MS - Chemical Engineering
[A Thesis / A Dissertation (pick one)]
by
Submitted to the College of Graduate Studies
Texas A&M University-Kingsville
in partial fulfillment of the requirements for the degree of
Major Subject:
vi
TITLE OF MANUSCRIPT SHOULD BE IN ALL CAPS, BOLD, AND DOUBLE SPACED
[A Thesis / A Dissertation (pick one)]
by
FIRST NAME LAST NAME [CENTERED; ALL CAPS SAME AS TITLE PAGE]
Approved as to style and content by:
First Name Last Name, Ph.D.
Committee Chair
First Name Last Name, Ph.D.
Committee Member
First Name Last Name, Ph.D.
Committee Member
First Name Last Name, Ph.D.
Department Chair
George Allen Rasmussen, Ph.D.
Vice President for Research
and Graduate Studies
Month and year of your graduation
Note: Department Chair is optional depending on your department
ABSTRACT
Manuscript Title in Title Case Format
[Graduation Term ex., May/August/December 20XX]
Student Name, Undergraduate and/or Graduate Degree(s) [Spelled Out]
University Name(s)
Chair of Advisory Committee: Dr. Chair Name
Indent one tab and start typing. Type up to 300 words for a thesis abstract and up to 400 words for a dissertation abstract. Be sure the tense has been updated from future tense in the proposal stage to past tense since you have now done the research activities.
There should only be one Abstract in this document, located after the Signature Page. It should summarize the research and findings in your thesis/dissertation manuscript. Your Abstract must not include formal citations, images, or complex equations.
DELETE THIS BOX BEFORE SUBMITTING
DEDICATION
Begin Typing Here
The Dedication page is optional and should be no longer than one page.
The text in the Dedication should be in the same font style
as the other text in the thesis/dissertation.
DELETE THIS PAGE
IF NOT INCLUDING A DEDICATION
DELETE THIS BOX BEFORE SUBMITTING
ACKNOWLEDGEMENTS
Begin Typing Here
The Acknowledgements page is optional and limited to four pages. It follows the Dedication page (or Abstract, if no Dedication). It is in the same font style as the main text. The vertical spacing, paragraph style, margins, and right alignment are also the same as used in main text. You must use complete sentences.
DELETE THIS PAGE IF NOT INCLUDING ACKNOWLEDGEMENTS
DELETE THIS BOX BEFORE SUBMITTING
(Sample Wording)
I would like to thank my committee chair, Dr. Hernandez and my committee members, Dr. Ortega, Dr. Brennen, Dr. Anderson, and Prof. Benner, for their guidance and support throughout the course of this research.
Thanks also go to my friends and colleagues and the department faculty and staff for making my time at Texas A&M University-Kingsville a great experience.
Finally, thanks to my mother and father for their encouragement and to my wife/husband for her/his patience and love.
CONTRIBUTORS AND FUNDING SOURCES
Begin Typing Here
Contributors Section: Consists of two sections. Part 1 will name all members of the thesis or dissertation committee. Part 2 will acknowledge individual student contributions and/or the contributions of others.
Funding Section: Include all support that was provided by the university, or any other source, to conduct your thesis or dissertation research and compilation. If you received no funding, state that here.
DELETE THIS PAGE IF NOT INCLUDING FUNDING INFO
DELETE THIS BOX BEFORE SUBMITTING
(Sample Wording)
Contributors
This work was supervised by a thesis (or) dissertation committee consisting of Professor XXXX [advisor – also note if co-advisor] and XXXX of the Department of [Home Department] and Professor(s) XXXX of the Department of [Outside Department].
The data analyzed for Chapter 3 was provided by Professor XXXX. The analyses depicted in Chapter 4 were conducted in part by [name] of the Department of [department name] and were published in (year).
All other work conducted for the thesis (or) dissertation was completed by the student independently.
Funding Sources
Graduate study was supported by a fellowship from Texas A&M University-Kingsville and a dissertation research fellowship from XXX Foundation.
This work was also made possible in part by [funding source] under Grant Number [insert grant number]. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the [name of awarding office].
NOMENCLATURE
Begin Typing Here
This optional list may be placed in the following places: before the Table of Contents, as the last preliminary page, after the main text, or as an Appendix. The list is in the same font style as text.
DELETE THIS PAGE IF NOT INCLUDING NOMENCLATURE
DELETE THIS BOX BEFORE SUBMITTING
(Sample Nomenclature)
HSUS Humane Society of the United States
LOF List of Figures
LOT List of Tables
NSF National Science Foundation
P Pressure
T Time
TOC Table of Contents
TEA Texas Education Agency
TxDOT Texas Department of Transportation
TABLE OF CONTENTS
Page
ABSTRACT iii
DEDICATION iv
ACKNOWLEDGEMENTS v
CONTRIBUTORS AND FUNDING SOURCES vi
NOMENCLATURE viii
TABLE OF CONTENTS ix
LIST OF FIGURES xi
LIST OF TABLES xii
CHAPTER 1. [CHAPTER 1 TITLE GOES HERE (ALL CAPS)] 1
CHAPTER 2. [CHAPTER 2 TITLE GOES HERE (ALL CAPS)]........................................... # 2.1 Level One Heading in Title Case Format #
2.2 Level One Heading in Title Case Format #
2.3 Level One Heading in Title Case Format #
CHAPTER 3. [CHAPTER 3 TITLE GOES HERE (ALL CAPS)] #
3.1 Level One Heading in Title Case Format #
3.2 Level One Heading in Title Case Format #
3.3 Level One Heading in Title Case Format #
3.4 Level One Heading in Title Case Format. If Level One Heading is lengthy and
continues to the next line, you will single space and indent #
CHAPTER 4. [CHAPTER 4 TITLE GOES HERE (ALL CAPS)] #
4.1 Level One Heading in Title Case Format #
Page
CHAPTER 5. [CHAPTER 5 TITLE GOES HERE (ALL CAPS)] #
5.1 Level One Heading in Title Case Format #
5.2 Level One Heading in Title Case Format #
5.2.1 Level two heading in sentence case format #
5.2.2 Level two heading in sentence case format #
REFERENCES #
VITA #
This template does NOT have an automatic ToC, which means you will need to refine it and input the page numbers by hand.
You may try an auto-formatted ToC, but are responsible for ensuring that the auto-formatting does not change text from 12 points Times New Roman or change the color from 100% black.
The ToC in this template DOES have some coding that will help you:
· Press ENTER after a page number and the next line should be formatted the same as the previous line.
· Pressing the TAB key will bring you to the different places on that line where you may need to type or paste in titles.
· You do not need to manually type the leader dots (…..) when you press TAB after text. They will be added for you.
DELETE THIS BOX BEFORE SUBMITTING
LIST OF FIGURES
Page
Figure 1. Example portrait.
4
Please use this style for your List of Figures. Be sure that the figure title in the List of Figures matches exactly what is in the actual caption. Please ensure that the figures in the manuscript correspond with the page number listed on List of Figures.
DELETE THIS BOX BEFORE SUBMITTING
xi
LIST OF TABLES
Page
Table 1. Table title in sentence case format. #
Table 2. Table title in sentence case format #
Table 3. Table title in sentence case format. #
Please use this style for your List of Tables. Be sure that the table title in the List of Tables matches exactly what is in the actual caption. Please ensure that the tables in the manuscript correspond with the page number listed on List of Tables.
If you have only one table, you do not need a LIST OF TABLES.
DELETE THIS BOX BEFORE SUBMITTING
xii
CHAPTER 1. FORMATTING
1.1 Font Specifications
Even when a journal is used as the model for the manuscript, the student must not attempt to copy the journal's use of various sizes and styles. Uniformity and legibility of typeface are still the primary concerns. TAMUK manuscripts are to use the Times New Roman font style at a size of 12 points throughout.
In most cases, the same font style must be used throughout the manuscript; mixing font styles is not acceptable. However, italic type is acceptable for those words and/or short phrases, which would be italicized, in a published format. Underlining, of course, provides the same emphasis but should be used sparingly and with discretion. Boldface type is required for chapter titles and all section headings.
Text color will be 100% black throughout.
1.2 Justified Right‐hand Margins
Justified right-hand margins are not acceptable. You cannot block the narrative text.
1.3 Line Spacing
The narrative text should be typed with double spacing throughout. Mixing spacing types is not acceptable. Double space is used between paragraphs.
Single spacing is used only for such specific and appropriate purposes as long, blocked, and inset quotations; footnotes; endnotes; and itemized or tabular materials. Any quotations of four or fewer typed lines should use the same spacing as the narrative text. Single spacing is also used in the TOC, LOF, and LOT for titles more than one line in length.
1.4 Page Margins
All body text, figures, and tables must fit within a 1-inch margin on all four sides of a page. The page number is to be set inside the page footer, centered, one-half inch from the bottom of each page that is numbered.
All computer data, illustrations, figuresand tables in the manuscript must conform to the margin requirements in every way.
1.5 Pagination
Every page in the manuscript except the Copyright page, Title page and the Signature page must be numbered. The Title page is considered to be page “i” and the Signature page is considered page “ii”, but no pagination numerals are shown on these two pages.
All page numbers should be centered and placed at ½ inch from the bottom of the page inside the Footer. All page numbers should be 12 point font size.
1.5.1 Preliminary pages
Lower case Roman numerals (iii, iv, v, vi, etc.) are used to number the preliminary pages. The first numbered page is the Abstract page, which is numbered “iii”, and follows the unnumbered Title page and Signature page.
1.5.2 Text and supplementary pages
Arabic numerals (1, 2, 3, etc.) are used in numbering all narrative text and supplementary pages. The first page of the narrative text begins with the numeral 1, and the numbering runs consecutively with the last numbered page being the VITA page.
1.6 Manuscript
After successfully defending the final thesis/dissertation and completing all committee member edits, the final manuscript must be uploaded to the One Drive as a Word doc by the student by no later than the set deadline which are posted on the Graduate Studies website. The link to the One Drive will be posted on the Graduate Studies website www.tamuk.edu/grad under the Current Graduate Students tab then click on Final Graduation Requirements.
It is the responsibility of the student to secure original signatures of all committee members before submitting to the College of Graduate Studies for final approval. All committee members must be on the graduate faculty and all signatures must be in black ink.
FIGURES AND TABLES
Figure 1. Example portrait.
REFERENCES
Begin References Here
References can be located at the end of the main text (here) or at the end of each chapter. The reference list should be consistent, accurate, and complete. We recommend using single spacing within each citation and double space between each new reference. The reference list should be organized either by number or by author’s last name.
DELETE THIS BOX BEFORE SUBMITTING
APPENDIX A
insert appendix title here
Place text, figures or tables here. If you have more than one appendix, the format is the same and the appendix designation follows the alpha order. You do not have to list the appendix in the Table of Contents, and you do not have to list the appendix tables or figures in the List of Tables and List of Figures.
Delete this page if not using appendices.
VITA
Center your name here in Title Case Format
(DO NOT include personal information)
Begin text here.
7
AUTOMATED SYSTEM FOR PRESSURE DROP MEASUREMENT
AND FLOW REGIMES DETERMINATION IN PACKED BEDS
WITH SINGLE AND MULTIPHASE GAS-LIQUID FLOW
A Dissertation
by
MRUDALINI moturu
Submitted to the College of Graduate Studies
Texas A&M University-Kingsville
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
December 2018
Major Subject: Chemical Engineering
48
AUTOMATED SYSTEM FOR PRESSURE DROP MEASUREMENT
AND FLOW REGIMES DETERMINATION IN PACKED BEDS
WITH SINGLE AND MULTIPHASE GAS-LIQUID FLOW
A Thesis
by
MRUDALINI MOTURU
Approved as to style and content by:
_________________________ _______________________
Patrick L. Mills, D.Sc. Matthew Alexander, Ph.D.
(Chairman of Committee) (Member of Committee)
_________________________ _______________________
Horacio A. Duarte, Ph. D. Patrick L. Mills, D.Sc.
(Member of Committee) (Chair of Department)
_____________________________
George Allen Rasmussen, Ph.D.
(Vice President for Research and
Graduate studies)
December 2018
ABSTRACT
Automated System for Pressure Drop Measurements and, Flow Regimes Determination in Packed Beds with Single and Multiphase Gas-Liquid Flow Comment by Graduate Studies.: All the text throughout the manuscript should be in Times New Roman, 12 points font.
December 2018
Mrudalini Moturu, Chemical Engineering, R.V.R.&J.C. College of Engineering Comment by Graduate Studies.: All the content throughout the manuscript should be with line spacing of 2.0.
If there are any change in the page numbers, fix it.
Chairman of Advisory Committee: Dr. Patrick L. Mills
A research program is described on the modernization of the manually operated packed column system located in the Unit Operations Laboratory into an automated system to support both student training and research in single and multiphase flows through porous media. The system provides an advanced platform to measure pressure drop and to investigate flow regimes for single-phase flow of a gas or liquid, or for multiphase gas-liquid flows. The automation package is based upon a Siemens 505 PLC with a Wonderware Intouch™ Human Machine Interface (HMI) and is configured for either manual or automatic operational modes. The instruments used to measure the various process parameters, the process and instrumentation diagram, operator interface and experimental protocols are described. Pressure drop experiments were performed using air and water through the packed column to illustrate limitations associated with the current setup, and to provide data needed for comparison to existing correlations for single and two-phase flow pressure drop. The results of this research will provide a novel experimental facility for hydrodynamic measurements of single and multiphase flows in the presence of various granular media and more complex fluids in various flow regimes to support development and validation of advanced computational fluid dynamic models.
Comment by Graduate Studies.: All the page numbers should be of 12 points fort and at ½ inch margin from the bottom of the page.
ACKNOWLEDGMENTS
I would like to thank my committee chair, Dr. Patrick L. Mills, for his technical guidance and support throughout the course of this research and for his suggestions during the hands-on work in the lab. I also thank Mr. Brian West from West Consulting Automation for his expert assistance in designing the PLC-based system and implementing a unique Human Machine Interface (HMI) for data acquisition and control of the packed column system located in the Kleberg 139 Unit Operations Laboratory. Comment by Graduate Studies.: Line spacing of 2.0
I would also like to thank my committee members and other department faculty for sharing their knowledge in this field.
Finally, I wish to thank all my friends, colleagues, and the department faculty and staff for making my time at Texas A&M University-Kingsville a great experience.
TABLE OF CONTENTS
ABSTRACT…………………………………………………………………………………….iii
ACKNOWLEDGEMENTS…………………………………………………………………...iv
LIST OF FIGURES……………………………………………………………………………v
LIST OF TABLES…………………………………………………………………………......vii
1 CHAPTER 1. 1
1.1 Overview of Packed Columns 1
1.2 Types of Packings 2
Random packings 2
Structured packings 3
1.3 Overview of Packed Column Design 3
2 CHAPTER 2. 6
2.1 LITERATURE REVIEW 6
2.1.1 Hydrodynamics 6
2.1.2 Pressure Drop: 6
2.1.3 Flow Regime 14
2.1.4 Flow Regime Transition 17
2.1.5 Liquid Holdup 18
3 CHAPTER 3. 19
3.1 RESEARCH OBJECTIVES 19
3.1.1 General Objectives 19
3.2 Specific Objectives 19
3.3 EXPERIMENTAL SETUP 20
Overview. 20
3.3.1 Experimental Procedure 23
3.4 Key Results and Discussion 24
3.4.1 Single phase cold flow conditions 24
3.4.2 Multiphase Cold Flow Conditions: 27
3.4.3 Flow Regime Transitions 31
3.4.4 Drawbacks for Existing Packed Column 33
3.4.5 Automation of Packed Bed 35
3.4.6 Human Machine Interface 37
4 CHAPTER 5. 40
4.1 SUMMARY AND CONCLUSIONS 40
4.2 FUTURE WORK 41
5 REFERENCES 42
6 NOMENCLATURE 46
7 APPENDICES 48
7.1 APPENDIX A 48
7.1.1 Sample Calculations 48
7.2 APPENDIX B: 50
7.3 APPENDIX C: 74
7.4 APPENDIX D: 80
7.5 APPENDIX E: 86
8 VITA 87
LIST OF FIGURES Comment by Graduate Studies.: Move to next page.
Where is figure 1,3,5?
Figure 2
:
Random Packings [36]
3
Figure 4: Excel simulator proposed by Larachi et al (1993)
13
Figure 6: Flow regimes in a trickle bed reactor: Fig. 6a: Trickle-flow regime; Fig. 5b: Pulse flow regime; Fig. 6c: Spray flow regime, and Fig 6d: Dispersed bubble flow regime [29].
