Capillary pressure data can be used to determine initial fluid saturations, fluid distributions in reservoirs, and residual oil saturations. It is related to properties like pore size, wettability, interfacial tension, and fluid densities. Capillary pressure curves show hysteresis between drainage and imbibition processes. Laboratory data must be converted to reservoir conditions using equations accounting for property differences. The J-function can average capillary pressure data for a given rock type.
INCLUDES SPREADING COEFFICIENT AND ITS THEORY AND ALSO FEW OF ITS APPLICATION IN PHARMACEUTICAL FIELD
WILL BE HELPFUL FOR B PHARMACY STUDENTS
INCLUDES HOW IT IS DERIVED AND ALSO HOW IT IS RELATED TO SPREADING OF A CREAM OR OINTMENT ON OUR SKIN
IMPORTANCE OF SPREADING COEFFICIENT
In this presentation:
Surface Tension
Interfacial Tension
Definition of inerfacial tension in different ways
Measurement of interfacial and surface tesion
B. Pharm 2nd year IIIrd Sem
Subject- Pharmaceutical Engineering
As per PCI syllabus
Content: Types of manometers, Reynolds number and its significance,
Bernoulli’s theorem and its applications, Energy losses, Orifice meter,
Venturimeter, Pitot tube and Rotometer
Surface and Interfacial tension [Part-3(a)](Measurement of Surface and Inter...Ms. Pooja Bhandare
MEASUREMENT OF SURFACE AND INTERFACIAL TENSION
Capillary Rise Method, Drop Count and Weight Method.
Wilhelmy Plate Methods ,The DuNouy Ring Method.
Capillary Rise Method: Upward force due to surface tension: Drop count and Weight method Downward Force: Drop weight method: Drop count method
INCLUDES SPREADING COEFFICIENT AND ITS THEORY AND ALSO FEW OF ITS APPLICATION IN PHARMACEUTICAL FIELD
WILL BE HELPFUL FOR B PHARMACY STUDENTS
INCLUDES HOW IT IS DERIVED AND ALSO HOW IT IS RELATED TO SPREADING OF A CREAM OR OINTMENT ON OUR SKIN
IMPORTANCE OF SPREADING COEFFICIENT
In this presentation:
Surface Tension
Interfacial Tension
Definition of inerfacial tension in different ways
Measurement of interfacial and surface tesion
B. Pharm 2nd year IIIrd Sem
Subject- Pharmaceutical Engineering
As per PCI syllabus
Content: Types of manometers, Reynolds number and its significance,
Bernoulli’s theorem and its applications, Energy losses, Orifice meter,
Venturimeter, Pitot tube and Rotometer
Surface and Interfacial tension [Part-3(a)](Measurement of Surface and Inter...Ms. Pooja Bhandare
MEASUREMENT OF SURFACE AND INTERFACIAL TENSION
Capillary Rise Method, Drop Count and Weight Method.
Wilhelmy Plate Methods ,The DuNouy Ring Method.
Capillary Rise Method: Upward force due to surface tension: Drop count and Weight method Downward Force: Drop weight method: Drop count method
Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force. Stoke's Law can be used to predict emulsion stability.
The CSC duNouy Tensiometer is a laboratory Instrument for the purpose of determining the strength of a liquid surface. Test is used in coatings and industries. Applications are also in chemical, pharmaceutical and electric power applications.
The movement of molecules from one phase to another is called partitioning.
If two immiscible phases are placed adjacent to each other, the solute will distribute itself between two immiscible phases until equilibrium is attained; therefore no further transfer of solute occurs.
When phases exist together, the boundary between two of them is known as interface.
When the phase is in contact with atmosphere it is termed as surface.
Surfactant is a surface active agent which are used to prevent surface tension and interfacial tension. It is important prevent interfacial fluidity, it is amphiphilic molecule having Hydrophilic head and Lipophilic tail. It is important for poorly water soluble drug and it is important to influencing water solubility of poorly water soluble drug. It is important to prevent the inter and intra subject variability.
It act as solubilizing agent, suspending and emulsifying agent, stabilizing agent, wetting agent, detergent, Foaming agent.
It is important for preparation of Nanoemulsion, Nanosuspension, Microemulsion.
It is important to show antibacterial as well as antimicrobial activity.
It is important for Novel drug delivery system, oral drug delivery system, Targeted drug delivery system.
It is important to influencing oral bioavailability of poorly water soluble drug.
Surfactants and their applications in pharmaceutical dosage formMuhammad Jamal
This presentation is very much helpful for the medical students,pharmacists, researchers and other health care providers. i hope it will provide important information regarding surfactants and their applications in pharmaceutical dosage forms.
Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force. Stoke's Law can be used to predict emulsion stability.
The CSC duNouy Tensiometer is a laboratory Instrument for the purpose of determining the strength of a liquid surface. Test is used in coatings and industries. Applications are also in chemical, pharmaceutical and electric power applications.
The movement of molecules from one phase to another is called partitioning.
If two immiscible phases are placed adjacent to each other, the solute will distribute itself between two immiscible phases until equilibrium is attained; therefore no further transfer of solute occurs.
When phases exist together, the boundary between two of them is known as interface.
When the phase is in contact with atmosphere it is termed as surface.
Surfactant is a surface active agent which are used to prevent surface tension and interfacial tension. It is important prevent interfacial fluidity, it is amphiphilic molecule having Hydrophilic head and Lipophilic tail. It is important for poorly water soluble drug and it is important to influencing water solubility of poorly water soluble drug. It is important to prevent the inter and intra subject variability.
It act as solubilizing agent, suspending and emulsifying agent, stabilizing agent, wetting agent, detergent, Foaming agent.
It is important for preparation of Nanoemulsion, Nanosuspension, Microemulsion.
It is important to show antibacterial as well as antimicrobial activity.
It is important for Novel drug delivery system, oral drug delivery system, Targeted drug delivery system.
It is important to influencing oral bioavailability of poorly water soluble drug.
Surfactants and their applications in pharmaceutical dosage formMuhammad Jamal
This presentation is very much helpful for the medical students,pharmacists, researchers and other health care providers. i hope it will provide important information regarding surfactants and their applications in pharmaceutical dosage forms.
This document provides a basic overview of the fundamental rock properties. It delivers a detailed analysis of the basic reservoir rock properties like porosity, permeability, Fluid saturation , wettability, etc.
21 Rock Fluid Interactions Capillary Rise, Capillary Pressure, J.docxeugeniadean34240
21 Rock Fluid Interactions Capillary Rise, Capillary Pressure, J Functions.pdf
107
Petr 3520: Rock-Fluid Interactions (such as capillary rise, capillary pressure…) Class 21
So far in this class we have studied rock properties (, k, cf, etc.) and fluid properties. But reservoir
engineers must also understand immiscible fluid-fluid interactions and rock-fluid interactions.
In petroleum reservoirs we have:
1. Microscopic-sized pores + two or more (immiscible) fluids (oil-water, gas-water, or oil-gas-
water) which typically do not mix (they are immiscible, not miscible). The rocks are water-wet or oil-wet
(which means that the rock is preferentially wetted by water or oil).
Because the pores are so small, the surface area (fluid-rock contact, and fluid-fluid contact (for example,
oil to water)) to volume (of fluid and/or rock) is very high, thus surface forces become significant.
Example Calculation: 1 ft
3
cube of rock, assume to be bundle of 1 mm dia tubes each 1 ft = 304.8 mm
long. There are 300
2
= 90,000 tubes in this cube. Surface area in mm
2
, convert to ft
2
: A = 1000 ft
2
.
2. What are surface forces? Surface forces exist at (immiscible) liquid-liquid and liquid-solid interfaces.
Surface forces arise due to relative Adhesion vs. Cohesion.
Cohesion (“stick or stay together”) is a property of a fluid whose molecules have high intermolecular
attraction. The fluid’s molecules would rather stick to themselves rather than another fluid or nearby
surface.
Adhesion is the degree to which a fluid will “stick” to a nearby solid surface.
3. Wetting, Contact Angle: These are the result of the relative cohesion vs. adhesion of two fluids and a
solid surface.
Fluid “wets” a surface: Adhesion > Cohesion. The fluid’s molecules preferentially attracted to
surface.
Fluid does not “wet” the surface: Cohesion > Adhesion. The fluid’s molecules preferentially
attracted to fluid.
Contact Angle: Angle formed between a fluid drop and a solid surface, measured through the fluid.
4. Examples of wettability, contact angle (): A fluid’s interaction with a solid surface:
Rain-X on automobile windshields
Gore Tex fabric
Non-stick fry pans
5. Examples of a fluid’s cohesion vs. adhesion (relative affinity of a fluid’s molecules to itself or to a solid
surface)
Round drops on plant leaves, on non-stick frying pans (for a fluid to form drops like this, the
fluid’s molecules would rather cohere with other fluid molecules than adhere to a solid surface)
6. Surface tension (): Between a fluid’s surface and air. Units: [work/area] = [dyne-cm/cm
2
] A fluid
wants to minimize its free surface. It takes work or energy to create additional surface area.
