Page 283 - gas transport in porous media

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Subsurface scenario
Q (t) Rossabi
patm (t)

Z
Sand
Clay
Sand P
Contaminant z
Clay
Water table

Figure 16.1. Scenario for analytical solution to barometrically induced flow through a well

slowly. If the VOC concentration in the gas is known and the flow out of the well
can be predicted, the mass removal of the system can be calculated. Similarly if the
nutrient uptake rate (e.g., oxygen utilization rate) is known and the flow into the
subsurface can be predicted, the mass of contaminant consumed by bioremediation
can be calculated.
Many researchers have devised analytical solutions to the equations describing
pressure and flow in porous media with certain boundary and initial conditions. From
Theis (1935) to Jacob (1940) to Cooper and Jacob (1946) and to Hantush (1964),
analytical solutions to groundwater flow are still generally the first methods used to
describe pumping test data. Although numerical methods can more easily solve the
equationsthatdescribeparticularsetsofsubsurfaceconditions, heterogeneityandlack
of data often limit development of a precise and unique set of descriptive equations on
which to apply these methods. In these situations an analytical solution can provide a
comparable degree of accuracy and the computational advantages of exact solutions
in comparison with iterative methods. When predicting the operation of inexpensive
remediation systems, the value of simple analytical solutions is particularly poignant.
Analytical solutions to subsurface pressure as a result of atmospheric pressure changes
have been developed and successfully applied to field data by several researchers
(Weeks, 1978; Rossabi and Riha, 1994; Shan, 1995). These solutions (often adapted
from solutions derived for heat conduction) can predict the magnitude and direction
of the pressure differential between the surface and subsurface, and have been used
for estimating the effective vertical permeability (k z ) of the intervening materials.