This document provides an overview of reservoir engineering fundamentals including:
- Three types of reservoir fluids based on compressibility: incompressible, slightly compressible, and compressible.
- Three flow regimes in reservoirs: steady-state, unsteady-state, and pseudosteady-state.
- Common reservoir geometries that influence fluid flow including radial, linear, spherical, and hemispherical.
- Darcy's law and its applications to steady-state fluid flow in reservoirs, including for different fluid types and geometries.
The problem of water and gas coning has plagued the petroleum industry for decades. Water or gas encroachment in oil zone and thus simultaneous production of oil & water or oil & gas is a major technical, environmental and economic problems associated with oil and gas production. This can limit the productive life of the oil and gas wells and can cause severe problems including corrosion of tubulars, fine migration, hydrostatic loading etc. The environmental impact of handling, treating and disposing of the produced water can seriously affect the economics of the production. Commonly, the reservoirs have an aquifer beneath the zone of hydrocarbon. While producing from oil zone, there develops a low pressure zone as a result of which the water zone starts coning upwards and gas zone cones down towards the production perforation in oil zone and thus reducing the oil production. Pressure enhanced capillary transition zone enlargement around the wellbore is responsible for the concurrent production. This also results in the loss of water drive and gas drive to a certain extent.
Numerous technologies have been developed to control unwanted water and gas coning. In order to design an effective strategy to control the coning of oil or gas, it is important to understand the mechanism of coning of oil and gas in reservoirs by developing a model of it. Non-Darcy flow effect (NDFE), vertical permeability, aquifer size, density of well perforation, and flow behind casing increase water coning/inflow to wells in homogeneous gas reservoirs with bottom water are important factors to consider. There are several methods to slow down coning of water and/or gas such as producing at a certain critical rate, polymer injection, Downhole Water Sink (DWS) technology etc.
Shubham Saxena
B.Tech. petroleum Engineering
IIT (ISM) Dhanbad
The problem of water and gas coning has plagued the petroleum industry for decades. Water or gas encroachment in oil zone and thus simultaneous production of oil & water or oil & gas is a major technical, environmental and economic problems associated with oil and gas production. This can limit the productive life of the oil and gas wells and can cause severe problems including corrosion of tubulars, fine migration, hydrostatic loading etc. The environmental impact of handling, treating and disposing of the produced water can seriously affect the economics of the production. Commonly, the reservoirs have an aquifer beneath the zone of hydrocarbon. While producing from oil zone, there develops a low pressure zone as a result of which the water zone starts coning upwards and gas zone cones down towards the production perforation in oil zone and thus reducing the oil production. Pressure enhanced capillary transition zone enlargement around the wellbore is responsible for the concurrent production. This also results in the loss of water drive and gas drive to a certain extent.
Numerous technologies have been developed to control unwanted water and gas coning. In order to design an effective strategy to control the coning of oil or gas, it is important to understand the mechanism of coning of oil and gas in reservoirs by developing a model of it. Non-Darcy flow effect (NDFE), vertical permeability, aquifer size, density of well perforation, and flow behind casing increase water coning/inflow to wells in homogeneous gas reservoirs with bottom water are important factors to consider. There are several methods to slow down coning of water and/or gas such as producing at a certain critical rate, polymer injection, Downhole Water Sink (DWS) technology etc.
Shubham Saxena
B.Tech. petroleum Engineering
IIT (ISM) Dhanbad
Reservoir engineering is the field to evaluate field performance by performing reservoir modeling studies and explore opportunities to maximize the value of both exploration and production properties to enhance hydrocarbon production.
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.
