Decline Curve Analysis

Brief

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

DCA is applied for Wells and Reservoirs production forecasting.

Math & Physics

Note	Rate	Cumulative
Hyperbolic decline, 0 < b < 1	$q(t) = \frac{q_i}{(1+b\ D_i\ t)^{1/b}}$	$Q = \frac{q^b_i}{D_i\ (1-b)} (q^{1-b}_i-q(t)^{1-b})$
Exponential decline, b = 0	$q(t) = {q_i}\ e^{-D_i\ t}$	$Q = \frac{q_i-q(t)}{D_i}$
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 D_i to the actual annual decline in %:

$if\ b > 0, a = (1 - (1 + b\ D_i)^{- 1 / b}) \times 100$

$if\ b = 0, a = (1 - e^{-D_i}) \times 100$

Workflow

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

$Q$ = cumulatve rate at time t, any rate units applies

$t$ = forecast time, days