Hvorslev Slug Test Conductivity

A slug test is the cheapest measurement in hydrogeology. Drop a solid slug into a monitoring well, or bail one out, and watch the water level recover. No pump, no discharge to manage, no permit, and about twenty minutes on site. Hvorslev published the interpretation in 1951 as US Army Corps of Engineers Waterways Experiment Station Bulletin 36, and because it is a US government document it has been freely available ever since, which is a large part of why the method is everywhere.

The recovery is exponential, so plotting the head ratio $H/H_0$ on a logarithmic axis against time gives a straight line, and the time at which that line reaches 0.37 is the basic time lag $T_0$. The 0.37 is $1/e$: one time constant. From it, $K = \rac{r_c^{2}\ln(L/R)}{2LT_0}$. The $\ln(L/R)$ is Hvorslev's shape factor for a long cylindrical intake, and it is derived on the assumption that the screen is much longer than it is wide, which is why $L/R$ should exceed about 8. Below that, flow around the ends of the screen stops being negligible and the shape factor understates the area available, so the conductivity comes out low.

Get the two radii right, because they are different things and mixing them up is the standard error. $r_c$ is the inside radius of the casing that the water actually rises and falls in, and it sets how much water has to move for the level to change. $R$ is the outside radius of the screen and its filter pack, and it sets the surface through which that water enters the formation. In a well with a 50 mm casing sitting in a 150 mm borehole with a sand pack, $r_c$ is 25 mm and $R$ is 75 mm. If the pack is much more permeable than the formation, which it should be, $R$ is the outside of the pack rather than the outside of the screen.

Now the honest limitation. A slug test measures a metre or two of aquifer immediately around the screen, and that material has been drilled through, smeared, and then replaced by a sand pack somebody chose. It is a point sample of a disturbed point. A pumping test measures hundreds of metres of aquifer in every direction. When the two disagree, and they routinely disagree by a factor of several, the pumping test is describing the aquifer and the slug test is describing the borehole. There is no brain here for the screen length $L$, for the same reason there is none for $T$ on the Cooper-Jacob page: $L$ appears inside the logarithm and in the denominator outside it, so that direction is transcendental. Read $L$ off the borehole log, where it belongs.