This document summarizes key concepts from a reservoir engineering course, including pseudosteady-state (PSS) flow regimes for radial flow of slightly compressible (SC) and compressible (C) fluids. It discusses how the PSS flow condition is reached after transient flow, and how average reservoir pressure changes at a constant rate in PSS. Equations are provided for calculating flow rates of SC and C fluids in PSS, along with approximations that account for skin effect and non-ideal assumptions.
prediction of original oil in place using material balance simulation. It's also useful for future reservoir performance and predict ultimate hydrocarbon recovery under various types of primary driving mechanisms.
That is my presentation for my grad research about reservoir geomechanics, hope you find it useful, and my source book was reservoir geomechanics for prof Mark Zoback, soon the PDF copy will be available as well.
Overview of Reservoir Simulation by Prem Dayal Saini
Reservoir simulation is the study of how fluids flow in a hydrocarbon reservoir when put under production conditions. The purpose is usually to predict the behavior of a reservoir to different production scenarios, or to increase the understanding of its geological properties by comparing known behavior to a simulation using different geological representations.
All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.
Reservoir engineers cannot capture full value from waterflood projects on their own. Cross-functional participation from earth sciences, production, drilling, completions, and facility engineering, and operational groups is required to get full value from waterfloods. Waterflood design and operational case histories of cross-functional collaboration are provided that have improved life cycle costs and increased recovery for onshore and offshore waterfloods. The role that water quality, surveillance, reservoir processing rates, and layered reservoir management has on waterflood oil recovery and life cycle costs will be clarified. Techniques to get better performance out of your waterflood will be shared.
prediction of original oil in place using material balance simulation. It's also useful for future reservoir performance and predict ultimate hydrocarbon recovery under various types of primary driving mechanisms.
That is my presentation for my grad research about reservoir geomechanics, hope you find it useful, and my source book was reservoir geomechanics for prof Mark Zoback, soon the PDF copy will be available as well.
Overview of Reservoir Simulation by Prem Dayal Saini
Reservoir simulation is the study of how fluids flow in a hydrocarbon reservoir when put under production conditions. The purpose is usually to predict the behavior of a reservoir to different production scenarios, or to increase the understanding of its geological properties by comparing known behavior to a simulation using different geological representations.
All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.
Reservoir engineers cannot capture full value from waterflood projects on their own. Cross-functional participation from earth sciences, production, drilling, completions, and facility engineering, and operational groups is required to get full value from waterfloods. Waterflood design and operational case histories of cross-functional collaboration are provided that have improved life cycle costs and increased recovery for onshore and offshore waterfloods. The role that water quality, surveillance, reservoir processing rates, and layered reservoir management has on waterflood oil recovery and life cycle costs will be clarified. Techniques to get better performance out of your waterflood will be shared.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Numerical Calculation of Solid-Liquid two-Phase Flow Inside a Small Sewage Pumptheijes
Based on a mixture multiphase flow model,theRNG k–εturbulencemodelandfrozen rotor method were used to perform a numerical simulation of steady flow in the internal flow field of a sewage pump that transports solid and liquid phase flows. Resultsof the study indicate that the degree of wear on the front and the back of the blade suction surface from different densities of solid particles shows a completely opposite influencing trend. With the increase of delivered solid-phase density, the isobaric equilibrium position moves to the leading edge point of the blade, but the solid-phase isoconcentration point on the blade pressure surface and suction surface basically remains unchanged. The difference between hydraulic lift and water lift indelivering solid- and liquid-phase flows shows a rising trend with the increase of working flow
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
We follow "Rigorous Publication" model - means that all articles appear on IJERD after full appraisal, effectiveness, legitimacy and reliability of research content. International Journal of Engineering Research and Development publishes papers online as well as provide hard copy of Journal to authors after publication of paper. It is intended to serve as a forum for researchers, practitioners and developers to exchange ideas and results for the advancement of Engineering & Technology.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2. 1. USS(LT) Regime for Radial flow of SC Fluids:
Finite-Radial Reservoir
2. Relation between pD and Ei
3. USS Regime for Radial Flow of C Fluids
A. (Exact Method)
B. (P2 Approximation Method)
C. (P Approximation Method)
4. PSS regime Flow Constant
3. 1. PSS
A.
B.
C.
D.
Average Reservoir Pressure
PSS regime for Radial Flow of SC Fluids
Effect of Well Location within the Drainage Area
PSS Regime for Radial Flow of C Fluids
2. Skin Concept
3. Using S for Radial Flow in Flow Equations
4.
5. Average Reservoir Pressure in PSS
Because the pressure at every point in the reservoir
is changing at the same rate, it leads to the
conclusion that the average reservoir pressure is
changing at the same rate.
This average reservoir pressure is essentially set equal to
the volumetric average reservoir pressure p– r.
