusion + absorption of the gas

$A_P$ Surface area of the particle
<table>
   <tr>
    <td>f</td>
    <td>Dissolved gas fugacity</td>
   </tr>
   <tr>
    <td>f<sub>EQ</sub></td>
    <td>Three-phase equilibrium fugacity of the gas</td>
   </tr>
   <tr>
    <td>K</td>
    <td>Coefficient of mass transfer</td>
   </tr>
   <tr>
    <td>A</td>
    <td>Surface area of the gas normal to flow direction</td>
   </tr>
   <tr>
    <td>C<sub>S</sub></td>
    <td>Dissolved saturation gas concentration inside the control-volume</td>
   </tr>
   <tr>
    <td>C<sub>0</sub></td>
    <td>Dissolved gas concentration inside the control-volume</td>
   </tr>
   <tr>
    <td>m<sub>l</sub></td>
    <td>Mass of liquid of plume</td>
   </tr>
   <tr>
    <td>m<sub>b</sub></td>
    <td>Mass of gas of plume</td>
   </tr>
   <tr>
    <td>m<sub>h</sub></td>
    <td>Mass of hydrates inside the plume</td>
   </tr>
   <tr>
    <td>u</td>
    <td>Horizontal velocity of plume at x direction</td>
   </tr>
   <tr>
    <td>u<sub>a</sub></td>
    <td>Ambient horizontal velocity of plume at x direction</td>
   </tr>
   <tr>
    <td>v</td>
    <td>Horizontal velocity of plume at y direction</td>
   </tr>
   <tr>
    <td>v<sub>a</sub></td>
    <td>Ambient horizontal velocity of plume at y direction</td>
   </tr>
   <tr>
    <td>w</td>
    <td>Vertical velocity of plume</td>
   </tr>
   <tr>
    <td>w<sub>a</sub></td>
    <td>Ambient vertical velocity</td>
   </tr>
   <tr>
    <td>w<sub>b</sub></td>
    <td>Gas bubbles velocity</td>
   </tr>
   <tr>
    <td>ρ<sub>l</sub></td>
    <td>Liquid density of plume</td>
   </tr>
   <tr>
    <td>ρ<sub>a</sub></td>
    <td>Density of ambient seawater</td>
   </tr>
   <tr>
    <td>ρ<sub>com</sub></td>
    <td>Density of hydrates and gas</td>
   </tr>
   <tr>
    <td>Q<sub>e</sub></td>
    <td>Entrainment water flux</td>
   </tr>
   <tr>
    <td>Q<sub>g</sub></td>
    <td>Gás flux</td>
   </tr>
   <tr>
    <td>g</td>
    <td>Acceleration of gravity</td>
   </tr>
   <tr>
    <td>b</td>
    <td>Plume ratio</td>
   </tr>
   <tr>
    <td>ε</td>
    <td>Gas fraction</td>
   </tr>
   <tr>
    <td>β</td>
    <td>Ratio between the bubble core width and the buoyant jet diameter</td>
   </tr>
   <tr>
    <td>h</td>
    <td>Depth of control volume</td>
   </tr>
  </table>
<table><tr><td>P</td><td>Ambient pressure</td></tr><tr><td>M<sub>g</sub></td><td>Gas mol weight</td></tr><tr><td>ρ<sub>b</sub></td><td>Gas density</td></tr><tr><td>T</td><td>Temperature</td></tr><tr><td>B</td><td>Buoyancy of gas plume</td></tr><tr><td>N<sub>BV</sub></td><td>Brunt-Vaisala frequency</td></tr><tr><td>Q<sub>B</sub></td><td>Gas flux</td></tr><tr><td>U<sub>N</sub></td><td>Nondimensional velocity</td></tr><tr><td>U<sub>S</sub></td><td>Bubble slip velocity</td></tr><tr><td>H<sub>A</sub></td><td>Atmospheric pressure head</td></tr><tr><td>H</td><td>Local depth</td></tr><tr><td>Z<sub>REF</sub></td><td>Reference depth in the temperature and salinity vertical profiles, It is used for the computation of MLD, ILD and OHC.</td></tr></table>
CONTENTS

<table><tr><td>1</td><td>INTRODUCTION</td><td>27</td></tr><tr><td>1.1</td><td>OBJECTIVE</td><td>30</td></tr><tr><td>2</td><td>THEORETICAL ASPECTS ON DEEPWATER OIL/GAS BLOWOUTS</td><td>32</td></tr><tr><td>2.1</td><td>OIL/GAS PLUME EVOLUTION</td><td>38</td></tr><tr><td>2.2</td><td>HYDRATE FORMATION</td><td>41</td></tr><tr><td>2.3</td><td>RELATIONSHIP OF KINETICS OF HYDRATE FORMATION WITH MASS AND HEAT TRANSFER</td><td>42</td></tr><tr><td>2.4</td><td>NON IDEAL GAS BEHAVIOR IN DEEP WATER</td><td>43</td></tr><tr><td>2.5</td><td>PHASE SEPARATION</td><td>45</td></tr><tr><td>2.6</td><td>SOLUBILITY</td><td>46</td></tr><tr><td>2.7</td><td>LIFTING SPEED OF OIL PARTICLES</td><td>47</td></tr><tr><td>3</td><td>DATA AND METHODOLOGY</td><td>49</td></tr><tr><td>3.1</td><td>STUDY AREA</td><td>49</td></tr><tr><td>3.2</td><td>OBSERVATIONAL DATA</td><td>51</td></tr><tr><td>3.2.1</td><td>World Ocean Atlas (WOA)</td><td>51</td></tr><tr><td>3.2.2</td><td>Comprehensive Ocean-Atmosphere Data Set (COADS)</td><td>51</td></tr><tr><td>3.2.3</td><td>Simple Ocean Data Assimilation (SODA)</td><td>51</td></tr><tr><td>3.2.4</td><td>Prediction and Research Moored Array in the Tropical Atlantic (PIRATA)</td><td>53</td></tr><tr><td>3.2.5</td><td>Bathymetry</td><td>53</td></tr><tr><td>3.2.6</td><td>Tide TPXO7</td><td>53</td></tr><tr><td>3.2.7</td><td>Freshwater river runoff. Dai and Trenberth Global River Flow and Continental Discharge Dataset</td><td>54</td></tr><tr><td>3.3</td><td>SURFACE CURRENTS FROM DIAGNOSTIC MODEL (SCUD)</td><td>54</td></tr><tr><td>3.4</td><td>NUMERICAL SIMULATION TOOLS</td><td>55</td></tr><tr><td>3.4.1</td><td>ROMS model</td><td>55</td></tr><tr><td>3.4.1.1</td><td>Basic equations of the ROMS AGRIF model</td><td>55</td></tr><tr><td>3.4.1.2</td><td>Horizontal boundary conditions</td><td>58</td></tr><tr><td>3.4.1.3</td><td>Vertical boundary conditions</td><td>58</td></tr><tr><td>3.4.1.4</td><td>Vertical coordinates</td><td>60</td></tr><tr><td>3.4.1.5</td><td>Spatial and temporal discretization</td><td>60</td></tr><tr><td>3.4.1.6</td><td>Pre and post-processing of data</td><td>60</td></tr><tr><td>3.4.1.7</td><td>Lateral boundary and initial conditions</td><td>60</td></tr><tr><td>3.4.1.8</td><td>Experiment configuration</td><td>61</td></tr><tr><td>3.4.2</td><td>GAS_DOCEAN model</td><td>61</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>3.4.2.1</td>
      <td>Basic equations of the GAS_DOCEAN model</td>
      <td>62</td>
    </tr>
    <tr>
      <td>3.4.2.2</td>
      <td>Parameterization of GAS_DOCEAN model</td>
      <td>67</td>
    </tr>
    <tr>
      <td>3.5</td>
      <td>MIXED LAYER DEPTH (MLD), ISOTHERMAL LAYER DEPTH (ILD) AND BARRIER LAYER THICKNESS (BLT) CRITERION</td>
      <td>69</td>
    </tr>
    <tr>
      <td>3.6</td>
      <td>OCEANIC HEAT CONTENT (OHC) CRITERION</td>
      <td>69</td>
    </tr>
    <tr>
      <td>4</td>
      <td>HYDRODYNAMIC MODEL: RESULTS AND DISCUSSIONS</td>
      <td>71</td>
    </tr>
    <tr>
      <td>4.1</td>
      <td>VALIDATION OF THE HYDRODYNAMIC MODEL</td>
      <td>71</td>
    </tr>
    <tr>
      <td>4.2</td>
      <td>INFLUENCES OF THE AMAZON AND PARÁ RIVERS ON HYDRODYNAMICS</td>
      <td>78</td>
    </tr>
    <tr>
      <td>5</td>
      <td>DEEPWATER OIL/GAS BLOWOUTS SIMULATIONS: RESULTS AND DISCUSSIONS</td>
      <td>86</td>
    </tr>
    <tr>
      <td>5.1</td>
      <td>OIL AND GAS PLUMES EVOLUTION</td>
      <td>89</td>
    </tr>
    <tr>
      <td>6</td>
      <td>CONCLUSIONS</td>
      <td>96</td>
    </tr>
    <tr>
      <td></td>
      <td>REFERENCES</td>
      <td>99</td>
    </tr>
    <tr>
      <td></td>
      <td>APPENDIX A PAPER "INFLUENCE OF UNDERWATER HYDRODYNAMICS ON OIL AND GAS BLOWOUTS OFF AMAZON RIVER MOUTH"</td>
      <td>113</td>
    </tr>
    <tr>
      <td></td>
      <td>ANNEX A PAPER "AMAZON RIVER PLUME INFLUENCE IN THE WESTERN TROPICAL ATLANTIC DYNAMIC VARIABILITY"</td>
      <td>14</td>
    </tr>
  </tbody>
</table>
# 1 INTRODUCTION

In recent decades, oil spills have occurred throughout the world and marine flora and fauna have been a frequent source of environmental impacts caused by these events (TEAL; HOWARTH, 1984). Contamination of marine and coastal environments by oil has been a concern for environmentalists around the world and has been the subject of much debate. This type of impact causes real environmental catastrophes, with incalculable and often irreversible damage to the environment. Human activities such as fishing and the recreational use of the environment are also compromised, causing great economic damages (GARZA-GIL; PRADA-BLANCO; VÁZQUEZ-RODRÍGUEZ, 2006).

From 1978 to 2010, the 12 major disasters occurred due to oil spills, of which only one was in an oil field on land, the rest occurred in marine environments, 9 of them were due to tanker or carrier accidents and 2 in oil rig marine exploration, shedding approximately 3901000 tonnes of oil into the sea (Figure 1).

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Map of the world's largest oil spills (from 1978 to 2010). Only Fergana Valley oil spill was terrestrial.</figcaption></figure>

Source: http://www.cbc.ca/news/multimedia/map-12-of-the-worst-oil-spills-1.3037952

The Ixtoc I oil spill involving an oil exploration well drilled by the Mexico's government-owned oil company (Pemex) offshore before an explosion occurred, causing oil to ignite and the drilling rig collapsed. From 10,000 to 30,000 barrels of oil per day went out of the well in the
Bay of Campeche, Gulf of Mexico for almost a whole year. The platform was located about 60 km northwest of Ciudad del Carmen (Bahia de Campeche) in the water (JERNELÖV; LINDÉN, 1981), about 48 m depth. The spill occurred when the drilling rig lost mud circulation and the pressure reduction in the tank caused an explosion, the oil caught fire and the platform collapsed into the ocean. The estimated amount of oil spilled was 476000 tonnes (JERNELÖV; LINDÉN, 1981).

The British Petroleum (BP) Deepwater Horizon oil spill occurred on April 20, 2010 in the Gulf of Mexico. It began when an explosion destroyed the Deepwater Horizon drilling rig, causing a pressurized oil flow near the wellhead at more than 1524 m depth. Many attempts were made to stop the oil leak, but alone they were partially successful, managing to sell the well on July 15, 2010. Oil gushed from the broken well for more than 85 days, spanning about 920 km of the Gulf Coast and killed hundreds of birds and several marine species (SMITH; SMITH; ASHCROFT, 2011). The estimated amount of oil spilled was 492000 tonnes ea (Figure 1).

Oil residues and by-products can have serious consequences for human life, coastal ecosystems and socioeconomic activities. In recent decades, there has been a progressive decrease in the number of accidents and in the volume of oil discharged internationally (ITOPF, 2016). The reduction of accidents is associated with greater control and care in operations involving the exploration, exploitation, transport and oil storage, which reflects an increase in the level of environmental responsibility of society (KIRBY; LAW, 2010; ETKIN, 1999).

Environmental sensitivity to oil spills has been studied some decades ago by Gundlach & Hayes (1978), sensitivity maps contain three types of spatial information: the classification of the sensitivity of environments, biological resources and recreational human resources, subsistence or commercial value. The classification of the environment is made according to its physical characteristics, oil permanence and conditions of cleaning and removal.

The Environmental Sensitivity Charts to Oil Spills, are essential tools and a primary source of information for contingency planning and for the implementation of response actions to oil pollution incidents, allowing the identification of environments with protection priority and possible areas of sacrifice, allowing the correct allocation of resources And the proper mobilization of containment and cleaning equipment (MICHEL; HAYES; BROWN, 1978; CARVALHO; GHERARDI, 2003).

The exploration and production of oil at sea is a risk-filled activity. It requires dangerous tasks such as drilling rocks in ultra-deep regions, facing very high pressures and handling large volumes of oil and gas. It analyzes the large volume of information generated in the initial stages of the investigation, gathering a reasonable knowledge about the depth, thickness and variation of existing rock layers in a sedimentary basin and the hydrodynamics of the region. Based on this knowledge, the best places to drill in the basin are chosen. Research for the exploration and production of oil at sea is considered a high risk activity (JAHN; COOK; GRAHAM, 2008).
The impact of an oil spills and blowout can be minimized if locations most sensitive to contact with the oil can be protected. Knowing previously the variations of spills and explosions of oil help in the distribution of available resources to give a more effective response to these types of accidents.

On the other hand, the dependence of industry and life with the use of oil and gas is very significantly, the demand for these two products and their derivatives is extremely high. Large oil and gas extraction corporations are increasingly expanding into new areas, exploring and exploiting more and more natural gas and oil reserves in the deep ocean. These explorations and exploitation processes are subjects to risk of accidents, which can endanger human life and contaminate the ocean and the coastal line. The understanding of oceanographic processes in the oil and gas blowouts is fundamental for its prevention and mitigation. In case of oil and gas blowouts, companies would have contingency planning and mitigation to reduce the impact on the environment (KIRBY; LAW, 2010).

With the discovery of the pre-salt (Figure 2), the exploration and exploitation of oil in the open sea boosts Brazil’s economy by increasing the good prospects of development for the Brazilian coastal states (RODRIGUES; SAUER, 2015). Consequently, also increase the risk of accidents that can produce a threat to the biological resources and socioeconomic development. When a leak occurs in the ocean, oil has a high potential for contamination and the damage it produces in the environment generally has disastrous dimensions, the severity of an accident is closely linked to factors that can make it more drastic, among them, meteorological and oceanic conditions (surface currents, wind, sea surface temperature, etc.), river runoff, seasonal period, area’s vulnerability, petroleum type and volume, response time, etc. In order to respond to an oil spill or oil/gas blowout, one must be prepared and planned enough time to minimize the impact of leakage taking into account all possible conditions (LIMA, Novembro, 2008).
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Schematic representation of the seabed layers: Pre-salt, salt and post-salt layers.</figcaption></figure>

**Source:** https://innovationhouserio.wordpress.com/2013/09/27/pre-salt-bidders-defined-12th-rounds-details-published/

Therefore, this research contributes to analyze and quantify the risk situations arising from possible oil spills or oil/gas blowouts on the northern continental shelf of Brazil, taking into account the hydrodynamics in the region of study and the flows of the Amazon and Pará Rivers. This type of analysis is essential to reduce the environmental consequences of an oil spill or blowout, to make efficient the containment and cleaning/removal efforts of accidents, simulating both the hydrodynamics of ocean currents forced by the atmosphere and the transport of the hydrocarbon plume as support for contingency plans.