Wireline (WL) and Logging-While-Drilling (LWD) formation tester measurements provide a link between the static petrophysical measurements and dynamic rock-fluid properties for enhanced formation evaluation. However, despite the significant advancements in these services, there are still barriers. The analysis of Wireline (WL) and Logging-While-Drilling (LWD) formation testing has traditionally been performed by a skilled testing analyst using specialized software and theoretical models to generate results and assess the data vitality. This can be a time-consuming process involving analyzing over 100 pressure transients. In practice, the petrophysicists and geoscientists rarely have access to a detailed analysis in the time frame required and typically revert to other methods. Some of the methods are ad hoc, but there is a growing consensus that several convenient, simple, and effective real-time measurements can be used for an objective evaluation of the dynamic data. This talk demonstrates a straightforward automated process that has been developed by which real-time measurements, which are routinely recorded, are used to automatically generate the results. Basic principles are used to develop quality parameters and a test rating system that can guide the analyst in the objective determination of the vitality of the results for each test. In this way, the highest quality testing results are used for fluid gradients and log correlations to improve the integration of the dynamic data into the petrophysical analysis. This also enables standards to be established for real-time data acquisition that can save testing time while improving data and quality. This automated method is being applied routinely and several field examples are used to illustrate the utility and time savings of this new workflow.
Reserve Estimation of Initial Oil and Gas by using Volumetric Method in Mann ...ijtsrd
This research paper is focused to estimate the current production rate of the wells and to predict field remaining reserves. The remaining reserve depends on the production points that selected to represent the real well behavior, the way of dealing with the production data, and the human errors that might happen during the life of the field. Reserves estimating methods are usually categorized into three families analogy, volumetric, and performance techniques. Reserve Estimators should utilize the particular methods, and the number of methods, which in their professional judgment are most appropriate given i the geographic location, formation characteristics and nature of the property or group of properties with respect to which reserves are being estimated ii the amount and quality of available data and iii the significance of such property or group of properties in relation to the oil and gas properties with respect to which reserves are being estimated. In this research paper, the calculation of collecting data and sample by volumetric method are suggested to estimate the oil and gas production rate with time by using the geological configuration and the historical production data from CD 3700 3800 sand in Mann Oil Field. San Win "Reserve Estimation of Initial Oil and Gas by using Volumetric Method in Mann Oil Field" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27945.pdfPaper URL: https://www.ijtsrd.com/engineering/petroleum-engineering/27945/reserve-estimation-of-initial-oil-and-gas-by-using-volumetric-method-in-mann-oil-field/san-win
Reservoir engineering is the field to evaluate field performance by performing reservoir modeling studies and explore opportunities to maximize the value of both exploration and production properties to enhance hydrocarbon production.
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.
Wireline (WL) and Logging-While-Drilling (LWD) formation tester measurements provide a link between the static petrophysical measurements and dynamic rock-fluid properties for enhanced formation evaluation. However, despite the significant advancements in these services, there are still barriers. The analysis of Wireline (WL) and Logging-While-Drilling (LWD) formation testing has traditionally been performed by a skilled testing analyst using specialized software and theoretical models to generate results and assess the data vitality. This can be a time-consuming process involving analyzing over 100 pressure transients. In practice, the petrophysicists and geoscientists rarely have access to a detailed analysis in the time frame required and typically revert to other methods. Some of the methods are ad hoc, but there is a growing consensus that several convenient, simple, and effective real-time measurements can be used for an objective evaluation of the dynamic data. This talk demonstrates a straightforward automated process that has been developed by which real-time measurements, which are routinely recorded, are used to automatically generate the results. Basic principles are used to develop quality parameters and a test rating system that can guide the analyst in the objective determination of the vitality of the results for each test. In this way, the highest quality testing results are used for fluid gradients and log correlations to improve the integration of the dynamic data into the petrophysical analysis. This also enables standards to be established for real-time data acquisition that can save testing time while improving data and quality. This automated method is being applied routinely and several field examples are used to illustrate the utility and time savings of this new workflow.
