UNIT 11 -- TRANSIENT MODFLOW MODELING:
Transient analytical solutions provide insight into the rate of change in a system, that is the length of time required to reach steady state conditions. This is of value because we may only be interested in the temporary application of a stress to the ground-water system. For example, the life of a mine may be 50 years and the response of the system may be slow enough that we do not even begin to approach steady state during that time frame. The steady state solution provides the maximum impact of the stress. The impacts during the transient period while the system is approaching steady state can only be less than those that prevail under steady state conditions.

Some problems do not have a steady state result. For example if a basin is pumped at a rate greater than the recharge, eventually the basin will go dry and the pumping cannot continue. A balanced steady state condition cannot be reached and so a steady state solution for pumping the basin at that rate does not exist.

The OBJECTIVE of UNIT 11 is for you to:

* BECOME FAMILIAR with ASPECTS OF NUMERICAL MODELING that are UNIQUE to TRANSIENT PROBLEMS

* UNDERSTAND the need for and significance of INITIAL CONDITIONS

* UNDERSTAND the DIFFERENCE between TIME-AVERAGED SOLUTIONS and SOLUTIONS with a GREATER DEGREE of TIME DISCRETIZATION and how this IMPACTS your CONCLUSION

DISCUSSION

As we discussed previously, definition of a specific ground-water problem requires that BOUNDARY CONDITIONS be imposed on the flow equations for the domain of interest. If the problem is transient, INITIAL CONDITIONS must also be defined. This can be thought of as specifying boundary conditions in time.

The transient analytical solutions we were discussing at that time employed relatively simple hydrostatic conditions, often yielded solutions in terms of drawdown, and called upon superposition to apply the results to alternative initial conditions if the problem was linear.

If a solution is expressed in terms of head rather than drawdown, then the initial heads must be defined. Numerical modeling is conducted in terms of head and allows us to define complex initial conditions. There are some important concepts to keep in mind, so go on to the transient numerical solution main page to consider these concepts.

TRANSIENT NUMERICAL SOLUTION MAIN PAGE

EXERCISES

If you chose to purchase Applied Ground-water Modeling,

If you chose to purchase Introduction to Ground-water Modeling,

If you didn't explore the following exercises in the discussion section, or wish to revisit any of them, the following links take you directly to the exercises:

Exercise 5 - Steady State Simulation of Pumping (end point of transient simulation under average conditions)
Exercise 6 - Transient Simulation of Average Annual Pumping starting from average steady state heads
Exercise 7a - Cyclic Transient Simulation of Variable Recharge without Pumping
Exercise 7b - Transient Simulation of Variable Pumping with Variable Recharge

How might transient modeling have helped our calibration and prediction?

Recall the steady state calibration results by (clicking here)

Prepare a transient calibration given the results of a 7 day pumping test here are data that you can copy. The test includes pumping both aquifers at a rate of 0.0625 cms at observation locations 2and 6, and 0.125cms at location 5.

Has the parameter estimation improved? Results of transient calibration.

compare:
- results of the steady state regression
- results of the transient regression
- true parameter values

Compare Transient and Steady State Residual Analysis.

Is the Transient model more or less linear than the Steady State calibration model? COMPARE Transient_SteadyState Linearity

Have the predictions or the confidence in them changed? Set up the same predictive situation as for the steady state calibration in unit 9 (pumping 1cms from the upper and lower layers at x=9500, y=9500 (row 9 column 10). This time make a transient predictions at the same locations (row 9 column 5 and row 9 column 15 as well as the flow along the entire reach of stream). Predict after pumping 1 day, 1month, 1 year and 5 years. Results. Comparison with Steady State Predictions Table Format, Graphic Format (xls). Download the files to assess these predictions.

COMMUNICATION

Please bring up any questions you may have about regarding transient numerical modeling. epoeter@mines.edu

ON TO LESSON 12

BACK TO LESSON LIST

BACK TO MAIN PAGE