## Research – Hydraulic Tomography – Examples

### Steady State 3D Hydraulic Tomography

This example, from Yeh and Liu, 2000, illustrates the principle of hydraulic tomography for a small, steady-state synthetic case. Sandbox experiments were also performed using a both a simple stratification and a more realistic heterogeneous media. Inversion of the data collected from these laboratory experiments produced similar results (Liu, Yeh and Gardner, 2000). This method would be well suited for sites where multi-port (e.g., continuous multichannel tubing, Westbay, or Waterloo multilevel systems) observation wells have been installed for characterizing aquifer contamination. Superfund sites, where characterization of the heterogeneity of the subsurface, and the distribution of contaminants is important, would benefit greatly from this efficient method.

Actual distribution of hydraulic conductivity. | Results of hydraulic tomography. | Pumping and observation locations. |

### Transient 2D Hydraulic Tomography

#### Estimate Hydraulic Conductivity (K)

In the above example, pressure data collected at observations after a long duration of pumping (at or near steady-state) were used. This is because at steady-state the response of the aquifer is only a function of hydraulic conductivity, not specific storage (the two components of the hydraulic diffusivity). This makes the analysis much more straight forward, and makes the dependence of pressure response to K alone more apparent. Current my research group is doing work which is showing that efficient analysis of transient tomographic pumping data is a reality.

Actual distribution of hydraulic conductivity (K) | Estimated K from Hydraulic Tomography with pumping and observation locations |

#### Estimate Specific Storage (S)

A variation of the procedure used for estimating a distribution of K in the domain, can be used to estimate the specific storage. Typically K is estimated only from longer-term (near steady-state) observations from a pumping test, while S is obtained only from the early-time data, but using our algorithm and inverse methods, we can use any transient data (early or late) to improve both estimates.

Actual distribution of Specific Storage (S). | Estimated S from Hydraulic Tomography with pumping and observation locations |

### Transient 3D Hydraulic Tomography

The concepts introduced with the two-dimensional hydraulic tomography are generalized to three dimensions, so that a block of aquifer with heterogeneous properties can be characterized by using this method to analyze the data collected from several small pumping tests.

This method utilizes all of the data collected during a pumping test, not just the steady-state data, collected at the end of test, but using all data. Realistically, pumping tests cannot be run until they reach steady-state (which may be days or weeks for some aquifers), so this is quite useful for shorter real-world pumping tests.