Decline Curve & EUR Calculator

About This Calculator

Decline curve analysis (DCA) is the workhorse of production forecasting and reserves estimation. The Arps (1945) equations describe how a well's production rate falls over time and provide closed-form expressions for cumulative production (the basis of the Estimated Ultimate Recovery, or EUR).

Rate vs Time

• Exponential (b = 0): q(t) = q_i · e^−D_it
• Hyperbolic (0 < b < 1): q(t) = q_i · (1 + b·D_i·t)^−1/b
• Harmonic (b = 1): q(t) = q_i / (1 + D_i·t)

Cumulative Production (EUR)

Integrating the rate from the initial rate down to the economic limit q_lim gives the closed-form cumulative production:

• Exponential: N_p = (q_i − q_lim) / D_i
• Hyperbolic: N_p = q_i^b / [(1−b)·D_i] · (q_i^1−b − q_lim^1−b)
• Harmonic: N_p = q_i/D_i · ln(q_i/q_lim)

Unit Handling

The nominal decline D_i is always entered per year, so the closed-form cumulative comes out in (rate × year). When the rate is a per-day rate (e.g. bbl/d), the result is multiplied by 365 days/year so that EUR is expressed in the rate's own volume unit (barrels, Mscf, etc.). Choose "per-year" to skip that conversion.

Limitations

• Boundary-dominated flow assumption — does not model transient or linear flow regimes.
• Single-segment decline; multi-segment (e.g. b switching at a terminal decline) is not modelled.
• Harmonic and hyperbolic EUR can be large; always cap with an economic limit or horizon.
• Not a substitute for history-matched, probabilistic reserves estimation.

Need Professional Reserves & Forecasting Support?

For probabilistic decline analysis, multi-segment forecasts, type-curve generation, and field-level economics integration, we offer professional consulting with validated workflows.

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