The Effect of Fractures on the Reclamation ofNAPL
59
injection and pumping wells, each pumping at equal rates (powers et al. 1991).
Following the startup of such a system, a short transient flushing period is
expected during which "apparent steady-state conditions" are established (Rubin
et al. 1997). Due to the short duration of the transient period and the low
solubility of the NAPL, very little NAPL dissolution occurs during the transient
stage. After the establishment of an apparent steady state concentration profile,
however, the NAPL saturation will gradually diminish over an extended period
due to dissolution and solute transport by flow through the contaminated domain.
Changes in the entrapped NAPL saturation are spatially nonuniform in the
domain.
In this study, the initial entrapped NAPL saturation is assumed to be
comparatively small (Le., Sn :::; 0.1) such that changes in NAPL saturation can be
assumed to have negligible effect on the conductivity of the permeable blocks
(Faust 1985). Diminishing NAPL saturation will, however, significantly affect the
rate of mass transfer to the mobile water phase, due to the change in the interphase
contact area. These effects are considered in the present study.
3 Basic Formulation
Due to the symmetry of the domain represented in Fig. 2a, simulations and
analyses are conducted on the subdomain shown in Fig. 2b. This subdomain is
characterized by fracture segments, permeable blocks, and matrix sections. The
set of successive fracture segments comprises the fracture network of the
subdomain. The permeable medium occupying the space between adjacent
fracture segments is termed the permeable block. The rectangular space
incorporating two halves of adjacent blocks and a single fracture segment is
referred to as a matrix section. In each permeable block there is a specific crosssection at the centerline of the block, which represents the interface between
adjacent matrix sections.
The specific discharge contributed by the fractures, qr is obtained by dividing
the fracture flow rate, Qr by the cross-sectional area of the block, perpendicular to
the flow direction (see Fig. 2b):
q =-.!d.L.
f
BsinO
(la)
The total discharge flowing through each cross-section perpendicular to the
flow direction, Q" is composed of the fracture segment flow rate, Qfi and the
single permeable block flow rate, Qb. The relationships between these three types
of flow-rates are given by:
Qt =Qf +Qb; Qf,Qb = (qf,qb)BsinO.
(lb)
Description of solute transport through the fracture network is formulated with
reference to the elementary fracture volume shown in Fig. 2c. Here, qb is the
59
injection and pumping wells, each pumping at equal rates (powers et al. 1991).
Following the startup of such a system, a short transient flushing period is
expected during which "apparent steady-state conditions" are established (Rubin
et al. 1997). Due to the short duration of the transient period and the low
solubility of the NAPL, very little NAPL dissolution occurs during the transient
stage. After the establishment of an apparent steady state concentration profile,
however, the NAPL saturation will gradually diminish over an extended period
due to dissolution and solute transport by flow through the contaminated domain.
Changes in the entrapped NAPL saturation are spatially nonuniform in the
domain.
In this study, the initial entrapped NAPL saturation is assumed to be
comparatively small (Le., Sn :::; 0.1) such that changes in NAPL saturation can be
assumed to have negligible effect on the conductivity of the permeable blocks
(Faust 1985). Diminishing NAPL saturation will, however, significantly affect the
rate of mass transfer to the mobile water phase, due to the change in the interphase
contact area. These effects are considered in the present study.
3 Basic Formulation
Due to the symmetry of the domain represented in Fig. 2a, simulations and
analyses are conducted on the subdomain shown in Fig. 2b. This subdomain is
characterized by fracture segments, permeable blocks, and matrix sections. The
set of successive fracture segments comprises the fracture network of the
subdomain. The permeable medium occupying the space between adjacent
fracture segments is termed the permeable block. The rectangular space
incorporating two halves of adjacent blocks and a single fracture segment is
referred to as a matrix section. In each permeable block there is a specific crosssection at the centerline of the block, which represents the interface between
adjacent matrix sections.
The specific discharge contributed by the fractures, qr is obtained by dividing
the fracture flow rate, Qr by the cross-sectional area of the block, perpendicular to
the flow direction (see Fig. 2b):
q =-.!d.L.
f
BsinO
(la)
The total discharge flowing through each cross-section perpendicular to the
flow direction, Q" is composed of the fracture segment flow rate, Qfi and the
single permeable block flow rate, Qb. The relationships between these three types
of flow-rates are given by:
Qt =Qf +Qb; Qf,Qb = (qf,qb)BsinO.
(lb)
Description of solute transport through the fracture network is formulated with
reference to the elementary fracture volume shown in Fig. 2c. Here, qb is the