Lawrence Berkeley Laboratory
`
`UNIVERSITY OF CALIFORNIA
`Engineering & Technical
`.. Services Division
`
`* r c
`
`VISCOSITY OF NaCl AND OTHER SOLUTIONS UP TO
`350" C AND 50 Wa PRESSURES
`
`-S. L. P h i l l i p s , H. Ozbek, A . Igbene, G. L i t t o n
`
`' November 1980
`
`Prepared for the U.S. Department of Energy under Contr
`
`ALKERMES EXH. 2008
`Luye v. Alkermes
`IPR2016-1095 & IPR2016-1096
`
`

`
`Lawrence Berkeley Laboratory
`
`UNIVERSITY OF CALIFORNIA
`Engineering & Technical
`.. Services Division
`
`* r c
`
`VISCOSITY OF NaCl AND OTHER SOLUTIONS UP TO
`350" C AND 50 Wa PRESSURES
`
`-S. L. P h i l l i p s , H. Ozbek, A . Igbene, G. L i t t o n
`
`' November 1980
`
`Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48
`
`

`
`DISCLAIMER
`
`This report was prepared as an account of work sponsored by an
`agency of the United States Government. Neither the United States
`Government nor any agency Thereof, nor any of their employees,
`makes any warranty, express or implied, or assumes any legal
`liability or responsibility
`for
`the accuracy, completeness, or
`usefulness of any information, apparatus, product, or process
`disclosed, or represents that its use would not infringe privately
`owned rights. Reference herein to any specific commercial product,
`process, or service by trade name, trademark, manufacturer, or
`otherwise does not necessarily constitute or imply its endorsement,
`recommendation, or favoring by the United States Government or any
`agency thereof. The views and opinions of authors expressed herein
`do not necessarily state or reflect those of the United States
`Government or any agency thereof.
`
`

`
`DISCLAIMER
`
`
`Portions of this document may be illegible in
`electronic image products. Images are produced
`from the best available original document.
`
`
`

`
`i
`1
`1
`1
`a , , 1.
`4 i
`i
`i
`i i
`i ,
`/
`i
`i
`
`1
`
`I
`
`j
`
`LEGAL NOTICE
`This book was prepared as an account of work
`sponsored by an agency of the United States
`Government. Neither the United States Govern-
`ment nor any agency thereof, nor any of their
`employees, makes any warranty, express or im-
`plied, or assumes any legal liability or responsibility
`for the accuracy, completeness, or usefulness of
`any information, apparatus, product, or process
`disclosed, or represents that its use would not
`infringe privately owned rights. Reference herein
`to any specific commercial product, process, or
`service by trade name, trademark, manufacturer,
`or otherwise, does not necessarily constitute or
`imply its endorsement, recommendation, or favor-
`ing by the United States Government or any agency
`thereof. The views and opinions of authors ex-
`pressed herein do not necessarily state or reflect
`those of the United States Government or any
`agency thereof.
`
`

`
`w
`
`Presented a t the Second Chemical
`Congress o f the North American
`Continent, Las Vegas, NV.
`August 24-29, 1980
`
`LBL-11586
`
`Viscosity o f NaCl and Other Solutions
`up t o 35OOC and 50 MPa Pressures
`
`S.L. P h i l l i p s , H. Ozbek, A.
`
`Igbene, G. L i t t o n
`
`Lawrence Berkeley Laboratory
`Uni versi t y of Cali f o r n i a
`Berkeley, CA 94720
`
`November 1980
`
`U
`
`Supported by the U.S. Department o f Energy, O f f i c e o f Basic Energy Sciences,
`D i v i s i o n o f Engineering , Mathematical . and Geosciences under Contract W-7405-ENG-48
`
`

`
`Abstract
`
`Experimental values for the viscosity of sodium chloride solutions are critically
`reviewed for application t o geothermal energy. Data pub1 i shed recently by
`Kestin, Las, Pepinov, and Semenyuk as well as earlier data are included. A
`theoretically based equation for calculating relative viscosity was devgloped
`and used t o generate tables of smoothed values over the ranges 20 C-350 C,
`0 - 5 m and pressures up t o 50 MPa. The equation reproduces selected data
`t o an average of better than 2 percent over the entire range of tempergtures
`Selected gables of data are included for KC1 up t o 150 C,
`and pressures.
`solutions up t o 100 C, and for mixtures o f NaCl with KC1 and CaC12.
`CaCl
`Recokendations are given for additional data needs.
`
`n
`
`

