Aquifer Tests

8/8/2019 Aquifer Tests

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AQUIFER TESTS Estimation of T, K and S for an aquifer

CONFINED AQUIFERGraphical solutions to flow equations: Theis type curve method, (Cooper) Jacob timedrawdown and distance drawdown methods

Introduction:- Previous emphasis: Predicting drawdown based on known aquifer parameters.

Examples:- You get a call from a client, they want to know why their well went dry- You need to design a de-watering project- You need to predict drawdown from multiple wells or aquifers with

hydraulic boundaries- Now: We will look at another aspect of flow to wells: making estimates of

aquifer parameters (T, K, S) based on field data, aquifer tests

- 2 basic approaches to the solution:- Use type curves that represent graphical solutions for our flow equations- Use straight line graphical solutions

- The objective in both methods: find T, K and S

Point to remember: all of these methods are for non-equilibrium flow (non-steady-state)

- Cone of depression is still expanding

I) Non equilibrium flow in a confined aquifer: Theis method

- Take the Theis equation, solve for T

ho-h = Q W(u)

4Tbecomes:

T = Q W(u)4 (ho -h)

- Also need to rearrange our well function solution equation, solve for S:

u = r2 S becomes S = 4 T t u(4Tt) r

2

- So: how do we get these numbers from an aquifer test?- Answer: the well function for the Theis solution has been plotted on graph

paper. Compare this curve to actual field (drawdown) data


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A) Steps to a type curve solution:1) Plot results from an aquifer test on graph paper. Use the same scale

as the type curve plot.

- Plot drawdown (3 log cycles on y axis scale) vs. time (4 or 5 logcycles on x axis scale)

- Result should look similar to type curve- Note: time is plotted in minutes here

2) Overlay type curve and plot aquifer test results- (light table or transparent type curve helps)


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- Carefully slide type curve until it matches shape of pumping test- Keep axes parallel (don't twist the type curve to make it match)

3) Pick a match point- Match point is any intersecting line set on the overlay curve- A common choice: point represented by W(u) = 1 and 1/u = 1- Note: any match point should produce similar results

4) Read values for:- W (u), 1/u, (ho - h) and t

5) Do necessary conversions (so that values from curve fit can beplugged into our altered version of Theis' equation)

- Convert 1/u to u- Convert t from minutes to days (divide by 1440 min/day)

6) Plug values into Theis' rearranged equation to solve for T:- Must know Q- Convert discharge (Q) units to ft

3/day if necessary

7) Plug values into Storativity equation to solve for storativity- Use the value for T calculated above

S = 4 Ttu / r2

- Must be given a value for r (radial distance to an observation well)- Note: you MUST have an observation well to calculate storativity using this


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method-

8) Solve for K:T = K b or K = T/b

Other graphical solutions to this problem: estimating aquifer parameters under non-equilibrium flow conditions

II) (Cooper) and Jacob straight line time-drawdown method for non-equilibrium flow in aconfined aquifer:

- Timedrawdown part is important: will compare to distance-drawdown method- This approach uses the infinite series from the Theis solution (see eqtn. 5-11

in text)

-

-- Recognizes that the last terms are insignificant IFwe are dealing with longer

term pumping. Combining some terms and converting to base 10 logs (to use with ourgraphing) see pg. 173 text

- The result:

T = 2.3 Q log (2.25 T t)4 (ho - h) (r

2S)

- The log function lets us plot this as a straight line on semi-log paper- Note: the 2.3 is a relict of the conversion from natural logs to base 10 logarithm- Typically: arithmetic scale on y axis (plot drawdown here)

3 cycle log scale on x axis (plot time here in minutes, remember toconvert to days in the following equations)


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- New equations for this solution:

A) Equation for transmissivity:

T = 2.3 Q4 (ho h)

- Note: (ho - h) refers to the change in h over1 log cycle

B) Equation for storativity:

S = 2.25 T tor2

- Note: to refers to the time where the straight line intersects the zerodrawdown line (upper x axis on the graph)

- This is tricky: must project the straight part of the line backward to find to- r = distance to an observation well. Once again, this storativity calculation

requires an observation well, while estimates of T and K do not need an observationwell.

- You must be given: Q, r- You must read (ho h), to from graph- to must be converted to days (again!)