## 1.1 OBJECTIVE

The main objective of this research is to analyze the variation of hydrocarbon plumes in deepwater oil/gas blowouts on the northern Brazil continental shelf. To get this result specific aims were realized:

* Simulation and verification of a hydrodynamic numerical model in the Western Tropical North Atlantic by comparing numerical data with SODA, PIRATA and SCUD datasets.

* Determine the variability in the marine currents, temperature, salinity, mixed layer depth, isothermal layer depth, formation of barrier layer and oceanic heat content due to the presence of the Amazon and Pará Rivers.
* Execute the GAS_DOCEAN numerical model to characterize the evolution of hydrocarbon plumes in deepwater oil/gas blowouts.
## 2 THEORETICAL ASPECTS ON DEEPWATER OIL/GAS BLOWOUTS

The circulation in the Western Tropical North Atlantic (WTNA) ocean perform an important role in the interhemispheric transport of mass, heat, and salt and in the thermohaline overturning cell (Schmitz Jr.; MCCARTNEY, 1993; BOURLES et al., 1999; VELEDA et al., 2012). Furthermore, a strong western boundary current, the North Brazil Current (NBC) is the main conduit for cross-equatorial transport of South Atlantic upper-ocean waters, as part of the Atlantic meridional overturning cell (JOHNS et al., 1998). This current flows northwestward, intercepting the Amazon and Pará Rivers freshwater discharges along the Brazilian north coast.

The Amazon River plume enters the WTNA near the equator and is carried northwestward along the Brazilian Shelf by the NBC (SALISBURY et al., 2011; Müller-Karger; MCCLAIN; RICHARDSON, 1988).

The Amazon River is the main source of freshwater in the world, with a discharge that ranges between 200000 $m^3 s^{-1}$ and 2 240000 $m^3 s^{-1}$ (RICHEY; NOBRE; DESER, 1989; MOLINIER et al., 1996; SALISBURY et al., 2011), depositing almost 20% of the global discharge of rivers into the continental shelf of the equatorial Atlantic Ocean (GOULDING; BARTHEM; FERREIRA, 2003; BARTHEM et al., 2004). The plume of Amazon River extends thousands of kilometers over the North Atlantic Ocean arriving to Caribbean Sea (Müller-Karger et al., 1989; Johns, W. E. et al., 1990).

The magnitude of Amazon freshwater source is unique in the global oceans. Typically, river discharge is a small component of the open ocean salinity balance, but the Amazon discharge volume is twice the evaporation minus precipitation budget (FERRY; REVERDIN, 2004). The influence of Amazon water is felt far from the river mouth through enhancement of surface stratification leading to the formation of barrier layers (FFIELD, 2007; COLES et al., 2013; GRODSKY et al., 2014). Thus, the Amazon River Plume is thought to contribute to the dynamics of ocean atmosphere interaction and climate in WTNA.

In addition to the physical climate impacts of the Amazon River on the region, the river also injects terrestrially derived sediments, nutrients, and colored as well as transparent dissolved organic matter, which can be traced thousands of kilometers from the Amazon River mouth (HU et al., 2004). Biological community structure is strongly influenced by these dissolved organic matter and nutrient inputs as well as by the plume's role in stratifying the upper ocean (STUKEL et al., 2014), leading to globally significant uptake of atmospheric carbon dioxide in the river
plume (COOLEY et al., 2007; SUBRAMANIAM et al., 2008).

Several recent studies have used observed data, satellite products, general circulation models (OGCMs) and regional models to explain the spatial and temporal variability of the Amazon plume and its interaction with the NBC rings (FRATANTONI; GLICKSON, 2002; FFIELD, 2007; KOROSOV; COUNILLON; JOHANNESSEN, 2015). Schmidt et al. (2011) implemented an operational forecasting system using a high resolution model to resolve the migration rate of the NBC rings in a short time scale. Recent studies link the intensification of hurricanes to the spreading of freshwater discharge due to the impact of haline stratification on reduction of vertical heat flux (BALAGURU et al., 2012; GRODSKY et al., 2012; NEWINGER; TOUMI, 2015) and the periodic movement of the NBC rings (FFIELD, 2007).

The WTNA is an area with intense river-sea-land interaction, characterized by complex material transport, mixed layer depth changes (GRODSKY et al., 2012; COLES et al., 2013) and biogeochemical processes (LEFÈVRE; DIVERRÈS; GALLOIS, 2010; IBÁNHEZ; FLORES; LEFÈVRE, 2017). In this context, the Amazon and Pará Rivers are the main continental forcing to the adjacent coastal waters, giving rise to alterations in local and remote physical and biogeochemical processes. However, more studies are necessary to quantify the role of the Amazon and Pará River plumes on the dynamic of this region. Thus, to better understand the role of the plume rivers in the WTNA is crucial to quantify how much it impacts on the dynamics of this region.

The first efforts of Fannelop & Sjoen (1980) focused on the case of the evolution of a single gas plume in the ocean. These authors proposed a simplified analytical modeling approach, with nondimensional solutions, and applicable in cases of spills in shallow waters. In this first model, the gas expansion all through the water column was estimated considering the classical theory of ideal gas. As a result, the solution for this model brings the dimensions of the cone of gas formed along the water column (starting from the ocean floor), and in consequence, the diameter of the gas plume in the surface. Meanwhile, the Fannelop & Sjoen (1980) approach does not consider horizontal advection of gas through the currents. Some advance on this first idea was proposed by Friedl & Fanneløp (2000), when routines were added that considered the elevation in the surface of the sea provoked by the reaching of the gas to the surface (fountain effect, Figure 3).
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Standard framework and notation adopted in GAS_DOCEAN model.</figcaption></figure>

Source: Friedl & Fanneløp (2000)

The increase of the oil and gas production in marine environment verified above all in the mid-year 2000 (E&P Forum/UNEP, 1997; U. S. DOE, 1999; U. S. EIA, 1998; U. S. NOIA., 2005) brought the need of more precise models for evaluation of the transport and dispersion of these mixtures in the oceans, as well as their effects on the environment. In deeper waters, for instance, the gas cannot be treated as an ideal mixture (CHEN; YAPA, 2001), and new interaction processes were observed between the two media (gas and liquid), mainly when the local pressure is very different from the atmospheric pressure. In this new generation of mathematical models, created to represent simultaneously oil and gas plumes in marine environment, two more important physicochemical processes were considered. It is the gas (TOPHAM, 1984a; CHEN; YAPA, 2001) and gas dissolution (JOHANSEN, 2003; ZHENG; YAPA, 2002) in sea.

In shallow waters, the gas dissolution is neglectable (JOHANSEN, 2000). However, in deep waters, the travel time for the gas through the water column is longer, also rising the dysphasic flow time. Adding to this the fact that the gas solubility increases with the environmental pressure (JOHANSEN, 2000), it is observed frequently that under natural conditions of low temperature and high pressure, the gas tends to form hydrates, which significantly change the ascension velocity of the gaseous plume along the water column (TOPHAM, 1984a; CHEN; YAPA, 2001; JOHANSEN, 2003).
The first models of evolution of a plume of gas developed did not foresee in their equations these two mechanisms (dissolution and hydration), limiting itself to its application in deeper ocean areas (CHEN; YAPA, 2001). Yapa & Zheng (1997), for instance, proposed a set of equations to predict the space-time evolution of plumes formed by spills in intermediate waters, considering only the advective transport of the gas as function of its characteristics (volumetric composition) and the environmental thermodynamic conditions (temperature fields, salinity, pressure and density). In the 90s these important mechanisms were introduced into the modeling of a plume of gas in the marine environment (REED et al., 1999; ZHENG; YAPA, 2000; CHEN; YAPA, 2001; YAPA; ZHENG; CHEN, 2001).

The main variables influencing in the variations of oil spills and blowouts are temperature, salinity and marine currents. The Atlantic (central North Atlantic) is the saltiest of the world's major oceans (TALLEY, 2002). The sea surface salinity in the open ocean is 33 – 37 *psu* and varies with latitude and season. The values of surface salinity are influenced by evaporation, rainfall and river affluence. Although the minimum values of salinity are only to the north of Ecuador (TOMCZAK; Stuart Godfrey, 2003), Because of heavy tropical rainfall, the lowest values are in the high latitudes and along the coasts, where large rivers (Amazon) drain into the ocean (HU et al., 2004). Maximum salinity values occur at approximately 25°N and 25°S, in subtropical regions with low rainfall and high evaporation. The sea surface temperature varies with latitude, marine current, season and other parameters, ranges from below –2°C to 29°C. The Maximum temperatures occur to the north of the Equator (Figure 4) and the minimum values are found in the polar regions.

The tropical Atlantic region is a complex system of zonal currents and counter-currents (Figure 4) forced by the subtropical gyres and by the action of the trade winds in both hemispheres (STRAMMA et al., 2005). The Benguela current flows north to feed on the southern side of the South Equatorial Current (SEC). The SEC flows westward toward the Brazilian platform and is divided in two branches at Cabo de São Roque, one branch (strongest branch) heading northward as the North Brazil Current (NBC), and the other as the Brazil Current (BC). According to Stramma & England (1999) the SEC is divided into four branches: the southern South Equatorial Current (sSEC), the central South Equatorial Current (cSEC), the northern South Equatorial Current (nSEC) and equatorial South Equatorial Current (eSEC). The eSEC and cSEC give origin to NBC, the latter is fed too by nSEC. At each season the SEC has a strong flow to the westward (about 0.3 *m s*⁻¹) near the equator and weaker (0.1 – 0.15 *m s*⁻¹) in a broad band south of 10°S (PETERSON; STRAMMA, 1991).
**Figure 4.** Schematic representation of the main surface (solid lines), subsurface (dashed lines) currents and average SST, 1998 – 2011 (OA_Flux at http://oaflux.whoi.edu/). BC (Brazilian Current). NBC (North Brazilian Current). NBCR (North Brazilian Current Retroflection). NEC (North Equatorial Current). NECC (North Equatorial Countercurrent). nSEC (northern branch of South Equatorial Current). cSEC (central branch of South Equatorial Current). sSEC (southern branch of South Equatorial Current). EUC (Equatorial Undercurrent). NEUC (North Equatorial Undercurrent). SEUC (South Equatorial Undercurrent). NBUC (North Brazil Undercurrent). GD (Guinea Dome). AD (Angola Dome).

<figure><img src="image_5.png" /></figure>

Source: Bruto et al. (2017)

The NBC is considered a low latitude strong western-boundary current (GARZOLI et al., 2004; FRATANTONI; RICHARDSON, 2006; AKUETEVI; WIRTH, 2015), which retroflects and separate away from the boundary turning anti-cyclonically for more than 90° (Figure 4), and form anti-cyclonic eddies. NBC flows from Northeastern to Northwest along the northwestern continental margin of Brazil as a coastal current developing a retroflexion in rings form (DESSIER; DONGUY, 1994; Johns, W. E. et al., 1990; FRATANTONI; JOHNS; TOWNSEND, 1995), this makes a turn to the East driven by the wind and feeds the North Equatorial Counter Current (NECC). Reaching speeds between 0.75 – 1.0 m s⁻¹ (ARNAULT et al., 1999).
The NBC seasonally retroflects near 6–8°N and sheds eddies exceeding 450 km in overall diameter (RICHARDSON et al., 1994; GARZOLI et al., 2004; FRATANTONI; RICHARDSON, 2006). The NBC retroflection feeds the North Equatorial Counter Current (NECC), an eastward zonal current, which contributes to the formation of the anticyclone current rings (CASTELÃO; JOHNS, 2011). The NBC rings are a significant contributor to transporting water across current gyres and between hemispheres in the tropical Atlantic (BOURLES et al., 1999; JOHNS et al., 1998; SCHOTT et al., 2003; STRAMMA et al., 2005).

During the boreal summer, in response to a shift towards the north of the trade winds, the NECC forms eastwards (Figure 4), near 6°N, intensifying significantly during the boreal winter (GRODSKY; CARTON, 2002; RICHARDSON; WALSH, 1986). The NECC is located between 3°N and 10°N, it is considered as the northern boundary for SEC (PETERSON; STRAMMA, 1991).

Strong seasonal variations in these currents occur in response to the annual migration of the atmospheric Intertropical Convergence Zone (ITCZ) between its southern position in winter, and its northern position in boreal summer (XIE; CARTON, 2004). This leads to northward transport of Amazon water in boreal winter, and eastward transport of Amazon water in the NECC in boreal spring through boreal fall (Müller-Karger; MCCLAIN; RICHARDSON, 1988; LENTZ, 1995b; FRATANTONI; GLICKSON, 2002; COLES et al., 2013; FOLTZ; SCHMID; LUMPKIN, 2015).

The NSEC is a water source that reinforces the NECC (STRAMMA; ENGLAND, 1999). The northern limit of NECC (when it is present) is the North Equatorial Current (NEC). The mean speed to eastward of NECC is $0.42 \text{ m s}^{-1}$ (FRATANTONI, 2001). The NEC comes from the northwest coast of Africa (Figure 4), where it is fed mainly by the cooler waters that flow from the northeastern Atlantic towards the tropic in the West direction transporting the waters coming from the Canary Current. It is located between 7° and 20°N, at 10°N is the southern part of the subtropical gyre flowing westward as a broad current with a mean velocity about $0 - 0.15 \text{ m s}^{-1}$ (RICHARDSON; WALSH, 1986).

Pollutant dispersion models have been developed in the ocean, combining analytical expressions, Eulerian and Lagrangian formalism, e. g. MEDSLIK-II (De Dominicis et al., 2013a; De Dominicis et al., 2013b). One of the advantages of these models is their flexibility to be assimilated from different datasets, as is the case with the output data of other models, such as ROMS (Regional Ocean Modeling System) (NORTH et al., 2011) or data collected in situ with ADCP (Acoustic Doppler Current Profiler) and CTD (Conductivity, Temperature and Depth), e. g. Leite et al. (2014).
## 2.1 OIL/GAS PLUME EVOLUTION

In agreement with Chen et al. (2015) the underwater oil spill process is divided into three successive stages, namely the turbulent jet stage, the buoyant plume stage and the advection-diffusion stage (Figure 5). The turbulent jet stage exists in the event that the oil and gas mixture is released from a violent underwater burst where the velocity at the orifice can reach $5 - 10m \cdot s^{-1}$. At this stage, the movement of the jet is dominated by the initial moment by which the oil breaks into a large number of drops of uneven size due to the high turbulence.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Sketch of underwater oil spill process</figcaption></figure>

Source: Chen et al. (2015)

As the ambient water is also drawn into the stream, a rapid loss of momentum occurs within a few meters of the release position and then the turbulent jet stage ends. In the buoyant plume stage, the momentum is no longer significant with respect to buoyancy, which then becomes the driving force for the rest of the oil plume.

The plume continues to rise towards the surface of the sea due to buoyancy while the ambient water is continuously drawn into the plume. As a result, the plume is enlarged and its density approaches the ambient density. When the plume is fully developed, a considerable amount of water containing the oil droplets is pumped to the most superficial region because in the deep sea area the sea water environment is usually much denser in the deeper region, the oil plume can reach a level of neutral buoyancy at a certain depth, where buoyancy no longer dominates the movement of the plume.

Thereafter, the dynamics of the plume become insignificant and the oil moves as individual droplets of oil passively following current and ambient turbulence and increasing due
to the buoyancy of the droplets. This is the so-called advection-diffusion stage. It should be noted
that there is no obvious limit between two successive stages. In fact, the three factors mentioned
above exist at each stage and the dominant factor is simply different at a different stage.