`
`u Pro1 ogue
`
`L
`
`'v.
`
`I
`
`The Lawrence Serkeley Laboratory is funded by the U,S. Department of
`Energy, Division of Engineering, Mathematical and Geosciences for an
`aqueous solutions database. The objective of this work is to provide
`critically evaluated data relevant to the utilization of geothermal energy
`for both power production and direct utilization.
`The larger work covers
`solids, liquids and gases to include the following: rocks, minerals and
`deposited scales ; methane , isobutane , hydrogen sul fide , steam and carbon
`dioxide; sodium chloride, potassium chloride and calcium chloride solutions;
`. t o .aqueous solutions o f the
`However, this work is -. limited
`and, water.
`materials and properties shown i n Table 1,
`Tables of smoothed values generated from correlation equations are
`provided to cover a range of conditions up to 350°c, 50 MPa pressures and
`concentrations generally to 5 molal. The properties are those thermodynamic,
`transport and physical parameters shown i n Table 1 e.g., heat of solution,
`viscosity and solubility.
`Chemical analyses show that site-specific
`geothermal brines are comprised mainly of dissolved sodium chloride, w i t h
`significant concentrations of potassium and calcium chlorides. See Table 2.
`Thus, this aqueous solutions database centers on these three materials as
`the major electrolytes which determine such properties as viscosity, density
`and enthalpy.
`The data for aqueous solutions are used t o model and predict the flow
`of heat from a production well, through a power plant and heat exchanger,
`and back to the reservoir vi a injection we1 1 S. Engineering and economic
`
`L
`
`~
`
`~
`
`< _ - -
`
`

`
`geothermal plants are
`decisions up to and including the construction o f
`c data. While this
`based on both the availability and quality o f bas
`report is intended to be both comprehensive and in-depth, it is recognized
`that there may be important omissions. The reader is urged to forward
`important pub1 ications and comments to our aqueous solutions database
`for
`inclusion in a subsequent updating o f this report.
`
`Sidney L. Phillips
`
`i i
`
`

`
`Table 1. Selected materials and properties included i n the aqueous
`solutions database.
`
`Material
`
`NaCl
`KC1
`CaCl2
`FeC13
`FeCl2
`Na2S04
`Ca HCO 3t
`HSO4'
`HCO 3;
`CaOH
`FeCl 2f2
`FeCl2
`FeCl4-
`Fe(0H)"
`Fe(OH)2t
`HS'
`FeS
`H2Ss NH3
`CaC03
`Si02
`
`*Property
`AHd Cp V h d
`s A Q
`
`AHs
`
`Kf
`
`yf
`
`J
`J
`J
`J
`
`' 4
`J
`.J
`J
`
`J
`.J
`J
`
`J
`J
`J
`J
`J
`J
`J
`J
`J
`J
`
`J
`J
`J
`J
`
`*Key :
`
`r
`
` AH^ = heat of solution
`AHd = heat Of dilution
`= heat capacity
`= vapor pressure
`thermal conductivity
`=
`= density
`= solubility
`= electrical conductivity
`= viscosity
`formation constant
`=
`= activity coefficient
`
`cP
`V
`A
`d
`S
`A
`
`Kf
`y+
`
`i i i
`
`

`
`Table '2,Sodium, potassium, calcium and chloride content o f selected geothermal
`reservoir water, Concentrations in ppm (12).
`
`LId
`
`Area
`Baca, NM
`Beowawe, NV
`Brawley, CA
`Cerro Prieto, Mexico
`East Mesa, CA
`
`Heber, CA
`Mono-Long Val 1 ey , CA
`Raft River, ID
`Sal ton Sea, CA
`
`Na
`2010
`2 14
`13900
`4175
`798
`9002
`4720
`236
`433
`54800
`10600
`
`K
`541
`9
`2400
`575
`49
`1047
`231
`62
`36
`18400
`1250
`
`Ca
`36 -
`2560
`212
`47
`896
`1062
`2
`48
`27600
`1130
`
`c1
`377 0
`50
`31000
`7470
`825
`15868
`8242
`266
`804
`160000
`19700
`
`i. Y
`
`

`
`How happy i s the man who f i n d s wisdom,
`The man who gains understanding!
`
`...
`She i s more precious than corals,
`...
`and none o f your heart's desires can compare w i t h her,
`Her ways are ways o f pleasantness
`And a l l her paths are peace.
`She i s a t r e e o f l i f e t o those who grasp her,
`And happy i s every one who holds her f a s t .
`
`Proverbs
`
`R i g i d i t y threatens a1 1 r e a l i zation : what 1 i ves and
`glows today may be crusted over tomorrow and, becoming
`* . - 1 0 1 o f F the day a f t e r .
`all-powerful, suppress the s t r i v i n g s
`Martin Buber
`
`I
`
`

