Industrial Oilfield Chemistry Short Course
Two-Day ACPA Short Course in
Scaling Chemistry Wednesday and Thursday November 2 and 3, 2011 Edmonton Hotel & Convention Centre 4520 – 76 Avenue Edmonton, Alberta
About the ACPA Chemistry touches and interacts with every part of our lives. Everything from pharmaceuticals, clothing, plastic, petroleum to the food you eat has probably been created, checked or modified by a chemist. Chemists also play crucial roles in environmental monitoring and remediation, helping to protect your health and safety by ensuring the quality of the water you drink and the purity of the air you breathe. For those reasons and many more, the practice of chemistry is regulated by the Province of Alberta through the Association of the Chemical Profession of Alberta (ACPA). Only chemists who are registered members of the ACPA may use the titles P.Chem. (Professional Chemist) or C.I.T. (Chemist in Training) as appropriate. These titles provide immediate assurance to government, industry and the public that specific levels of education and experience have been met. The objectives of the ACPA are the following: ● To ensure that our members meet the high standards of professional competence and ethics needed for protection of industry and the public; ● To increase the knowledge, skills and proficiency of our members in all things relating to chemistry; ● To foster greater general interest in chemistry and a better understanding of the chemical profession by industry and the public at large; and ● To provide a recognized voice for professional chemists in Alberta. The ACPA is one of only six professional organizations whose members are permitted to sign off on environmental reports or sites for closure in Alberta. For more information about the ACPA, please see our website at www.pchem.ca. Copyright Notice All rights reserved. No part of this publication may be reproduced in any form, print or electronic, for the purposes of resale without the prior written permission of either the author involved or the copyright holder noted on the slide.
ACPA 2011 Short Course
A2
Scaling Chemistry (Edmonton)
Celebrating the International Year of Chemistry The International Year of Chemistry 2011 (IYC 2011) is a worldwide celebration of achievements in chemistry and its contributions to the well‐being of humankind. Under the unifying theme “Chemistry — Our Life, Our Future,” IYC 2011 will offer a range of interactive, entertaining and educational activities for all ages. The International Year of Chemistry is intended to reach across the globe, with opportunities for public participation at the local, regional and national level. The year 2011 will coincide with the 100th anniversary of the Nobel Prize awarded to Madame Marie Curie — an opportunity to celebrate the contributions of women to science. The year will also be the 100th anniversary of the founding of the International Association of Chemical Societies, which was succeeded by IUPAC a few years later, providing a chance to highlight the benefits of international scientific collaboration. The goals of IYC 2011 are the following: ● To increase the public appreciation of chemistry in meeting world needs; ● To encourage interest in chemistry among young people; ● To generate enthusiasm for the creative future of chemistry; and ● To help enhance international cooperation by serving as a focal point or information source for activities by national chemical societies, educational institutions, industry, and governmental and non‐governmental organizations. IYC 2011 events will emphasize that chemistry is a creative science essential for sustainability and improvements to our way of life. Activities such as lectures, exhibits, and hands‐on experiments will explore how chemical research is critical for solving our most vexing global problems of food, water, health, energy, transportation and more. The Chemical Institute of Canada (CIC) has taken the lead to bring together chemistry professionals to spread the IYC message. It has helped to create a Canada‐wide organizing committee that is working with science outreach organizations, science centers, museums, government agencies and trade associations to promote IYC and its activities. For more information, please see the IYC 2011 website at www.iyc2011.ca. (Adapted from International Year of Chemistry 2011: A Canadian Celebration of Chemistry (Overview) at http://www.iyc2011.ca/index.php?ci_id=2283&la_id=1.)
ACPA 2011 Short Course
A3
Scaling Chemistry (Edmonton)
Program Contents Course Schedule ........................................................................................................ A5 Speaker Biographies .................................................................................................. A6 Summaries and Slides for Day 1 ................................................................................. A9 1. Scaling Chemistry and Theory of Saturation Indices ...................................... A10 Maurice Shevalier, University of Calgary 2. Kinetics of Nucleation (Precipitation) ............................................................ A29 Maurice Shevalier, University of Calgary 3. Criteria for Determining Good Water Analysis ............................................... A42 Maurice Shevalier, University of Calgary 4. Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 .................... A53 Maurice Shevalier, University of Calgary Summaries and Slides for Day 2 .................................................................................. B1 5. Quality of Thermodynamic Databases ............................................................. B2 Maurice Shevalier, University of Calgary 6. Chemical Analysis of Scales ........................................................................... B14 Ken Schmidt (Wilson Analytical) and Neil Warrender (Sanjel Corp.) 7. Dissolution of Scales ...................................................................................... B47 Tom McCartney (Clean Harbors) 8. Chemistry of Scale Inhibitors ......................................................................... B83 Tom Ignacz (Baker Hughes [Petrolite])
ACPA 2011 Short Course
A4
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry Wednesday and Thursday, November 2 and 3, 2011
Course Schedule Day 1 08:00–08:25 Registration and continental breakfast 08:25–08:30 Welcome and introductions 08:30–10:00 1. Scaling Chemistry and Theory of Saturation Indices — Maurice Shevalier (U. of Calgary) 10:00–10:30 Coffee 10:30–12:00 2. Kinetics of Nucleation (Precipitation) — Maurice Shevalier (U. of Calgary) 12:00–13:00 Lunch 13:00–14:30 3. Criteria for Determining Good Water Analysis — Maurice Shevalier (U. of Calgary) 14:30–15:00 Coffee 15:00–16:30 4. Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 — Maurice Shevalier (U. of Calgary)
Day 2
08:00–08:25 Registration and continental breakfast 08:25–08:30 Welcome and introductions 08:30–10:00 5. Quality of Thermodynamic Databases — Maurice Shevalier (U. of Calgary) 10:00–10:30 Coffee 10:30‐12:00 6. Chemical Analysis of Scales — Ken Schmidt (Wilson Analytical) and Neil Warrender (Sanjel Corp.) 12:00–13:00 Lunch 13:00–14:30 7. Dissolution of Scales — Tom McCartney (Clean Harbors) 14:30–15:00 Coffee 15:00–16:30 8. Chemistry of Scale Inhibitors — Tom Ignacz (Baker Hughes [Petrolite])