Yapa & Zheng (1997) explained a model to simulate oil spills from underwater accidents, their model could also simulate the presence of gas with oil for relatively vertical plume. In Zheng & Yapa (1998), the model simulations were compared in detail with numerous laboratory data and some data obtained from small-scale field experiments using compressed air. A modified version of this model was then used to compare the results of two field experiments conducted in the Norwegian Sea by SINTEF (Norway), consisted of releases of oil and gas at 100 m (RYE; BRANDVIK; STRØM, 1997). The results of these comparisons are set forth in Yapa, Zheng & Nakata (1999).

Yapa & Zheng (1997) is not suitable for deepwater simulations due to important
differences in gas variations in relatively shallow water. As stated in Cooper, Forristall &
Joyce (1990) the existence of strong currents in some deepwater regions may cause the gas
phase to separate from the plume. Another argument by which the previous model needed a
major modification. Yapa, Zheng & Chen (2001) developed a module for the formation and
decomposition of the hydrate by coupling it with its previous model (YAPA; ZHENG, 1997)
to calculate several scenarios of deepwater blowouts. Johansen (2000) developed a deepwater
oil/gas blowouts model based only on thermodynamics capable of simulating the formation and
decomposition of gas hydrates, the dissolution of the gas and the separation of the gas from the
main plume, ignoring reaction rates of formation and decomposition.

Yapa, Zheng & Chen (2001) developed a model that did not include the complete model formulation or comparisons with data from the field experiment "Deepspill" (JOHANSEN; RYE; COOPER, 2003). Spaulding et al. (2000) presented a model in deep waters that could simulate the formation of hydrates, without detailing this one. Vysniauskas & Bishnoi (1983) developed a model taking into account the empirical hydration formation that was later integrated by Barbosa Jr, Bradbury & Silva Freire (1996) and by Topham (1984a), Topham (1984b) with a plume model to simulate scenarios of deepwater blowouts. None of these studies compared the results of numerical simulations with field data.

Zheng, Yapa & Chen (2002) describes a complete mathematical model to simulate the variations of oil and gas released from deep water, the formulation of the model integrates the hydrodynamics and thermodynamics of the plume; the thermodynamics and the kinetics of the formation and decomposition of the hydrate and the dissolution of the gas, uses an improvement for the calculation of the buoyant velocity of gases and hydrates and the dissolution of gases, obtaining good results. Gas behavior may be no-ideal.

The model can simulate the variations of oil and gas under conditions of a strong
transverse flow where gases can be separated from the main plume. Each module was tested by
comparing the numerical results with the available data. Zheng, Yapa & Chen (2002) called for
convenience "CDOG" to this model. Subsequently, Chen & Yapa (2003) used CDOG model for computing and compare results with large-scale field experiments, "Deepspill".

**Figure 6.** Sketch of control element of PDM submodel. $b_k$ is the plume radius and $h_k$ is the plume thickness

<figure><img src="image_7.png" /></figure>

**Source:** Taken and modified from Lee & Cheung (1990)

Conforming to Dasanayaka & Yapa (2009), the time for oil to appear on the surface and its approximate location are two key aspects that must be solved with the oil spill model for contingencies and emergency responses. This requires that the explanation of the underwater oil spill process be as accurate as possible. Yapa et al. (2012) summarized the most recent models of underwater oil spills, making successive improvements to the simulations that illustrate the behavior of the oil, demonstrates the impact of the dimensions of oil drops, also explains how the behavior of the oil changes when additives are supplied as dispersants. The results of the simulations reveal that underwater plumes with low concentrations of oil can form and remain submerged for long periods of time when very small oil droplets with diameters less than 0.5 mm are present.

The oil slick model presented by Chen et al. (2015) is formed by two submodels: the dynamics model of the plume (PDM) and the advection-diffusion model (ADM). The PDM submodel is used to simulate the turbulent jet phase and the floating plume phase where the water mixture and a small amount of spilled oil is treated as a whole and takes into account the interaction between the oil and its environment. The Lagrangian integral technique is used to simulate the turbulent jet stage and the floating plume phase. The duration of the oil spills is divided into a series of equal time intervals (Figure 6) and each time interval corresponds to a small amount of oil spilled (LEE; CHEUNG, 1990).

As a result, the oil and water plume is represented by a series of non-interfering control
elements. At some point, the line connecting the central points of all control elements is considered as the oil path. It is assumed that each control element is a cylindrical section of a curved cone and its lower plane is perpendicular to the trajectory of the plume. In the submodel ADM the oil spilled is divided into a large number of discrete particles, each particle represents a set of oil droplets of equal size and is characterized by its spatial coordinate, velocity, volume, oil concentration, drop diameter, etc. These particles are introduced into the water, in the last place of the plume and then move in response to the shear current, turbulence and buoyancy.

When the oil plume moves up to a certain depth, its density may be very close to the density of the environment because a large amount of water has been drawn into the plume, mainly in a water environment stratified by density, when the oil boom rises to the depth where the water is less dense, the fluid of the boom can reach a level of neutral or even negative buoyancy below of the sea surface.

## 2.2 HYDRATE FORMATION

According to Zheng, Yapa & Chen (2002) in low temperatures and high pressures in the deep ocean, oil/gas blowouts, in addition to their long travel to the surface, are more subject to more complex processes than if they were on the surface or in shallow waters (Figure 7), including hydrate formation, non-ideal gas behavior, etc. Gas hydrates consist of gas and water, and it is a compound. For CH₄, the hydrate formation can be described as equation (2.1).

$$ (CH_4)_{gas} + n_h(H_2O)_{water} \leftrightarrow (CH_4 \cdot n_h H_2O)_{hydrate} \quad (2.1) $$

Where $n_h = 5.75$ for CH₄. When a plume rises to a lower pressure level, the hydrate can decompose in water and gas again. Figure 7 shows the variation of potential temperature and thermodynamic equilibrium conditions for CH₄ and natural gas (80% methane, 10% ethane, 10% propane) in the Norwegian Sea and Gulf of Mexico. Below the thermodynamic equilibrium line, the pressure and temperature satisfy the hydrate formation conditions, above this, the hydrates will begin to decompose. In these places, the thermodynamic conditions to form hydrates will gather close to 500 m (CH₄) and 200 m (natural gas) at Norwegian Sea; and near 600 m (CH₄) and 300 m (natural gas) at Gulf of Mexico. The formation and decomposition of the hydrate significantly affects the buoyancy of the plume.
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Diagrams of thermodynamic equilibrium for hydrate from CH₄ and natural gas (80% methane, 10% ethane, 10% propane) superimposed on the temperature distribution at a place in the Norwegian Sea and Gulf of Mexico.</figcaption></figure>

Conforming to Zheng, Yapa & Chen (2002) the free gas can dissolve in water during its long journey, changing the buoyancy of the plume. Under high pressures the behavior of the gas is best described by an equation of non ideal gas state. The size of the gas bubbles and their buoyancy velocities cannot be approximated as constants, considering the processes of hydrate formation, decomposition, dissolution and gas expansion. The gas can be separated from the plume due to the slip velocity of the gas bubble if the plume is significantly bent in a transversal flow.

## 2.3 RELATIONSHIP OF KINETICS OF HYDRATE FORMATION WITH MASS AND HEAT TRANSFER

To model the rate of hydrate formation in the gas phase of the plume the relationship between hydrate kinetics, mass and heat transfer should be considered. The mass transfer carries the gas for the formation of hydrates to the point of reaction. Heat transfer redistributes the
released heat of hydrate formation around the solid hydrate to change the temperature of the water.

Before integrating the hydrate kinetics with the hydrodynamics and thermodynamics of the plume, Englezos et al. (1987) constructed a module for the hydrate kinetics that helped to verify the adaptation and the numerical algorithms, this module takes into account that the gas molecules diffuse through the porous hydrate layer due to the concentration gradient of the gas and react with the water to form hydrates at the hydrate-water interface; the hydrate layer is at the same temperature as the hydrate-water interface, the heat released by the hydrate formation at the hydrate-water interface is transferred only through the aqueous phase since the thermal conductivity of the phase gaseous phase is much lower than that of the liquid phase; the transfer of mass and heat in any cross-section is the same for a given time; the pressure on the inside and the outside of the bubble is the same; any hydrate particles that emanate from the border of the bubbles are not taken into account in the calculations and the hydrate sheathing evenly covers the surface of the bubble (Figure 8). This module is for a single bubble and is applied in the same way to several bubbles. The nucleation process is not taken into account because the experimental data show that the period of this process is very short (BISHNOI; NATARAJAN, 1996; BREWER et al., 1998).

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Scheme of a gas bubble with a homogeneous sheathing of hydrate</figcaption></figure>

Source: Taken and modified from Zheng, Yapa & Chen (2002)

## 2.4 NON IDEAL GAS BEHAVIOR IN DEEP WATER

The gas behavior is not ideal in deep water because of the high ambient pressure, the solubility of the gas in water depends to a large extent on the ambient pressure, temperature and salinity (ZHENG; YAPA; CHEN, 2002; JOYE et al., 2011). Therefore, a correction for
compressibility factor ($F_c$) is necessary.

$$PV = F_c nRT \qquad (2.2)$$

Where:

$F_c = 1$ for ideal gas

P Ambient pressure (Pa)

V Gas volume (m³)

n Number of gas moles

R = 8.314 Pa · mol⁻¹ · K⁻¹ Universal gas constant

T Ambient temperature (K)

The values of $F_c$ for $CH_4$, $CO_2$ and an ideal gas are shown in figure 9 up to 500 m depth in the Gulf of Mexico, where can see a significant difference between the ideal gas and the real gases $CH_4$ and $CO_2$, this difference increases with the increase of depth.

**Figure 9.** Comparison of the compressibility factor of an ideal gas with the real $CH_4$ and $CO_2$ gases in the Gulf of Mexico. The compressibility factor is computed according to Sloan Jr & Koh (2008) method.

<figure><img src="image_10.png" /></figure>

Source: Taken and modified from Zheng, Yapa & Chen (2002)
## 2.5 PHASE SEPARATION

In a transverse flow the difference in velocity between the sliding bubbles and rising entrained fluid can lead to a phase separation. Figure 10 shows single-phase and biphasic plume in a uniform cross-flow. If the cross-flow is strong enough to push the fluid out of the plume and advect it with the flow, the bubbles will separate from the entrained fluid at some height $h_s$, forming a column of bubbles that rises as a result of the velocity of sliding the bubble alone. Above $h_s$, fluid diverted at the front of the bubble column by the current rises a short distance while interacting with the floating bubbles before it is thrown to leeward of the plume (SOCOLOFSKY; ADAMS, 2002).

<figure><img src="image_11.png" /><figcaption>**Figure 10.** Representation of single-phase and biphasic plumes in a uniform cross-flow. $h_s$ is the phase separation height</figcaption></figure>

Source: Socolofsky (2001)

Cross-flows affect a wide range of plume properties, changing the basic dynamics of the plume. Even in the case of single-phase plume, cross flows improve entrainment, divert the plume center line, deform it into a pair of vortices and can cause fluid to leak in the downstream wake of the plume (FISCHER et al., 1979; DAVIDSON; PUN, 1999). The bubble plumes are similarly affected and have additional complications due to the sliding velocity of the dispersed phase.

Socolofsky & Adams (2002) performed several experiments confirming fractionation and separation, determining the coding for phase separation taking into account the cross-flow force, for plumes with high buoyancy and low cross-flow velocity (weak cross-flows), the separation did not occur at the time the bubbles reached the surface of the water, occurring the separation in other experiments with high cross-flow rate (strong cross-flows).
## 2.6 SOLUBILITY

Experimental values for the water-solubility of natural gases are available as a function of pressure and temperature (FOGG; GERRARD, 1991), for small pressures, the solubility increases in proportion to the pressure in the gas phase according to Henry's law, while at higher pressures, this simple law must be substituted by the modified form of Henry's law (Krichevsky & Kasarnovsky (1935) relation). In this law, the pressure term is replaced by the fugacity that accounts for non-ideal gas behavior (LEKVAM; BISHNOI, 1997).

Figure 11 shows the Comparison between the calculated data of CH₄ solubility in water through Henry's law and the modified Henry's law and those observed by Lekvam & Bishnoi (1997). In this comparison has taken into account 3 different temperatures ( 1.20 °C, 10.22 °C and 12.46 °C ). Evidently it can be seen that for higher temperatures and for higher pressures the observed data are much closer to the modified Henry's law. Therefore, at higher pressures modified Henry's law provide better computational values for solubility. The higher pressures in this plot correspond to what is expected in deepwater spills.
**Figure 11.** Comparison between calculated CH₄ solubility in water data and those observed by Lekvam & Bishnoi (1997)

<figure><img src="image_12.png" /></figure>

Source: Zheng & Yapa (2002)

## 2.7 LIFTING SPEED OF OIL PARTICLES

When the oil drop are in the water column, its trajectory is described by the advection-diffusion equation with a buoyant velocity as part of the vertical velocity (YAPA; ZHENG; NAKATA, 1999). The buoyant velocity of the oil particles using Stokes's law or Reynolds's law was calculated by Elliott (1986) and depends on the particle diameter *d* relative to the critical diameter *d*<sub>c</sub> given by:

$$d_c = \frac{9.52\nu^{2/3}}{[g(1 - \rho_d/\rho_w)]^{1/3}} \quad (2.3)$$

Where:

* *d* particle diameter (*m*)

* *d*<sub>c</sub> critical diameter (*m*)
ν Viscosity of seawater (m²·s⁻¹)

ρ<sub>d</sub> Density of the drop (kg·m⁻³)

ρ<sub>w</sub> Seawater density (kg·m⁻³)

$$
W = \begin{cases}
\frac{gd^2\left(1 - \frac{\rho_d}{\rho_w}\right)}{18\nu} & \text{Stokes law if } d < d_c \\
\left[\frac{8}{3} - gd\left(1 - \frac{\rho_d}{\rho_w}\right)\right]^{1/3} & \text{Reynolds law if } d \ge d_c
\end{cases}
\qquad (2.4)
$$

Using equation (2.4), Elliott (1986) successfully simulated the vertical mixing of oil
particles in the North Sea.
# 3 DATA AND METHODOLOGY

## 3.1 STUDY AREA

The Atlantic Ocean is limited to the west by North and South America, in the north and northeast is separated by the Arctic Ocean and by the Canadian Arctic Islands, Iceland, Greenland, Jan Mayen, Svalbard Islands and continental Europe. It connects to the Arctic Ocean through the Strait of Denmark, the Greenland Sea, the Norwegian and Barents Seas. To the east, the boundaries of the ocean are Europe, the Strait of Gibraltar (which connects it with the Mediterranean Sea) and Africa. In the southeast, the Atlantic merges with the Indian Ocean, divided by the eastern meridian, running south of the Cape Agulhas to Antarctica. While some authorities show the Atlantic Ocean, extending south to Antarctica, others show it as delimited to the south by the South Ocean (IHO, 1953). In the southwest, the Drake Pass connects to the Pacific Ocean. The Caribbean Sea, the Gulf of Mexico, the Hudson Bay, the Mediterranean Sea, the North and the Baltic Seas are the large bodies of water adjacent to the Atlantic Ocean.

The Atlantic Ocean with its adjacent seas occupies an area of about 106.4 million square kilometers and without them, 82.6 million square kilometers. The width of the Atlantic ranges from 2848 km (between Brazil and Liberia) to about 4830 km (between the United States and North Africa) (AKINDE; OBIRE, 2011). The average depth of the Atlantic Ocean without its adjacent seas is 3926 m. The mean depth between 60°N and 60°S is 3730 m, finding the modal depth between 4000 m and 5000 m (LEVIN; GOODAY, 2003) and the maximum depth in the Puerto Rico Trench with a value of 8605 km (FOX et al., 2009).

