Hydro Geo Solutions LLP — Theis (1935) non-equilibrium analytical model for industrial / mining groundwater withdrawal impact assessment
* mandatory — fields marked with a red asterisk must be filled before the model will compute or save.
Aquifer type is descriptive here — the Theis solution below is applied directly (confined assumption) with the entered Transmissivity and Storativity. For an unconfined aquifer with large drawdown relative to saturated thickness, correct observed/target drawdown using the Jacob correction (s′ = s − s²/2b) before comparing against saturated thickness, per Kruseman & de Ridder (1994).
Table HGS_AnalyticalDrawdown (ID mxepwjffc273ccy) is live in the HGS base. Save/Load work whenever this page is opened from a machine that can reach the NAS.
Every read/write is scoped by Project Code (Project Details, above) — set it before saving. If "Connect" fails (different NocoDB layout/version, or table already exists under a different name), see the manual fallback logged above: create the table by hand in the NocoDB UI with the listed fields, then paste its Table ID into the box that appears.
The map does two jobs and nothing else: it measures receptor distances for you when you click them, and it draws the RoI / drawdown-contour rings used as a report figure. Every drawdown, RoI and export figure is identical without it.
Coordinates default to a placeholder (22.5°N, 78.9°E) — set them to the actual well before producing any report figure, as the RoI rings and receptor distances are drawn from this point.
Click the map in "Set well location" mode to place the pumping/production well. Switch to "Add receptor" mode and click again to drop nearby wells, habitations or surface-water points — distance from the pumping well is computed automatically (great-circle) and a row is added to the Receptors table below.
| Name | Type | Distance from well (m) | Local pre-monsoon DTW (m), optional |
|---|
Receptor drawdown, impact ratio and whether it falls within the computed radius of influence are evaluated automatically on the "RoI & Impact Assessment" tab.
* mandatory
These sets reproduce two HGS field observations: in productive alluvium, 30–40 lps for 10 days leaves no measurable drawdown at 1000 m; in hard rock, a 3–4 lps well shows a much deeper but markedly shorter cone. They are starting values, not substitutes for a site pumping test.
Cite source of T & S in the report (pumping test analysis, aquifer performance test, or CGWB/NAQUIM regional values). Reference: Theis, C.V. (1935), "The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage," Trans. AGU 16, 519–524.
* mandatory
"Pumping period considered" drives the main distance–drawdown table, the RoI computation and the report. "Study periods" additionally produces a distance × time matrix so long-term development can be shown in one table — enter any set of years, e.g. 1, 2, 5, 10, 30. Elapsed time in the Theis solution is taken as study years × days of pumping per year, following the workbook convention.
What to enter: a test you have actually run. You pumped a well at a known rate for a known number of
days, and there was some distance beyond which no observation well showed any response. Enter that discharge, that
duration, and that distance. The last box is what "no response" means on your sounder — typically 0.02 m.
What it returns: the storage coefficient S that would put drawdown exactly at your detection limit
at that distance and time. Any larger S is equally consistent with seeing nothing; any smaller S would have produced a
drawdown you would have measured. So it is a defensible lower bound on S taken from your own site data, and a
check on whatever value is entered above.
* mandatory
Recharge is always acting on the aquifer, and it is what stops the cone of depression growing: expansion ceases once the recharge captured inside the cone equals the abstraction. That balance fixes the capture radius R = √(Q / πw), inside which the steady profile is s(r) = Q/(2πT)·ln(R/r) − w(R²−r²)/(4T), reaching zero at r = R. Drawdown develops per the selected pumping method until recharge balances abstraction, then holds — the same RCH-against-WEL balance a numerical model closes. The Theis solution alone has no recharge term and its cone grows as √t for ever; that case is not offered here. For a genuinely confined aquifer that receives no leakage over the cone, this bounded-cone treatment does not apply — use a leaky (Hantush–Jacob) or numerical model instead.
RIF must come from the GEC-2015 table for the assessment unit and formation — the values suggested when you change lithology are typical only (alluvium ~22%, weathered granite/gneiss ~11%, basalt ~7–13%, shale ~5%) and are not a substitute for the published figure; the HGS Groundwater Recharge Calculator holds the full 39-formation catalogue. Two cautions on interpretation: (1) a genuinely confined aquifer receives no direct areal recharge over the cone — recharge enters at the distant outcrop — so applying this to a confined S is inconsistent; use it where the aquifer is unconfined or leaky. (2) Recharge inside R is not free water: it already sustains baseflow, existing users and regional outflow, so R is a lower bound on the true zone of contribution and does not by itself demonstrate sustainability — that remains a GEC-2015 stage-of-extraction question for the assessment unit.
If a local replenishable-recharge figure is available (e.g. from a GEC-2015 assessment or the HGS Groundwater Recharge Calculator), this ratio gives a first-order screening indicator of stress added by the proposed withdrawal. It is not a substitute for the block/watershed-level GEC-2015 stage-of-extraction computation.