Reserve Estimation of Initial Oil and Gas by using Volumetric Method in Mann ...ijtsrd
This research paper is focused to estimate the current production rate of the wells and to predict field remaining reserves. The remaining reserve depends on the production points that selected to represent the real well behavior, the way of dealing with the production data, and the human errors that might happen during the life of the field. Reserves estimating methods are usually categorized into three families analogy, volumetric, and performance techniques. Reserve Estimators should utilize the particular methods, and the number of methods, which in their professional judgment are most appropriate given i the geographic location, formation characteristics and nature of the property or group of properties with respect to which reserves are being estimated ii the amount and quality of available data and iii the significance of such property or group of properties in relation to the oil and gas properties with respect to which reserves are being estimated. In this research paper, the calculation of collecting data and sample by volumetric method are suggested to estimate the oil and gas production rate with time by using the geological configuration and the historical production data from CD 3700 3800 sand in Mann Oil Field. San Win "Reserve Estimation of Initial Oil and Gas by using Volumetric Method in Mann Oil Field" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27945.pdfPaper URL: https://www.ijtsrd.com/engineering/petroleum-engineering/27945/reserve-estimation-of-initial-oil-and-gas-by-using-volumetric-method-in-mann-oil-field/san-win
The forth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.
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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.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
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Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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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
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.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
2. 1.
2.
3.
4.
5.
6.
7.
8.
9.
Darcy Law: Linear Flow Model
Permeability Measurements
Darcy Law: Radial Flow Model
Permeability-Averaging Techniques
Effective Permeabilities
Rock Compressibility
Homogeneous and Heterogeneous Reservoirs
Two-Phase Permeability
Reservoir Characteristics
3. 1. Reservoir Characteristics
A.
B.
C.
D.
Reservoir Fluid Types According To Compressibility
Types of Flow Regimes
Types of Reservoir Geometries
Darcy’s Law Remarks
2. SS Regime for:
A. Linear Flow and Tilted Reservoirs
B. Radial Flow of
a. Incompressible and Slightly Compressible Fluids
b. Compressible Fluids
4.
5. Types of Fluids in the Reservoir
The isothermal compressibility coefficient is
essentially the controlling factor in identifying the
type of the reservoir fluid.
In general, reservoir fluids are classified into three
groups:
Incompressible fluids
Slightly compressible fluids
Compressible fluids
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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6. Incompressible Fluids
Incompressible fluids do not exist; this behavior,
however, may be assumed in some cases to simplify
the derivation and the final form of many flow
equations.
An incompressible fluid is defined as the fluid
whose volume (or density) does not change with
pressure, i.e.:
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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7. Slightly Compressible Fluids
These “slightly” compressible fluids exhibit small
changes in volume, or density, with changes in
pressure.
Knowing the volume Vref of a slightly compressible
liquid at a reference (initial) pressure pref, the changes in
the volumetric behavior of this fluid as a function of
pressure p can be mathematically described by:
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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8. Slightly Compressible Fluids (Cont.)
It should be pointed out that crude oil and water
systems fit into this category.
The ex may be represented by a series expansion
as:
Because the exponent x [which represents the term c
(pref−p)] is very small, the ex term can be approximated
by truncating to ex = 1 + x
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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9. Compressible Fluids
These are fluids that experience large changes in
volume as a function of pressure.
All gases are considered compressible fluids.
The truncation of the series expansion is not valid in this
category and the complete expansion is used.
The isothermal compressibility of any compressible
fluid is described by the following expression:
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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10. Schematic Illustrations of
the V and ρ vs. P
Pressure-volume relationship
Fall 13 H. AlamiNia
Fluid density vs. p for different fluid types
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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11.
12. Flow Regimes
There are basically three types of flow regimes that
must be recognized in order to describe the fluid
flow behavior and reservoir pressure distribution as
a function of time.
There are three flow regimes:
Steady-state flow
Unsteady-state flow
Pseudosteady-state flow
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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13. Steady-State Flow
The flow regime is identified as a steady-state flow
if the pressure at every location in the reservoir
remains constant, i.e., does not change with time.
Mathematically, this condition is expressed as:
In reservoirs, the steady-state flow condition can
only occur when the reservoir is completely
recharged and supported by strong aquifer or
pressure maintenance operations.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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14. Unsteady-State Flow
The unsteady-state flow
(frequently called transient flow)
is defined as the fluid flowing condition at which the
rate of change of pressure with respect to time at any
position in the reservoir is not zero or constant.