ACPA 2011 Short Course
A5
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011
Speaker Biographies
Maurice Shevalier, P.Chem. Maurice is a Research Scientist and Project Manager for the Applied Geochemistry Group in the Department of Geoscience at the University of Calgary. He graduated with B.Sc. in Chemistry from the University of Calgary in 1982, adding an M.Sc. in Electrochemistry in 1985 and an M.Sc. in Physics specializing in Computer Modeling in 1992. In 1985, he secured a Research Assistant position in the Diagenesis Research Group in the Department of Geology and Geophysics at the U of C. His responsibilities included sampling and chemical analysis of oilfield brines as well as ground and surficial waters. Maurice was later promoted to Research Scientist when his duties shifted more to computer modeling. He has been involved in various types of geochemical computer modeling for the past 20 years. Current projects include the International Energy Agency Green House Gas Weyburn CO2 Monitoring and Storage Project, a long‐term project looking at CO2 sequestration in a depleted carbonate oil reservoir. Maurice is also involved in the PennWest CO2 Enhanced Oil Recovery Pilot project, as well as coal bed methane, environmental, and heavy oil projects involving water and gas sampling, analysis, and geochemical computer modeling. Maurice Shevalier, P.Chem. Applied Geochemistry Group Dept. of Geoscience, University of Calgary Calgary, AB T2N 1N4
Tel: 403‐220‐7873 Fax: 403‐220‐8514 E‐mail: [email protected]
ACPA 2011 Short Course
A6
Scaling Chemistry (Edmonton)
Ken Schmidt, Ph.D., P. Chem. Ken Schmidt is a professional chemist working out of Fort Saskatchewan, AB. He is the president of Wilson Analytical Services Inc., a chemical analysis and field instrumentation company serving the oil and gas industry. He has over twenty years of R&D and management experience in industry in Alberta working in areas such as ceramics, coatings, sulphur chemistry, spectroscopy, chemical analysis, and the design of analytical instrumentation. Ken holds a Ph.D. in inorganic chemistry from the University of Calgary and a combined Honours BSc in chemistry and biochemistry from McMaster University. He served for seven years on the board of the Association of the Chemical Profession of Alberta, and is currently the Industrial Liaison Director on the Canadian Society for Chemistry board. He been on the board of the Calgary or Edmonton CIC Local Sections since 1986, and served as the Chair of the Edmonton Section in 2004 and again in 2009. He is the author or co‐author of over 50 scientific publications and presentations, and has co‐organized (and occasionally presented at) nearly 30 technical workshops or short courses. Over the years, he has also been involved in many outreach activities aimed at highlighting the wonders of chemistry to students and the general public. Ken Schmidt, Ph.D., P.Chem. Wilson Analytical Services Inc. #2075, 61 Broadway Boulevard Sherwood Park, AB T8H 2C1
Tel: 780‐702‐0610 Toll‐Free: 1‐866‐3wilson (394‐5766) Fax: 780‐998‐5327 E‐mail: [email protected] Web: www.wilsonanalytical.com
Neil Warrender, Ph.D., P.Chem. Neil holds a Ph.D. in Physical Chemistry and is a registered Professional Chemist (P.Chem.) in the Province of Alberta. Neil has been lost in the tortured maze of oilfield chemistry for almost twenty years, seeking chemical solutions for various oilfield service companies along the way. He is currently leading the technical team at Sanjel Corporation to the promised land of innovative technology and environmental friendliness. Neil’s Ph.D. is in X‐ray diffraction, a technique that he has applied to a wide variety of projects and problems—especially the debris associated with corrosion failures and related issues. Such insight as he has managed to glean from these deliberations he will be delighted to share with participants of this ACPA short course. Neil Warrender, Ph.D., P.Chem. Sanjel Corporation Sanjel Professional Park, 10774 ‐ 42 Street SE Calgary, AB T2C 0L5 ACPA 2011 Short Course
Tel: 403‐723‐6060 Cell: 403‐479‐1670 E‐mail: [email protected]
A7
Scaling Chemistry (Edmonton)
Tom McCartney, P.Chem. Tom McCartney graduated with a B.Sc. in Honours Chemistry from the University of Alberta in 1978. After a couple of years working in the oil field and industrial services industry, Tom returned to study for a masters degree in metallurgical engineering, returning to industry in 1982. For the subsequent 28 years, Tom has worked in the research and development of chemical solutions for removing or preventing deposits. His experience in chemical and industrial cleaning has been in a wide range of industries, from refineries and power plants to chemical process systems and pulp and paper. In 1998, Tom became Chief Chemist for Woodrising Resources, a supplier of chemistry and consulting services for the industrial cleaning industry. There he successfully developed or invented processes and systems to dissolve or remove deposits ranging from complex organic mixtures to iron polysulfides. He also worked on developing processes to use in the new field of ultrasonic chemical cleaning while continuing to support previous inventions. In 2011, Tom accepted a new position as Technical Services Manager for the Paratene Products Group at Clean Harbors (Calgary). Tom McCartney, B.Sc., P.Chem. Clean Harbors Energy and Industrial Services Corp. #2, 321 ‐ 37th Avenue NE Calgary, AB T2E 6P6
Tel: 403‐216‐2131 Fax: 403‐216‐2132 E‐mail: [email protected] Web: www.paratene.com and www.cleanharbors.com
Thomas (Tom) Ignacz, Technical Account Executive Tom graduated from Concordia University (Montreal) with a M.Sc. in Chemistry in 1978. He entered the oil and gas industry in 1980 as a research chemist developing corrosion inhibitors for petroleum production and industrial cleaning. Over the next eight years, he progressed to a Technical Services Representative providing technical support to field personnel, including total system analysis, trouble‐shooting, product development, program recommendations, and customer presentations. In subsequent roles as a Technical Manager at production chemical companies, Tom was responsible for all aspects of technical issues, including analytical services laboratory, research and development, regulatory concerns, product stewardship, and training. He provided these services not only in the domestic market but also in the oilfields of Ecuador and Mexico. In his present role at Baker Hughes [Petrolite], Tom supports special projects and directs product development on paraffin and asphaltene control chemicals. Tom Ignacz, Technical Account Executive Baker Hughes [Petrolite] 2323 – 91 Avenue Edmonton, AB T6P 1L1
ACPA 2011 Short Course
Tel: 780‐416‐6440 Fax: 780‐416‐1824 Cell: 780‐242‐1047 E‐mail: [email protected] Web: www.bakerhughes.com
A8
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011
Summaries and Slides for Day 1 1. 2. 3. 4.