Drawdown at radial distance r and time t from the start of pumping: s(r,t) = Q/(4πT) · W(u), u = r²S / (4Tt). W(u) is the Theis well function, evaluated here as the exact exponential integral E₁(u) (series expansion for u<1; Abramowitz & Stegun 5.1.56 rational approximation, error ≤ 2×10⁻⁸, for u≥1) — not a coarse lookup table, so no interpolation error is introduced at any distance or time.
Where pumping is intermittent (site power availability limits pumping to part of the day, as is typical for Indian industrial/mining bore/tube wells), HGS applies the effective daily discharge volume Qd = Q × (hours pumped/day) in place of a 24-hour continuous rate, and superimposes a non-pumping-period term using a recovery-style factor so that Net drawdown = Qd/(4πT) · W(u) · [1 + e−u] at the end of each pumping day, reflecting the additional transient drawdown from daily on/off cycling that a simple continuous-average-rate Theis run would understate. This term is omitted (Net = Qd/(4πT)·W(u)) when the pumping regime is set to Continuous.
| Distance r (m) | u | W(u) | Drawdown during pumping, sp (m) | Non-pumping term, sr (m) | Net drawdown (m) |
|---|
Distance from the well runs both ways on a linear axis; drawdown hangs below the static water level (the line at zero). Each shaded band is the growth between two snapshots in time. The cone deepens and widens, then stops widening at the recharge capture radius (dashed verticals) — after that, further pumping only fills the cone in, it does not extend it.
The same snapshots as surfaces of revolution: horizontal distance on the two base axes, drawdown downward. Each time is a different colour; later cones nest inside earlier ones. Drag to rotate, scroll to zoom. The cutaway removes the near half so the nested profiles are visible on the section face; the ring at the water table is the capture radius.
Net drawdown (m) at every distance for each study period set on the Aquifer & Pumping tab. This is the table to lift straight into an impact-assessment chapter when long-term development has to be demonstrated.
The pump runs for the set hours each day and builds drawdown; when it stops, the water level recovers part of the way back; whatever has not recovered by the next morning is carried forward, and the next day's drawdown builds on top of that residual. This is computed by Theis superposition: each pump-start is a discharging well and each pump-stop superposes a recharging (image) well of equal rate, so the recovery and the carried-forward residual fall out of the mathematics rather than being estimated:
s(r,t) = Qinst/(4πT) · Σi [ W(u(t − ton,i)) − W(u(t − toff,i)) ], u(Δt) = r²S / (4T·Δt), summed over every pumping cycle that has begun by time t, with Qinst the actual pumping rate while running (not the daily average). Recovery terms enter only after the pump stops. This is the standard superposition/image-well treatment of intermittent abstraction and of the Theis recovery method (Theis 1935; Kruseman & de Ridder, ILRI 1994). Where days of pumping per year is less than 365, the annual shutdown block is honoured as a long recovery period.
Simulation cost rises with the square of the number of days (every day superposes on every earlier cycle). 365 days is instant; beyond about 1500 days expect a short pause.
Upper points are the water level at the end of each day's pumping; lower points are after the overnight recovery. The gap between the two envelopes is the daily recovery; the rise of the lower envelope is the residual accumulating.
| Day | Status | DD at end of pumping (m) | Recovery during off-hours (m) | Residual DD carried to next day (m) | Net gain over previous day (m) | Recovery (%) |
|---|
The reported figure is the distance to the threshold drawdown on the Theis curve, bounded by the recharge capture radius by recharge capture. That is the number that goes to the summary and the exports. Recharge is always applied; the cone cannot be reported unbounded.
Both assume an infinite aquifer with no recharge, so they are kept out of the report. Cooper & Jacob (1946) is the log-approximation's extrapolation to zero drawdown — useful to confirm the order of magnitude of the unbounded cone, nothing more. Sichardt (1928) is an empirical dewatering-excavation rule that needs K = T/b; it is often quoted in Indian NOC/EIA submissions, which is the only reason it is shown. A large disagreement between the two and the reported radius is the usual sign that S is wrong.
Rings show the drawdown contours entered below and the reported radius of influence, centred on the pumping well.
The analytical equivalent of a MODFLOW mass balance / ZONEBUDGET listing: cumulative abstraction split between water released from aquifer storage and water drawn from captured areal recharge. Storage depletion saturates once the cone stabilises; everything after that is capture. Compare against the model's own budget — if the numerical model shows a large share arriving from constant-head or general-head boundaries instead, the boundaries are feeding the well and the predicted drawdown is boundary-controlled rather than recharge-controlled.
| Elapsed time | Cumulative abstraction (m³) | From aquifer storage (m³) | From captured recharge (m³) | % from storage | % from recharge |
|---|
| Receptor | Type | Distance (m) | Net drawdown at end of period (m) | Pre-monsoon DTW (m) | Drawdown as % of DTW | Within reported RoI |
|---|
The reported RoI is the distance to the threshold drawdown, bounded by the recharge capture radius when the limit is on. Where a local pre-monsoon depth-to-water is entered, drawdown is expressed as a percentage of that column for screening only; there is no universal regulatory threshold for this ratio, so treat it as a discussion point against site-specific EIA/CGWA conditions rather than a pass/fail rule.