Large Diameter Wells with WellBore Storage - Papadopulos-Cooper |
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Large Diameter Wells with WellBore Storage - Papadopulos-Cooper |
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Standard methods of aquifer data analysis assume storage in the well is negligible; however, for large-diameter wells this is not the case. At the beginning of the pumping test, the drawdown comes not only from the aquifer, but also from within the pumping well itself, or from the annular space surrounding the well (i.e. the gravel/filter pack). Thus the drawdown that occurs is reduced compared to the standard Theis solution. However, this effect becomes more negligible as time progresses, and eventually there is no difference when compared to the Theis solution for later time drawdown data.
Papadopulos devised a method that accounts for well bore storage for a large-diameter well that fully penetrates a confined aquifer (Kruseman and de Ridder, 1990). Using the Jacob Correction factor, this method can also be applied to unconfined aquifers.
The diagram below shows the required conditions for a large-diameter well:
where,
D: initial saturated aquifer thickness
rew: effective radius of the well screen or open hole
rc: radius of the unscreened portion of the well over which the water level is changing
The mathematical model for the solution is described in Papadopulos & Cooper (1967). The drawdown in the pumping well (r=rw) is calculated as follows:
with
sw: drawdown in the pumping well
rew: effective radius of the filter/well
rc: radius of the full pipe, in which the water level changes
CD: dimensionless well storage coefficient. For the Papadopulos method, the symbol a is used.
As shown in the above equations, the well storage coefficient CD correlates with the storage coefficient S.
If only early time-drawdown data are available, it will be difficult to obtain a match to the type curve because the type curves differ only slightly in shape. The data curve can be matched equally well with more than one type curve. Moving from one type curve to another results in a value of S (storativity) that differs an order of magnitude. For early time data, storativity determined by the Papadopulos curve-fitting method is of questionable reliability. (Kruseman and de Ridder, 1990)
An example of a Papadopulos-Cooper Solution graph has been included in the following figure:
An example of a Papadopulos - Cooper analysis is available in the project:
C:\Users\Public\Documents\AquiferTest Pro\Examples\WellBoreStorage.HYT
Data requirements for the Papadopulos-Cooper solution are:
•Time vs. Drawdown data at a pumping well
•Pumping well dimensions
•Pumping rate
For Papadopulos the dimensionless curve parameter SD is defined as.
with
rc: Radius of the full pipe in that the water level changes
rw: Radius of the screen
The effective radius of the well typically lies somewhere between the radius of the filter and the radius of the borehole (i.e. it is a calculated value). The exact value depends on the usable pore volume of the filter pack.
In AquiferTest, the following values are defined in the wells table.
B: Radius of the borehole
R: Radius of the screen
r: Radius of the riser pipe (casing)
n: Effective porosity of the annular space (gravel/sand pack)
Though not specifically indicated, AquiferTest uses the value R (i.e. screen radius) as effective radius; however, if the option to “use effective well radius (use r(w))” is selected in the Wells table, AquiferTest computes this value according to the formula
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