Scaling Chemistry and Theory of Saturation Indices ...................................... A10 Maurice Shevalier, University of Calgary Kinetics of Nucleation (Precipitation) ............................................................ A29 Maurice Shevalier, University of Calgary Criteria for Determining Good Water Analysis ............................................... A42 Maurice Shevalier, University of Calgary Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 .................... A53 Maurice Shevalier, University of Calgary
ACPA 2011 Short Course
A9
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011 Day 1, 08:30–10:00
1. Scaling Chemistry and Theory of Saturation Indices — Maurice Shevalier (University of Calgary) The saturation index shows whether a solution will tend to dissolve or precipitate a particular mineral. In this session, participants will learn how saturation indices can be calculated for dilute solutions using the Debye‐Hückel theory. The use of the B‐dot and Pitzer equations for more concentrated solutions will also be reviewed. Based on these theories, the activity coefficients of the various ions present in a solution can be calculated and the saturation indexes of minerals can be determined. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
ACPA 2011 Short Course
A10
Scaling Chemistry (Edmonton)
Scaling Chemistry Maurice Shevalier, P.Chem. Department of Geoscience University of Calgary [email protected] (403)220‐7873
Scaling Chemistry
Who am I? Why are you up front? • Maurice Shevalier – MSc in Physical Chemistry & Physics (Computer Modeling) – 25 years in Dept 25 years in Dept of Geoscience, University of of Geoscience University of Calgary – 25 years sampling, analyzing and modeling waters – Past 10+ years involved in CCS projects: sampling and modeling
Scaling Chemistry
Why are we here?
To hopefully prevent this from forming! Scale in a separator Scaling Chemistry
ACPA 2011 Short Course
A11
Scaling Chemistry (Edmonton)
How are we going to do this? • Going back to basics! – Detailed review of the theory
Scaling Chemistry
Why do this? • To prevent the ‘black box’ syndrome – Where you use a model without an understanding of the theory used in writing a program • Understanding of the theory helps you make better predictions from the model
Scaling Chemistry
Introduction • What is scale? – Scale is the precipitation (usually minerals) deposited on surfaces due to changes in water chemistry – Changes can be caused by mixing of waters, changes in temperature, pressure etc. p ,p – Scale interferes with heat exchangers, restricts flows in pipes
Scaling Chemistry
ACPA 2011 Short Course
A12
Scaling Chemistry (Edmonton)
Introduction (cont.) • What are the most common INORGANIC scales? – Calcium carbonate • CaCO3 (calcite, aragonite) (calcite aragonite)
– Calcium/barium sulphate: • CaSO4 (anhydrite) • CaSO4•2H2O (gypsum) • BaSO4 (barite)
Scaling Chemistry
Introduction (cont.) • What factors control scale formation? – Changes in water chemistry caused by MIXING (either different formation waters or formation waters and process fluids) usually by INJECTION or p ) y y processing at the surface – Changes in physical conditions (pressure, temperature) usually due to production
Scaling Chemistry
Introduction (cont.) • Not all scales behave as expected! • Calcium sulphate minerals exhibit retrograde solubility, i.e. solubility decreases as temperature increases! temperature increases! • Drops in pressure will also decrease solubility. • Calcium carbonate solubility decreases as temperature increases and pressure decreases
Scaling Chemistry
ACPA 2011 Short Course
A13
Scaling Chemistry (Edmonton)
Calcium sulfate solubility as a function of temperature and pressure (Source: Blount and Dickson 1973).
Scaling Chemistry
Calcium carbonate solubility as a function of temperature and pressure (Source: Duan and Li 2008).
Scaling Chemistry
References • Blount, C.W., and Dickson, F.W. (1973), Gypsum‐anhydrite equilibria in systems CaSO4‐H2O and CaSO4‐NaCl‐H2O, Amer. Mineral. 58, pp. 323–331. • Duan, Z., and Li, D. (2008). Coupled phase and aqueous species ( ) p p q p equilibrium of the H2O–CO2–NaCl–CaCO3 system from 0 to 250ºC, 1 to 1000 bars with NaCl concentrations up to saturation of halite. Geochim. Cosmochim. Acta, 72 (20): 5128‐5145.
Scaling Chemistry
ACPA 2011 Short Course
A14
Scaling Chemistry (Edmonton)
Theory of Saturation Indices
Scaling Chemistry
Activities of Ions • Thermodynamic properties of ions depend on chemical potential μi • Ideally, chemical potential would be related to molality mi by: μi = μio + RT ln(mi/mo)
(1)
• Chemical potential of a real solution can be written in a similar way: μi = μio + RT ln ai
(2) Scaling Chemistry
Activity of Ions • We have defined activity and the molarity by the following: ai = γimi/mo
(3)
• Activity and molality are related by the activity coefficient γi • What is γi and how does it relate to …?