15
Figure 8: Lab Scale Packed Column 22
Figure 9.1: Experimental Pressure Drop vs Superficial Gas Velocity
24
Figure 10.2:
Experimental vs Predicted Values of Pressure Drop (Ɛ=0.68)
26
Figure 11.2:
Experimental vs Predicted Values of Pressure Drop (Ɛ=0.51
26
Figure 12
: Experimental Pressure Drop vs Air Mass Velocity
27
Figure 14: Determination of Loading and Flooding Points
28
Figure 15(a)
: Experimental vs Predicted Pressure Drop for L=1.079 kg/m
2
-s
29
Figure 16(a)
: Experimental vs Predicted Pressure Drop for L=2.158 kg/m
2
-s
30
Figure 17
: Pressure Drop Correlation by Eckert
31
Figure 19
: Flow Regime Map by Fukushima-Kusaka
32
Figure 21: Human Machine Interface of Automated System
37
Figure B 1
: Experimental vs Predicted Pressure Drop for L=3.236 kg/m
2
-
56
Figure B 2
: Experimental vs Predicted Pressure Drop for L=4.315 kg/m
2
-s
57
Figure B 3
): Experimental vs Predicted Pressure Drop for L=5.394 kg/m
2
-s
58
Figure B 4
: Experimental vs Predicted Pressure Drop for L=6.473 kg/m
2
-s
60
Figure B 5
: Experimental vs Predicted Pressure Drop for L=7.552 kg/m
2
-s
61
Figure B 6
: Experimental vs Predicted Pressure Drop for L=8.631 kg/m
2
-s
62
Figure B 7
): Experimental vs Predicted Pressure Drop for L=9.709 kg/m
2
-s
63
Figure B 8
: Experimental vs Predicted Pressure Drop for L=10.788 kg/m
2
-s
64
LIST OF TABLES
Table 1
: Pros and Cons of Random and Structured Packings.
4
Table 2: Pressure Drop Correlations for Two-phase Flow in Packed beds.
8
Table 3: Summary of Pressure Drop Data & Model Predictions
25
Table 4: Minimum a
n
d Maximum Operating Ranges
39
Table B 1: Pres
s
ure Drop Calculations for Single Phase Flow
50
Table B 2
: Pressure Drop vs Air Mass Velocity
50
Table B 3
50
Table B 4 .
51
Table B 5
52
Table B 6
: Comparison of Experimental vs Predicted Pressure Drop
54
Table B 7
(a): For Liquid Mass Velocity, L = 1.079 kg/m
2
-s
54
Table B 8
(b): For Liquid Mass Velocity, L = 2.158 kg/m
2
-s
54
Table B 9
(c): For Liquid Mass Velocity, L = 3.236 kg/m
2
-s
55
Table B 10
(d): For Liquid Mass Velocity, L = 4.315 kg/m
2
-s
56
Table B 11
(e): For Liquid Mass Velocity, L = 5.394 kg/m
2
-s
57
Table B 12
(e)
58
Table B 13
(f): For Liquid Mass Velocity, L = 6.473 kg/m
2
-s
59
Table B 14
(g): For Liquid Mass Velocity, L = 7.552 kg/m
2
-s
60
Table B 15
(h): For Liquid Mass Velocity, L = 8.631 kg/m
2
-s
61
Table B 16
(i): For Liquid Mass Velocity, L = 9.709 kg/m
2
-s
62
Table B 17
(j): For Liquid Mass Velocity, L = 10.788 kg/m
2
-s
63
Table B 18
: Pressure Drop Correlation by Eckert
64
Table B 19
: Flow Regime Map by Charpentier-Favier
67
Table B 20
68
Table B 21
69
Table B 22 .
70
Table B 23
: Flow Regime Map by Fukushima-Kusaka
71
Table B 23
72
Table B 23
73
Table C 1
:
Equipment Table
74
Comment by Graduate Studies.: Remove continued titles for all.
Table C 1
75
Table C 1
76
Table C 1
77
CHAPTER 1. Comment by Graduate Studies.: All the content should start from 1 inch margin at the top of the page.
1.1.
Overview of Packed Columns Comment by Graduate Studies.: Where is topic number.
Review and correct for all the topics throughout the manuscript.
Packed towers are a particular type of fluid-fluid contactor that have been widely used in the process industries mainly for either gas absorption or liquid stripping operations. For example, packed columns are used in pollution abatement to remove one or more toxic gaseous species from stack gases by scrubbing with a suitable scrubbing liquid.
A schematic of a typical packed column is shown in Figure 1. A typical packed tower consists of vertical process vessel equipped with various external ports for introduction and removal of the process fluids, such as gases and liquids or partially miscible liquid phases. The column internals consist of various hardware for distribution, redistribution and separation of the gas and liquid phases or other process fluids, a grid system for supporting the column packing, and possibly special-purpose hardware for control of column temperature. In the countercurrent mode of fluid-fluid contacting, the process gas is introduced at the bottom of column and the process liquid is introduced at the top.
Packed towers are sometimes chosen over tray towers since they can exhibit a lower pressure drop than tray towers and can exhibit higher efficiency when compared to tray columns using one or more mass transfer parameters as the basis, such as height equivalent to a theoretical plate. Also, packed column configurations can provide substantially larger fluid-fluid specific contacting area for interphase heat and mass transport, they can handle a broader range of liquid to gas mass velocities without a deterioration in performance, the packing can be fabricated using a wider range of materials of construction for improved corrosion resistant, and they are more suitable for foaming systems.
For the countercurrent mode of contacting, the liquid flows downward the column and the gas move upward the column through the packing. In the case of the low gas-liquid interaction regime, the liquid phase is the discontinuous phase, and the gas is the continuous phase [34]
There are two types of packings in packed towers, structural and random. The packing provides a surface where the two fluids can come into intimate contact so that local mass and heat transfer processes can occur. Also, the packing is commonly an inert material, such as ceramic or plastic rings, which is explained below in more detail.
Comment by Graduate Studies.: Below 1 inch margin. Move up.
Figure 1: Packed Column [33] Comment by Graduate Studies.: 12 points, black font.
Remove italics.
The performance of a packed column depends on various parameters, including the macroscopic and microscopic liquid and gas distribution, pressure drop, liquid holdup, gas-liquid flow regime, extent of liquid-solid contacting, heat and mass transfer rates, and gas-liquid specific interfacial area. One source of energy loss that occurs is largely manifested in the form of pressure drop. Therefore, knowledge of pressure drop and flow regime are crucial in predicting the performance of packed column.
1.2.
Types of Packings
Random packings: Random packings have been used for fractionation, absorption and stripping in gas, refinery, and chemical plants. Ease of replacement and storage makes random packing the ideal choice for systems with heavy fouling or corrosion where packing should be frequently replaced. They are available in metal, plastic, ceramic and glass. Figure 2 shows some examples of packings including Pall rings, Raschig rings, Intalox saddles, Berl saddles, snowflake plastic, flexi saddles, and ballast saddles.[35].
Figure 2: Random Packings [36]
Structured packings: Structured packings are packing elements made from perforated metal sheets or from a wire mesh. Material is arranged with regular geometry to provide high surface area with high void fraction. They are available in metal, glass, ceramic and plastics. Figure 3 shows some examples of structured packings, such as Mellapak, Mellagrid, BX gauze paking, CYgauze packing, Mella carbon, Rambopak, DX laboratory, and Katapak. Structured packing has an advantage over random packing for their lower HETP and low pressure drop [35]. A comparison between the process parameters random and structured packings is given in Table 1.
Figure 3: Structured Packings [37] Comment by Graduate Studies.: Center.
1.3.
Overview of Packed Column Design
Important hydrodynamic parameters that are needed either for packed column design or rating of performance include overall pressure drop, flow regime, flow regime transition, and liquid holdup. In the case of two-phase countercurrent flow, these parameters have been the subject of numerous experimental studies as well as efforts to develop empirical correlations using data that was measured under a variety of conditions. In a number of cases, the scope of experimental variables investigated, such as gas and liquid mass velocities, gas and liquid fluid transport properties and other related physical properties, column diameter and height, column packing material of construction, shape, and size, and flow regime has been very limited. In addition, the experimental systems often employ various manually operated control systems along with very basic instruments for measurement of key response variables, such as the differential pressure drop across the packed section. Hence, a need exists for an experimental facility where a more modern approach to system operation is utilized and the parameter space can be defined by a broader scope of experimental parameters. This would allow students to obtain a better understanding of the physics associated with packed column systems and to acquire response data that covers a broader range of parameter space.
Table 1: Pros and Cons of Random and Structured Packings.
Process Parameters
Random Packing
Structured Packing
Raschig Rings & Saddles
Through Flow
Relative Cost
Low
Moderate
High
Pressure Drop
Moderate
Low
High
Efficiency
Moderate
High
Very High
Vapor Capacity
Fairly High
High
High
Typical Turndown Ratio (max/min vapor capacity)
2
2
2
*Data is collected from web-sited of companies that manufacture column packings [38]
This research is focused upon modification of the existing packed column system located in the Unit Operations Laboratory in Kleberg Hall 139 as part of a larger effort aimed at modernization of various experiments used for teaching the unit operations sequence of courses. The proposed configuration will allow pressure drop measurements to be performed using a high frequency response transducer for a user-defined set of gas and liquid flow rates using either a single-phase air or an air-water multiphase system. The resulting pressure drop data will allow investigation of flow regime, flow regime transitions, and other flow phenomena, such as column flooding, thereby providing students with more in-depth knowledge on the hydrodynamics of single-phase and multiphase flow through porous media.
Comment by Graduate Studies.: Remove extra blank page.
CHAPTER 2.
LITERATURE REVIEW Comment by Graduate Studies.: Center.
Hydrodynamics
Various transport processes in packed columns depend upon the fluid flow regime, which in turn depends on the gas and liquid mass velocities and packing dimensions. Various flow regimes exist for countercurrent gas-liquid flow such as trickle flow, pulsing flow, spray flow and wavy flow [34]. In the trickle-flow regime or low gas interaction regime, a discontinuous flowing liquid phase trickles over the packing in the form of streams, rivulets and droplets while the continuous flowing gas phase fills the remaining void space that is not occupied by the liquid and packing.
Understanding the hydrodynamics of packed columns is a key aspect associated with prediction of their design and performance. The hydrodynamics in this fluid-fluid contactor can be described through a mechanistic approach rather than a complex fundamental viewpoint. A description of macroscale and microscale phenomena in trickle-bed reactors, which consist of a packed bed of catalyst with cocurrent downflow of gas and liquid, are provided by Dudukovic and Mills.[21] The performance of a trickle-bed reactor can be partly characterized based on the macroscopic hydrodynamic parameters such as pressure drop, flow regime, liquid holdup, and liquid-solid contacting. All these parameters must be quantitatively evaluated to support the evaluation of reactor performance on various scales of operation. To analyze the performance of packed towers, the same parameters must be evaluated to support the solution of the overall mass, specie, and energy balance relationships that described the packed column performance. This research focuses on development of an automated system for measurement of pressure drop and flow regime where measurements are first performed using the existing manual system to identify existing limitations that must be overcome.
Pressure Drop:
A knowledge of pressure drop is important for estimation of feed pressure, pump and compressor capacities, and for predicting parameters such as liquid holdup, and transport coefficients [1, 2, 18, 19]. A large number of correlations and theoretical models can be found in the literature for prediction of two-phase pressure drop through a packed bed. Table 1 summarizes selected pressure drop correlations for multiphase gas-liquid flow through packed beds. A majority of the correlations are based on the Ergun equation [21] as shown below in eq. (1). In many cases, the modified Lockhart-Martinelli two-phase flow parameters were utilized to capture the presence of both gas and liquid phases as well as the effect of fluid physical properties. Comment by Graduate Studies.: Indent.
Indent all the new paragraphs.
38
Table 2: Pressure Drop Correlations for Two-phase Flow in Packed beds. Comment by Graduate Studies.: Remove italics.
Refer thesis template/manual for guidance.
Equation
Information
Gas-Liquid System
Reference
Column Dimensions
Packings
Pressure Drop & Liquid Holdup Correlation
Air-water, and other fluids
[10]
Spheres (3/8", 3mm), Cylinders (1/8")
2" and 4" ID,
7 ft. high
Pressure Drop & Liquid Holdup Correlation, Flow map
Air-water
[11]
Glass spheres (2.59-16.5 mm)
122mm and 65.8 mm ID
Pressure Drop &
Liquid Holdup (All flow regimes)
Air-water
[12]
0.3-in. tabular alumina
2", 4" and 6" dia, 7ft high columns
Table 2. Continued Comment by Graduate Studies.: Below 1 inch margin. Move up .
Remove parenthesis.
Liquid Holdup (High and Low Interaction Regimes)
Air-water, and other liquids
[13]
Glass Spheres (6mm), Cylinders
(5.4 mmx5.4 mm,
2.7 mmx2.7 mm)
0.08 m dia,
1.05 m high
Pressure Drop & Liquid Holdup Correlation (Trickle & Pulsing
Flow)
Air-silicone
[14]
1.04 mm, 1.39 mm, 3.35 mm extrudates
55 mm ID and 1.5 m high
Table 2. Continued
Liquid Holdup (High and Low Interaction Regimes)
Air-water, and other liquids
[15]
Glass Spheres (6mm), Cylinders
(5.4 mmx5.4 mm,
2.7 mmx2.7 mm)
0.08 m diameter,
1.05 m height
New Pressure Drop Correlations for Industrial
Reactors
Air-water, and other liquids
[16]
Spheres and cylinders (1.16-3.06 mm)
23-100 mm ID, 0.49 - 2
m high
A=6.96; B=53.27; C=200; D=85; j=-2; k=-1.5; m=-1.2; n=-0.5
New Pressure Drop Correlations for Industrial
Reactors
Air-water, and other liquids
[17]
Spheres and cylinders (1.16-3.06
mm)
23-100 mm ID, 0.49 - 2
m height
Table 2. Continued
Pressure Drop, Liquid Holdup and Flow Regimes
Various
[18]
Various
Various
As explained in a later section, pressure drop data was collected using the packed column system located in Kleberg Hall room 139. The experimental data were compared to values predicted from the correlations of Midoux et al. (1997) and also the generalized correlation described by Larachi et al. (1993). These two correlations are summarized below for later reference. Comment by Graduate Studies.: Indent all new paragraphs.
Midoux et al. (1997) [31]
Larachi et al. (1993) [17]
The above correlation for the friction factor given above was developed by Larachi et al. (1997) using NNfit software with over 60,000 literature data points. The resulting equations were implemented in MS Excel and are available at the following URL:
http://www.gch.ulaval.ca/flarachi
/
. The user interface is shown below in Figure 4.
Referring to Figure 4, the cells highlighted in blue correspond to data that must be input by the user, such as the liquid-phase properties, the gas-phase properties, and the bed properties. The liquid and gas phase properties include various transport and thermodynamic properties as well as the liquid and gas mass velocities. The bed properties include the diameter and height of the packed column section. The calculated results are highlighted in red and include the flooding capacity, the loading capacity, the liquid holdup, the overall pressure drop, the flow regime and the various volumetric mass transfer coefficients at the gas-liquid interface. Comment by Graduate Studies.: Remove boldface.
The Excel simulator can be used in one of two alternate ways. In the first method, predictions can be made using existing packings that are already available in data bank. Alternately, predictions can be made by using packing characteristic supplied by the user. The packing properties can be varied in the box highlighted in color, green.
Figure 4: Excel simulator proposed by Larachi et al (1993)
Flow Regime
A packed bed or a trickle bed reactor can be operated in various flow regimes that were broadly classified as the low interaction regime and the high interaction regime. A popular flow regime map developed by Charpentier and Favier (24) is shown in Figure 4. It is based on the so-called Baker coordinates in which the dimensionless group Lλφ/G is plotted against G/λ where λ and φ are parameters that are dependent on fluid properties. Each of these parameters assumes a value of unity when the fluids are air and water. Depending on the values for these dimensionless groups, three flow regimes can exist, namely, the trickling flow regime, the pulsing flow regime, and the spray flow regime. Qualitative features of these flow regimes will be discussed later in this section. The qualitative features of each flow regime are illustrated in Figure 5.
Figure 5: Flow map proposed by Charpentier & Favier, 1975 [24] Comment by Graduate Studies.: Remove extra blank spacing.
One significant aspect associated with identification of the flow regime is that the magnitudes of various key reactor parameters, such as the axial and radial mixing characteristics of the gas and liquid phases, pressure drop, particle-scale liquid-solid contacting efficiency, reactor-scale gas and liquid distributions, and heat and mass transfer coefficients, will depend on the particular flow regime where the reactor is operating [1]. However, the transition from one flow regime to another may differ for foaming and non-foaming systems, along with other hydrodynamic parameters [22, 23].
Figure 6: Flow regimes in a trickle bed reactor: Fig. 6a: Trickle-flow regime; Fig. 5b: Pulse flow regime; Fig. 6c: Spray flow regime, and Fig 6d: Dispersed bubble flow regime [29]. Comment by Graduate Studies.: 12 points font.
