.depletion-calculator-container {
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max-width: 800px;
margin: 0 auto;
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line-height: 1.6;
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Understanding Depletion Rates
Whether you are managing natural resource reserves (like oil, gas, or water), analyzing inventory turnover, or calculating the lifespan of a battery, understanding the Depletion Rate is critical for forecasting and planning. A depletion rate quantifies how quickly a finite resource is being exhausted over a specific period.
This calculator assists engineers, analysts, and planners in determining the lifespan of a stock based on current usage patterns. It supports both Linear Depletion (constant amount removed) and Exponential Depletion (percentage removed), which mimics the natural decline curves found in geology and physics.
Linear vs. Exponential Depletion
Choosing the correct model is essential for accurate forecasting:
- Linear Depletion: Assumes a fixed amount is removed every period regardless of the remaining stock. This is common in manufacturing inventory or fixed-budget spending. Example: Drinking 2 liters of water per day from a 100-liter tank.
- Exponential Depletion: Assumes a fixed percentage is removed. As the stock decreases, the absolute amount removed decreases. This is standard in oil and gas reservoirs (Decline Curve Analysis), radioactive decay, or battery discharge curves.
Formulas Used
1. Linear Depletion Rate ($d_L$):
$$ d_L = \frac{\text{Consumption}}{\text{Initial Stock}} \times 100 $$
2. Time to Empty (Linear):
$$ T = \frac{\text{Initial Stock}}{\text{Consumption}} $$
3. Exponential Decay Model:
For natural resources following Arps' decline curves or similar physics, the remaining amount $V_t$ at time $t$ is calculated as:
$$ V_t = V_0 \times (1 – r)^t $$
Where $r$ is the depletion rate expressed as a decimal.
Applications of Depletion Calculation
Resource Management
Mining & Drilling: Estimating the productive life of a well or mine based on extraction rates.
Environmental Science: Calculating the depletion of groundwater aquifers during drought seasons.
Inventory Control: Determining "Day Sales of Inventory" to prevent stockouts.
Frequently Asked Questions
What is a healthy depletion rate?
This depends entirely on the context. For a renewable resource (like a forest), the depletion rate should never exceed the regeneration rate. For non-renewable resources (like an oil well), a lower depletion rate implies a longer asset life, while a higher rate implies faster cash flow but shorter lifespan.
Does this calculate tax depletion?
No. While "Percentage Depletion" is a tax term used by the IRS for mineral properties, this calculator focuses on the physical volume and mathematical exhaustion of a resource, not the financial tax deduction.
Why does the exponential model never reach exactly zero?
Mathematically, exponential decay approaches zero but theoretically never touches it (asymptote). In practical terms, the resource is considered "depleted" when it falls below a usable threshold (economic limit).
function calculateDepletion() {
// 1. Get Inputs
var initialStock = document.getElementById('initialResource').value;
var consumption = document.getElementById('consumptionRate').value;
var projTime = document.getElementById('projectionTime').value;
var mode = document.getElementById('calcMode').value;
// 2. Validate Inputs
if (initialStock === "" || consumption === "") {
alert("Please enter both Initial Resource Stock and Consumption Rate.");
return;
}
var stock = parseFloat(initialStock);
var rateVal = parseFloat(consumption); // usage amount per period
var time = parseFloat(projTime);
if (isNaN(stock) || isNaN(rateVal) || stock <= 0 || rateVal < 0) {
alert("Please enter valid positive numbers.");
return;
}
if (isNaN(time)) {
time = 0; // Default to 0 if empty
}
// 3. Variables for Results
var depletionRatePercent = 0;
var lifespan = 0;
var remaining = 0;
var statusMsg = "";
// 4. Calculate based on Mode
if (mode === "linear") {
// Linear Logic
if (rateVal === 0) {
depletionRatePercent = 0;
lifespan = Infinity;
remaining = stock;
statusMsg = "No depletion occurring.";
} else {
depletionRatePercent = (rateVal / stock) * 100;
lifespan = stock / rateVal;
// Linear Remaining Calculation
remaining = stock – (rateVal * time);
if (remaining = 1) {
lifespan = 1; // Depleted in 1 period or less
remaining = 0;
statusMsg = "Immediate depletion (Rate >= 100%).";
} else {
// Lifespan usually defined as time to reach 1 unit or 1%
// Let's use 1% of initial stock as the "Economic Limit"
var limit = stock * 0.01;
// Formula: limit = stock * (1 – r)^t => log(limit/stock) = t * log(1-r)
// t = log(limit/stock) / log(1-r)
lifespan = Math.log(limit / stock) / Math.log(1 – r);
// Remaining after time t
remaining = stock * Math.pow((1 – r), time);
statusMsg = "Decays rapidly, then slows.";
}
}
}
// 5. Update UI
document.getElementById('resultsOutput').style.display = "block";
// Format Percent
document.getElementById('resRate').innerText = depletionRatePercent.toFixed(2) + "% / period";
// Format Lifespan
if (lifespan === Infinity) {
document.getElementById('resLifespan').innerText = "Infinite";
} else {
document.getElementById('resLifespan').innerText = lifespan.toFixed(1) + " periods";
}
// Format Remaining
document.getElementById('resRemaining').innerText = remaining.toFixed(2) + " units";
// Update Labels
document.getElementById('resProjTimeLabel').innerText = time;
document.getElementById('resStatus').innerText = statusMsg;
}