Lyons W.C. (ed.). Standard handbook of petroleum and natural gas engineering.2001- Volume 1
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Geological Engineering
255
NNE
ssw
LOW RELIEF SALT PILLOW
NANCY
FIELD
CLARKE
COUNTY,
MISSISSIPPI
B
B'
BTW
PWciO
KACO
SEA
LEVEL
WONIII
WEmOlI
11
AnLrOlilt
10
CENOZOIC
EUIAW
TUSCALOOSA
lUKi
-5
000
I
I
I
I
I.
I
I
I
I
WASHITA
IREDERICKSBURC
(LKi
PALUXY
ILK)
-10
000
COTTON VALLEV
(Ji
-15.aoo
Tx ;x
XT
-x
LOUANN
SALT(J)
-
Ax~xxxxxxxx xx
*
xx xx
XXhh
I
Figure
2-50.
Low relief salt pillow trap (Nancy Field, Mississippi).
(from
Gulf
Coast
Association
of
Geological Societies).
Sedimentary deposits are usually carried to the region
of
deposition by water and
are deposited in water. (In some cases deposits are carried by wind or ice.)
It
is within
these water-deposited sediments that hydrocarbons are likely generated from the
plant and animal life that exists in these environments. Two principal properties
of
the sedimentary rocks that form from such deposits are porosity and permeability.
256
General Engineering and Science
ss
SH
LM
ss
SH
SH
CHANNEL
FILL
ss
Figure
2-51.
River channel sand trap.
c
SH
ss
1
SH
LM
SH
Figure
2-52.
Reef trap.
Porosity
Porosity is a measure
of
the void space within a rock, which is expressed
as
a
The general expression for porosity
41
is
fraction (or percentage)
of
the bulk volume
of
that rock
[31].
(2-155)
where
V,
is the bulk volume of the rock,
Vs
is the volume occupied
by
solids (also
called grain volume), and
Vp
is the pore volume.
Geological
Engineering
257
SH
ss
LM
Figure
2-53.
Unconformity trap.
Figure
2-54.
Combination trap.
258
General Engineering and Science
From an engineering point of view, porosity
is
classified as:
Absolute porosity-total porosity of a rock, regardless of whether or not the
Effective porosity-only that porosity due to voids that are interconnected.
It
is the effective porosity that is of interest. All further discussion of porosity
will
From a geologic point of view, porosity
is
classified as:
1.
Primary porosity-porosity formed at the time the sediment was deposited.
Sedimentary rocks that typically exhibit primary porosity are the clastic (also
called fragmental or detrital) rocks, which are composed of erosional fragments
from older beds. These particles are classified by grain size.
2.
Secondary porosity-voids formed after the sediment was deposited. The
magnitude, shape, size, and interconnection of the voids bears little or no relation
to thc form of the original sedimentary particles. Secondary porosity
is
subdivided into three classes.
Solution porosity refers to voids formed by the solution of the more soluble
portions of the rock in the presence of subsurface migrating (or surface
percolating) waters containing carbonic and other organic acids. Solution
porosity is also called vugulurporosity where individual holes are called vugs.
Fractures, fissures, and joints are openings in sedimentary rocks formed by
the structural (mechanical) failure of the rock under loads caused by earth
crust tectonics. This form of porosity is extremely hard to evaluate
quantitatively due to its irregularity.
Dolomitization is the process by which limestone (CaCO,) is transformed
into dolomite CaMg
(CO,),.
During the transformation (which occurs under
pressure), crystal reorientation occurs, which results in porosity in dolomite.
The typical value of porosity for a clean, consolidated, and reasonably uniform
sand is
20%.
The carbonate rocks (limestone and dolomite) normally exhibit lower
values, e.g.,
6-8%.
These are approximate values and do not fit all situations. The
principal factors that complicate intergranular porosity magnitudes are uniformity
of grain size, degree of cementation, packing of the grains, and particle shape.
Permeability
individual voids are connected.
pertain to effective porosity.
Permeability is defined
as
a measure of
a
rock’s ability to transmit fluids. In addition
to a rock’s being porous, sedimentary rock can also be permeable. Permeability refers
to
the property
of
a rock that allows fluids to flow through its pore network at practical
rates under reasonable pressure differentials. The quantitative definition
of
permeability was first given in an empirical relationship developed by the French
hydrologist Henry D’Arcy who studied the flow
of
water through unconsolidated
sands
[31].
This law in differential form is
(2-
156)
where
v
is the apparent flow velocity (cm/sec), is the viscosity of the flowing fluid
(centipoise), p is pressure (atmospheres), Pis the length (cm),
k
is permeability of the
porous
media (darcies).
Geological Engineering
259
Consider the linear flow system of Figure 2-55. The following assumptions are
necessary
to
establish the basic flow equations:
Steady-state flow conditions.
