1
Special thanks:
Abdulsaboor Khan
Sara Al-Marzouqi
Mohammed Al-MohannadiMohamed IdrisRand Alagha
Afsha ShaikhMaryam Al-Suwaidi
Mashaal Al-SalemMariam Obidan
Tarek SaadWajdi Al oush
RESERVOIR ROCKPROPERTIESEssentialsEdited by Dr. Nayef Alyafei
2 Editionnd
22
ContentsConversion of units 4Porosity 5Rock compressibility 6Liquid permeability 7Gas permeability 8Flow in layered systems 9Fluid saturation 11Electrical properties 12Wettability 13Capillary pressure 14Relative permeability 17Volumetric estimation of hydrocarbons
18
3
What is this booklet?This booklet summarizes the different topics covered in the Fundamentals of Reservoir Rock Properties book in a simple and easy-to-follow format with a one-page article covering each concept. The booklet highlights each property with a basic knowledge that intends to convey a general understanding of the covered topics. The purpose of this booklet is to give a quick overview of the reservoir rock properties. The Fundamentals of Reservoir Rock Properties book can be downloaded from the following link:
https://www.qscience.com/content/books/9789927137273
Why studying Reservoir Rock Properties is important?Reservoir rock properties are part of petrophysics, which is the study of rock properties and rock-fluid properties. Reservoir rock properties are essential aspects of understanding hydrocarbon reservoirs. Those properties should help in estimating the amount of hydrocarbons in reservoirs as well as understanding the production behavior of hydrocarbons.
ContentsConversion of units 4Porosity 5Rock compressibility 6Liquid permeability 7Gas permeability 8Flow in layered systems 9Fluid saturation 11Electrical properties 12Wettability 13Capillary pressure 14Relative permeability 17Volumetric estimation of hydrocarbons
18
DOI: https://doi.org/10.5339/Reservoir_Rock_Properties_Essentials
44
CONVERSION OF UNITS
1 ft = 0.3048 m = 12 in
1 m = 3.281 ft = 39.37 in = 100 cm
Length
Metric Prefixes
Area
Volume
Mass
Oilfield Prefixes
Force
Interfacial Tension Permeability
Pressure
Density
Viscosity
1 ft2 = 0.092903 m2 = 144 in2
1 m2 = 10.7649 ft2 = 10000 cm2
1 cP = 0.01 poise = 0.01 g/cm.s = 0.001 kg/m.s = 0.001 n.s/m2 = 0.001 Pa.s
= 0.01 dyne.s/cm2 = 6.72 x 10-4 lbm/ft.s = 2.09 x 10-5 lbf.s/ft2
1 ft3 = 0.02831 m3 = 28.3168 L = 0.178 bbl = 0.178 RB
1 m3 = 35.29 ft3 = 1000 L
1 = 0.45359 kg
1 kg = 2.2046 lbm = 1000 g
1 lbf = 4.44822 N = 32.2 lbm.ft/s2
1 N = 0.2248 lbf = 1 kg.m/s2
1 N/m = 1000 mN/m = 1000 dyne/cm 1 D = 1000 mD = 9.869233 x 10-13 m2
1 atm = 101.3 kPa = 1.013 bar = 14.696 lbf/in2 (psia)
1 psia = 6.89 kPa = atm/14.696
1 Pa = 1 N/m2 = 1 kg/m.s2 = 10-5 bar = 1.450 x 10-4 lbf/in2 = 10 dyne/cm2
1 g/cc = 1000 kg/m3 = 62.427 lb/ft3 = 8.345 lb/gal = 0.03361 lb/in3
Prefix Symbol Multiplication Factor
giga G 109
mega M 106
kilo k 103
centi c 10-2
milli m 10-3
micro µ 10-6
nano n 10-9
Prefix Symbol Multiplication Factor
Thousand M 103
Million MM 106
Billion MMM or B 109
Trillion T 1012
psia = psig +14.7
5
POROSITY
What is Porosity?Porosity (ф) is the fraction or percentage of empty volume that exists in a rock over the total volume. This is where water, oil and gas reside in a rock. Think of the reservoir like a sponge, the way a sponge absorbs water in the empty spaces is the same way that the fluids occupy the pore spaces in a rock. The general formula for porosity is:
where:ф = porosity [fraction or %]Vp = pore volume [cm3 or ml]Vb = bulk volume [cm3 or ml]Vm = matrix volume [cm3 or ml]
Types of PorosityThere are two types of porosity:• Total porosity (фt) • Effective porosity (фe)
The total porosity takes all the pore space in a rock into consideration. Whereas, effective porosity, is the fraction of the volume of interconnected space in a rock over the bulk volume. As petroleum engineers, we mostly care about the effective porosity. Imagine a school with an area of 100 m2, 25 m2 of those 100 m2 are occupied by five hallways, and for simplicity let us say all the hallways have the same area. Now imagine that two of those hallways are closed. Students then can only walk through three of the hallways, or 15 m2. In the same sense, fluids in the rock can only flow through pores that are not closed but are connected.
