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7. Adsorption under Partially-Saturated Conditions
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Impermeable boundary conditions are imposed along the sides parallel to the
main direction of flow.
We follow the procedure explained in Section 6.3 to perform drainage and
applying a steady state flow fluid, under a different saturations, to calculate
the total volumetric flow though the network and the relative permeability.
7.4 Simulating adsorptive transport within the
network
In order to take limited mixing, due to existence of the non-wetting phase, into
account, we subdivided a drained pore body into corner units. In the case of a
cubic pore body, we have eight corner units, each comprised of a corner domain
together with half of the three neighboring edges (Figure 6.3a).
In our formulation, the unknowns will be either concentrations of saturated
pore bodies, c i , and saturated pore throats, c ij , or concentrations of edges of
drained pore throats, c ij,k , and corner units of drained pore bodies, c CU,i . The
adsorbed mass concentration will be either adsorbed mass concentrations of
saturated pore bodies, s sw
i
, and saturated pore throats, s sw , or adsorbed mass
ij
, and,
concentrations at SW and AW interfaces of drained pore throats, s sw
ij
s aw , respectively, or corner units of drained pore bodies, ssw
CU,i CU,i
respectively.
, and, saw
CU,i ,
To describe the formulation, we introduce mass balance equations for a system
of two drained pores connected by a drained angular pore throat, as the most
general case, shown in Figure (6.3a). We assume that the flow is from corner
unit j towards corner unit i through corners of drained pore throat ij. For a
given corner unit (with concentration c CU,i and volume V CU,i ), we can write
the mass balance equation
V CU,i
d
dt (c CU,i) =
Nin∑
tube
j=1
N ij
edge
∑
k=1
q ij,k c ij,k +
N CU,i
in,edge
∑
n=1
( ) ( )
d
−V CU,i dt
s sw
d
− V
CU,i CU,i dt
s aw
CU,i
q i,n c n − Q CU,i c CU,i (7.1)
where the first term on the r.h.s. is due to the mass arriving via N ij
edge
edges of
throats with flow towards the corner unit. The second term on the r.h.s.
N tube
in
accounts for the mass arriving from N CU,i
in,edge
166
neighboring corner units (within