1. Suez University
Faculty of Petroleum & Mining Engineering
Porosity and Permeability
Student
Belal Farouk El-saied Ibrahim
Class / III
Section / Engineering Geology and Geophysics
Presented to
Prof. Dr. / Ali Abbas

2. Porosity and Permeability
Both are important properties that are related to fluids in sediment and
sedimentary rocks.
Fluids can include: water, hydrocarbons, spilled contaminants.
Most aquifers are in sediment or sedimentary rocks.
Virtually all hydrocarbons are contained in sedimentary rocks.
Porosity: the volume of void space (available to contain fluid or air) in a
sediment or sedimentary rock.
Permeability: related to how easily a fluid will pass through any
granular material.

3. I. Porosity (P)
The proportion of any material that is void space, expressed as a
percentage of the total volume of material.
VP
P = ×100
VT
Where VP is the total volume of pore space
and VT is the total volume of rock or
sediment.
In practice, porosity is commonly based on measurement of the total
grain volume of a granular material:
VT − VG
P=
× 100
VT
Where VG is the total volume of
grains within the total volume of
rock or sediment.
∴VP = VT − VG

26. Porosity varies from 0% to 70% in natural sediments but exceeds 70%
for freshly deposited mud.
Several factors control porosity.
a) Packing Density
Packing density: the arrangement of the particles in the deposit.
The more densely packed the particles the lower the porosity.
e.g., perfect spheres of uniform size.
Porosity can vary
from 48% to 26%.

27. Shape has an important effect on packing.
Tabular rectangular particles can vary from 0% to just under 50%:
Natural particles such as shells can have very high porosity:

28. In general, the greater the angularity of the particles the more open the
framework (more open fabric) and the greater the possible porosity.
b) Grain Size
On its own, grain size has no influence on porosity!
Consider a cube of sediment of
perfect spheres with cubic
packing.
VT − VG
P=
× 100
VT
d = sphere diameter; n = number of grains along a side (5 in this example).

29. VT − VG
P=
× 100
VT
Length of a side of the cube = d × n = dn
Volume of the cube (VT):
VT = dn × dn × dn = d 3n3
Total number of grains: n × n × n = n3
Volume of a single grain: V =
π 3
d
6
Total volume of grains (VG):
π 3
3π
VG = n × d = n d 3
6
6
3

30. VT − VG
P=
×100
VT
Where: VT = d n
3 3
π 3
d n −n d
6 × 100
P=
d 3 n3
3 3
Therefore:
and
π 3
VG = n d
6
3
3
 π
d n 1 − ÷
 6  ×100
P=
d 3 n3
3 3
Rearranging:
Therefore:
 π
P = 1 − ÷× 100 = 48%
 6
d (grain size) does not affect the porosity so that porosity is independent
of grains size.
No matter how large or small the spherical grains in cubic packing have
a porosity is 48%.

31. There are some indirect relationships between size and porosity.
i) Large grains have higher settling velocities than small grains.
When grains settle through a fluid the large grains will impact the
substrate with larger momentum, possibly jostling the grains into tighter
packing (therefore with lower porosity).
ii) A shape effect.
Unconsolidated sands tend to
decrease in porosity with
increasing grain size.
Consolidated sands tend to
increase in porosity with
increasing grain size.

32. Generally, unconsolidated sands undergo little burial and less
compaction than consolidated sands.
Fine sand has slightly higher porosity.
Fine sand tends to be more angular than coarse sand.
Therefore fine sand will support a more open framework (higher
porosity) than better rounded, more spherical, coarse sand.

33. Consolidated sand (deep burial, well compacted) has undergone
exposure to the pressure of burial (experiences the weight of overlying
sediment).
Fine sand is angular, with sharp edges, and the edges will break under
the load pressure and become more compacted (more tightly packed
with lower porosity).
Coarse sand is better rounded and less prone to breakage under load;
therefore the porosity is higher than that of fine sand.

34. c) Sorting
In general, the better sorted the sediment the greater the porosity.
In well sorted sands fine grains are not available to fill the pore spaces.
This figure shows the relationship between sorting and porosity for
clay-free sands.