`
`!
`
`I
`
`A.
`B.
`
`C.
`
`D.
`
`E.
`
`F.
`G.
`
`H.
`
`I.
`J.
`
`K.
`L.
`Tables
`Figures
`
`Con tents
`Introduction
`Scope
`Viscosity of Sodium Chloride Solutions
`1. Dilute Solutions
`Moderate t o High Concentrations
`2.
`Interpolating Equations
`1. Othmer Rule
`Jones-Dole Equation
`2.
`Laboratory Measurements of Viscosity
`Density of Water and Sodium Chloride Solutions
`Correl a t i on Equati on for Sodi urn Chl ori de Soluti ons
`Effect of Pressure
`1.
`Viscosity of Other Solutions
`Potassi urn Chloride
`1.
`Calcium Chloride
`2.
`3. Mixtures
`Sea Water
`4.
`Summary and Conclusions
`Recommendations
`Symbols and Units
`Literature Cited
`
`I . I
`
`v i
`
`

`
`-1 -
`
`/
`
`A.
`
`Introduction
`
`The u t i l i z a t i o n o f geothermal energy resources requires calculations
`
`and modeling of the flow o f heat from production wells, through power plants
`
`and heat exchangers, and back t o the e a r t h v i a i n j e c t i o n wells (1,2). The
`
`flow o f heat i s by water, aqueous e l e c t r o l y t e solution, steam or
`
`hydrocarbon.
`
`Important properties which determine both the flow and
`
`transfer o f heat include enthalpy and heat capacity (3,4), density ( 5 ) ,
`thermal conductivity (6), s o l u b i l i t y ( I ) , e l e c t r i c a l conductivity (8), vapor
`pressure (9), and v i s c o s i t y (10,ll). This paper reports the r e s u l t s of a
`review o f the available data on the y i s c o S i t y o f sodium chloride solutions
`
`covering the f o l l o w i n g ranges o f geothermal conditions:
`temperatures up t o
`35OoC, pressures up t o 50 MPa, and concentrations t o 5 m (27 percent
`The i n t e r e s t i n sodium chloride solutions stems p a r t l y from the
`weight).
`
`fact t h a t NaCl i s the major dissolved e l e c t r o l y t e i n geothermal brines.
`
`For
`example, wells i n Baca Location No. 1 i n New Mexico, .contain over 2000 ppm
`
`Na and over 3000 ppm C1; wells i n East Mesa i n C a l i f o r n i a have over 700 ppm
`Na and over 800 ppm C1; and wells i n the Salton Sea area o f C a l i f o r n i a
`t o 160,000 ppm C1 (12).
`10,000 t o 50,000 ppm Na and 20,000
`The lack o f r e l i a b l e data on the basic properties o f geothermal brines
`
`i s a r e f l e c t i o n o f the d i f f i c u l t y , or even impossibility, o f obtaining brine
`
`samples which have not l o s t dissolved gases and solids, o r have not
`e chemical r e a c t i o s after the sampling step (13).
`t h a t measurements o f the basic properties o f site-specific brines only
`
`It i s l i k e l y
`
`approximates values f o r the i n situ, unreacted brines.
`
`I n any case, data
`
`obtained a t one s i t e cannot be used w i t h confidence f o r calculating the flow
`On the other hand, data obtained from laboratory
`
`o f heat a t other sites.
`
`-
`
`

`
`-2-
`
`measurements on solutions of d i s t i l l e d water and p u r i f i e d s a l t s e.g., NaC1,
`
`KC1 are reliable, and can be used t o model the heat flow f o r any geothermal
`brine. Data on the e f f e c t s o f other constituents (e.g., CH4,CaC12,
`COP) as well as mixtures o f these dissolved s a l t s and gases permit
`
`estimating the properties o f brines a t a l l temperatures, pressures and
`
`concentrations i n the ranges o f geothermal interest.
`
`Viscosity o f a l i q u i d i s a measure o f the resistance o f the l i q u i d t o
`
`flow; the reciprocal o f v i s c o s i t y i s the f l u i d i t y (14). The addition o f
`electrolytes t o water e i t h e r increases or decreases the viscosity of the
`r e s u l t i n g solution. For example, addition o f NaC1, BaClp, LaC13, KC1 o r
`
`CaCIP increases the viscosity, while CsN03 can decrease the v i s c o s i t y of
`
`aqueous solutions (14).
`
`The magnitude o f the change i n v i s c o s i t y differs
`
`f o r each electrolyte.
`
`Data on the change i n viscosity o f NaCl solutions w i t h temperature,
`
`concentration, pressure and w i t h other dissolved constituents are used f o r
`
`example t o calculate f l u i d volumes when i n j e c t i n g brines (15). A 139OC
`(282OF) change i n temperature f o r a 1.11 s p e c i f i c g r a v i t y brine w i
`an estimated 88.5 percent decrease i n viscosity f o r a geothermal f l u i d
`
`l
`
`l cause
`
`(15). This change may be compensated by a decrease i n pumping capacity. A
`
`note of caution:
`
`the temperature change w i
`
`l
`
`l also cause a decrease i n
`
`density and thereby increase the f l u i d volume;
`
`t h i s could necessitate an
`
`increase i n pumping capacity.
`
`Thus, on r e l a t i n g the e f f e c t s o f changes i n
`
`v i s c o s i t y for predictive modeling, other properties such as density changes
`
`need t o be considered.
`
`Viscosity data are also used t o calculate other properties o f
`
`solutions, such as kinematic viscosity, and t o i n t e r p r e t the structure o f
`
`e l e c t r o l y t e solutions (14).
`
`I n t h i s case, the data are interpreted i n terms
`
`