The designation of a foaming system suggests that a frothy mass of fine bubbles forms at liquid surfaces or at the gas-liquid interface in the presence of flowing gas phase. For example, certain hydrocarbons, such as kerosene, desulfurized and non-desulfurized gas oils, have a tendency to foam whereas organic compounds, such as cyclohexane, gasoline, and petroleum ether do not exhibit this behavior [24]. In industrial practice, some hydrocarbon systems may begin to foam depending on fluid properties, such as surface tension and viscosity. Sometimes, anti-foaming agents or so-called defoamers are added to inhibit foam formation [23]. Therefore, some studies in the literature on pressure drop, flow regime, and flow regime transition have utilized non-foaming systems in experiments. Since air and water are the two fluids used in this work, the results apply to non-foaming systems only. The key characteristics of various flow regimes for a non-foaming system are described below.
a. Low interaction regime. This regime (Figure 5a) is also known as the trickle-flow regime and is observed at low gas and liquid flow velocities in which the liquid phase trickles over the packing in the form of streams and thin films with a minimum interaction with the continuous flowing gas phase. This flow regime promotes stable reactor operation and longer residence times for the liquid phase as desired for chemistries in which observed local reaction rate is relatively slow when compared to other local transport processes. However, reactor operation in the trickle-flow regime may not be preferred when higher heat and mass transfer coefficients are required for reactions whose observed rate may be limited by external transport resistances [26].
b. High interaction regime. This regime is characterized by a significant amount of gas-liquid interaction that is induced by an appropriate combination of gas and liquid mass velocities, gas and liquid fluid properties, packing geometry, packing characteristics, bed voidage distribution, temperature and pressure. The high gas interaction regime can be further classified into the pulse flow, dispersed bubble flow, and spray flow regimes. Each of these regimes is briefly described below.
a. Pulse flow regime. This flow regime (Figure 5b) is characterized by high gas and liquid mass velocities that produces a high degree of interaction between the flowing gas and liquid phases and the stagnant solid catalyst. It is sometimes referred to the pulsing flow
regime. At sufficiently high liquid flow rates, the catalyst surfaces are substantially wetted, which leads to the formation of bridges of liquid phase between the catalyst particles. These liquid bridges are ruptured and subsequently pushed downward by the gas flowing through the bed as soon as they grow to a sufficiently large size. As a result, alternating liquid and gas rich slugs (or “pulses”) can be observed flowing through the catalyst bed. This leads to an increased pressure drop across the packed bed and generates fluctuations in the liquid holdup. Comment by Graduate Studies.: Align left.
Fix. Comment by Graduate Studies.: Fix.
b. Spray flow regime. The spray or mist flow regime (Figure 5c) is achieved at very high gas-to-liquid flow ratios and is characterized by a very high degree of gas-liquid interactions as a result of significant drag at the local gas-liquid interface. The magnitude of the drag is large enough the liquid phase is broken down into tiny drops that are subsequently entrained in the downward flowing continuous gas flow. This regime is not very common in the industry because most reactions conducted in practical applications require higher liquid to gas flow ratios for significant reactant conversion to occur. Since it is very difficult to discern a boundary between the spray flow and trickle-flow regimes by simple visual observations, both are sometimes grouped together and described as the gas continuous flow regime [12, 25].
c. Dispersed bubble flow regime. The dispersed bubble flow regime (Figure 5d) occurs at sufficiently low gas velocities and high liquid-to-gas flow ratios. These ratios cause the gas phase to be broken down into small bubbles that flow through the continuous liquid phase as a dispersed phase. This phenomenon also results in a high level of interaction between the flowing gas and liquid phases and the stagnant catalyst particles. This flow regime is characterized by rapid fluctuations in the column hydrodynamic, such as the pressure drop, liquid holdup, and the gas-liquid specific interfacial area.
Flow Regime Transition
Flow regime transition is generally concerned with the various multiphase flow phenomena that occur when changes in various system parameters, such as the gas and liquid mass velocities, physical properties of the gas and liquid phases, and catalyst bed characteristics, results in a transformation in the flow regime from one regime to another. This change either may or may not be readily discernible by normal visual observations. Nevertheless, the ability to predict flow regime transition is important in the analysis and prediction of reactor performance and operation. Other parameters, such as pressure drop, liquid holdup, liquid-solid contacting, and mass transfer coefficients, to name a few, are also dependent on the flow regime. Therefore, significant research has focused on identifying the transition from trickle flow to pulse flow or bubble flow, and on quantifying the associated hydrodynamic parameters. Many authors have proposed flow maps and correlations to identify transition from one regime to another. For example, Figure 1 shows the first flow map proposed by Charpentier & Favier, 1975 that is accepted widely in literature.
Liquid Holdup
There are two different types of liquid holdup in a packed bed since the total liquid hold up is the sum of both the static and dynamic holdup.
a. Static Holdup. Static holdup represents the volume of liquid per volume of packing that remains in the bed after the gas and liquid flows are brought to an abrupt stop and the bed has drained. It depends on packing surface area, roughness of packing surface, contact angle between the packing surface and the liquid and system properties. The static holdup has been correlated using the Eötvos number (Saez et al., 1991).[39]
b. Operating/Dynamic Holdup. The dynamic holdup corresponds to the volume of liquid per volume of packing that drains out of the bed after the gas and liquid flows to the column are abruptly stopped. Liquid holdup is an important parameter in packed column design and operation since it is related to the residence time of the actively flowing liquid phase and also contributes to the effective local thermal capacity of the combined packing and fluid that are present. Dynamic holdup is generally a function of the gas and liquid flow rates, gas and liquid physical properties, and packing characteristics.
CHAPTER 3.
RESEARCH OBJECTIVES Comment by Graduate Studies.: Center.
General Objectives
Main research objective is to identify the shortcomings associated with the controls, instrumentation, and operation of the existing packed column system in the Unit Operations Laboratory in view of the ABET assessment and perform experiments (1) to determine pressure drop (2) to observe flow regime transitions and (3) to compare the measured pressure drops with those calculated using existing correlations for both single phase gas flow and two-phase gas-liquid flow.
Specific Objectives
Identify the shortcomings associated with the controls, instrumentation, and operation of the existing packed column system in the Unit Operations Laboratory in view of the ABET assessment.
Perform experiments to determine allowable range of operation for existing system in terms of gas and liquid mass velocities, pressure drop, flooding and flow regime transition. Then, compare the experimental measurements to existing correlations for pressure drop and flow regime to assess the validity of these correlations and to expand the scope of existing methods used for data analysis since this is currently based on simple Ergun equation-like analysis.
Design a modern PLC-based process control and data acquisition system using the existing packed column system as the initial platform that can be expanded in the future. Design and implement a unique Human Machine Interface (HMI) for control of the overall system, various sub-systems, and implementation of experiments and develop recommendations for future work.
EXPERIMENTAL SETUP
The experimental setup currently used in the Unit Operations Laboratory is described in this section. This includes an overview of the experimental objectives of interest for this particular application and the limitations of the current experimental setup shown in the process and instrumentation diagram (P&ID) and as well as a photograph reference.
Overview.
The primary objectives of this experiment are: (1) to determine overall pressure drops at various gas and liquid rates; (2) to determine the loading point and the flooding point at various liquid flow rates starting with “dry” conditions; (3) to observe flow regime transitions; (4) to compare the measured pressure drops with those calculated using existing correlations for both single phase gas flow and two-phase gas-liquid flow; and (5) to compare experimental data for flow transition in two-phase gas-liquid flow with predictions using existing correlations.
By varying the gas and liquid inlet flow rates, the pressure drop behavior, gas-liquid flow regimes and flow-regime transitions can be studied. Manual controls are used for flow rate settings using basic process control elements such as rotameters, pressure regulators and gauges. A U-tube manometer is utilized for pressure drop measurements. This manometer is not capable of capturing high frequency pressure drop fluctuations. Also, Flooding point at various liquid flow rates could not be determined due to gas bypassing, and this setup is limited to countercurrent mode of gas liquid contacting.
Rotameter for Air Flow
Rotameter for Water Flow
Ballast Tank
City Water Supply
Figure 7: Piping and Instrumentation Diagram of Existing Packed Column System
Comment by Graduate Studies.: Figure out of 1 inch margin.
Move in .
Figure 8: Lab Scale Packed Column
Raschig Rings
Pump
Rotameter for Water
Rotameter for Air
Air Inlet
Air Outlet
Water Inlet
Water Outlet
Manometer
Figure 5: Lab Scale Packed Column
3-in. ID x 60-in. H
Figure 8. Lab Scale Packed Column
Experimental Procedure
The experiment involves determination of pressure drop (inches of H2O) per foot of packing (∆P/L) for various air and water flow rates. The dimensions of the packed column are 5 ft. long with an inner diameter of 3-in. that is packed with ¼-in. by 3/8-in. Raschig rings. Air is fed from the bottom of column from the compressed air lab header and water from the top of column from the city water supply. Both air and water flow rates are controlled by rotameters on a scale of 0 to 100 with a scaling factor of 0.0418 for air to convert flow in terms of SCFM and a scaling factor of 0.0078 for water to convert in terms of gpm.
a. Single phase operation:
With damp packing and no water flow, turn on the air flow and wait until a steady state is attained. Then note down the manual reading given by manometer, which shows difference in water column in terms of inches of water column (units for pressure drop). This process is repeated by increasing the gas flow rate and note down the respective manometer readings.to determine pressure drop, loading and flooding points.
b. Multi-phase operation:
With damp packing and no water flow, turn on the air flow and wait until steady state is attained, then turn on the water flow. Make sure to wait some time till steady state is attained and then note the manometer readings. This process is repeated for various flow rates of air and water to determine the pressure drop, gas mass velocity, superficial velocity and also study hysteresis effect.
Key Results and Discussion
Single phase cold flow conditions
Data was collected for following operating range, analyzed for trends and compared experimental data with predicted correlations.
Gas Flow: 0.418 to 4.18 SCFM
Air compressor is turned on, keeping the water flow at zero. Gas flow rates are increased gradually, and corresponding pressure drop is noted from manometer. Figure 9.1 depicts the behavior of superficial velocity on pressure drop for a single-phase flow.
Also, for single phase flow, experimental pressure drop is not in correlation with Ergun equation for given porosity of system (Ɛ=0.68). But, for a reduced voidage (Ɛ=0.51), most of the experimental data is in correlation with predicted values based on Ergun equation. It is evident that the voidage has been reduced due to local accumulation of fouling material in packing (figure 9.3), because the system is installed 40 years ago and has not been cleaned since then.
Figure 9: Experimental Pressure Drop vs Superficial Gas Velocity
Ergun equation used to calculate pressure drop for voidage of 0.68 and sphericity of 0.85
Table 3: Summary of Pressure Drop Data & Model Predictions
Mode
Gm
Lm
P/L
P/L
P/L
lbm/ft2-hr
lbm/ft2-hr
Experimental
Predicted Model 1
Predicted Model 2
min
max
min
max
in H2O/ft
in H2O/ft
in H2O/ft
min
max
min
max
min
max
Single-Phase Flow
ε = 0.68
0
396
-
-
0
0.62
0
0.17
-
-
Single-Phase Flow
ε = 0.51
0
396
-
-
0
0.62
0
0.67
Multiphase Flow ε = 0.68
38
383
795
3181
0.03
2.76
0.01
0.05
0.005
0.2
Multiphase Flow ε = 0.51
38
383
795
3181
0.03
2.76
0.02
0.1
0.016
2.0
Figure10.1: Experimental vs Predicted Values of Pressure Drop (Ɛ=0.68)
Figure10.2: Experimental vs Predicted Values of Pressure Drop (Ɛ=0.51)
Multiphase Cold Flow Conditions:
Data was collected for following operating range, analyzed for trends and compared experimental data with predicted correlations.
Gas Flow: 0.418 to 4.18 SCFM
Liquid Flow: 0.078 to 0.312 gpm
For multi-phase operation, gas flow rate is first set to zero and column is allowed to wet for some time. Now, rotameter for gas flow is turned on and manometer reading is noted for a given flow rate of air and water. Liquid flow rate is kept constant and gas flow rate is increased gradually, while noting the manometer readings, and then readings are noted for the same liquid flow rate and decreasing the air flow rate. Figures 11 and 12 shows how pressure drop increases with increase in gas flow rate, but the data is limited for higher flow rates of gas and for cold flow conditions. Graphically, flooding and loading points are determined by plotting pressure drop of column against gas mass velocity. A point where the orientation of graph is changed is located as loading point and the path where it takes sudden peak is located as flooding point.
Figure 11: Experimental Pressure Drop vs Air Mass Velocity
4772
Figure 12: Experimental Pressure Drop vs Air Mass Velocity
Figure 13: Determination of Loading and Flooding Points
Mode of operation is same as described above for a multi-phase flow. Figures 14(a) and 14(b) shows the comparison of experimental values vs predicted using two correlations by Midoux and Larachi. Because of fouling in packing, porosity of existing system is changed to 0.51 (as observed for single phase operation). Larachi’s excel simulator is used to generate results for various gas and liquid flow rates for porosities 0.68 and 0.51 in multiphase flow. A huge error was observed between experimental and predicted values for given porosity of system, but the system is in correlation with Larachi’s predicted data, generated for porosity of 0.51.
Hysteresis was also exhibited by the system, mainly at higher gas flow rates. This observation is reported by many authors [4,5,32]. Figure 14 (a-b) shows the hysteresis effects observed a various gas and liquid flow rates. At high gas and liquid flow rates, liquid flows down in form of channeled rivulets through relatively dry packing and spreads to other parts of packing that were not in contact with liquid earlier (at low liquid flow rates). Once the liquid flow rate is high enough, a portion of packing gets covered in a thin film of fluid. This film should be broken by gas flow. Therefore, liquid flow is decreased, and the gas encounters higher pressure drop than, when compared to higher liquid flow rates.
Figure 14(a): Experimental vs Predicted Pressure Drop for L=1.079 kg/m2-s
Comment by Graduate Studies.: Below 1 inch margin. Move up.
Figure 14(b): Experimental vs Predicted Pressure Drop for L=2.158 kg/m2-s
Figure 15 is re-defined plot of pressure drop correlation by Eckert for the existing system. This graph helps in predicting the pressure drop for given gas and liquid flow rates.
Figure 15: Pressure Drop Correlation by Eckert
Flow Regime Transitions
Using the same mode of operation for multi-phase flow, flow regime maps developed with experimental data and are compared to the maps developed by Charpentier-Favier [24] and Fukushima-Kusaka[30]. From the plot, one can see that the existing system only operates in trickling and pulsing flow regime. The operating conditions correspond to a very low gas to liquid ratio, quite common in the industry but rarely encountered in literature Operation at higher flow rates in packed column should be studied to know more about flow regime transitions (visually).
To obtain more consistent readings (represents industrial columns), column should be subjected to high interaction regimes. So, there is a need to upgrade the existing system to automation.
Pulsing Flow
Spray Flow
Trickling Flow
Figure 16: Flow Regime Map by Charpentier-Favier Comment by Graduate Studies.: Placement of figures is consistent.
Figure 17: Flow Regime Map by Fukushima-Kusaka
Drawbacks for Existing Packed Column
System is controlled manually, pressure drop (∆P) measurements and flow regime transition from low interaction to high interaction are limited by ranges for gas and liquid flow rates. Flooding cannot be approached due to gas bypassing at liquid seal of system (“U” neck installation at bottom). Simple manometer is used for pressure drop measurements and (manual data collection) it cannot capture higher frequency fluctuations which are indicative of flow regime transition. Also, experimental values are noted manually, and data collection has limited the scope of experimental studies. System is also limited to single column size (H, D, H/D), single packing type (Raschig rings) and single mode of gas-liquid contacting (countercurrent).
I. AUTOMATION OF PACKED COLUMN
Figure 18: Piping and Instrumentation Diagram of Automated System
Automation of Packed Bed Comment by Graduate Studies.: This should be on page 35 according to ToC.
Carefully review all the page numbers for all titles/figures/tables and make corrections accordingly.
Determination of pressure drop can be carried out in an automated system of packed column for a single-phase gas flow and two-phase liquid-gas flow under different contacting modes. Dimensions of column are 8ft long and 9 inch diameter (derived using excel worksheet of packed bed simulation by F.Larachi and B.P.A. Grandjean, Laval University, Canada). Types of packings to be used in this experiment can be started with spheres, pall rings and raschig rings with three different diameters (to maintain constant D/dp), and further study of pressure drop on fluid properties can be determined by changing the liquid media like ethylene glycol, methocel.
Air is introduced into the system from compressor to a 10-gallon ballast tank (T-1) through a ¾” PVC pipeline. The ballast tank provides a buffer volume between the header and the downstream piping system so that any upstream fluctuations in the header supply pressure, such as those due to intermittent operation of the compressor, are minimized. Both the pressure and temperature of air that enter the ballast tank are measured by a pressure transducer (PT-2) and temperature transmitter (TT-1). A manually operated forward pressure regulator (FPR-1) is located ahead of the ballast tank so air is supplied to the downstream test section at a relatively constant pressure. The exit side of the ballast tank is connected to a supply line that contains a mass flow controller (MFC-1) having an upper limit of 2000 SLPM based on air. The pressure upstream of the mass flow controller is measured with a pressure transducer (PT-3) while the pressure downstream of the mass flow controller is regulated by a manually operated back pressure regulator (BPR-1). The pressure on the exit side of the mass flow controller is measured with another pressure transducer (PT-4). A tee is located downstream of the back pressure regulator with a manually operated ball-valve (V-2) so the gas flow can be diverted to a wet test meter for calibration of the mass flow controller. A thermocouple (TT-2) is in close proximity of the column side port for a final measurement of the air temperature before it is introduced to the column. The air exit is located at the top of the column since the air and water flow in countercurrent flow. A pressure transducer (PT-7) is used to measure the pressure in the air vent line while the temperature is measured using an in-line thermocouple (TT-3).
Water is introduced to the system from the laboratory deionized water supply header. The tank level is monitored using a differential pressure transmitter (DPT-2) which is also used to actuate a level control valve (LCV-1). The water temperature in the tank is monitored using a thermocouple (TT-4). The tank can be drained through a two-way ball valve (BV-10) that is attached to one side of a tee in the tank exit line. The electrical power for the pump can be turned on or off through an 115V solid-state relay that is actuated from the HMI of the PLC. The fluid pressures at both the inlet and exit sides of the pump are measured by pressure transducers PT-9 and PT-10, respectively and fluid temperature at the pump exit is measured by an in-line thermocouple (TT-5). Under normal operation, the water is directed to the top of the column where the temperature is measured before being introduced using an in-line thermocouple (TT-6). The water exits the column through a glass pipe that is connected to the bottom head. The water temperature at the exit of the column is measured using another in-line thermocouple (TT-7).
