|
 Introduction
|
|
The saltpool problem is a lab experiment conducted by S. Oswald at the ETH Zuerich and documented in [OSWALD] The experiment begins with a stable system of layers of saltwater of differing densities below a freshwater layer, and then allows an additional discharge of freshwater on the top. The system's reaction is observed via MRI (Magnetic Resonance Imaging). The comparison of actual measured data with the computed results provides a good verification standard for software that computes density-driven flow.
|
|
|
|
 Experimental Setup
|
|
In the first phase, saltwater is injected into the block via opening O5 (see figure below). The displaced freshwater can run off via the holes O1-O4. The amount of saltwater is sufficient to replace about 30% of the freshwater. In the second phase, all holes are sealed. After certain amount of time has elapsed, a stable layering is achieved. An equilibrium with almost horizontal layers and only minor disturbances is reached. The holes O1-O4 are opened again for phase three. A constant flow rate is established with inflow through the holes O1 and O3 and a run-off through the opposing holes O2 and O4. From: [OSWALD].
The experiment was conducted with various salt concentrations. For this verification, the experiment was modelled with two different concentrations, in accordance with the data available:
| Saltp_l |
Salt mass fraction C=1%
(Change in Density Drho/rho0=0.0071) |
| Saltp_d |
Salt mass fraction C=10%
Change in Density Drho/rho0=0.071) |
|
|
Parameters
|
|
According to [OSWALD] the experiments were conducted with the following parameters:
| Hydraulic Conductivity |
kf = 9.325*10-3 m/s |
| Porosity |
n = 0.372 |
| Longitudinal Dispersitivity |
aL = 1.2*10-3 m |
| Transverse Dispersitivity |
aL = 1.2*10-4 m |
| Effective Diffusion |
dm = 8.7*10-10 m2/s |
|
| |
saltp_l |
saltp_d |
| Salt Mass fraction |
1.0 % |
10.0 % |
| Flow Rate 1st Phase |
1.2 ml/s |
1.26 ml/s |
| Flow Rate 3rd Phase |
1.89 ml/s |
1.83 ml/s |
| Duration 1st Phase |
12.0 min |
11.9 min |
| Duration 3st Phase |
33.5 min |
34.6 min |
| Last Picture 3rd Phase |
140.2 min |
159.9 min |
|
|
The results of the computations can be compared to the values measured during the experiments. Two different data sets are available for comparison: the solute concentration of the fluid running out in phase 3, and the spatial distribution of the solute concentration at various points of time of the experiment measured with an experimental MRI-based visualization method.
|
|
|
Discretization
|
|
Numeric models of the saltp_d and saltp_l experiments were generated and computed as models of transient solute transport. The horizontal FE-mesh contains 2060 nodes and 2125 elements and is shown in the figure below. The lengths of the element edges range from 0.0005 m to 0.005 m. The vertical discretization involves up to 71 layers, some of them being realized as partial layers. Here, too, the lengths of the element edges range from 0.0005 m to 0.005 m. Altogether, the three-dimensional FE mesh consists of 155,298 nodes and 110,348 elements.
Horizontal FE mesh
Vertical FE mesh (O1 - O3)
|
|
Computed Results
|
|
To verify the calculated results of the density-dependent layering investigation, the third phases of saltp_l and saltp_d are computed. The computing component SITRA relies on pressure-dependent flow algorithms and Picard's iterations for the density-based interconnection of the equations for flow and solute transport.
The time steps for the calculations were 3 seconds for flow computation, and 1 second for solute transport computation. Every time step in computing the flow automatically refreshes the assumed density distribution for the system.
The layer of saltwater below the freshwater is assumed to have an initial thickness of 0.25 m for both experiments, saltp_l and saltp_d.
In the following sections, the results of the SPRING computation are compared with the data measured in the SALTPOOL project and with the results of the computations in d3f, both according to [OSWALD]. The results from d3f (please refer to [FEIN (Hrsg.)] in [OSWALD]) and from SPRING were computed under similar conditions.
|
|
Computed Results for the 3rd Phase of saltp_l
|
|
The figure below shows the breakthrough curves of the concentration at the opening O3 with the actual measurements and the results computed with d3f (according to [OSWALD]), supplemented by the results obtained with SPRING.
|
|
To visualize the distribution of the solute concentration inside the block, the course of a isoline for C = 0.5 % is illustrated in a cross-section of the block in [OSWALD]. The figure below contains this visualization, supplemented with the results computed with SPRING:
|
|
Computed Results for the 3rd Phase of saltp_d
|
|
The figure below shows the breakthrough curves of the concentration at the opening O3 with the actual measurements and the results computed with d3f (according to [OSWALD]), supplemented with the results computed with SPRING.
|
|
Referencs
|
|
[FEIN (Hrsg.)] E. Fein (Hrsg.); d3f - A Simulator for Density Driven Flow Modelling. User's Manual. GRS, Braunschweig, 1988.
[OSWALD] S. Oswald; Dichteströmungen in porösen Medien. ETH Zürich, 1999
[SPRING] SPRING; Simulation of Processes in Groundwater. Programmbeschreibung. GKW, Bochum, 2000
|
|
