Q931+rrl reference en le cs

Reservoir Rock Laboratory Course
2nd Ed. , 2nd Experience

1. About This Course
2. Course Learning Outcome
3. Presentation and assessment
A. Class Projects (CLS PRJ)
4. Laboratory related issues
5. Review of Syllabus
6. Resources
7. Training Outline (beta)
8. Communication

A quote on Beginnings
"Before you begin a thing, remind yourself that
difficulties and delays quite impossible to foresee
are ahead.
If you could see them clearly, naturally you could do
a great deal to get rid of them but you can't.
You can only see one thing clearly and
that is your goal.
Form a mental vision of that and
cling to it through thick and thin"
Kathleen Norris
Fall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 4

Course Scope
Systematic theoretical
and laboratory study of
physical properties of
petroleum reservoir
rocks;
STRUCTURE AND
PROPERTIES OF POROUS
MEDIA
Coring and Rock sample
preparation
Porosity
• Measurement of
Porosity by saturation
method and helium
porosimeter
• Compressibility
• grain size and pore size
distribution of
formation
Permeability
• effective permeability
by using liquid & gas

Course Scope (Cont.)
STATICS OF FLUIDS IN
POROUS MEDIA
Saturation
• Measurement of fluid
Saturation by extraction
method, retort method
• Resistivity
Multiphase Phenomena
(Fluid flow in porous
media, fluid-rock
interaction)
• Surface tension and
wettability
• Capillary pressure
o capillary
characteristics by
porous plate
method and
mercury injection
method
• Relative permeability
Heterogeneity

Course Description
This course is prepared for:
 1 semester (or credit) hours and meets for a total of 2
hours a week.
Sophomore or junior level students (BS degrees)
(Major) Petroleum engineering students
(Minors) Production, Drilling and reservoir engineering students
Prerequisites: general petrology.
Main objectives:
The aim of the laboratory experiments is to give the
students better understanding of reservoir rocks and the
factors that affect the fluid flow within the porous media

Learning and Teaching Strategies
This course promotes interactive and thorough
engagement in the learning process.
It is essential that you take responsibility for your
own learning, and that I facilitate that learning by
establishing a supportive as well as challenging
environment.

Proposed study method
When studying petroleum engineering,
it is important to realize that
the things you are learning today
will be important to you for the rest of your career.
Hence,
you shouldn’t just learn things simply to pass exams!
You will gain maximum benefit from this course by
approaching each lecture and in-class activity
with an inquiring mind and a critical, analytical attitude.

Study recommendations
In covering the material in the course, I recommend
that you follow the procedure outlined below:
Carefully read the entire chapter
to familiarize yourself with the material.
Locate the topic area in your text book and study this material
in conjunction with the course material.
Attempt the examples before all tutorials.
When you feel that you have mastered a topic area,
attempt the problem for the topic.
You are required to complete the assigned readings prior to
lectures.
This will help your active participation in class activities.
Self-study in advance is always more beneficial.

Main Objectives (minimum skills to be
achieved/demonstrated)
By the last day of class, the student should be able to:
Define porosity, discuss the factors which effect porosity, and
describe the methods of determining values of porosity.
Define the coefficient of isothermal compressibility of reservoir
rock and describe methods for determining values of formation
compressibility.
describe methods for determining values of absolute
permeability.
Explain boundary tension and wettability and their effect on
capillary pressure, describe methods of determining values of
capillary pressure, and convert laboratory capillary pressure
values to reservoir conditions.
Describe methods of determining fluid saturations in reservoir
rock and show relationship between fluid saturation and capillary
pressure.

Main Objectives (minimum skills to be
achieved/demonstrated) (Cont.)
Define resistivity, electrical formation resistivity factor,
resistivity index, saturation exponent, and cementation
factor and show their relationship and uses; discuss
laboratory measurement of electrical properties of
reservoir rocks; and demonstrate the calculations
necessary in analyzing laboratory measurements.
Define effective permeability, relative permeability,
permeability ratio; reproduce typical relative
permeability curves and show effect of saturation
history on relative permeability; illustrate the
measurement of relative permeability; and
demonstrate some uses of relative permeability data.

Minor Objectives (other skills to be
achieved/demonstrated)
Describe three-phase flow in reservoir rock and
explain methods of displaying three-phase effective
permeabilities, including ternary diagrams.
Demonstrate the techniques of averaging porosity,
permeability, and reservoir pressure data.
Demonstrate capability to perform calculations
relating to all concepts above.

Laboratory related outcomes
Apply the knowledge of mathematics, geology,
physics, chemistry as well as other engineering
sciences.
Conduct experiments safely and accurately and to
be able to correctly analyze the results.
Design an engineering process or system to meet
desired needs.
Identify, formulate and solve engineering problems.
Understand the impact of engineering solutions in
a global, economic, environmental and societal
contest.

Side Objectives
Communicational skills
Communicate
successfully and
effectively.
Understand professional
and ethical
responsibilities.
Work in a team
environment
Familiarize with English
language
Academic skills
Systematic research
Reporting
Management skills
Project
time
Computer knowledge
Understand the use of
modern techniques, skills
and modern engineering
tools
Application of internet
and Email
Microsoft Office
Professional software

Presentations (Lectures)
Each session
Consists of different sections (about 4-5 sections)
Consists of about 35 slides
Is divided into 2 parts with short break time
Would be available online
The teaching approach to be employed will involve
lectures and tutorials.
Lecture presentations cover theoretical and practical
aspects, which are also described in the supporting
academic texts and teaching resources.
You are encouraged to ask questions and express feedback
during classes. You are expected to read prescribed materials
in advance of classes to enable active participation.

