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# Diagnostic Plots and Interpretation

Calculating hydraulic characteristics would be relatively easy if the aquifer system (i.e. aquifer plus well) were precisely known. This is generally not the case, so interpreting a pumping test is primarily a matter of identifying an unknown system. System identification relies on models, the characteristics of which are assumed to represent the characteristics of the real aquifer system (Kruseman and de Ridder, 1991).

In a pumping test the type of aquifer, the well effects (well losses and well bore storage, and partial penetration), and the boundary conditions (barrier or recharge boundaries) dominate at different times during the test. They affect the drawdown behavior of the system in their own individual ways. So, to identify an aquifer system, one must compare its drawdown behavior with that of the various theoretical models. The model that compares best with the real system is then selected for the calculation of the hydraulic parameters (Kruseman and de Ridder, 1991).

AquiferTest includes tools to help you to determine the aquifer type and conditions before conducting the analysis. In AquiferTest, the various theoretical models are referred to as Diagnostic plots. Diagnostic plots are plots of drawdown vs. the time since pumping began; these plots are available in log-log or semi-log format. The diagnostic plots allow the dominating flow regimes to be identified; these yield straight lines on specialized plots. The characteristic shape of the curves can help in selecting the appropriate solution method (Kruseman and de Ridder, 1991).

Furthermore, the Diagnostic plots also display the theoretical drawdown derivative curves (i.e. the rate of change of drawdown over time). Quite often, the derivative data can prove to be more meaningful for choosing the appropriate solution method.

NOTE: Diagnostic Graphs are only available for Pumping Tests when using AquiferTest Pro.

To view the Diagnostic Plots, load the Analysis tab, select the Diagnostic Graphs tab, and the following window will appear:

The main plot window will contain two data series:

1. the time-drawdown data

2. the drawdown derivative data (time vs. change in drawdown).

The drawdown derivative data series will be represented by a standard symbol with the addition of an X through the middle of the symbol.

To the right of the graph window, you will see 6 diagnostic plot windows, with a variety of type curves. The plots are named diagnostic, since they provide an insight or “diagnosis” of the aquifer type and conditions. Each plot contains theoretical drawdown curves for a variety of aquifer conditions, well effects, and boundary influences, which include:

Confined

Leaky

Recharge Boundary

Barrier Boundary

Unconfined or Double Porosity

Well Effects

In the Diagnostic plots, the time (t) is plotted on the X axis, and the drawdown (s) is plotted on the y axis. There are two different representations are available:

1. Log-Log scale

2. Semi-log (also known as lin-log), whereby the drawdown (s) is plotted on a linear axis.

The scale type may be selected directly above the time-drawdown graph templates. Changing the plot type will display a new set of the graph templates, and also plot the observed drawdown data in the new scale.

Each diagnostic graph contains two lines:

 Type curve (solid blue line) Derivative of type curve (dashed black line).

In some diagnostic plots, there is no distinguishable difference between the time vs. drawdown curves, and it may be difficult to diagnose the aquifer type and conditions. In this case, study the time vs. drawdown derivative curves, as they typically provide a clearer picture of the aquifer characteristics.

The diagnostic plots are available as a visual aid only; your judgment should coincide with further hydrogeological and geological assessment.

The theoretical drawdown graph templates are further explained below.

By default, the Diagnostic plot will assume a constant discharge rate. If you are using variable discharge rate for your pumping test, then you must turn on the "Variable Discharge" check box above the Diagnostic graph, which normalizes the drawdown using the relative pumping rate. If “Include recovery” is checked, the data points during recovery (between the steps) are shown as well. The methodology to accommodate this is based on the techniques described in Birsoy and Summers (1980).

## Identifying Flow Regimes

In the log-log mode of the Diagnostic Graph tab, you can display trend lines representing a flow regime which can be helpful in determining well/aquifer conditions. These lines have a particular slope on a log-log plot, which represents the slope of the derivative during a given period of time, so they should be parallel with the derivative of the (smoothed) measured data when the represented flow regime is active.  The various flow regimes are described by Renard et al (2009) and in the Diagnostic_plots entry at http://petrowiki.org.

The following flow regimes have well defined slopes that can be plotted in AquiferTest:

Wellbore storage: (slope = 1) occurs at initial times when the well bore is draining or when a pseudo-steady state condition has been reached (e.g. boundary dominated flow)

Radial: (slope = 0) typically occurs after wellbore storage and prior to boundary effects

Linear flow: (slope = 1/2) occurs in channelized aquifers, (hydraulically) fractured wells, and horizontal wells

Bilinear (slope = 1/4) occurs in fractured wells with low-conductivity fractures

Spherical (slope = -1/2) occurs in partially penetrating wells with a low penetration ration (i.e. the screen length in the aquifer is small relative to the aquifer thickness)

### Confined Aquifer

In an ideal confined aquifer (homogeneous and isotropic, fully penetrating, small diameter well), the drawdown follows the Theis curve. When viewing the semi-log plot, the time-drawdown relationship at early pumping times is not linear, but at later pumping times it is.

 log-log lin-log

If a linear relationship like this is found, it should be used to calculate the hydraulic characteristics because the results will be much more accurate than those obtained by matching field data points with the log-log plot (Kruseman and de Ridder, 1991).