This definition suggests that the pressure derivative
with respect to time is essentially a function of both
position i and time t, thus
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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15. Pseudosteady-State Flow
When the pressure at different locations in the
reservoir is declining linearly as a function of time,
i.e., at a constant declining rate, the flowing
condition is characterized as the pseudosteadystate flow.
It should be pointed out that the pseudosteadystate flow is commonly referred to as semisteadystate flow and quasisteady-state flow.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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16. Schematic Comparison of
Flow Regimes
Figure shows
a schematic
comparison of
the pressure
declines as a
function of
time of the
three flow
regimes.
Flow regimes
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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17.
18. Reservoir Geometry
The shape of a reservoir has a significant effect on
its flow behavior.
Most reservoirs have irregular boundaries and a rigorous
mathematical description of geometry is often possible
only with the use of numerical simulators.
For many engineering purposes, however, the actual
flow geometry may be represented by one of the
following flow geometries:
Radial flow
Linear flow
Spherical and hemispherical flow
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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19. Radial Flow
In the absence of severe reservoir
heterogeneities, flow into or away
from a wellbore will follow radial
flow lines from a substantial
distance from the wellbore.
Because fluids move toward the well
from all directions and coverage at
the wellbore, the term radial flow is
given to characterize the flow of
fluid into the wellbore.
Figure shows idealized flow lines
and iso-potential lines for a radial
flow system.
Ideal radial flow
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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20. Linear Flow
Linear flow occurs when
flow paths are parallel
and the fluid flows in a
single direction.
In addition, the cross
sectional area to flow
must be constant.
A common application of
linear flow equations is
the fluid flow into vertical
hydraulic fractures.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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21. Spherical and Hemispherical Flow
Depending upon the type
of wellbore completion
configuration, it is possible
to have a spherical or
hemispherical flow near the
wellbore.
A well with a limited
perforated interval could
result in spherical flow in the
vicinity of the perforations.
A well that only partially
penetrates the pay zone,
could result in hemispherical
flow. The condition could
arise where coning of
bottom water is important.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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22.
23. Number of
Flowing Fluids in the Reservoir
The mathematical expressions that are used to
predict the volumetric performance and pressure
behavior of the reservoir vary in forms and
complexity depending upon the number of mobile
fluids in the reservoir.
Single-phase flow (oil, water, or gas)
Two-phase flow (oil-water, oil-gas, or gas-water)
Three-phase flow (oil, water, and gas)
The description of fluid flow and subsequent
analysis of pressure data becomes more difficult as
the number of mobile fluids increases.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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24. Fluid Flow Equations
The fluid flow equations that are used to describe
the flow behavior in a reservoir can take many
forms depending upon the combination of variables
presented previously,
(i.e., types of flow, types of fluids, etc.).
By combining the conservation of mass equation
with the transport equation (Darcy’s equation) and
various equations-of-state, the necessary flow
equations can be developed.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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25. Darcy’s Law Circumstances
Darcy’s Law applies only when the following
conditions exist:
Laminar (viscous) flow
Steady-state flow
Incompressible fluids
Homogeneous formation
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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26. Deviation from Laminar Flow
in Darcy’s Law
For turbulent flow, which occurs at higher
velocities, the pressure gradient increases at a
greater rate than does the flow rate and a special
modification of Darcy’s equation is needed.
When turbulent flow exists, the application of
Darcy’s equation can result in serious errors.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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27.
28.
29. Steady-State Flow
The applications of the steady-state flow are:
Linear flow of :
incompressible fluids
slightly compressible fluids
compressible fluids (gases)
Radial flow of :
incompressible fluids
slightly compressible fluids
compressible fluids
Multiphase flow
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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30. SS Regime for Linear Flow of IC Fluids
It is desirable to
express the above
relationship in
customary field units,
or:
Fall 13 H. AlamiNia
Where q = flow rate,
bbl/day
k = absolute
permeability, md
p = pressure, psia
μ = viscosity, cp
L = distance, ft
A = cross-sectional
area, ft2
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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31. Fluid Flow in Tilted Reservoirs
The difference in the pressure (p1−p2) in Darcy’s
Equation is not the only driving force in a tilted
reservoir.