The system is designed so the gas and liquid flow rates can be varied over wide ranges so the gas and liquid interaction can be varied from the low gas-liquid interaction (trickling flow) regime to the high gas-liquid interaction (pulsing flow or spray flow) regime. A differential pressure transmitter (DPT-1) connected across the packed section of the column provides a means of measuring the overall column pressure drop during process.
Since the system is automated, one can specify up to 15 different air flow rate and water flow rate data pairs at which pressure drop data would be recorded. In addition, each of air-water flow rate settings would be maintained for specified dwell times where the maximum dwell time is 10 minutes. Once all the flow rate settings have been selected, the flow rate sequence would be initiated, and the system would then proceed to record pressure drop vs flow rate data for the user-specified dwell-time. The resulting pressure drop versus flow rate data are then stored in a user-specified file on the computer system hard drive for subsequent data analysis. A standard operating procedure (SOP) for identifying column flooding will require development after the automation system is completed since this has not been done before with the current experimental setup.
Key Features for Automated System
1. Using of high-capacity liquid pump and gas mass flow controllers with greater ranges will expand the scope of differentia pressure (∆P) and flow regime measurements.
2. Installation of Liquid-level control system in column sump will prevent gas bypassing at all gas and liquid flow rates, thereby allowing flooding to be investigated.
3. Digital differential pressure transmitter has a response time that will measure higher frequency pressure fluctuations both in time domain and frequency domain.
4. HMI-PLC system allows user to specify up to 10 gas-liquid settings where data is recorded for a user-specified time and display in real time.
5. System is configured so that columns having various dimensions, column packing, column internals, and modes of gas-liquid contacting can be installed in the future.
Human Machine Interface
HMI is based upon Wonderware InTouch™ System Platform where system is installed with Siemens 505 Series Programmable Logic Controllers (PLC) with Control Technology, Inc. (CTI) input/output modules and supporting technology.
Key Features & Capabilities of this PLC are.
1. Analog Input/Output of Voltage or Current
2. Digital Input/Output for solenoids, relays, etc.
3. Wide range of temperature sensing devices
4. RS-232or RS-485 protocols for instruments
5. Ethernet to PC interface module
6. Other specialty modules and PID control
Figure 19: Human Machine Interface of Automated System
Figure 20: HMI Process Historian
Statistical Design for Experiment
Table 4: Minimum and Maximum Operating Ranges
Variables
Minimum
Maximum
QG
0
2000 slpm
QL
0
150 lpm
dp (in.)
1/4-in.
2-in.
Packing (S/V) (/m)
Variable
Packing material of construction
Ceramic, Plastic, Metal, or Catalyst support
Viscosity, (kg/m-sec)
1 x 10-3
1 x 10-2
Density, (kg/)
750
1500
CHAPTER 4.
SUMMARY AND CONCLUSIONS
Packed columns are one of the most capital-intensive components of commercial process technology and student training on various aspects, especially that gained through hands-on training, is well-justified and a useful addition to their education. Manual operation has notable merit and has been integrated into the automated system through proper design of the process control and data acquisition system. Existing packed columns that are commercially available for teaching purposes have limited capabilities and still require significant capital resources.
Significant progress has been made toward the completion of the packed column automation. The overall design automation control system has been finalized. The HMI and its underlying programming parameters for control have been developed with only minor adjustments and improvements remaining. The final programming parameters may not be available until the physical set-up is completed. The automation instruments and equipment needed have been ordered and received
The path forward largely depends on the available budget for the project and the overall installation of equipment, which will be an extremely involved process because of the number of instruments and the fact that support structures will need to be added to the current structure for some of the heavier equipment (namely control valves), adding to the already labor-intensive processes of piping and wiring the system. The two main possible options for moving forward with the installation of equipment and validation of HMI would be to request bids from professional contractors, or to establish a team of engineering students in relevant disciplines (chemical/mechanical/electrical). A combination of these two scenarios may be possible. For instance, the university may be able to find instrumentation/piping/control technicians or engineers working in the Corpus Christi area that would be willing to serve as advisers to an engineering team; then the completion of the project would provide a valuable learning experience to students. Also, the university would benefit by saving labor costs while still having professional oversight.
Upgrading the existing packed column system provides flexibility with desirable features and provides an attractive alternative for academic program improvement. Automation of a pilot-scale packed column for teaching and other training purposes requires significant effort as well as various financial and human resources for successful implementation.
FUTURE WORK
Raschig rings are used in current experiment to determine the pressure drop across column for single and multiphase mixtures. Pressure drop is not only a function of flowrates, phase properties but also voidage and packing/catalyst size. As our main aim is to fill the knowledge gap between low gas-liquid and high gas-liquid interaction regime, development of automated system is resourceful
Use the automated system to measure the pressure drop for different packings using single and multiphase fluid mixtures.
· Using various protocols for different contacting/flowrate modes.
· Implement tracer method for measurement of liquid holdup.
Columns having different diameters and heights with fluids having a wide range of fluid properties (µ, σ, ρ). can be installed to study the effect of column dimensions on pressure drop and flow regime transitions. Various dumped and structured packings that produce bed structures having various voidage distributions and ranges for packing surface to volume ratios can also be used.
Use various liquid and gas flow rates so that the flow regime is varied from low gas-liquid interaction regime to the high gas-liquid interaction regime and vice-versa to study hysteresis effects. Studying the hydrodynamic parameters at higher liquid and air flow rates can also be made for different column dimensions.
Compare the experimental measurements to existing correlations for pressure drop, flow regime and liquid holdup and update the existing Larachi data bank with newer data.
REFERENCES
1. Shah, Yatish T. Gas liquid solid reactor design. Vol. 327. McGraw-Hill International Book Company, 1979.
2. Ranade, Vivek V., Raghunath Chaudhari, and Prashant R. Gunjal. Trickle bed reactors: Reactor engineering and applications. Elsevier, 2011.
3. Kan, Kin-Mun, and Paul F. Greenfield. "Multiple hydrodynamic states in cocurrent two-phase downflow through packed beds." Industrial & Engineering Chemistry Process Design and Development 17.4 (1978): 482-485.
4. Levec, Janez, A. E. Saez, and R. G. Carbonell. "The hydrodynamics of trickling flow in packed beds. Part II: Experimental observations." AIChE journal 32.3 (1986): 369-380.
5. Kan, Kin-Mun, and Paul F. Greenfield. "Pressure drop and holdup in two-phase cocurrent trickle flows through beds of small packings." Industrial & Engineering Chemistry Process Design and Development 18.4 (1979): 740-745.
6. Rao, V. Govardhana, and A. A. H. Drinkenburg. "Pressure drop and hydrodynamic properties of pulses in two‐phase gas‐liquid downflow through packed columns." The Canadian Journal of Chemical Engineering 61.2 (1983): 158-167.
7. Ratheesh, S., and A. Kannan. "Holdup and pressure drop studies in structured packings with catalysts." Chemical Engineering Journal 104.1-3 (2004): 45-54.
8. Ellenberger, J., and R. Krishna. "Counter-current operation of structured catalytically packed distillation columns: pressure drop, holdup and mixing." Chemical Engineering Science54.10 (1999): 1339-1345.
9. Larkins, Robert Pruett, R. R. White, and D. W. Jeffrey. "Two‐phase concurrent flow in packed beds." AIChE Journal 7.2 (1961): 231-239.
10. Sai, P. S. T., and Y. B. G. Varma. "Pressure drop in gas‐liquid downflow through packed beds." AIChE journal 33.12 (1987): 2027-2036.
11. Larkins, Robert Pruett, R. R. White, and D. W. Jeffrey. "Two‐phase concurrent flow in packed beds." AIChE Journal 7.2 (1961): 231-239.
12. Sato, Yuji, et al. "Pressure loss and liquid holdup in packed bed reactor with cocurrent gas-liquid down flow." Journal of Chemical Engineering of Japan 6.2 (1973): 147-152.
13. Turpin, Jim L., and R. L. Huntington. "Prediction of pressure drop for two‐phase, two‐component concurrent flow in packed beds." AIChE Journal 13.6 (1967): 1196-1202.
14. Specchia, V., and G. Baldi. "Pressure drop and liquid holdup for two phase concurrent flow in packed beds." Chemical Engineering Science 32.5 (1977): 515-523.
15. Clements, L. D., and P. C. Schmidt. "Two‐phase pressure drop in cocurrent downflow in packed beds: Air‐silicone oil systems." AIChE Journal 26.2 (1980): 314-317.
16. Ellman, M. J., et al. "A new, improved pressure drop correlation for trickle-bed reactors." Tenth International Symposium on Chemical Reaction Engineering. 1988.
17. Larachi, F., et al. "Experimental study of a trickle-bed reactor operating at high pressure: two-phase pressure drop and liquid saturation." Chemical Engineering Science 46.5-6 (1991): 1233-1246.Dudukovic, Milorad P., and P. L. Mills. "Contacting and hydrodynamics in trickle-bed reactors." Encyclopedia of fluid mechanics 3 (1986): 969.
18. Gianetto, A. and V. Specchia, Absorption in packed towers with concurrent downward high-velocity flows: I-interfacial areas. Quaderni Dell'ingegnere Chimico Italiano, 1970. 6: p. 125-133.
19. Ergun, S. and A.A. Orning, Fluid flow through randomly packed columns and fluidized beds. Industrial & Engineering Chemistry, 1949. 41(6): p. 1179-1184
20. Eckert, J. S. "Trays and packings: selecting the proper distillation column packing." Chem. Eng. Prog. 66 (1970): 39-44.
21. Dudukovic, Milorad P., and P. L. Mills. "Contacting and hydrodynamics in trickle-bed reactors." Encyclopedia of fluid mechanics 3 (1986): 969.
22. Chou, T. S., F. L. Worley, and D. Luss. "Transition to pulsed flow in mixed-phase cocurrent downflow through a fixed bed." Industrial & Engineering Chemistry Process Design and Development 16.3 (1977): 424-427.
23. Sodhi, Vijay, and Ajay Bansal. "Analysis of Foaming Flow Instabilities for Dynamic Liquid Saturation in Trickle Bed Reactor." Analysis 356 (2011): 2736.
24. Charpentier, Jean‐Claude, and Michel Favier. "Some liquid holdup experimental data in trickle‐bed reactors for foaming and nonfoaming hydrocarbons." AIChE Journal 21.6 (1975): 1213-1218.
25. Sicardi, S., H. Gerhard, and H. Hoffmann. "Flow regime transition in trickle-bed reactors." The Chemical Engineering Journal 18.3 (1979): 173-182.
26. Ramachandran, P. A., M. P. Duduković, and P. L. Mills. "Recent advances in the analysis and design of trickle-bed reactors." Sadhana 10.1-2 (1987): 269.
27. Honda, Gregory S., et al. "Effects of prewetting on bubbly-and pulsing-flow regime transitions in trickle-bed reactors." Industrial & Engineering Chemistry Research 54.42 (2015): 10253-10259.
28. Larachi, F., et al. "Onset of pulsing in trickle beds: evaluation of current tools and state‐of‐the‐art correlation." The Canadian Journal of Chemical Engineering 77.4 (1999): 751-758.
29. Reinecke, Nicolas, and Dieter Mewes. "Investigation of the two-phase flow in trickle-bed reactors using capacitance tomography." Chemical Engineering Science 52.13 (1997): 2111-2127.
30. FUKUSHIMA, SUSUMU, and KATSUHIKO KUSAKA. "Interfacial area and boundary of hydrodynamic flow region in packed column with cocurrent downward flow." Journal of Chemical Engineering of Japan 10.6 (1977): 461-467.
31. Benkrid, K., S. Rode, and N. Midoux. "Prediction of pressure drop and liquid saturation in trickle-bed reactors operated in high interaction regimes." Chemical Engineering Science52.21-22 (1997): 4021-4032.
32. Honda, Gregory S., et al. "Effects of pre wetting on bubbly-and pulsing-flow regime transitions in trickle-bed reactors." Industrial & Engineering Chemistry Research 54.42 (2015): 10253-10259.
33. Virtual Labs. “Packed Column”. vlabs.iitb.ac.in, (Accessed on 20 Nov 2018)
http://vlabs.iitb.ac.in/vlab/chemical/exp2/index.html#
34. Douek, R. S., G. F. Hewitt, and A. G. Livingston. "Hydrodynamics of vertical co-current gas-liquid-solid flows." Chemical engineering science 52.23 (1997): 4357-4372.
35. Duss, M., H. Meierhofer, and P. Bomio. "Comparison between random and structured packings and a model to predict the efficiency of structured packing in distillation and absorption applications." INSTITUTION OF CHEMICAL ENGINEERS SYMPOSIUM SERIES. Vol. 142. HEMSPHERE PUBLISHING CORPORATION, 1997.
36. Tower Packing. “Packed Column and Packings”.Tower-packin.cn, (Accessed on 20 Nov 2018)
http://www.tower-packing.cn/s02/affiche/2015/03/05/1135252.html
37. Rubber Sealing. “Metal Structured Packings”. Rubbersealing.com, (Accessed on 17 Nov 2018).
http://www.rubbersealing.com/TCI/goods-645-Metal+Structured+Packing+125Y250Y350Y500Y.html
38. Hyper-Thermische Verfahrens Technik. “Gas Liquid Contactors”. hyper-tvt.etzh.ch (Accessed on 21 Nov 2018)
http://www.hyper-tvt.ethz.ch/contactors-packing.php
39. Saez, A. E., et al. "Static liquid holdup in packed beds of spherical particles." AIChE journal 37.11 (1991): 1733-1736.
NOMENCLATURE
ap
Mass transfer surface area per unit volume
ft-1
A
Cross sectional area
ft2
dp
Effective particle diameter
ft
deq
Equivalent diameter of a particle based on a sphere
ft
D
Diameter of column
ft
f
Friction factor for flow through packed bed
FP
Packing factor
ft-1
Fr
Froude number
gc
Gravitational constant
lbm-ft/lbf-s2
G
Gas mass velocity
lbm/ft2-hr
hL
Liquid holdup
lT
Effective length of tower
ft
L
Liquid mass velocity
lbm/ft2-hr
m
Mass flow rate
lbm/hr
Q
Volumetric flow rate
ft3/hr
Re
Reynolds number
u
Velocity
ft/hr
We
Weber Number
XG
Modified Lockhart-Martinelli parameter
Greek Letters
∆P
Pressure drop
in H2O wc
ε
Bed void fraction
μ
Absolute viscosity
lbm/ft-hr
ρ
Density
lbm/ft3
σ
Surface tension
lbf/in
ψ
Charpentier-Favier constant
λ
Charpentier-Favier constant
φ
Sphericity
ϵT
Total liquid holdup
%
ϵL,S
Static liquid holdup
%
ϵD,S
Dynamic liquid holdup
%
Subscripts
f
Denotes flooding
g
Denotes gas
l
Denotes liquid
s
Denotes superficial
APPENDICES
APPENDIX A
Sample Calculations
Sample Calculations for Single Phase Gas Flow
Density of air, ρG = 0.075 lbm/ft3
Viscosity of air, µG = 2.419 lbm/ft-hr
Column diameter, d = 0.25 ft
Cross sectional area, A = = 0.049 ft2
Flow rate of air, QG = 1.254 SCFM = 75.24 ft3/hr
Superficial velocity of air, uSG = QG/A = 1532.78 ft/hr
Diameter of particle, dp = 0.014328 ft
Porosity of column, Ɛ = 0.68
Sphericity, φ = 0.51
Substituting above inputs in Ergu’s equation,
Pressure Drop = 0.022 in H2O/ft
Sample Calculations for Charpentier-Favier Flow Regime Map
Flow rate of air, QG = 0.836 SCFM = 50.16 ft3/hr
Flow rate of water. QL =0.078 gpm = 0.6256 ft3/hr
Gas mass velocity, G = (QG )(ρ)/A = 76.6388 lbm/ft2-hr
Liquid mass velocity, L = (QL )(ρ)/A = 795.2927 lbm/ft2-hr =1
Charpetier constant, λ =
=1
Charpentier constant, ψ =
Sample Calculations for Fukushima-Kusaka Flow Regime Map
Equivalent diameter of particle, deq = 0.27 ft
Viscosity of water, µL = 2.419 lbm/ft-hr
Reynolds number for air = ReG = (deq)(µG)/G = 47.03
Reynolds number for water = ReL = (deq)(µL)/L = 8.88
APPENDIX B:
Table 5: Pressure Drop Calculations for Single Phase Flow
% Flow rate of Air (measured)
SCFM (calculated) (0.0418)
Diameter of Column (ft)
Cross Sectional Area (ft²)
Gas Velocity (lbm/ft²*s)
Superficial Velocity (ft/hr)
∆P/L (in.H₂O/ft) measured
Ergun Correlation, ∆P/L (in H2O/ft)
Q(G)
Q(G)
D
A
G
Usg
∆P/L
∆P/L (calc)
0
0
0.25
0.05
0.00
0.00
0
0.00
10
0.418
0.25
0.05
0.01
510.93
0.02
0.00
20
0.836
0.25
0.05
0.02
1021.85
0.06
0.01
30
1.254
0.25
0.05
0.03
1532.78
0.1
0.02
40
1.672
0.25
0.05
0.04
2043.70
0.14
0.03
50
2.09
0.25
0.05
0.05
2554.63
0.2
0.05
60
2.508
0.25
0.05
0.06
3065.55
0.26
0.07
70
2.926
0.25
0.05
0.07
3576.48
0.34
0.09
80
3.344
0.25
0.05
0.09
4087.40
0.42
0.11
90
3.762
0.25
0.05
0.10
4598.33
0.52
0.14
100
4.18
0.25
0.05
0.11
5109.26
0.62
0.17
Table 6.1: Pressure Drop vs Air Mass Velocity
Gas MassVelocity
Liquid Mass Velocity
Experimental Pressure Drop
G, lbm/ft²-hr
L, lbm/ft²-hr
∆P/L, in.H2O/ft
38.32
795
0.02
38.32
1591
0.04
38.32
2386
0.04
38.32
3181
0.05
Table 6.1 continued.