The study area of this work is located in the equatorial band of the tropical Atlantic, limited in the southeast by the north coast of Brazil, where the rivers Amazonas and Pará release freshwater. This area is framed in 60.5°W – 24°W/5°S~16°N (Figure 12), covering an area of $4916 \times 10^3 \text{ Km}^2$. Special attention is given to these two oceanic regions: REG1, the retroflexion area of NBC and REG2, which corresponds to the plume of the Amazon River spreading eastwards. Figure 13 shows the Amazon river delta with very irregular coast and where are located multiple islands that define four fundamental inputs: North channel, Santa Rosa Bay, Dangerous channel and Jurupari channel.
**Figure 12.** The model domain framed in 60.5°W – 24°W/5°S – 16°N, bathimetry and regions for data validation (Red rectangles). REG1(48° – 45°W/4° – 12°N). REG2 (40° – 28°W/6° – 10°N)

<figure><img src="image_13.png" /></figure>

Source: The author

**Figure 13.** Map of location of the Amazon River delta and its four inputs (North channel, Santa Rosa Bay, Dangerous channel and Jurupari channel)

<figure><img src="image_14.png" /></figure>

Source: The author
## 3.2 OBSERVATIONAL DATA

### 3.2.1 World Ocean Atlas (WOA)

World Ocean Atlas (WOA) is a climate data service created in 1994 by the Ocean Climate Laboratory (OCL) of the National Oceanographic Data Center (NODC), includes monthly, seasonal and annual data of temperature (LOCARNINI et al., 2013), salinity (ZWENG et al., 2013), dissolved oxygen, apparent oxygen utilization, oxygen saturation (GARCIA et al., 2014b) and dissolved inorganic nutrients (GARCIA et al., 2014a) in a global grid with spatial resolution of 1° and 33 levels of standard depths between 0 and 5500 m. This climatology is made from 1900 to 2013. Development of the World Ocean products has been updated in 1994, 1998, 2001, 2005, 2009, and 2013.

### 3.2.2 Comprehensive Ocean-Atmosphere Data Set (COADS)

Comprehensive Ocean-Atmosphere Data Set is the result of a cooperative project to collect observations of weather measurements near to ocean's surface. The first observations were made by merchant ships. The variables observed are air temperature, SST, wind, pressure, humidity and cloudiness, from these are generated other variables such as surface forcings. From these variables a monthly climatology is made, which are used as inputs of the ROMS model. The spatial resolution of COADS is 2°x2° and the period of time used for this dataset was from 1945 to 1989 (SLUTZ et al., 1985; WOODRUFF et al., 1987).

### 3.2.3 Simple Ocean Data Assimilation (SODA)

There are several datasets that can be used to validate of the SST and SSS result of the ROMS model, such as SMOS (SST and SSS), Aquarius (Only SSS) and SODA (SST, SSS and currents). In this work it is not convenient to use the data of SMOS and Aquarius because in both there is absence of data in the regions that correspond to the Amazon River mouth and to the band that forms the NBC (blue polygon in figure 14). Being SODA selected for the validations of SST and SSS throughout the study region.

The SODA reanalysis dataset (CARTON; GIESE, 2008) is composed of temperature, salinity, ocean currents and other physical oceanographic variables, these data are produced by a general ocean circulation model based on Smith, Dukowicz & Malone (1992), with a spatial resolution of 0.25°x0.4° and 40 vertical levels with a spacing of 10 meters on the surface. Salt, heat and vertical diffusion of momentum are done through K-profile parameterization (KPP) mixing with modifications to address issues such as diurnal heating, meanwhile lateral subgrid-scale processes are resolved using biharmonic mixing (LARGE; MCWILLIAMS; DONEY, 1994). Sea level is computed by a linearized continuity equation, determined for small ratios of
sea level to fluid depth (DUKOWICZ; SMITH, 1994). Daily surface wind speed data is provided by the ERA-40 project of ECMWF (SIMMONS; GIBSON, 2000; UPPALA et al., 2005) and surface freshwater flow is provided by GPCC.

<figure><img src="image_15.png" /><figcaption>**Figure 14.** Representation of the SSS of SMOS and Aquarius in November. The blue polygon represents the area where there is no data in both datasets.</figcaption></figure>

Source: The author

Data assimilation is done every 10 days using incremental analysis (BLOOM et al., 1996), where a time analysis is performed, followed by a simulation of 5 days. On the fifth day there is an update of temperature and salinity. The simulation is repeated from time to time with gradual corrections of temperature and salinity. This maintains a relationship between the geostrophic component of the flux and the pressure and velocity fields. In this way, the average fields are remapped to a uniform global field of horizontal grid with a resolution of 0.5°x0.5° (CARTON; CHEPURIN; CAO, 2000a; CARTON; CHEPURIN; CAO, 2000b). Temperature, salinity, and zonal and meridional velocity components of ocean currents are three-dimensional
and Sea Surface Height (SSH) and zonal and meridional components of the vertically integrated velocity are two-dimensional.

SST operational data from AVHRR (NASA) and NOAA are used to update the SODA SST, binned into 1° × 1° bins (CARTON; GIESE, 2008; VAZQUEZ; PERRY; KILPATRICK, 1998; REYNOLDS et al., 2002). The Reynolds & Smith (1994) SST are also used for update SODA SST. The SST of Reynolds & Smith (1994) is obtained from the combination of the satellite, shipboards and buoys observations. The period of time used for this dataset was from 1991 to 2010.

### 3.2.4 Prediction and Research Moored Array in the Tropical Atlantic (PIRATA)

The Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) dataset (SERVAIN et al., 1998; BOURLÈS et al., 2008) was implemented in the mid-1990s to measure the oceanographic and atmospheric variables in the tropical Atlantic Ocean that affect the climatic variability of this region in seasonal, interannual and longer duration scales. The name of the project was renamed in 2008 as Prediction and Research Moored Array in the Tropical Atlantic. It is supported by INPE, DHN, NOAA, IRD, IFREMER, Meteo-France and CNRS. The period of time used for this dataset was from 2000 to 2015.

### 3.2.5 Bathymetry

Ocean circulation models, the effect of bathymetry on ocean dynamics is essential. There are international databases obtained from satellite altimetry and depth soundings with ships (SMITH; SANDWELL, 1997) that are used by most models, in this study we use eTOPO2v2 (NCEI, 2006). The vertical datum is Mean Sea Level with 1 meter of precision. The horizontal datum is WGS-84, the horizontal grid spacing is 2-minutes of latitude and longitude, averaged over the cell's area.

### 3.2.6 Tide TPXO7

TPXO7 is a version 7 of a TOPEX/Poseidon Global Inverse Solution model of ocean tides described by Egbert, Bennett & Foreman (1994) and also by Egbert & Erofeeva (2002). The tides are supplied as amplitudes of earth-relative sea-surface elevation. The main harmonic constituents provided are: Principal lunar ($M_2$), Principal solar ($S_2$), Major lunar elliptical ($N_2$), Luni-solar declinational ($K_2$), Luni-solar declinational ($K_1$), Principal lunar ($O_1$), Principal solar ($P_1$) and Major lunar elliptical ($Q_1$); harmonic constituents of long period, Lunar fortnightly ($Mf$) and Lunar monthly ($Mm$); and harmonic constituents nonlinear Shallow water overtides of principal lunar constituent ($M_4$), Shallow water quarter diurnal constituent ($MN_4$) and Shallow water quarter diurnal constituent ($MS_4$). The spatial resolution of TPXO7 is 0.25°.
### 3.2.7 Freshwater river runoff. Dai and Trenberth Global River Flow and Continental Discharge Dataset

Temporary series of monthly river flows at the furthest downstream station of the world's largest 925 rivers (mean and climatological monthly volume at stations), more long-term river flows and continental discharge into the global and individual oceans (DAI; TRENBERTH, 2002). The period of time used for this dataset was from 1948 to 2004. Figure

**Figure 15.** (a) Monthly distribution of discharge (m³s⁻¹) of Amazon River (blue lines) and Pará River (black line), from Obidos and Tucuruí gauge stations. (b) Monthly distribution of temperature (°C) of Amazon River (blue line) and Pará River (black line).

<figure><img src="image_16.png" /></figure>

Source: The author

### 3.3 SURFACE CURRENTS FROM DIAGNOSTIC MODEL (SCUD)

The surface velocities are taken from the SCUD program (MAXIMENKO; HAFNER, 2010), implemented by the Asia Pacific Data Research Center of the International Pacific Research Center (APDRC/IPRC). The SCUD dataset, with spatial resolution of 0.25°, comprises nearly global and daily surface velocities as a result of a simple diagnostic model that combines three sources of scientific information: geostrophic components produced by the sea level anomaly from the Archiving Validation and Interpretation of Satellite Data in Oceanography (AVISO) project and mean dynamic ocean topography from Maximenko et al. (2009). Wind components using satellite daily winds (QuikSCAT) and drifter trajectories which provide consistent data for tuning the diagnostic model. The period of time used for this dataset was from 2000 to 2008.
## 3.4 NUMERICAL SIMULATION TOOLS

Numerical models are a tool to evaluate and understand the dynamics of the natural environment, simulating computational physical conditions of the same, allowing preventive and corrective to evaluate alternatives for technical and scientific environmental studies, to reach the improvement and protection of the conditions of the marine - river ecosystem. Numerical models are very useful in assessing impacts on environmental impact studies in the marine environment.

Ocean numerical models are useful for the study of ocean dynamics and are applied to characterize hydrodynamics, for the assessment of environmental impact in the marine environment, for the design of marine works, submarine issuers, dredging, etc.

### 3.4.1 ROMS model

The ROMS (Regional Oceanic Modeling System) model is an open source software that is actively developed by a large community of programmers and scientists (UCLA, IDR and Rutgers University), with hundreds of thousands of lines of FORTRAN code, which integrates primitive equations into a rotational, surface system free, using the Boussinesq approximation, the hydrostatic approximation and the vertical momentum balance (SHCHEPETKIN; MCWILLIAMS, 2005; SONG; HAIDVOGEL, 1994; PANZER et al., 2013).

ROMS uses orthogonal curvilinear coordinates in the horizontal dimension and generalized sigma coordinates that follow the shape of the ocean floor in the vertical dimension. This was adapted to different geographic regions of the world where good results were obtained (HAIDVOGEL et al., 2000; PENVEN et al., 2000; Malanotte-Rizzoli et al., 2000; SHE; KLINCK, 2000; SHE; KLINCK, 2001; PENVEN et al., 2001; LUTJEHARMS; PENVEN; ROY, 2003; CORREA et al., 2008; SILVA et al., 2009).

#### 3.4.1.1 Basic equations of the ROMS AGRIF model

Figure 16 shows several computational pathways for the execution of the ROMS model, the OCEAN model can be used standalone or coupled to waves (WAVE_OCEAN) and/or atmospheric (AIR_OCEAN) models. These follow the Earth System Modeling Framework (ESMF) conventions for coupling models in the execution sequence (INITIALIZE, RUN and FINALIZE). ROMS dynamic kernel consists of four independent models, including:

**NLM** Non-Linear model.

**TLM** Tangent Linear Model.

**RPM** RePresenter tangent linear Model.
**AM** Adjoint Model.

There are several drivers to run each model (NLM, TLM, RPM and AM) separately and together. The drivers that are shown in the **PROPAGATOR** group are used for the analysis of Generalized Stability Theory (GST) (MOORE et al., 2004) to study the dynamics, sensitivity and stability of oceanic circulations to naturally occurring perturbations, errors or uncertainties in the system of forecasting and adaptive sampling. The driver for adjoint sensitivities (**ADSEN_OCEAN**) calculates the response of a chosen function of the model's circulation to variations in all physical attributes of the system (MOORE et al., 2004). Includes drivers for strong (**IS4DVAR_OCEAN**) and weak (**W4DVAR_OCEAN**) constraint variational data assimilation (Di Lorenzo et al., 2006). Strong Constraint drivers: Conventional S4DVAR, outer loop, NLM, AM; Incremental S4DVAR_OCEAN, inner and outer loops, NLM, TLM, AM (Courtier et al., 1994) and efficient incremental S4DVAR (WEAVER; VIALARD; ANDERSON, 2003). Weak Constraint drivers: Inverse Ocean Modeling (IOM), Indirect Representer Method, inner and outer loops, NLM, TLM, RPM, AM (EGBERT; BENNETT; FOREMAN, 1994). A driver for ensemble prediction is available to perturb forcing and/or initial conditions along the most unstable directions of the state space using singular vectors. Finally, several controllers are included in the sanity check group to test the accuracy and correctness of the TLM, RPM, and AM algorithms.

<figure><img src="image_17.png" /><figcaption>**Figure 16.** Working structure of the ROMS model.</figcaption></figure>

Source: https://www.myroms.org/wiki/Regional_Ocean Modelling System_(ROMS)
The primitive equations in Cartesian coordinates are:

$$ \frac{\partial u}{\partial t} + \mathbf{v} \cdot \nabla u - f\mathbf{v} = -\frac{\partial \phi}{\partial x} - \frac{\partial}{\partial z}(K_M \frac{\partial u}{\partial z}) + \mathcal{F}_u + \mathcal{D}_u \quad (3.1) $$

and

$$ \frac{\partial v}{\partial t} + \mathbf{v} \cdot \nabla v - f u = -\frac{\partial \phi}{\partial y} - \frac{\partial}{\partial z}(K_M \frac{\partial v}{\partial z}) + \mathcal{F}_v + \mathcal{D}_v \quad (3.2) $$

The temperature and salinity equations can be written as:

$$ \frac{\partial T}{\partial t} + \mathbf{v} \cdot \nabla T = \frac{\partial}{\partial z}(K_H \frac{\partial T}{\partial z}) + \mathcal{F}_T + \mathcal{D}_T \quad (3.3) $$

and

$$ \frac{\partial S}{\partial t} + \mathbf{v} \cdot \nabla S = \frac{\partial}{\partial z}(K_H \frac{\partial S}{\partial z}) + \mathcal{F}_S + \mathcal{D}_S \quad (3.4) $$

The advective-diffusive equation is:

$$ \rho = \rho(S, T, P) \quad (3.5) $$

The equation of state is given by:

$$ \frac{\partial \phi}{\partial z} = -\frac{\rho g}{\rho_o} \quad (3.6) $$

Finally, the continuity equation is:

$$ \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 \quad (3.7) $$

The equation (3.5) is the general equation of state, it is taken into account the form of the international equation of state of the sea water (GILL, 1982). The notation used in these equations is:

u, v, w Components of the velocity vector v.

T(u, v, w, t) Potential temperature.

S(u, v, w, t) Salinity.

$\rho_o + \rho(x, y, z, t)$ Total density.

$\phi(x, y, z, t)$ Dynamic pressure. $\phi = P/\rho_o$

P Total pressure. $P \approx \rho_o gz$

f Parameter of Coriolis.

g Acceleration of gravity.

$K_M(x, y, z, t)$ Eddy vertical viscosity.
$K_H(x, y, z, t)$ Eddy vertical diffusivity.

$D_u, D_v, D_T, D_S$ Vertical Eddy viscosity and diffusivity.

$F_u, F_v, F_T, F_S$ Forcing terms.

$t$ Time.

### 3.4.1.2 Horizontal boundary conditions

The domain of the model is logically rectangular, but it is possible to mask the land areas in the contour and in the interior. The boundary conditions on these masked regions are straightforward, with a choice of no-slip or free-slip walls.

If biharmonic friction is used, a higher order boundary condition must also be provided. The model currently has this built-in code where the biharmonic terms are calculated. The higher-order contour conditions used for $u$ are:

$$ \frac{\partial}{\partial x} \left( \frac{hv}{mn} \frac{\partial^2 u}{\partial x^2} \right) = 0 \qquad (3.8) $$

on the east and west limits.

and

$$ \frac{\partial}{\partial y} \left( \frac{hv}{mn} \frac{\partial^2 u}{\partial y^2} \right) = 0 \qquad (3.9) $$

on the north and south limits. Where $v$ is the horizontal viscosity.