Timing
Last Session (Review)
Areas Covered in This
Lecture
Presentation A
Break Time
Presentation B
Next Session Topics
Last session
(Review)
Session
Outlook
Presentation ABreak
Time
Presentation B
Next Session
Topics
Roll Call

Assessment Criteria
Basis for Course Grade:
Final exam
(Close book)
Attendance
Class activities
Class Projects
Examinations
Grade Range:
90 ≤ A ≤100 (18 ≤ A ≤20)
80 ≤ B ≤ 90 (16 ≤ B ≤18)
70 ≤ C ≤ 80 (14 ≤ C ≤16)
60 ≤ D ≤ 70 (12 ≤ D ≤14)
F < 60 (F <12)
Final
exam
Attendance
Class
activities

Previous Term Scores out of 20 (Q922)
10.0
15.0
20.0
F DE1 F DE2 F LOG F RE2 F RFP

Previous Term (Q922)
Attendance percentage
Students are
expected to
be regular and
punctual in
attendance at
all lectures
and tutorials.
Attendance
will be
recorded
when
applicable.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
DE1 DE2 LOG RE2 RFP

CLS PRJ Topics:
These are intended topics,
addition and/or deletion
of certain problems may
occur as other problems
become available. Multiple
assignments from each
topic are possible.
Porosity (fundamentals and
laboratory measurements).
Permeability (fundamentals
and laboratory
measurements).
Compressibility of reservoir
rocks
(derivations/applications).
Flow in channels and
layered reservoir systems
(derivations/applications).
Capillary pressure
(fundamentals, laboratory
measurements, and
correlations).
Electrical properties
(fundamentals and
laboratory measurements).
Relative permeability
(fundamentals, laboratory
measurements, and
correlations).
Statistical analysis and
correlation of reservoir
data.

Format of the Report:
 Title page:
 Course number, course name,
Experiment number & title, Lab date,
Names of the lab group
 Sections to include in each report
 Introduction
 Objective/purpose of the experiment
 Scope of the experiment / Importance
of the parameters measured
 How (in general) you obtained the
information you are reporting
 Methods
 Describe Equipment
 Experimental procedure (write it in your
own words)
 Methods of analysis (if appropriate)
 How did you analyze the data (principle
/ equations used)
 Results:
 State/tabulate/plot results as applicable
 Report both observed and measured
results
 Discussion:
 Discuss the importance of results
 Tie the results of this study to previous
knowledge/works
 Comment on the quality of results
 Conclusions:
 Findings in the study (stick to the results
you measured)
 References
 Appendices
 Raw Data tables
 Must include sample calculations
 Derivation of equations (if applicable)
 Report late submission Policy:
 Report must be submitted one week
after experiment unless asked
otherwise. Deduction of 10% grade per
late submission will be applied.

Deliverable Format Guidelines
General Instructions:
You must use predefined templates for reporting the
projects
Follow predefine instructions

Safety:
Wear safety goggles when working in the lab
 Lab coats or aprons should be worn when appropriate
 Flip flops and sandals are prohibited
 Restrain loose clothing, hair and jewelry
 Never work alone or without an instructor present
 Never leave heat sources unattended
 Do not eat, drink or smoke in the lab
 Dispose of waste properly
 Wash hands after spill
 Report any accidents to the instructor
 Avoid direct contacts with chemicals and reagents

‫مخزن‬ ‫سنگ‬ ‫خواص‬ ‫آزمایشگاه‬ ‫سرفصل‬
(‫علوم‬ ‫وزارت‬ ‫مصوب‬)
‫گیری‬ ‫مغزه‬
‫روش‬‫برداری‬ ‫مغزه‬ ‫های‬
‫آزمایش‬‫مغزه‬ ‫های‬
‫مغزه‬ ‫آنالیز‬ ‫و‬ ‫داری‬ ‫نگه‬‫سنگی‬ ‫های‬
‫تخلخل‬
‫اندازه‬‫گیری‬‫تخلخل‬ ‫آزمایشگاهی‬
‫تعیین‬‫توزیع‬‫خلل‬‫فرج‬ ‫و‬‫با‬‫استفاده‬‫از‬
‫تراوایی‬
‫اندازه‬‫گیری‬‫آزمایشگاهی‬‫تراوایی‬‫مطلق‬
(‫گاز‬+‫مایع‬)
‫اشباع‬
‫روشهای‬‫آزمایشگاهی‬‫تعیین‬‫اشباع‬‫سنگ‬
‫مخزن‬
‫بیان‬‫معایب‬
‫مزایا‬ ‫بیان‬
‫ارزیابی‬‫اعتبار‬‫داده‬‫اشباع‬ ‫های‬
‫پذیری‬ ‫تراکم‬
‫اندازه‬‫آزمایشگاهی‬ ‫گیری‬‫تراکم‬‫پذیری‬
‫الکتریکی‬ ‫خواص‬
‫اندازه‬‫گیری‬‫آزمایشگاهی‬‫ضریب‬‫مقاومت‬
‫الکتریکی‬‫سازند‬

(‫علوم‬ ‫وزارت‬ ‫مصوب‬( )‫ادامه‬)
‫مویین‬ ‫فشار‬
‫آزمایشگاهی‬ ‫روشهای‬‫اندازه‬‫گیری‬
‫فشار‬،‫مویینگی‬
‫ویژگیهای‬‫منحنی‬‫فشار‬،‫مویینگی‬
‫تبدیل‬‫داده‬‫آزمایشگاهی‬ ‫های‬‫فشار‬
‫مویینگی‬‫جهت‬‫استفاده‬‫در‬،‫میدان‬
‫تعیین‬‫متوسط‬‫فشار‬‫مویینگی‬‫با‬
‫استفاده‬‫از‬‫رابطه‬J،
‫تعیین‬‫میزان‬‫اشباع‬‫نفت‬‫عمق‬ ‫با‬
‫متوسط‬‫منحنی‬‫فشار‬،‫مویینگی‬
‫توسعه‬‫رابطه‬‫ریاضی‬‫فشار‬‫مویینگی‬
‫در‬‫آزمایش‬،‫سانتریفوژ‬
‫سیال‬ ‫جابجایی‬ ‫و‬ ‫فازی‬ ‫دو‬ ‫تراوایی‬
‫روشهای‬‫آزمایشگاهی‬‫اندازه‬‫گیری‬
‫تراوایی‬‫نسبی‬
(‫روش‬‫یکنواخت‬‫و‬‫یکنواخت‬ ‫غیر‬)
‫تعیین‬‫تراوایی‬‫نسبی‬‫از‬‫داده‬‫فشار‬ ‫های‬
،‫مویینگی‬
‫عوامل‬‫موثر‬‫بر‬‫اندازه‬‫گیری‬‫تراوایی‬
،‫نسبی‬
‫ویژگیها‬‫خاص‬‫در‬‫داده‬‫تراوایی‬ ‫های‬
،‫نسبی‬
‫ارزیابی‬‫داده‬‫تراوایی‬ ‫های‬‫نسبی‬‫و‬
‫تعیین‬‫توان‬‫رابطه‬ ‫های‬corey،
‫اهمیت‬‫داده‬‫تراوایی‬ ‫های‬‫نسبی‬‫در‬
‫سیستمهای‬‫محاسبه‬‫فازی‬

