﻿ Pumping Test: Theory and Analysis Methods > Pumping Test Analysis Methods - Flexible Assumptions > Leaky - Hantush-Jacob (Walton)

# Leaky - Hantush-Jacob (Walton)

Most confined aquifers are not totally isolated from sources of vertical recharge. Less permeable layers, either above or below the aquifer, can leak water into the aquifer under pumping conditions. Walton developed a method of solution for pumping tests (based on Hantush-Jacob, 1955) in leaky-confined aquifers with unsteady-state flow. The conditions for the leaky aquifer are shown below.

In the case of leaky aquifers, the well function described by Theis (1935) can be replaced by the functions described by Walton or Hantush , and the solution becomes:

where:

is the drawdown at a point        [L]

is the distance to the well        [L]

is the pumping rate        [L3/T]

is the aquifer transmissivity        [L2/T]

is the Hantush dimensionless curve parameter,        [-]

is the leakage factor, , (note is also referred to as in the Hantush function)        [1/L]

is the hydraulic resistance,        [1/T]

is the thickness of the leaky aquitard        [L]

is the vertical hydraulic conductivity of the leaky aquitard        [L/T]

In AquiferTest, the model parameter (hydraulic resistance, units [time]) is used with the Hantush method. The larger , the smaller and/or more slowly the infiltration is due to leakage. The value must be defined for each data set, in the Results frame of the Analysis Navigator panel.

## Example

An example of a Hantush-Jacob analysis graph has been included below:

In this example, the dimensionless view is shown. An example of a Hantush-Jacob analysis is available in the project:

C:\Users\Public\Documents\AquiferTest Pro\Examples\Leaky.HYT

## Assumptions

The Hantush-Jacob method can be used if the following assumptions and conditions are satisfied:

The aquifer:

ohomogeneous and isotropic

ois infinite in areal extent

ohas uniform thickness

ois leaky confined

oreleases water from storage instantaneously with declines in hydraulic head

The leaky aquitard:

ohas a homogenous vertical hydraulic conductivity

ois infinite in areal extent

ohas uniform thickness

ois overlain or underlain by an infinite constant head plane source

ois incompressible (has no storage)

The pumping well:

ofully penetrates the aquifer

ohas a sufficiently small diameter such that storage in the well can be neglected

Flow:

oin the aquifer is horizontally radial towards the well

ohas no vertical component

oin the aquitard is vertical

The water table is flat

## Data Requirements

The data requirements for the Hantush-Jacob (no aquitard storage) Solution are:

Drawdown vs. time data at an observation well

Distance from the pumping well to the observation well

Pumping rate

value: dimensionless leakage factor

## Dimensionless Parameters

For Hantush the dimensionless curve parameter which characterizes the leakage is defined as:

where:

The leakage factor () must be greater than 3 times the saturated aquifer thickness () and the dimensionless leakage factor () must be less than or equal to 0.05 (Kruseman and de Ridder, 1991). If the aquifer is not leaky (i.e. ), then and the solution reduces to the Theis solution for a confined system.

Similar to the Theis method, type curves are generated on a log/log scale plot of the relationship between values of along the Y-axis versus values of along the X-axis. The data analysis is done by curve matching the field measurements, which are plotted with drawdown () values along the Y-axis and time () values along the X-axis, to a type curve. The following window can be located by expanding the Type curves section of the Analysis Navigator Panel and selecting "Add type curve..." button.