### Unconfined Aquifer

The curves for the unconfined aquifer demonstrate a delayed yield. At early pumping times, the log-log plot follows the typical Theis curve. In the middle of the pumping duration, the curve flattens, which represents the recharge from the overlying, less permeable aquifer, which stabilizes the drawdown. At later times, the curve again follows a portion of the theoretical Theis curve.

 log-log lin-log

The semi-log plot is even more characteristic; it shows two parallel straight-line segments at early and late pumping times. (Kruseman and de Ridder, 1991).

### Double Porosity

The theoretical curve for double porosity is quite similar to that seen in an unconfined aquifer, which illustrates delayed yield. The aquifer is called double porosity, since there are two systems: the fractures of high permeability and low storage capacity, and the matrix blocks of low permeability and high storage capacity. The flow towards the well in this system is entirely through the fractures is radial and in unsteady state. The flow from the matrix blocks into the fractures is assumed to be in pseudo-steady-state.

 log-log lin-log

In this system, there are three characteristic components of the drawdown curve. Early in the pumping process, all the flow is derived from storage in the fractures. Midway through the pumping process, there is a transition period during which the matrix blocks feed their water at an increasing rate to the fractures, resulting in a (partly) stabilized drawdown. Later during pumping, the pumped water is derived from storage in both the fractures and the matrix blocks (Kruseman and de Ridder, 1991).

### Leaky

In a leaky aquifer, the curves at early pumping times follow the Theis curve. In the middle of the pumping duration, there is more and more water from the aquitard reaching the aquifer. At later pumping times, all the water pumped is from leakage through the aquitard(s), and the flow to the well has reached steady-state. This means that the drawdown in the aquifer stabilizes (Kruseman and de Ridder, 1991).

 log-log lin-log

### Recharge Boundary

When the cone of depression reaches a recharge boundary, the drawdown in the well stabilizes. The field data curve then begins to deviate more and more from the theoretical Theis curve (Kruseman and de Ridder, 1991).

 log-log lin-log

### Barrier (Impermeable) Boundary

With a barrier boundary, the effect is opposite to that of a recharge boundary. When the cone of depression reaches a barrier boundary, the drawdown will double. The field data curve will then steepen, deviating upward from the theoretical Theis curve. (Kruseman and de Ridder, 1991). Analytically this is modeled by an additional pumping well (an image well). After this phase (in which the two drawdowns accumulate) and the curve again adapts itself to the Theis function.

 log-log lin-log

### Well Effects

Well effects, in particular storage in the pumping well, can contribute to delayed drawdown at the beginning of the pumping test. At early pumping, the drawdown data will deviate from the theoretical Theis curve, since there will be a storage component in the well. After this, in mid to late pumping times, the drawdown curve should represent the theoretical Theis curve. These well effects are more easily identified in the lin-log plot.

 log-log lin-log

## Analysis Plots and Options

The Analysis plots are the most important feature in AquiferTest. In the analysis graph, the data is fit to the type curve, and the corresponding aquifer parameters are determined. In the graph the data can be plotted linearly or logarithmically. The program calculates the Type curve automatically, and plots it on the graph. Above the graph, the analysis method is listed. To the right of the graph, in the Analysis Navigator panel, the aquifer parameters for each well are displayed in the Results frame, and can be manually modified using parameter controls. (for more information see "Manual Curve Fitting").

### Model Assumptions

The model assumptions control which solution method will be chosen for your data, and what superposition factors will be applied.

Using the diagnostic plots as a guide, select the appropriate model assumptions, and AquiferTest will select the appropriate Analysis Method from the Analysis Navigator panel. From here, you may continue to adjust the model assumptions in order to reach a more representative solution. Alternately, you may directly select the Analysis Method and AquiferTest will then select the corresponding model assumptions.

The following model assumptions are available for the pumping test solutions:

Type: Confined, Unconfined, Leaky, Fractured

Extent: Infinite, Recharge Boundary, Barrier Boundary

Isotropy: Isotropic, Anisotropic

Discharge: Constant, Variable

Well Penetration: Fully, Partially

Each time a model assumption is modified, AquiferTest will attempt to recalculate the theoretical drawdown curve, and a new automatic fit must be applied by the user. If the automatic fit fails, then a manual curve fit can be done using the parameter controls.

Also, adjusting model assumptions may result in the addition of a new aquifer parameter(s), or removal of existing ones (apart from the usual parameters Transmissivity [T] and Storativity [S]). For example, if you change the aquifer type from confined to leaky, an additional parameter for hydraulic resistance (c) will be added for each well in the Results frame of the Analysis Navigator panel, and its value will be calculated. Alternately, changing the aquifer type back to confined will hide this parameter, and the c value will no longer appear in the Results frame.

NOTE: Model assumptions are not available for slug test solutions, nor for the Theis Recovery or Cooper-Jacob methods.

### Dimensionless Graphs

AquiferTest also provides a dimensionless representation of the analysis graph. In this graph, time () and drawdown () are plotted without dimensions.

NOTE: Similar to the diagnostic plots, the dimensionless graph is appropriate for constant pumping rates only, and a single pumping well.

The following definitions are specified:

Dimensionless time, and dimensionless drawdown,

where:

T is the aquifer transmissivity        [L2/T]

t is the elapsed time since the start of pumping        [T]

r is the distance to the well        [L]

S is the aquifer storage coefficient        [-/L]

s is the drawdown at a point        [L]

Q is the discharge from the well        [L/T]