# Application of the Model to the Case of Continuous Flow of Oil

During the accident at Macondo well in the Gulf of Mexico in April 2010, oil leaked at a rate of 57,000 barrels per day on a continuous basis until the well was closed on July 15, 2010. This was the worst oil spill accident in US history and released 4.9 million barrels of oil until it was sealed after 86 days on July 15, 2010 (about 57,000 bbl/day or 377 m'Vh) as reported by NOAA. Information about this oil spill and the properties of the oil released and meteorological data were presented in Chapter 4. A large portion of this oil (40°API) was vaporized during a period in which temperature varied between 20 and 34°C.

The model presented in this chapter is applied to this case in which oil is flowing for a period of nearly 3 months. In this modeling approach, temperature and wind speed are considered variable on a daily basis, and a time step of 12 hours (half a day) is chosen for the calculation of the rate of evaporation of hydrocarbons from the oil spill floating on the sea surface coming from a source on a continuous basis. The most readily available data for the crude oil produced from the Macondo Well are its density or API gravity. However, Reddy et al. (2011) reported a detailed GC analysis of oil and gas produced from the well at 5,000 ft below' the water surface. They found that the fluid flowung out of the Macondo well had a gas-to-oil ratio (GOR) of 1,600 standard cubic feet per barrel. The compositions of the oil, gas, and reservoir fluid are given in Table 4.3, while the general characteristics of the oil are given in Table 4.4 in Chapter 4. The oil API gravity is 40 (equivalent to a density of 0.85 g/cm3) as reported by Reddy and US government organizations (NOAA, 2010). These data were used with the density function given by Equation 5.17 to generate molar

FIGURE 7.14 Molar distribution of hydrocarbons in the oil.

distribution. Based on the normalization of the data, the molar distribution of the crude is presented in Figure 7.14. The crude oil in the GOM spill was divided into 19 pseudocomponents with those heavier than water considered sedimented and the remaining components involved in the vaporization process according their vapor pressure and mass transfer coefficient in the air as described by Riazi (2016).

The variation of temperature and wind speed in Venice, La., from May to July 2010 was recorded, and it is given in Chapter 4 (Table 4.6). The spread between low and high temperatures for this period is shown in Figure 7.15 as reported by Riazi (2016). For the computational calculations, these temperature variations have been correlated to time (day) as given in Table 7.5. The variation of wind speed for the same period is shown in Figure 7.16. Based on the area of spill and its volume as reported by NOAA, the initial slick thickness can be estimated.

An Excel sheet was specifically developed to perform the calculations for this problem. The calculation results for the volume of oil vaporized versus time are presented in Figure 7.18. The days are counted starting from April 20 when the oil flow' began. The volume of oil was calculated from the sum of volume of all pseudocomponents. In Figure 7.18, the horizontal parts indicate no vaporization due to zero wind speed for those specific days as explained above.

In the proposed model the initial oil thickness (y) is needed. This was calculated from Equation 7.1 and based on the spill area from Figure 7.17 on April 26. The initial oil thickness was calculated as 0.03 mm. According to Table 5.3, the last tw'o components have SG> 1 and therefore account for 24.9% of the total oil volume removed before vaporization began. So the model prediction for the amount of sedimentation (which may be considered as the amount dispersed) is about 25% of the initial volume. According to the data released by NOAA (2010), about 24% total oil

FIGURE 7.15 The variation of temperature versus time in days (April 20,2010, Day = 0).

TABLE 7.5

Low and High Temperature Based on Data from Table 4.6 (Chapter 4) and Figure 7.15

 T (°C) = a + b (Day/100) + c (Day/100)2 a b c d AD, °C Low temperature 15.73 36.55 - 39.96 14.85 0.56 High temperature 21.47 47.71 -73.71 36.59 1.00

was dispersed (16% naturally and 8% by chemicals) while 25% vaporized and 26% remained at the sea or on shore as shown in Figure 7.19.

In the calculations using the above models it was assumed that the oil is either vaporized or sedimented, and Figure 7.18 shows that about 50% of the total oil released into the sea was vaporized while 25% was sedimented and 25% remained in the sea under natural conditions. According to NOAA data (Figure 7.19), 50% of the oil was removed or burned or dispersed. If this amount (half of 4.9 million barrels of oil released) is considered in these calculations (after 25% of the initial oil was dispersed or sunk) then the model estimate would be 25% vaporized, which agrees with the NOAA estimate. It is not expected to achieve identical predictions, as in the actual case, the rate of oil released varied in the early and final stages of the accident. In the last few weeks, as attempts to seal the pipe were underway, the amount of oil

FIGURE 7.16 The variation of wind speed versus time in days (April 20, 2010, Day=0).

FIGURE 7.17 Position and area of the oil spill after four days (source: NOAA [2010]). Based on the area of this slick the oil thickness is calculated as 0.03 mm.

released was reduced gradually until July 15, when oil flow was completely stopped. In addition, other factors such as dissolution, the timing of removal, or burning also affect the calculation results which are not considered here.