The boundary conditions for $v$, $T$ and $S$ are similar. These contour conditions were chosen because they preserve the property of no gain or loss of momentum of the integrated volume, temperature or salinity.

### 3.4.1.3 Vertical boundary conditions

The vertical boundary conditions can be prescribed as follows:

On the surface ($z = \zeta(x, y, t)$)

$$ K_M \frac{\partial u}{\partial z} = \tau_s^x(x, y, t) \qquad (3.10) $$

$$ K_M \frac{\partial v}{\partial z} = \tau_s^y(x, y, t) \qquad (3.11) $$

$$ K_T \frac{\partial T}{\partial z} = \frac{Q_T}{\rho_o c_p} + \frac{1}{\rho_o c_p} \frac{dQ_T}{dT} (T - T_{ref}) \qquad (3.12) $$
$$K_s \frac{\partial S}{\partial z} = (E - P_r)S \qquad (3.13)$$

$$w = \frac{\partial \zeta}{\partial t} \qquad (3.14)$$

On the seabed ($z = -h(x, y)$)

$$K_M \frac{\partial u}{\partial z} = \tau_b^x(x, y, t) \qquad (3.15)$$

$$K_M \frac{\partial v}{\partial z} = \tau_b^y(x, y, t) \qquad (3.16)$$

$$K_T \frac{\partial T}{\partial z} = 0 \qquad (3.17)$$

$$K_s \frac{\partial S}{\partial z} = 0 \qquad (3.18)$$

$$-w + \mathbf{v} \cdot \nabla h = 0 \qquad (3.19)$$

Where:

$h(x, y)$ Depth.

$\zeta(x, y, t)$ Surface elevation.

$\tau_s^x, \tau_s^y$ Surface wind stress.

$\tau_b^x, \tau_b^y$ Bottom stress.

$E - P_r$ Evaporation minus precipitation.

$Q_T$ Surface heat flux.

$T_{ref}$ Surface reference temperature.

$Q_T$ is a strong function of surface temperature, it is also prudent to include a correction term for the $Q$ change, as the surface temperature moves away from the reference temperature that was used to calculate $Q_T$. In the background, $z = -h(x, y)$, the horizontal velocity components are limited to accommodate the background forcing which is a sum of linear and quadratic terms:

$$\tau_b^x = (\gamma_1 + \gamma_2 \sqrt{u^2 + v^2})u \qquad (3.20)$$
$$ \tau_b^y = (\gamma_1 + \gamma_2 \sqrt{u^2 + v^2})\nu \qquad (3.21) $$

$\gamma_1, \gamma_2$ are the linear and quadratic coefficients of the bottom forcing.

A better description of the ROMS model can be found in Hedstrom (1997), Hedstrom (2009).

### 3.4.1.4 Vertical coordinates

ROMS vertically uses the so-called sigma-coordinate ($\sigma$ coordinate) system (SONG; HAIDVOGEL, 1994; HAIDVOGEL et al., 2000). The $\sigma$ coordinate models, or "terrain-following" are especially suitable in regions with variable bottom topography and in which the processes of interaction with the background boundary layer are important. The main attraction of such models lies in the smooth representation of topography and in its ability to simulate the interactions between flow and bathymetry (EZER; ARANGO; SHCHEPETKIN, 2002).

### 3.4.1.5 Spatial and temporal discretization

The model is discretized horizontally in a rectangular and isotropic Arakawa type C structured mesh (ARAKAWA; LAMB, 1977), is discretized vertically in a curvilinear $\sigma$ coordinate system that follows the shape of the bottom and the coastline (SONG; HAIDVOGEL, 1994). It uses two time steps, one for the barotropic external oscillation mode (with a shorter time interval) that satisfies the continuity equation and another baroclinic internal (with a longer time interval), both fulfilling the CFL convergence condition (SHCHEPETKIN, 2015).

### 3.4.1.6 Pre and post-processing of data

The grids of bathymetry, forcing, initial and contour conditions were constructed using the ROMSTOOLS package developed by the IRD (PENVEN et al., 2007). This package includes tools like **nestgui** for nesting the meshes and **roms_gui** for visualizing the results. Finally it has scripts to run it in inter-annual and climatic modes. The operation of such tools is described in Penven et al. (2010).

### 3.4.1.7 Lateral boundary and initial conditions

The grid generated from the bathymetry has a spatial resolution of 0.25° and 32 vertical levels in sigma-coordinates. The four lateral boundaries are considered open, in the lateral boundary and initial conditions all variables were obtained from the monthly mean of World
Ocean Atlas 2009 (WOA09) with a resolution of 1°. The surface forcings were obtained from monthly mean climatology of Comprehensive Ocean-Atmosphere Data Set (COADS05) (Da Silva; YOUNG; LEVITUS, 1994) with 0.5° of resolution. Tides are an important process in mixing the river freshwater plumes with the open ocean and are obtained from the TPXO7 (EGBERT; BENNETT; FOREMAN, 1994; EGBERT; EROFEEVA, 2002), which has altimetry data from several satellites to improve the accuracy of the results obtained through the hydrodynamic model (WANG, 2004; D'ONOFRIO; OREIRO; FIORE, 2012). The monthly means river discharge were obtained from Obidos and Tucurui gauge stations (DAI; TRENBERTH, 2002), the monthly climatology of SST in the rivers discharge points was also obtained from WOA09.

### 3.4.1.8 Experiment configuration

We have carried out two numerical experiments to estimate the potential impact of Amazons and Pará rivers in the salinity, temperature and surface currents on the WTNA. In the first experiment, River Runoff (RRF), the Amazon and Pará Rivers release freshwater into the WTNA, given the geographical configuration of Amazon River Delta, there are four inputs from the river to WTNA (Figure 13): Canal do Norte, Baía de Santa Rosa, Canal Perigoso and Canal do Jurupari, the inputs are placed in four cells of the grid, considering the width of each channel the contribution was calculated for each one, distributed in 14.47%, 37.27%, 29.13% and 19.13% respectively (Figure 15(a)), with the same monthly temperature distribution for the four inputs nodes in the Amazon River Delta and different in the input node of the Pará River (Figure 15(b)). In the second experiment, No-River Runoff (NRF), the Amazon and Pará Rivers do not release freshwater into the WTNA, with the same parametrization as the first experiment. We run each experiment for 11 years, but our analyses are restricted to the last 3 years.

## 3.4.2 GAS_DOCEAN model

In this study the evolution of the plumes of oil and gas through the water column was estimated based on the theory proposed by Leite et al. (2014), Fannelop & Sjoen (1980), Zheng & Yapa (1998), Friedl & Fanneløp (2000), Zheng & Yapa (2000), Yapa, Zheng & Chen (2001), Zheng & Yapa (2002), Chen & Yapa (2004). These studies were used for the elaboration of computational routines that could represent the simultaneous transport of oil and natural gas. This model was also previously used in the evaluation of the evolution of plumes of natural gas and/or oil resulting from an eventual blowout on the oceanic floor (LEITE et al., 2014).

The new implementations to the GAS_DOCEAN code (version 3.0) allow the simulations of engaged/simultaneous evolution of the plumes of oil and natural gas. The adopted methodology follows the theoretical-experimental approach proposed by Chen & Yapa (2004). The decrease of the pressure that makes the gas expand in volume, the temperature decrease may induce the formation of hydrates starting from lighter hydrocarbon chains (ZHENG; YAPA, 2002; CHEN;
YAPA, 2004). So, under these new conditions of pressure and temperature, the mixture tends to hydrate. With the formation of hydrates, the upwelling time for the gas along the water column will be incremented since their presence will induce the reduction of ascending velocity of the gas plume (TOPHAM, 1984a; CHEN; YAPA, 2001; JOHANSEN, 2003). The physical-chemical characteristics of the oil, necessary for simulations, were then calculated from each depth through parameterized equations inserted in the mathematical model, and taken from experimental curves obtained in laboratory (LEITE et al., 2014).

### 3.4.2.1 Basic equations of the GAS_DOCEAN model

The equations are discretized using a lagrangean control-volume, and local variations of mass inside the plumes are treated taking into account the prime mechanisms of water entrainment, oil dissolution and gas hydrate formation. In order to follow the usual framework and notations concerning previous modelling approaches we have adopted here the scheme proposed by Friedl & Fanneløp (2000) (Figure 3).

The position of each control volume along the simulation is obtained as follows:

$$h = |V|\Delta t \qquad (3.22)$$

$$\Delta t = \frac{0.1 \cdot b_0}{|V_0|} \qquad (3.23)$$

where:

* h Depth of control volume (m).

* V Total velocity (m · s⁻¹).

* Δt Time step (s).

* b₀ Ratio of initial control-volume (m).

* V₀ Initial blowout velocity (m · s⁻¹).

Recent implementations in the GAS_DOCEAN code are mainly related to the inclusion of the coupled/simultaneous dynamics of evolution of the plumes of oil and gas. The adopted methodology follows the theoretical-experimental approach proposed by Chen & Yapa (2004) and illustrated in figure 17.

Separation between the two plumes occurs in regard to their speed of ascension and the strength of horizontal advection imposed by the oceanic currents. The critical length, from which the separation is observed between the plumes of oil and gas, is calculated comparing the momentum in the control-volume (gas and oil) with the horizontal momentum induced by environmental current fields.
The GAS_DOCEAN model uses the theoretical concept developed by Davidson & Pun (1999) and Davidson & Wang (2002) for estimating the eventual separation between oil and gas plumes along the seawater column. This approach defines, for each step of time, the excess momentum (per unit density - $M_0$) of the mixture according to the environment forcing, as follows:

**Figure 17.** Theoretical-experimental scheme for displacement of oil and gas plumes used in simulations.

<figure><img src="image_18.png" /></figure>

Source: Chen & Yapa (2004)

$$M_0 = \pi \cdot (U_0 - U_A) \cdot U_0 \cdot b_0^2 \quad (3.24)$$

where:

$M_0$ Momentum excess in the control-volume (gas + oil) ($m^4 \cdot s^{-4}$).

$U_0$ Velocity of the mixture oil + gas ($m \cdot s^{-1}$).

$U_A$ Velocity of the currents in the ocean ($m \cdot s^{-1}$).

The characteristic length scale $X_{SW}$ ($m$) that relates the excess momentum in the mixture (oil + gas) to the ocean momentum (always by units of density) is given by:

$$X_{SW} \approx \frac{M_0^{1/2}}{U_A} \quad (3.25)$$

The characteristic length scale $X_{SW}$, estimated by the equation 3.25 and calculated at each numerical step of time, furnishes an indication of the location along the water column
of the transition between the strong advective behavior and the weak advection. Laboratory experiments indicate that the separation between the two plumes (oil and gas) occurs, indeed $X_{SEP}$, when the excess of momentum in the external environment (in this case the ocean) is about 100-fold the plumes momentum, or:

$$ \frac{X_{SEP}}{M_0^{1/2}/U_A} \le 100 \qquad (3.26) $$

A second upgrade in this new version of the GAS_DOCEAN model is the routines that consider hydration mechanisms of the gas (TOPHAM, 1984a; CHEN; YAPA, 2001) and the dissolution of the gas (JOHANSEN, 2003; ZHENG; YAPA, 2002) in the liquid environment.

In the hydration mechanism of the gas, each particle (considered spherical) is treated considering that it is involved by a diffusive layer, superimposed to an absorption layer. From this sub-model, the transformation of the gas into hydrates is driven by the equation 3.27. More details can be found in the works of Englezos et al. (1987).

$$ \left(\frac{dn}{dt}\right)_p = K^* \cdot A_p \cdot (f - f_{EQ}) \qquad (3.27) $$

where:

n Number of moles of consumed gas (moles).

$K^*$ Rate of diffusion + absorption of the gas ($m \cdot s^{-1}$).

$A_p$ Surface area of the particle ($m^2$).

$f$ Dissolved gas fugacity ($mol \cdot m^{-3}$).

$f_{EQ}$ Three-phase equilibrium fugacity of the gas ($mol \cdot m^{-3}$).

The process of gas dissolution in the liquid environment is considered through the following expression (ZHENG; YAPA, 2002):

$$ \frac{dn}{dt} = K \cdot A \cdot (C_s - C_0) \qquad (3.28) $$

where:

K Coefficient of mass transfer ($m \cdot s^{-1}$).

A Surface area of the gas normal to flow direction ($m^2$).

$C_s$ Dissolved saturation gas concentration inside the control-volume ($mol \cdot m^{-3}$).

$C_0$ Dissolved gas concentration inside the control-volume ($mol \cdot m^{-3}$).

The main set of derivative mass-balance equations in GAS_DOCEAN model are presented following and more details can be found in Yapa & Zheng (1997).
$$
\begin{align}
\frac{d}{dt}[(m_l + m_b + m_h)u] &= u_a \rho_a Q_e - u \rho_{com} Q_g \nonumber \\
\frac{d}{dt}[(m_l + m_b + m_h)v] &= v_a \rho_a Q_e - v \rho_{com} Q_g \nonumber \\
\frac{d}{dt}[m_l w + (m_b + m_h)(w + w_b)] &= w_a \rho_a Q_e - w \rho_{com} Q_g + \tag{3.29} \\
&\quad + (\rho_a - \rho_l)g\pi b^2 (1 - \beta\epsilon)h + \nonumber \\
&\quad + (\rho_a - \rho_{com})g\pi b^2 \beta^2 \epsilon h \nonumber
\end{align}
$$

where:

$m_l$ Mass of liquid of plume (kg).

$m_b$ Mass of gas of plume (kg).

$m_h$ Mass of hydrates inside the plume (kg).

u Horizontal velocity of plume at x direction (m · s⁻¹).

$u_a$ Ambient horizontal velocity of plume at x direction (m · s⁻¹).

v Horizontal velocity of plume at y direction (m · s⁻¹).

$v_a$ Ambient horizontal velocity of plume at y direction (m · s⁻¹).

w Vertical velocity of plume (m · s⁻¹).

$w_a$ Ambient vertical velocity (m · s⁻¹).

$w_b$ Gas bubbles velocity (m · s⁻¹).

$\rho_l$ Liquid density of plume (kg · m⁻³).

$\rho_a$ Density of ambient seawater (kg · m⁻³).

$\rho_{com}$ Density of hydrates and gas(kg · m⁻³).

$Q_e$ Entrainment water flux (m³ · s⁻¹).

$Q_g$ Gás flux (m³ · s⁻¹).

g Acceleration of gravity (m² · s⁻¹).

b Plume ratio (m).

$\epsilon$ Gas fraction, defined as $\epsilon = (\rho_l - \rho)/(\rho_l - \rho_{com})$.

β Ratio between the bubble core width and the buoyant jet diameter, varies from 0.65 to 0.8

h Depth of control volume (m).

At the deep ocean the gas is considered as non-ideal, so we have:

$$
PM_g = \rho_b F_c R T \tag{3.30}
$$

where:

P Ambient pressure from (Pa).

$M_g$ Gas mol weight (kg · mol⁻¹).
$F_c$ Compress factor.

R Universal gas constant (8,314 J · mol⁻¹ · K⁻¹).

$\rho_b$ Gas density (kg · m³).

T Temperature (K).

In geophysical deep ocean situations, the important independent variables are the total kinematics buoyancy flux (B) and the buoyancy frequency (N), defined by Socolofsky & Adams (2005) as:

$$B = \frac{gQ_B(\rho_a - \rho_b)}{\bar{\rho}_a} \qquad (3.31)$$

$$N_{BV} = \left[ -\frac{g}{\bar{\rho}_l} \left( \frac{\partial \rho_l}{\partial z} \right) \right]^{1/2} \qquad (3.32)$$

where:

B Buoyancy of gas plume (m⁴ · s⁻³).

