Water Extraction Volume Estimator

ANA›Life Services Authority›National Calculator Authority›Water Extraction Volume Estimator

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Water Extraction Volume Estimator

Estimates the sustainable extraction volume from an aquifer using the Theis equation and aquifer storage/transmissivity parameters.

Aquifer Type

Confined Aquifer Unconfined Aquifer

Transmissivity (T) [m²/day]

Rate at which water is transmitted through a unit width of aquifer

Storativity (S) [dimensionless]

Confined: 10⁻⁵ – 10⁻³ | Unconfined: 0.01 – 0.35

Pumping Rate (Q) [m³/day]

Desired or planned extraction rate from the well

Pumping Duration (t) [days]

Total duration of pumping period

Well Radius (r_w) [m]

Radius of the pumping well (typically 0.05 – 0.5 m)

Radius of Influence (r) [m]

Distance from well to point of interest or aquifer boundary

Saturated Thickness (b) [m]

Initial saturated thickness (unconfined aquifer only)

Annual Recharge Rate [mm/year]

Average annual groundwater recharge (0 = no recharge considered)

Recharge Catchment Area [km²]

Area contributing recharge to the aquifer

Calculate Results will appear here.

function watUpdateFields() { var type = document.getElementById('wat-aquifer-type').value; var satRow = document.getElementById('wat-sat-thickness-row'); var sInput = document.getElementById('wat-storativity'); if (type === 'unconfined') { satRow.style.display = ''; sInput.placeholder = 'e.g. 0.15'; } else { satRow.style.display = 'none'; sInput.placeholder = 'e.g. 0.0005'; } }

// Well function W(u) approximation using polynomial series (Abramowitz & Stegun) function watWellFunction(u) { if (u 100) return 0; // For small u (u 0."); if (isNaN(S) || S 1) errors.push("Storativity must be between 0 and 1."); if (isNaN(Q) || Q 0."); if (isNaN(t) || t 0."); if (isNaN(rw) || rw 0."); if (isNaN(r) || r 0."); if (r 0 for unconfined aquifer."); }

if (errors.length > 0) { document.getElementById('wat-result').innerHTML = 'Input Errors:' + errors.map(function(e){ return ''; }).join('') + ''; return; }

// --- Theis drawdown at well face (r = rw) --- var u_well = (rw * rw * S) / (4 * T * t); var Wu_well = watWellFunction(u_well); var drawdown_well = (Q / (4 * Math.PI * T)) * Wu_well; // metres

// --- Theis drawdown at radius of influence --- var u_r = (r * r * S) / (4 * T * t); var Wu_r = watWellFunction(u_r); var drawdown_r = (Q / (4 * Math.PI * T)) * Wu_r; // metres

// --- Total extraction volume --- var totalExtraction = Q * t; // m³

// --- Annual recharge volume --- var recharge_m_per_day = (recharge_mm / 1000) / 365; var area_m2 = area_km2 * 1e6; var rechargeVolume = recharge_m_per_day * area_m2 * t; // m³ over pumping period

// --- Sustainable yield check --- var annualExtraction = Q * 365; var annualRecharge = (recharge_mm / 1000) * area_m2; var sustainabilityRatio = (annualRecharge > 0) ? (annualExtraction / annualRecharge) : Infinity;

// --- Aquifer storage volume (confined) or drainable volume (unconfined) --- var aquiferStorageVol = NaN; var storageLabel = ''; if (aquiferType === 'confined') { // Storage volume within radius of influence: V = S * π * r² * drawdown_avg // Approximate: V_storage = S * π * r² * drawdown_r (conservative) aquiferStorageVol = S * Math.PI * r * r * drawdown_well; storageLabel = 'Aquifer Storage Released (within r)'; } else { // Unconfined: drainable volume = Sy * π * r² * drawdown_avg aquiferStorageVol = S * Math.PI * r * r * drawdown_well; storageLabel = 'Drainable Storage (within r)'; }

// --- Drawdown check for unconfined --- var warnings = []; if (aquiferType === 'unconfined' && !isNaN(b)) { if (drawdown_well > 0.5 * b) { warnings.push('⚠️ Drawdown at well (' + drawdown_well.toFixed(2) + ' m) exceeds 50% of saturated thickness. Theis equation may underestimate actual drawdown; consider using Jacob correction.'); // Jacob correction for unconfined: s' = s - s²/(2b) var s_corrected = drawdown_well - (drawdown_well * drawdown_well) / (2 * b); warnings.push('Jacob-corrected drawdown at well: ' + s_corrected.toFixed(3) + ' m'); } } if (drawdown_well 1 && annualRecharge > 0) { warnings.push('⚠️ Annual extraction (' + annualExtraction.toFixed(0) + ' m³/yr) exceeds annual recharge (' + annualRecharge.toFixed(0) + ' m³/yr). Extraction may not be sustainable long-term.'); } if (u_well > 0.05) { warnings.push('⚠️ u = ' + u_well.toExponential(3) + ' at well face. For accuracy, Theis equation requires u 0) { sustainStr = 'Annual Recharge Volume' + annualRecharge.toFixed(0) + ' m³/yr' + 'Annual Extraction Volume' + annualExtraction.toFixed(0) + ' m³/yr' + 'Extraction / Recharge Ratio' + sustainabilityRatio.toFixed(2) + (sustainabilityRatio '; }

var warnHtml = warnings.length > 0 ? '' + warnings.map(function(w){ return '' + w + '

'; }).join('') + ''
'';

document.getElementById('wat-result').innerHTML = '### Results ' + '' + 'ParameterValue' + 'Aquifer Type' + (aquiferType === 'confined' ? 'Confined' : 'Unconfined') + '' + 'Theis u (at well face)' + u_well.toExponential(4) + '' + 'Well Function W(u) at well' + Wu_well.toFixed(4) + '' + 'Drawdown at Well Face (s_w)' + drawdown_well.toFixed(3) + ' m' + 'Drawdown at r = ' + r + ' m' + drawdown_r.toFixed(4) + ' m' + 'Total Extraction Volume' + totalExtraction.toLocaleString(undefined,{maximumFractionDigits:1}) + ' m³' + 'Total Extraction Volume' + (totalExtraction/1000).toFixed(2) + ' thousand m³ | ' + (totalExtraction/1e6).toFixed(4) + ' Mm³' + '' + storageLabel + '' + aquiferStorageVol.toFixed(1) + ' m³' + (rechargeVolume > 0 ? 'Recharge Volume (over ' + t + ' days)' + rechargeVolume.toFixed(1) + ' m³' : '') + sustainStr + '' + warnHtml; }

#### Formulas Used

Theis (1935) Equation — Drawdown:

s(r, t) = Q / (4πT) × W(u)

where u = r²S / (4Tt)

Well Function W(u): Exponential integral approximated by polynomial series (Abramowitz & Stegun, 1964):

W(u) = −0.5772 − ln(u) + u − u²/4 + u³/18 − ... (for u ≤ 1)

Total Extraction Volume: V = Q × t

Jacob Correction (unconfined, large drawdown): s' = s − s²/(2b)

Annual Recharge Volume: V_r = R × A where R = recharge depth [m/yr], A = catchment area [m²]

Sustainability Ratio: SR = Q_annual / V_r — SR ≤ 1 indicates sustainable extraction

#### Assumptions & References

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References

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