(‫علوم‬ ‫وزارت‬ ‫مصوب‬( )‫ادامه‬)
‫محیط‬ ‫در‬ ‫سیاالت‬ ‫جریان‬‫های‬
‫متخلخل‬
‫استفا‬ ‫با‬ ‫سیاالت‬ ‫جریان‬ ‫مطالعه‬‫ده‬
‫مدل‬ ‫از‬‫و‬ ‫الکتریکی‬ ‫ساده‬ ‫های‬
‫مخ‬ ‫سازی‬ ‫شبیه‬ ‫در‬ ‫الکترولیتی‬‫زن‬
‫ناهمگونی‬(Heterogeneity)
‫در‬‫مخازن‬
‫اهمیت‬
‫تعریف‬
‫ناهمگونی‬،‫سطحی‬
‫ناهمگونی‬،‫عمقی‬
‫کمی‬‫ناهمگونی‬ ‫سازی‬
‫از‬‫روشهای‬‫دایکسترا‬‫پارسونر‬‫و‬‫لورنز‬
‫کشش‬‫سطحی‬‫و‬‫ترشوندگی‬
‫اندازه‬‫گیری‬،‫ترشوندگی‬
‫روشهای‬‫آموت‬ ‫شاخص‬
‫و‬USBM،
‫آموت‬‫هاروی‬
‫و‬‫زاویه‬‫تماس‬

Extra (Beyond scope)
Statistical analysis and correlation of reservoir data
Treating Experimental Data
Simulating experiments using relevant software

‫خواص‬ ‫آزمایشگاه‬ ‫درس‬ ‫پیشنهادی‬ ‫منابع‬
‫مخزن‬ ‫سیاالت‬
‫است‬ ‫نشده‬ ‫ارایه‬ ‫منابعی‬.

Texts and Materials:
(ABT) Torsæter, O., and M. Abtahi. "Experimental
reservoir engineering laboratory work book."
(Q931+RRL+L00) Lecture notes from class
These materials may include
handouts provided in class.
computer files available on the course weblog
…

Class Lectures

Major References
(ABT) Torsæter, O., and
M. Abtahi.
"Experimental reservoir
engineering laboratory
work book."
Department of
Petroleum Engineering
and Applied
Geophysics,
Norwegian University
of Science and
Technology (NTNU),
Trondheim (2003).

Major References (Cont.)
Mostafa Mahmoud
Abdel Latief Kinawy,
"Lecture of Reservoir
Engineering
Laboratory“ Petroleum
and Natural Gas
Engineering
Department of King
Saud University (2009).

Side References
Ahmed, T. (2010).
Reservoir engineering
handbook
(Gulf Professional
Publishing).
Chapters:

‫فارسی‬ ‫منابع‬(‫کمکی‬)
(‫ترجمه‬)‫رحیم‬ ،‫سیالوی‬.
1386.‫مخازن‬ ‫مهندسی‬
‫هیدروکربوری‬

Class Schedule (Beta)
Lec. 1
 Introduction
Lec. 2
Lec. 3
Lec. 4
Lec. 5
Lec. 6

Lec. 7
Lec. 8
Lec. 9
Lec. 10

Details (Beta)
Date Lecture Topic Reading Assignment (prior to class)
01
02
03

Communication Methods
Preferred methods
Break time and mid class
First Point of Contact via
email (Limited)
Will be answered with
some delay
(an hour to a week
according to importance
and requirements)
Mention your personal
and educational info in
emails (Name, Student #,
Course title, Subject)
Avoid following
communication methods
Appointments
Phone calls
Short Message Service
(SMS)
Instant message (IM)
chats

Frequently Asked Questions (FAQ)
Class schedule:
Almost all sessions will
be held
Preferred topics:
Course related
Research study
Paper for International
conferences
Articles for national
journals
Avoided helps:
Other courses
Sources, exams, exercises,
class works and so on
B.Sc. Thesis
Aside supervised ones
M.Sc. Conquer
Trainee
Private class
Educational problems
Personal problems
National conference
paper

1. Petrophysics
2. Coring and Plugging

Petrophysics definition
Petrophysics
(from the Greek petra, "rock" and physis, "nature")
is the study of physical and chemical rock properties and their
interactions with fluids.
A major application of petrophysics is in studying
reservoirs for the hydrocarbon industry.
Petrophysicists are employed
to help reservoir engineers and geoscientists
understand the rock properties of the reservoir,
particularly how pores in the subsurface are interconnected,
controlling the accumulation and migration of hydrocarbons.
Some of the key properties studied in petrophysics are
lithology, porosity, water saturation, permeability and density.

key aspect of petrophysics
A key aspect of petrophysics
is measuring and evaluating these rock properties
by acquiring
well log measurements - in which a string of
measurement tools are inserted in the borehole,
core measurements - in which rock samples are
retrieved from subsurface, and
seismic measurements.
These studies are then combined with geological
and geophysical studies and reservoir engineering
to give a complete picture of the reservoir.

Categories of measured properties
While most petrophysicists
work in the hydrocarbon industry, some also
work in the mining and water resource industries.
The properties measured or computed fall into
three broad categories:
conventional (or reservoir) petrophysical properties,
Reservoir models are built upon their measured and derived
properties to estimate the amount of hydrocarbon present in
the reservoir, the rate at which that hydrocarbon can be
produced to the Earth’s surface.
rock mechanical properties, and
ore quality

conventional (or reservoir)
petrophysical properties,
Lithology: rock's physical characteristics:
grain size, composition and texture and etc.
By using log measurements,
such as natural gamma, neutron, density and resistivity
Porosity:
from neutrons or by gamma rays, also sonic and NMR logging.
Water saturation:
from an instrument that measures the resistivity of the rock
Permeability:
From Formation testing, and empirical relationships with
other measurements such as porosity, NMR and sonic logging.
“Net Pay”

Rock mechanical properties
Some petrophysicists use acoustic and density
measurements of rocks to compute their
mechanical properties and strength.
They measure the compressional (P) wave velocity of
sound through the rock and the shear (S) wave velocity
and use these with the density of the rock to compute
the rocks' compressive strength
These measurements are useful to design programs to drill
wells that produce oil and gas.
also used to design dams, roads, foundations for buildings,
They can also be used to help interpret seismic signals from the
Earth, either man-made seismic signals or those from
earthquakes.