φ =Vp
Vb=
Vb − Vm
Vb
Factors Affecting Porosity1. Primary porosity – developed during the burial of the rock:
Sorting
2. Secondary porosity (induced) – developed after deposition due to external factors:
a. Compaction due to stress (decreases porosity):
b. Fractures (increase porosity):
c. Dissolutions (Vugs) (increase porosity):
Well sorted Poorly sorted
Unpacked packed
66
ROCK COMPRESSIBILITY
Porosity is the fraction of a rock that consists of void space. A key aspect in studying porosity is studying rock compressibility.
Rock Compaction Porosity is reduced by compaction, and the reduction is a function of the burial depth of the rock. Isothermal compressibility is defined as the change of volume per unit pressure change at constant temperature.
Effects of Compaction• Changes in packing• Deformation of rock fragments
Simplifying Assumptions• Reservoirs are isothermal • As pressure increases, material volume
decreases • As pressure decreases, material volume
increases
These assumptions are used to derive the compressibility equation shown below
where:
c = coefficient of isothermal compressibility [1/psia]V = volume [ft3]P = pressure [psia]
Types of CompressibilityCompressibility plays a major role on reservoir performance. It is divided into three types:
• Matrix Compressibility, cm • Pore or formation Compressibility, cp/f• Bulk Compressibility, cb
For static conditions;The summation of forces should equal zero
Fov = Fm + Ff
Where Fov is the overburden force, Fm is the matrix force resisting deformation, and Ff is the fluid force.
Similarly for pressures,
Pov = Pm + Pf
As fluids are produced from a reservoir, the fluid pressure in the pores decreases; however, the overburden pressure remains constant causing the following effect:
1. Force on matrix increases2. Bulk volume decreases 3. Pore volume decreases
This effect pushes some fluids out of the reservoir, as the pore volume is decreasing with compaction. Also, this might cause subsidence, where formation thickness decreases to compensate for the produced fluids.
Fov
FmFf
c = − 1
V
dV
dP
7
LIQUID PERMEABILITY
What is Liquid Permeability? Pores usually contain water in them referred to as brine. Brine is water that contains more dissolved salt than typical seawater. In other words, brine is a solution of salt in water.
Permeability is a measure of the fluid conductivity of the rock, which means that permeability is the term used for fluid transport.
Understanding Permeability It is important to understand permeability, as it influences the production of hydrocarbons. As previously discussed hydrocarbons are stored in the pores of the reservoir rocks.
Now you might be wondering what the relationship between porosity and permeability is. Permeability is the ability of fluids to be transported through porous rocks. If the pore spaces in rocks are not connected, then the rock is not permeable. The fluid then, will be trapped and unable to move. If the pore spaces in rocks are connected, then fluid can be transported so it is permeable. The figure below provides an illustration of how low and high permeability look like.
Low permeability reigon
High permeability reigon
Permeability can be calculated using Darcy’s law for 1-D, single phase liquid (in Darcy’s units):
Where
k = permeability [D]
= pressure gradient [atm/cm]
A = cross sectional area [cm2]µ = viscosity of liquid [cP]q = volumetric flow [cm3/s] When finding the permeability using Darcy’s law, there are certain conditions that must be assumed for Darcy’s law to be valid:
• The pore spaces should be fully saturated with a single phase; water, oil, or gas.
• The flow must be laminar.• The flow must be at steady-state condition.
q =kA
µ
dP
dx
q =kA
µ
dP
dx
88
GAS PERMEABILITY
IntroductionOften dry gas (He, N2, air) is used in the laboratory for permeability determination since it is readily available and is relatively less reactive with the rock.
