Decline Curve Analysis

Decline curve analysis (DCA) is the workhorse of production forecasting in the oil and gas industry. By fitting a mathematical model to a well's historical production history, engineers can extrapolate future production rates and estimate the total recoverable volume over the well's producing life.

The Arps Equations

The industry standard framework, developed by J.J. Arps in 1945, describes production decline using three curve types governed by the b-factor:

• Exponential (b = 0): The simplest model. Decline rate is constant over time. Commonly used for conventional, pressure-depleted reservoirs. Formula: q(t) = qᵢ · e^(−Dᵢt)
• Hyperbolic (0 < b < 2): The most common model for unconventional shale wells. Decline rate decreases over time, producing a long, flattening tail. Formula: q(t) = qᵢ / (1 + b·Dᵢ·t)^(1/b)
• Harmonic (b = 1): A special case of hyperbolic decline, rarely used in isolation.

For shale wells, b-factors typically range from 0.8 to 1.5, reflecting the complexity of hydraulically fractured reservoirs where multiple flow regimes occur simultaneously.

Key Inputs

Important Limitations

A b-factor greater than 1.0 produces mathematically infinite EUR when integrated to infinity — a physically impossible result. Best practice is to apply a terminal exponential decline once the rate drops below a threshold, or to cap the well life at a reasonable economic limit. Use the calculator below to see how b-factor choices affect EUR estimates for your well inputs.