Lesson 20: Succession
12 Pages
Downloading requires you to have access to the YouScribe library
Learn all about the services we offer

Lesson 20: Succession


Downloading requires you to have access to the YouScribe library
Learn all about the services we offer
12 Pages


  • leçon - matière potentielle : 12 -21
Lesson 20: Succession • Definitions – Seres and stages – Autogenic vs. allogenic succession – Progressive vs. retrogressive succession – Facilitation, inhibition, life-history traits • Examples of primary and secondary succession • Methods of documenting succession – Historical long-term data from permanent plots – Examination of plots along a chronosequence – Pollen record – Dendrochronolgy • Models of succession • Facilitation vs. inhibition (Cowles vs. Clements) • Relay floristics vs.
  • quartzite rock with grimmia clones
  • vegetation change through time
  • sand dune sere
  • sere
  • suggest stages of succession from herbs to low shrubs to tall shrubs as the fracture planes weather
  • time scales
  • succession



Published by
Reads 20
Language English


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

Graphical solutions to flow equations: Theis type curve method, (Cooper) Jacob time
drawdown and distance drawdown methods

- Previous emphasis: Predicting drawdown based on known aquifer parameters.
- 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-
- Cone of depression is still expanding

I) Non equilibrium flow in a confined aquifer: Theis method
- Take the Theis equation, solve for T

h -h = Q W(u) o

T = Q W(u)
4π (h -h) o

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

2u = r S becomes S = 4 T t u
2 (4Tt) r
- 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

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 log
cycles 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) 3
- 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, (h - h) and t o

5) Do necessary conversions (so that values from curve fit can be
plugged 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
3- Convert discharge (Q) units to ft /day if necessary
7) Plug values into Storativity equation to solve for storativity
- Use the value for T calculated above
2S = 4 Ttu / r
- 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 4
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 a
confined aquifer:
- Time drawdown 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 IF we are dealing with longer
term pumping. Combining some terms and converting to base 10 logs (to use with our
graphing) – see pg. 173 text
- The result:

T = 2.3 Q log (2.25 T t)
2 4 π(h - h) (r S) o

- 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 to
convert to days in the following equations) 5

- New equations for this solution:

A) Equation for transmissivity:

T = 2.3 Q
4 π ∆ (h –h) o

- Note: ∆(h - h) refers to the change in h over 1 log cycle o

B) Equation for storativity:

S = 2.25 T t o
2 r

- Note: t refers to the time where the straight line intersects the zero o
drawdown 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 observation

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

C) Solve for K if needed:

T = Kb 6

- This method is only valid for long pumping times
- 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. May
find 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 distance drawdown method
- Requires data from several wells
- Plot on semi-log paper
- Wells must be properly spaced for this method to be effective. The ideal
spacing: have at least 3 wells, with distances between the wells that plot on 3
different log cycles.
- - Example: observation well with 3 wells spaced at 10 ft, 100 ft and 1000 ft.

- New formulas: 7
A) Equation for transmissivity:

T = 2.3 Q
2 π ∆ (h -h) o

- Note: (h - h) refers to the change in h over 1 log cycle o

B) Equation for storativity:

2S = 2.25 T t / r o

r = distance where straight line intersects the zero drawdown axis o
t = some time “t” into the test (in days) where drawdown is recorded
in all wells

- 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
- 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

simultaneous data from a series of wells (distance drawdown) or a series of
measurements from one well (time drawdown) are used to plot a semi-log drawdown
curve from which the values needed to solve the equations are taken (straight line
Time-drawdown data is plotted on a log-log plot and then matched to a type curve or
series of type curves to derive the unknown parameters. (type curve method)

Type curve method:

K’ = vertical hydraulic conductivity of leaky confining layer
B’ = thickness of leaky confining layer

Source of water “leaking” to confined aquifer is an upper unconfined aquifer (in pictured

• Drawdown response in leaky confined aquifers
o Hantush-Jacob formula
2r S
u =
where W(u, r/B) is the well function for leaky aquifer; K’ and b’ are the
hydraulic conductivity and thickness of the confining layer, respectively

Match type curve and aquifer tests data to get W(u,r/B), 1/u, t, s and r/B
Substitute values into Hantush-Jacob equations to obtain T, S, K’


Type A curves = early part of curve match to early data to obtain specific storage
Type B curves = mid to late part of curve match to latern specific yield
T estimate from both match points should be similar
Obtain vertical K from lambda value match point 10


The problem with having a partially penetrating pumping well is that flow near the well
will 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 fully
If the observation wells are also partially penetrating, then they effect of having a
vertical flow component is negligible if the following relationship is true:

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

water in the well by lowering into it a solid piece of pipe called a slug (ahhh! So that’s where An
alternative to a pump test is a slug test (also called a baildown test). In this test the
water level in a small diameter well is quickly raised or lowered. The rate at which the
water in the well falls (as it drains back into the aquifer) or rises (as it drains from the
aquifer 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 water
level. However, perhaps the easiest way to raise the water level in the well is to
displace some of the the name comes from!)