A modified version of SUTRA is introduced that is capable of simulating variable-density flow and transport of heat and multiple dissolved species through variably to fully saturated porous media. The original version of SUTRA is capable or simulating variable-density flow and transport of either heat or one dissolved species through variably to fully saturated porous media. This modified version was developed because of the importance of temperature and solute concentrations in many variable-density flow environments and the desire to implicitly simulate the transport of multiple dissolved species that may or may not affect fluid density. Users familiar with SUTRA should have little difficulty applying this version of SUTRA to multi-species transport problems.
All modifications to SUTRA are general, the number of dissolved species that can be simulated is unrestricted by the program, any of the simulated species can affect fluid density and or viscosity, and simulation of heat transport is unrestricted by the number of simulated dissolved species. The model assumes density and viscosity are linear functions of solute concentration. For simulation of energy transport, the model assumes density is a linear function of temperature but the relation between temperature and viscosity is non-linear. A limitation of the current temperature-viscosity relationship is that it can be scaled only with user-specified parameters unless the code is modified and recompiled. However, alternative temperature-viscosity relationships can be easily incorporated in the source code. In addition to modifications that allow for multi-species transport, SUTRA has been modified to allow use of a spatially distributed solid matrix thermal conductivity and the option to use a geometric-mean approximation for bulk thermal conductivity that accounts for partial saturation. The geometric-mean approximation for bulk thermal conductivity was added because of supporting empirical evidence (Sass and others, 1971).
In addition to modifications to the numerical algorithms in SUTRA, a number of optional functions have been added to minimize solution non-convergence, minimize user coding to simulate time-varying boundary conditions, reduce output file size, allow specification of hydraulic parameters using zones, and specify observation locations with spatial coordinates. A simplified automatic time-step algorithm has been added that reduces the time-step length, if the number of iterations exceeds a user-specified value, and can rerun time steps if the specified maximum number of iterations is exceeded. A simple algorithm has been added that allows any boundary condition to be time varying without the need for user-programmed functions, with the limitation that boundary conditions between the times when conditions are changed (at the beginning of stress periods) are not interpolated. Time steps are reduced to the minimum time step when new boundary-condition values are read. A simple technique has been implemented that permits the user to specify the exact time to write data to the nodal and elemental output files. Functionality has been added that allows hydraulic parameters to be specified using zones in order to reduce the memory requirements for large two- and three-dimensional simulations and to better facilitate the use of model-independent parameter-estimation codes (e.g., UCODE, Poeter and Hill, 1998; PEST, Doherty, 1994). A simple routine that allows observation locations to be specified using coordinates rather than node numbers also has been included.
The modified version of SUTRA has retained all the functionality of the original SUTRA and can solve the flow and transport equations in either two or three dimensions. This version of SUTRA is backward compatible with standard two- and three-dimensional SUTRA single species input data sets. Multi-species data sets are different from standard data sets only when additional data are required for each simulated species.
Three examples are presented that demonstrate the ability of the modified version of SUTRA to simulate multi-species transport. Two of these examples demonstrate the ability to simulate fluid density affected by more than one species, and one example shows several additional applications of the modified version of SUTRA. Where possible, the modified code is compared to observed data, the standard version of SUTRA (Voss and Provost, 2002), or other codes capable of simulating variable-density flow and heat and solute transport. Comparisons indicate the modified version of SUTRA is comparable to HST3D (Kipp, 1997) for a coupled heat and solute variable-density-flow problem, and is capable of simulating a coupled variable-density multi-species Hele-Shaw experiment.
1.0 Introduction
1.1 Purpose
1.2 SUTRA Fundamentals and Previous Applications
1.3 The Current Study
2.0 Physical-Mathematical Basis of SUTRA-MS Modifications
2.1 General Mass-Balance Formulation
2.1.1 Fluid Mass-Balance Equation
2.1.2 Modified Form of the Fluid Mass- Balance Equation
2.1.3 Unified Energy- and Solute- Balance Equation
2.1.4 Modified Form of the Unified Energy- and Solute- Balance Equation
2.1.5 Modified Form of the Energy- Balance Equation used with Geometric-Mean Approximation for Bulk Thermal Conductivity
3.0 Numerical Methods
3.1 Numerical Approximation of SUTRA-MS Fluid Mass Balance
3.2 Numerical Approximation of SUTRA-MS Unified Energy- and Solute-Balance Equation
3.3 Temporal Evaluation of Adsorbate Mass Balance
3.4 Solution Sequencing
4.0 Additional SUTRA-MS Options
4.1 Simple Time-Varying Boundary Conditions
4.2 Specified User Output Times
4.3 Simple Automatic Time-Stepping Algorithm
4.4 Specified Observation Locations
4.5 Specification of Hydraulic Parameters Using Zones
5.0 SUTRA-MS Simulation Examples
5.1 Density-dependent flow, heat transport, and solute transport, Solution for multi-component fluid flow in a saline aquifer system
5.1.1 Physical Setup
5.1.2 Simulation Setup
5.1.3 Parameters
5.1.4 Boundary Conditions
5.1.5 Initial Conditions
5.1.6 Results
5.2 Solution for double-diffusive finger convection induced by different fluid dispersivities and viscosities
5.2.1 Physical Setup
5.2.2 Simulation Setup
5.2.3 Parameters
5.2.4 Boundary Conditions
5.2.5 Initial Conditions
5.2.6 Results
5.3 Density-dependent flow with transport of a non-reactive tracer and zero-order production and transport of a solute to simulate ground-water age
5.3.1 Physical Setup
5.3.2 Simulation Setup
5.3.3 Parameters
5.3.4 Boundary Conditions
5.3.5 Initial Conditions
5.3.6 Results
6.0 SUTRA-MS Data Input
6.1 SUTRA Input Data List
6.2 General Format of the ".inp", ".ics", ".tbc", ".otm", ".ats", ".sob", and ".zon" Input Files
6.3 List of Input Data for the ".inp" (Main Input) File
6.4 List of Input Data for ".ics" (Initial Conditions) File
6.5 List of Input Data for ".tbc" (Simple Transient Boundary Conditions) File
6.6 List of Input Data for ".otm" (Specified User Output Times) File
6.7 List of Input Data for ".ats" (Simple Automatic Time-Stepping Algorithm) File
6.8 List of Input Data for ".sob" (Specified Observation Locations) File
6.9 List of Input Data for ".zon" (Node and Element zone parameters) File
7.0 References.
Appendix 1: Notation
Generic Units
Units 133
Special Notation
Roman Lowercase
Roman Uppercase
Greek Lowercase
Greek Uppercase
For product and ordering information:
World Wide Web: http://www.usgs.gov/pubprod
Telephone: 1-888-ASK-USGS
For more information on the USGS— the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment:
World Wide Web: http://www.usgs.gov
Telephone: 1-888-ASK-USGS
This report is available online in Portable Document Format (PDF). If you do not have the Adobe Acrobat PDF Reader, it is available for free download from Adobe Systems Incorporated.
Download the report (PDF, 1.6 MB)
Document Accessibility: Adobe Systems Incorporated has information about PDFs and the visually impaired. This information provides tools to help make PDF files accessible. These tools convert Adobe PDF documents into HTML or ASCII text, which then can be read by a number of common screen-reading programs that synthesize text as audible speech. In addition, an accessible version of Acrobat Reader 5.0 for Windows (English only), which contains support for screen readers, is available. These tools and the accessible reader may be obtained free from Adobe at Adobe Access.
| AccessibilityFOIAPrivacyPolicies and Notices | |
  |
|