Scaling Chemistry
ACPA 2011 Short Course
A15
Scaling Chemistry (Edmonton)
Activity of Ions • Consider a compound composed of a monovalent anion (μ−) and cation (μ+), then the total chemical potential of the electrically neutral solution is neutral solution is μ+ + μ−= μ+o +μ-o + RT ln a+ + RT ln a- (4) = μ+o + μ-o + RT ln(m+/mo) + RT ln(m-/mo) + RT lnγ+γ‐ (5)
Scaling Chemistry
Activity of Ions • It is almost impossible to separate the product γ+γ− into anion and cation components • Define ‘mean ionic activity coefficient’ as γ± = (γ+γ‐)1/2
(6)
When the salt is MpXq, then γ± = (γ+pγ‐q)1/n
(7)
where n = p + q Scaling Chemistry
Activity of Ions • For an ideal case, the energy of interaction of two uncharged molecules falls off as r−6 but Coulombic interaction between two charged ions falls off as r−1. • Opposite charged ions attract each other but cations tend to be near anions, so there is an abundance of the counter ion around a given ion. • On average, more counter ions pass a given ion and the time‐averaged haze of opposite charged ions creates the ionic atmosphere of the ion. Scaling Chemistry
ACPA 2011 Short Course
A16
Scaling Chemistry (Edmonton)
Activity of Ions • The departure from an ideal solution is due to the electrostatic interactions • Consider solution where the electrostatic interactions have been turned off and ions interactions have been turned off and ions maintain their positions • The difference in the chemical potentials is a difference in the molar Gibbs function, ΔG, between the uncharged and charged state, which represents the work done on charging the system Scaling Chemistry
Activity of Ions • The chemical potential of an ideal dilute solution is μo(mi) and activity coefficient of the true solution is: μ(mi) = μo(mi) + RT ln γ± (8) or ln γ± = (1/RT) {μ(mi) ‐ μo(mi)} (9) or ln γ± = (we/RT) (10) So… what is we? Scaling Chemistry
Activity of Ions • The Coulombic potential at a distance r from an ion of charge zie in a vacuum is: ϕ(r) = (zie/4πεo)(1/r)
(11)
• In In a solution the solvent decreases the a solution the solvent decreases the strength of the field and ϕ(r) = (zie/4πε)(1/r)
(12)
Scaling Chemistry
ACPA 2011 Short Course
A17
Scaling Chemistry (Edmonton)
Activity of Ions • In an ionic atmosphere, the central charge is shielded, and the potential is the shielded Coulomb potential where 1/r → (1/r)exp(‐r/rD)
(13)
ϕ(r) = (zie/4πε)(1/r)exp(‐r/rD)
(14)
So where rD is the unknown parameter. Scaling Chemistry
Activity of Ions • In a spherically symmetrical charge distribution, charge density at distance r is ρi(r), the potential depends only on the radius, so the following simplification is possible: so the following simplification is possible: (1/r2)(d/dr)(r2dϕi/dr) = ‐ρi(r)/ε resulting in ϕi(r)/rD2= ‐ρi(r)/ε
(15) (16)
Scaling Chemistry
Activity of Ions • To solve equation (16) for rD we need to know charge density, ρi(r) • Charge density at point r is due to competition between electrostatic attractive forces of central ion for its counter ions and disruptive effects of thermal agitation it ti • Energy of interaction of ion of charge zje with central ion of charge zie separated by a distance r is ΔE = zjeϕi(r)
(17)
where ϕi(r) = potential generated by the ion i Scaling Chemistry
ACPA 2011 Short Course
A18
Scaling Chemistry (Edmonton)
Activity of Ions • Boltzmann distribution gives proportion of ions with this energy at temperature T as Nj(r)/Noj = number of ions of type j per unit vol with potential = ϕi(r) number of ion of of type j per unit vol with potential number of ion of of type j per unit vol with potential = 0 0
= exp(‐ΔE/kT) = exp (‐zjeϕi(r)/kT)
(18)
Scaling Chemistry
Activity of Ions • Charge density at a distance r from ion I is the concentration of ions of each type multiplied by charge of each ion: ρi(r) = N (r) = N+(r)z+e + N + N‐(r)z‐e o = N +z+e exp(‐z+eϕi(r)/kT) + No‐z‐e exp(‐z‐eϕi(r)/kT) (19)
Scaling Chemistry
Activity of Ions • Consider the electrostatic interaction energy to be small compared with kT. If this were not the case, the attraction of the ions would overcome the scattering influence of the overcome the scattering influence of the thermal motion and the ions would condense into a crystal lattice • Thus, exp(x) ≈ 1 + x + h.o.t.
Scaling Chemistry
ACPA 2011 Short Course
A19
Scaling Chemistry (Edmonton)
Activity of Ions • Thus (19) can be rewritten as ρi(r) = (No+z+ + No‐z‐)e – {(No+z+2 + No‐z‐2)e2ϕi(r)}/kT + ... The first term on the right hand side of the equation is zero since it is a concentration of charge and the solution is electrically neutral: ρi(r) = – {(No+z+2 + No‐z‐2)e2ϕi(r)}/kT
(20)
Scaling Chemistry
Activity of Ions • (No+z+2 + No‐z‐2) can be simplified by expressing number concentrations (Noj) in terms of molalities: Noj = m = mjLρ (21) where L = Avogadro’s number mj = amount per unit mass ρ = solvent density and I = ½Σj mjzj2 = ionic strength Scaling Chemistry
Activity of Ions • The charge density in the vicinity of i is now ρi(r) = –(2ρe2LI/kT)ϕi(r)
(22)
and rD is
rD2 = εRT/2ρL2e2I (23)
Scaling Chemistry
ACPA 2011 Short Course
A20
Scaling Chemistry (Edmonton)
Activity of Ions • We started by trying to determine the activity coefficient and we are not quite there yet! • We started by considering the electrical work of charging a central ion when it is surrounded g g by an ionic atmosphere • We need to know the potential at the ion arising from the atmosphere, ϕatmos, which is the difference between the total potential (14) and the central ion potential Scaling Chemistry
Activity of Ions 4 ϕatmos(r) = ϕi(r) – ϕcentral ion(r) = {(zie/4πε)/r}[exp(‐r/rD) – 1] (24) • Consider the potential at the ion of interest ((r = 0), then limit r→0 is ), ϕatmos(0) = ‐(zie/4πε)(1/rD) (25) • Also, consider the central charge to be q not ze. Then the work involved in adding a charge dq to a region with a potential of ϕatmos(0) is dwe = ϕatmos(0) dq (26) Scaling Chemistry
Activity of Ions we = L∫0zie ϕatmos(0) dq = ‐zi2e2L/8πεrD (27) • Recalling (10), ln γ± = (we/RT), we have the following: ln γ± = ‐(zi2e2L)/(8πεrDRT)
(28)
• Substituting (23) into (28) (and assuming the general formula for ionic salt is MpXq) gives the following for ln γ±: Scaling Chemistry
ACPA 2011 Short Course
A21
Scaling Chemistry (Edmonton)
Activity of Ions ln γ± = ‐|z+z‐|(Le2/8πεrDRT)
(29)
• Substituting (23) into (29) yields (30) after converting to log from ln: log γ± = ‐A|z+z‐|(I)½
Debye‐Hückel Limiting Law (30)
• Above equation, although important, is only useful for very low concentration data, I SI > −0.3: equilibrium, no dissolution or precipitation p p SI
Scaling Chemistry Wednesday and Thursday November 2 and 3, 2011 Edmonton Hotel & Convention Centre 4520 – 76 Avenue Edmonton, Alberta
About the ACPA Chemistry touches and interacts with every part of our lives. Everything from pharmaceuticals, clothing, plastic, petroleum to the food you eat has probably been created, checked or modified by a chemist. Chemists also play crucial roles in environmental monitoring and remediation, helping to protect your health and safety by ensuring the quality of the water you drink and the purity of the air you breathe. For those reasons and many more, the practice of chemistry is regulated by the Province of Alberta through the Association of the Chemical Profession of Alberta (ACPA). Only chemists who are registered members of the ACPA may use the titles P.Chem. (Professional Chemist) or C.I.T. (Chemist in Training) as appropriate. These titles provide immediate assurance to government, industry and the public that specific levels of education and experience have been met. The objectives of the ACPA are the following: ● To ensure that our members meet the high standards of professional competence and ethics needed for protection of industry and the public; ● To increase the knowledge, skills and proficiency of our members in all things relating to chemistry; ● To foster greater general interest in chemistry and a better understanding of the chemical profession by industry and the public at large; and ● To provide a recognized voice for professional chemists in Alberta. The ACPA is one of only six professional organizations whose members are permitted to sign off on environmental reports or sites for closure in Alberta. For more information about the ACPA, please see our website at www.pchem.ca. Copyright Notice All rights reserved. No part of this publication may be reproduced in any form, print or electronic, for the purposes of resale without the prior written permission of either the author involved or the copyright holder noted on the slide.
