Fracture Porosity From Pressure Transient Data
Authors: Tiab Djebbar , Igbokoyi Alpheus Olorunwa , Restrepo Dora Patrici 
Published: February 2016

Abstract
The storage capacity ratio (w) measures the flow capacitance of the secondary porosity and the interporosity flow parameter (l) is related to the heterogeneity scale of the system. Currently, both parameters l and w are obtained from well test data by using the conventional semilog analysis, type-curve matching or the TDS Technique. Warren and Root showed how the parameter w can be obtained from semilog plots. However, no accurate equation is proposed in the literature for calculating fracture porosity.
This paper presents an equation for the estimation of the l parameter using semilog plots. A new equation for calculating the interporosity flow parameter, the storage capacity ratio and fracture porosity from the coordinates of the minimum point of the trough on the pressure derivative is presented. The influence of the wellbore storage on the trough was investigated and a new equation was derived to correct the coordinates of the minimum point. The equations are applicable to both pressure buildup and pressure drawdown tests. The interpretation of these pressure tests follows closely, the classification of naturally fractured reservoirs into four types, as suggested by Nelson.
The paper also discusses new procedures for interpreting pressure transient tests for three common cases: the pressure test is too short to observe the early-time radial flow straight line and only the first straight line is observed,the pressure test is long enough to observe the late-time radial flow straight line, but the first straight line is not observed due to inner boundary effects, such as wellbore storage and formation damage, andNeither straight line is observed for the same reasons, but the trough on the pressure derivative is well defined.
Analytical equations are derived in all three cases for calculating permeability, skin, storage capacity ratio and interporosity flow coefficient, without using type curve matching.
In naturally fractured reservoirs, the matrix pore volume, therefore the matrix porosity, is reduced as a result of large reservoir pressure drop due to oil production. This large pressure drop causes the fracture pore volume, therefore fracture porosity, to increase. This behavior is observed particularly in reservoir where matrix porosity is much greater than fracture porosity. Fractures in reservoirs are more vertically than horizontally oriented, and the stress axis on the formation is also essentially vertical. Using these principles, a new method is introduced for calculating fracture porosity from the storage capacity ratio, without assuming the total matrix compressibility is equal to the total fracture compressibility.
Several numerical examples are presented for illustration purposes.

Introduction
Nelson1 identifies four types of naturally fractured reservoirs; based on the extent the fractures have altered the reservoir matrix porosity and permeability.
In Type 1 reservoirs, fractures provide the essential reservoir storage capacity and permeability. Typical Type-1 naturally fractured reservoirs are the Amal field in Libya, the LaPaz and Mara fields in Venezuela, and pre-Cambrian basement reservoirs in Eastern China. All these fields contain high fracture density.
In Type 2 naturally fractured reservoirs, fractures provide the essential permeability, and the matrix provides the essential porosity, such as in the Monterey fields of California, the Spraberry reservoirs of West Texas, and Agha Jari and Haft Kel oil fields of Iran.
In Type 3 naturally fractured reservoirs, the matrix has an already good primary permeability. The fractures add to the reservoir permeability and can result in considerable high flow rates, such as in Kirkuk field of Iraq, Gachsaran field of Iran, and Dukhan field of Qatar. Nelson includes Hassi Messaoud (HMD) in this list. While indeed there are several low-permeability zones in HMD that are fissured; in most zones however the evidence of fissures is not clear or unproven.
In Type 4 naturally fractured reservoirs, the fractures are filled with minerals and provide no additional porosity or permeability. These types of fractures create significant reservoir anisotropy, and tend to form barriers to fluid flow and partition formations into relatively small blocks.