35. Overall porosity decreases with increasing sorting coefficient (poorer
sorting).
For clay-free sands the reduction in porosity with increasing sorting
coefficient is greater for coarse sand than for fine sand.
The difference is unlikely if clay was also available to fill the pores.

36. For clay-free sands the silt and fine sand particles are available to fill
the pore space between large grains and reduce porosity.

37. Because clay is absent less
relatively fine material is not
available to fill the pores of fine
sand.
Therefore the pores of fine sand
will be less well-filled (and have
porosity higher).

38. d) Post burial changes in porosity.
Includes processes that reduce and increase porosity.
Porosity that develops at the time of deposition is termed primary
porosity.
Porosity that develops after deposition is termed secondary porosity.
Overall, with increasing
burial depth the porosity of
sediment decreases.
50% reduction in porosity
with burial to 6 km depth due
to a variety of processes.

39. i) Compaction
Particles are forced into closer packing by the weight of overlying
deposits, reducing porosity.
May include breakage of grains.
Most effective if clay minerals are present (e.g., shale).
Freshly deposited mud may have 70% porosity but burial under a
kilometre of sediment reduces porosity to 5 or 10%.
http://www.engr.usask.ca/~mjr347/prog/geoe118/geoe118.022.html

40. ii) Cementation
Precipitation of new minerals from pore waters causes cementation of
the grains and acts to fill the pore spaces, reducing porosity.
Most common cements are calcite and quartz.
Here’s a movie of cementation at Paul Heller’s web site
.

41. iii) Clay formation
Clays may form by the chemical alteration of pre-existing minerals after
burial.
Feldspars are particularly common clay-forming minerals.
Clay minerals are very fine-grained and may accumulate in the pore
spaces, reducing porosity.
Eocene Whitemud
Formation, Saskatchewan

42. iv) Solution
If pore waters are undersaturated with respect to the minerals making up
a sediment then some volume of mineral material is lost to solution.
Calcite, that makes up limestone, is relatively soluble and void spaces
that are produced by solution range from the size of individual grains to
caverns.
Quartz is relatively soluble when pore waters have a low Ph.
Solution of grains reduces VG, increasing porosity.
Solution is the most effective means of creating secondary porosity.
v) Pressure solution
The solubility of mineral grains increases under an applied stress (such
as burial load) and the process of solution under stress is termed
Pressure Solution.
The solution takes place at the grain contacts where the applied stress is
greatest.

43. Pressure solution results in a reduction in porosity in two different ways:
1. It shortens the pore spaces as the grains are dissolved.
2. Insoluble material within the grains accumulates in the pore spaces as
the grains are dissolve.

44. v) Fracturing
Fracturing of existing rocks creates a small increase in porosity.
Fracturing is particularly important in producing porosity in rocks with
low primary porosity.

46. POROSITY DETERMINATION
FROM LOGS
Most slides in this section are modified primarily from NExT PERF Short Course Notes, 1999.
However, many of the NExT slides appears to have been obtained from other primary
sources that are not cited. Some slides have a notes section.

47. OPENHOLE LOG EVALUATION
Well Log
SP
Resistivity

48. POROSITY DETERMINATION BY LOGGING
Increasing
radioactivity
Increasing Increasing
resistivity
porosity
Shale
Oil sand
Shale
Gamma
ray
Resisitivity Porosity

49. POROSITY LOG TYPES
3 Main Log Types
• Bulk density
• Sonic (acoustic)
• Compensated neutron
These logs do not measures porosity directly. To
accurately calculate porosity, the analyst must
know:
•Formation lithology
• Fluid in pores of sampled reservoir volume

50. DENSITY LOGS
• Uses radioactive source to generate
gamma rays
• Gamma ray collides with electrons in
formation, losing energy
• Detector measures intensity of backscattered gamma rays, which is related
to electron density of the formation
• Electron density is a measure of bulk
density

51. DENSITY LOGS
• Bulk density, ρb, is dependent upon:
– Lithology
– Porosity
– Density and saturation of fluids in pores
• Saturation is fraction of pore volume
occupied by a particular fluid (intensive)