It is the pressure that is used to perform flow calculations
during the semisteady state flowing condition.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
5
6. Average Reservoir Pressure
Calculation in PSS
In the above discussion, p– r indicates that, in
principal, the above Equation can be used to
estimate by replacing the pressure decline rate
dp/dt with (pi − p– r)/t, or:
(t is approximately the elapsed time since the end
of the transient flow regime to the time of interest.)
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
6
7. Volumetric Average Pressure
of the Entire Reservoir
It should be noted that when performing material
balance calculations, the volumetric average
pressure of the entire reservoir is used to calculate
the fluid properties. This pressure can be
determined from the individual well drainage
properties as follows:
Where Vi = pore volume of the ith drainage volume
p–ri = volumetric average pressure within the ith
drainage volume.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
7
8. Using the Flow Rate
in Volumetric Avg Reservoir Pressure
Figure illustrates the
concept of the
volumetric average
pressure.
In practice, the Vi’s are
difficult to determine
and, therefore, it is
common to use the
flow rate qi.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
8
9. Applications
of the Pseudosteady-State Flow
The practical applications of using the
pseudosteady-state flow condition to describe the
flow behavior of the following two types of fluids
are presented below:
Radial flow of slightly compressible fluids
Radial flow of compressible fluids
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
9
10.
11. Diffusivity Equation in PSS
The diffusivity equation as expressed previously for
the transient flow regime is:
For the semisteady-state flow, the term (∂p/∂t) is
constant so:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
11
12. Radial Flow of Slightly Compressible
Fluids Calculation
Where c1 is the constant of the integration and can
be evaluated by imposing the outer no-flow
boundary condition [i.e., (∂p/∂r) re = 0] on the
above relation to give:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
12
13. Flow Rate for Radial Flow of Slightly
Compressible Fluids (PSS)
Performing the above
integration and assuming
(rw 2 /re 2) is negligible
gives:
A more appropriate form
of the above is to solve
for the flow rate, to give:
2013 H. AlamiNia
Where Q = flow rate,
STB/day
B = formation volume
factor, bbl/STB
k = permeability, md
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
13
14. Q Vs. Average Reservoir Pressure for
PSS Regime
The volumetric average reservoir pressure p– r is
commonly used in calculating the liquid flow rate
under the semisteady-state flowing condition.
Introducing the p– r into previous Equation gives:
(the volumetric average pressure p–r occurs at about 47% of
the drainage radius during the semisteady-state condition.)
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
14
15.
16. Using Pd Solution (PSS)
It is interesting to notice that the dimensionless
pressure pD solution to the diffusivity equation can
be used to derive previous Equation.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
16
17. Effect of Geometry on PSS Flow
It should be pointed out that the pseudosteadystate flow occurs regardless of the geometry of the
reservoir.
Irregular geometries also reach this state when
they have been produced long enough for the
entire drainage area to be affected.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
17
18. Shape Factor
Rather than developing a separate equation for
each geometry, Ramey and Cobb (1971) introduced
a correction factor that is called the shape factor,
CA, which is designed to account for the deviation
of the drainage area from the ideal circular form.
The shape factor, accounts also for the location of
the well within the drainage area.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
18
19. Shape Factor Tables
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
19
20. Solutions Using CA
Introducing CA into following Equation and
performing the solution procedure gives the
following two solutions:
In terms of the volumetric average pressure p–r:
In terms of the initial reservoir pressure pi:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
20
21.
22. Radial Flow of
Compressible Fluids (Gases) (PSS)
The radial diffusivity equation was developed to study the performance
of compressible fluid under unsteady-state conditions. The equation has
the following form:
For the semisteady-state flow, the rate of change of the real gas
pseudopressure with respect to time is constant, i.e.,
Using the same technique identical to that described previously for
liquids gives the following exact solution to the diffusivity equation:
Where Qg = gas flow rate, Mscf/day
T = temperature, °R
k = permeability, md
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
22
23. Approximations for
Radial Flow of Gases (PSS)
Two approximations to the above solution are
widely used. These approximations are:
Pressure-squared approximation
Pressure-approximation
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
23
24. P2 Approximation
As outlined previously, the method provides us
with compatible results to that of the exact solution
approach when p < 2000.
The solution has the following familiar form:
The gas properties z– and μ are evaluated at:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
24
25. P Approximation
This approximation method is applicable at p>3000
psi and has the following mathematical form:
With the gas properties evaluated at:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
25
26.
27.
28. Assumptions
in Deriving the Flow Equations
In deriving the flow equations, the following two
main assumptions were made:
Uniform permeability throughout the drainage area
Laminar (viscous) flow
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
28
29. Correction Factors for Assumptions
Before using any of the previous mathematical
solutions to the flow equations, the solution must
be modified to account for the possible deviation
from the above two assumptions.
