Input Parameters

Enter initial production data and decline parameters

Typical: 0.3-0.5 for oil, 0.5-0.7 for gas
Minimum economic production rate (same units as qi)

Arps Decline Types

  • Exponential (b=0): Constant % decline, most conservative
  • Hyperbolic (0<b<1): Declining % decline, most common
  • Harmonic (b=1): Slowest decline, often for water drive

Results

Enter values and click Calculate to see results

Formula Reference

Arps Decline Equations

The general Arps hyperbolic decline equation:

q(t) = qi / (1 + b * Di * t)^(1/b) Where: q(t) = Production rate at time t qi = Initial production rate Di = Initial decline rate (nominal) b = Hyperbolic exponent (0 <= b <= 1) t = Time

Exponential Decline (b = 0)

q(t) = qi * e^(-Di * t) Cumulative Production: Np(t) = qi / Di * (1 - e^(-Di * t)) EUR (as t -> infinity): EUR = qi / Di

Hyperbolic Decline (0 < b < 1)

q(t) = qi / (1 + b * Di * t)^(1/b) Cumulative Production: Np(t) = qi^b / ((1-b) * Di) * (qi^(1-b) - q(t)^(1-b))

Harmonic Decline (b = 1)

q(t) = qi / (1 + Di * t) Cumulative Production: Np(t) = (qi / Di) * ln(1 + Di * t) Note: EUR is infinite for harmonic decline (requires economic limit)

Decline Rate Conversions

Nominal to Effective: D_eff = 1 - e^(-D_nom) [for exponential] D_eff = 1 - (1 + b*D_nom)^(-1/b) [for hyperbolic] Annual to Monthly: D_monthly = D_annual / 12 [nominal]