52. DENSITY LOG
0
GR
API
6
CALIX
IN
16
6
CALIY
IN
16
200
2
RHOB
G/C3
-0.25
3
DRHO
G/C3
0.25
4100
Gamma ray
Density
correction
4200
Caliper
Density

53. Mud cake
(ρ mc + hmc)
Formation (ρ b)
Long spacing
detector
Short spacing
detector
Source

54. BULK DENSITY
ρb = ρma ( 1 − φ) + ρ f φ
Matrix
•Measures electron density of a formation
•Strong function of formation bulk density
•Matrix bulk density varies with lithology
–Sandstone 2.65 g/cc
–Limestone 2.71 g/cc
–Dolomite 2.87 g/cc
Fluids in
flushed zone

55. POROSITY FROM DENSITY LOG
Porosity equation
ρma − ρb
φ=
ρma − ρ f
Fluid density equation
ρ f = ρmf Sxo + ρh ( 1 − Sxo )
We usually assume the fluid density (ρf) is between 1.0 and 1.1. If gas is present, the
actual ρf will be < 1.0 and the calculated porosity will be too high.
ρmf
is the mud filtrate density, g/cc
ρh
is the hydrocarbon density, g/cc
Sxo
is the saturation of the flush/zone, decimal

56. DENSITY LOGS
Working equation (hydrocarbon zone)
ρb = φ S xo ρmf + φ ( 1 − S xo ) ρhc
+ Vsh ρ sh + ( 1 − φ − Vsh ) ρma
ρb
=
Recorded parameter (bulk volume)
φ Sxo ρmf
=
Mud filtrate component
φ (1 - Sxo) ρhc =
Hydrocarbon component
Vsh ρsh
Shale component
=
1 - φ - Vsh =
Matrix component

57. DENSITY LOGS
• If minimal shale, Vsh ≈ 0
• If ρhc ≈ ρmf ≈ ρf, then
∀ ρb = φ ρf - (1 - φ) ρma
ρma − ρb
φ = φd =
ρma − ρ f
φd = Porosity from density log, fraction
ρma = Density of formation matrix, g/cm3
ρb = Bulk density from log measurement, g/cm3
ρf = Density of fluid in rock pores, g/cm3
ρhc = Density of hydrocarbons in rock pores, g/cm3
ρmf = Density of mud filtrate, g/cm3
ρsh = Density of shale, g/cm3
Vsh = Volume of shale, fraction

58. BULK DENSITY LOG
001) BONANZA 1
GRC
0
150
SPC
-160 MV
40
ACAL
6
16
10700
0.2
0.2
0.2
ILDC
SNC
MLLCF
200
200
RHOC
1.95
2.95
CNLLC
0.45
-0.15
DT
150 us/f 50
200
RHOC
1.95
10800
10900
Bulk Density
Log
2.95

59. NEUTRON LOG
• Logging tool emits high energy
neutrons into formation
• Neutrons collide with nuclei of
formation’s atoms
• Neutrons lose energy (velocity) with
each collision

60. NEUTRON LOG
• The most energy is lost when colliding
with a hydrogen atom nucleus
• Neutrons are slowed sufficiently to be
captured by nuclei
• Capturing nuclei become excited and
emit gamma rays

61. NEUTRON LOG
• Depending on type of logging tool either gamma
rays or non-captured neutrons are recorded
• Log records porosity based on neutrons
captured by formation
• If hydrogen is in pore space, porosity is related
to the ratio of neutrons emitted to those counted
as captured
• Neutron log reports porosity, calibrated
assuming calcite matrix and fresh water in
pores, if these assumptions are invalid we must
correct the neutron porosity value