Gas PermeabilitySince gases are compressible, the average pressure Pm needs to be used, where:
Considering an ideal gas behavior of gas, we can assume:
Thus, Darcy’s law equation becomes:
where, qsc = gas flowrate at standard conditions [cm3/s]Psc = pressure at atmospheric conditions [≈ 1atm]k = absolute permeability [D]A = cross sectional area [cm2]P1 = inlet pressure [atm]P2 = outlet pressure [atm]µg = gas viscosity [cP]L = length of core [cm]
Pm =P1 + P2
2
P1q1 = P2q2 = Pmqm
Pscqsc = Pmqm
qsc =kA(P 2
1 − P 22 )
2µgLPsc
Klinkenberg EffectKlinkenberg (1941) noticed that permeability measurements using liquids and gases gave different results. Permeability with air gave a higher value than permeability measurement with water. This phenomenon was attributed to gas slippage at the pore walls. Liquids have zero velocity at the sand grain surface; however, gases have some finite velocity at the sand grain surface. The slippage results in a higher flowrate for a given pressure differential for the gases. Klinkenberg related the liquid permeability kL to gas permeability kg by the following equation:
If we observe from the graph, the higher the value of Pm, the lower the value of 1/Pm. At extremely high pressures (infinite pressure), gases are believed to behave like liquids. Thus if we extrapolate our 1/Pm to zero, it would mean the permeability would be approximately equal to the liquid permeability. The slope c of the line is a function of absolute permeability, type of gas, and average radius of the rock capillaries.
kg = c1
Pm+ kL
Slippage
kg
Absloute or Liquid Permeability
1Pm
9
FLOW IN LAYERED SYSTEMS
The objective of understanding the flow in a layered system is to find the average permeability of the system and its various beddings. The average permeability calculation will be centered around Darcy’s law but will vary based on the configuration of the layers as described in the following cases:
Case 1: Linear Flow in Parallel Consider the three-layer system below where the layers are in parallel and each layer has a different permeability. In this case, the pressure drop in each layer is the same. The flow rate and thickness, however, are unique and sum up to the total flow rate and thickness of the system. Combining these relationships with Darcy’s law results in the average permeability formula for this system.
Case 2: Linear Flow in SeriesIn this case, each bedding still has a different permeability but they are in series to each other. As a result, the flow rate that passes through each rock is the same but the pressure drop across each rock is different. Furthermore, the total length of the system is composed of the length of each rock. These conditions can be combined to calculate the average permeability of the system.
Case 3: Radial Flow in ParallelThe flow in parallel systems for liner and radial cases is similar. Consider the system below, the overall flow rate and total thickness is the summation of the flow rate and thickness value of each layer. The pressure drop, however, is common. Combining these conditions with Darcy’s law for radial flow results in a calculation of average permeability for this case.
Case 4: Radial Flow in SeriesFinally, consider the radial system below. In this case, the flow rate across each layer is the same, however the pressure difference in each layer varies. Combining these conditions allows for the average permeability for this system.
P2P1
k1 h1
h2
h3
k2
k3
q1
q2
q3
W
L
h
h1
h2
h
h3
re
rW
q2
q1
q3
k1
k2
k3
rW
re
r1
h k1k2
P2P1
k3
L3
W
L
q q
h
k1
L1
k2
L2
P3P2P1
k =
n∑i=1
kihi
h
k =L∑n
i=1Li
ki
k =
n∑i=1
kihi
h
k =ln(
rerw
)
∑ni=1
ln( r(i+1)
ri
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ki
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∆Tm
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Vb
φ=
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c=
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)
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kihi
h
k=
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ki
k=
ln( r
e
rw
)
∑n i=
1
ln( r
i+
1ri
)
ki
k=
r2 8
k=
h2
12
ρ=
m V
P=
F A
11
FLUID SATURATION
What is Saturation?Pores usually contain more than one fluid in them. The fraction of pore space occupied by a specific fluid is called saturation. Saturation is the ratio of fluid volume to the pore volume.
where:
Sw = water saturation [fraction or %] So = oil saturation [fraction or %]Sg = gas saturation [fraction or %]Vw = water volume [cm3 or ml]Vo = oil volume [cm3 or ml]Vg = gas volume [cm3 or ml]Vp = pore volume [cm3 or ml]
We could then notice that saturations are fractions, and collectively in pores the summation of all saturations should equal 1:
Look at the figure below for an idea on how fluids look like in a pore
Sw =Vw
Vp
So =Vo
Vp
Sg =Vg
Vp
Rock water Oil or gas
Important Definitions • Connate water (Swc): it is the minimum
water saturation which would remain adhered to the pores and not become mobile. During deposition, water saturation is 100% which declines by the migration of oil/gas to (20-30%) and that is the connate water saturation.
