7.3. Coupled Inverse Problems of Groundwater Flow and Mass Transport
223
taken as 10 m and the other parameters are the same as those in Figure 7.13.
From the figure it is seen that, if Kr/K z is over 50, the results of a threedimensional model are alm ost the same as those of a two-dimensional model.
If Kr/K z is relatively smaIl, the results ealculated from these two models differ
greatly. This means that when we fit the model to the observed eurves, we
should not simplify the model without taking into eonsideration the value of
Kr/Kz·
A reasonable design may be found after analyzing a great number of
sensitivity eurves. The best way is to drill one weIl first, do some single
weIl tests to reduee the ranges of the unknown parameters, and then use the
results of sensitivity analyses to determine a suitable distanee for the seeond
weIl. As a result, it is more possible to obtain a sueeessful design than drilling
two wells at the same time. Obviously, the CAD method ean and should be
used to obtain more eomplex experimental designs.
7.3 Coupled Inverse Problems of Groundwater Flow and
Mass Transport
7.3.1 The Definition of Coupled Inverse Problems
Aeeording to Seetion 7.1.1, the groundwater flow and mass transport in
the saturated zone of an isotropie aquifer are governed by the following
equations:
oh 0 ( Oh)
Ss- - -
K - + Q = 0,
ot oXi oXi
(7.3.1)
O(OC)
0 (
OC)
0
-i)- - -i) DijO-i) + -i) (V;OC) + ;'BC + M = 0,
t
Xi
Xj
Xi
(7.3.2)
where water head hand eoneentration C satisfy the following initial
eonditions:
t = 0, XE (0)
(7.3.3)
and boundary eonditions:
XE (S!), t ~ °
(7.3.4)
-K:: i ni =/2' (-DufJ:~ + v;oc)ni =g2; XE(S2), t~O. (7.3.5)
In Eqs. (7.3.1) to (7.3.5), Q is the souree/sink term of the flow equation; M the
souree/sink term of the quality equation; 10' go, 11' g!, 12' g2 all known
funetions; (0) the flow domain; and (S1) and (S2) its boundary surfaees. The
other symbols are the same as before. The eomponents of mean veloeity V
223
taken as 10 m and the other parameters are the same as those in Figure 7.13.
From the figure it is seen that, if Kr/K z is over 50, the results of a threedimensional model are alm ost the same as those of a two-dimensional model.
If Kr/K z is relatively smaIl, the results ealculated from these two models differ
greatly. This means that when we fit the model to the observed eurves, we
should not simplify the model without taking into eonsideration the value of
Kr/Kz·
A reasonable design may be found after analyzing a great number of
sensitivity eurves. The best way is to drill one weIl first, do some single
weIl tests to reduee the ranges of the unknown parameters, and then use the
results of sensitivity analyses to determine a suitable distanee for the seeond
weIl. As a result, it is more possible to obtain a sueeessful design than drilling
two wells at the same time. Obviously, the CAD method ean and should be
used to obtain more eomplex experimental designs.
7.3 Coupled Inverse Problems of Groundwater Flow and
Mass Transport
7.3.1 The Definition of Coupled Inverse Problems
Aeeording to Seetion 7.1.1, the groundwater flow and mass transport in
the saturated zone of an isotropie aquifer are governed by the following
equations:
oh 0 ( Oh)
Ss- - -
K - + Q = 0,
ot oXi oXi
(7.3.1)
O(OC)
0 (
OC)
0
-i)- - -i) DijO-i) + -i) (V;OC) + ;'BC + M = 0,
t
Xi
Xj
Xi
(7.3.2)
where water head hand eoneentration C satisfy the following initial
eonditions:
t = 0, XE (0)
(7.3.3)
and boundary eonditions:
XE (S!), t ~ °
(7.3.4)
-K:: i ni =/2' (-DufJ:~ + v;oc)ni =g2; XE(S2), t~O. (7.3.5)
In Eqs. (7.3.1) to (7.3.5), Q is the souree/sink term of the flow equation; M the
souree/sink term of the quality equation; 10' go, 11' g!, 12' g2 all known
funetions; (0) the flow domain; and (S1) and (S2) its boundary surfaees. The
other symbols are the same as before. The eomponents of mean veloeity V