`
`-3-
`
`o f ion-water
`
`interactions, f o r example the degree o f hydration of a
`
`dissolved e l e c t r o l y t e such as LaC13 when solution concentrations exceed
`about 1 m (16), and f o r more d i l u t e solutions o f other electrolytes e.g.,
`
`NaCl (17,18).
`
`The available experimental data on the v i s c o s i t y o f NaCl solutions up
`
`temperatures and 50 MPa pressures i s not large.
`t o 350°C
`Within the past
`f i v e years three sets o f data above 100°C have been published:
`by Kestin e t a1 (11) t o 15OoC and 35 MPa,
`t h a t reported by Pepinov,
`Yusufova and Lobkova covering temperatures up t o 35OoC and pressures t o 30
`.
`MPa (19), and the r e s u l t s by Semenyuk, Zarembo and Fedorov up t o 356OC and
`
`the work
`
`L e I ' _ _ > 3
`
`150 MPa (20). Ove
`e past decade these three sets of data together w i t h
`the e a r l i e r and widely referenced measurements by Korosi and Fabuss (21)
`
`c o n s t i t u t e most o f the available data f o r temperatures exceeding 100°C.
`
`A t high pressure
`
`e work by Kestin e t a1 (111,
`
`ave been publ i shed.
`
`lues were obtained from the
`
`o r i g i n a l publ ications. These experimental data were converted where
`
`necessary t o uni
`
`OC, molal concen ations, ,centipoise viscosity
`
`I
`
`units, and t o me
`
`molar t o molal q
`
`res. The dens y values needed t o convert
`r database (22). Data on the
`v i s c o s i t y o f water were calculated using the recent c o r r e l a t i o n published by
`Kestin f o r temperatures up t o 15OoC and saturated vapor pressures (23), or
`
`obtained from
`
`calculated from the equation recommended by the Eighth International
`
`Association f o r the P r
`Detailed studies o f the v i s c o s i t y o f e l e c t r o l y t e solutions such as
`
`those o f NaCl were begun by P o i s e u i l l e i n 1847. The derivation o f equations
`
`'cd
`
`-
`-
`
`-
`.
`
`bi
`
`

`
`-4-
`
`directed toward predicting electrolyte viscosities for dilute solutions a t
`temperatures near 25OC began about 100 years ago w i t h publications by
`Arrhenius, and 75 years ago by Gruneisen. However, the commonly accepted
`equation is that published by Jones and Dole in 1929 which is based i n p a r t on
`the Debye-Huckel theory (14); this equation was further developed on a
`theoretical basis by Falkenhagen and Vernon i n 1932 (25); and, more recently
`by others including O u t and Los (26), Krumgalz for nonaqueous solutions (27)
`and Leyendekkers (28). For solut9ons exceeding about 1 m concentrations, the
`theoretical approach developed by Vand i n 1948 (29) and analyzed by Thomas
`(30) for colloids and nonelectrolyte solutions (e.g., sucrose) has been
`applied t o electrolyte solutions, for example by Spedding and Pika1 (16) and
`Breslau and Miller (31). Alternate approaches for concentrated solutions
`utilizing transport equations were used by Angel1 and Bressel (32), Slama and
`Kodejs (33), and by Leyendekkers (28).
`However, the viscosity o f NaCl or
`other electrolyte solutions cannot yet be calculated from theoretically based
`equations for temperatures exceeding about 95OC, concentrat ions above about
`1 m, and pressures higher than saturated vapor pressures.
`Information on the theory of viscosity of NaCl solutions i s found i n the
`paper "The Viscosity of Aqueous Solutions of Strong Electrolytes w i t h Special
`Reference to Barium Chloride" by Jones and Dole (14); on experimental
`measurements by Kestin and Khalifa (34), Pepinov, Yusufova and Lobkova (35),
`Semenyuk, Zarembo and Federov (20), and Touloukian, Saxena and Hestermans
`(36); and treatment of data from Dynamic Viscosity of Water Substance (23,24),
`Thermophysical Properties of Matter, Vol . 11, Viscosity (36) , "Tables of the
`Dynamic and Kinematic Viscosity of Aqueous NaCl Solutions i n the Temperature
`Range 20-150°C and the Pressure Range 0.1-35 MPa" (37), and ''Viscosity of
`NaCl Solutions" (10). O u t and Los give a comprehensive discussion on the A, B
`
`