Methods of analysis
Coring and core analysis is a direct measurement of
petrophysical properties.
In the petroleum industry rock samples are retrieved
from subsurface and measured by core labs of oil
company or some commercial core measurement
service companies.
This process is time consuming and expensive, thus cannot be
applied to all the wells drilled in a field.
Well Logging is used as a relatively inexpensive
method to obtain petrophysical properties
downhole.
Measurement tools are conveyed downhole using either
wireline or LWD method.

routine core analysis (RCAL)
routine core analysis is
The set of measurements
normally carried out on core plugs or whole core.
These generally include
porosity, grain density, horizontal permeability,
fluid saturation and a lithologic description.
Routine core analyses often include
a core gamma log and measurements of vertical permeability.
Measurements are made at room temperature and
at either atmospheric confining pressure,
formation confining pressure, or both.
Recommended practices for routine core analysis
are available in the API document RP40.

Special core analysis laboratory (SCAL)
In the petroleum industry, special core analysis,
often abbreviated SCAL or SPCAN,
is a laboratory procedure for conducting flow
experiments on core plugs taken from a petroleum
reservoir.
Special core analysis is distinguished from "routine
or conventional core analysis" by adding more
experiments, in particular including
measurements of two-phase flow properties,
determining relative permeability and
capillary pressure.

major sources of petrophysical
properties
Knowledge of petrophysical and hydrodynamic
properties of reservoir rocks are of fundamental
importance to the petroleum engineer.
These data are obtained from two major sources:
core analysis and well logging.
In this course we present some details about the analysis of
cores and review the nature and quality of the information
that can be deduced from cores.
Cores are obtained during the drilling of a well by
replacing the drill bit with a diamond core bit and a
core barrel.
The core barrel is basically a hollow pipe receiving the
continuous rock cylinder, and the rock is inside the core barrel
when brought to surface.

Coring
Continuous mechanical coring is a costly procedure due
to:
The drill string must be pulled out of the hole to replace the
normal bit by core bit and core barrel.
The coring operation itself is slow.
The recovery of rocks drilled is not complete.
A single core is usually not more than 9 m long, so extra trips
out of hole are required.
Coring should therefore be detailed programmed,
especially in production wells.
In an exploration well the coring cannot always be
accurately planned due to lack of knowledge about the
rock.

sidewall coring
Now and then there is a need for sample in an
already drilled interval, and then sidewall coring can
be applied.
In sidewall coring a wireline-conveyed core gun is used,
where a hollow cylindrical “bullet” is fired in to the wall
of the hole.
These plugs are small and usually not very valuable
for reservoir engineers.

The fluid content of the core
During drilling, the core becomes contaminated
with drilling mud filtrate and
the reduction of pressure and temperature
while bringing the core to surface
results in gas dissolution and further expansion of fluids.
The fluid content of the core observed on the
surface cannot be used as a quantitative measure
of saturation of oil, gas and water in the reservoir.
However, if water based mud is used the presence of oil
in the core indicates that the rock information is oil
bearing.

routine core analysis
When the core arrives in the laboratory
plugs are usually drilled 20-30 cm apart throughout the
reservoir interval .
All these plugs are analyzed with respect to
porosity, permeability, saturation and lithology.
This analysis is usually called routine core analysis.
The results from routine core analysis are used in
interpretation and evaluation of the reservoir.

1. “Petrophysics.” Wikipedia, the free
encyclopedia 13 July 2014. Wikipedia. Web. 22
July 2014.
2. (KSU) M. Kinawy. “Reservoir engineering
laboratory manual" Petroleum and Natural
Gas Engineering Department, King Saud
University, Riyadh (2009).

1. Without Distillation methods
2. Soxhlet Extraction method
3. Dean-Stark Distillation-Extraction and
Vacuum Distillation
A. Saturation Determination Experiment
4. Conclusions and Recommendations

Cleaning and Saturation
Determination
Objectives:
Cleaning and drying the core samples
Introduction and Theory:
Before measuring porosity and permeability,
the core samples must be cleaned of residual fluids and
thoroughly dried.
The cleaning process may also be a part of fluid saturation
determination.
Fluid saturation is defined as the ratio of the volume of fluid in a
given core sample to the pore volume of the sample
Note that fluid saturation may be reported either as a fraction of
total porosity or as a fraction of effective porosity.
• Since fluid in pore spaces that are not interconnected cannot be
produced from a well, the saturations are more meaningful
if expressed on the basis of effective porosity.

Saturation calculation
The weight of water
collected from the sample
is calculated from
the volume of water
by the relationship
The weight of oil removed
from the core may be
computed as the weight of
liquid less weight of water
WL is the weight of liquids
removed from the core
sample in gram.
Oil volume may then
be calculated as Wo/ρo.
Pore volume Vp is
determined by
a porosity measurement.
and oil and water
saturation
may be calculated by
Gas saturation can be
determined using

Direct Injection & centrifugal
methods
Direct Injection of Solvent
The solvent is injected into the sample
in a continuous process.
The sample is held in a rubber sleeve
thus forcing the flow to be uniaxial.
Centrifuge Flushing
A centrifuge which has been fitted with a special head
sprays warm solvent onto the sample.
The centrifugal force then moves the solvent through
the sample.
The used solvent can be collected and recycled.

Gas Driven method
Gas Driven Solvent Extraction
The sample is placed
in a pressurized atmosphere
of solvent containing dissolved gas.
The solvent fills the pores of sample.
When the pressure is decreased,
the gas comes out of solution,
expands,
and drives fluids out of the rock pore space.
This process can be repeated as many times as
necessary.

Soxhlet extractor
A Soxhlet extractor is a piece of
laboratory apparatus invented
in 1879 by Franz von Soxhlet.
It was originally designed for
the extraction of a lipid from a
solid material.
Typically, a Soxhlet extraction is
only required where the
desired compound has a limited
solubility in a solvent, and the
impurity is insoluble in that
solvent.Soxhlet mechanism

Soxhlet Extraction Apparatus
A Soxhlet extraction
apparatus is the most
common method for
cleaning sample, and is
routinely used by most
laboratories.
As shown in the Figure,
samples to be cleaned
are placed in a porous
thimble inside the
Soxhlet.

