Hydraulic Gradient – Fundamentals and Wandering Groundwater in a Tidally Impacted AquiferJonathan Johnson, PhD, ENVIRON, Princeton NJ; Jinjun Wang, PhD, PE, ENVIRON, Houston TX

ABSTRACTHydraulic gradient is a vector quantity having both magnitude and direction. Fundamentally, magnitude and direction of a gradient vector can be determined by using a set of three wells with concurrent water level measurements. Average gradient, over a speci�c time scale, can be obtained from a series of gradient vectors calculated over shorter time scales using vector algebra. In practice, this simple analysis is underutilized. The concept becomes a very powerful analytical tool when applied in conjunction with pressure transducer readings. This study demonstrates an application of this fundamental concept for �ow and transport analysis in a tidally in�uenced aquifer.

Multiple pressure transducers were installed in an aquifer in�uenced by a tidal river. Surprisingly complex groundwater �ow patterns arose from plotting the hydraulic gradient series for each well triplet. Dynamics occurred at time scales and spatial scales important to groundwater �ow and transport, which are often entirely ignored when analysis methods require the assumption of average uniform steady groundwater �ow.

Plots of the gradient vectors from this study show that different �ow patterns result depending on location and distance from the tidal body. Plotted vectors describe groundwater �ow paths that are wandering as compared to the average path. These wanderings occur at shorter time scales than that of the average gradient. Importantly, these wanderings contain gradient angles perpendicular to and opposite to the average gradient direction.

Water Level Data: 15 wells5 minute intervals 870 water levels for each well

Hydraulic Gradient is a Vector Quantity with Magnitude and Direction

Three Point Gradient Computation (Heath, 1983)

Head measurements at time t1 Resulting gradient vector at time t1

Vectors Placed Head to TailFor example, water levels are taken at times t1,t2,t3, at an equal interval apart Dt.

Last Example: Different Site — Recharge Event

SHALLOW ZONE

INTERMEDIATE ZONE

1

DEEP ZONE

Shallow Data: 4 wellsThickness 3-5 ftHistoric �ll and �ne to medium sand

Intermediate Data: 7 wellsThickness 16 ftFine to medium sand with �ne gravel

Deep Data: 4 wellsThickness 5 ftFine sand

Gradient at time t1

Gradient at time t2

Gradient at time t3

Vector Sum

Vector Average

Development of TheoryThe complexity of the �ow system does not diminish our desire for simpli�ed solutions to the transport equations in these systems. The “average” concentration is still a meaningful quantity with respect to exposure and transport to receptors. The equations below illustrate the potential use of the measured changing directions of �ow applied to the two-dimensional transport equation.

Conservative solute transport in two dimensions can be written as Equation 1:

The dispersion tensors in Equation 1 are de�ned as follows:

Our measurement technique suggests a method of incorporating the impact of changes in direction. Assuming constant hydraulic conductivity (K), and effective porosity (ne) and using our hydraulic data from the transducers allows us to write:

Where the subscript TS indicates that dispersion is Time Scale Dependent.

Terms in the form of

are normalized gradient components over time scale TS, which can be directly calculated from the gradient analysis data. This suggests closed form analytical solutions may still be possible at a given speci�c time scale.

INTERMEDIATE ZONE

2

CONCLUSIONGroundwater/surface water interaction can result in highly complex �ow

patterns that present a challenge to modeling the groundwater hydrology

and contaminant transport. Our calculation of gradient and changes in

gradient over time illustrates the complexity of the system, and may provide

for a technique to predict both the average direction of �ow and average

concentration in these inherently dynamic environments. In tidally impacted

aquifers, or in areas with suspected changes in �ow direction, extra care

should be taken to evaluate the hydrogeological characteristics, such as

hydraulic gradient and hydraulic dispersion. Continuous-logging devices

are suggested as a method to better understand the hydrology and

interactions at time and space scales of interest.

REFERENCEHeath R. C., Basic Groundwater Hydrology, WSP 2220, USGS, 1983

0.0176

0.0011

0.0005

0.0018

Generalized Boring Log

0.005

hydraulic gradient

magnitude

direction

JohnsonPosterv8.indd 1 11/30/12 9:48 AM