. 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 2.

The summary of contaminant soil vapor transport models including biodegradation.

Governing equation

Models

Steady state diffusion & biodegradation (1 species)

0 = \nabla \cdot (D_{i} \nabla c_{ig}) - R_{i}

(22)

Ririe and Sweeney (64),
R-UNSAT (65),
Johnson et al. (20),
Davis et al. (66)

Transient diffusion & biodegradation (1 species)

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

(23)

Jeng et al. (67),
VIM (68),
Sanders and Stern (#1) (69)

Constant convection & transient diffusion & biodegradation (1 species)

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

(24)

Ünlü et al. (70),
Jury et al. (4–7),
van Genuchten et al. (71–74),
Sanders and Stern (#2) (69),
Anderson et al. (75),
T & R model (76),
Lin and Hildemann (77)

Steady state diffusion & biodegradation (2 species)

0 = \nabla \cdot (D_{i} \nabla c_{ig}) - R_{i}

(25)

Ostendorf and Kampbell (60),
Roggemans et al. (57, 78),
Devaull (79),
Parker (80),
Verginelli and Baciocchi (81)

Convection & diffusion & biodegradation (2 species)

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

(26)

R-UNSAT (64)²ⁿ,
VADBIO (82)²ⁿ,
IMPACT (83–85)²ⁿ,
The Brown model (Yao (86)³ⁿ),
The ASU model (Abreu and Johnson
(87)³ⁿ, Abreu et al. (88)),
CompFlow Bio (89)²ⁿ

Note: ²⁽³⁾ⁿ means 2(3)-D numerically solve model; models shown without superscript symbols are all 1-D, steady state, analytical models