N<sub>BV</sub> Brunt-Vaisala frequency (s⁻¹).

Q<sub>B</sub> Gas flux (m³ · s⁻¹).

The dimensional analysis performed by Socolofsky & Adams (2005) introduces a single nondimensional number that describes the first-order effects of the dispersed phase:

$$U_N = \frac{U_S}{(B \cdot N)^{1/4}} \qquad (3.33)$$

where:

U<sub>N</sub> Nondimensional velocity.

U<sub>S</sub> Bubble slip velocity (m · s⁻¹).

Asaeda & Imberger (1993) presents three different plume types as observed in laboratory studies and Socolofsky & Adams (2005) identified the behavior of another type of plume (Figure 18). For each kind of plume shape, it is possible to estimate the corresponding U<sub>N</sub> as presented in Table 1 (SOCOLOFSKY; ADAMS, 2005). The plume Type 1* is different to Type 1, defined by:

$$H_T = H + H_A \qquad (3.34)$$
**Figure 18.** Schematic of plume type classification: $H_T$ is trap height of the first peel and $H$ is reservoir depth.

<figure><img src="image_19.png" /></figure>

Source: Socolofsky & Adams (2005)

$H_T$ is the local $H$ depth plus the atmospheric pressure head $H_A$. If the height of the plume trap is higher than $H_T$ (i.e., $h > H_T$) the plume is classified as Type 1. Otherwise if $h < H_T$, the plume has a Type 1* behavior.

<table><caption>**Table 1.** $U_N$ intervals for plume classification</caption><thead><tr><td>$U_N$ range</td><td>Type</td></tr></thead><tbody><tr><td>$0 < U_N < 1.5$</td><td>1</td></tr><tr><td>$0 < U_N < 1.5$</td><td>1*</td></tr><tr><td>$1.5 \le U_N < 2.5$</td><td>2</td></tr><tr><td>$U_N \ge 2.5$</td><td>3</td></tr></tbody></table>

Source: Socolofsky & Adams (2005)

### 3.4.2.2 Parameterization of GAS_DOCEAN model

Table 2 shows the values of the main parameters of the GAS_DOCEAN model.

<table><caption>**Table 2.** Parameterization of GAS_DOCEAN</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>Ratio between the bubble core width and the buoyant jet diameter</td><td>0.8</td></tr><tr><td>Gas density</td><td>5 × 10<sup>-3</sup> kg·m<sup>-3</sup></td></tr><tr><td>Density of hydrates and gas</td><td>912, kg·m<sup>-3</sup></td></tr><tr><td>Initial shear entrainment coefficient</td><td>0.083</td></tr><tr><td>Gas flow</td><td>50 kg·s<sup>-1</sup></td></tr><tr><td>Oil flow</td><td>100 kg·s<sup>-1</sup></td></tr><tr><td>Mass transfer coefficient of dissolution</td><td>10<sup>-9</sup> m·s<sup>-1</sup></td></tr></tbody></table>

Source: Yapa & Chen (2004)
The points P1, P2 and P3 (Figure 19) were selected according to the position of the oil and gas exploration blocks in the north continental shelf of Brazil and the analysis of oil sensitivity charts (SAO charts) of the areas subject to oil spill and blowouts in the region comprising the continental shelves of Amazonas and Pará - Maranhão - Barreirinhas. The Amazon Continental Shelf (ACS) is a high priority area for the conservation of biodiversity (JUNIOR; MAGRINI, 2014; SANTOS; MENDES; SILVEIRA, 2016), the Amazon River mouth represents the limit of the distribution of several sponges, lobster, stony corals and snapper and others shallow water fish, among other groups of coastal and reef organisms (MOURA et al., 2016).

**Figure 19.** The bathymetry and distribution of the slope in the continental shelf northwest of Brazil. The green rectangle represent the Amazon mouth basin and the magenta rectangle represent Pará-Maranhão-Barreirinhas basin. The oil and gas exploration blocks are represented by black polygons. The location of P1, P2 and P3 is represented by blue points above of exploration blocks where P1, P2 and P3 are placed, block FZA-M-88 (P1), block PAMA-M-337 (P2) and block BAR-M-21 (P3). The coral reef appears in red color.

<figure><img src="image_20.png" /></figure>

Source: The author

P1 is located on it, at (50.12°W, 5, 12°N) and belongs to the exploration block FZA-M-88; P2 is in the Pará - Maranhão basin at (44.63°W, 0.38°N), coinciding with the exploration block PAMA-M-337 and P3 it's located in exploration block BAR-M-21 at (42.75°W, 1°S) in the Barreirinhas basin.

The dilution capacity of the effluent overflow will be analyzed in a blowout event at
P1, P2 and P3 as a result of the simultaneous effects of sea currents, winds and surface and subsurface thermodynamic processes acting at the adjacent oceanic area. This analysis will be held through hydrodynamics simulation, mathematical modeling and numeric simulation of the dispersion mechanism acting over the plumes of oil and natural gas in the study region. The simulations of the oil and gas blowouts were performed taking into account a flow of 100 and 50 kg · s⁻¹ respectively (Table 2) and the other parameters were taken from (YAPA; CHEN, 2004).

## 3.5 MIXED LAYER DEPTH (MLD), ISOTHERMAL LAYER DEPTH (ILD) AND BARRIER LAYER THICKNESS (BLT) CRITERION

MLD defined as the depth where the density increases from the surface value due to a prescribed temperature decrease of 0.2°C (ΔT = -0.2°C) from the surface value while maintaining constant surface salinity value. The MLD was mathematically defined by Sprintall & Tomczak (1992) and Montégut et al. (2007) as:

$$ \Delta\sigma = \sigma(T + \Delta T, S, P_0) - \sigma(T, S, P_0) \qquad (3.35) $$

where Δσ is densities difference for the same change in temperature (ΔT) at constant salinity, T, S are the values of temperature and salinity at ZREF (reference depth in the temperature and salinity vertical profiles) and P₀ is the pressure at the ocean surfaces.

In this study we consider ZREF = 5 m, also used by Hounsou-Gbo et al. (2016) and different from that used by other authors, e.g. Montégut et al. (2007), this value was chosen because in the region of the Atlantic the MLD can be found at depths less than 10 m; and in the outputs of the RRF and NRF experiments we have 32 vertical levels, corresponding the level 32 to the ocean surface and the level 31 to 4.8 m depth. The ILD is the depth at which the temperature is equal to T + ΔT.

The Barrier Layer (BL) prevents heat exchange between the Oceanic Mixed Layer (OML) and deeper water, influencing the SST, ensuring greater isolation of the OML, while thicker it is, less heat exchange will exist between deep water and the OML. The BLT can be calculated according Montégut et al. (2007) as:

$$ BLT = ILD - MLD $$

## 3.6 OCEANIC HEAT CONTENT (OHC) CRITERION

The transfer of mass, momentum and energy through the mixing layer is the source of almost all oceanic movements, and its thickness determines the heat content and the mechanical
inertia of the layer that interacts directly with the atmosphere (MONTÉGUT et al., 2004). Changes in oceanic heat content play an important role in sea level rise due to thermal expansion. The quantity of energy stored per unit area in the ocean (OHC) between levels $Z_{REF}$ and $h$ is defined according to Jayne, Wahr & Bryan (2003) as:

$$OHC = \rho_0 C_p \int_{Z_{REF}}^{h} T(Z) dZ$$

where: OHC is the Oceanic Heat Content in $J m^{-2}$, $\rho_0 = 1025 kg m^{-3}$ is the density of seawater at the sea surface, $C_p = 4 \cdot 10^3 J (kg^{-\circ} C)^{-1}$ is the specific heat of seawater at constant pressure at the sea surface, according to Levitus, Antonov & Boyer (2005), $T(Z)$ is the potential temperature (°C), $Z$ is the depth (m) and $Z_{REF} = 5 m$.

As the depth increases, the temperature oscillation decreases and below the active ocean layer, there are practically no annual variations in temperature, so we are only going to study the quantity of heat in the active layer of the ocean, numerically integrating the temperature in each vertical profile in the grids of the RRF and NRF experiments, from $Z_{REF}$ to $h = ILD$. For the determination of MLD, ILD, BLT and OHC, the temperature and salinity are linearly interpolated every 1 m depth from $Z_{REF}$, following the procedures and equations described above.
# 4 HYDRODYNAMIC MODEL: RESULTS AND DISCUSSIONS

In this chapter the following results are detailed:

* Hydrodynamical model: Two hydrodynamical simulations are carried out with the ROMS model, in the first one (RRF experiment), the release of freshwater from the Amazon and Pará rivers in the tropical Atlantic is taken into account; and the second one (NRF experiment) is supposed not to release freshwater.

* Validation of model results with rivers: The salinity, temperature and currents of the ROMS model (RRF experiment) are compared with the SODA, PIRATA and SCUD datasets.

* Influence of rivers on WTNA: The variations produced by the rivers in the SST, SSS, MLD, ILD, BLT and OHC fields are quantified, finally, the NECC offset is determined due to the influence of the rivers.

These results correspond to the article "Amazon River plume influence in the western Tropical Atlantic dynamic variability" that was submitted in the Dynamics of Atmospheres and Oceans journal.

## 4.1 VALIDATION OF THE HYDRODYNAMIC MODEL

The difference of SSS between the model simulation with river (RRF) and SODA is shown in figure 20. Modeled mean SSS present lower salinities than SODA in the area of the NBC retroflection mainly during April to June. From September to December, the lower salinities are following the NECC.
<figure><img src="image_21.png" /><figcaption>**Figure 20.** Mean monthly cycle of the difference between SSS (psu) of RRF experiment and SODA dataset.</figcaption></figure>

Source: The author

Table 3 (columns 1 and 2) shows a summary of the seasonal cycles averaged for the area REG2 (defined in figure 12). The SSS maximum difference is from June to August (0.27 *psu*) and a minimum difference is from March to May (0.06 *psu*).
<table><caption>**Table 3.** Comparison between the SSS RRF and SODA in REG2, area defined in figure 12. In the first rows mean value ± standard deviation and in the second rows minimum – maximum.</caption><thead><tr><th></th><th>SODA<br>(psu)</th><th>RRF<br>(psu)</th><th>SODA<br>(°C)</th><th>RRF<br>(°C)</th></tr></thead><tbody><tr><td>DJF</td><td>35.86 ± 0.02<br>(35.56 – 36.10)</td><td>35.63 ± 0.07<br>(34.94 – 36.19)</td><td>26.90 ± 0.04<br>(26.02 – 27.48)</td><td>28.17 ± 0.14<br>(26.47 – 29.12)</td></tr><tr><td>MAM</td><td>36.09 ± 0.02<br>(35.87 – 36.32)</td><td>36.15 ± 0.01<br>(35.81 – 36.47)</td><td>26.74 ± 0.10<br>(25.60 – 27.61)</td><td>27.05 ± 0.27<br>(25.73 – 28.31)</td></tr><tr><td>JJA</td><td>35.82 ± 0.03<br>(35.43 – 36.15)</td><td>36.09 ± 0.05<br>(35.46 – 36.51)</td><td>27.77 ± 0.07<br>(27.15 – 28.30)</td><td>27.77 ± 0.23<br>(26.27 – 28.84)</td></tr><tr><td>SON</td><td>35.41 ± 0.07<br>(34.89 – 35.87)</td><td>35.23 ± 0.13<br>(34.19 – 36.26)</td><td>28.26 ± 0.04<br>(27.84 – 28.74)</td><td>28.63 ± 0.13<br>(27.63 – 29.69)</td></tr><tr><td>Annual</td><td>35.79 ± 0.03<br>(35.44 – 36.11)</td><td>35.78 ± 0.08<br>(35.10 – 36.36)</td><td>27.42 ± 0.07<br>(26.65 – 28.03)</td><td>27.91 ± 0.19<br>(26.53 – 28.99)</td></tr></tbody></table>

Source: The author

The difference of SST between the model simulation with river (RRF) and SODA is shown in figure 21. Modeled mean SST present higher temperatures than SODA in the area of the NBC retroflection, mainly during October to February and also in the NECC area. The cause of this large seasonal variation is assumed to be a dynamic adjustment due to changes in wind forcing over the tropical Atlantic and both local and remote wind stress that may play a role in the SST variability (JOHNS et al., 1998; BOURLES; GOURIOU; CHUCHLA, 1999b; SHARMA et al., 2009).
<figure><img src="image_22.png" /><figcaption>**Figure 21.** Mean monthly cycle of the difference between SST (°C) of RRF experiment and SODA dataset.</figcaption></figure>

Source: The author

The Table 3 (columns 3 and 4) resume the main results of modeled SST and SODA, evidencing higher difference in December to February, when we have the plume feeding the NECC. The RRF is well adjusted in June to August.

The figure 22 shows the comparison of RRF simulation and PIRATA salinity and temperature profiles. The modeled salinity at the position 8°N 38°W (Figure 22(a)) shows similar vertical structure, mainly from August to December, period of lower salinities from the plume. The main differences are from June to October, mainly in the first 40 m, which is coincident with the period that the freshwater of the Amazon plume flows into the NECC (COLES et al., 2013; GRODSKY et al., 2014).
<figure><img src="image_23.png" /><figcaption>**Figure 22.** Hovmüller diagram of RRF (red dashed lines) and PIRATA buoy (blue solid lines), monthly mean calculated from 2000 to 2015 at 38°W8°N (a) salinity vertical profile (psu) and (b) temperature vertical profile (°C) and at 38°W12°N (c) salinity vertical profile (psu) and (d) temperature vertical profile (°C).</figcaption></figure>

Source: The author

In order to compare the vertical profiles of salinity and temperature of the RRF experiment with the PIRATA dataset, we used the two-sample t-student test. Prior to performing the t-test, data were normalized by dividing each profile by its norm, since the initial dataset showed a non-normal distribution (one-sample Kolmogorov-Smirnov test). The t-student test also no statistically significant differences were found between salinity vertical profile of RRF experiment and PIRATA dataset ($p = 0.9966, \alpha = 0.05$). The temperature vertical profile is well adjusted to the measurements (Figure 22(b)). However, the RRF underestimate the measurements between 80 and 180 m depth. There were no significant differences between potential temperature of RRF experiment and PIRATA dataset ($p = 0.8287, \alpha = 0.05$).

At the position 38°W12°N (Fig. 22(c)), the vertical profile of modeled salinity is consistent with measurements, with mean difference of 0.4 psu. No significant differences
were found between potential salinity of RRF experiment and PIRATA ($p = 0.9857, \alpha = 0.05$). The temperature vertical structure is similar to the measurement along the year (Figure 22(d)), With main differences between 100 – 180 m. The main differences found in these results are limited by the thermocline depth. The t-student test also did not show significant differences ($p = 0.8137$) for a significance level of 0.05.

The NECC is the main current that transports the Amazon plume eastward (GRODSKY et al., 2014). We compare the resulting zonal components in the RRF simulation in the area REG2 (Figure 23(a)), associated to the NECC pathway, with SCUD zonal components (Figure 23(b)). The values of the zonal component are gradually decreasing in the RRF experiment, from 0.3 to $0.2 \text{ ms}^{-1}$, from July to October, between 4.5 and $9.5^\circ \text{N}$. The maximum difference with SCUD was found between 5.5 and $6.5^\circ \text{N}$ in July and between 4 and $5^\circ \text{N}$ in October (Figure 23(b)), being $0.2 \text{ ms}^{-1}$. The mean differences are $0.1 \text{ ms}^{-1}$. These results reveal the RRF simulation is representing quite well the dynamics of the NECC variability.