62. NEUTRON LOG
Theoretical equation
φN = φ S xo φNmf + φ ( 1 −S xo ) φNhc
+ Vsh φ sh + ( 1 − φ − Vsh ) φNma
φN
= Recorded parameter
φNma = Porosity of matrix fraction
φ Sxo φNmf
= Mud filtrate portion
φNhc = Porosity of formation saturated with
φ (1 - Sxo) φNhc = Hydrocarbon portion
Vsh φNsh
= Shale portion
(1 - φ - Vsh) φNhc = Matrix portion where φ = True
porosity of rock
φN = Porosity from neutron log measurement, fraction
hydrocarbon fluid, fraction
φNmf = Porosity saturated with mud filtrate, fraction
Vsh = Volume of shale, fraction
Sxo = Mud filtrate saturation in zone invaded
by mud filtrate, fraction

63. POROSITY FROM NEUTRON LOG
001) BONANZA 1
GRC
0
150
SPC
-160 MV
40
ACAL
6
16
10700
0.2
0.2
0.2
ILDC
SNC
MLLCF
200
200
RHOC
1.95
2.95
CNLLC
0.45
-0.15
DT
150 us/f 50
200
CNLLC
0.45
10800
10900
Neutron
Log
-0.15

64. ACOUSTIC (SONIC) LOG
Upper
transmitter
R1
R2
R3
R4
Lower
transmitter
• Tool usually consists of
one sound transmitter
(above) and two receivers
(below)
• Sound is generated,
travels through formation
• Elapsed time between
sound wave at receiver 1
vs receiver 2 is dependent
upon density of medium
through which the sound
traveled

65. Compressional
waves
E1
E3
E2
T0
50
µsec
Rayleigh
waves
Mud waves

66. COMMON LITHOLOGY MATRIX
TRAVEL TIMES USED
Lithology
Sandstone
Limestone
Dolomite
Anydridte
Salt
Typical Matrix Travel
Time, ∆, µ
tma sec/ft
55.5
47.5
43.5
50.0
66.7

67. ACOUSTIC (SONIC) LOG
Working equation
∆t L = φ S xo ∆t mf + φ ( 1 − S xo ) ∆t hc
+ Vsh ∆t sh + ( 1 − φ − Vsh ) ∆t ma
∆tL
= Recorded parameter, travel time read from log
φ Sxo ∆tmf = Mud filtrate portion
φ (1 - Sxo) ∆thc = Hydrocarbon portion
Vsh ∆tsh
= Shale portion
(1 - φ - Vsh) ∆tma = Matrix portion

68. ACOUSTIC (SONIC) LOG
• If Vsh = 0 and if hydrocarbon is liquid
(i.e. ∆tmf ≈ ∆tf), then
∀ ∆tL = φ ∆tf + (1 - φ) ∆tma
or
∆t L − ∆t ma
φs = φ =
∆t f − ∆t ma
φs = Porosity calculated from sonic log reading, fraction
∆tL = Travel time reading from log, microseconds/ft
∆tma = Travel time in matrix, microseconds/ft
∆tf = Travel time in fluid, microseconds/ ft

69. ACOUSTIC (SONIC) LOG
0
GR
API
6
CALIX
IN
DT
200
140
40
30
16
USFT
SPHI
%
10
4100
Sonic travel time
Gamma
Ray
Sonic
porosity
4200
Caliper

70. SONIC LOG
The response can be written as follows:
t log = t ma ( 1 − φ) + t f φ
φ=
t log − t ma
t f − t ma
tlog = log reading, µsec/ft
tma = the matrix travel time, µsec/ft
tf = the fluid travel time, µsec/ft
φ = porosity

71. SONIC LOG
001) BONANZA 1
GRC
0
150
SPC
-160 MV
40
ACAL
6
16
0.2
0.2
0.2
ILDC
SNC
MLLCF
200
200
RHOC
1.95
2.95
CNLLC
0.45
-0.15
DT
150 us/f 50
200
10700
150
10800
Sonic
Log
10900
DT
us/f
50

72. EXAMPLE
Calculating Rock Porosity
Using an Acoustic Log
Calculate the porosity for the following intervals. The measured travel times from the
log are summarized in the following table.
At depth of 10,820’, accoustic log reads travel time of 65 µs/ft.
Calculate porosity. Does this value agree with density and neutron
logs?
Assume a matrix travel time, ∆tm = 51.6 µsec/ft. In addition, assume the formation is
saturated with water having a ∆tf = 189.0 µsec/ft.

