By Linda M. Abriola
Groundwater has lengthy been one of many world's most crucial assets. It bills for about ninety six% of all clean water within the usa and provides greater than 50% of the inhabitants with potable water. traditionally, this water resource has often been considered as pristine. besides the fact that, in recent times, infection of floor water by way of commercial items has turn into an issue of turning out to be drawback. prior to now 4 a long time, the range and volume of natural chemical substances produced within the U. S. has progressively elevated. at the moment, greater than 40,000 diverse natural compounds are being synthetic, trans ported, used and finally disposed of within the surroundings (Wilson, et !l (1981». creation and intake of petroleum items has additionally risen during this related period of time. lots of those business compounds are hugely poisonous and somewhat water soluble. therefore, they pose a poten tial risk to giant volumes of groundwater in the event that they are one way or the other intro duced into the subsurface. elevated creation of chemical substances implies the elevated possibility of unintended spills or leakage to the soil, and certainly, the literature abounds with infection case histories. 2 Incidences of petroleum infection of groundwater were documented by way of many authors. for instance, see: Schwi11e (1967); Toms (1971); Guenther (1972); McKee, et!l (1912); Williams and Wilder (1971); Van100cke, et ~]-
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Additional info for Multiphase Migration of Organic Compounds in a Porous Medium: A Mathematical Model
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Ri ca lly. 7. Note that some terms have been more fully expanded and all equations have been written in terms of the two capillary pressures Pow and Pwg • The soil species equation has been incorporated into the other balance equations and will not be listed separately here. 55) 17 P ~. 9'!!.. + ~~] 9 2 9 at 2 aP ow at aP wg at E 0 \I. ( p - ES 0 0 w w D· \I w2 + PES w:::D. \I _ 0::; w + PES 9 W2 9 9:::D· \I _ is known as the a-phase mobility. 57). 59) where u is the vector of unknowns A and Bare :::: ::;;: 3 x 3 nonlinear coefficient matrices with functional dependence on ~, ~ and ~~; and F encompasses the lower-order terms.
Work of Vachaud (1967) and Watson (1966) verified the applicability of Darcy's law with steady state permeability values to the unsaturated, transient case. Leverett and Lewis (1941) and Corey, et ~ (1956) conducted three phase (oil, gas, water) permeability determinations in sands and sandstones for use in oil reservoir modeling. All of the above experimental work found hydraulic conductivities to be functions of fluid saturations for the mu1tiphase case. generalized Darcy equation is nonlinear.
Recall that the convective movement of the gas phase has been neglected. 49) Since the system is isothermal and the pressure in the gas phase remains constant, the density of this phase is controlled solely by its composition. 50) The functional dependence of gas saturation on capillary pressure will also be assumed. 30) have been employed. 8 - Equation Summary), reveals that they can be represented as non-linear partial differential equations in 6 unknovms (two capillary pressures and four mass fractions).