• Irreducible water saturation (Swir): it is the minimum water saturation in a rock forming a layer of water stuck to the rock surface and that does not move. Therefore, Swc = Swir
• Residual oil (Sor): it is the oil left behind (could not be produced) after immscible displacement. This oil is trapped in the pore spaces and cannot move.
Types of MeasurementsThere are two methods to determine or measure fluid saturation
• Direct: using core samples through: - Retort distillation - Solvent extraction (Dean-Stark method)
• Indirect: capillary pressure and well log analysis (resistivity logs)
Factors Affecting SaturationThere are many factors that affect saturation. For example, core samples from reservoir get affected by filtrate from drilling mud. The mud can usually be water or oil based and depending on the wettability of the rock could affect saturation differently.
Another factor that affects fluid saturation would be the differences in pressure and temperature that are caused by bringing the core sample from the reservoir to the surface. Those differences in pressure and temperature cause fluids such as gas trapped in oil to be released. This is especially important to know when conducting direct measurements to find the fluid saturation using core samples. The reason fluid saturation is very important is that it helps in estimating the amount of hydrocarbons stored in the reservoir.
1212
ELECTRICAL PROPERTIES
The formation water (brine) contains dissolved salts which make up the electrolytes and help it conduct current within. These salts dissolve and break up into cations (Na+, Ca2+), and anions (Cl- and SO42-). The higher the salt concentration, the better it is at conducting electricity. ResistivityResistivity is a measure of the material’s ability to resist the flow of electricity. The unit of resistivity is ohm.m [Ω.m]. The range for a poorly consolidated sand is 0.2 ohm.m to several ohm.m. For well consolidated sands the resistivity ranges from 1 ohm.m to 1000 ohm.m. Notations for resistivityRw = formation water resistivity [Ω.m]Ro = resistivity of rock with 100% water saturation [Ω.m]Rt = true formation resistivity [Ω.m] Factors that affect resistivity • Water Resistivity • Formation Porosity • Formation Lithology • Type and Amount of Clay Formation FactorFormation factor relates Rw to Ro based on an empirical formula/relation developed by Archie (1942). He found out that this correlation is related to three parameters: a, ф, and m as shown in the following equation:
where:a = constant ≈ 1.0 for most formationsф = porosity [fraction]m = cementation factor ≈ 2 for most formations
F =Ro
Rw= aφ−m
Saturation EquationArchie also found out the saturation equation (resistivity index) which relates Rt to Ro. He found out that this correlation is related to water saturation (Sw) and n is the saturation exponent.
Archie’s EquationArchie’s equation is the combination of the formation factor and the saturation equation since Ro is common in both equations. It is used to calculate the water saturation of un-invaded zones near the bore hole using wireline resistivity logs.
Archie’s equation:
Resistivity of Earth Materials
Ir =Rt
Ro= S−n
w
Sw = n
√aRw
φmRt
ELECTRICAL PROPERTIES ___________________________________________________________________________________
Electriccurrentistransmittedthrougharockduetotheconnatewateritcontainsinoilorgaszones.Theformation water, brine, contains dissolved saltswhichmakesuptheelectrolytesandhelpsitconductcurrentwithin.Thesesaltsdissolveandbreakupintocations, Na+, Ca2+, and anions, Cl- and SO4
2-. Thehigher the salt concentration, the better it is atconductingelectricity.ResistivityUnitisohm.m[Ω.m].The range for a poorly consolidated sand is 0.2ohm.mtoseveralohm.m.For well consolidated sands the resistivity rangesfrom1ohm-mto1000ohm.m.NotationsforresistivityRw=formationwaterresistivity[Ω.m].Ro = Resistivity of rock with100% water saturation[Ω.m].Rt=Trueformationresistivity[Ω.m].Factorsthataffectresistivity
• WaterResistivity• FormationPorosity• FormationLithology• TypeandAmountofClay
FormationFactorFormation factor relates Rw to Ro based on anempirical formula/relation developed by Archie(1942).Hefoundoutthatthiscorrelationisrelatedto three parameters:a,ф, andm as shown in thefollowingequation:
𝐹𝐹 =𝑅𝑅/𝑅𝑅K
= 𝑎𝑎ɸO(
Where:a=constant≈1.0formostformationsф=porosity[fraction]m=cementationfactor≈2formostformations
SaturationEquationArchie also found out the saturation equation(resistivityindex)whichrelatesRttoRo.Hefoundoutthat this correlation is related to water saturation(Sw)andnisthesaturationexponent.