Pore volume is 100% filled with flowing fluid; therefore,
k
is the absolute
permeability.
Viscosity of the flowing fluid is constant. In general, this is not true for most
real fluids. However, the effect is negligible if
p
at the average pressure is used.
Isothermal conditions prevail.
Flow is horizontal and linear.
Flow is laminar.
Using the foregoing restrictions:
(2- 157)
q
A
\
=-
where
q
is
the volumetric rate of fluid flow (cm"/s);
A
is the total cross-sectional area
perpendicular
to
flow direction (cm').
This fiirther assumption concerning velocity and the volumetric rate of flow restricts
flow
to
the pores and not the full area. Therefore,
v
is an apparent velocity. The
actual velocity, assuming a uniform medium, is
where
$
is porosity defined in Equation 2-155.
Substituting Equation 2-157 into Equation 2-156 yields
Separation
of'
variables and using limits from Figure 2-55 gives
=
d4
-4
.I
Figure
2-55.
Linear
flow
system.
(2-158)
(2-159)
(2-160)
260
General Engineering and Science
Integrating the preceding yields
or
(2-161)
(2-
162)
Equations 2-161 and 2-162 are the basic forms of the permeability relationship,
and the following example serves to define the darcy unit:
If q
=
1
cml/s
A=
lcm2
F=
1cp
Ap/P=
1
atm/cm
then from Equation 2-162
k
=
1
darcy
A
permeability of 1 darcy is much higher than that commonly found in sedimentary
rock, particularly reservoir rocks. Consequently, a more common unit is the milli-
darcy, where
1
darcy
=
1,000
millidarcies
Typical values for sedimentary rock permeability for the flow of hydrocarbons
and other fluids are 100 millidarcies (md) or greater. Rocks exhibiting permeabilities
of
50
md or less are considered tight, relative to the flow
of
most fluids.
Subsurface Temperature
The earth is assumed to contain a molten core; therefore, it is logical to assume
that the temperature should increase with depth below the surface. This temperature-
depth relationship is commonly assumed to be a linear function.
t,
=
tS
+
pd
(2-
163)
where
t,
is the temperature of the rock at depth, d(OF),
ts
is the average surface
temperature
(OF),
p
is the temperature gradient (OF/ft), and
d
is the depth (ft).
In general there is considerable variation in the geothermal gradient throughout
the United States and the world.
Also,
in many regions of the world where there
is evidence
of
rather thin crust, the relationship between temperature at depth
and depth may not be approximated by the linear function given in Equation
2-163.
The increase in temperature with depth has important consequences for drilling
and production equipment that is used in the petroleum industry. The viscosity
Geological Engineering
261
of drilling and production fluids will, in general decrease with high temperatures.
The sitting time for well cement will generally decrease with increased
temperature, as will the strength and fracture toughness
of
steels used in drilling,
well completion, and production.
Temperature logs can be taken as wells are drilled and the temperature gradient
determined for the particular region. These temperature logs taken at depth are
used
to
determine the types of drilling fluids used as drilling progresses. Also, the
temperatures at depth will determine the cements used in well completion operations.
The average geothermal gradient used in most areas of the United States for initial
predictions of subsurface temperatures is a value
of
0.01G0F/ft
[32].
Example
2-25
Determine the temperature at 20,000 ft using the approximate geothermal gradient
Assume t5
=
60°F.
t<,
=
t>
+
0.016d
t,
=
60
+
0.016(20,000)
t<,
=
380°F
p
=
0.016 "F/ft.
Subsurface Fluid Pressure (Pore Pressure Gradient).
The total overburden
pressure
is
derived from the weight of the materials and fluids that lie above any
particular depth level in the earth. Of interest to the petroleum industry are the
sedimentary rocks derived from deposits in water, particularly, in seawater. Such
sedimentary rocks contain rock particle grains and saline water within the pore spaces.
Total theoretical maximum overburden pressure,
P
(lb/ft'),
is
(2-164)
where
W,
is weight
of
rock particle grains (lb),
W,%
is weight of water
(Ib),
and
A
is
area (ft').
The term
W,
can be approximated by
w
=
(1
-
@)
Ady,,,
(2-165)
where
@
is the fractional porosity, d is depth (ft), and
y,
is average mineral specific
weight (Ib/ft5).
The term
W
can be approximated by
where
y,,
is the average saltwater specific weight (lb/ft3)).
Substitution of Equations 2-165 and 2-166 into Equation 2-164 yields
(2-166)
(2-167)
Equation 2-167 can be rewritten in terms of the specific gravities
of
average minerals
Sm
and salt water
S5w:
262
General Engineering and Science
(2-168)
where
y,
is the specific weight of fresh water (i.e., 62.4 lb/fti).