Free fluids form drops (minimum surface area)
Round drops on plants (cohesion
Water bugs
Coin or paper clip float on water
108
7. Interfacial tension (): Between two fluids, e.g. .
Boiler Drum level measurement in Thermal Power StationsManohar Tatwawadi
The paper describes the basics of Boiler Drum water Level measurement in a Thermal Power Station. The Single element and three element control has been described in a very simple manner. Useful for the Thermal Engineers
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.
1
KNE351 Fluid Mechanics 1
Laboratory Notes
Broad-Crested Weir
This booklet contains instructions and notes for the experiment listed above.
Additional material relating to laboratory work will be delivered during the
course. The expectations regarding lab work and reporting are described in a
separate document,‘KNE351. FLUIDMECHANICS: Laboratory Method and
Reporting’, which will also be circulated at the beginning of the course. It is
expected that all students study these notes and complete the pre-lab component
prior to the laboratory session. An overview of the laboratory equipment will
be provided at the beginning of each session.
A D Henderson
2
1. Learning Objectives
1. Observe and understand the behaviour of a real fluid flowing over a broad-crested weir,
2. Model this behaviour employing the Continuity and Bernoulli (Energy) Principles to
predict the flow rate from depth measurements.
3. Evaluate these predictions by comparing with measured values and use Specific Energy
to explain the changing nature of the flow over the weir.
2. Introduction
The theory of non-uniform flow in channels is covered by the course text, by many other fluid
mechanics texts, and by several web sites.
The specific energy, E, is the energy at a channel cross-section referred to the base of the
channel (in contrast to the Bernoulli equation, which is referred to a fixed horizontal datum).
The expression given for E is actually an approximation valid for small bed slopes. You've
measured the flume slope, and should examine this approximation in your report. A hydrostatic
pressure distribution is assumed, and you should also examine the validity of this assumption. If
the streamlines are not parallel, then the accelerative forces will modify the pressure - depth
relationship.
In general, two conjugate flows depths satisfy the specific energy equation for a given value of
the specific energy. The greater depth is associated with subcritical flow, and the shallower
depth with supercritical flow. At the critical depth the conjugate depths are equal, and the
discharge for the given specific energy is a maximum.
Broad crested weirs are used as a method of flow measurement in open channel flows. If the
weir is sufficiently high and long, the free surface will drop to critical depth. If the height of
the upstream flow is measured, then the flow rate can be determined.
3
3. Apparatus
• Water flume comprising of pump, control valve, venturi and v-notch flow meters,
downstream control gate.
• depth gauges
• 2 vertical water manometers
• 2 total head tubes
4. Preparation
Examine and sketch the layout of the channel and associated flow measuring equipment.
Measure the channel width and note significant geometrical parameters of the nozzle venturi
meter and V-notch weir. Note the directions of readings of all measuring scales.
a. Measure the channel, weir dimensions, a.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
1. Capillary Pressure
Objectives:
- List the uses of capillary pressure data.
- Define hysteresis.
- Sketch capillary pressure curves for typical drainage and imbibition processes.
- Explain the relation between capillary pressure data and reservoir fluid saturation
- Define oil-water and gas-oil transition zones.
- Convert capillary pressure lab data to reservoir conditions.
- Define the J-function.
- List the different methods for measuring capillary pressure in the lab
Uses of Capillary Pressure Data:
• Determine initial water saturation in the reservoir.
• Determine fluid distribution in the reservoir.
• Determine residual oil saturation for water flooding applications
• Determine pore size distribution index.
• May help in identifying zones or rock types.
• Input for reservoir simulation calculations
Capillary pressure measurements determine the initial water saturation. This is the saturation at which the
increase in capillary pressure does not affect the saturation.
Capillary pressure data can also determine the vertical fluid distribution in the reservoir by establishing the
relation between the capillary pressure and height above the free water level.
Imbibition capillary pressure measurements determine the residual oil saturation in water flooding application.
We can infer the pore size Distribution index, λ, from capillary pressure data. This index can be used to
calculate relative permeability using industry correlations.
Capillary pressure curves are similar for the same rock type. The shape also gives indication about the rock
permeability.
Capillary pressure curves are used to initialize simulation runs and in flow calculations between and blocks.
Capillary Pressure Concept:
Water exists at all levels below 2, and both water and oil exist at all levels above 2
Oil and water pressure gradients are different because their density is different
At level 2, pressure in both the water and oil phases is the same.
At any level above 2, such as level 3, water and oil pressures are different
This difference in pressure is called the capillary pressure.
Capillary Pressure 1
2. Capillary Pressure Definition:
• The pressure difference existing across the interface separating two immiscible fluids.