73. EXAMPLE SOLUTION SONIC LOG
001) BONANZA 1
GRC
0
150
SPC
-160 MV
40
ACAL
6
16
0.2
0.2
0.2
ILDC
SNC
MLLCF
200
200
RHOC
1.95
2.95
CNLLC
0.45
-0.15
DT
150 us/f 50
SPHI
45
ss
-15
200
10700
10800
SPHI
10900

74. FACTORS AFFECTING SONIC
LOG RESPONSE
• Unconsolidated formations
• Naturally fractured formations
• Hydrocarbons (especially gas)
• Rugose salt sections

75. RESPONSES OF POROSITY LOGS
The three porosity logs:
– Respond differently to different matrix
compositions
– Respond differently to presence of gas or
light oils
Combinations of logs can:
– Imply composition of matrix
– Indicate the type of hydrocarbon in pores

76. GAS EFFECT
• Density - φ is too high
• Neutron - φ is too low
• Sonic - φ is not significantly
affected by gas

77. ESTIMATING POROSITY FROM
WELL LOGS
Openhole logging tools are the most common method
of determining porosity:
• Less expensive than coring and may be less
risk of sticking the tool in the hole
• Coring may not be practical in unconsolidated
formations or in formations with high secondary
porosity such as vugs or natural fractures.
If porosity measurements are very important, both
coring and logging programs may be conducted so
the log-based porosity calculations can be used to
calibrated to the core-based porosity measurements .

78. Influence Of Clay-Mineral Distribution
On Effective Porosity
Dispersed Clay
• Pore-filling
• Pore-lining
• Pore-bridging
φe
Clay
Minerals
Detrital Quartz
Grains
φe
φe
Clay Lamination
Structural Clay
(Rock Fragments,
Rip-Up Clasts,
Clay-Replaced Grains)
φ
φee

79. GEOLOGICAL AND PETROPHYSICAL
DATA USED TO DEFINE FLOW UNITS
Core Lithofacies
Core Pore
Plugs Types
Petrophysical
Data
Gamma Ray Flow
Log
Units
φ vs k Capillary
Pressure
5
4
3
2
1

80. Schematic Reservoir Layering Profile
in a Carbonate Reservoir
Baffles/barriers
SA -97A
Flow unit
SA -251
3150
3200
SA -356 SA -71 SA -344
3150
3100
SA -371
3100
SA -348
3250
SA -346
SA -37
3150
3100
3200
3250
3200
3200
3150
3300
3150
3200
3150
3250
3300
3250
3250
3200
3250
3250
3200
3300
3350
3300
3250
3300
3250
3350
3350
From Bastian and others

81. Why is porosity important?
Especially because it allows us to make estimations of the amount of
fluid that can be contained in a rock (water, oil, spilled contaminants,
etc.).
Example from oil and gas exploration:

82. Why is porosity important?
Especially because it allows us to make estimations of the amount of
fluid that can be contained in a rock (water, oil, spilled contaminants,
etc.).
Example from oil and gas exploration:

83. Why is porosity important?
Especially because it allows us to make estimations of the amount of
fluid that can be contained in a rock (water, oil, spilled contaminants,
etc.).
Example from oil and gas exploration:

84. Why is porosity important?
Especially because it allows us to make estimations of the amount of
fluid that can be contained in a rock (water, oil, spilled contaminants,
etc.).
Example from oil and gas exploration:

85. Why is porosity important?
Especially because it allows us to make estimations of the amount of
fluid that can be contained in a rock (water, oil, spilled contaminants,
etc.).
Example from oil and gas exploration:
How much oil is contained in the discovered unit?
In this case, assume that the pore
spaces of the sediment in the oilbearing unit are full of oil.
Therefore, the total volume of oil is
the total volume of pore space (VP)
in the oil-bearing unit.

86. VP
P = ×100
VT
Total volume of oil = VP, therefore solve for VP.
VT = 800m × 200m ×1m = 160, 000m3
P × VT
VP =
100
P = 10%
Therefore:
10 ×160, 000
VP =
100
= 16, 000m
3
of oil

87. II. Permeability (Hydraulic Conductivity; k)
Stated qualitatively: permeability is a measure of how easily a fluid will
flow through any granular material.
More precisely, permeability (k) is
an empirically-derived parameter
in D’Arcy’s Law, a Law that
predicts the discharge of fluid
through a granular material.