Procedure
The solvent (toluene) is
brought to a slow boil in
a Pyrex flask;
Electric or gas heaters
are used to vaporize the
solvent.
its vapors move upwards
and the core becomes
engulfed in the toluene
vapors
(at approximately 110 C).
Eventual water within the
core sample in the
thimble will be vaporized.
water falls from
the base of the
condenser onto the core
sample in the thimble;
the toluene soaks the
core sample and
dissolves any oil with
which it come into
contact.
When the liquid level
within
the Soxhlet tube
reaches the top ofFall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 78

Procedure (Cont.)
The extraction process continues for several hours
and is terminated
when no more oil remains in the samples.
This is recognized when the condensing vapors remain
clean because no oils is left in the cores to be dissolved.
After the extraction,
samples are dried in an electric oven.
Sometimes vacuum may also be applied to the oven.
The dried samples are kept
in a desiccator sealed with grease and
has some moisture absorbents at its bottom.

Remarks
A complete extraction may take several days to
several weeks in the case of low API gravity crude
or presence of heavy residual hydrocarbon deposit
within the core.
Low permeability rock may also
require a long extraction time.

Dean-Stark apparatus
The Dean-Stark apparatus or
Dean-Stark receiver or distilling
trap or Dean-Stark Head is a
piece of laboratory glassware
used in synthetic chemistry to
collect water (or occasionally
other liquid) from a reactor.
It was invented by E. W. Dean
and D. D. Stark in 1920 for
determination of the water
content in petroleum.

Dean-Stark distillation procedure
The Dean-Stark
distillation provides a
direct determination of
water content.
The oil and water area
extracted by dripping a
solvent, usually
toluene or
a mixture of acetone
and chloroform,
over the plug samples.

Calculation of water and oil
content
In this method,
the water and solvent are vaporized,
recondensed in a cooled tube in the top of the
apparatus and
the water is collected in a calibrated chamber.
The solvent overflows and
drips back over the samples.
The oil removed from the samples
remains in solution in the solvent.
Oil content is calculated by
the difference between the weight of water recovered
and the total weight loss after extraction and drying.

Vacuum Distillation
The oil and water
content of cores may
be determined by this
method.
As shown in the Figure,
a sample is placed
within a leak-proof
vacuum system and
heated to a maximum
temperature of 230 C.
Liquids within the
sample are vaporized
and
passed through
Vacuum distillation Apparatus

The Experiment Description
Description:
The objective of the experiment is to determine the oil,
water and gas saturation of a core sample.
Procedure:
Weigh a clean, dry thimble.
Use tongs to handle the thimble.
Place the cylindrical core plug inside the thimble,
then quickly weigh the thimble and sample.
Fill the extraction flask two-thirds full with toluene.
Place the thimble with sample into the long neck flask.

The Experiment Procedure
Tighten the ground joint fittings,
but do not apply any lubricant for creating tighter joints.
Start circulating cold water in the condenser.
Turn on the heating jacket or plate and adjust the rate of
boiling so that the reflux from the condenser is a few
drops of solvent per second.
The water circulation rate should be adjusted so that excessive
cooling does not prevent the condenser solvent from reaching
the core sample.
Continue the extraction until the solvent is clear.
Change solvent if necessary.

The Experiment Procedure (Cont.)
Read the volume of collected water in the graduated
tube.
Turn off the heater and cooling water and place the sample into
the oven (from 105 C to 120 C),
• until the sample weight does not change.
The dried sample should be stored in a desiccater.
Obtain the weight of the thimble and the dry core.
Calculate the loss in weight WL,
of the core sample due to the removal of oil and water.
Measure the density of a separate sample of the oil.
Calculate the oil, water and gas saturations after the
pore volume Vp of the sample is determined.

Saturation Determination from The
Experiment
Data and calculations:
Worg: Weight of original saturated sample
Wdry: Weight of desaturated and dry sample
Equations:
D and L are diameter and length of the core sample,
respectively.

direct-injection, centrifugal and
gas driven-extraction methods
The direct-injection method is effective, but slow.
The method of flushing by using centrifuge is
limited to plug-sized samples.
The samples also must have sufficient mechanical
strength to withstand the stress imposed by centrifuging.
However, the procedure is fast.
The gas driven-extraction method is slow.
The disadvantage here is that it is not suitable for poorly
consolidated samples or chalky limestones.

Distillation methods
The distillation in a Soxhlet apparatus is slow, but is
gentle on the samples.
The procedure is simple and very accurate water content
determination can be made.
Vacuum distillation is often used for full diameter
cores because the process is relatively rapid.
It is also frequently used for poorly consolidated cores
since the process does not damage the sample.
The oil and water values are measured directly and
dependently of each other.

solvents
In each of these methods,
the number of cycles or amount of solvent which must
be used depends on
the nature of
the hydrocarbons being removed and
the solvent used.
Often, more than one solvent must be used to
clean a sample.
The solvents selected must not react with the
minerals in the core.

Common solvents
The commonly used
solvents are:
Acetone
Benzene
Benzen-methol Alcohol
Carbon-tetrachloride
Chloroform
Methylene Dichloride
Mexane
Naphtha
Tetra Chloroethylene
Toluene
Trichloro Ethylene
Toluene and benzene
are most frequently used
to remove oil and
methanol and water
is used to remove salt
from interstitial or filtrate
water.
The cleaning procedures
used are specifically
important in special core
analysis tests,
as the cleaning itself may

Drying remarks
The core sample is dried
for the purpose of
removing connate water
from the pores, or
to remove solvents used
in cleaning the cores.
When hydratable
minerals are present,
the drying procedure is
critical since interstitial
water must be removed
without mineral
alteration.
Drying is commonly
performed
in a regular oven or
a vacuum oven at
temperatures between
50 C to 105 C.
If problems with clay
are expected,
drying the samples
at 60 C and
40 % relative humidity
will not damage
the samples.

