Difference between revisions of "Decline Curve Analysis"

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== Discussion  ==
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If one has a need to convert decline factor D<sub>i</sub> to the actual annual decline in %:
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:<math> a =  1 - (1 + b\ D_i) - 1 / b </math> for b > 0
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:<math> a =  1 - e^{-D_i} </math> for b =1
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=== Nomenclature ===
 
=== Nomenclature ===
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:<math> a </math> = annual decline, %
 
:<math> b </math> = decline curve parametr, dimensionless
 
:<math> b </math> = decline curve parametr, dimensionless
 
:<math> D_i </math> = decline factor per time t, dimensionless
 
:<math> D_i </math> = decline factor per time t, dimensionless

Revision as of 15:55, 26 October 2017

Brief

Decline Curve Analysis DCA is an empirical method for rate decline analysis and rate forecasting published by Arps in 1945 [1].

DCA is applied for Wells and Reservoirs production forecasting.

Math & Physics

Note Rate Cumulative
Hyperbolic decline, 0 < b < 1 [2] q(t) = \frac{q_i}{(1+b\ D_i\ t)^{1/b}} Q = \frac{q^b_i}{D_i\ (1-b)} (q^{1-b}_i-q(t)^{1-b})
Exponential decline, b = 0 q(t) = {q_i}^{-D_i\ t} Q = \frac{q_i-q(t)}{D_i}
Harmonic decline, b = 1 q(t) = \frac{q_i}{1+D_i\ t} Q = \frac{q_i}{D_i} ln{\frac{q_i}{q(t)}}

Discussion

If one has a need to convert decline factor Di to the actual annual decline in %:

a = 1 - (1 + b\ D_i) - 1 / b for b > 0
a = 1 - e^{-D_i} for b =1

Nomenclature

a = annual decline, %
b = decline curve parametr, dimensionless
D_i = decline factor per time t, dimensionless
q_i = initial rate, any rate units applies
q(t) = rate at time t, any rate units applies
t = forecast time, days

References

  1. ↑ Arps, J. J. (1945). "Analysis of Decline Curves"Paid subscription required. Transactions of the AIME. Society of Petroleum Engineers. 160 (01). 
  2. ↑ "KAPPA Dynamic Data Analysis (DDA) book"Paid subscription required. 
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