Arp's Decline | predico

Introduction

Arp’s equations are empirical (1944), but have been somewhat correlated to theory. According to Boulis et al [2009], exponential rate-decline case can be derived theoretically; for the case of constant compressibility liquid in a closed reservoir flowing at a constant wellbore flowing pressure during boundary-dominated flow conditions.

Rate Relations

	Rate	Cumulative Production
Exponential (b=0)
Hyperbolic: (0<b<1)
Harmonic: (b=1)
Other Identities
Loss Ratio
b-factor

Arp’s Observations

Arp’s observations for the decline curve exponent (b) were for solution gas-drive reservoirs

Arp’s Exponent
b = 0	Reservoir is highly undersaturated (p > p_b) Single Phase Liquid Expansion Poor Waterflooding Performance Tubing Restricted Gas Production In the example below, three (3) of the four (4) declines are quite suitable, with the fourth (b=0) looking pessimistic - hence, significant uncertainty based on choice of b-value.
b = 0.1 to 0.4 (maybe up to 0.6)	Solution Gas Drive
b = 0.4 to 0.5	Single Phase Gas Expansion
b = 0.5	Gravity drainage with free surface Effective Edge Water Drive

Table reproduced after T. A. Blasingame (2023)

Others Observations

Using traditional Arps decline, Log [decline rate] vs log [time], introduced in 1942, validates the power-law concept found in Decline for Unconventional Reservoirs . The image below (the loss Ratio) shows a power law trend observed from shale gas data.

References

T. A. Blasingame, Analysis Well Performance, v20230723, Texas A&M
T.A. Blasingame, Pressure Transient Analysis (PTA) , Rate Transient Analysis (RTA) & Decline Curve Analysis (DCA) Methods for Wells in Unconventional Reservoirs. SPE Denver Section. General Meeting 16 December 2020.
A New Series of Rate Decline Relations Based on the Diagnosis of Rate-Time Data, A. S. Boulis, B. Ilk, and T. A. Blasingame, Paper 2009-202 [June 2009]
Juan Manuel Lacayo Ortiz, Pressure Normalization of Production Rates Improves Forecasting Results, M.Sc. Texas A&m University 2013.