Starting plume

The height of the rising plume can be determined from a conservation of mass for a control volume, enclosing the plume as it rises. From Equation (3.15), it follows that 

We make the following assumptions in order to estimate each term  

The rate of fuel supply is small compared to the rate of air entrained, m 0. 

The plume properties can be treated as quasi-steady. This is equivalent to applying Equation (10.60) with tQ small or negligible compared to t. Then at an instant of time the steady state solutions apply. 

In keeping with assumption 2, the plume cap is ignored, and the top of the rising plume is treated as a steady state plume truncated at zp. 

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More specific results are beyond the scope of our limited presentation for plumes. However, we will examine some gross features of transient plumes namely (a) the rise of a starting plume and (b) the dynamics of a fire ball due to the sudden release of a finite burst of gaseous fuel. Again, our philosophy here is not to develop exact solutions, but to represent the relevant physics through approximate analyses. In this way, experimental correlations for the phenomena can be better appreciated. 

Griffiths R. W. and Campbell I. H. (1990) Stirring and structure in mantle starting plumes. Earth Planet. Set Lett. 99, 66-78. 

Hill R. I. (1991) Starting plumes and continental break-up. Earth Planet Sci. Lett. 104, 398-416. 

As a flrst guess, a starting plume may be represented by a volume Q of material ponding beneath a flat base of the lithosphere. Initially the material has radius Ro and central height Hq, that is, dimensionally... 

For purposes of computation we used parameters obtained by Ebinger Sleep (1998) for the East African plume. The material properties assumed are a viscosity, h = 0.3x 10 Pas thermal diffusivity k = 0.8 x 10 m s , and specific weight contrast 200 Nm . The scaling constant is = 1/16. The starting plume head volume in the infinite radial model is g = 0.2 x 10 m , which yields Apond = 39 km. The finite widths Ro and Xq are assumed to be 250 km. This... 

Sleep, N. H. 1997. Lateral flow and ponding of starting plume material. Journal of Geophysical Research, 102, 10001-10012. 

This occurs when the nocturnal inversion is dissipated by heat from the morning sun. The lapse layer usually starts at the ground and works its way upward (less rapidly in winter than in summer). Fumigation may also occur in sea-breeze circulations during late morning or early afternoon. The shaded zone of strong concentration is that portion of the plume which has not yet been mixed downward. 

Installation of the pumping well is more time consuming than digging a trench. There is a lag period between the start of pumping, the formation of the depression cone, and containment of the plume. This limits its use as a rapid containment measure. The water table depression must be kept constant otherwise, if the water table is allowed to fluctuate, gasoline droplets may adhere to soil particles and get trapped below the water table, especially when the depth of the cone of depression gets lower. 

Figure 10.21 Rise time of starting fire plumes (from Tanaka, Fujita and Yamaguchi [31])...

When a recovery well is located within a contaminant plume and the pump is started, the initial concentration of contaminant removed is close to the maximum level during preliminary testing. As the pump continues to operate, cleaner water is drawn from the plume perimeter through the aquifer pores toward the recovery well. Some of the contaminant is released from the soil into the water in proportion to the equilibrium coefficient. For example, if the Kd is 1000, at equilibrium, 1 part is in the water and 1000 parts are retained in the soil. If the water-soil contact time is sufficient, complete equilibrium will be established. After the first pore volume flush (theoretically), the concentration in the water will be 0.9 and that on the soil will be 999. With each succeeding flush, the 1000 1 ratio will remain the same. If the time of water-soil contact is not sufficient to establish equilibrium, the recovered water will contain a lesser concentration. A typical decline curve is shown on Figure 9.2. Note the asymptotic shape of the curve where the decline rate is significantly reduced. 

This result may also be obtained by starting with Eq. (4.11), assuming a source at z = h and a fictitious source at z = -h, and adding the two expressions in the region 2 > 0. If we assume a totally absorbing earth, the corresponding form of the Gaussian plume equation is... 

By careful optimization of the MAPLE deposition conditions (laser wavelength, repetition rate, solvent type, concentration, temperature, background gas and gas pressure), this process can occur without any significant chemical decomposition. When a substrate is positioned directly in the path of the plume, a coating starts to form from the evaporated organic molecules, while the volatile solvent molecules, which have very low sticking coefficients, are evacuated by the pump in the deposition chamber. 

The two contaminant plumes are represented in the first stage of the optimization formulation with a set of 110 control points along the plume boundaries. These same control point locations are used as starting points for particles when forward tracking is used in the second stage of the solution process. For the unconfined simulation, additional constraints are included to require a minimum saturated thickness of 1.5 m at each well cell. Both confined and unconfined assumptions are simulated under two sets of penalty parameters. Recall that the solution algorithm uses the penalty method for the plume capture constraints, in which each constraint violation is multiplied by a penalty parameter and added to the objective function. 

The NMED approved an operation and maintenance plan in November 1995, and DBS A started operation of the SVE system in early December 1995. On April 29, 1996, monitor well MW-9 was incorporated into the SVE network to provide further control of the groundwater plume (Fig. 6). 

Fig. 5.2 Simulated development of the ETEX-1 tracer plume at 12, 24, 36 and 48 h after start of release (ngm ), corresponding measurements can be found in Graziani et al. (1998)...

At 24 h after the start of the release the plume maximum had spht into two separate parts (Fig. 5.2). The head received cyclonic rotational momentum from a meso-scale disturbance and reached DK02 after 26 h giving rise to the first peak. As the latter part of the cloud progressed it received anti-cyclonic momentum and after 36 h the plume attained a U-shaped deformation which was advected towards DK02. The rotational time scale of the eddies was not large enough (compared to the advective time scale of the plume) to cause a full revolution in the plume. 

Fig. 5.5 Relative vorticity (x 10 s ) in lowest model layer at the start of the release. Arrows indicate eddies influencing the plume during transport...

Gibson S. A. (2002) Major element heterogeneity in Archean to Recent mantle plume starting-heads. Earth Planet. Sci. Lett. 195, 59-74. 

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