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Reservoir EngineeringReserves and Recovery

Arps Harmonic Decline Rate Formula

q(t)=qi1+Ditq(t)=\frac{q_i}{1+D_it}

Arps Harmonic Decline Rate calculates production rate at time for reserves and recovery workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (q_i, D_i, t) are known and the assumptions behind the cited reserves and recovery relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, q_t equals 732.600733 STB/day.

q_iSTB/day

1000

D_i1/day

0.001

tday

365

Inputs

q_i

STB/day

Initial Production Rate

D_i

1/day

Initial Nominal Decline Rate

t

day

Elapsed Production Time

Outputs

q_t

STB/day

Production Rate at Time

q_i

STB/day

Initial Production Rate

Source and review

reviewed

Arps, J.J. 1945. Analysis of Decline Curves, Trans. AIME. Harmonic decline model.

Source

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