1. (ABT) Torsæter, O., and M. Abtahi.
"Experimental reservoir engineering
laboratory work book." Department of
Petroleum Engineering and Applied
Geophysics, Norwegian University of Science
and Technology (NTNU), Trondheim (2003).
Chapter 2
A. (KSU) M. Kinawy. “Reservoir engineering
laboratory manual" Petroleum and Natural Gas
Engineering Department, King Saud University,
Riyadh (2009).
2. “Soxhlet Extractor.” Wikipedia, the free
encyclopedia 5 July 2014. Wikipedia. Web. 22
July 2014.
3. “Dean-Stark Apparatus.” Wikipedia, the free

1. Porosity definitions
2. Porosity determination
3. Determination of Bulk Volume
A. Determination of Bulk Volume By Mercury Pump
4. Determination of Grain Volume
5. Pore Volume Determination
A. Pore Volume Determination (Gas Expansion)
6. Effective Porosity Determination by
Helium Porosimeter Method
7. Porosity Determination by Liquid Saturating
Method

Porosity importance
One of the essential properties of a reservoir rock
is that it must be porous.
Porosity is therefore an important property and
its accurate determination is relevant
to reserve estimates and
other petroleum engineering calculations.
The porosity of a material defined as the fraction
(or the percentage) of the bulk volume occupied by
pores.
Thus porosity is a measure of the storage capacity of the
rock.
The more porous is the rock, the more is its capacity
to store fluids (oil, gas and water) in its pores.Fall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 102

Definition of the total (absolute)
porosity and effective porosity
Some of the pores in a rock may be
sealed off from other pores by cementing materials.
These pores, although present and contribute to the
porosity, do not allow passage or withdrawal of fluids.
Two types of porosity may be measured:
total or absolute porosity and effective porosity.
Total porosity is the ratio of
all the pore spaces in a rock
to the bulk volume of the rock.
Effective porosity ϕe is the ratio of
interconnected void spaces to the bulk volume.

Differences between
Absolute and Effective Porosity
Thus, only the effective porosity contains fluids
that can be produced from wells.
For granular materials such as sandstone,
the effective porosity may approach the total porosity,
however, for shales and for highly cemented or
vugular rocks such as some limestones,
large variations may exist
between effective and total porosity.
The difference
between absolute and effective porosity
is known as the dead porosity.

primary vs. secondary porosity
Porosity may be classified according to its origin as
either primary or secondary.
Primary or original porosity
is developed during deposition of the sediment.
Secondary porosity is caused by some geologic process
subsequent to formation of the deposit.
These changes in the original pore spaces
may be created by ground stresses, water movement, or
various types of geological activities
after the original sediments were deposited.
Fracturing or formation of solution cavities
often will increase the original porosity of the rock.

Porosity of different packing types
A maximum theoretical
porosity of 48% is
achieved
with cubic packing (a)
of spherical grains.
The porosity of the
Rhombohedral packing
(b),
which is more
representative of
reservoir conditions, is
26%.
If a second, smaller sizeFall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 106

Effective parameters on porosity
For a uniform rock grain size,
porosity is independent of the size of the grains.
Thus, porosity is dependent on
the grain size distribution and
the arrangement of the grains,
as well as the amount of cementing materials.
Not all grains are spherical, and grain shape also
influences porosity.

Effect of Compaction on Porosity
Compaction
is the process of volume reduction
due to an externally applied pressure.
For extreme compaction pressures,
all materials show some irreversible change in porosity.
This is due to
distortion and crushing of the grain or matrix elements
of the materials, and in some cases, recrystallization.

Formation compressibility
The variation of porosity
with change in pressure
can be represented by
ϕ2 and ϕ1 are porosities
at pressure P2 and P1
respectively, and
cf is formation
compressibility.
Formation
compressibility
is defined as summation
of both grain and pore
compressibility.
For most petroleum
reservoirs, grain
compressibility is
considered to be
negligible. Formation
compressibility can be
expressed as
• dP is change in reservoir
pressure.
• For porous rocks,
the compressibility
depends explicitly on
porosity.

Porosity definition
By definition
It is sometimes convenient to express porosity in
percent. So
Since a rock is composed from pores and grains or
rock matrix, it is obvious that
Bulk volume = grain volume + pore volume
Vb = Vg + Vp and
Vp = Vb – Vg

Porosity calculation
It is clear from the above relations that any two of
the three values Vp, Vg and Vb are sufficient to
determine the value of porosity.
Porosity from pore and bulk volumes
Porosity from pore and grain volumes
Porosity from grain and bulk volumes

Some Notes about Porosity
It must be noticed that
the two volumes used to determine the porosity
must be for the same sample.
Sometimes the bulk and grain densities
may be used instead of bulk and grain volumes.
Depending on the method used,
either absolute or effective porosity will result.

Porosity determination techniques
The porosity of reservoir rock may be determined
by
Core analysis, Well logging technique, Well testing
The question of which source of porosity data is
most reliable cannot be answered without
reference to a specific interpretation problem.
These techniques can all give correct porosity values
under favorable conditions.
The core analysis porosity determination has the advantage
that
no assumption need to be made as to
mineral composition, borehole effects, etc.
However, since the volume of the core is less than the rock
volume which is investigated by a logging device,
porosity values derived from logs

Measurement Methods for
the porosity determination
PoreVolume
Gas Expansion
• Mercury Pump with
a vacuum
• helium Gas
Saturation
Method
Mercury Pump
Washburn
Bunting
GrainVolume
Dry, ϕe
(Unsaturated)
• Gas Expansion
• helium Gas
Saturated, ϕe
• Gravimetric
(Loss of Weight)
• Russell Volumeter
• Pycnometer
Crushed , ϕt
• Pycnometer
BulkVolume
Dimensional
Coated Sample
• Gravimetric
(Loss of Weight)
Method
• Mercury
Pycnometer
• Mercury Pump

Bulk Volume Measurement
Although the bulk volume
may be computed from measurements of the
dimensions of a uniformly shaped sample,
the usual procedure utilizes the observation of
the volume of fluid displaced by the sample.
The fluid displaced by a sample can be observed
either volumetrically or gravimetrically.
Gravimetric determinations of bulk volume can be
accomplished by observing the loss in weight of
the sample when immersed in a fluid or by change in
weight of a pycnometer with and without the core
sample.

Sample isolation methods
In either procedure it is necessary to prevent the
fluid penetration into the pore space of the rock.
This can be accomplished
(1) by coating the sample
with paraffin or a similar substance,
(2) by saturating
the core with the fluid into which it is to be immersed, or
(3) by using mercury.

Bulk Volume Determination:
By Measuring the Dimensions
For a regularly shaped sample, the bulk volume is
found by measuring the dimensions of the sample.
For a cylindrical sample with diameter D and length L,
the bulk volume is given by:
For a sample with rectangular cross section
A sliding caliper is used to measure the dimensions.
Different reading are usually taken for the diameter and
length and the average values are used.

