Rate Transient and Decline Curve Analyses for Continuously (Dual-Porosity) and Discretely Naturally Fractured Reservoirs
Authors: Kuchuk Fikri , Biryukov Denis , Fitzpatrick Tony 
Published: October 2014

Abstract
Forecasting production rates and reserves is important for reservoir management. Analysis of long-term production data has traditionally been performed using the empirical Arps (1945) decline curves to predict future production. Fetkovich (1980) combined Arps decline curves with constant-wellbore pressure solutions to offer a new method for decline-curve analysis. Furthermore, both rate-transient and decline-curve analyses for naturally fractured reservoirs were performed using Arps (1945) decline curves or Warren and Root (1963) dual-porosity-type models. These approaches have yielded unsatisfactory results for naturally fractured reservoirs. Recent studies show that the Warren and Root (1963) dual-porosity-type models, which do not contain fractures, cannot characterize highly diverse transient behaviors of continuously and discretely fractured reservoirs because they are inappropriate and incomplete for most naturally fractured reservoirs. Furthermore, no investigation has been performed on rate-transient behavior of discretely fractured reservoirs.
We investigate rate-transient behavior of continuously (dual-porosity) and discretely naturally fractured reservoirs using semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite-and/or infinite-conductivity fractures, of different lengths and orientations. Our results demonstrate that, in terms of rate transients, neither continuously nor discretely fractured reservoirs behave like the Warren and Root (1963) dual-porosity type model. There are many factors that dominate the rate-transient behavior of naturally fractured reservoirs, such as fracture conductivities, dip angles, lengths, and distributions, as well as whether or not fractures intersect the wellbore. Rate transients associated with these factors are shown for a few continuously and discretely fractured reservoirs with different well and fracture configurations.
The inverse of the dimensionless pressure (pD) is not a good approximation for the dimensionless rate (qD), but for most cases, their derivatives [tDd(1/qD)dtD and dpD)dln(tD) behave similarly, and exhibit same or similar flow regimes. For some cases, they behave very differently. The similarities or variations are true for any type of reservoirs.
For any reservoir, Arps' decline curves yield unreasonably high production rates and cumulative productions, except the exponential decline curve. The exponential decline curve should not be used without taking into account the change of the wellbore pressure as a function of time. Arps' decline curves analysis should not be used for both discretely and continuously fractured reservoirs. An integrated interpretation methodology is outlined for rate transient analysis in fractured reservoirs.
A few examples for the rate transient behavior of the continuously and discretely fractured fractured reservoirs are presented. They exhibit different flow regimes depending on fracture distribution, intensity, and conductivity. We also compare the rate transient derivatives with pressure transient derivatives of these examples. For most cases, they exhibit similar behaviors. These derivatives and flow regimes presented are valuable diagnostic tools for rate transient analysis.