<figure><img src="image_24.png" /><figcaption>**Figure 23.** Hovmüller diagram of the zonal component in REG2 (a) RRF experiment, (b) SCUD dataset</figcaption></figure>

Source: The author

We also calculated the average of the zonal component in WNECC (framed in $50^\circ - 40^\circ \text{W}/5^\circ - 8^\circ \text{N}$) and ENECC (framed in $30^\circ - 25^\circ \text{W}/5^\circ - 8^\circ \text{N}$) regions, in the boreal fall, being $0.384 \text{ ms}^{-1}$ and $0.226 \text{ ms}^{-1}$ respectively. Similar averages in the same regions were reported by Richardson & Reverdin (1987), being $0.410 \text{ ms}^{-1}$ and $0.215 \text{ ms}^{-1}$ respectively.

Figures 24(a) and (b) show the monthly mean differences between the zonal and meridional components of ROMS model and SODA dataset at $38^\circ \text{W}, 8^\circ \text{N}$. The zonal component of ROMS at the surface is $0.1 \text{ m} \cdot \text{ s}^{-1}$ higher than SODA, in January and from July to October, conversely SODA is stronger $0.1 \text{ m} \cdot \text{ s}^{-1}$, in March from 600 m to just over 1000 m; and in
May and November around 3500 m. In the meridional component the biggest differences are found in the first 250 m, from April to June and August, reaching a little more than 500 m in March. In December ROMS is $0.1 \cdot m \cdot s^{-1}$ higher than SODA. Predominating the differences between $-0.05 \cdot m \cdot s^{-1}$ and 0 for both components.

Figures 24(c) and (d) show the monthly mean differences between the zonal and meridional components of ROMS model and SODA at 38°W, 12°N. For both components the maximum variation range of this difference is between $-0.13, m s^{-1}$ and $0.12, m s^{-1}$, locating the extreme values only in the first 500 m, from this depth the difference oscillates between $-0.05, m s^{-1}$ and $0.07, m s^{-1}$, being the ROMS model consistent with SODA.

<figure><img src="image_25.png" /><figcaption>**Figure 24.** Monthly mean differences between the vertical profile of (a) zonal ($m s^{-1}$) and (b) meridional components ($m s^{-1}$) at 38°W, 8°N, the vertical profile of (c) zonal ($m s^{-1}$) and (d) meridional components ($m s^{-1}$) at 38°W, 12°N.</figcaption></figure>

Source: The author
## 4.2 INFLUENCES OF THE AMAZON AND PARÁ RIVERS ON HYDRODYNAMICS

In the figure 25, the seasonal cycles of SSS differences are compared in the RRF and NRF experiments. The RRF experiment shows lower salinities confined to the coast from December to February. From March to May, the RRF experiment shows lower salinities in the NBC retroflection area, from June to August the plume spreads northward and from September to November the plume is eastward along the NECC. The RRF experiment is 10 – 12 *psu* lower along the coast than NRF, which represents well the seasonal cycle of the Amazon freshwater discharge into the WTNA. In the NECC area the RRF create a lower SSS area of 4 *psu*. These results are in agreement with others authors (COLES et al., 2013; KOROSOV; COUNILLON; JOHANNESSEN, 2015; NEWINGER; TOUMI, 2015).

<figure><img src="image_26.png" /><figcaption>**Figure 25.** Mean seasonal cycle of difference of SSS between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November).</figcaption></figure>

Source: The author

There is no significant change in SST, except near the Amazon River mouth (Figure 26). The differences show variable river temperatures (0 – 2 °C) at the left side of the Amazon mouth from September to November. In the open ocean the SST changes are not sensitive to the river temperature. These results are in agreement with others authors (NEWINGER; TOUMI, 2015).
<figure><img src="image_27.png" /><figcaption>**Figure 26.** Mean seasonal cycle of difference of SST between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November).</figcaption></figure>

Source: The author

Figure 27 shows the differences between RRF and NRF velocities of surface currents. The seasonal cycle shows a strong impact of the river plume on the WTNA. These strongest velocities are from June to November. From September to November a well-defined rings structure eastward is highlighted. These differences emphasize the role of the Amazon plume in the dynamics of the NBC retroflection as well as in the NBC rings into the NECC, with maximum differences of 1 ms⁻¹.
**Figure 27.** Mean seasonal cycle of difference of surface currents between RRF and NRF simulations. Boreal winter (DJF-December, January, February), boreal spring (MAM-March, April, May), boreal summer (JJA-June, July, August), and boreal fall (SON-September, October, November).

<figure><img src="image_28.png" /></figure>

Source: The author

Comparing the zonal component of RRF and NRF experiments (Figure 28(a) RRF and (b) NRF), similar patterns are present in the zonal current intensities, reaching a maximum value of 0.5 ms⁻¹. These areas have a phase shift, in the RRF experiment the maximum value appears in February (between 7° and 8°N), from middle of August to end of September and from middle October to middle November.
**Figure 28.** Comparison of zonal component between RRF and NRF simulations in REG1, area defined in figure 12. The black arrow represents the phase shift of the zonal component of the current.

<figure><img src="image_29.png" /></figure>

Source: The author

In the NRF experiment (Figure 28) a phase shift exists. From January to February the maximum values are similar to the RRF experiment (between 6.5° and 7.5°N). However, in the second part of the year the strongest velocities occur after September, lagging in two months relating to the RRF experiment, where the maximum values start in August. This phase shifts in the second part of the year reveals that the river plume changes the seasonal cycle of the zonal currents.

Figure 29 shows how the OML is shallower in the RRF experiment than in the NRF, due mainly to the low-density layer formed by the freshwater input discharged by the rivers. The MLD in the RRF experiment is 20 – 50 m shallower over the entire extension of the plume. The MLD minimum for the RRF experiment is 6 m throughout the year and the maximum fluctuates between 88 – 102 m, being deeper in the SON period, while for the NRF experiment the MLD minimum is between 6 – 22 m and the maximum oscillates between 99 – 120 m, found the most extreme values in the SON period.
<figure><img src="image_30.png" /><figcaption>**Figure 29.** Mean seasonal cycle of difference in MLD (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November).</figcaption></figure>

Source: The author

Figure 30 shows the spatial distribution of ILD between the RRF and NRF experiments, here we also find that the ILD is 20 – 50 m shallower in the RRF experiment, mainly in the periods JJA and SON. In the variation of ILD there is a clear influence of SST, being up to 1 °C higher in the RRF experiment (Figure 26).
<figure><img src="image_31.png" /><figcaption>**Figure 30.** Mean seasonal cycle of difference in ILD (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November).</figcaption></figure>

Source: The author

Figure 31 shows the spatial distribution of the difference of BLT between the RRF and NRF experiments. The discharge of fresh water from the rivers plays a fundamental role in the formation of BL, following the extension of the plume. In the NRF experiment, the BL is almost non-existent in the extension of the plume, when the maximum thickness of the BL is at the mouth of the river and extending northwestward, gradually decreasing its thickness as it moves away in the same direction of the river discharge, mainly in the MAM and JJA periods. In SON the BL extends towards the Northwest and then makes a turn to the East accompanying the plume and the NECC. In the NRF experiment we can find 100% of the BLT between 1 – 35 m. In the RRF experiment the BLT reaches 82 – 94 m in the periods DFJ, MAM and JJA and up to 110 m in the SON period. A similar result was reported by Pailler, Bourlès & Gouriou (1999).
**Figure 31.** Mean seasonal cycle of difference in BLT (m). Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November). The nodes of the grid where the thickness of the layer is less than 10% of the maximum depth (ILD or MLD) are shown with value 0 and in white color.

<figure><img src="image_32.png" /></figure>

Source: The author

It was calculated the OHC between $Z_{REF}$ and ILD, the biggest difference was between -0.7 and -0.3 × 10¹⁰ J m⁻², storing more energy in the NRF experiment, mainly in the periods MAM, JJA and SON (Figure 32). These differences stand out fundamentally in the region near the nodes of the grid and northwest region in the periods MAM and JJA; in the SON period the biggest difference is observed in the region of the plume extension eastward, the opposite phenomenon is also highlighted in the same direction, coinciding with the maximum values of the BLT near river mouth and with the retroflection, with higher energy stored in that region in the experiment RRF. The largest accumulation of energy in the NRF experiment was from 1.1 to 1.3 × 10¹⁰ J m⁻², while in the RRF experiment it was from 1.0 to 1.2 × 10¹⁰ J m⁻², with maximum difference of 0.1 × 10¹⁰ J m⁻². Variations in ILD are the main factor influencing the OHC difference between the RRF (shallower) and NRF experiments.
<figure><img src="image_33.png" /><figcaption>**Figure 32.** Mean seasonal cycle of difference in OHC(J m⁻²) integrated from ZREF to ILD. Boreal winter (DJF - December, January, February), boreal spring (MAM - March, April, May), boreal summer (JJA - June, July, August), and boreal fall (SON - September, October, November).</figcaption></figure>

Source: The author
# 5 DEEPWATER OIL/GAS BLOWOUTS SIMULATIONS: RESULTS AND DISCUSSIONS

This chapter presents the results of the temporal evolution of plumes generated from oil/gas blowouts at points located on the continental shelf of the northern coast of Brazil. These results correspond to the article "Influence of underwater hydrodynamics on oil and gas blowouts off Amazon River mouth" that was accepted by the Tropical Oceanography journal.

In order to perform the numerical simulations, the GAS_DOCEAN model was used, which has three-dimensional fields of marine currents, temperature and salinity as input. These three three-dimensional fields were obtained from the RRF experiment.

Before running the GAS_DOCEAN model, it was necessary to evaluate the temperature and current speed in the vertical profiles of the ROMS model at points P1, P2 and P3. Resulting in good agreement when compared with the SODA dataset.

Figure 33(a) shows the vertical profiles of the temperature at point P1 of the SODA dataset and the ROMS model in the DJF and JJA periods. The vertical profiles of the temperature are better adjusted below 300 m depth in both periods. In depths above 300 m the ROMS model overestimates the temperature and the main differences range between 0.7 to 1.7°C.
<figure><img src="image_34.png" /><figcaption>**Figure 33.** (a) Temperature and (b) current speed vertical profiles in DJF (December-January-February) and JJA (June-July-August) periods for SODA and ROMS at point P1.</figcaption></figure>

Source: The author

In JJA period there is a maximum difference of 0.04 $ms^{-1}$ below 300 m and above this depth, the average difference was 0.17 $ms^{-1}$ with a maximum difference of 0.21 $ms^{-1}$ from 150 to 180 m depth (Figure 33(b)). The profile of the current speed is well adjusted below the 300 m depth in the DJF period. The maximum difference in the DJF period was 0.18 $ms^{-1}$ on the surface.

Once the results of the ROMS model were validated, the GAS_DOCEAN model it ran with the parameters summarized in table 2. In the interest of improve the understanding of the results of oil/gas plumes simulations, the figure 34(a) shows the mean seasonal velocity of the marine current, averaged between the surface and 100 m depth.
**Figure 34.** ROMS output of mean seasonal cycle of the currents measured (a) between the surface and 100 m depth; and (b) between 1000 and 1200 m depth during the winter (DJF-December, January, February), spring (MAM-March, April, May), summer (JJA-June, July, August), and fall (SON-September, October, November). The centers of the red circle represent the positions of the simulation points P1, P2 and P3.

<figure><img src="image_35.png" /></figure>

Source: The author

The most intense currents form a wide band and confined to the coastline, corresponds to the NBC. This current is more intense in the winter especially over the northwest part of the coast, where it turns toward the east (following the NBC retroflection), reaching speeds higher than 0.9 $ms^{-1}$. In the boreal spring, we found the less intense currents of the whole year with maximum values eastward of the Amazon River mouth, reaching up to 0.7 $ms^{-1}$. In the boreal summer, the NBC velocities vary from 0.5 $ms^{-1}$ to speeds higher than 0.9 $ms^{-1}$. In the autumn, as in the winter, the eastward turning appears, better defining the NBC retroflection. Higher speeds are found along the coast more to the northwest and in the NBC retroflection, oscillating the current speed from 0.5 $ms^{-1}$ to speeds higher than 0.9 $ms^{-1}$.

The center of the red circles represents the positions of the P1, P2 and P3 simulation points. In winter the average speed is 0.25 $ms^{-1}$, at P1, extremely low (0.01 ms$^{-1}$) at P2 and it reaches 0.15 $ms^{-1}$ at P3. In the spring, we find the lowest speeds of the year at P1, P2 and P3, oscillating between 0.01 and 0.25 $ms^{-1}$. In the boreal summer and autumn at P2 and P3, current speeds reach the minimum value (0.01-0.15 $ms^{-1}$), increasing at P1 with respect to spring.

Figure 34(b) shows the mean seasonal behavior of currents dynamic between 1000 and
1200 m depth. In general, at these depths the currents are very slow, oscillating their speed between 0.01 and 0.15 ms⁻¹. These currents are slightly less intense in the spring and a little more intense in the fall, mainly above 4°N and between 47 and 50°W; and between 0.5-2°N and 42-45°W, reaching 0.15 ms⁻¹, moving this last pattern towards the southeast in the winter.

In the winter we find speeds of 0.15 ms⁻¹ at P3 and between 0.01-0.03 ms⁻¹ at P1 and P2. The least intense currents are in the spring at all 3 points (0.03-0.04 ms⁻¹). Similar speeds are found at P2 and P3 in the summer, increasing slightly at P1 to 0.06 ms⁻¹. In the autumn, speeds at P3 do not differ from the summer, being somewhat lower at P1 and reaching up to 0.15 ms⁻¹ at P2.

## 5.1 OIL AND GAS PLUMES EVOLUTION

Figure 35 shows the monthly evolution of oil/gas plumes at P1. During the entire evaluated period, the plumes were type 3, with exception to September, where they reached the maximum entrainment below 1000 m depth. Above this level, the radius of the plumes began to decrease gradually until reaches the surface, oscillating between 54-76.5 m. The plumes reached the largest radius in August, November and December and the lowest radius was observed between May-July (table 4).
**Figure 35.** Oil/gas plumes evolution in the middle of each month (simulation day 15) at P1. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south.

<figure><img src="image_36.png" /></figure>

Source: The author

The largest displacements of the plume from the blowout point were approximately 1 m in January and May. The mean arrival time of the oil/gas plumes to the surface was *7.99 hours* and difference between the months was minimal.