The gravitational force is the other important
driving force that must be accounted for to
determine the direction and rate of flow.
The fluid gradient force (gravitational force) is always
directed vertically downward while the force that results
from an applied pressure drop may be in any direction.
The force causing flow would then be the vector
sum of these two.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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32. Fluid Potential
In practice, we obtain this result by introducing a
new parameter, called fluid potential, which has the
same dimensions as pressure, e.g., psi. Its symbol is
Φ.
The fluid potential at any point in the reservoir is
defined as the pressure at that point less the
pressure that would be exerted by a fluid head
extending to an arbitrarily assigned datum level.
Fall 13 H. AlamiNia
Reservoir Engineering 1 Course: Fundamentals of Reservoir Fluid Flow and SS Regime
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33. Fluid Potential (Cont.)
Letting Δzi be the vertical distance from a point i in
the reservoir to this datum level.
Where ρ is the density in lb/ft3.
Expressing the fluid density in gm/cc
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34. Datum in Fluid Potential
The datum is usually selected at the gas-oil contact,
oil-water contact, or at the highest point in
formation.
In using Equations to calculate the fluid potential
Φi at location i, the vertical distance Δzi is assigned
as a positive value when the point i is below the
datum level and as a negative when it is above the
datum level, i.e.:
If point i is above the datum level:
If point i is below the datum level:
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35. Darcy’s Equation in Tilted Reservoirs
It should be pointed out that
the fluid potential drop (Φ1 − Φ2) is equal to
the pressure drop (p1 − p2)
only when the flow system is horizontal.
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36. SS Regime for Linear Flow of SC Fluids
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37. SS Regime for Linear Flow
of C Fluids (Gases)
For a viscous (laminar) gas flow in a homogeneouslinear system, the real-gas equation-of-state can be
applied to calculate the number of gas moles n at
pressure p, temperature T, and volume V:
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38. SS Regime for Linear Flow
of C Fluids (Gases) (Cont.)
It is essential to notice that those gas properties z
and μg are a very strong function of pressure, but
they have been removed from the integral to
simplify the final form of the gas flow equation.
The above equation is valid for applications when
the pressure < 2000 psi.
The gas properties must be evaluated at the
average pressure p– as defined below.
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39.
40. SS Regime for Radial Flow of IC Fluids
Because the fluid is incompressible, the flow rate q
must be constant at all radii.
Due to the steady-state flowing condition, the
pressure profile around the wellbore is maintained
constant with time.
Let pwf represent the maintained bottom-hole
flowing pressure at the wellbore radius rw and pe
denote the external pressure at the external or
drainage radius.
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41. SS Regime for Radial Flow of IC Fluids
(Cont.)
Darcy’s equation can be used to determine the flow
rate at any radius r:
The flow rate for a crude oil system is customarily
expressed in surface units, i.e., stock-tank barrels
(STB), rather than reservoir units.
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42. SS Regime for Radial Flow of IC Fluids
(Cont.)
Where:
Frequently the two
Qo = oil, flow rate,
radii of interest are the
STB/day
wellbore radius rw and
pe = external pressure, psi
the external or drainage
pwf = bottom-hole
flowing pressure, psi
radius re.
k = permeability, md
Then:
μo = oil viscosity, cp
Bo = oil formation volume
factor, bbl/STB
h = thickness, ft
re = external or drainage
radius, ft
rw = wellbore radius, ft
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43. The External (Drainage) Radius
The external (drainage) radius re is usually
determined from the well spacing by equating the
area of the well spacing with that of a circle, i.e.,
Where A is the well spacing in acres.
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44. Pressure P at Any Radius R
In practice, neither the external radius nor the
wellbore radius is generally known with precision.
Fortunately, they enter the equation as a logarithm,
so that the error in the equation will be less than
the errors in the radii.
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45. Average Reservoir Pressure
The external pressure pe cannot be measured
readily, but Pe does not deviate substantially from
initial reservoir pressure if a strong and active
aquifer is present.
The average reservoir pressure pr, which often is
reported in well test results, should be used in
performing material balance calculations and flow rate
prediction.
