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	$q(t) = {q_i}^{-D_i\ t}$	$Q = \frac{q_i-q(t)}{D_i}$
Harmonic decline, b = 1	$q(t) = \frac{q_i}{1+D_i\ t}$	$Q = \frac{q_i}{D_i} ln{\frac{q_i}{q(t)}}$

Nomenclature

$A_1..A_{11}$ = coefficients

$\rho_r$ = reduced density, dimensionless

$P$ = pressure, psia

$P_{pc}$ = pseudo critical pressure, psia

$P_{pr}$ = pseudoreduced pressure, dimensionless

$SG_g$ = gas specific gravity, dimensionless

$T$ = temperature, °R

$T_{pc}$ = pseudo critical temperature, °R

$T_{pr}$ = pseudoreduced temperature, dimensionless

$z$ = gas compressibility factor, dimensionless