Figure 36 shows the monthly evolution of the oil/gas plumes at P2. As already verified in P1, all the plumes are of type 3. All the plumes reach their maximum entrainment
<table><caption>**Table 4.** Monthly radius and displacement of oil/gas plumes at points P1, P2 and P3</caption><thead><tr><th rowspan="2"></th><th colspan="3">P1</th><th colspan="3">P2</th><th colspan="3">P3</th></tr><tr><th>Mean radius (m)</th><th>Displacement (m)</th><th>Evolution time (hours)</th><th>Mean radius (m)</th><th>Displacement (m)</th><th>Evolution time (hours)</th><th>Mean radius (m)</th><th>Displacement (m)</th><th>Evolution time (hours)</th></tr></thead><tbody><tr><td>Jan</td><td>56.4</td><td>(0.71,-0.70)</td><td>8.04</td><td>75.5</td><td>(-0.30,0.20)</td><td>7.26</td><td>58.9</td><td>(0.37,-0.32)</td><td>6.30</td></tr><tr><td>Feb</td><td>65.3</td><td>(0.50,-0.45)</td><td>7.97</td><td>60.1</td><td>(-0.35,0.26)</td><td>7.25</td><td>58.7</td><td>(-0.13,0.22)</td><td>6.30</td></tr><tr><td>Mar</td><td>62.1</td><td>(0.71,-0.71)</td><td>8.06</td><td>54.1</td><td>(-0.33,0.24)</td><td>7.25</td><td>58.7</td><td>(-0.09,0.23)</td><td>6.30</td></tr><tr><td>Apr</td><td>63.3</td><td>(0.36,-0.36)</td><td>7.96</td><td>58.4</td><td>(0.14,-0.15)</td><td>7.26</td><td>58.7</td><td>(-0.19,0.26)</td><td>6.30</td></tr><tr><td>May</td><td>54.5</td><td>(0.69,-0.73)</td><td>8.05</td><td>60.7</td><td>(-0.10,0.15)</td><td>7.25</td><td>58.8</td><td>(0.20,-0.18)</td><td>6.30</td></tr><tr><td>Jun</td><td>54.0</td><td>(0.30,-0.28)</td><td>7.95</td><td>55.3</td><td>(-0.52,0.34)</td><td>7.26</td><td>58.8</td><td>(0.18,0.24)</td><td>6.30</td></tr><tr><td>Jul</td><td>54.3</td><td>(0.38,-041)</td><td>7.96</td><td>73.1</td><td>(-0.54,0.32)</td><td>7.27</td><td>58.8</td><td>(0.10,-0.03)</td><td>6.30</td></tr><tr><td>Aug</td><td>74.1</td><td>(-0.24,0.22)</td><td>7.96</td><td>61.0</td><td>(-0.56,0.30)</td><td>7.26</td><td>58.8</td><td>(-0.44,0.64)</td><td>6.33</td></tr><tr><td>Sep</td><td>60.3</td><td>(-0.02,-0.01)</td><td>7.96</td><td>56.5</td><td>(-0.47,0.25)</td><td>7.26</td><td>58.7</td><td>(-0.28,0.36)</td><td>6.30</td></tr><tr><td>Oct</td><td>61.4</td><td>(0.35,-0.33)</td><td>7.97</td><td>79.5</td><td>(-0.44,0.26)</td><td>7.25</td><td>58.7</td><td>(-0.39,0.47)</td><td>6.31</td></tr><tr><td>Nov</td><td>70.6</td><td>(0.36,-0.24)</td><td>7.97</td><td>54.5</td><td>(-0.42,0.19)</td><td>7.25</td><td>58.7</td><td>(-0.19,0.32)</td><td>6.30</td></tr><tr><td>Dec</td><td>76.5</td><td>(0.54,-0.69)</td><td>8.02</td><td>79.7</td><td>(-0.26,0.16)</td><td>7.26</td><td>58.7</td><td>(-0.37,0.55)</td><td>6.32</td></tr></tbody></table>

Source: The author
below 1000 m, decreasing their radius until they reach the surface (54.1-79.7 m). The largest diameters in the surface corresponded to the months of January, October and December. The largest displacements of P2 plume occurred from June to August and were approximately 0.64 m (table 4). The average time of arrival at the surface was 7.26 hours.

**Figure 36.** Oil/gas plumes evolution in the middle of each month (simulation day 15) at P2. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south.

<figure><img src="image_37.png" /></figure>

Source: The author

The pattern of oil/gas plume evolution already observed at the points P1 and P2 (type
3) was also verified at P3 (Figure 37). The plumes at P3 reaching its largest entrainment below 1000 m depth except for the months of May and July, where the diameter at the surface was almost invariant during all months (58.7-58.9 m). As shown in table 4, the displacement of the plumes from its point of origin occurred in August and was 0.78 m. The plumes evolution time was practically the same, oscillating between 6.30 and 6.33 hours.

<figure><img src="image_38.png" /><figcaption>**Figure 37.** Oil/gas plumes evolution in the middle of each month (simulation day 15) at P3. The solid lines represent the west (-) and east (+) directions. The dashed lines represent the north (-) and south (+) directions. The red color is the displacement of the plumes from the bottom. The black color represents the radius to the west and north. The blue color represents the radius to the east and south.</figcaption></figure>

Source: The author
Figure 38(a) shows the vertical profiles of the current velocity for March at point P1 and for November at point P3. In both profiles, the plume simulations show that the maximum entrainment of these were reached below 1000 m depth (Figure 35 and figure 37). The bottom speed of points P1 and P3 is greater than 0.1 $ms^{-1}$ and less than 0.2 $ms^{-1}$, thus maintaining the entire water column up to 200 m depth. This behavior is very similar to the rest of the profiles at all points, with the exception of September, at point P1, and of May and July, at point P3.

<figure><img src="image_39.png" /><figcaption>**Figure 38.** Vertical profiles of the current speed (a) at P1 (March) and P3 (November) and (b) at P1 (September) and P3 (May and July).</figcaption></figure>

Source: The author

In September, at P1 (Figure 38(b)), the current speed at the bottom was almost zero (approximately 0.02 $ms^{-1}$). From the bottom, the velocity grew very slowly as the depth decreased to 1000 m (0.12 $ms^{-1}$). The speed began to increase a little faster from 1000 m depth to the surface, which means that the maximum entrainment was reached between 900 and 1000 m depth. In May at P3 (Figure 38(b)) the behavior of the plume in the bottom was also almost zero, but the increase in speed began near the 1500 m depth, which was much slower than in the previous case. Up to almost 200 m depth the speed did not exceed 0.2 $ms^{-1}$ and, above that, where the plume reached its maximum entrainment, it began to grow sharply until exceeding 0.5 $ms^{-1}$ on the surface. At this same point, in July (Figure 38(b)), the current speed was less than 0.1 $ms^{-1}$ and maintained that value up to 1500 m depth. It began to decrease to approximately 850 m depth and then, it increased from above this depth, reaching its maximum entrainment.

Using the coefficient 0.2 in the equation 3.23 did not get good results because the bottom current speed at the three points was very small, $|V_0| \to 0$, which this implied that $\Delta t \to \infty$. Thus it was necessary to adjust the coefficient to estimate $\Delta t$. The equation 5.1 below was then
considered

$$ \Delta t = \begin{cases} 0.025 b_0/|V_0| & \text{for P1 and P2} \\ 0.0375 b_0/|V_0| & \text{for P3} \end{cases} \qquad (5.1) $$

where $\Delta t$ is the time step in $s$, $b_0$ is the ratio of initial control-volume in $m$ and $V_0$ is the initial blowout velocity in $ms^{-1}$.
# 6 CONCLUSIONS

In the first place, this study quantify how much the Amazon plume impacts on the dynamics of the Western Tropical North Atlantic. We investigate the role of Amazon and Pará River plumes in the temperature, salinity and dynamics of the main surface currents, as the North Brazil Current retroflection, rings and North Equatorial Countercurrent, using a regional ocean model with and no-river input.

The rivers freshwater impact on the WTNA is evident in the SSS fields. The seasonal cycle of the experiment with rivers is in good agreement with profiles of the PIRATA buoys and with spatial distribution of satellite and reanalysis products. Compared to some previous studies about salinity fields in the region of the WTNA, we find similar patterns of the plume distribution, as the salinity, temperature and mixed layer depth values (COLES et al., 2013; KOROSOV; COUNILLON; JOHANNESSEN, 2015; NEWINGER; TOUMI, 2015). The structure of the SSS on the area of the NBC retroflection and NECC is clearly identified in the seasonal cycle, showing a confinement of the lower salinities close to the coast from December to February and spreading eastward along the NECC region from September to November.

The SST fields don't show significant changes, except near the Amazon River mouth. A warm core of SST is concentrated at the left side of the Amazon mouth from September to November, following the NBC retroflection area. This river output warming core is due to the influence of the river temperature. However, in the open ocean, SST changes are not sensitive to the river temperature. The seasonal cycle of the differences in the experiments with river and no-river is stronger from October to November.

The seasonal cycle of the differences between RRF and NRF experiments in the surface current fields show a strong impact of the river plume on the WTNA dynamics. The strongest velocities are from June to November and a well-defined rings structure eastward is highlighted from September to November. The differences in the surface currents emphasize the role of the Amazon plume in the dynamics of the NBC retroflection, as well as in the NBC rings following the NECC. The experiment with river increase the surface currents in $1 \text{ ms}^{-1}$ compared to the experiment with no-river.

In the comparisons of zonal components of RRF and NRF experiments we found similar patterns in the zonal current intensities, reaching a maximum value of $0.5 \text{ ms}^{-1}$. However, the maximum values in the second semester of the year show a phase delay of the experiment NRF
relating to the RRF. The zonal component of the NRF lags the RRF in two months, with strongest
values occurring after September. This phase shifts in the second part of the year reveals that the
river plumes change the period of maximum intensities of the zonal currents, anticipating the
seasonal cycle.

The MLD and ILD in the RRF experiment is 20–50 m shallower over the entire extension of the plume. The discharge of fresh water from the rivers plays the fundamental role in the formation of BL. The maximum thickness of the BL is at the mouth of the rivers and extending northwestward, gradually decreasing its thickness as it moves away following the plume, mainly in the MAM and JJA periods. In SON, the plume extends northwestward and then retroflects eastward accompanying the plume and the NECC.

In the RRF experiment less energy is accumulated than in the NRF, there being a
maximum difference of the OHC of 0.1 × 10¹⁰ J m⁻² between both experiments, mainly due to
the variations of the ILD, being shallower in the RRF experiment.

In this work, the physical properties, as the dynamic variability of the Amazon River
plume are well represented by the ocean regional modeling. The results with-river and no-river
show a significative difference of the thermodynamic at the Amazon plume. The SSS spatial
pattern is much altered by the river presence, reducing the salinity in about 8 psu.

Besides, the surface currents are intensified with the river input. The main difference is
along the plume trajectory, where strong velocities are found. Other important characteristic
are the rings formation. Considering river input, the presence of the Amazon rings are evident,
highlighting the importance of the river in the rings dynamic into the WTNA region.

The formation and intensification of these rings due to the presence of the river, as well as
the low salinities, evidence the role of the river in the dynamics, stratification and its contribution
to heat transport in the WTNA.

As a summary, figure 39 shows a diagram of the logical sequence in which the processes
described above in the study area are manifested.
<figure><img src="image_40.png" /><figcaption>**Figure 39.** Outline of the logical sequence of oceanic processes due to the effect of the Amazon and Pará rivers in WTNA</figcaption></figure>

Source: The author

In the second place, the behavior of the oil/gas plumes of the deepwater blowout, located on the continental shelf of northern Brazil, was analyzed. Three parameters were estimated, the time of arrival at the surface, the plume radius on the surface and the deviation at surface from its origin.

All the plumes were type 3. At P1 the mean radius at the surface varied between 54–76.5 *m*, displacement the plume approximately 1 *m* from its origin in the bottom, the average time it delayed to reach the surface was 7.99 *hours*, this time was a little lower in P2, delaying 7.26 *hours*, the greatest distance displaced from its point of origin was 0.64 *m* and its average radius on the surface ranged from 54.1 – 79.7 *m*. At P3 the displacement of the plume with respect to its origin was 0.78 *m*, at this point the mean radius on the surface and the time of evolution to the surface of the plume remained almost invariant, oscillating between 58.7–58.9 *m* and 6.30 – 6.33 *hours* respectively. The little displacement of the plume with respect to their origin is due to the low speeds in the vertical profile.

To obtain good results in the numerical simulations of the plumes, it was necessary to adjust the coefficient for computation $\Delta t$. The equation suggested by Lee & Cheung (1990) will be modified as $\Delta t = 0.025 b_0/|V_0|$ for P1 and P2; and $\Delta t = 0.0375 b_0/|V_0|$ for P3.
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A PAPER "INFLUENCE OF UNDERWATER HYDRODYNAMICS ON OIL AND GAS BLOWOUTS OFF AMAZON RIVER MOUTH"

This annex presents the manuscript entitled *Influence of underwater hydrodynamics on oil and gas blowouts off amazon river mouth*, submitted Feb 21, 2018 in *Tropical Oceanography*.
Current status: Accepted.

the main objective is to determine the behavior of the oil/gas plumes of the deepwater blowout, located on the continental shelf of northern Brazil, was analyzed. Three parameters were estimated, the time of arrival at the surface, the plume radius on the surface and the deviation at surface from its origin.
<figure><img src="image_41.png" /></figure>

Tropical Oceanography
ISSN 1679-3013 (online) / ISSN 1679-3005 (print)

# INFLUENCE OF UNDERWATER HYDRODYNAMICS ON OIL AND GAS BLOWOUTS OFF AMAZON RIVER MOUTH

Humberto L. VARONA<fnref n="1" />,<fnref n="2" />*; Marcus A. SILVA<fnref n="1" />,<fnref n="2" />; Dóris VELEDA<fnref n="1" />,<fnref n="2" />; Fabiana S. LEITE<fnref n="1" />,<fnref n="2" />; Márcio das Chagas MOURA<fnref n="3" />; Moacyr ARAUJO<fnref n="1" />,<fnref n="2" />

**RESUMO.** O estudo está focado na análise do comportamento das plumas de vazamento de óleo/gás em águas profundas, localizadas na plataforma continental do norte do Brasil. O modelo Regional Ocean Modeling System (ROMS) é utilizado para simular a dinâmica oceânica na região 60.5°-24°W/5°S-16°N com 0.25° de resolução, 32 níveis verticais e considerando as descargas dos rios Amazonas e Pará. A saída do modelo ROMS é comparada com o conjunto de dados SODA (Simple Ocean Data Assimilation). Três pontos foram selecionados para fazer as simulações numéricas, localizados em (50°W, 5.25°N), (44.5°W, 0.5°N) e (42.75°W, 1°S). O passo do tempo sugerido por Lee e Cheung (1990) foi ajustado devido às condições oceanográficas particulares em cada ponto, em que a velocidade inicial tende a zero. O coeficiente 0.1 da equação original foi substituído por 0.0250 e 0.0375. Todas as plumas se comportaram como tipo 3. A velocidade de corrente sazonal foi pequena do fundo á superfície, não excedendo 0.25 ms⁻<fnref n="1" />; o deslocamento máximo das plumas de seu ponto de origem não foi maior do que 1 m. O diâmetro médio das plumas na superfície variou de 54 a 79.7 m e o tempo de chegada à superfície foi de 7.25 a 8.05 horas.

**Palavras-Chave:** Vazamento de Óleo/Gás, Foz do Rio Amazonas, Oceano Atlântico, Modelo ROMS, Modelo GAS_DOCEAN.

**ABSTRACT.** This study is focused on analyzing the behavior of oil/gas plumes from blowouts into deepwater, located at the northern Brazil continental shelf. The Regional Ocean Modeling System (ROMS) model is used to simulate ocean dynamics in the region 60.5°-24.0°W/5°S-16°N with 0.25° of resolution. 32 vertical levels and considering the discharges of the Amazon and Pará Rivers. The ROMS output are compared to Simple Ocean Data Assimilation (SODA) dataset. Three points were selected to make the numerical simulations, located at (50°W, 5.25°N), (44.5°W, 0.5°N) and (42.75°W, 1°S). The time step suggested by Lee and Cheung (1990) was adjusted due to the particular oceanographic conditions at each point, in which, the initial velocity tends to zero and the coefficient 0.1 of the original equation was replaced by 0.0250 and 0.0375. All the plumes behaved as type 3. The seasonal current speed was small from the bottom to the surface, usually not exceeding 0.25 ms⁻<fnref n="1" />; the maximum displacement of the plumes from its point of origin was not greater than 1 m. The mean plumes diameter on the surface ranged 54 - 79.7 m and the arrival time to the surface was from 7.25 to 8.05 hours.

**Keywords:** Oil/Gas Blowouts, Amazon River mouth, Atlantic Ocean, ROMS model, GAS_DOCEAN model.

<footnote n="1">¹Department of Oceanography, DOCEAN, Federal University of Pernambuco, Recife, PE, Brazil. E-mail: humberto.varona@yandex.com, marcus.oceano@gmail.com, doris.veleda@ufpe.br, fasoaresl@yahoo.ca, moa.ufpe@gmail.com</footnote>

<footnote>*Autor correspondente</footnote>

<footnote n="2">²Center for Risk Analysis and Environmental Modeling - CEERMA. Federal University of Pernambuco, Recife, PE, Brazil.</footnote>

<footnote n="3">³Department of Production Engineering, Federal University of Pernambuco, Recife, PE, Brazil. E-mail: marcio@cerma.org</footnote>