The average specific gravity of minerals in the earth's crust is taken
to
be 2.7. The
average specific gravity of saltwater is taken to be 1.07. If the average sedimentary
rock porosity is assumed to be lo%, then the total theoretical maximum overburden
pressure gradient (lb/ft2)/ft becomes
=
(1
-
0.10)(2.7)(62.4)
+
0.10(
1.07)(61.4)
d
=
158.3
d
(2-
169)
Equation 2-169 can be expressed in normal gradient terms of psi/ft. Equation 2-169,
which is the theoretical maximum overburden pressure gradient, becomes
&=
1.10
d
(2-1 70)
where pob is pressure in (psi).
The foregoing theoretical overburden pressure gradient assumes that the
sedimentary deposits together with the saline water are a mixture of materials and
fluid. Such a mixture could be considered as a fluid with
a
new specific weight of
y,
=
158.3 lb/ft
which in terms of drilling mud units would be
158.3
7.48
7,
=--
-
21.1 ppg
where
1
fti
=
7.48 gal.
After sedimentary deposits are laid down in saline water, cementing processes
commence. These cementing processes take place through geologic time. In general
the cementing process results in sedimentary rock that has structural competency.
The cementing of the particles results in a structure that contains the saline in the
rock pores. Therefore, if the sedimentary column of rock below the surface were a
mature rock column in which cementing is complete throughout the entire column,
the theoretical minimum pressure gradient basically would be the saltwater gradient
(lb/ft2)/ft.
P
-
=
1.07(62.4)
d
or
P
-
=
66.8
d
(2-1 71)
Geological Engineering 263
Equation
2-171
can be expressed in normal gradient terms of psi/ft. Equation
2-171,
which is the minimum pressure gradient, becomes
=
0.464
d
(2-1
72)
The foregoing minimum pressure gradient assumes also that the sedimentary column
pores are completely filled with saline water and that there
is
communication from
pore
to
pore within the rock column from surface to depth.
Figure
2-56
shows a plot of the theoretical maximum overburden pressure and
the theoretical minimum pressure as a function
of
depth. Also plotted are various
bottomhole fluid pressures from actual wells drilled in the Gulf Coast region
[33].
These experimentally obtained pressures are the measurements
of
the
pressures in the fluids that result from a combination of rock overburden and the
fluid hydraulic column to the surface. These data show the bottomhole fluid
pressure extremes. The abnormally high pressures can be explained by the fact
that the sedimentary basins in the Gulf Coast region are immature basins and are
DEPTH.
0
2000
4000
so00
8000
IOOOC
I2
ooc
14000
I I
I I
I I I
LEBENO
MIOCENE
@
JACKSON
A
ANAHUAC
0
COCKFIELD
FRlO CROCKETT
v
VICKSBURG
0
WlLcOx
I
I
I I I
1
I
EARTH
PRESSURE
BRAOIENT
(0.464
LWSO.
IN/f
l.)
00
ESTIMATED
FORMATION PRESSURE
:
LBS. PER
SO.
IN.
GAGE
Figure
2-56.
Magnitude
of
abnormal pressure encountered in Gulf Coast region
(from Cannon and Sullins, “Problems Encountered in Drilling Abnormal Pressure
Formations,” in
API Drilling and Production Practices,
1946).
264
General Engineering and Science
0
2000
4000
6000
c
a
2
8000
l-
a
0
10.000-
I
W
12.000
I4,OW-
16,000
-
therefore unconsolidated relative to older basins. In such basins the cementing
process is by no means complete, which results in pressures at depths approaching
the maximum theoretical overburden pressures.
The fluid pressure in the rock at the bottom of a well is commonly defined as pore
pressure (also called formation pressure, or reservoir pressure). Depending on the
maturity of the sedimentary basin, the pore pressure will reflect geologic column
overburden that may include a portion of the rock particle weight (i.e., immature
basins), or a simple hydrostatic column
of
fluid (i.e., mature basins). The pore pressure
and therefore its gradient can be obtained from well log data as wells are drilled.
These pore pressure data are fundamental for the solution of engineering problems
in drilling, well completions, production, and reservoir engineering.
Because the geologic column of sedimentary rock is usually filled with saline water,
the pore pressure and pore pressure gradient can be obtained for nearly the entire
column. Figure
2-57
shows a typical pore pressure gradient versus depth plot for a
Gulf
Coast
region well.
0.4
0.5
0.6
0.7
0.8
0.9
1.0
I
1
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I
1
Ill'
\I
\
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\\
-
\,
FRACTURE PRESSURE
-
\\J
GRADIENT
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1
\
\
-
\
-
\
\
-
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\
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PRESSURE
I
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