ACPA 2011 Short Course
A2
Scaling Chemistry (Edmonton)
Celebrating the International Year of Chemistry The International Year of Chemistry 2011 (IYC 2011) is a worldwide celebration of achievements in chemistry and its contributions to the well‐being of humankind. Under the unifying theme “Chemistry — Our Life, Our Future,” IYC 2011 will offer a range of interactive, entertaining and educational activities for all ages. The International Year of Chemistry is intended to reach across the globe, with opportunities for public participation at the local, regional and national level. The year 2011 will coincide with the 100th anniversary of the Nobel Prize awarded to Madame Marie Curie — an opportunity to celebrate the contributions of women to science. The year will also be the 100th anniversary of the founding of the International Association of Chemical Societies, which was succeeded by IUPAC a few years later, providing a chance to highlight the benefits of international scientific collaboration. The goals of IYC 2011 are the following: ● To increase the public appreciation of chemistry in meeting world needs; ● To encourage interest in chemistry among young people; ● To generate enthusiasm for the creative future of chemistry; and ● To help enhance international cooperation by serving as a focal point or information source for activities by national chemical societies, educational institutions, industry, and governmental and non‐governmental organizations. IYC 2011 events will emphasize that chemistry is a creative science essential for sustainability and improvements to our way of life. Activities such as lectures, exhibits, and hands‐on experiments will explore how chemical research is critical for solving our most vexing global problems of food, water, health, energy, transportation and more. The Chemical Institute of Canada (CIC) has taken the lead to bring together chemistry professionals to spread the IYC message. It has helped to create a Canada‐wide organizing committee that is working with science outreach organizations, science centers, museums, government agencies and trade associations to promote IYC and its activities. For more information, please see the IYC 2011 website at www.iyc2011.ca. (Adapted from International Year of Chemistry 2011: A Canadian Celebration of Chemistry (Overview) at http://www.iyc2011.ca/index.php?ci_id=2283&la_id=1.)
ACPA 2011 Short Course
A3
Scaling Chemistry (Edmonton)
Program Contents Course Schedule ........................................................................................................ A5 Speaker Biographies .................................................................................................. A6 Summaries and Slides for Day 1 ................................................................................. A9 1. Scaling Chemistry and Theory of Saturation Indices ...................................... A10 Maurice Shevalier, University of Calgary 2. Kinetics of Nucleation (Precipitation) ............................................................ A29 Maurice Shevalier, University of Calgary 3. Criteria for Determining Good Water Analysis ............................................... A42 Maurice Shevalier, University of Calgary 4. Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 .................... A53 Maurice Shevalier, University of Calgary Summaries and Slides for Day 2 .................................................................................. B1 5. Quality of Thermodynamic Databases ............................................................. B2 Maurice Shevalier, University of Calgary 6. Chemical Analysis of Scales ........................................................................... B14 Ken Schmidt (Wilson Analytical) and Neil Warrender (Sanjel Corp.) 7. Dissolution of Scales ...................................................................................... B47 Tom McCartney (Clean Harbors) 8. Chemistry of Scale Inhibitors ......................................................................... B83 Tom Ignacz (Baker Hughes [Petrolite])
ACPA 2011 Short Course
A4
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry Wednesday and Thursday, November 2 and 3, 2011
Course Schedule Day 1 08:00–08:25 Registration and continental breakfast 08:25–08:30 Welcome and introductions 08:30–10:00 1. Scaling Chemistry and Theory of Saturation Indices — Maurice Shevalier (U. of Calgary) 10:00–10:30 Coffee 10:30–12:00 2. Kinetics of Nucleation (Precipitation) — Maurice Shevalier (U. of Calgary) 12:00–13:00 Lunch 13:00–14:30 3. Criteria for Determining Good Water Analysis — Maurice Shevalier (U. of Calgary) 14:30–15:00 Coffee 15:00–16:30 4. Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 — Maurice Shevalier (U. of Calgary)
Day 2
08:00–08:25 Registration and continental breakfast 08:25–08:30 Welcome and introductions 08:30–10:00 5. Quality of Thermodynamic Databases — Maurice Shevalier (U. of Calgary) 10:00–10:30 Coffee 10:30‐12:00 6. Chemical Analysis of Scales — Ken Schmidt (Wilson Analytical) and Neil Warrender (Sanjel Corp.) 12:00–13:00 Lunch 13:00–14:30 7. Dissolution of Scales — Tom McCartney (Clean Harbors) 14:30–15:00 Coffee 15:00–16:30 8. Chemistry of Scale Inhibitors — Tom Ignacz (Baker Hughes [Petrolite])
ACPA 2011 Short Course
A5
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011
Speaker Biographies
Maurice Shevalier, P.Chem. Maurice is a Research Scientist and Project Manager for the Applied Geochemistry Group in the Department of Geoscience at the University of Calgary. He graduated with B.Sc. in Chemistry from the University of Calgary in 1982, adding an M.Sc. in Electrochemistry in 1985 and an M.Sc. in Physics specializing in Computer Modeling in 1992. In 1985, he secured a Research Assistant position in the Diagenesis Research Group in the Department of Geology and Geophysics at the U of C. His responsibilities included sampling and chemical analysis of oilfield brines as well as ground and surficial waters. Maurice was later promoted to Research Scientist when his duties shifted more to computer modeling. He has been involved in various types of geochemical computer modeling for the past 20 years. Current projects include the International Energy Agency Green House Gas Weyburn CO2 Monitoring and Storage Project, a long‐term project looking at CO2 sequestration in a depleted carbonate oil reservoir. Maurice is also involved in the PennWest CO2 Enhanced Oil Recovery Pilot project, as well as coal bed methane, environmental, and heavy oil projects involving water and gas sampling, analysis, and geochemical computer modeling. Maurice Shevalier, P.Chem. Applied Geochemistry Group Dept. of Geoscience, University of Calgary Calgary, AB T2N 1N4