𝐼𝐼 = QRQS= 𝑆𝑆KOT
Archie’sEquationArchie’s equation is the combination of theformationfactorandthesaturationequationsinceRoiscommoninbothequations.It is used to calculate the water saturation of un-invaded zones near the bore hole using wirelineresistivitylogs. Archie’sequation:
𝑆𝑆K = U VQWɸ(QR
X ResistivityofEarthMaterials Rock
Gas Oil
Fresh Water
Salt Water
8
Res
istiv
ity
Conductivity
13
WETTABILITY
What is Wettability?Wettability is a fluid’s tendency to adhere on a solid surface, while co-existing with another immiscible fluid.
ImmiscibilityImmiscible fluids are fluids that do not mix with one another. This is due to an imbalance in the molecular forces between two fluids in contact with one another. These molecular forces present at the interface of two fluids are known as the interfacial tension.
Interface between Immiscible Fluids
Adhesion TensionA key factor in determining the wettability of a rock is adhesion, also known as the difference between two solid-fluid interfacial tensions, is expressed with the following equation:
If the Adhesion tension is positive the denser fluid will wet the rock becoming the wetting phase fluid. For instance, water is the wetting phase in the figure below.
AT = σsw − σso = σwocos θ
θ
σwo
-x +xσsw σso σso
How to determine the wettability of a rock?If a water droplet is surrounded by oil then;
What affects wettability?• Composition of pore-lining minerals• Composition of the fluids• Saturation history
What are the types of wettability?• Oil- or water-wet• Neutral- or intermediate-wet• Fractional- or mixed-wet
Wettability Affects• Capillary Pressure• Residual oil saturation• Relative permeability
Wetting phase fluid Non-wetting phase fluidOccupy smallest pores Occupy largest pores
Has low mobility Usually of higher mobility
Water-Wet Oil-Wet
os > ws os < ws
AT > 0 (positive) AT < 0 (negative)
0 < < 90 90 < < 180
1414
CAPILLARY PRESSURE: PART 1
What is Capillary Pressure?Most of hydrocarbon reservoirs contain a minimum of two immiscible fluids. For water and oil, the interface at which the separation happens is called the oil-water contact. Capillary pressure is defined as the pressure difference between the two immiscible fluids at the interface.
To further define the capillary pressure, wettability needs to be recalled. In a heterogeneous system where one fluid wets the surface (wetting phase) in preference to the other fluid (non-wetting phase), the capillary pressure can be calculated as:
where: Pc = capillary pressure [Pa]Pnw = pressure of the non-wetting phase [Pa]Pw = pressure of the wetting phase [Pa]
Understanding Capillary Pressure from Capillary TubesTo simplify the study of capillary pressure, porous media in a reservoir can be modeled as a collection of capillary tubes as shown below.
For a water-gas system in a collection of capillary tubes, like in a reservoir, water (wetting phase) rises filling smaller pores and leaves the larger pores to be filled by air (non-wetting phase).The height of the water (shown below) in a capillary tube is a function of the adhesion tension between the air and water, the radius of the tube (shown below), and the density difference between air and water (the two immiscible fluids present).
Pc = Pnw − Pw
Water
Δh
h = 0
Air
r
θ
The height of the water in the capillary tube can be calculated using the following formula:
where: σwa = surface tension between air and water [N/m]g = gravitational acceleration [9.8 m/s2]Δρwa = density difference between air and water [kg/m3]θ = contact angle between the surface and water [˚]
Combining the two previous equations, capillary pressure can also be computed using:
Capillary Pressure CurvesAs can be inferred, capillary pressure is very dependent on the wetting phase saturation. To graphically represent the capillary pressure, the capillary pressure curves can be drawn as a function of this saturation. To do that, two fluid flow processes need to be defined over which the capillary pressure varies. These are drainage and Imbibition.Drainage: The process through which the saturation of the non-wetting phase increases.
