 |
| Titel |
Semi-analytical solution of three-dimensional transient flow in a coupled N-layer aquifer system |
| VerfasserIn |
E. J. M. Veling, C. Maas |
| Konferenz |
EGU General Assembly 2009
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250027397
|
|
|
|
|
|
| Zusammenfassung |
| We present an efficient strategy for solving semi-analytically the transient groundwater head
in a coupled N-layer aquifer system Ïi(r,z,t), i = 1,-
-
-
,N, with radial symmetry, with full
z-dependency, and partially penetrating wells. Aquitards are treated as aquifers with their
own horizontal and vertical permeabilities. Since the vertical direction is fully taken into
account, we do not need to pose the Dupuit assumption, i.e. that the flow is mainly horizontal.
At the common boundaries of the layers we assume continuity of the head and the
flux. At the top and the bottom of the system we assume boundary conditions of
Robin type (i.e. flow is proportional to the head), including Dirichlet and Neumann
conditions.
To solve this problem, we employ the Laplace transform for the t variable (with transform
parameter p), the Hankel transform for the r variable (with transform parameter α) and a
particular form of a Generalized Fourier transform for the vertical direction z with an
infinite set of eigenvalues λm2 (with the discrete index m). We solve this problem in
the form of a semi-analytical solution by specifying an analytical expression in
terms of the variables r and z, transform parameter p, and eigenvalues λm2(p) of
the Generalized Fourier transform. The calculation of the eigenvalues λm2 and
the inversion of these transformed solution to the time domain can only be done
numerically.
In this context the application of the Generalized Fourier transform is novel. By means of
this Generalized Fourier transform transient problems with horizontal symmetries other than
radial can be treated as well.
We demonstrate the capabilities of this technique by an example of particle tracking to
and from an partially penetrating well in a system of 6 layers and 3 wells, both under
stationary as under transient conditions. |
|
|
|
|
|
|