Tel: 403‐220‐7873 Fax: 403‐220‐8514 E‐mail: [email protected]
ACPA 2011 Short Course
A6
Scaling Chemistry (Edmonton)
Ken Schmidt, Ph.D., P. Chem. Ken Schmidt is a professional chemist working out of Fort Saskatchewan, AB. He is the president of Wilson Analytical Services Inc., a chemical analysis and field instrumentation company serving the oil and gas industry. He has over twenty years of R&D and management experience in industry in Alberta working in areas such as ceramics, coatings, sulphur chemistry, spectroscopy, chemical analysis, and the design of analytical instrumentation. Ken holds a Ph.D. in inorganic chemistry from the University of Calgary and a combined Honours BSc in chemistry and biochemistry from McMaster University. He served for seven years on the board of the Association of the Chemical Profession of Alberta, and is currently the Industrial Liaison Director on the Canadian Society for Chemistry board. He been on the board of the Calgary or Edmonton CIC Local Sections since 1986, and served as the Chair of the Edmonton Section in 2004 and again in 2009. He is the author or co‐author of over 50 scientific publications and presentations, and has co‐organized (and occasionally presented at) nearly 30 technical workshops or short courses. Over the years, he has also been involved in many outreach activities aimed at highlighting the wonders of chemistry to students and the general public. Ken Schmidt, Ph.D., P.Chem. Wilson Analytical Services Inc. #2075, 61 Broadway Boulevard Sherwood Park, AB T8H 2C1
Tel: 780‐702‐0610 Toll‐Free: 1‐866‐3wilson (394‐5766) Fax: 780‐998‐5327 E‐mail: [email protected] Web: www.wilsonanalytical.com
Neil Warrender, Ph.D., P.Chem. Neil holds a Ph.D. in Physical Chemistry and is a registered Professional Chemist (P.Chem.) in the Province of Alberta. Neil has been lost in the tortured maze of oilfield chemistry for almost twenty years, seeking chemical solutions for various oilfield service companies along the way. He is currently leading the technical team at Sanjel Corporation to the promised land of innovative technology and environmental friendliness. Neil’s Ph.D. is in X‐ray diffraction, a technique that he has applied to a wide variety of projects and problems—especially the debris associated with corrosion failures and related issues. Such insight as he has managed to glean from these deliberations he will be delighted to share with participants of this ACPA short course. Neil Warrender, Ph.D., P.Chem. Sanjel Corporation Sanjel Professional Park, 10774 ‐ 42 Street SE Calgary, AB T2C 0L5 ACPA 2011 Short Course
Tel: 403‐723‐6060 Cell: 403‐479‐1670 E‐mail: [email protected]
A7
Scaling Chemistry (Edmonton)
Tom McCartney, P.Chem. Tom McCartney graduated with a B.Sc. in Honours Chemistry from the University of Alberta in 1978. After a couple of years working in the oil field and industrial services industry, Tom returned to study for a masters degree in metallurgical engineering, returning to industry in 1982. For the subsequent 28 years, Tom has worked in the research and development of chemical solutions for removing or preventing deposits. His experience in chemical and industrial cleaning has been in a wide range of industries, from refineries and power plants to chemical process systems and pulp and paper. In 1998, Tom became Chief Chemist for Woodrising Resources, a supplier of chemistry and consulting services for the industrial cleaning industry. There he successfully developed or invented processes and systems to dissolve or remove deposits ranging from complex organic mixtures to iron polysulfides. He also worked on developing processes to use in the new field of ultrasonic chemical cleaning while continuing to support previous inventions. In 2011, Tom accepted a new position as Technical Services Manager for the Paratene Products Group at Clean Harbors (Calgary). Tom McCartney, B.Sc., P.Chem. Clean Harbors Energy and Industrial Services Corp. #2, 321 ‐ 37th Avenue NE Calgary, AB T2E 6P6
Tel: 403‐216‐2131 Fax: 403‐216‐2132 E‐mail: [email protected] Web: www.paratene.com and www.cleanharbors.com
Thomas (Tom) Ignacz, Technical Account Executive Tom graduated from Concordia University (Montreal) with a M.Sc. in Chemistry in 1978. He entered the oil and gas industry in 1980 as a research chemist developing corrosion inhibitors for petroleum production and industrial cleaning. Over the next eight years, he progressed to a Technical Services Representative providing technical support to field personnel, including total system analysis, trouble‐shooting, product development, program recommendations, and customer presentations. In subsequent roles as a Technical Manager at production chemical companies, Tom was responsible for all aspects of technical issues, including analytical services laboratory, research and development, regulatory concerns, product stewardship, and training. He provided these services not only in the domestic market but also in the oilfields of Ecuador and Mexico. In his present role at Baker Hughes [Petrolite], Tom supports special projects and directs product development on paraffin and asphaltene control chemicals. Tom Ignacz, Technical Account Executive Baker Hughes [Petrolite] 2323 – 91 Avenue Edmonton, AB T6P 1L1
ACPA 2011 Short Course
Tel: 780‐416‐6440 Fax: 780‐416‐1824 Cell: 780‐242‐1047 E‐mail: [email protected] Web: www.bakerhughes.com
A8
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011
Summaries and Slides for Day 1 1. 2. 3. 4.