`
`b
`
`II
`
`*
`
`.
`
`-5-
`
`i n the Jones and Dole equation (26); new values for the A,
`and D coefficient
`B coefficients a t 5OC were measured by Dordick, Korson and Drost-Hansen
`data on the viscosity of aqueous NaCl solutions
`i tional sourc
`at elevated temperatures i
`ntained i n the publication Pressure Buildups and
`Flow Tests i n Wells (39). The data are presented as a family of curves
`he temperatures 4OC t o 204OC, and NaCl concentrations from zero
`bout 6 molal.. However, the data used t o construct these plots are
`not available.
`The Saline Water Conversion Engineering Data Book contains
`
`plots of viscosity up t o 100°C (40) .
`
`widely referenced books:
`(41), Ionic Processes i n
`Solutions (42), and Electrolyte Solutions (43). The International Joint
`1 1 Properties which includes liquids will be held i n
`Conference on Thermop
`, i n June 1981.
`Gai thersburg,
`
`The time span covered i s mainly from 1929 t o July 1980; earlier data are
`found i n the International Critical Tables (44). Besides basic data on the
`thermal applications this review also
`viscosity of NaCl solutions for
`sity for KC1 and
`CaC12 solutions, sea water and petroleum brines that meet one or more of the
`following criteria: (1) theory, and methods f o r calculating viscosity,
`(2)instrumentation for measuring viscosity up t o 35OOC; (3) the effects of
`l u i d s ; and, (4) effect of m
`vi scos ity on
`electrolytes such as KC1 on the viscosity of NaCl solutions. Selected
`
`

`
`-6-
`
`tabulated values consisting o f extensive data f o r the v i s c o s i t y of KC1, and
`
`LJ
`
`CaC12 are given i n t h i s report, and the reader i s referred t o the o r i g i n a l
`
`publications for detai 1s.
`
`The paper published by Jones and Dole contains an excellent background
`
`sumnary o f v i s c o s i t y measurements and theory f o r d i l u t e a
`
`ous solutions
`
`beginning with the work of P o i s e u i l l e i n 1847, and on up t o 1929 (14). The
`
`papers by Spedding and Pika1 (16). and by Thomas (30) provide a good discussion
`
`o f Vand's theory both f o r nonelectrolytes (29) and as modified f o r a p p l i c a t i o n
`
`t o concentrated solutions o f electrolytes.
`
`C.
`
`Viscosity o f Sodium Chloride Solutions
`
`Selected t h e o r e t i c a l l y based and empirical equations which have been used
`
`t o describe the change i n v i s c o s i t y o f aqueous NaCl solutions as a f u n c t i o n o f
`
`temperature, concentration and pressure are reviewed i n t h i s sect ion. The
`
`theoretical approaches include those based on Jones and Dole f o r 0.005-1 m
`
`solutions, the application o f Vand's equation t o electrolytes, and the
`
`semi-empirical approach developed by Leyendekkers and Angel1 f o r concentrated
`
`solutions (28, 32). More emphasis i s placed on the f i r s t two.
`
`1. D i l u t e Solutions
`
`Based on the Debye-Huckel theory, Jones and Dole introduced a square r o o t
`
`term for concentration i n t o the equation f o r the f l u i d i t y , f, o f an
`e l e c t r o l y t e t o obtain
`
`Eq 1 represented the available data for BaC12 a t 25OC t o a maximum
`deviation o f 0.032 percent, over the range 0.005 - 1 molal (14). The equation
`KI, LiN03); however,
`i s v a l i d f o r other e l e c t r o l y t e s (e.g.,
`f o r solutions of
`
`Li
`
`