Gas MassVelocity
Liquid Mass Velocity
Experimental Pressure Drop
G, lbm/ft²-hr
L, lbm/ft²-hr
∆P/L, in.H2O/ft
38.32
3976
0.06
38.32
4772
0.08
38.32
5567
0.09
38.32
6362
0.1
38.32
7158
0.14
38.32
7953
0.18
76.64
795
0.06
76.64
1591
0.07
76.64
2386
0.1
76.64
3181
0.12
76.64
3976
0.16
76.64
4772
0.22
76.64
5567
0.26
76.64
6362
0.32
76.64
7158
0.44
76.64
7953
0.64
114.96
795
0.12
114.96
1591
0.14
114.96
2386
0.18
114.96
3181
0.22
114.96
3976
0.3
114.96
4772
0.38
114.96
5567
0.5
114.96
6362
0.66
114.96
7158
1.04
114.96
7953
1.66
Table 6.1 continued.
Gas MassVelocity
Liquid Mass Velocity
Experimental Pressure Drop
G, lbm/ft²-hr
L, lbm/ft²-hr
∆P/L, in.H2O/ft
153.28
795
0.20
153.28
1591
0.23
153.28
2386
0.28
153.28
3181
0.36
153.28
3976
0.52
153.28
4772
0.66
153.28
5567
0.84
153.28
6362
1.36
153.28
7158
1.90
191.60
795
0.28
191.60
1591
0.34
191.60
2386
0.42
191.60
3181
0.53
191.60
3976
0.78
191.60
4772
1.08
191.60
5567
1.46
191.60
6362
2.28
229.92
795
0.38
229.92
1591
0.46
229.92
2386
0.56
229.92
3181
0.74
229.92
3976
1.16
229.92
4772
1.62
229.92
5567
2.64
268.24
795
0.52
Table 6.1 continued.
Gas MassVelocity
Liquid Mass Velocity
Experimental Pressure Drop
G, lbm/ft²-hr
L, lbm/ft²-hr
∆P/L, in.H2O/ft
268.24
1591
0.63
268.24
2386
0.76
268.24
3181
0.82
268.24
3976
1.66
268.24
4772
2.24
306.56
795
0.62
306.56
1591
0.80
306.56
2386
1.00
306.56
3181
1.38
306.56
3976
2.24
306.56
4772
3.44
344.87
795
0.76
344.87
1591
1.00
344.87
2386
1.24
344.87
3181
1.84
344.87
3976
3.04
383.19
795
0.96
383.19
1591
1.23
383.19
2386
1.64
Table 6.2: Comparison of Experimental vs Predicted Pressure Drop
Table 6.2(a): For Liquid Mass Velocity, L = 1.079 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
7.95
4.20
13
16
24
0.10
8.05
9.30
42.4
49
57
0.16
8.08
14.70
86.9
98
106
0.21
8.10
21.00
146.9
163
180
0.26
8.11
27.50
221.7
229
245
0.31
8.11
34.60
315
310
327
0.36
8.12
42.50
429.6
425
441
0.42
8.12
50.60
565.5
506
539
0.47
8.13
59.10
725
620
669
Table 6.2(b): For Liquid Mass Velocity, L = 2.158 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
17.60
7
21.7
32.66
32.66
0.10
18.01
15
65.5
57.15
65.31
0.16
18.16
22
130.0
114.30
130.62
0.21
18.23
30
216.9
187.77
212.27
0.26
18.28
38
326.3
277.58
293.91
0.31
18.31
47
434.1
375.55
408.20
0.36
18.33
57
592.6
514.33
538.83
0.42
18.35
67
785.2
653.12
685.78
0.47
18.36
78
1017.0
816.40
865.39
Table 6.2(c): For Liquid Mass Velocity, L = 3.236 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
28.86
11
24
32.66
48.98
0.10
29.83
22
59
81.64
89.80
0.16
30.19
31
128
146.95
163.28
0.21
30.37
41
207
228.59
261.25
0.26
30.48
52
309
342.89
375.55
0.31
30.56
63
467
457.19
522.50
0.36
30.61
75
634
620.47
702.11
0.42
30.65
87
933
816.40
898.04
0.47
30.69
100
1203
1012.34
1126.64
Figure 21: Experimental vs Predicted Pressure Drop for L=3.236 kg/m2-
Table 6.2(d): For Liquid Mass Velocity, L = 4.315 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
41.67
17
50
40.82
48.98
0.10
43.46
31
132
97.97
122.46
0.16
44.13
43
275
179.61
244.92
0.21
44.48
56
401
293.91
408.20
0.26
44.69
68
599
432.69
604.14
0.31
44.84
81
853
604.14
832.73
0.36
44.95
96
1174
669.45
1175.62
0.42
45.03
110
1761
1126.64
1665.46
0.47
45.09
125
2301
1502.18
2155.31
Figure 22: Experimental vs Predicted Pressure Drop for L=4.315 kg/m2-s
Table 6.2(e): For Liquid Mass Velocity, L = 5.394 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
55.97
23
74
48.98
57.15
0.10
58.83
42
184
130.62
146.95
0.16
59.94
57
372
244.92
293.91
0.21
60.52
73
538
424.53
489.84
0.26
60.88
88
801
636.80
767.42
0.31
61.13
104
1140
947.03
1175.62
0.36
61.31
121
1670
1355.23
2253.28
0.42
61.44
138
2371
1828.75
2449.21
0.47
61.55
156
3116
2481.87
2481.87
Figure 23: Experimental vs Predicted Pressure Drop for L=5.394 kg/m2-s
Table 6.2(f): For Liquid Mass Velocity, L = 6.473 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
71.70
31
104
65.31
65.31
0.10
75.92
55
249
179.61
195.94
0.16
77.58
74
445
310.23
375.55
0.21
78.47
94
706
538.83
702.11
0.26
79.03
112
1048
881.72
1845.07
0.31
79.41
131
1490
1322.57
2383.90
0.36
79.68
151
2188
1828.75
2775.77
0.42
79.89
171
3119
2808.43
2808.43
Figure 24: Experimental vs Predicted Pressure Drop for L=6.473 kg/m2-s
Table 6.2(g): For Liquid Mass Velocity, L = 7.552 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
88.83
39
141
73.48
81.64
0.10
94.66
71
329
212.27
244.92
0.16
97.02
95
639
408.20
522.50
0.21
98.30
119
989
685.78
1093.98
0.26
99.10
141
1448
1191.95
1812.42
0.31
99.64
163
2045
2155.31
2155.31
Figure 25: Experimental vs Predicted Pressure Drop for L=7.552 kg/m2-s
Table 6.2(h): For Liquid Mass Velocity, L = 8.631 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
107.32
49
141
81.64
114.30
0.10
115.04
89
329
261.25
342.89
0.16
118.23
120
639
538.83
669.45
0.21
119.97
148
989
1110.31
2106.32
0.26
121.07
174
1448
1861.40
1861.40
Figure 26: Experimental vs Predicted Pressure Drop for L=8.631 kg/m2-s
Table 6.2(i): For Liquid Mass Velocity, L = 9.709 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
127.14
58
242
114.30
130.62
0.10
137.01
110
542
359.22
473.51
0.16
141.17
148
1023
849.06
930.70
0.21
143.46
182
1567
1551.17
1551.17
Figure 27: Experimental vs Predicted Pressure Drop for L=9.709 kg/m2-s
Table 6.2(j): For Liquid Mass Velocity, L = 10.788 kg/m2-s
Gas Mass Velocity
Predicted Pressure Drop by Midoux (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.68)
Predicted Pressure Drop by Larachi (Ɛ=0.51)
Experimental Pressure Drop (Increase in Gas Mass Velocity)
Experimental Pressure Drop (Decrease in Gas Mass Velocity)
G
∆P/L
∆P/L
∆P/L
∆P/L
∆P/L
kg/m2s
Pa/m
Pa/m
Pa/m
Pa/m
Pa/m
0.05
148.26
63
305
146.95
179.61
0.10
160.53
121
677
522.50
653.12
0.16
165.81
163
1267
1355.23
1355.23
Figure 28: Experimental vs Predicted Pressure Drop for L=10.788 kg/m2-s
Table 7: Pressure Drop Correlation by Eckert
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Pressure Drop
lbm/ft2-hr
lbm/ft2-hr
in. H2O/ft
38.32
795.29
0.02
0.72
10656.68
38.32
1590.59
0.04
1.44
10656.68
38.32
2385.88
0.04
2.16
10656.68
38.32
3181.17
0.05
2.88
10656.68
38.32
3976.46
0.06
3.60
10656.68
38.32
4771.76
0.08
4.32
10656.68
38.32
5567.05
0.09
5.04
10656.68
38.32
6362.34
0.1
5.76
10656.68
38.32
7157.63
0.14
6.48
10656.68
38.32
7952.93
0.18
7.20
10656.68
76.64
795.29
0.06
0.36
42626.72
76.64
1590.59
0.07
0.72
42626.72
76.64
2385.88
0.1
1.08
42626.72
76.64
3181.17
0.12
1.44
42626.72
76.64
3976.46
0.16
1.80
42626.72
76.64
4771.76
0.22
2.16
42626.72
76.64
5567.05
0.26
2.52
42626.72
76.64
6362.34
0.32
2.88
42626.72
76.64
7157.63
0.44
3.24
42626.72
76.64
7952.93
0.64
3.60
42626.72
114.96
795.29
0.12
0.24
95910.13
114.96
1590.59
0.14
0.48
95910.13
114.96
2385.88
0.18
0.72
95910.13
114.96
3181.17
0.22
0.96
95910.13
114.96
3976.46
0.3
1.20
95910.13
114.96
4771.76
0.38
1.44
95910.13
114.96
5567.05
0.5
1.68
95910.13
114.96
6362.34
0.66
1.92
95910.13
114.96
7157.63
1.04
2.16
95910.13
114.96
7952.93
1.66
2.40
95910.13
153.28
795.29
0.2
0.18
170506.89
153.28
1590.59
0.23
0.36
170506.89
153.28
2385.88
0.28
0.54
170506.89
153.28
3181.17
0.36
0.72
170506.89
153.28
3976.46
0.52
0.90
170506.89
153.28
4771.76
0.66
1.08
170506.89
153.28
5567.05
0.84
1.26
170506.89
153.28
6362.34
1.36
1.44
170506.89
Table B continued.
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Pressure Drop
lbm/ft2-hr
lbm/ft2-hr
in. H2O/ft
153.28
7157.63
1.9
1.62
170506.89
191.60
795.29
0.28
0.14
266417.02
191.60
1590.59
0.34
0.29
266417.02
191.60
2385.88
0.42
0.43
266417.02
191.60
3181.17
0.53
0.58
266417.02
191.60
3976.46
0.78
0.72
266417.02
191.60
4771.76
1.08
0.86
266417.02
191.60
5567.05
1.46
1.01
266417.02
191.60
6362.34
2.28
1.15
266417.02
229.92
795.29
0.38
0.12
383640.51
229.92
1590.59
0.46
0.24
383640.51
229.92
2385.88
0.56
0.36
383640.51
229.92
3181.17
0.74
0.48
383640.51
229.92
3976.46
1.16
0.60
383640.51
229.92
4771.76
1.62
0.72
383640.51
229.92
5567.05
2.64
0.84
383640.51
268.24
795.29
0.52
0.10
522177.36
268.24
1590.59
0.63
0.21
522177.36
268.24
2385.88
0.76
0.31
522177.36
268.24
3181.17
0.82
0.41
522177.36
268.24
3976.46
1.66
0.51
522177.36
268.24
4771.76
2.24
0.62
522177.36
306.56
795.29
0.62
0.09
682027.57
306.56
1590.59
0.8
0.18
682027.57
306.56
2385.88
1
0.27
682027.57
306.56
3181.17
1.38
0.36
682027.57
Table B continued.
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Pressure Drop
lbm/ft2-hr
lbm/ft2-hr
in. H2O/ft
306.56
3976.46
2.24
0.45
682027.57
306.56
4771.76
3.44
0.54
682027.57
344.87
795.29
0.76
0.08
863191.15
344.87
1590.59
1
0.16
863191.15
344.87
2385.88
1.24
0.24
863191.15
344.87
3181.17
1.84
0.32
863191.15
344.87
3976.46
3.04
0.40
863191.15
383.19
795.29
0.96
0.07
1065668.08
383.19
1590.59
1.23
0.14
1065668.08
383.19
2385.88
1.64
0.22
1065668.08
383.19
3181.17
2.76
0.29
1065668.08
Table B 19: Flow Regime Map by Charpentier-Favier
Mass flow of water
Mass flow of air
Cross sectional area
Liquid Mass Velocity
Gas Mass Velocity
G/λ
L/Gλψ
m(L)
m(G)
A
L
G
X-axis
Y-axis
kg/hr
kg/hr
m2
kg/m2-s
kg/m2-s
17.71
0.85
0.005
1.08
0.05
0.05
20.79
35.42
0.85
0.005
2.16
0.05
0.05
41.58
53.13
0.85
0.005
3.24
0.05
0.05
62.36
70.85
0.85
0.005
4.32
0.05
0.05
83.15
88.56
0.85
0.005
5.39
0.05
0.05
103.94
106.27
0.85
0.005
6.47
0.05
0.05
124.73
123.98
0.85
0.005
7.55
0.05
0.05
145.51
141.69
0.85
0.005
8.63
0.05
0.05
166.30
Table B 20 continued.
Mass flow of water
Mass flow of air
Cross sectional area
Liquid Mass Velocity
Gas Mass Velocity
G/λ
L/Gλψ
m(L)
m(G)
A
L
G
X-axis
Y-axis
kg/hr
kg/hr
m2
kg/m2-s
kg/m2-s
159.40
0.85
0.005
9.71
0.05
0.05
187.09
177.11
0.85
0.005
10.79
0.05
0.05
207.88
17.71
1.70
0.005
1.08
0.10
0.10
10.39
35.42
1.70
0.005
2.16
0.10
0.10
20.79
53.13
1.70
0.005
3.24
0.10
0.10
31.18
70.85
1.70
0.005
4.32
0.10
0.10
41.58
88.56
1.70
0.005
5.39
0.10
0.10
51.97
106.27
1.70
0.005
6.47
0.10
0.10
62.36
123.98
1.70
0.005
7.55
0.10
0.10
72.76
141.69
1.70
0.005
8.63
0.10
0.10
83.15
159.40
1.70
0.005
9.71
0.10
0.10
93.54
177.11
1.70
0.005
10.79
0.10
0.10
103.94
17.71
2.56
0.005
1.08
0.16
0.16
6.93
35.42
2.56
0.005
2.16
0.16
0.16
13.86
53.13
2.56
0.005
3.24
0.16
0.16
20.79
70.85
2.56
0.005
4.32
0.16
0.16
27.72
88.56
2.56
0.005
5.39
0.16
0.16
34.65
106.27
2.56
0.005
6.47
0.16
0.16
41.58
123.98
2.56
0.005
7.55
0.16
0.16
48.50
141.69
2.56
0.005
8.63
0.16
0.16
55.43
159.40
2.56
0.005
9.71
0.16
0.16
62.36
177.11
2.56
0.005
10.79
0.16
0.16
69.29
17.71
3.41
0.005
1.08
0.21
0.21
5.20
35.42
3.41
0.005
2.16
0.21
0.21
10.39
Table B 21 continued.
Mass flow of water
Mass flow of air
Cross sectional area
Liquid Mass Velocity
Gas Mass Velocity
G/λ
L/Gλψ
m(L)
m(G)
A
L
G
X-axis
Y-axis
kg/hr
kg/hr
m2
kg/m2-s
kg/m2-s
53.13
3.41
0.005
3.24
0.21
0.21
15.59
70.85
3.41
0.005
4.32
0.21
0.21
20.79
88.56
3.41
0.005
5.39
0.21
0.21
25.98
106.27
3.41
0.005
6.47
0.21
0.21
31.18
123.98
3.41
0.005
7.55
0.21
0.21
36.38
141.69
3.41
0.005
8.63
0.21
0.21
41.58
159.40
3.41
0.005
9.71
0.21
0.21
46.77
17.71
4.26
0.005
1.08
0.26
0.26
4.16
35.42
4.26
0.005
2.16
0.26
0.26
8.32
53.13
4.26
0.005
3.24
0.26
0.26
12.47
70.85
4.26
0.005
4.32
0.26
0.26
16.63
88.56
4.26
0.005
5.39
0.26
0.26
20.79
106.27
4.26
0.005
6.47
0.26
0.26
24.95
123.98
4.26
0.005
7.55
0.26
0.26
29.10
141.69
4.26
0.005
8.63
0.26
0.26
33.26
17.71
5.11
0.005
1.08
0.31
0.31
3.46
35.42
5.11
0.005
2.16
0.31
0.31
6.93
53.13
5.11
0.005
3.24
0.31
0.31
10.39
70.85
5.11
0.005
4.32
0.31
0.31
13.86
88.56
5.11
0.005
5.39
0.31
0.31
17.32
106.27
5.11
0.005
6.47
0.31
0.31
20.79
123.98
5.11
0.005
7.55
0.31
0.31
24.25
17.71
5.96
0.005
1.08
0.36
0.36
2.97
35.42
5.96
0.005
2.16
0.36
0.36
5.94
Table B 22 continued.
