N Ca , N B , and N T are obtained under the assumption that the shear forces can be
neglected (Ng et al. 1978; Pennell et al. 1996). These forces, which depend on the
viscosity contrast between wetting and non-wetting liquids, cannot be neglected for
viscous liquids such as coal tar, motor oil, and some crude oils (Ng et al. 1978). In
those cases, using the mobility ratio is proposed (m) (Dullien 1992) (Eq. 3.18).
m ¼
k 2r μ 1
k 1r μ 2
ð3:18Þ
where,
m: mobility ratio
k 1r : relative permeability of the displaced phase (À)
k 2r : relative permeability of the displacing phase (À)
μ 1 : fluid dynamic viscosity of the displaced phase (kgÁm
À1
Ás
À1 )
μ 2 : fluid dynamic viscosity of the displacing phase (kgÁm
À1
Ás
À1 )
Viscous fingering tends to reduce with increased temperatures; this phenomenon
is related to the fact that, given the reduced NAPL viscosity, the ratio of the mobility
of the displacing fluid to the displaced fluid is lower (Lenormand 1985; Munson
et al. 2009).
3.2.4 Effects of Temperature on Adsorption onto Solid Phase
Adsorption involves the attachment of molecules present in a fluid onto a solid
surface. Adsorption is a mechanism that affects the transport of compounds in
aqueous phase. The soil–water distribution coefficient, K d , characterizes the adsorption capacity of a dissolved substance i onto a solid substrate at equilibrium
(Eq. 3.19):
K d ¼
C i,s
C i,w
ð3:19Þ
where,
K d : soil–water distribution coefficient (LÁkg
À1 )
C i, s : concentration of compound i onto the solid phase (mgÁkg
À1 )
C i, w : concentration of compound i in the aqueous phase (mgÁL
À1 )
Various models are used to characterize the adsorption of an organic compound
onto solid surfaces, such as the nonlinear model (Langmuir, Freundlich, and
Langmuir–Hinshelwood isotherm models). Generally, the organic carbon–water
partition, K oc , is more often used to better determinate the adsorption capacity
onto organic matter (Eq. 3.20):
3 In Situ Thermal Treatments and Enhancements: Theory and Case Study
169
neglected (Ng et al. 1978; Pennell et al. 1996). These forces, which depend on the
viscosity contrast between wetting and non-wetting liquids, cannot be neglected for
viscous liquids such as coal tar, motor oil, and some crude oils (Ng et al. 1978). In
those cases, using the mobility ratio is proposed (m) (Dullien 1992) (Eq. 3.18).
m ¼
k 2r μ 1
k 1r μ 2
ð3:18Þ
where,
m: mobility ratio
k 1r : relative permeability of the displaced phase (À)
k 2r : relative permeability of the displacing phase (À)
μ 1 : fluid dynamic viscosity of the displaced phase (kgÁm
À1
Ás
À1 )
μ 2 : fluid dynamic viscosity of the displacing phase (kgÁm
À1
Ás
À1 )
Viscous fingering tends to reduce with increased temperatures; this phenomenon
is related to the fact that, given the reduced NAPL viscosity, the ratio of the mobility
of the displacing fluid to the displaced fluid is lower (Lenormand 1985; Munson
et al. 2009).
3.2.4 Effects of Temperature on Adsorption onto Solid Phase
Adsorption involves the attachment of molecules present in a fluid onto a solid
surface. Adsorption is a mechanism that affects the transport of compounds in
aqueous phase. The soil–water distribution coefficient, K d , characterizes the adsorption capacity of a dissolved substance i onto a solid substrate at equilibrium
(Eq. 3.19):
K d ¼
C i,s
C i,w
ð3:19Þ
where,
K d : soil–water distribution coefficient (LÁkg
À1 )
C i, s : concentration of compound i onto the solid phase (mgÁkg
À1 )
C i, w : concentration of compound i in the aqueous phase (mgÁL
À1 )
Various models are used to characterize the adsorption of an organic compound
onto solid surfaces, such as the nonlinear model (Langmuir, Freundlich, and
Langmuir–Hinshelwood isotherm models). Generally, the organic carbon–water
partition, K oc , is more often used to better determinate the adsorption capacity
onto organic matter (Eq. 3.20):
3 In Situ Thermal Treatments and Enhancements: Theory and Case Study
169