`
`-7-
`
`non-electrolytes such as methyl acetate, the value o f A was found t o be zero.
`
`Eq 1 i s generally
`
`ten w i t h the f l u i d i t y replaced by the r e l a t i v e
`
`viscosity, qr
`
`); the concentration,
`i s i n e i t h e r molar o r
`nal term, Dc , i s sometimes added t o eq 1 t o give
`2
`the extended Jones-Dole equation.
`
`molal units.
`
`The A term o f eq 1, the l i m i t i n g slope
`
`Falkenhagen and Vernon. For binary 1 - 1 e l e c t r o l y t e s (46)
`
`a l l y derived by
`
`Ao i s thc limiting conductivity of thc electrolyte
`0
`XI and X 2 are the limiting conductivitics of the ions.
`0
`
`29.16 x 2 a
`B =
`
`n,(DT)
`
`1/2
`
`where
`
`and
`
`where
`
`i s the viscosity of the solvent
`D is the dielectric constant
`
`As shown by eq 2 the A parameter i s a function o f both temperature and
`The B c o e f f i c i e n t i s an
`p i r i c a l q u a n t i t y whose value depends
`the B coe
`ure;
`i e n t has been r e l a t e d t o the size
`
`nd t o e l e c t r o l y t e - water interactions. The Dc 2
`interactions (26,38). The B and D
`term accounts f o r solute-solute
`c o e f f k i e n t s are discussed with c l a r i t y i n the publications by Spedding and
`
`

`
`-8-
`
`Pika1 (16), and by Out and Los (26). Table 3 lists A, B and D values for
`NaC1, KC1 and CaC12 up to 95OC and 1 m. Much work has been done to
`theoretically calculate the - B coefficient; see, for example, the 1 i terature
`review by Mandal, Seal and Basu (46), and by Out and Los (26).
`2. Moderate to High Concentrations
`In three widely referenced publications Vand derived an equation for
`the relative viscosity o f both a suspension o f rigid spheres, and dissolved
`nonelectrolytes in the absence of either Brownian motion or mutual
`attraction:
`
`.I
`
`Eq 3 may be written as a power series
`
`2 +
`= 1 + 2.5 6 + 7,349 4
`
`"r
`
`...
`
`In qr =
`
`A3
`1 -Q'
`
`(4)
`
`(5)
`
`Eq 5 has been used by Stokes and co-workers for highly hydrated
`electrolytes at moderate to high concentration levels, and by Spedding and
`Likal for rare earth chlorides up to saturation concentrations.
`For solutions
`of electrolytes, the particle volume is replaced by the term cV, where c =
`molar concentration, and V = molar volume of the electrolyte (16,26). Eq 4
`was applied to NaCl and other solutions up to 95OC and 1.2 m concentrations
`by Breslau and Miller (31) and by Out and Los (26) using the results of Thomas
`where the 0 coefficient was calculated to be 10.05 (30).
`
`z
`
`Lad
`
`

`
`-9-
`
`a;d
`
`Another approach t o developing an equation f o r the v i s c o s i t y o f
`
`e l e c t r o l y t e s t o high concentration involves exponential expressions. These
`
`include the models discussed i n the recent publications by Leyendekkers (28),
`
`Slama and Kodejs (33), and e a r l i e r work by Thomas (30) and Angel1 and Bressel
`
`Leyendekkers applied the Tamman-Tait-Gibson (TTG) model t o calculate the
`
`v i s c o s i t y o f 20 e l e c t r o l y t e s including NaCl solutions, over the range 0-6 m a t
`
`20°C.
`
`The central idea o f the TTG model i s any change i n the volume o f the
`
`water solvent i s due t o pressure applied by the dissolved electrolyte.
`
`For
`
`v i s c o s i t y the appropriate equation' i s -04 the-form
`
`The calculated values based on Eq (6) f i t experimental data f o r NaC
`t o b e t t e r than 1-2 percent up t o 6 m concentration a t 20°C
`
`(28).
`
`solutions
`
`I n sumnary,
`
`the t h e o r e t i c a l l y based equations available can be applied
`
`o n l y t o a l i m i t e d range of temperatures, concentrations and pressures. The
`
`Jones-Dole equation i s mainly f o r d i l u t e solutions and temperatures up t o
`
`95OC,
`
`the Vand equations
`
`concentrated solutions and temperatures around
`
`25OC, Spedding and Pika1 developed an equation f o r r a r e earth chlorides
`
`based on the Vand model, but containing a term f o r the square r o o t o f
`
`concentration.
`
`reproduced w i t h i n the l i m i t s o f
`n t r a t i o n s between 0.01 - 3.9 m
`there i s c u r r e n t l y neither a t h e o r e t i c a l l y based equation nor
`
`experimental e r r
`(16). However,
`a model t h a t can be used t o calculate the v i s c o s i t y o f NaCl or other solutions
`
`up t o 35OoC and 50 MPa pressures.
`
`c
`
`c
`
`