Mass flow of water
Mass flow of air
Cross sectional area
Liquid Mass Velocity
Gas Mass Velocity
G/λ
L/Gλψ
m(L)
m(G)
A
L
G
X-axis
Y-axis
kg/hr
kg/hr
m2
kg/m2-s
kg/m2-s
53.13
5.96
0.005
3.24
0.36
0.36
8.91
70.85
5.96
0.005
4.32
0.36
0.36
11.88
88.56
5.96
0.005
5.39
0.36
0.36
14.85
106.27
5.96
0.005
6.47
0.36
0.36
17.82
17.71
6.82
0.005
1.08
0.42
0.42
2.60
35.42
6.82
0.005
2.16
0.42
0.42
5.20
53.13
6.82
0.005
3.24
0.42
0.42
7.80
70.85
6.82
0.005
4.32
0.42
0.42
10.39
88.56
6.82
0.005
5.39
0.42
0.42
12.99
106.27
6.82
0.005
6.47
0.42
0.42
15.59
17.71
7.67
0.005
1.08
0.47
0.47
2.31
35.42
7.67
0.005
2.16
0.47
0.47
4.62
53.13
7.67
0.005
3.24
0.47
0.47
6.93
70.85
7.67
0.005
4.32
0.47
0.47
9.24
88.56
7.67
0.005
5.39
0.47
0.47
11.55
17.71
8.52
0.005
1.08
0.52
0.52
2.08
35.42
8.52
0.005
2.16
0.52
0.52
4.16
53.13
8.52
0.005
3.24
0.52
0.52
6.24
70.85
8.52
0.005
4.32
0.52
0.52
8.32
Table B 23: Flow Regime Map by Fukushima-Kusaka
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Equivalent diameter d(eq)
Reynolds Number for Air Re(G)
Reynolds Number for Water Re(L)
lbm/ft2-hr
lbm/ft2-hr
ft
-
-
38.32
795.29
0.03
23.51
8.88
38.32
1590.59
0.03
23.51
17.75
38.32
2385.88
0.03
23.51
26.63
38.32
3181.17
0.03
23.51
35.51
38.32
3976.46
0.03
23.51
44.38
38.32
4771.76
0.03
23.51
53.26
38.32
5567.05
0.03
23.51
62.14
38.32
6362.34
0.03
23.51
71.01
38.32
7157.63
0.03
23.51
79.89
38.32
7952.93
0.03
23.51
88.77
76.64
795.29
0.03
47.03
8.88
76.64
1590.59
0.03
47.03
17.75
76.64
2385.88
0.03
47.03
26.63
76.64
3181.17
0.03
47.03
35.51
76.64
3976.46
0.03
47.03
44.38
76.64
4771.76
0.03
47.03
53.26
76.64
5567.05
0.03
47.03
62.14
76.64
6362.34
0.03
47.03
71.01
76.64
7157.63
0.03
47.03
79.89
76.64
7952.93
0.03
47.03
88.77
114.96
795.29
0.03
70.54
8.88
114.96
1590.59
0.03
70.54
17.75
114.96
2385.88
0.03
70.54
26.63
114.96
3181.17
0.03
70.54
35.51
114.96
3976.46
0.03
70.54
44.38
Table B 23 continued
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Equivalent diameter d(eq)
Reynolds Number for Air Re(G)
Reynolds Number for Water Re(L)
lbm/ft2-hr
lbm/ft2-hr
ft
-
-
114.96
4771.76
0.03
70.54
53.26
114.96
5567.05
0.03
70.54
62.14
114.96
6362.34
0.03
70.54
71.01
114.96
7157.63
0.03
70.54
79.89
114.96
7952.93
0.03
70.54
88.77
153.28
795.29
0.03
94.06
8.88
153.28
1590.59
0.03
94.06
17.75
153.28
2385.88
0.03
94.06
26.63
153.28
3181.17
0.03
94.06
35.51
153.28
3976.46
0.03
94.06
44.38
153.28
4771.76
0.03
94.06
53.26
153.28
5567.05
0.03
94.06
62.14
153.28
6362.34
0.03
94.06
71.01
153.28
7157.63
0.03
94.06
79.89
191.60
795.29
0.03
117.57
8.88
191.60
1590.59
0.03
117.57
17.75
191.60
2385.88
0.03
117.57
26.63
191.60
3181.17
0.03
117.57
35.51
191.60
3976.46
0.03
117.57
44.38
191.60
4771.76
0.03
117.57
53.26
191.60
5567.05
0.03
117.57
62.14
191.60
6362.34
0.03
117.57
71.01
229.92
795.29
0.03
141.09
8.88
229.92
1590.59
0.03
141.09
17.75
229.92
2385.88
0.03
141.09
26.63
Table B 23 continued
Mass Velocity of Air (G)
Mass Veloity of Water (L)
Equivalent diameter d(eq)
Reynolds Number for Air Re(G)
Reynolds Number for Water Re(L)
lbm/ft2-hr
lbm/ft2-hr
ft
-
-
229.92
3181.17
0.03
141.09
35.51
229.92
3976.46
0.03
141.09
44.38
229.92
4771.76
0.03
141.09
53.26
229.92
5567.05
0.03
141.09
62.14
268.24
795.29
0.03
164.60
8.88
268.24
1590.59
0.03
164.60
17.75
268.24
2385.88
0.03
164.60
26.63
268.24
3181.17
0.03
164.60
35.51
268.24
3976.46
0.03
164.60
44.38
268.24
4771.76
0.03
164.60
53.26
306.56
795.29
0.03
188.11
8.88
306.56
1590.59
0.03
188.11
17.75
306.56
2385.88
0.03
188.11
26.63
306.56
3181.17
0.03
188.11
35.51
306.56
3976.46
0.03
188.11
44.38
306.56
4771.76
0.03
188.11
53.26
344.87
795.29
0.03
211.63
8.88
344.87
1590.59
0.03
211.63
17.75
344.87
2385.88
0.03
211.63
26.63
344.87
3181.17
0.03
211.63
35.51
344.87
3976.46
0.03
211.63
44.38
383.19
795.29
0.03
235.14
8.88
383.19
1590.59
0.03
235.14
17.75
383.19
2385.88
0.03
235.14
26.63
383.19
3181.17
0.03
235.14
35.51
APPENDIX C:
PLC Instruments:
Table C 1: Equipment Table
Tag
PLC Tag
Description
Manufacturer
Part No.
Range
BV 1
c10241 - Y201
Water from make up line to feed tank, 3/4"
McMasterCarr
4711K842
BV 2
c10242 - Y202
Water from feed tank to pump, 3/4"
McMasterCarr
4711K842
BV 3
C10243 - Y203
Switches water feed to FT 1, 3/4"
Valworx
565647A
BV 4
Same as 3, slaved
Switches water feed to FT 2, 3/4"
Valworx
565647A
BV 5
C10245 - Y205
Compressed air feed flow, 3/4"
McMasterCarr
4711K842
BV 6
C10246 - Y206
Water inlet to packed column, 3/4"
McMasterCarr
4711K842
BV 7
C10247 - Y207
Water to drain at Column Exit. 3/4"
McMasterCarr
4711K842
BV8
C10247 - Y208
Air into Column, 3/4"
McMasterCarr
4711K842
Table C 1 continued
Tag
PLC Tag
Description
Manufacturer
Part No.
Range
BV9
C10249 - Y209
Air Exit from Column
Wonderware
C10266
Unit Startup - sets RCVs
Wonderware
c10267 - Y227
Air Only Experiment
Wonderware
C10268 - Y228
Water Only Experiment
Wonderware
C10269 - Y229
Air and Water Experiment
Wonderware
C10270 - Y230
Turns Pump ON/Off
Wonderware
PT 1
WX401
Compressor pressure
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 2
WX402
Ballast tank pressure
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 3
WX403
Upstream pressure to MFC for air feed
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 4
WX404
Downstream pressure from MFC for air feed
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 5
WX405
Column air flow inlet pressure
Dwyer
626-09-CH-P1-E5-S1
0-50 psig
Table C 1 continued
Tag
PLC Tag
Description
Manufacturer
Part No.
Range
PT 6
WX406
Column Pressure
Dwyer
626-09-CH-P1-E5-S1
0-50 psig
PT 7
WX407
Column air flow outlet pressure
Dwyer
673-3
0-5 psig
PT 8
WX408
Water Supply Pressure
Dwyer
626-09-CH-P1-E5-S1
0-50 psig
PT 9
WX409
Upstream pressure to pump for water feed
Dwyer
626-07-CH-P1-E5-S1
0-15 psig
PT 10
WX410
Downstream pressure from pump for water feed
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 11
WX411
Water Supply to Column
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
PT 12
WX412
Water Exit Line from Column
Dwyer
626-12-CH-P1-E5-S1
0-160 psig
DPT 1
WX413
Differential pressure across packed column
ColePalmer
EW-98073-72
0-10 psig
DPT 2
WX414
Differential pressure across water feed tank
Dwyer
616W-6-LCD
0-100"
Table C 1 continued
Tag
PLC Tag
Description
Manufacturer
Part No.
Range
DPT 3
WX415
Differential pressure in column sump
Dwyer
616W-6-LCD
0-100"
MFC 1
WX417 - WY601
Air mass flow controller for air inlet, 3/4"
Omega
PV-34B
0-1000 slpm
TT 1
WX505
Air temperature in ballast tank
Omega
TC-T-1/4NPT-U-72DUAL
0-650 F
TT 2
WX506
Inlet air temperature to column
Omega
TC-T-1/4NPT-U-72DUAL
0-650 F
TT 3
WX507
Air temperature at outlet of packed column
Omega
TC-T-1/4NPT-U-72DUAL
0-650 F
TT 4
WX508
Temperature of feed water in tank
Omega
TC-T-1/4NPT-U-72DUAL
0-650 F
FT 1
WX417
Inlet air flow rate, 3/4"
Omega
FLR7710D
0.13-1.3 gpm
FT 2
WX416
Inlet water flow rate, 1"
Omega
FLR8340D
0.53-9.2 gpm
FCV 1
WX415 - WY602
Inlet water flow control valve for FT 1
Badger meter
1002 GC N 36 SV CS ALN 36 Time size B
max CV 2.0
FCV 2
WX416 - WY603
Inlet water flow control valve for FT 2
Badger meter
1002 GC N 36 SV CS ALN 36 Time size B
max CV 2.0
LCV 1
WX413 - WY604
Inlet feed tank level control valve
Badger meter
1002 GC N 36 SV CS ALN 36 Time size B
max CV 2.0
LCV 2
WX414 - WY605
Outlet control valve
Badger meter
1002 GC N 36 SV CS ALN 36 Time size B
max CV 2.0
Pump
C10270 - Y230
Water tank feed pump
Cole-Parmer
EW-79733-00
44 gpm head
Manual Devices:
TAG
Manufaturer
Part No.
Control Function Description
V-1
Grainger
49EZ67
Compressed air feed flow two way ball valve (3/4')
V-2
Grainger
49EZ67
Air flow calibration valve downstream of BPR-1 (3/4')
V-3
Grainger
49EZ67
Air flow two way valve downstream of BPR-1 (3/4')
V-4
Grainger
49EZ67
Water from makeup line to feed tank two way ball valve (3/4 inch)
V-5
Grainger
49EZ67
Water tank bottom drain line two way ball valve (3/4 inch)
V-6
Grainger
49EZ67
Water tank bottom feed line two way ball valve (3/4 inch)
V-7
Grainger
49EZ67
Pump discharge line two way valve (3/4 inch)
V-8
Grainger
49EZ67
Water feed line calibration two way valve (3/4 inch)
V-9
Grainger
49EZ67
Water feed line two way valve to column before FCV 1/2 (3/4 inch)
V-10
Grainger
49EZ67
Water feed line to column after FCV 1/2 (3/4 inch)
CV-1
McMasterCarr
47715K24
Check valve downstream of BPR-1, 3/4"
TI 1
McMasterCarr
3946K11
Air local gauge temperature in ballast tank
TI 2
McMasterCarr
3946K11
Inlet air local gauge temperature to column
TI 3
McMasterCarr
3946K11
Exit air local gauge temperature from column
TI 4
McMasterCarr
3946K11
Feed water local gauge temperature in tank
TI 5
McMasterCarr
3946K11
Pump outlet water local gauge temperature
TI 6
McMasterCarr
3946K11
Inlet water local gauge temperature to column
TI 7
McMasterCarr
3946K11
Exit water local gauge temperature to column
PI 1
Ametek
163281
Ballast tank pressure local gauge pressure
PI 2
Ametek
163281
Upstream local gauge pressure to MFC for air feed
PI 3
Ametek
163281
Downstream local gauge pressure from MFC for air feed
PI 4
Ametek
047102A
Upstream local gauge pressure to pump for water feed
PI 5
Ametek
163279
Downstream local gauge pressure from pump for water feed
PI 6
Ametek
163279
Column air flow inlet local gauge pressure
PI 7
Ametek
161970A
Column air flow outlet local gauge pressure
BPR-1
Straval
3/4" BPH05-07T
Back pressure regulator for air flow feed line downstream of MFC-1
FPR-1
Valworx
ARO R37351-100
Forward pressure regulator for air flow to ballast tank
V-1
McMasterCarr
9827K8
Lightweight Compressed Air Storage Tank
Filter
McMasterCarr
4274K34
Compressed Air Filter for Water and Particles
TK-1
USPlastics
5200
Domed bottom cyl poly-e tank
APPENDIX D:
Table 10: Procedure Logic Table
Single phase (air only operation)
Step
Description
Tags
Action/
Set point
Required Condition
Remove any water present in column
1
Check and make sure pump is turned off
P-1
2
Close water inlet and outlet of tank
BV-1, BV-2
Automated
3
Close water inlet to column
BV-6
Automated
Close BV-3, BV-4
4
Drain any water left in column
Open BV-7
Automated
Close BV-7
Initiating air flow by maintaining pressure drop
5
Close inlet air to air filter
BV-5
Open V-1
6
Turn on air compressor if not turned on already
7
Check/maintain pressure in PT 1
PT-1
Close BV-5
Open V-1
8
Close air inlet to column
V-3
Manual
BV-8
Automated
9
Open air inlet to filter/ballast tank
BV-5
10
Open calibartion valve (after BPR-1)
V-2
Manual
11
Open the back pressure and forward presure regulators
BPR-1
FPR-1
12
Set mass flow rate
MFC-1
100 SLPM
13
Maintain the pressure
FPR-1
80psi
BPR-1
40psi
Air inlet to column
14
Open air exit from column
BV-9
Automated
15
Open Air inlet stream to column
V-3
Manual
Close calibration valve V-2
BV-8
Automated
16
Set Level control valve at bottom of column
LCV-2
0
Close BV-6 and BV-7
17
Go to autorun mode/experimental set up page. Click "ON". Click "AIR". Set water flow to "ZERO"
Single Phase (Water only operation)
Step
Description
Tags
Action/
Set point
Required Condition
Remove any air trapped in column
1
Ensure air compressor is on/available for another experiment
2
Turn off air compressor if not in use
3
Close air inlet to ballast tank (T-1)
V-1
Manual
BV-5
Automated
4
Open calibration valve
V-2
Manual
5
Open air exit from column
BV-9
Automated
Open BV-8
6
Wait for system to purge
PT-7
PT-7 = ZERO
7
Close calibration valve
V-2
Manual
8
Close air inlet , exit to column
BV-8, BV-9
Automated
9
Open water outlet from column to remove any air trapped
BV-7
Automated
Close BV-6 (water inlet to column)
Maintaining water level in tank (T-2)
10
Close water drain from tank (T-2)
BV-10
Automated
11
Close water inlet to pump
BV-2
Automated
V-6
Manual
12
Open water inlet to tank (T-2)
V-4
Manual
BV-1
Automated
13
Maintain tank level
T-2
If DPT-2 ≥ 75"
Close LCV-1
If DPT-2 ≤ 25"
Open LCV-1
Water flow to column
14
Open water exit from column
BV-7
Automated
15
Open water inlet stream to pump
V-6
If DPT-2 ≥ 75"
Close LCV-1
BV-2
If DPT-2 ≤ 25"
Open LCV-1
16
Open water inlet to column
V-7, V-9
Manual
Close V-8
BV-6
Automated
17
Turn on the pump
P-1
18
Set water flow rate
FT-1
0.1 gpm
19
For maximum flow
FT-2
FT-1 ≥ 0.9 times maximum of FT-1
Open BV-3, BV-4
20
For minimum flow
FT-1
FT-2 ≤ 1.2 times minimum of FT-2
21
Maintain pressure at bottom of column
DPT-3
If DPT-3 ≥ 25"
Open LCV-2
If DPT-2 ≤ 5"
Close LCV-2
22
Go to autorun mode/experimental set up page. Click "ON". Click "WATER". Set air flow to "ZERO"
Multiphase flow:
Step
Description
Tags
Action/
Set point
Required Condition
Set the water flow first
1
Ensure air compressor is on/available for another experiment
2
Turn off air compressor if not in use
3
Close air inlet to ballast tank (T-1)
V-1
Manual
BV-5
Automated
4
Open calibration valve
V-2
Manual
5
Open air exit from column
BV-9
Automated
Open BV-8
6
Wait for system to purge
PT-7
PT-7 = ZERO
7
Close calibration valve
V-2
Manual
8
Close air inlet , exit to column
BV-8, BV-9
Automated
9
Open water outlet from column to remove any air trapped
BV-7
Automated
Close BV-6 (water inlet to column)
10
Close water drain from tank (T-2)
BV-10
Automated
11
Close water inlet to pump
BV-2
Automated
V-6
Manual
12
Open water inlet to tank (T-2)
V-4
Manual
BV-1
Automated
13
Maintain tank level
T-2
If DPT-2 ≥ 75"
Close LCV-1
If DPT-2 ≤ 25"
Open LCV-1
14
Open water exit from column
BV-7
Automated
15
Open water inlet stream to pump
V-6
If DPT-2 ≥ 75"
Close LCV-1
BV-2
If DPT-2 ≤ 25"
Open LCV-1
16
Open water inlet to column
V-7, V-9
Manual
Close V-8
BV-6
Automated
17
Turn on the pump
P-1
18
Set water flow rate
FT-1
0.1 gpm
19
For maximum flow
FT-2
FT-1 ≥ 0.9 times maximum of FT-1
Open BV-3, BV-4
20
For minimum flow
FT-1
FT-2 ≤ 1.2 times minimum of FT-2
21
Maintain pressure at bottom of column
DPT-3
If DPT-3 ≥ 25"
Open LCV-2
If DPT-2 ≤ 5"
Close LCV-2
Now set the air flow
22
Close air inlet to air filter/Ballast tank
V-1
Manual
BV-5
Automated
23
Close air inlet to column
V-3
Manual
BV-8
Automated
24
Open calibration valve (after BPR-1)
V-2
Manual
25
Open air inlet to air filter
V-1
Manual
Close BV-5
26
Maintain pressure in PT-1
PT-1
80 psig
27
Open air inlet to air filter
BV-5
Automated
28
Open air exit from column
BV-9
Automated
29
Open the back pressure and forward pressure regulators
BPR-1
FPR-1
30
Set mass flow rate
MFC-1
100 SLPM
31
Maintain the pressure
FPR-1
80psi
BPR-1
40psi
32
Open Air inlet stream to column
V-3
Manual
Close calibration valve V-2
BV-8
Automated
33
Maintain pressure at bottom of column
DPT-3
If DPT-3 ≥ 25"
Open LCV-2
Process Shutdown:
Step
Description
Tags
Action/
Set point
1
Close water flow
P-1
Turn off Pump 1
2
Close air flow
MFC-1
Turn off mass flow rtae
3
Drain the water (open water outlet from column)
BV-7
Open
4
Release the air (open air exit from column)
BV-9
Open
5
Close air, water inputs to column
BV-6. BV-8
Close
6
Close air,water outputs to column
BV-7, BV-9
Close
7
Close air input to air filter
V-1, BV-5
Close
8
Close water input to tank
V-4, BV-1
Close
9
Empty the water tank (open drain valve)
BV-10
Open, close when T-2 is empty
APPENDIX E:
Table 11: Alarm Table
Tag
Description
Alarm
Condition
Action
Action Stop Condition
DPT-1
Differential Pressure
High-High
DPT-1 > 95% MAX
Close MFC-1
DPT-1 = 95% MAX
Show User
DPT-2
Differential Pressure
High
DPT-2 > 85% MAX
Close LCV-1
DPT-2 = 90% MAX
Show User
Low
DPT-2 < 25% MAX
Open LCV-1
DPT-2 = 30% MAX
Show User
DPT-3
Differential Pressure
High-High
DPT-3 > 90% MAX
Turn off P-1
Close BV-2
Show User
Low
DPT-3 < 20% MAX
Close LCV-2
DPT-3 = 25% MAX
Low-Low
DPT-3 < 10% MAX
Turn off P-1
DPT-3 = 15% MAX
Show User
VITA
Mrudalini Moturu received her Bachelor of Technology degree in Chemical Engineering (2014) from Rayapati Venkata Rangarao and Jagarlamudi Chandramouli (RVR & JC) College of Engineering in Andhra Pradesh, India. In January 2016, she joined Chemical Engineering Master’s Program at Texas A&M University-Kingsville. She has been working on this research under Dr. Patrick L. Mills, chair, and head of the department.