Craft and Hawkins (1959) showed that the average
pressure is located at about 61% of the drainage radius
re for a steady-state flow condition.
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46. Oil Flow Rate as a Function of Pr
SS Regime for Radial Flow of IC Fluids
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47. SS Regime for Radial Flow of SC Fluids
Choosing the bottomhole flow pressure pwf as
the reference pressure
and expressing the flow
rate in STB/day gives:
Where qref is oil flow rate
at a reference pressure
pref.
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Where co = isothermal
compressibility
coefficient, psi−1
Qo = oil flow rate, STB/day
k = permeability, md
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48.
49. SS Regime for Radial Flow of C Fluids
The basic differential
form of Darcy’s Law for
a horizontal laminar
flow is valid for
describing the flow of
both gas and liquid
systems. For a radial
gas flow, the Darcy’s
equation takes the
form:
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Where:
qgr = gas flow rate at
radius r, bbl/day
r = radial distance, ft
h = zone thickness, ft
μg = gas viscosity, cp
p = pressure, psi
0.001127 = conversion
constant from Darcy
units to field units
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50. SS Regime for Radial Flow of C Fluids
(Cont.)
The gas flow rate is usually expressed in scf/day.
Referring to the gas flow rate at standard condition
as Qg, the gas flow rate qgr under pressure and
temperature can be converted to that of standard
condition by applying the real gas equation-of-state
to both conditions, or
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51. SS Regime for Radial Flow of C Fluids
(Cont.)
Integrating from the wellbore conditions (rw and
pwf) to any point in the reservoir (r and p) to give:
Imposing Darcy’s Law conditions on the Equation,
i.e.:
Steady-state flow, which requires that Qg is constant at
all radii
Homogeneous formation, which implies that k and h are
constant
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52. Real Gas Potential or
Real Gas Pseudopressure
The integral is called the real gas potential or real gas
pseudopressure, and it is usually represented by m (p) or
ψ. Thus
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53. Real Gas Potential or
Real Gas Pseudopressure Calculation
To calculate the integral,
the values of 2p/μgz are
calculated for several
values of pressure p.
Then (2p/μgz) versus p is
plotted on a Cartesian
scale and the area under
the curve is calculated
either numerically or
graphically, where the
area under the curve
from p = 0 to any
pressure p represents the
value of ψ corresponding
to p.
Real gas pseudopressure data
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54. Gas Flow Rate in scf/Day
The Equation indicates that a graph of ψ vs. ln r/rw
yields a straight line of slope (QgT/0.703kh) and
intercepts ψw. The flow rate is given exactly by
In the particular case when r = re, then: (Qg [scf/D]
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55. Gas Flow Rate in Mscf/Day
The gas flow rate is
commonly expressed in
Mscf/day, or
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Where:
ψe = real gas potential
as evaluated from 0 to
pe, psi2/cp
ψw = real gas potential
as evaluated from 0 to
Pwf, psi2/cp
k = permeability, md
h = thickness, ft
re = drainage radius, ft
rw = wellbore radius, ft
Qg = gas flow rate,
Mscf/day
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56. Exact Gas Flow Rate in Terms of Pr
The Equation can be expressed in terms of the
average reservoir pressure pr instead of the initial
reservoir pressure pe as:
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57. Approximation of
the Gas Flow Rate (P2 Method)
The exact gas flow rate as expressed by the
different forms of Darcy’s Law, can be approximated
by removing the term 2/μgz outside the integral as
a constant.
It should be pointed out that the zμg is considered
constant only under a pressure range of < 2000 psi.
The term (μg z) avg is evaluated at an average pressure
p– that is defined by the following expression:
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58. 1. Ahmed, T. (2010). Reservoir engineering
handbook (Gulf Professional Publishing).
Chapter 6
59. 1. Multiple-Phase Flow
2. Pressure Disturbance in Reservoirs
3. USS Flow Regime
A. USS: Mathematical Formulation
4. Diffusivity Equation
A. Solution of Diffusivity Equation
a.
Ei- Function Solution