Introducing the following two correction factors
into the solution of the flow equation can eliminate
the above two assumptions:
Skin factor
Turbulent flow factor
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
29
30. Wellbore Damage
It is not unusual for materials such as mud filtrate,
cement slurry, or clay particles to enter the
formation during drilling, completion, or workover
operations and reduce the permeability around the
wellbore.
This effect is commonly referred to as a wellbore
damage and
The region of altered permeability is called the skin
zone.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
30
31. Skin Zone
Skin zone can extend from a few inches to several
feet from the wellbore.
Many other wells are stimulated by acidizing or
fracturing, which in effect increase the permeability
near the wellbore.
Thus, the permeability near the wellbore is always
different from the permeability away from the well
where the formation has not been affected by
drilling or stimulation.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
31
32. Near Wellbore Skin Effect
A schematic
illustration of
the skin zone
is shown in
Figure.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
32
33. Skin Effect
Those factors that cause damage to the formation
can produce additional localized pressure drop
during flow.
This additional pressure drop is commonly referred to as
Δpskin.
On the other hand, well stimulation techniques will
normally enhance the properties of the formation
and increase the permeability around the wellbore,
so that a decrease in pressure drop is observed.
The resulting effect of altering the permeability
around the well bore is called the skin effect.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
33
34. Skin Types
Figure compares the
differences in the skin
zone pressure drop for
three possible outcomes:
Δpskin > 0, indicates an
additional pressure drop
due to wellbore damage,
i.e., kskin < k.
Δpskin < 0, indicates less
pressure drop due to
wellbore improvement,
i.e., kskin > k.
Δpskin = 0, indicates no
changes in the wellbore
condition, i.e., kskin = k.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
34
35. Skin Zone Pressure Drop
Hawkins (1956) suggested that the permeability in
the skin zone, i.e., kskin, is uniform and the
pressure drop across the zone can be approximated
by Darcy’s equation. Hawkins proposed the
following approach:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
35
36. Skin Factor
The additional pressure drop expression is
commonly expressed in the following form:
Where s is called the skin factor and defined as:
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
36
37. Positive Skin Factor
Positive Skin Factor, s > 0
When a damaged zone near the wellbore exists, kskin is
less than k and hence s is a positive number.
The magnitude of the skin factor increases as kskin
decreases and as the depth of the damage rskin
increases.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
37
38. Negative Skin Factor
Negative Skin Factor, s < 0
When the permeability around the well kskin is higher
than that of the formation k, a negative skin factor exists.
This negative factor indicates an improved wellbore
condition.
a negative skin factor will result in a negative value of
Δpskin.
This implies that a stimulated well will require less pressure
drawdown to produce at rate q than an equivalent well with
uniform permeability.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
38
39. Zero Skin Factor
Zero Skin Factor, s = 0
Zero skin factor occurs when no alternation in the
permeability around the wellbore is observed, i.e., kskin
= k.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
39
40.
41. Modification of the Flow Equations
The proposed modification of the previous flow
equation is based on the concept that the actual
total pressure drawdown will increase or decrease
by an amount of Δpskin.
Assuming that (Δp) ideal represents the pressure
drawdown for a drainage area with a uniform
permeability k, then:
The concept can be applied to all the previous flow
regimes to account for the skin zone around the
wellbore.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
41
42. S in SS Regime
for Radial Flow of SC Fluids
Where
Qo = oil flow rate, STB/day
k = permeability, md
h = thickness, ft
s = skin factor
Bo = oil formation volume factor, bbl/STB
μo = oil viscosity, cp
pi = initial reservoir pressure, psi
pwf = bottom hole flowing pressure, psi
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
42
43. S in USS Regime
for Radial flow of SC Fluids
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
43
44. S in USS Regime
of Radial Flow of C Fluids
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
44
45. S in PSS regime
for Radial Flow of SC Fluids
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
45
46. S in PSS Regime
for Radial Flow of C Fluids
Where:
Qg = gas flow rate, Mscf/day
k = permeability, md
T = temperature, °R
(μ–g) = gas viscosity at average pressure p–, cp
z–g = gas compressibility factor at average pressure p–
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
46
47. Effective (Apparent) Wellbore Radius
Matthews and Russell (1967) proposed an
alternative treatment to the skin effect by
introducing the effective or apparent wellbore
radius rwa that accounts for the pressure drop in
the skin. They define rwa by the following equation:
All of the ideal radial flow equations can be also
modified for the skin by simply replacing wellbore
radius rw with that of the apparent wellbore radius
rwa.
2013 H. AlamiNia
Reservoir Engineering 1 Course: PSS Regime for Radial Flow of SC & C Fluids and Skin
Effect
47
48. 1. Ahmed, T. (2006). Reservoir engineering
handbook (Gulf Professional Publishing). Ch6
49. 1. Turbulent Flow
2. Superposition
A. Multiple Well
B. Multi Rate
C. Reservoir Boundary