**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.**Consider the tasks that need to be accomplished. Click here to get the completed files.**

Has the parameter estimation improved? Results of transient calibration.**Run Residual_Analysis. Which observations made the difference? (click here to see transient Residual_analysis results) Steady State results.**

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.

**
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, **

read Chapter 7

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

read Chapter 4

**
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: **

compare:

- results of the steady state regression

- results of the transient regression

- true parameter values

**COMMUNICATION**

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