. Author manuscript; available in PMC: 2014 Mar 19.

Published in final edited form as: Environ Sci Technol. 2013 Feb 27;47(6):2457–2470. doi: 10.1021/es302714g

TABLE 1.

The summary of contaminant soil vapor transport models without biodegradation.

Main governing equation

Examples of model use

Steady state advection

0 = - \nabla \cdot (q_{g} c_{ig})

(6)

Little et al. (#3) (34)

Steady state diffusion

0 = \nabla^{2} c_{ig}

(7)

OCHCA (35),
J-E model (28), Park (36),
CSOIL (37),
Atteia and Hohener (33),
Yao et al. (22)², Yao and Suuberg (38)²,
Wrighter and Howell (39),
Lowell and Eklund (40)²

Transient diffusion

ϕ_{g, w, s} \frac{\partial c_{ig}}{\partial t} = \nabla^{2} c_{ig}

(8)

Little et al. (#1, 2 model) (34)
Symms et al. (41)

Steady state uniform advection & diffusion

q_{g} \nabla c_{ig} = \nabla \cdot (D_{i} \nabla c_{ig})

(9)

Murphy and Chan (42),
VOLASOIL (43–44),
CSOIL 2000 (45)

Steady state advection & diffusion

\nabla \cdot (q_{g} c_{ig}) = \nabla \cdot (D_{i} \nabla c_{ig})

(10)

The Brown model (Bozkurt (46)³ⁿ, Bozkurt et al. (47)³ⁿ,
Pennell et al. (48)³ⁿ, Yao et al. (49)³ⁿ),
The ASU model (Abreu (50)³ⁿ, Abreu and Johnson (21)³ⁿ)

Transient advection & diffusion

ϕ_{g, w, s} \frac{\partial c_{ig}}{\partial t} = - \nabla \cdot (q_{g} c_{ig}) + \nabla \cdot (D_{i} \nabla c_{ig})

(11)

The Brown model (Yao et al. (51)³ⁿ),

Note: while some models were developed in more complete form, what is show here is how the models were actually used in the indicated references. ²⁽³⁾ⁿ means 2(3)-D numerically solved models; models shown without superscript symbols are all 1-D, steady state, analytical models