Scaling Chemistry and Theory of Saturation Indices ...................................... A10 Maurice Shevalier, University of Calgary Kinetics of Nucleation (Precipitation) ............................................................ A29 Maurice Shevalier, University of Calgary Criteria for Determining Good Water Analysis ............................................... A42 Maurice Shevalier, University of Calgary Basics of Geochemical Programs: SOLMINEQ88 and PHREEQC1 .................... A53 Maurice Shevalier, University of Calgary
ACPA 2011 Short Course
A9
Scaling Chemistry (Edmonton)
Two‐Day ACPA Short Course in Scaling Chemistry November 2 and 3, 2011 Day 1, 08:30–10:00
1. Scaling Chemistry and Theory of Saturation Indices — Maurice Shevalier (University of Calgary) The saturation index shows whether a solution will tend to dissolve or precipitate a particular mineral. In this session, participants will learn how saturation indices can be calculated for dilute solutions using the Debye‐Hückel theory. The use of the B‐dot and Pitzer equations for more concentrated solutions will also be reviewed. Based on these theories, the activity coefficients of the various ions present in a solution can be calculated and the saturation indexes of minerals can be determined. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
ACPA 2011 Short Course
A10
Scaling Chemistry (Edmonton)
Scaling Chemistry Maurice Shevalier, P.Chem. Department of Geoscience University of Calgary [email protected] (403)220‐7873
Scaling Chemistry
Who am I? Why are you up front? • Maurice Shevalier – MSc in Physical Chemistry & Physics (Computer Modeling) – 25 years in Dept 25 years in Dept of Geoscience, University of of Geoscience University of Calgary – 25 years sampling, analyzing and modeling waters – Past 10+ years involved in CCS projects: sampling and modeling
Scaling Chemistry
Why are we here?
To hopefully prevent this from forming! Scale in a separator Scaling Chemistry
ACPA 2011 Short Course
A11
Scaling Chemistry (Edmonton)
How are we going to do this? • Going back to basics! – Detailed review of the theory
Scaling Chemistry
Why do this? • To prevent the ‘black box’ syndrome – Where you use a model without an understanding of the theory used in writing a program • Understanding of the theory helps you make better predictions from the model
Scaling Chemistry
Introduction • What is scale? – Scale is the precipitation (usually minerals) deposited on surfaces due to changes in water chemistry – Changes can be caused by mixing of waters, changes in temperature, pressure etc. p ,p – Scale interferes with heat exchangers, restricts flows in pipes
Scaling Chemistry
ACPA 2011 Short Course
A12
Scaling Chemistry (Edmonton)
Introduction (cont.) • What are the most common INORGANIC scales? – Calcium carbonate • CaCO3 (calcite, aragonite) (calcite aragonite)
– Calcium/barium sulphate: • CaSO4 (anhydrite) • CaSO4•2H2O (gypsum) • BaSO4 (barite)
Scaling Chemistry
Introduction (cont.) • What factors control scale formation? – Changes in water chemistry caused by MIXING (either different formation waters or formation waters and process fluids) usually by INJECTION or p ) y y processing at the surface – Changes in physical conditions (pressure, temperature) usually due to production
Scaling Chemistry
Introduction (cont.) • Not all scales behave as expected! • Calcium sulphate minerals exhibit retrograde solubility, i.e. solubility decreases as temperature increases! temperature increases! • Drops in pressure will also decrease solubility. • Calcium carbonate solubility decreases as temperature increases and pressure decreases
Scaling Chemistry
ACPA 2011 Short Course
A13
Scaling Chemistry (Edmonton)
Calcium sulfate solubility as a function of temperature and pressure (Source: Blount and Dickson 1973).
Scaling Chemistry
Calcium carbonate solubility as a function of temperature and pressure (Source: Duan and Li 2008).
Scaling Chemistry
References • Blount, C.W., and Dickson, F.W. (1973), Gypsum‐anhydrite equilibria in systems CaSO4‐H2O and CaSO4‐NaCl‐H2O, Amer. Mineral. 58, pp. 323–331. • Duan, Z., and Li, D. (2008). Coupled phase and aqueous species ( ) p p q p equilibrium of the H2O–CO2–NaCl–CaCO3 system from 0 to 250ºC, 1 to 1000 bars with NaCl concentrations up to saturation of halite. Geochim. Cosmochim. Acta, 72 (20): 5128‐5145.
Scaling Chemistry
ACPA 2011 Short Course
A14
Scaling Chemistry (Edmonton)
Theory of Saturation Indices
Scaling Chemistry
Activities of Ions • Thermodynamic properties of ions depend on chemical potential μi • Ideally, chemical potential would be related to molality mi by: μi = μio + RT ln(mi/mo)
(1)
• Chemical potential of a real solution can be written in a similar way: μi = μio + RT ln ai
(2) Scaling Chemistry
Activity of Ions • We have defined activity and the molarity by the following: ai = γimi/mo
(3)
• Activity and molality are related by the activity coefficient γi • What is γi and how does it relate to …?