By Russell Volumeter
In this case a sample must by
saturated completely with
a non-reacative fluid or coated
by paraffin wax and then placed
in the volumeter.
The difference in the fluid level
before and after the sample gives
the bulk volume of the sample.
If the sample is coated
the volume of the coating
material must be found and
subtracted from the reading.
This obtained by noting the weight
of the coating wax which is
the difference between the weight

Gravimetric (Loss of Weight)
MethodA coated sample is weighed suspended in air and
then suspended in a liquid (water or kerosene).
The difference in weight is the buoyancy force
which is equal to the volume of displaced fluid
multiplied by the density of the fluid.
Since the volume of the displaced fluid is the same
as the volume of immersed solid, then:
 volume of coated sample = (W1 – W2) / ρ
 W1 = weight in air
W2 = weight in liquid
 ρ = density of liquid
The volume of the coating material must be found
and subtracted as explained earlier.

By Mercury Pycnometer
A special steel pycnometer is
used Figure.
It is first filled with mercury.
The top is removed and the
sample placed at the mercury
surface.
The top is then pressed down
allowing excess mercury to
overflow into a beaker.
The excess mercury is then
collected and its volume
determined in a graduated
cylinder.
For more accuracy, the mercuryFall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 122

the bulk density
If the weight of a dry clean sample is determined
before coating or saturating the sample,
the bulk density of the sample
is found from the measured bulk volume.

Mercury porometer
Mercury porometer is designed
to measure the gas space and
bulk volume of a freshly
recovered core sample.
The instrument consists of
a hand operated pump,
a sample cell
The cell
can accommodate a sample
with a bulk volume of 10 to 15 cm3
(a sample with 2.5cm length).
equipped with a needle valve
mounted on its lid.

Mercury Pump, Procedure
The pump consists of
a core chamber, pump cylinder with piston and
wheel, scales and gauges.
First mercury is brought
to a fixed mark above the sample chamber and
the pump is brought to zero reading.
The piston is removed
withdrawing mercury from the chamber.
The sample is then placed in the chamber and
mercury is brought back to the fixed mark.
The reading of the pump scale gives
the bulk volume of the sample.

Mercury injection pump (a) and
porosity through mercury injection
(b)

Methods of
Grain Volume Measurement
The grain volume of pore samples
is sometimes calculated
from sample weight and knowledge of average density.
Formations of varying lithology and, hence,
grain density limit applicability of this method.
Boyle’s law is often employed with helium
as the gas to determine grain volume.
The technique is fairly rapid, and
is valid on clean and dry sample.

Methods of
Grain Volume Measurement
(Cont.)The measurement of the grain volume of
a core sample may also be
based on the loss in weight of
a saturated sample plunged in a liquid.
Grain volume may be measured by
crushing a dry and clean core sample.
The volume of crushed sample is then determined by
(either pycnometer or) immersing in a suitable liquid.

By Russell Volumeter
The Russell Volumeter may be used in the same
way as described in bulk volume determination to
determine the grain volume of a crushed sample.
A part of a clean (extracted) dry sample
is crushed into individual grains.
The grains are weighed by analytical balance and
the volume is determined by Russell Volumeter
(as in the case of bulk volume determination.)

By Pycnometer
Procedure
The pycnometer
is weighed empty (W0)
and then filled with
water
(or kerosene) (W1).
The crushed sample is
weighed then placed
in the empty pycnometer
and the weight
is determined (W2).
(W2 – W0) is the weight
of the crushed grains.
This is more accurate than
the use of the weight
and the total weight is
determined (W3).
The grain volume is then
calculated as follows:
W1 = weight of
pycnometer filled with
fluid
W0 =
weight of empty
pycnometer
W2 =Fall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 133

Grain volume: Saturating samples
in
Russell Volumeter and pycnometerThe grain volume of a sample (uncrushed) can also
be obtained by Russell Volumeter or
the pycnometer methods
provided the sample is unsaturated (dry) and enough
time is allowed for the fluid to penetrate the pores of
the sample before the readings are taken.

Grain volume: Loss of Weight
Method
The weight of a dry clean sample W1 is
determined.
The sample is then fully saturated with a non-
reactive liquid (instead of a coated sample as in
bulk volume).
The weight of the sample
suspended in the liquid W2 is then determined.
The difference (loss) of weight is divided by the
density of the liquid to find the grain volume of the
sample.
The grain volume determined by this method is theFall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 135

Gas Expansion Method (General)
Many porosimeters are designed to use the
principle of Boyle’s law of gas expansion to
determine the grain volume.
The idea is to allow the remaining volume of a chamber
in which a core is placed (V1 – Vg) at pressure P1 to
expand by an additional volume V2 and read the final
pressure P2.
From Boyle’s Law (at constant temperature).
(V1 – Vg) P1 = (V1 – Vg + V2) P2
knowing V1, V2, P1 and P2 allows the calculation of grain
volume Vg.
Vg = V1 – [(P2 / (P1 – P2)] V2

The helium porosimeter
The helium porosimeter uses the principle of gas
expansion, as described by Boyle’s law.
A known volume (reference cell volume) of helium gas
[V2], at a predetermined pressure [PA], is isothermally
expanded into a sample chamber.
After expansion,
the resultant equilibrium pressure is measured [PB].
This pressure depends on the volume of the sample
chamber [V1] minus the rock grain volume [Vg], and
then the porosity can be calculated.
PA*V2=PB*(V2+V1-Vg)
Vg=V1+V2-(PA/PB)V2=V1-[(PA-PB)/PB]V2

Calculation of grain density
If we know the weight of the dry clean sample for
which the grain volume is determined, the grain
density can be calculated by:

Pore Volume Measurement
All the methods measuring pore volume yield
effective porosity. The methods are based on
either the extraction of a fluid from the rock or
the introduction of a fluid
into the pore spaces of the rock.

Saturation Method Procedure
A dry clean sample is weighed and placed in a
suction flask with two connections to a vacuum
pump and a Separatory funnel.
First the valve is closed and vacuum is applied.
After sufficient vacuum is reached the vacuum pump is
shut off, the valve to the funnel is opened and the liquid
is allowed to saturate the sample.
The sample is kept immersed in the liquid for some time
to allow complete saturation.
The saturated sample is drained from excess liquid and
weighed.