`
`-1 0-
`
`LJ
`
`D.
`
`Interpolating Equations
`There are two interpolating equations which have been developed for
`generating tables of smoothed values for NaCl and other solutions up to h i g h
`temperatures and pressures. These include those based on the Othmer Rule used
`by Korosi and Fabuss, and Kestin e t a1 in logarithmic form, and the
`expressions developed by Fabuss and Korosi and by Pepinov, Yusufova and
`Lobkova, based on the Jones-Dole equation.
`1. Othmer Rule
`The Othmer rule relates the viscosity of an aqueous solution t o changes
`-
`.
`
` ~ -
`i n the viscosity of water according t o the logarithmic equation
`
`r -
`
`where A and B coefficients are functions of concentration (11,Zl).
`Eq 7
`reproduces experimental data from seven laboratories for NaCl solutions t o a
`maximum difference of less than *2 percent up t o 150°C, 35 MPa and 6 m
`concentrations; Kestin and Khalifa have used the following form for eq 7
`(zero pressure)
`
`Eq 7 has also been used t o correlate data on the viscosity of KC1 and other
`solutions. See references 37, 48 and 55.
`Jones - Dole Equation
`2.
`Fabuss and Korosi (45) and more recently Pepinov, Yusufova and Lobkova
`used the extended Jones and Dole equation t o develope empirical correlations
`for their measurements of viscosity
`
`

`
`-11-
`
`Pepinov et a1 retained up to six terms for the constants A, B, D, their
`correlation includes a pressure term for interpolating data up to 30 MPa and
`35OoC, with a stated accuracy of 1 percent:
`1-1
`A - A ~ +CAat"+pC Ant("-&), ,
`n r l
`
`8-4
`
`n-4
`
`where the coefficients An, Bn and Dn are given by:
`
`Ab = 0.5649011~10-2
`A1 = 0.2011989~10-~
`A 2 =-0.1200112~10-~
`A3 = 0.4514873~10-9
`A4 = 0.1999090~10-6
`A5 =-0.7889921~10-8
`
`Bo
`= 0.5112900~10-~
`61 = 0.9948465~10-3
`Be =4,3451046~10-5
`B3 = 0.6835311~10-~
`B4 = 0.6105840~10-4
`B5 =-0.6531548~10-7
`86 =a. 1447941 X10-8
`
`Do = 0.2061946~10-1
`D1 =-0.1717302~10-~
`D2 = 0.8796201~10-6
`D3 =-0.1740261~10-~
`D4 =-0.1362641~10-4
`05 =-0.1650395~10-~
`06 = 0.3002503~10-~
`
`'
`
`In summary, empirical correlation equations are available for the
`viscosity of NaCl and other solutions (e.g., KC1) up to 350°C, 35 MPa and
`An alternate approach t o the Jones-Dole equation i s the Othmer rule:
`6 m.
`correlations are available up to 15OoC, 35 MPa and 6 m. Kestin and
`coworkers have used this approach for NaC1, and KC1 solutions and for
`mixtures of NaCl + -KC1 solutions up to 150' gnd 35 MPa (23,47, 48).
`However, these statistically developed empirical equations are valid only
`for in terpo 1 at ion an machine computation .fn the concentration and
`the experimental data.
`Laboratory Measurements of Viscosity
`This section summarizes laboratory instrumentation used to measure
`the viscosity of aqueous NaCl and other electrolyte solutions. The
`
`E.
`
`-
`
`J
`
`c
`
`i
`
`4 d
`
`

