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### Multi-Layered Aquifer Systems

Chapter Nine

Analysis and Evaluation of Pumping Test Data

Revised Second Edition

Aquifer System #1

- Consists of two or more aquifer layers separated by aquicludes. Therefore, we have two possibilities:
- Two confined aquifers
- An unconfined aquifer overlying a confined aquifer
- If data on the transmissivity and storativity of the individual layers are needed, a pumping test can be performed in each layeras long as the well does not fully penetrate the entire system.
- For an aquifer system consisting of multiple confined aquifers separated by an aquiclude, Papadopulosderived asymptotic solutions for non-steady state flow to a well that fully penetrates the system.
- For an aquifer system that consists of an unconfined aquifer overlying a confined aquifer, Khader and Veerankutty derived a solution for non-steady state flow to a fully penetrating well.

Aquifer System #2

- Consists of two or more aquifers- each with its own hydraulic characteristics- that are separated by interfaces that allow for unrestricted flow between them, or crossflow.
- A response to pumping will be analogous to that of a single-layered whose transmissivity and storativity are equal to the sum of the transmissivity and storativity of the individual layers.

Javandel-Witherspoon Method

This is for aquifer system #2: a confined two-layered aquifer systems with unrestricted crossflowbetween the two aquifer layers.

This method is applicable if the following assumptions and conditions are satisfied:

- The aquifer is confined
- The aquifer has a seemingly infinite areal extent
- The system consists of two aquifer layers. Each layer has its own hydraulic characteristics, is of apparent infinite areal extent, is homogeneous, isotropic, and of uniform thickness over the area influenced by the test. The interface between the two layers is an open boundary.
- Prior to pumping, the piezometric surface is considered horizontal
- The aquifer is pumped at a constant discharge rate.
- The flow to the well is in non-steady state
- The piezometers are placed at a depth that coincides with the middle of the well screen.
- Drawdown data are available for small and large values of pumping time
- Small data values of pumping time measured by: t < or = (D1 – b)2 / (10K1D1 / S1)
- Late-time drawdown data values measured by: r > or = 1.5{D1 + (K2D2) / K1}
- The pumped well does not penetrate the entire thickness of the aquifer system, but it partially screened.

Javandel-Witherspoon Method (cont’d)

The analytical solution was developed for the drawdown in both layers of a confined two-layered aquifer system pumped by a partially screened well in either setting in the diagram.

Javandel-Witherspoon Method (cont’d)

For small values of pumping time (t < or = (D1 – b)2 / {10K1D1) / S1}), the drawdown equation for the pumped layer is the same as the equation for unsteady-state flow in a confined single-layered aquifer with a partially penetrating pumping well:

Where:

Javandel-Witherspoon Method (cont’d)

For large values of pumping time and at distances from the pumped well beyond

R > or = 1.5 {D1 + (K2D2) / K1}, the partial penetration effects of the well can be ignored and the drawdown in the pumped layer approaches the following expression, which has the same form of the Theis equation for unsteady flow in a confined single-layered aquifer pumped by a fully penetrating well:

A semi-log drawdown-time plot will show a straight line for large values of time, with the slope equivalent to:

Aquifer System #3

Consists of multiple aquifers layers separated by aquitards.

In this leaky system, pumping one layer has measureable effects in other layers of the aquifer system. The effects are dependent upon the hydraulic characteristics of the individual layers and the aquitards.

For short pumping tests in these systems, drawdown in the unpumped layers can be considered negligible, and we would use methods from chapter 4 to find aquifer properties.

For longer pumping times, Bruggeman developed a method for the analysis of pumping data from leaky two-layered aquifer systems in steady state conditions.

Bruggeman’s Method

The Bruggeman method is based on the following assumptions and conditions:

- The aquifer system consists of two layers separated by an aquitard. Each layer is homogenous, isotropic, and of uniform thickness over the area influenced by the test. The aquifer system is overlain by an aquitard.
- The aquifer has a seemingly infinite areal extent.
- The well receives water by horizontal flow from the entire thickness of the pumped layer.
- Prior to pumping, the piezometric surface is considered horizontal.
- The aquifer is pumped at a constant discharge rate.
- The flow to the well is in steady state.
- Distance from well (r) / Leakance (r/L) is small: r/L < 0.05
- C1 > C2 (c is the hydraulic resistance, which characterizes the resistance of an aquitard to vertical flow, and is the reciprocal of leakage. Thus, c = D / K.
- K2D2 > K1D1 (T2 > T1)
- C3is less than or equal to infiniti
- A pumping test is first conducted in the lower layer until a steady state is reached. Then, after complete recovery, a pumping test is conducted in the upper layer until steady state is reached.

Bruggeman’s Method (cont’d)

If the hydraulic resistance of the aquitard separating the layers is high compared with that of the overlying aquitard, and if the base layer is an aquiclude, the upper and lower parts of the system can be treated as two separate single-layered leaky aquifers.

However, if the hydraulic resistance of the separating aquitard is appreciably lower than that of the overlying aquitard, and the upper system is pumped, the discharged water would come from the pumped upper layer, the lower aquifer layer through the separating aquitard, and the overlying aquitard.

Bruggeman’s Method (cont’d)

The following relations are valid:

s’2,1 is the drawdown observed in the lower layer when the upper layer is pumped at a standard Q.

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