Exercise 4

Aerobic biodegradation of petroleum hydrocarbons present in the vadose zone is manifest by a predominately upward flux of carbon dioxide. The magnitude of CO2 flux is an indicator of the rate of depletion of the liquid-phase hydrocarbon. Among the various methods that have been used to estimate the CO2 flux in the field is the so-called gradient method, by which the upward flux is computed from a measured concentration distribution and the effective diffusion coefficient. More than two gas components are involved in the depletion of a liquid-phase hydrocarbon by aerobic biodegradation. Nevertheless, it is instructive to revise the gradient method using the flux equations for a binary gas in which air and carbon dioxide are assumed to be the only two constituents.

Refer to Figure Exercise 4-1 and derive an equation by which the steady CO2 flux can be calculated from a measured concentration distribution and a known effective diffusion coefficient. Assume the molecular regime prevails, pressure diffusion is negligible, and air can be considered to be a single species (species A).

Compute the mole flux of carbon dioxide, phase (bulk gas) flux, non-equimolar flux, and viscous flux using the following data from Tracy (2015).

p = 8.3 × 104 Pa

T = 21.6 °C

D = 4.7 × 10-6 m2/s

z2z1 = 1.29 m

xB(z1) = 0.0583

xB(z2) = 0.0013

\displaystyle M_{BA}^{0.5}= 1.232

 

Sketch of steady diffusion of carbon dioxide in the vadose zone from a source at the water table

Figure Exercise 41Sketch of steady diffusion of carbon dioxide in the vadose zone from a source at the water table.

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Flux Equations for Gas Diffusion in Porous Media Copyright © 2021 by David B. McWhorter. All Rights Reserved.