Imbibition: The process through which the saturation of the wetting phase increases. Parameters used in the figure above are the following:• Swir = irreducible wetting phase saturation
[fraction or %]• Sm = 1 – residual non-wetting phase
saturation [fraction or %]• Pct = threshold capillary pressure, the
minimum pressure required to force non-wetting fluid into the largest pore [Pa]
The shapes of these curves are affected by reservoir quality. This includes the pore size distribution, grain sorting, and permeability.
∆h =2σwacos θ
∆ρwagr
Pc =2σwacos θ
r
Drainage
Imbibition
Pc
Sw0 1
0
-
+
Swir Sm
Pct
15
CAPILLARY PRESSURE: PART 2
Measurement Capillary pressure laboratory measurements are a part of special core analysis (SCAL) and can be measured through three main methods:
• Porous Plate Technique: Uses a low permeability water wet ceramic disc to retain oil in a water wet core sample (containing both oil and water) while allowing water to pass through. In this setup, the inlet pressure will be the oil pressure and the outlet pressure will be the water pressure. The difference between the inlet and outlet pressure is the capillary pressure.
• Mercury Injection Capillary Pressure (MICP): The core sample is placed in a pressure chamber and mercury is injected through it. Mercury acts as the non-wetting phase while air acts as the wetting phase. The volume of mercury injected is calculated and can be converted to a non-wetting phase saturation. The wetting phase saturation will be one minus the non-wetting phase saturation.
• Centrifuge: This method can measure the drainage and waterflood capillary pressure curves. For drainage, a core sample filled with the wetting phase is placed in a cell surrounded by the non-wetting phase. The cell is centrifuged at various speeds and the fluid displaced is recorded at each speed. At each increment, the rotation speed is converted to pressure using specific equations.
Hydrostatic Pressure and Repeat Formation Tester (RFT) As can be inferred, capillary pressure is very dependent on the wetting phase saturation. To graphically represent the capillary pressure, the capillary pressure curves can be drawn as a function of this saturation. To do that, two fluid flow processes need to be defined over which the capillary pressure varies. These are drainage and Imbibition.Drainage: The process through which the saturation of the non-wetting phase increases.
Free oil level (FOL)
Gas
Oil
Water
Free water level (FWL)Dep
th
Pressure
( Pg , Zg )
( Po , Zo )
( Pw , Zw )
Porous Plate Technique MICP Centrifuge
• The most accurate method• Very time consuming and can take a few hours to a few weeks• Non-destructive
• The fasted method• Requires an extra conversion step and does not use reservoir fluids• Damaging to the core
• An intermediate method in terms of time and accuracy• Can use reservoir fluids
ZFOL =Po − Pg + ρggZg − ρogZo
(ρg − ρo)g
ZFWL =Pw − Po + ρogZo − ρwgZw
(ρo − ρw)g
16
FLUID
SATU
RATIO
N
WET
TABIL
ITY C
APILL
ARY P
RESS
URE
ELE
CTRIC
AL PR
OPER
TIES
The
Frac
tion
of p
ore
volu
me
occu
pied
by
a pa
rtic
ular
flui
d.Re
sist
ivity
: The
inve
rse
of th
e m
easu
re
of e
lect
rica
l flow
cap
acity
of r
ocks
(Int
ensi
ve P
rope
rty )
.
Fact
ors
affec
ting
elec
tric
al r
esis
tivity
:·R
esis
tivity
of fl
uids
·Por
osity
of f
orm
atio
n·T
ype
and
amou
nt o
f cla
y·L
ithol
ogy
of fo
rmat
ion
·Tem
pera
ture
Impo
rtan
ce:
To c
alib
rate
the
resi
stiv
ity lo
g an
d fin
d th
e flu
id s
atur
atio
n in
the
rese
rvoi
r.
Met
hods
Impo
rtan
ce: T
o qu
antif
y th
e am
ount
of
HC
in r
eser
voir
Issu
es w
ith e
xtra
ctio
nm
etho
ds w
hen
deal
ing
with
res
ervo
ir r
ocks
: ·D
rilli
ng m
uds.
·Flu
id p
rope
rtie
s.