Pore volume calculation by
Saturation Method
The pore volume is then calculated as:
Vp = (W2 – W1) / ρ
W2 = weight of saturated sample
W1 = weight of dry sample
ρ = density of saturating fluid
Notes:
A wetting non-reactive liquid must be used.
Kerosene or tetrachlorethane are usually used.

Washburn Bunting Method
Procedure (obsolete and seldom
used)This method is based on liberating the air from the
pores of the sample by creating vacuum.
This is achieved by first raising the mercury level above
the sample while the valve is open, closing the valve and
then lowering the mercury reservoir so that the mercury
falls below the sample in the chamber.
The collected air is measured under atmospheric
pressure by raising the mercury reservoir until the
mercury level is the same in the two sides.
Air is then allowed to escape and the process is repeated
until no more air is extruded.
The total volume of air (under atmospheric pressure) is
recorded.

Washburn –Bunting type
The experiment is first
run without a sample to
determine the volume
of air adsorbed on the
glass surface of the
apparatus.
This volume is
subtracted from the
total air volume
obtained before to get
the pore volume of the
sample.

Pore volume Determination:
By Mercury Pump
When a rock has a small fraction of void space,
it is convenience to measure porosity
by Mercury injection rather than other methods.
The principle consists of forcing mercury
under relatively high pressure in the rock pores.
A pressure gauge is attached to the cylinder
for reading pressure
under which measuring fluid is forced into the pores.
The volume of mercury entering the core sample is
obtained from the device with accuracy up to 0.01 cm3.
(Approximately a cube with the length of 2 mm)

Mercury Injection procedure
The mercury pump procedure is as follow:
After a dry sample is placed in the core chamber
and the bulk volume is determined,
pressure is applied by moving the piston clockwise
allowing mercury to enter the pores of the sample.
Pressure vs. volume of injected mercury is recorded
until a pressure of 1000 psia is reached.
The final volume reading
gives the pore volume of the sample.
Notes:
Macropores and fractures can be detected by a flat
curve
at the start where increase in volume is noted
without appreciable rise in pressure.Fall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 146

Gas Expansion Method:
by mercury pump (with a vacuum)
The mercury pump (with a vacuum) gauge is used.
After the bulk volume is determined and mercury
fills the chamber but does not penetrate the sample,
the air in the pores is allowed to expand
by withdrawing the mercury from the chamber.
If the volume of mercury withdrawn is V which is read
on the pump scale then from Boyle’s Law:
Vp P1 = (Vp + V) P2 So: Vp = V[(P2 / (P1 – P2)]
• P1 is initial pressure (atmospheric)
• P2 is the final pressure read on the vacuum gauge
It is clear that if P2 = ½ P1 then Vp = V
• So the pore volume would be equal to the volume of mercury
withdrawn from the chamber to reduce the pressure in the
chamber to half its original (atmospheric) value.

the helium Gas advantages
Helium has advantages over other gases because:
(1) its small molecules rapidly penetrated small pores,
(2) it is inert and
does not adsorb on rock surfaces as air may do,
(3) helium can be considered as an ideal gas (i.e., z = 1.0)
for pressures and temperatures usually employed in the test,
and
(4) helium has a high diffusivity and
therefore affords a useful means
for determining porosity of low permeability rocks.

the helium technique procedure
The helium porosimeter has a reference volume
V1,
at pressure p1, and a matrix cup
with unknown volume V2, and initial pressure p2.
(Pressure p1 and p2 are controlled by the operator;
usually p1 = 100 and p2 = 0 psig).
The reference cell and the matrix cup are
connected
by tubing;
the system can be brought to equilibrium
when the core holder valve is opened,
allowing determination of the unknown volume V2
by measuring the resultant equilibrium pressure p.Fall 14 H. AlamiNia Reservoir Rock Laboratory Course (2nd Ed.) 150

the helium technique calculation
Boyle’s law is applicable if the expansion takes
place isothermally.
Thus the pressure-volume products are equal before and
after opening the core holder valve:
P1V1 +P2V2 = P(V1+V2)
Solving the equation for the unknown volume, V2:
V2 = (P-P1)V1/(P2-P1)
Since all pressures in the equation must be absolute and
it is customary to set p1 = 100 psig and p2 = 0 psig,
the Eq. may be simplified as follows:
V2 = V1(100-P)/P
• V2 in cm3 is the unknown volume in the matrix cup, and
• V1 in cm3 is the known volume of the reference cell.
• p in psig is pressure read directly from the gauge.

the helium technique correction
factor
Small volume changes occur in the system,
including the changes in tubing and fittings
caused by pressure changes during equalization.
A correction factor, G, may be introduced to correct
for the composite system expansion.
The correction factor G is determined for porosimeters
before they leave the manufacturer, and this correction
is built into the gauge calibration in such a way that it is
possible to read the volumes directly from the gauge.

Schematic diagram of helium
porosimeter apparatus

Descriptions
The determination of the effective liquid porosity
of a porous plug
is the initial part of the measurement of capillary
pressure using porous plate method in core laboratories.
Before the capillary pressure is determined
the volume of the saturating liquid (brine or oil)
in the core must be known.
Thus, the effective liquid porosity of the core
can be calculated in the beginning of
capillary pressure measurement.

Procedure:
Weigh dry Berea plug Wdry,
measure its diameter D, and length L, with calliper
(1 core for each group).
Put the cores in the beaker inside a vacuum
container, run vacuum pump about 1 hour.
Saturate the cores with 36 g/l NaCl brine,
ρ brine = 1.02g/cm3.
Weigh the saturated cores, Wsat.

Calculations and report
Calculate the saturated brine weight,
Wbrine = Wsat-Wdry.
Calculate the pore volume
(saturated brine volume), Vp = Wbrine/ ρbrine.
Calculate effective porosity, ϕ e = Vp/Vb.

1. (ABT) Torsæter, O., and M. Abtahi.
"Experimental reservoir engineering
laboratory work book." Department of
Petroleum Engineering and Applied
Geophysics, Norwegian University of Science
and Technology (NTNU), Trondheim (2003).
Chapter 5
A. (KSU) M. Kinawy. “Reservoir engineering
laboratory manual" Petroleum and Natural Gas
Engineering Department, King Saud University,
Riyadh (2009).

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