Page 63 - Geology of Carbonate Reservoirs

44 CARBONATE RESERVOIR ROCK PROPERTIES

Fracture porosity is the result of brittle failure under differential stress. It varies
with the mechanical properties of the rock and the magnitude, type, and direction
of the differential stresses. Mechanical behavior of rocks can be grouped into a
variety of classes, three of which are the most common in most situations: brittle,
ductile, and plastic. Brittle behavior is associated with fractures, faults, and joints. It
occurs when the elastic limit of the brittle rock is exceeded and failure by rupture —
brittle failure — occurs. Ductile behavior can be modeled by a soft metal rod (e.g.,
lead or copper) under tensional stress. The center of the rod continually becomes
thinner and thinner under stress until it fails. Plastic behavior can be imagined as
the behavior of bread dough or putty. Plastic deformation requires little stress to
start deformation and once it begins, it continues with little additional stress. Ductile
and plastic behaviors are not generally associated with fracture porosity. Stress is

defined as force per unit area and stress categories include extension, compaction,
and shear. Stress magnitudes are classified as maximum, intermediate, and minimum

principal stress; they are represented by σ 1 , σ 2 , and σ 3 , respectively. Most fracture
porosity is associated with tectonic fractures, as will be discussed in Chapter 7 .
Fractures occur in predictable patterns and orientations on faults and folds, making
it possible to estimate the extent and orientation of fractures in reservoirs associated
with such tectonic features. However, there are special problems with fractured
reservoirs that will be discussed later. Fracture intensity varies with depositional bed
thickness and depositional texture to the extent that a hybrid category of fractures
influenced by depositional attributes can be useful. Characteristics of depositional,

diagenetic, and fracture porosity are discussed in more detail in Chapters 5 , 6 , and
7 , respectively.

2.4.3 Permeability
Nineteenth century engineers Henri Darcy and Charles Ritter conducted experi-
ments to establish the laws that govern the flow of water through sand. Their

purpose was to explain these principles as aids to planning and managing water

distribution for Dijon and other cities in France (Darcy, 1856 ). They filled a cylinder
with different mixtures of sand and gravel, packed the mixture, and passed water

through the column to determine flow rate. The experiments involved pure water
and atmospheric pressure such that the principal variables were sand and gravel
textural characteristics. Flow rates and pressure differences were small in the origi-
nal Darcy – Ritter experiments as compared to those in hydrocarbon reservoirs.

“ Darcy flow ” is defined as laminar fl ow.
Today the Darcy – Ritter expression is written with different letter designations
for parameters and measurements than in their 1856 paper but the method and the
outcome are unchanged. Discharge ( Q ) through a known cross - sectional area ( A )
and length ( L ) of a cylindrical, sand - packed cylinder is proportional to the hydraulic
gradient ( h 1 − h 2 )/ L along the cylinder, and Darcy ’ s law is given by
)
Q ( h − h 2
= k
1
A L
The Darcy – Ritter expression has to be modified for application to hydrocarbon

reservoirs because fluids other than water are involved and there are wide variations