100. Those are all properties that are independent of the granular material.
There are also controls on permeability that are exerted by the granular
material and are accounted for in the term (k) for permeability:
k is proportional to all sediment properties that influence the flow of
fluid through any granular material (note that the dimensions of k are
cm2).
Two major factors:
1. The diameter of the pathways through which the fluid moves.
2. The tortuosity of the pathways (how complex they are).

101. 1. The diameter of the pathways.
Along the walls of the pathway the velocity is zero (a no slip boundary)
and increases away from the boundaries, reaching a maximum towards
the middle to the pathway.
Narrow pathway: the region where the velocity is low is a relatively
large proportion of the total cross-sectional area and average velocity is
low.
Large pathway: the region where
the velocity is low is proportionally
small and the average velocity is
greater.
It’s easier to push fluid through a large
Pathway than a small one.

102. 2. The tortuosity of the pathways.
Tortuosity is a measure of how
much a pathway deviates from a
straight line.

104. 2. The tortuosity of the pathways.
Tortuosity is a measure of how
much a pathway deviates from a
straight line.
The path that fluid takes through a
granular material is governed by
how individual pore spaces are
connected.
The greater the tortuosity the
lower the permeability because
viscous resistance is cumulative
along the length of the pathway.

105. Pathway diameter and tortuosity are controlled by the properties of the
sediment and determine the sediment’s permeability.
The units of permeability are Darcies (d):
1 darcy is the permeability that allows a fluid with 1 centipoise
viscosity to flow at a rate of 1 cm/s under a pressure gradient of 1
atm/cm.
1
d )
Permeability is often very small and expressed in millidarcies (
1000

106. a) Sediment controls on permeability
i) Packing density
Tightly packed sediment has smaller
pathways than loosely packed
sediment (all other factors being
equal).
Smaller pathways reduce porosity and the size of the pathways so the
more tightly packed the sediment the lower the permeability.

107. ii) Porosity
In general, permeability increases with primary porosity.
The larger and more abundant the pore spaces the greater the
permeability.
Pore spaces must be well connected
to enhance permeability.

108. Shale, chalk and vuggy rocks (rocks with large solution holes) may have
very high porosity but the pores are not well linked.
The discontinuous pathways result in low permeability.
Fractures can greatly enhance permeability but do not increase porosity
significantly.
A 0.25 mm fracture will pass fluid
at the rate that would be passed
by13.5 metres of rock with 100 md
permeability.

109. iii) Grain Size
Unlike porosity, permeability increases with grain size.
The larger the grain size the larger the pore area.
For spherical grains in cubic packing:
Pore area = 0.74d2

110. A ten-fold increase in grain size yields a hundred-fold increase in
permeability.
iv) Sorting
The better sorted a sediment is the
greater its permeability.
In very well sorted sands the pore
spaces are open.
In poorly sorted sands fine grains
occupy the pore spaces between
coarser grains.

111. v) Post-burial processes
Like porosity, permeability is changed following burial of a sediment.
In this example permeability
is reduced by two orders of
magnitude with 3 km of
burial.
Cementation
Clay formation
Compaction
Pressure solution
All act to reduce permeability

112. b) Directional permeability
Permeability is not necessarily isotropic (equal in all directions)
Fractures are commonly aligned in the same direction, greatly
enhancing permeability in the direction that is parallel to the
fractures.

113. Variation in grain size and geological structure can create directional
permeability.
E.g., Graded bedding: grain
size becomes finer upwards in
a bed.
Fluid that is introduced at the surface will follow a path that is towards the
direction of dip of the beds.

114. Fabric (preferred orientation of the grains in a sediment) can cause
directional permeability.
E.g., A sandstone unit of prolate particles.
The direction along the long axes of grains will have larger pathways
and therefore greater permeability than the direction that is parallel to
the long axes.