Permanent Address:
D.No: 7-99,
Gorantla center, Near Masjid
Gorantla,
Guntur, Andhra Pradesh – 522034,
India.
0 510.92556451132606 1021.8511290226521 1532.7766935339785 2043.7022580453042 2554.6278225566307 3065.5533870679569 3576.4789515792822 4087.4045160906085 4598.3300806019352 51 09.2556451132614 0 4.7320144402113401E-3 1.2103171886261439E-2 2.2113472338150298E-2 3.4762915795877904E-2 5.0051502259444276E-2 6.7979231728849412E-2 8.8546104204093284E-2 0.11175211968517594 0.13759727817209735 0.16608157966485751 uSG x 10-2 , ft/hr
∆P/L, in. H₂O/ft
Ergun Equation (Measured) 0 1.0644282593985959E-2 2.1288565187971918E-2 3.1932847781957881E-2 4.2577130375943836E-2 5.3221412969929799E-2 6.3865695563915761E-2 7.450997815790171E-2 8.5154260751887673E-2 9.57985433458736 35E-2 0.1064428259398596 0 4.7320144402113401E-3 1.2103171886261439E-2 2.2113472338150298E-2 3.4762915795877904E-2 5.0051502259444276E-2 6.7979231728849412E-2 8.8546104204093284E-2 0.11175211968517594 0.13759727817209735 0.16608157966485751 Experimental Values 0 1.0644282593985959E-2 2.1288565187971918E-2 3.1932847781957881E-2 4.2577130375943836E-2 5.3221412969929799E-2 6.3865695563915761E-2 7.4509978157 90171E-2 8.5154260751887673E-2 9.5798543345873635E-2 0.1064428259398596 0 0.02 0.06 0.1 0.13999999999999999 0.2 0.26 0.33999999999999997 0.42000000000000004 0.52 0.62 Gas Mass Velocity, lbm/ft²*h
∆P, in. H₂O/ft
Ergun Equation (Measured) 0 1.0644282593985959E-2 2.1288565187971918E-2 3.1932847781957881E-2 4.2577130375943836E-2 5.3221412969929799E-2 6.3865695563915761E-2 7.450997815790171E-2 8.5154260751887673E-2 9.57985433458736 35E-2 0.1064428259398596 0 2.3755471317165724E-2 5.709005428515361E-2 0.10000374890396367 0.15249655517359587 0.21456847309405022 0.28621950266532681 0.36744964388742546 0.45825889676034637 0.55864726128408937 0.66861473745865452 Experimental Values 0 1.0644282593985959E-2 2.1288565187971918E-2 3.1932847781957881E-2 4.2577130375943836E-2 5.3221412969929799E-2 6.3865695563915761E-2 7.450997815790171E-2 8.5154260751887673E-2 9.5798543345873635E-2 0.1064428259398596 0 0.02 0.06 0.1 0.13999999999999999 0.2 0.26 0.33999999999999997 0.42000000000000004 0.52 0.62 Gas Mass Velocity, lbm/ft²*h
∆P, in. H₂O/ft
L = 795 38.319417338349453 76.638834676698906 114.95825201504837 153 .27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.02 0.06 0.12 0.2 0.27999999999999997 0.38 0.52 0.62 L = 1591 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.235921368446 16 306.55533870679562 0.04 6.9999999999999993E-2 0.13999999999999999 0.22999999999999998 0.33999999999999997 0.45999999999999996 0.63 0.8 L = 2386 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.2359213684461 6 306.55533870679562 0.04 0.1 0.18 0.27999999999999997 0.42000000000000004 0.55999999999999994 0.76 1 L = 3181 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.05 0.12 0.22000000000000003 0.36 0.53 0.74 0.82 1.3800000000000001 L = 3976 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.06 0.16 0.3 0.52 0.78 1.1599999999999999 1.6600000000000001 2.2399999999999998 L = 4772 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.08 0.22000000000000003 0.38 0.65999999999999992 1.08 1.6199999999999999 2.2399999999999998 3.44 L = 5567 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 0.09 0.26 0.5 0.84000000000000008 1.46 2.6399999999999997 L = 6362 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 0.1 0.32 0.65999999999999992 1.3599999999999999 2.2800000000000002 L = 7158 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 0.13999999999999999 0.44000000000000006 1.04 1.9 L = 7953 38.319417338349453 76.638834676698906 114.95825201504837 0.18 0.64 1.6600000000000001 G, lbm/ft2-hr
∆P/L, in H2O/ft
L = 4772 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.08 0.22000000000000003 0.38 0.65999999999999992 1.08 1.6199999999999999 2.2399999999999998 3.44 L = 5567 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 0.09 0.26 0.5 0.84000000000000008 1.46 2.6399999999999997 L = 6362 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 0.1 0.32 0.65999999999999992 1.3599999999999999 2.2800000000000002 L = 7158 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 0.13999999999999999 0.44000000000000006 1.04 1.9 L = 7953 38.319417338349453 76.638834676698906 114.95825201504837 0.18 0.64 1.66000000000000 01 L = 795 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.02 0.06 0.12 0.2 0.27999999999999997 0.38 0.52 0.62 L = 1591 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.04 6.9999999999999993E-2 0.13999999999999999 0.22999999999999998 0.33999999999999997 0.45999999999999996 0.63 0.8 L = 2386 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.04 0.1 0.18 0.27999999999999997 0.42000000000000004 0.55999999999999994 0.76 1 L = 3181 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.05 0.12 0.22000000000000003 0.36 0.53 0.74 0.82 1.3800000000000001 L = 3976 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 306.55533870679562 0.06 0.16 0.3 0.52 0.78 1.1599999999999999 1.6600000000000001 2.2399999999999998 G, lbm/ft2-hr
∆P/L, in H2O/ft
dP Vs G 38.319417338349453 76.638834676698906 114.95825201504837 153.27766935339781 191.59708669174728 229.91650403009675 268.23592136844616 0.04 6.9999999999999993E-2 0.13999999999999999 0.22999999999999998 0.33999999999999997 0.45999999999999996 0.63 G, lbm/ft2-hr
∆P/L, in H2O/ft
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.3113 8491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 7.9471654251759887 8.0453231019408324 8.0791342518358729 8.0962522814182272 8.1065921124934484 8.1135143306927375 8.1184730520217752 8.1221999318893872 8.1251032745516572 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 4.2 9.3000000000000007 14.7 21 27.5 34.6 42.5 50.6 59.1 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 16.328083989501312 48.984251968503933 97.968503937007867 163.28083989501312 228.59317585301832 310.23359580052494 424.53018372703417 506.17060367454064 620.46719160104988 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 24.492125984251967 57.148293963254581 106.13254593175854 179.60892388451444 244.92125984251967 326.56167979002623 440.85826771653547 538.82677165354323 669.45144356955382 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 13 42.4 86.9 146.9 221.7 315 429.6 565.5 725 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 17.595127976202203 18.009168261528856 18.156242226069406 18.231604567110058 18.27742357225226 18.308224425260562 18.330351201012668 18.347015800368702 18.360018581419059 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 7.3 14.6 21.9 30.1 38.4 47.2 57.2 67.2 77.7 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 32.656167979002625 57.148293963254581 114.2965879265091 6 187.77296587926506 277.57742782152229 375.54593175853012 514.33464566929138 653.12335958005247 816.40419947506564 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 32.656167979002625 65.312335958005249 130.6246719160105 212.26509186351709 293.90551181102359 408.20209973753282 538.82677165354323 685.77952755905517 865.38845144356947 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 21.7 65.5 130 216.9 326.3 434.1 592.6 785.2 1017 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
∆P=0.2 0.1799896700667854 0.71995868026714149 0.9599449070228554 2.8798347210685664 3.2398140612021376 170506.89308318589 95910.127359292077 95910.127359292077 42626.723270796472 42626.723270796472 ∆P=0.4 0.11999311337785692 0.2879834721068566 0.7199586802671416 0.89994835033392695 1.9198898140457108 2.1598760408014246 383640.50943716831 266417.02044247795 170506.89308318589 170506.89308318589 95910.127359292077 95910.127359292077 ∆P=0.6 0.10285124003816309 0.35997934013357075 0.57596694421371319 0.71995868026714149 1.0799380204007123 1.2599276904674979 2.3998622675571384 522177.36006725678 383640.50943716831 266417.02044247795 266417.02044247795 170506.89308318589 170506.89308318589 95910.127359292077 ∆P=0.8 7.9995408918571292E-2 8.9994835033392701E-2 0.30855372011448928 0.4799724535114277 0.86395041632056979 863191.14623362862 682027.57233274356 522177.36006725678 383640.50943716831 266417.02044247795 ∆P=1.0 7.1995868026714149E-2 0.15999081783714258 0.1799896700667854 0.26998450510017807 0.41140496015265238 0.5999655668892846 1.4399173605342832 1065668.0817699118 863191.14623362862 682027.57233274356 682027.57233274356 522177.36006725678 383640.50943716831 170506.89308318589 ∆P=1.5 1.0079421523739982 0.71995868026714149 0.51425620019081542 0.3599793401335708 0.23998622675571385 0.1439917360534283 266417.02044247795 383640.50943716831 522177.36006725678 682027.57233274356 863191.14623362862 1065668.0817699118 ∆P=0.1 0.3599793401335708 0.7199 586802671416 1.0799380204007123 1.4399173605342832 1.7998967006678539 5.7596694421371328 6.4796281224042751 7.1995868026714156 42626.723270796472 42626.723270796472 42626.723270796472 42626.723270796472 42626.723270796472 10656.680817699118 10656.680817699118 10656.680817699118
5.1897486280017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 5.18974862 80017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 5.1897486280017099E-2 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.1037949725600342 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.15569245884005128 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.2075899451200684 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.25948743140008546 0.31138491768010257 0.31138491768010257 0.31138491768010257 0.31138491768010257 0.31138491768010257 0.31138491768010257 0.31138491768010257 0.36328240396011968 0.36328240396011968 0.36328240396011968 0.36328240396011968 0.36328240396011968 0.36328240396011968 0.4151798902401368 0.4151798902401368 0.4151798902401368 0.4151798902401368 0.4151798902401368 0.4151798902401368 0.4670773765201538 0.4670773765201538 0.4670773765201538 0.4670773765201538 0.4670773765201538 0.51897486280017091 0.51897486280017091 0.51897486280017091 0.51897486280017091 20.787559808612439 41.575119617224878 62.362679425837321 83.150239234449757 103.9377990430622 124.72535885167464 145.51291866028706 166.30047846889951 187.08803827751194 207.8755980861244 10.39377990430622 20.787559808612439 31.18133971291866 41.575119617224878 51.9688995215311 62.362679425837321 72.756459330143528 83.150239234449757 93.544019138755971 103.9377990430622 6.9291866028708133 13.858373205741627 20.787559808612443 27.716746411483253 34.645933014354071 41.575119617224885 48.504306220095692 55.433492822966507 62.362679425837321 69.291866028708142 5.1968899521531098 10.39377990430622 15.59066985645933 20.787559808612439 25.98444976076555 31.18133971291866 36.378229665071764 41.575119617224878 46.772009569377985 4.1575119617224887 8.3150239234449774 12.472535885167467 16.630047846889955 20.787559808612443 24.945071770334934 29.102583732057415 33.26009569377991 3.4645933014354067 6.9291866028708133 10.393779904306221 13.858373205741627 17.322966507177036 20.787559808612443 24.252153110047846 2.9696514012303483 5.9393028024606966 8.9089542036910458 11.878605604921393 14.848257006151742 17.817908407382092 2.5984449760765549 5.1968899521531098 7.7953349282296651 10.39377990430622 12.992224880382775 15.59066985645933 2.3097288676236047 4.6194577352472095 6.9291866028708151 9.238915470494419 11.548644338118024 2.0787559808612444 4.1575119617224887 6.2362679425837335 8.3150239234449774 G/λ
L/Gλψ
Flow - Regime 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 71.014145187736887 79.890913336204008 88.767681484671101 8.876768148467 1108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 71.014145187736887 79.890913336204008 88.767681484671101 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 71.014145187736887 79.890913336204008 88.767681484671101 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 71.014145187736887 79.890913336204008 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 71.014145187736887 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 62.137377039269779 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 53.260608890802658 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 44.383840742335551 8.8767681484671108 17.753536296934222 26.630304445401329 35.507072593868443 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 23.514187912168982 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 47.028375824337964 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 70.542563736506963 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 94.056751648675927 117.57093956084492 117.57093956084492 117.57093956084492 117.57093956084492 117.57093956084492 117.57093956084492 117.57093956084492 117.57093956084492 141.08512747301393 141.08512747301393 141.08512747301393 141.08512747301393 141.08512747301393 141.08512747301393 141.08512747301393 164.59931538518288 164.59931538518288 164.59931538518288 164.59931538518288 164.59931538518288 164.59931538518288 188.11350329735185 188.11350329735185 188.11350329735185 188.11350329735185 188.11350329735185 188.11350329735185 211.62769120952086 211.62769120952086 211.62769120952086 211.62769120952086 211.62769120952086 235.14187912168984 235.14187912168984 235.14187912168984 235.14187912168984 Re (water)
Re (air)
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 28.859322153428963 29.830806500984153 30.186008509058603 30.370141152255886 30.482803788523984 30.558844395507684 30.613623005773686 30.654963505287348 30.687270520274073 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 11.4 21.6 31.1 41.4 51.7 62.6 74.7 86.8 99.5 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 32.656167979002625 81.640419947506558 146.9527 5590551179 228.59317585301832 342.88976377952758 457.18635170603665 620.46719160104988 816.40419947506564 1012.3412073490813 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 48.984251968503933 89.80446194225722 163.28083989501312 261.249343832021 375.54593175853012 522.498687664042 702.10761154855641 898.04461942257228 1126.6377952755904 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 23.6 58.8 127.8 207 308.89999999999998 466.9 633.79999999999995 933.1 1203.2 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 41.669489428831497 43.455120683110934 44.125998080691453 44.477686167765214 44.694204049359513 44.840918358352134 44.946899247381197 45.027042587133685 45.089770339438942 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 16.7 30.5 42.6 55.5 68.099999999999994 81.2 95.7 110.2 125.4 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 40.820209973753279 97.968503937007867 179.60892388451444 293.90551181102359 432.69422572178473 604.13910761154852 669.45144356955382 1126.6377952755904 1502.1837270341205 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 48.984251968503933 122.46062992125984 244.92125984251967 408.20209973753282 604.13910761154852 832.73228346456688 1175.6220472440943 1665.4645669291338 2155.3070866141729 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 50.4 132.4 274.7 400.5 599.29999999999995 853.1 1173.5999999999999 1760.5 2301.3000000000002 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 55.966775417707439 58.831971925017534 59.936431035396907 60.521699489042497 60.884201237648718 61.130786657045213 61.309391097149785 61.444721313228364 61.550805301308152 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 23.2 41.6 57 72.8 88 103.7 121 138.1 156.1 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 48.984251968503933 130.6246719160105 244.9212598425196 7 424.53018372703417 636.79527559055111 947.02887139107611 1355.2309711286089 1828.7454068241466 2481.8687664041995 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 57.148293963254581 146.95275590551179 293.90551181102359 489.84251968503935 767.4199475065617 1175.6220472440943 2253.2755905511808 2449.2125984251966 2481.8687664041995 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 73.599999999999994 183.9 371.8 537.6 800.8 1139.5999999999999 1670.4 2371.1 3116.4 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s)