`
`t
`
`-1 2-
`
`discussion includes instrumentation used a t 25OC, but emphasis i s on
`
`those methods which have been applied t o elevated temperatures and
`
`pressures.
`
`A good discussion on v i s c o s i t y measurements i s given i n the
`
`Encyclopedia o f Chemical Technology (49), and by Kestin and K h a l i f a (34).
`
`The four viscometers comnonly used t o measure the v i s c o s i t y o f NaCl
`
`aqueous solutions are the following:
`
`capillary, rotational, f a l l i n g
`
`sphere, and o s c i l l a t i n g disk. For temperatures above about 5OoC,
`
`the
`
`most widely used i s the capillary-type,
`
`for example,
`
`the Ostwald, Cannon
`
`and Ubbelohde v i scometers.
`
`Goncalves and Kestin used both the Ostwald and Ubbelohde viscometers
`
`i n measuring the v i s c o s i t y of NaCl and KC1 solutions over the range 25OC
`
`t o 5OoC. Calibration was performed w i t h respect t o water a t 20, 25, 30,
`
`40, and 6OoC, w i t h temperatures controlled t o *0.loC.
`
`The solutions
`
`were prepared by weighing the desired amount o f reagent grade NaCl i n
`
`double-disti l l e d water. The accuracy of the v i s c o s i t y measurements was
`taken t o be t0.1 percent (50).
`Korosi and Fabuss measured the v i s c o s i t y over the temperature range
`
`25OC t o 15OoC using a special l y b u i It Cannon glass capi 1 l a r y v i scometer
`
`w i t h 470 mm o v e r a l l length secured t o a metal support frame by means of two
`
`screw clamps.
`
`The ends o f the 3 / 8 i n . O.D.
`
`receiving tube and a 1/4 in.
`
`O.D.
`
`c a p i l l a r y side tube o f the viscometer were connected t o the manifold
`
`and valve system w i t h two Cajon 0 r i n g f i t t i n g s .
`
`The c a p i l l a r y side o f the
`
`viscometer joined a stainless s t e e l holder enclosing a palladium s i l v e r
`
`membrane, which was connected t o a normally open, a i r pressure-operated
`
`Nupro bellows valve.
`
`The l i n e rejoined the receiving side of
`
`the v i s c o s i t y
`
`i n a T f i t t i n g .
`
`From here connection was made t o the source o f pressurized
`
`hydrogen,
`
`through an a i r pressure operated, and normally closed, Whitey
`
`

`
`hj
`
`.
`
`3
`
`c
`
`e
`
`-1 3-
`
`valve, and through the panel terminal located on top o f the assembly.
`
`The
`
`whole assembly was submerged i n a thermostat f i l l e d w i t h o i l f o r
`
`temperature control (45).
`
`Ostwald-type viscometers were also used by Etrokhi i n measuring NaCl
`
`v i s c o s i t y at 25, 40, and 6OoC (51), by Postnikov f o r temperatures t o
`
`8OoC (52); by Suryanarayana and Venkatesan f o r temperatures t o 55OC
`
`(53), and by Jones and Christian at 25OC (54).
`
`Recent viscosity measurements a t pressures up t o 30 MPa reported by
`
`Kestin and coworkers (11,55) were made using a modified o s c i l l a t i n g disk
`
`viscometer. The instrument consisted o6.a high-pressure bomb of type 347,
`
`18-8 stainless steel, sealed w i t h the a i d o f t i e - b o l t s made from Inconel X,
`
`and provided w i t h a synthetic sapphire, Bridgman-type window. The
`
`o s c i l l a t i n g system was enclosed i n the bomb, and carried a r e f l e c t i n g
`
`mirror on a stem. The bomb was mounted on a titanium-carbide b a l l bearing,
`
`and enclosed i n an automatically controlled heater surrounded by a
`
`r a d i a t i o n shield. O s c i l l a t i o n was i n i t i a t e d by r o t a t i o n of the bomb on i t s
`
`bearing, and observed by a telescope which was trained on a precision
`
`For brines such as NaCl solutions, the f o l l o w i n g parameters were
`scale.
`stainless steel disk w i t h R = 33.9725
`used: natural period o f = 16 sec.,
`mm radius and d = 3.2131 mm thickness between two f i x e d plates o f spacing b
`
`= 2.9782 mm. Pressure measurements were made using high-precision Bourdon
`
`gauges, each accurate t o 0.2 percent o f i t s maximum range. Temperatures
`
`were measured w i t h calibrated thermocouples.
`
`I n other work, Pepinov,
`
`Yusufova and Lobkova used a modified c a p i l l a r y method t o measure NaCl
`
`viscosities. The amount of l i q u i d flowing through the c a p i l l a r y was varied
`
`LJ
`
`the capi l l a r y was made from corrosion-resistant nickel-rhenium
`w i t h a pump;
`alloy, and had an inside diameter o f 0.349 mm, w i t h a length of 553.07 mm
`( 35). Semenyu k ,
`
`

`
`-1 4-
`Zarembo and Federov used a capillary type titanium apparatus for
`temperatures t o 4OO0C and pressures to 200 MPa.
`Out and Los used a
`Ubbelohde (ASTM) type viscometer t o measure . v i scosi ties up t o 95OC w i t h
`0.02 percent precision.
`In summary, the oscillating disk, Ostwald, Cannon and Ubbelohde-type
`viscometers are the instruments mainly used for measuring the
`capillary
`of NaCl solutions for temperatures t o 15OoC, and a modified
`viscosity
`used for temperatures up t o 35OoC and pressures to 150 MPa.
`capi 11 ary
`
`is
`
`P
`
`I
`
`F.
`
`Density of Water and Sodium Chloride Solutions
`Density values for NaCl solutions and