• It is usually calculated as
Pc = Pnwt - Pwf
One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase).
Gas is always the non-wetting phase in both oil-gas and water-gas systems.
Oil is often the non-wetting phase in water-oil systems.
Example:
Define capillary pressure in the following systems:
• Water-gas system.
• Water-wet water-oil system.
• Oil-gas system.
Solution:
Water-gas system:
Pc =ρg-ρw
Water-wet water-oil system:
Pc =ρo-ρw
oil-gas system:
Pc =ρg-ρo
Relation between Capillary Pressure and Fluid Saturation
For uniform sands, reservoir fluid saturation is related to the height above the free-water level by the following
relation:
Capillary Pressure 2
3. Fluid Distribution in Petroleum Reservoirs:
Free water level (surface) is the level at which water-oil capillary pressure is zero. i.e. the pressures in both
water and oil phases are equal.
Above the free water level, oil and water can coexist. Above this level, there usually exists another level (or
surface) called the water-oil contact, WOC. Below the VVOC, only water can be produced. Above the WOC,
both oil and water can be produced. At some point above the WOC, water will reach an irreducible value and
will no longer be movable.
Likewise, a free oil level and an oil-gas contact (OGC) may exist as shown in the figure above.
Capillary Pressure 3
4. This processed log section shows the fluid distribution in the reservoir. Gas and oil are clearly identified from
water.
An oil-water transition zone of about 7 feet can be also seen on the log.
Transition zone height is partially a function of me density difference between the two fluids. For a given rock
quality, the transition zone will be smaller for larger density differences (e.g. gas and oil) and larger for smaller
density differences (e.g. heavy oil and water). This relationship is evident from the relation between capillary
pressure and the height above the free-water level.
Example:
Capillary pressure was measured to be 5 psia at connate water saturation. Water density is 66.5
Ibm/ft3 Calculate the length of the transition zone in the following two situations:
A. oil density = 59.3 fbm/ft3
B. oil density = 43.7 ibm/ft3
This example assumes the rock quality is the same in both situations.
Solution:
Rearranging the relation between capillary pressure and height:
A. Heavy oil
B. Light oil
Capillary Tube Model - Air-Water System:
We can imagine the porous media as a collection of capillary tubes. This model is useful for providing insight
into how fluids behave in the reservoir pore spaces.
Water rises in a capillary tube when that tube is placed in a beaker of water. Likewise, water (the wetting phase)
fills small pores leaving larger pores to non-wetting phases.
The height of water is a function of:
• The adhesion tension between the air and water.
• The radius of the tube.
• The density difference between fluids.
Capillary Pressure 4
5. The above relation can be derived from balancing the upward and downward forces. Upward force is due to
adhesion tension and downward force is due to the weight of the fluid.
Δh = Height of water rise in capillary tube, cm.
σaw = Interfacial tension between air and water, dynes/cm.
θ = Air/water contact angle, degrees.
r = Radius of capillary tube, cm.
g = Acceleration due to gravity, 980 cm/sec2.
Δρaw = Density difference between water and air, gm/cm3.
Contact angle, ft is measured in the denser phase (water in this case).
This relation shows that the wetting phase (water) rise will be larger in small capillaries.
Water rise in capillary tube depends on the density difference of fluid
Combining the two relations:
Capillary Pressure 5
6. Capillary Pressure - Oil-Water System:
From a similar derivation, the equation for capillary pressure for an oil/water system is:
Converting Laboratory Capillary Pressure Data to Reservoir Conditions:
Basic Equations:
Subscripts L and R refer to laboratory and reservoir conditions, respectively.
Setting rL = rR and combining equations yields:
Therefore, capillary pressure at reservoir conditions is given by:
Example:
Convert the laboratory capillary pressure data for sample 28 in the attached capillary pressure curve (obtained
using mercury injection method) to reservoir conditions for a formation containing oil and water.
Calculate reservoir capillary pressure data for mercury saturations of 70. 60, 50, 40,30, 20, and 10 percent.
Laboratory Data: σHg= 480 cynes/cm. θHg = 140°
Reservoir Data: σow = 24 dynes/cm. θow = 20°
Note. The reservoir data are very difficult to obtain. The reservoir data above are representative values based
upon industry literature.
Capillary Pressure 6
7. Solution;
Steps:
• Solve the equation that relates lab capillary pressure data to reservoir capillary pressure data for the
conditions we have.
• Obtain laboratory capittaiy pressure data from the curve for Sample 28.
• Convert the lab numbers to reservoir capillary pressure.
