All the methods below assume a confined, non-leaky, infinite, homogeneous aquifer — the standard
Theis/Jacob assumptions. Run them on an unconfined aquifer without a delayed-yield correction, or near
a recharge or barrier boundary, and you'll still get a number out. Whether it's the right number comes
down to picking a conceptual model that actually fits your site, and that call is yours to make.
Cooper-Jacob Straight-Line Method
Cooper & Jacob (1946) — the workhorse late-time approximation of the Theis solution
s = (2.303·Q)/(4πT) · log₁₀(t) + b → T = 2.303·Q / (4π·Δs) S = 2.25·T·t₀ / r²
Plot drawdown s against the log of time since pumping started. Once wellbore storage has
died out and before any boundary effect shows up, that plot runs straight: its slope per log cycle
(Δs) gives you transmissivity T directly. Where the line would cross s=0 (t₀)
gives storativity S — but that only works if drawdown was measured in a real observation well at
a known distance r. Well losses and effective-radius uncertainty swamp S when it's calculated
from the pumping well's own drawdown, so leave r blank and this tool will report T alone.
Only valid once u = r²S/(4Tt) drops below roughly 0.01–0.05 — picking which points
count as "late enough" is on you; this tool just fits whatever points you give it.
| t (days) | s (m) |
|---|
Theis Equation (Drawdown Prediction)
Theis (1935) — the non-equilibrium well function, valid at early time too (no Jacob approximation needed)
s(r,t) = Q/(4πT) · W(u) where u = r²S / (4Tt)
Give it a T and S for the aquifer, known or assumed, and it predicts drawdown s
at any distance r and time t. W(u) is the "well function" — the exponential
integral E₁(u) — computed here with the standard Abramowitz & Stegun rational approximation,
the same one most commercial pump-test software uses under the hood. Handy for predicting interference
at a nearby well, or just sanity-checking a T/S pair before you trust it.
Step-Drawdown Test (Jacob Step-Test)
Jacob (1947) — separates aquifer (formation) losses from well (turbulent) losses
sw = B·Q + C·Q² (fit via linear regression of s/Q against Q)
Pump at several increasing rates (steps) and record drawdown at each one. B, the formation-loss
coefficient, reflects laminar flow through the aquifer and stays roughly fixed. C, the well-loss
coefficient, captures turbulent losses at the screen, gravel pack, and casing — it's really telling you
about the well's construction. If well losses make up a big share of the drawdown at your design rate,
that points at the well before you start second-guessing the aquifer.
| Q (m³/h) | sw (m) |
|---|
Specific Capacity
The simplest yield metric — how much drawdown per unit of pumping
q = Q / s
A quick way to compare wells, or to track one well's condition over time — declining specific capacity
across repeat tests is a classic sign of fouling or clogging. It's construction-dependent though: two
wells with identical specific capacity can sit in aquifers of very different transmissivity if they're
developed differently, so treat it as a field indicator rather than a stand-in for T.
Sichardt's Radius of Influence
Sichardt (empirical) — a fast order-of-magnitude estimate, widely used for a first pass / dewatering design
R = 3000 · sw · √k
A purely empirical formula, but still the standard quick estimate for construction dewatering radius.
sw is drawdown at the well (m), k is hydraulic conductivity (m/s). Once you
have real T/S from a test, cross-check against the Theis-consistent radius below — the two can land a
long way apart, and that's just how these two approaches differ, nothing to worry about.
Theis-Consistent Radius of Influence
Solves the Theis equation for the radius where drawdown falls to a chosen threshold
solve for R: s(R,t) = sthreshold (root-finding, using the T/S your own test gave you)
Uses the actual T and S from your test instead of Sichardt's generic multiplier, so it's tied to your
specific site. Heads up: for transmissive, low-storativity confined aquifers this can come out
to several kilometres at a strict threshold like 1 cm — that's just how the Theis equation
behaves at these parameter values. The threshold you pick is a policy call, and moving it shifts the
answer substantially.
Slug tests displace the water level instantaneously — add or remove a solid slug, or do a fast bail —
and track how it recovers. Much faster and cheaper than a full pump test, though you're only sampling
the aquifer right around the well. Both methods below fit a straight line to the log-normalized
recovery curve; where they differ is the setup they're built for: Hvorslev is general-purpose, Bouwer-Rice
is built for partially-penetrating wells in unconfined or confined aquifers with a screen.
Hvorslev Method (Basic Time Lag)
Hvorslev (1951) — the classic piezometer slug-test method
K = r²·ln(Le/R) / (2·Le·T₀) where ln(y/y₀) = −t/T₀
The formula here is the standard long-screen approximation, valid for Le/R ≥ 8.
r is the casing radius, where the water level actually moves; R is the effective radius
of the screen or intake, gravel pack included if there is one; Le is the screen
length. The "basic time lag" T₀ comes from plotting the normalized head ratio y/y₀
(remaining displacement over initial displacement) against time — this tool fits that line by
regressing ln(y/y₀) against t and reports T₀ = −1/slope.
| t (seconds) | y (m, remaining displacement) |
|---|
Bouwer-Rice Method
Bouwer & Rice (1976) — for partially-penetrating wells, very common for monitoring-well slug tests
K = rc²·ln(Re/rw) / (2·Le) · (1/t)·ln(y₀/yt)
rc is the casing radius, rw is the well radius including any
filter pack, and Le is the screen length. Same as Hvorslev, this tool regresses
ln(y/y₀) against t to get the recovery rate — the two methods differ in where
ln(Re/rw) comes from, covered below.
You enter ln(Re/rw) directly below rather than having this tool derive it.
Bouwer & Rice's original method gets that "effective radius" term from empirical type-curves based
on well and aquifer geometry — screen length and depth relative to aquifer thickness — and reproducing
those curves accurately takes the primary reference (Bouwer, 1989, Ground Water 27(3)) or
dedicated software in hand, not something to trust from memory. If you've already pulled
ln(Re/rw) from a published curve, a table, or software like AQTESOLV, enter it
here and this tool handles the regression and K arithmetic from there.
| t (seconds) | y (m, remaining displacement) |
|---|
Literature ranges of hydraulic conductivity (K) and effective porosity (ne) by
lithology — ne is the value that governs seepage velocity (v = q/ne) for particle
tracking and travel-time estimates. Worth keeping ne and total porosity separate in your
head: for clay, most of that pore space is micropores that barely drain, and for karst or fissured
rock, flow runs through the fracture network while the rock matrix itself contributes almost nothing.
These ranges come from the usual references (Freeze & Cherry's Groundwater, 1979, checked
loosely against Domenico & Schwartz and Polish texts), and different textbooks disagree at the
margins by a factor of 2–3 for some lithologies — treat these as the commonly-cited ballpark rather
than gospel.
Suggested Effective Porosity
Positions a suggested ne within the lithology's literature range, based on where your site's K falls within that lithology's own typical K range