Dir
ect
Indi
rect elec
tric
al p
rope
rtie
s
capi
llary
pre
ssur
e
extr
actio
nSo
lven
t ext
ract
ion
Soxh
let e
xtra
ctio
nD
ean-
Star
kRe
tort
dis
tilla
tion
Mat
eria
l Bal
ance
accu
rate
, non
-dis
truc
tive
slow
, ext
ract
1 fl
uid
fast
, ext
ract
2 fl
uids
dam
ages
the
core
Met
hods
Dir
ect
Indi
rect
·Cap
illar
y pr
essu
re·R
elat
ive
perm
·Con
tact
ang
le·A
mot
t Ind
exTh
e te
nden
cy o
f a fl
uid
tosp
read
on
solid
sur
face
in
pre
senc
e of
ano
ther
im
mis
cibl
e flu
id.
The
diff
eren
ce b
etw
een
the
non-
wet
ting
phas
e &
the
wet
ting
phas
e pr
essu
res
acro
ss in
terf
ace.
Impo
rtan
ce:
·Con
trol
s sa
tura
tion
dist
ribu
tion.
·Con
trol
s oi
l rec
over
y by
wat
er in
ject
ion.
Imbi
bitio
n:Th
e in
crea
se o
f wet
ting
phas
e sa
tura
tion.
Dra
inag
e:Th
e de
crea
se o
f w
ettin
g ph
ase
satu
ratio
n.
Met
hods
Poro
us P
late
Cent
rifu
geM
ercu
ry In
ject
ion
M
ost a
ccur
ate
U
ses
rese
rvoi
rflu
ids
Ve
ry s
low
Fa
st
Use
s re
serv
oir
fluid
.
Requ
ires
calc
ulat
ion
ofpr
essu
re a
nd s
at
Fa
stes
t
Doe
s no
t use
re
serv
oir
fluid
Le
ast a
ccur
ate
Re
quir
es
inte
rpre
tatio
n
Less
acc
urat
e
0<90
⁰w
ater
-wet
0=90
⁰in
term
edia
te n
eutr
al0>
90⁰
oil-w
etm
ixed
-wet
Impo
rtan
ce:
Dra
inag
e ca
pilla
ry
pres
sure
is u
sed
to
dete
rmin
e flu
id
dist
ribu
tion
in
rese
rvoi
r (in
itial
co
nditi
on) a
bove
the
free
wat
er le
vel
F=
Ro
Rw
=aφ
−m
=a φm
Ir=
Rt
Ro
=S
−n
w=
1 Sn w
Sw
=n√
aR
w
φmR
t
17
RELATIVE PERMEABILITY
What is permeability? Permeability is a rock’s fluid conductivity, as its ability to allow fluid to flow through its pores. When a pore is completely saturated with only one fluid, the rock’s ability to allow that fluid to pass through it is called absolute permeability.However, pores are usually being occupied with more than one fluid (oil, water, and/or gas), and fluids compete to flow through a rock. This is why when producing hydrocarbons by water injection for example; we are interested in the relative permeability of each fluid. The figure below provides a simplistic view of how water is injected in oil filled pores.
What is relative permeability? Because pores contain multiple fluids that are interacting with one another, they do not all move through the rock at the same rate. This is why we need to know the relative permeability for each fluid. The effectiveness of a medium to allow a certain fluid (oil, water or gas) to move in it is called effective permeability.
This all comes to play when trying to determine the relative permeability or the ratio of the effective permeability of a fluid at a specific saturation over the absolute permeability.
t1 t2 t3 t1< t2< t3
Water injection
Permeability Relative permeability
Equation
1-D, linear flow for single phase liquid
, where f is
fluid and can be either water, oil, or gas.
Units mD, D, or m2 Dimensionless
Phase 1 phase flow Multiphase flow
What affects relative permeability?• Fluid saturation • Geometry of the pore spaces • Wettability
Using a relative permeability curve as the one shown below, we keep track of the relative permeability changes. The reason knowing relative permeability is very important is because it affects the flow characteristics of the reservoir fluids which in turn affect the recovery efficiency of the hydrocarbons when two or more fluids are flowing.
Looking at the figure provided above, we can tell that kro is reduced with the increase of krw. This is because they share the same area when they try to flow and when on fluid takes more space the other is forced to take less space. The irreducible water saturation is the minimum water saturation a rock could have, this water cannot be moved or reduced. On the other hand, residual oil saturation occurs during imbibition, where some of the oil we try to produce is trapped in the pore spaces of a rock.