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 71.701506255698078 75.915649955904087 77.57997812072621 78.471180029498584 79.026424787583977 79.405553718709101 79.680889197419106 79.889922312403158 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 30.8 55.1 74.400000000000006 93.8 112 130.69999999999999 151.1 171.3 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 65.312335958005249 179.60892388451444 310.23359580052494 538.82677165354323 881.71653543307093 1322.5748031496062 1828.7454068241466 2808.4304461942256 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 65.312335958005249 195.93700787401573 375.54593175853012 702.10761154855641 1845.0734908136483 2383.9002624671916 2775.7742782152231 2808.4304461942256 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 103.7 248.8 445.3 706.2 1047.7 1489.9 2188.4 3118.6 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 88.83146573242405 94.664394723838839 97.021574883218804 98.296575814722189 99.09550666596644 99.643057456455836 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 39.200000000000003 71 95.2 118.8 140.6 162.69999999999999 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 73.476377952755897 212.26509186351709 408.20209973753282 685.77952755905517 1191.9501312335958 2155.3070866141729 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 81.640419947506558 244.92125984251967 522.498687664042 1093.9816272965879 1812.4173228346451 2155.3070866141729 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 141.4 329 638.5 988.8 1448.2 2044.9 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 107.32054637653347 115.03997870422404 118.22825247545984 119.96970028904798 121.06703417900718 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 48.5 89.4 119.6 148.19999999999999 174.3 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 81.640419947506558 261.249343832021 538.82677165354323 1110.3097112860892 1861.4015748031497 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 114.29658792650916 342.88976377952758 669.45144356955382 2106.3228346456694 1861.4015748031497 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 141.4 329 638.5 988.8 1448.2 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 127.13768310350194 137.00734111011212 141.16898340742537 143.46365435634226 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 58.2 110.1 147.699999999 99999 182.4 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 114.29658792650916 359.21784776902888 849.06036745406834 1551.1679790026246 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 130.6246719160105 473.51443569553805 930.70078740157487 1551.1679790026246 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 241.9 541.9 1023.2 1566.5 Midoux e=0.51 5.189748628001710 6E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocity, kg/m2-s
Pressure Drop, Pa/m
Midoux (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.311 38491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 148.25600270120145 160.53426663289497 165.81454072447747 Larachi (Ɛ=0.68) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 63.2 121.3 163.19999999999999 Exp Inc 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 146.95275590551179 522.498687664042 1355.2309711286089 Exp Dec 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 179.60892388451444 653.12335958005247 1355.2309711286089 Larachi (Ɛ=0.51) 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 305 677.2 1267 Midoux e=0.51 5.1897486280017106E-2 0.10379497256003421 0.15569245884005128 0.20758994512006843 0.25948743140008551 0.31138491768010257 0.36328240396011968 0.41517989024013685 0.46707737652015385 1 Gas Mass Velocit, kg/m2-s
Pressure Drop, Pa/m
(
)
30
0
.
0
666
.
0
log
146
.
0
log
5
.
0
2
<
÷
÷
ø
ö
ç
ç
è
æ
=
<
+
=
÷
÷
ø
ö
ç
ç
è
æ
+
g
g
g
d
d
c
c
d
d
d
l
l
l
(
)
20
1
.
0
1
2
.
1
log
70
.
0
log
2
<
<
+
=
÷
÷
ø
ö
ç
ç
è
æ
+
c
c
d
d
d
g
g
l
l
(
)
(
)
500
Re
Re
2
.
0
;
1
3
2
;
2
ln
0078
.
0
ln
0021
.
0
ln
34
.
1
96
.
7
ln
767
.
0
167
.
1
2
3
2
<
=
<
=
-
=
=
+
+
-
=
L
g
ex
p
B
B
p
pe
g
g
pe
g
g
g
Z
S
d
d
d
u
d
f
Z
Z
Z
f
p
e
e
r
d
l
l
l
2
1
.
1
1
.
1
ln
0573
.
0
30
.
1
82
.
7
ln
ú
û
ù
ê
ë
é
÷
÷
ø
ö
ç
ç
è
æ
-
-
=
y
y
Z
Z
f
g
l
L
p
g
g
g
L
g
g
B
B
p
L
g
d
u
We
We
d
s
r
e
e
m
d
d
2
3
1
g
Re
Re
1
1507
=
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
-
=
-
l
(
)
[
]
(
)
(
)
(
)
bed)
the
of
osity
holdup/por
(dynamic
saturation
dynamic
bed)
the
of
osity
holdup/por
(static
saturation
residual
1
1
1
1
1
1
t
2
3
2
3
2
2
1
g
-
-
-
-
-
-
-
+
-
-
-
-
-
=
b
b
r
b
b
e
b
b
e
m
b
b
e
b
b
e
d
r
g
g
t
r
B
t
r
B
g
g
t
r
B
t
r
B
u
k
u
k
l
1
.
0
2
.
1
65
.
1
2
.
0
24
.
0
1
1
1
)
Re
17
.
3
1
(
Re
)
(
)
(
L
L
L
L
k
G
j
G
We
We
where
X
B
X
A
f
+
=
+
=
x
x
x
5
.
1
2
2
2
2
Re
001
.
0
Re
)
(
)
(
L
L
n
G
m
G
where
X
D
X
C
f
+
=
+
=
x
x
x
ú
ú
û
ù
ê
ê
ë
é
+
=
4
/
1
2
/
3
4
/
1
)
(Re
3
.
17
3
.
31
)
)
(Re
(
1
L
L
G
L
L
G
We
X
We
X
f
CATEGORIES
Economics
Nursing
Applied Sciences
Psychology
Science
Management
Computer Science
Human Resource Management
Accounting
Information Systems
English
Anatomy
Operations Management
Sociology
Literature
Education
Business & Finance
Marketing
Engineering
Statistics
Biology
Political Science
Reading
History
Financial markets
Philosophy
Mathematics
Law
Criminal
Architecture and Design
Government
Social Science
World history
Chemistry
Humanities
Business Finance
Writing
Programming
Telecommunications Engineering
Geography
Physics
Spanish
ach
e. Embedded Entrepreneurship
f. Three Social Entrepreneurship Models
g. Social-Founder Identity
h. Micros-enterprise Development
Outcomes
Subset 2. Indigenous Entrepreneurship Approaches (Outside of Canada)
a. Indigenous Australian Entrepreneurs Exami
Calculus
(people influence of
others) processes that you perceived occurs in this specific Institution Select one of the forms of stratification highlighted (focus on inter the intersectionalities
of these three) to reflect and analyze the potential ways these (
American history
Pharmacology
Ancient history
. Also
Numerical analysis
Environmental science
Electrical Engineering
Precalculus
Physiology
Civil Engineering
Electronic Engineering
ness Horizons
Algebra
Geology
Physical chemistry
nt
When considering both O
lassrooms
Civil
Probability
ions
Identify a specific consumer product that you or your family have used for quite some time. This might be a branded smartphone (if you have used several versions over the years)
or the court to consider in its deliberations. Locard’s exchange principle argues that during the commission of a crime
Chemical Engineering
Ecology
aragraphs (meaning 25 sentences or more). Your assignment may be more than 5 paragraphs but not less.
INSTRUCTIONS:
To access the FNU Online Library for journals and articles you can go the FNU library link here:
https://www.fnu.edu/library/
In order to
n that draws upon the theoretical reading to explain and contextualize the design choices. Be sure to directly quote or paraphrase the reading
ce to the vaccine. Your campaign must educate and inform the audience on the benefits but also create for safe and open dialogue. A key metric of your campaign will be the direct increase in numbers.
Key outcomes: The approach that you take must be clear
Mechanical Engineering
Organic chemistry
Geometry
nment
Topic
You will need to pick one topic for your project (5 pts)
Literature search
You will need to perform a literature search for your topic
Geophysics
you been involved with a company doing a redesign of business processes
Communication on Customer Relations. Discuss how two-way communication on social media channels impacts businesses both positively and negatively. Provide any personal examples from your experience
od pressure and hypertension via a community-wide intervention that targets the problem across the lifespan (i.e. includes all ages).
Develop a community-wide intervention to reduce elevated blood pressure and hypertension in the State of Alabama that in
in body of the report
Conclusions
References (8 References Minimum)
*** Words count = 2000 words.
*** In-Text Citations and References using Harvard style.
*** In Task section I’ve chose (Economic issues in overseas contracting)"
Electromagnetism
w or quality improvement; it was just all part of good nursing care. The goal for quality improvement is to monitor patient outcomes using statistics for comparison to standards of care for different diseases
e a 1 to 2 slide Microsoft PowerPoint presentation on the different models of case management. Include speaker notes... .....Describe three different models of case management.
visual representations of information. They can include numbers
SSAY
ame workbook for all 3 milestones. You do not need to download a new copy for Milestones 2 or 3. When you submit Milestone 3
pages):
Provide a description of an existing intervention in Canada
making the appropriate buying decisions in an ethical and professional manner.
Topic: Purchasing and Technology
You read about blockchain ledger technology. Now do some additional research out on the Internet and share your URL with the rest of the class
be aware of which features their competitors are opting to include so the product development teams can design similar or enhanced features to attract more of the market. The more unique
low (The Top Health Industry Trends to Watch in 2015) to assist you with this discussion.
https://youtu.be/fRym_jyuBc0
Next year the $2.8 trillion U.S. healthcare industry will finally begin to look and feel more like the rest of the business wo
evidence-based primary care curriculum. Throughout your nurse practitioner program
Vignette
Understanding Gender Fluidity
Providing Inclusive Quality Care
Affirming Clinical Encounters
Conclusion
References
Nurse Practitioner Knowledge
Mechanics
and word limit is unit as a guide only.
The assessment may be re-attempted on two further occasions (maximum three attempts in total). All assessments must be resubmitted 3 days within receiving your unsatisfactory grade. You must clearly indicate “Re-su
Trigonometry
Article writing
Other
5. June 29
After the components sending to the manufacturing house
1. In 1972 the Furman v. Georgia case resulted in a decision that would put action into motion. Furman was originally sentenced to death because of a murder he committed in Georgia but the court debated whether or not this was a violation of his 8th amend
One of the first conflicts that would need to be investigated would be whether the human service professional followed the responsibility to client ethical standard. While developing a relationship with client it is important to clarify that if danger or
Ethical behavior is a critical topic in the workplace because the impact of it can make or break a business
No matter which type of health care organization
With a direct sale
During the pandemic
Computers are being used to monitor the spread of outbreaks in different areas of the world and with this record
3. Furman v. Georgia is a U.S Supreme Court case that resolves around the Eighth Amendments ban on cruel and unsual punishment in death penalty cases. The Furman v. Georgia case was based on Furman being convicted of murder in Georgia. Furman was caught i
One major ethical conflict that may arise in my investigation is the Responsibility to Client in both Standard 3 and Standard 4 of the Ethical Standards for Human Service Professionals (2015). Making sure we do not disclose information without consent ev
4. Identify two examples of real world problems that you have observed in your personal
Summary & Evaluation: Reference & 188. Academic Search Ultimate
Ethics
We can mention at least one example of how the violation of ethical standards can be prevented. Many organizations promote ethical self-regulation by creating moral codes to help direct their business activities
*DDB is used for the first three years
For example
The inbound logistics for William Instrument refer to purchase components from various electronic firms. During the purchase process William need to consider the quality and price of the components. In this case
4. A U.S. Supreme Court case known as Furman v. Georgia (1972) is a landmark case that involved Eighth Amendment’s ban of unusual and cruel punishment in death penalty cases (Furman v. Georgia (1972)
With covid coming into place
In my opinion
with
Not necessarily all home buyers are the same! When you choose to work with we buy ugly houses Baltimore & nationwide USA
The ability to view ourselves from an unbiased perspective allows us to critically assess our personal strengths and weaknesses. This is an important step in the process of finding the right resources for our personal learning style. Ego and pride can be
· By Day 1 of this week
While you must form your answers to the questions below from our assigned reading material
CliftonLarsonAllen LLP (2013)
5 The family dynamic is awkward at first since the most outgoing and straight forward person in the family in Linda
Urien
The most important benefit of my statistical analysis would be the accuracy with which I interpret the data. The greatest obstacle
From a similar but larger point of view
4 In order to get the entire family to come back for another session I would suggest coming in on a day the restaurant is not open
When seeking to identify a patient’s health condition
After viewing the you tube videos on prayer
Your paper must be at least two pages in length (not counting the title and reference pages)
The word assimilate is negative to me. I believe everyone should learn about a country that they are going to live in. It doesnt mean that they have to believe that everything in America is better than where they came from. It means that they care enough
Data collection
Single Subject Chris is a social worker in a geriatric case management program located in a midsize Northeastern town. She has an MSW and is part of a team of case managers that likes to continuously improve on its practice. The team is currently using an
I would start off with Linda on repeating her options for the child and going over what she is feeling with each option. I would want to find out what she is afraid of. I would avoid asking her any “why” questions because I want her to be in the here an
Summarize the advantages and disadvantages of using an Internet site as means of collecting data for psychological research (Comp 2.1) 25.0\% Summarization of the advantages and disadvantages of using an Internet site as means of collecting data for psych
Identify the type of research used in a chosen study
Compose a 1
Optics
effect relationship becomes more difficult—as the researcher cannot enact total control of another person even in an experimental environment. Social workers serve clients in highly complex real-world environments. Clients often implement recommended inte
I think knowing more about you will allow you to be able to choose the right resources
Be 4 pages in length
soft MB-920 dumps review and documentation and high-quality listing pdf MB-920 braindumps also recommended and approved by Microsoft experts. The practical test
g
One thing you will need to do in college is learn how to find and use references. References support your ideas. College-level work must be supported by research. You are expected to do that for this paper. You will research
Elaborate on any potential confounds or ethical concerns while participating in the psychological study 20.0\% Elaboration on any potential confounds or ethical concerns while participating in the psychological study is missing. Elaboration on any potenti
3 The first thing I would do in the family’s first session is develop a genogram of the family to get an idea of all the individuals who play a major role in Linda’s life. After establishing where each member is in relation to the family
A Health in All Policies approach
Note: The requirements outlined below correspond to the grading criteria in the scoring guide. At a minimum
Chen
Read Connecting Communities and Complexity: A Case Study in Creating the Conditions for Transformational Change
Read Reflections on Cultural Humility
Read A Basic Guide to ABCD Community Organizing
Use the bolded black section and sub-section titles below to organize your paper. For each section
Losinski forwarded the article on a priority basis to Mary Scott
Losinksi wanted details on use of the ED at CGH. He asked the administrative resident