Scaling Chemistry
ACPA 2011 Short Course
A15
Scaling Chemistry (Edmonton)
Activity of Ions • Consider a compound composed of a monovalent anion (μ−) and cation (μ+), then the total chemical potential of the electrically neutral solution is neutral solution is μ+ + μ−= μ+o +μ-o + RT ln a+ + RT ln a- (4) = μ+o + μ-o + RT ln(m+/mo) + RT ln(m-/mo) + RT lnγ+γ‐ (5)
Scaling Chemistry
Activity of Ions • It is almost impossible to separate the product γ+γ− into anion and cation components • Define ‘mean ionic activity coefficient’ as γ± = (γ+γ‐)1/2
(6)
When the salt is MpXq, then γ± = (γ+pγ‐q)1/n
(7)
where n = p + q Scaling Chemistry
Activity of Ions • For an ideal case, the energy of interaction of two uncharged molecules falls off as r−6 but Coulombic interaction between two charged ions falls off as r−1. • Opposite charged ions attract each other but cations tend to be near anions, so there is an abundance of the counter ion around a given ion. • On average, more counter ions pass a given ion and the time‐averaged haze of opposite charged ions creates the ionic atmosphere of the ion. Scaling Chemistry
ACPA 2011 Short Course
A16
Scaling Chemistry (Edmonton)
Activity of Ions • The departure from an ideal solution is due to the electrostatic interactions • Consider solution where the electrostatic interactions have been turned off and ions interactions have been turned off and ions maintain their positions • The difference in the chemical potentials is a difference in the molar Gibbs function, ΔG, between the uncharged and charged state, which represents the work done on charging the system Scaling Chemistry
Activity of Ions • The chemical potential of an ideal dilute solution is μo(mi) and activity coefficient of the true solution is: μ(mi) = μo(mi) + RT ln γ± (8) or ln γ± = (1/RT) {μ(mi) ‐ μo(mi)} (9) or ln γ± = (we/RT) (10) So… what is we? Scaling Chemistry
Activity of Ions • The Coulombic potential at a distance r from an ion of charge zie in a vacuum is: ϕ(r) = (zie/4πεo)(1/r)
(11)
• In In a solution the solvent decreases the a solution the solvent decreases the strength of the field and ϕ(r) = (zie/4πε)(1/r)
(12)
Scaling Chemistry
ACPA 2011 Short Course
A17
Scaling Chemistry (Edmonton)
Activity of Ions • In an ionic atmosphere, the central charge is shielded, and the potential is the shielded Coulomb potential where 1/r → (1/r)exp(‐r/rD)
(13)
ϕ(r) = (zie/4πε)(1/r)exp(‐r/rD)
(14)
So where rD is the unknown parameter. Scaling Chemistry
Activity of Ions • In a spherically symmetrical charge distribution, charge density at distance r is ρi(r), the potential depends only on the radius, so the following simplification is possible: so the following simplification is possible: (1/r2)(d/dr)(r2dϕi/dr) = ‐ρi(r)/ε resulting in ϕi(r)/rD2= ‐ρi(r)/ε
(15) (16)
Scaling Chemistry
Activity of Ions • To solve equation (16) for rD we need to know charge density, ρi(r) • Charge density at point r is due to competition between electrostatic attractive forces of central ion for its counter ions and disruptive effects of thermal agitation it ti • Energy of interaction of ion of charge zje with central ion of charge zie separated by a distance r is ΔE = zjeϕi(r)
(17)
where ϕi(r) = potential generated by the ion i Scaling Chemistry
ACPA 2011 Short Course
A18
Scaling Chemistry (Edmonton)
Activity of Ions • Boltzmann distribution gives proportion of ions with this energy at temperature T as Nj(r)/Noj = number of ions of type j per unit vol with potential = ϕi(r) number of ion of of type j per unit vol with potential number of ion of of type j per unit vol with potential = 0 0
= exp(‐ΔE/kT) = exp (‐zjeϕi(r)/kT)
(18)
Scaling Chemistry
Activity of Ions • Charge density at a distance r from ion I is the concentration of ions of each type multiplied by charge of each ion: ρi(r) = N (r) = N+(r)z+e + N + N‐(r)z‐e o = N +z+e exp(‐z+eϕi(r)/kT) + No‐z‐e exp(‐z‐eϕi(r)/kT) (19)
Scaling Chemistry
Activity of Ions • Consider the electrostatic interaction energy to be small compared with kT. If this were not the case, the attraction of the ions would overcome the scattering influence of the overcome the scattering influence of the thermal motion and the ions would condense into a crystal lattice • Thus, exp(x) ≈ 1 + x + h.o.t.
Scaling Chemistry
ACPA 2011 Short Course
A19
Scaling Chemistry (Edmonton)
Activity of Ions • Thus (19) can be rewritten as ρi(r) = (No+z+ + No‐z‐)e – {(No+z+2 + No‐z‐2)e2ϕi(r)}/kT + ... The first term on the right hand side of the equation is zero since it is a concentration of charge and the solution is electrically neutral: ρi(r) = – {(No+z+2 + No‐z‐2)e2ϕi(r)}/kT
(20)
Scaling Chemistry
Activity of Ions • (No+z+2 + No‐z‐2) can be simplified by expressing number concentrations (Noj) in terms of molalities: Noj = m = mjLρ (21) where L = Avogadro’s number mj = amount per unit mass ρ = solvent density and I = ½Σj mjzj2 = ionic strength Scaling Chemistry
Activity of Ions • The charge density in the vicinity of i is now ρi(r) = –(2ρe2LI/kT)ϕi(r)
(22)
and rD is
rD2 = εRT/2ρL2e2I (23)
Scaling Chemistry
ACPA 2011 Short Course
A20
Scaling Chemistry (Edmonton)
Activity of Ions • We started by trying to determine the activity coefficient and we are not quite there yet! • We started by considering the electrical work of charging a central ion when it is surrounded g g by an ionic atmosphere • We need to know the potential at the ion arising from the atmosphere, ϕatmos, which is the difference between the total potential (14) and the central ion potential Scaling Chemistry
Activity of Ions 4 ϕatmos(r) = ϕi(r) – ϕcentral ion(r) = {(zie/4πε)/r}[exp(‐r/rD) – 1] (24) • Consider the potential at the ion of interest ((r = 0), then limit r→0 is ), ϕatmos(0) = ‐(zie/4πε)(1/rD) (25) • Also, consider the central charge to be q not ze. Then the work involved in adding a charge dq to a region with a potential of ϕatmos(0) is dwe = ϕatmos(0) dq (26) Scaling Chemistry
Activity of Ions we = L∫0zie ϕatmos(0) dq = ‐zi2e2L/8πεrD (27) • Recalling (10), ln γ± = (we/RT), we have the following: ln γ± = ‐(zi2e2L)/(8πεrDRT)
(28)
• Substituting (23) into (28) (and assuming the general formula for ionic salt is MpXq) gives the following for ln γ±: Scaling Chemistry
ACPA 2011 Short Course
A21
Scaling Chemistry (Edmonton)
Activity of Ions ln γ± = ‐|z+z‐|(Le2/8πεrDRT)
(29)
• Substituting (23) into (29) yields (30) after converting to log from ln: log γ± = ‐A|z+z‐|(I)½
Debye‐Hückel Limiting Law (30)
• Above equation, although important, is only useful for very low concentration data, I SI > −0.3: equilibrium, no dissolution or precipitation p p SI
