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Saturday, January 2, 2010

Well Drawdown Tutorial

Pump Types and Specific Flow Measurements for Well Discharge Pump Tests
& The Extrapolation for Long-term Drawdown


This report will cover what well pump tests are, what kinds of pumps are used in those well tests, and how tests can be used to make predictions for long-term drawdowns


A well pump test is a test that hydrologists use in order to determine the localized properties for an aquifer. These tests are generally performed by continually pumping a well at a specified flow rate for a length of time and making pressure or water table depth measurements at radial distances from the pumping well via smaller monitoring wells. There are a few different aquifer conditions to consider when deciding which kind of pump test is necessary such as whether the aquifer is confined or unconfined, how deep or shallow is the aquifer, if the well being tested is nearby any high-flow or no-flow recharge boundaries, and if there are any other pumping wells or discharge zones nearby.

For an unconfined aquifer, hydrologists employ the use of monitoring wells that they can measure the water table drawdown by taking a difference in the water table depth between the initial depth and the depth at a time after the pumping has started. In an unconfined aquifer, hydrologists are generally looking for the soil permeability and specific yield values. The value for permeability is generally found by using the Darcy’s Law equations for discharge and seepage velocity, while the value for specific yield is found by doing a laboratory drain test. The key here is as follows:


Where “N” is the porosity (dimensionless), “Sy” is the specific yield (dimensionless) determined by doing a laboratory drain test, and “Sr” is the specific retention (dimensionless) which is determined by evaporating the rest of the water in a fume-hood and then taking the difference in weight of the soil sample before and after the evaporation process and dividing by the density of water. The volume of water drained plus the volume of water evaporated divided by the initial volume of the soil sample will give you the porosity. Then, Darcy’s experiment is performed in order to find out the permeability of a sample:
K= (Q/A)*(L/dh)

Where a sample of soil is loaded into a Darcy Apparatus,

and then the flow rate “Q=> volume per time” and the head differential between two points “dh=> height of water against gravity” is measured while the area “A” and the length the points “L=> length” are known constants. From knowing the discharge velocity “Q/A=> distance per time” and the porosity “N=> volume/volume”, a hydrologist can find the seepage velocity “Vs=> distance per time” with this equation:

Vs= (Q/A)/N

For an unconfined aquifer, the seepage velocity can be surmised by assuming that the flow of the water, during a pump test, actually falls off as an inverse proportionality to distance from the well due to the assumption the flux of inflow (Q/A) through the surface area of a cylinder (A) is the same coming in from all directions. By integrating the flux of inflow over the area of a cylinder of any radius ought to give the pump flow rate due to a conservation of water volume. Well, the seepage velocity can be thought of as the same thing as the flux of the inflow in an unconfined aquifer, and it actually varies in space depending on the non-uniformities in the soil permeability, porosity, and hydraulic gradient and it varies in time with the changing of the porosity of the soil due to land subsidence, which is why it is important to dig a well near a boundary of high groundwater recharge such as a lake, river, and/or generally in a large unconfined aquifer basin with a higher permeability and lower specific retention. At any rate, computer programs are useful in the determination of permeability distributions with the input from monitoring well water levels based on 3d mathematical extrapolations of linear algebra and multivariable calculus.

For a confined aquifer, hydrologists utilize a piezometer to measure the difference in the hydraulic head in order to get the drawdown equivalency. In a confined aquifer, hydrologists are looking for the permeability (distance/time), transmissivity (area/time), and storativity (volume/volume) values of the aquifer, and can employ either the Theis “infinite series” method on a log-log plot (p.334-341)., the Cooper&Jacob linear approximation method on a semi-log plot (p.342-344), or the Distance-Drawdown linear approximation method on a semi-log plot as well (p.346-347){2}.

The Theis Method gives the most accurate results for transmissivity and storativity, and are is much easier to use with computers than to do by hand on graph paper, whereas the Cooper&Jacob Method is much easier to do by hand but generally doesn’t give as accurate of results. The Distance-Drawdown method is also easier to perform by hand and is more convenient when there are more monitoring wells set up. With the Theis Method, the difference in the hydraulic head from a single monitoring well at a radial distance is taken at incremental times since the pumping is initiated, or the potentiometric drawdown from multiple wells at incremental distances from the pumping well could simultaneously be recorded. Then, the hydraulic head vs. the time/radius^2 can be plotted on log-log graph in a spreadsheet-type software program and then fitted to a Theis curve. The Cooper&Jacob Method and the Distance-Drawdown Method are linear 1st order approximations of the Theis Method, and can thus be easily performed by hand using a straight line plot of the difference in hydraulic head on the straight axis vs. either the time/radius^2 or the distance (respectively) on the logarithmic axis. The time/radius^2 axis intercept is used in the Cooper&Jacob calculations for transmissivity and storativity of the aquifer, whereas distance axis intercept is utilized in the Distance-Drawdown method calculations in determining the aquifer storativity and transmissivity.

There are all sorts of pumps that are used in wells from hand pumps to deep well pumps. There does not need to be a pump test for manually operated hand pumps because these types of pumps are very low flow and therefore are considered to have a negligible effect on aquifer drawdown and the water table. The sorts of pumps that are used in well tests are typically higher flow pumps for shallower unconfined aquifers of about 25 feet deep or much deeper confined aquifers. The shallower wells can utilize centrifugal closed impellor of jet well pumps, whereas the deeper wells utilize submersible open impellor and positive displacement pumps. Other deep well pumps utilize a turbine impeller with the motor shaft at the top of the well{3}.

References and Bibliography:


2. Hydrology: An Environmental Approach; Ian Watson & Alister Burnett, CH 4, 14, 15


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