10 Sw
kr kro
krw
Swir Sor
0
1
Residual oil
saturation (Sor)
Irreducible water
saturation (Swir)
krw @ Sor
krw @ Swir
18
VOLUMETRIC ESTIMATION OF HYDROCARBONS
Estimating Oil and Gas in Place Dealing with an oil and gas reservoir is challenging because it is underground and obscure. An important application of petrophysical data is the ability to estimate the amount of hydrocarbons in the reservoir and provide some clarity to the commercial viability of its production. The first form of these estimates calculates Oil in Place (OIP), the volume of oil in the reservoir, by utilizing water saturation and porosity.
In the case of a reservoir containing water and gas, the Gas in Place can be calculated in a similar manner.
Fluid Properties An important phenomenon to consider when estimating volumes is the effect a change in pressure and temperature has on reservoir fluids as they are produced. For oil, as pressure is depleted, the dissolved gas in the oil begins to expand causing the total volume to increase. The oil expansion will continue until the bubble point pressure is reached, after which the gas begins to bubble out of the oil, reducing the oil volume. This phenomenon is encapsulated in the oil formation factor – a dimensionless value used to convert the oil volume from reservoir conditions to surface conditions.
The oil formation factor will always be greater than 1, as the volume at the surface will always be less than or equal to reservoir volumes. This parameter adjusts the OIP formula to calculate stock tank oil in place (STOIP or N).
Gas behaves in a different manner to oil. When the pressure acting on the gas is depleted, it begins to expand. To capture this behavior the gas formation volume factor is defined as:
Similar to the OIP formula, with the addition of the gas formation volume factor, the GIP formula can be adjusted to calculate stock tank gas in place (STGIP or G).
Unit Systems Oilfield units are the most common units used in the petroleum industry and, when utilized with the volumetric equation, require a conversion factor.
where, N: Stock tank oil in place [STB]G: Stock tank gas in place [SCF]A: Area of the reservoir [acres]h: Thickness of the reservoir [ft]Sw: Water saturation [dimensionless]Bo: Oil formation volume factor [RB/STB]Bg: Gas formation volume factor [ft3/SCF]
P
Bo
Pb
Bob
Pi
Boi
P
Bg
OIP = φVb(1− Sw)
Bo =Volume of oil in the reservoirVolume of oil on the surface
N =φVb(1− Sw)
Bo
G =φVb(1− Sw)
Bg
N =7758φAh(1− Sw)
Bo
G =43560φAh(1− Sw)
Bg
Bg =Volume of gas in the reservoirVolume of gas on the surface
GIP = φVb(1− Sw)
19
SUMMARY OF ROCK PROPERTIES
Parameter Symbol Definition Importance
Porosity ϕ Is the ratio of pore volume to bulk volume
We use porosity to quantify the volume of oil and/or gas in the reservoirs
Rock Compressibility
c The relative change of volume per unit pressure
It is part of the recovery mechanisms under primary hydrocarbon production. Also, can cause subsidence which has an environmental impact.
Single Phase permeability
k A measure of the ease which with which fluid flows through a porous rock
We use permeability in determining the rate at which the gas and oil flow to the surface.
Fluid Saturation Si , (where ican be water, oil, or gas)
The fraction of pore volume occupied by the fluid
We use fluid saturation to quantify the volume of oil and/or gas in the reservoirs
Electrical Properties F and Ir The rock properties to impede the follow of electric current through a rock. Electrical properties are a function of porosity and fluids in the pore space.
We use electrical properties to calibrate the resistivity log and find the fluid saturation in the reservoir.
Wettability - The tendency of a fluid to spread on a solid surface in the presence of another immiscible fluid
We use wettability to help us understand oil production when injecting water as wettability has a primary role in water injection performance.
Capillary Pressure Pc The pressure difference between the non-wetting phase and the wetting phase across the interface
We use capillary pressure to determine fluid distribution in the reservoir (initial condition) above the free water level.
Relative Permeability
kr Is the ratio of the effective permeability of that phase to the absolute permeability
We use relative permeability to study and understand the multi-phase flow in reservoirs. For instance, we use relative permeability to predict the recovery of oil by water injection.
20