Drainage and Imbibition Capillary Pressure Curves:
The drainage curve is always higher than the Imbibition curve
Si = initial or irreducible wetting phase saturation
Sm = critical non-wetting phase saturation.
Pd = entry pressure or displacement pressure.
The entry (displacement) pressure is defined as the pressure required to force the non-wetting fiutd through an
initially wetting-phase-saturated sample.
Drainage Process:
• Fluid flow process in which the saturation of the nonwetting phase increases.
• Mobility of nonwetting fluid phase increases as nonwetting phase saturation increases.
Imbibition Process:
• Fluid flow process m which the saturation of the wetting phase increases and the nonwetting phase
saturation decreases.
• Mobility of wettirg phase increases as wetting phase saturation increases.
Capillary Pressure 7
8. Effects of Rwrvoff Properties on Capillary Pressure:
- Capillary pressure characteristics in reservoir are affected by:
• Variations in permeability
• Grain size distribution
• Sataration "history
• Contact angle
• Interfacial tension
• Density difference between fluids
Effect of Permeability:
• Curves shift to the nght (i.e., larger water saturations at a given value of capillary pressure) as the
permeability decreases.
• Displacement pressure increases as permeability decreases.
• Minimum interstitial water saturation increases as permeability decreases.
Effect of Grain Size Distribution:
• Well-sorted grain sizes:
• Majority of grain sizes are the same size.
• Minimum Interstitial water saturation is lower.
• Displacement pressure is lower.
• Poorly sorted grain sizes:
• Significant variation in range of grain sizes.
• Minimum interstitial water saturation is higher.
• Displacement pressure is higher.
Capillary Pressure 8
9. Effect of Saturation History:
For the same saturation, capillary pressure is always higher for the drainage process (increasing the
non-wetting phase saturation) than the imbibition process (increasing the wetting phase saturation)
Effect of Contact Angle:
• Contact angle less than 90o indicates water-wet characteristics (refer to wettability notes).
• Curves shift to the right (i.e., larger water saturations at a given value of capillary pressure) as
the contact angle decreases.
• Displacement pressure increases as contact angle decreases.
• Minimum interstitial water saturation increases as contact angle decreases.
Effect of Interfacial Tension:
Capillary Pressure 9
10. Low interracial tension indicates higher tendency of phases to mix together.
With higher interfacial tension, transition zone is expected to be larger.
■
Effect of Density Difference:
Smaller density difference between fluids results in a larger transition zone (refer to Exercise 1).
Averaging Capillary Pressure Data Using the Leverett J-Function:
• A universal capillary pressure curve is impossible to generate because of the variation of
properties affecting capillary pressure reservoir.
• The Leverett J-function was developed in an attempt to convert ail capillary to a universal
curve.
Definition of Leverett J-Function:
J(Sw) = Leverett J-function, dimensionless.
Sw = Water saturation, fraction.
Pc = Capillary pressure, psia.
σ = interfacial tension, dynes/cm.
θ = Contact angle, degrees.
K = Formation permeability, md.
Φ = Porosity, fraction.
Capillary Pressure 10
11. Example of J-Function for West Texas Carbonate
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Jc
Jmatch
Jn1
Jn2
Jn3
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Water saturation, fraction
J-function
The cata represented by plus signs (+} are from an original capillary pressure experiments. The outer
data were for three new experiments, performed to cetermine the reliability of the original data.
The black line represents an average J-function that was initially used in a reservoir simulation study
for the field. Ultimately, the rock type was broken into smaller units, and five different capillary
pressure relationships were used to represent the ranges of carbonate rock quality observed in the
reservoir.
Uses of Leverett J-Function:
• J-function is useful for averaging capillary pressure data from a given rock type from a given
reservoir.
• J-function can sometimes be extended to different reservoirs having same lithoiogies.
• J-function usually does not predict an accurate correlation for different lithoiogies.
• If J-functions are not successful in reducing the scatter in a given set of data, then this
suggests that we are dealing with different rock types.
Example: Calculation of Leverett J-Function:
Using the average capillary pressure data from the table, calculate and plot the Leverett J-function. Use
the following rock and fluid properties:
σ = 72 dynes/cm k = 47 md
θ = 0o Φ = 19.4 %
Capillary Pressure 11
12. Solution:
In the table above.we have no multiplied through by the conversion factor 0.22
Example:Estimating Pc from the J-Function:
Estimate capillary pressures from Leverett J-function calculated in the previous example for a different
core sample.
Properties of core sample:
K =100md.
Φ =10%
Solution :
Laboratory Methods for Measuring Capillary Pressure:
• Porous diaphragm method
• Mercury injection
• Centrifuge method
• Dynamic method
Capillary Pressure 12