C) Solve for K if needed:

T = Kb


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- This method is only valid for long pumping times- MUST CHECK CRITERIA AFTER SOLVING

- Your text uses a criteria of less than 0.05- Check for all early times in the pumping data. May find that you should NOT

be using some of the early time pumping data to draw your straight line. Mayfind out that all your data is too early!

- Notice in graph above how the early time data do not plot on the straight line

III) Non-equilibrium flow: Cooper Jacob distancedrawdown method- Requires data from several wells- Plot on semi-log paper

- Wells must be properly spaced for this method to be effective. The idealspacing: have at least 3 wells, with distances between the wells that plot on 3different log cycles.

- - Example: observation well with 3 wells spaced at 10 ft, 100 ft and 1000 ft.

- New formulas:


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A) Equation for transmissivity:

T = 2.3 Q2 (ho -h)

- Note: (ho - h) refers to the change in h over1 log cycle

B) Equation for storativity:

S = 2.25 T t / ro2

where:ro = distance where straight line intersects the zero drawdown axist = some time t into the test (in days) where drawdown is recorded

in all wells

Summary:- These methods give a great regional summary of aquifer parameters- T, K and S are estimated for the entire area affected by the cone of depression- Theis method uses (relies on) good early time data (first few seconds or

minutes)- Distance-drawdown method uses an especially wide area- this is useful for

computer models that need a regional estimate of aquifer parameters. AND:uses later time data

SUMMARY FOR CONFINED AQUIFER

Either...

simultaneous data from a series of wells (distance drawdown) or a series ofmeasurements from one well (time drawdown) are used to plot a semi-log drawdowncurve from which the values needed to solve the equations are taken (straight linemethods)

or

Time-drawdown data is plotted on a log-log plot and then matched to a type curve orseries of type curves to derive the unknown parameters. (type curve method)


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Tt

Sru

4

2

=

LEAKY CONFINED AQUIFER

Type curve method:

K = vertical hydraulic conductivity of leaky confining layerB = thickness of leaky confining layer

Source of water leaking to confined aquifer is an upper unconfined aquifer (in picturedexample)

Drawdown response in leaky confined aquiferso Hantush-Jacob formula

o

o

where W(u, r/B) is the well function for leaky aquifer; Kand bare thehydraulic conductivity and thickness of the confining layer, respectively


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Match type curve and aquifer tests data to get W(u,r/B), 1/u, t, s and r/BSubstitute values into Hantush-Jacob equations to obtain T, S, K

UNCONFINED AQUIFER TYPE CURVE MATCHING

Type A curves = early part of curve match to early data to obtain specific storageType B curves = mid to late part of curve match to later data to obtain specific yieldT estimate from both match points should be similarObtain vertical K from lambda value match point


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EFFECT OF PARTIAL PENETRATION OF WELLS

The problem with having a partially penetrating pumping well is that flow near the wellwill not be completely horizontal as water is pulled upward toward the well opening.

Hantush has show that this is not a problem if the observation wells are fullypenetrating.

If the observation wells are also partially penetrating, then they effect of having avertical flow component is negligible if the following relationship is true:

When designing aquifer tests, it is important that these effects be taken intoconsideration if the pumping well is not going to be fully penetrating.

SLUG TESTS

water in the well by lowering into it a solid piece of pipe called a slug (ahhh! So thats where An

alternative to a pump test is a slug test (also called a baildown test). In this test thewater level in a small diameter well is quickly raised or lowered. The rate at which thewater in the well falls (as it drains back into the aquifer) or rises (as it drains from theaquifer into the well) is measured and these data are analyzed.

Water can be poured into the well or bailed out of the well to raise or lower the waterlevel. However, perhaps the easiest way to raise the water level in the well is todisplace some of the the name comes from!)


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Slug tests can be used to estimate transmissivity of the aquifer in the immediate vicinityof the well. Storativity can also be estimated, although storativity estimates are oftendifficult to make with any degree of accuracy.


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Differing solutions depending on set up of well (fully vs partial penetration, etc.) andwhether the aquifer response is overdamped (water level recovers in a smooth manner)or underdamped (water level oscillates with oscillations decreasing with time commonin highly transmissive aquifer)

Things to be careful about:Skin effect lower hydraulic conductivity material (clays, drilling muds, etc.) have beensmeared along the screen of the well. If this material is not removed by welldevelopment (pump or surge well to stir up fines and remove), slug tests will result in anincorrect low value of K.

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Aquifer Tests