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CEMENTandCONCRETERESEARCH. Vol.20, pp. 175-192,1990. Printedin the USA. 0008-8846/90. $3.00+00. Copyright(c) 1990PergamonPressplc.
AN ION I N T E R A C T I O N M O D E L FOR T H E D E T E R M I N A T I O N OF C H E M I C A L E Q U I L I B R I A IN C E M E N T / W A T E R SYSTEMS
E.J. Reardon Department of Earth Sciences University fo Waterloo Waterloo, Ontario, Canada N2L 3G1 (Refereed) (Received March 31, 1989) ABSTRACT A chemical equilibria model is proposed for the simulation of reactions between porewater and the various amorphous and crystalline minerals of cementitious material at 25°C. The model utilizes the Pitzer Ion Interaction model as a basis for the calculation of ion activity coefficients. This allows the simulation of chemical equilibria between minerals and water to high solute concentrations. A variable compositional model for CSH based on the data of Gartner and Jennings is also incorporated into the solving relations. An example simulation of the effect of progressive additions of sulfuric acid on a cement paste are presented to illustrate the basic workings of the model.
Introduction T h e major elemental constituents of cement are the same as the aggregates that are used to produce grouts and concretes from cement - Ca, Mg, Na, K, Fe, A1, Si, S, C and C1. Upon interaction of H 2 0 with cement-based materials, these elements are partitioned between the solid and solution phases. The solid phases that form are an assemblage of h y d r a t e d compounds that may be crystalline or gel-like in character. T h e gel-like phases, most notably CSH, characteristically exhibit a wide range in chemical composition. For gel/water systems, a change in the composition of the solution phase effects a change in the composition of the solid. Variable composition solids are difficult to incorporate into chemical models. Another complicating factor to the chemical modelling of c e m e n t / w a t e r systems relates to the dissolved constituents which can attain very high concentrations. The Debye-Huckel and Davies equations, which are used to calculate ion activity coefficients, are stretched to the limit at such concentrations. Yet there is considerable interest in the cement research community to describe reactions in c e m e n t / w a t e r systems at exceedingly high solute concentrations, such as encountered in seawater or oil-field brines. The construction of a chemical equilibria model that can accurately describe the partitioning of elements between the solid and solution phases in cementitious systems is, quite accu175
176
Vol. 20, No. 2 E.J. Reardon
rately, a formidable challenge. In this paper, a preliminary step is made in this direction. The paper provides the necessary thermodynamic information and modelling strategy to enable the quantitative analysis of chemical equilibria in cement/water systems. The Chemical Model Solution Speciation
The aqueous species that are produced when water comes in contact with grouts, concrete or cement are a collection of hydrolysis products, ion pairs and complexes. To determine the equilibrium state of such solutions, the actual number of aqueous species that one need recognize may be considerably smaller than the actual number of species present. For example, although Fe3+ and A1a+ ions form a wide variety of hydrolysis products in water, only Fe(OH)7 and AI(OH)~ are important species at the pH conditions representative of porewaters in contact with cementitious material (pH > 8.0). In addition, if an ion interaction model is used to calculate individual ion activity coefficients, the effects of loosely associated ion pairs such as NaC03, CaSO~ and MgSO~ on solution equilibria can be accounted for by the inclusion of interaction parameters in the activity coefficient expressions. The use of an ion interaction model to calculate activity coefficients can thus considerably simplify the speeiation picture and consequently the calculation of chemical equilibrium states. In this study, we have adopted the Pitzer ion interaction model with which to perform the calculation of ion activity coefficients. The suite of aqueous species that are explicitly recognized with this model are shown in Table 1. In performing chemical equilibria calculations for a gas/water/solid system, all reactions between the solution and either the solid or the gas phase must be written in terms of, and only in terms of, these species. The pertinent activity coefficient expressions for the Pitzer ion interaction model have been published elsewhere [1,2,3]. and are not presented in thisreport. The reader is referred to Harvie et al. [3] for the particular formulation of the equations used in this study. The solution of the Pitzer equations to yield ion activity coefficient values requires ion interaction parameter data. For each cation/anion pair, up to four parameters are required - flo, fl~j,/3,% and C~, where i and j refer to cation and anion, respectively. For each cation/cation pair and anion/anion pair, such as Na+-Ca 2+ or CI--OH-, a single parameter is required (0~i or 0jj). For each cation/neutral species or anion/neutral species Table 1: Principal aqueous species in cement/water systems Cations
Anions
NeutralSpecies
Ca2+
CISO~HCO~ Fe(OH)7
H4SiO~
M g ~+ Na + K+
H+
AI(OH)7
MgOH +
H3SiO7
H~SiO~OH-
co~-
H~CO~
Vol.
20,
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2
177 CHEMICAL E Q U I L I B R I A ,
ION INTERACTION MODEL
a single p a r a m e t e r is required (Ain or Ajn). Finally, for each three ion interaction of either two cations and an anion or two anions and one cation, an additional parameter is required (¢iij or Cjjl). The strength of the Pitzer approach is its ability to accurately describe equilibria in multicomponent solutions based on data collected from binary and ternary salt systems. It is found that because the probability of interaction among three ions of the same charge or four or more ions is so low, additional interaction parameter data other than those cited above are not necessary to describe multicomponent solutions. Although much of the parameter data required to solve for the activity coefficients of the ions listed in Table 1 are available in the compilations provided by Pitzer [1] or Harvie et al. [3], some data are not available. This is the case for the interaction of iron, aluminum and silica species with other ions in solution. In this study, these missing data have been
Table 2: Values of single electrolyte interaction parameters at 25°C. Ion
Na +
K+
C a 2+
Mg2+
H+
MgOH +
CI-
~ ~ B2 C¢
0.0765 0.2664 0 0.0013
0.0483 0.2122 0 -0.0008
0.3159 1.6140 0 -0.0003
0.3523 1.6815 0 0.0052
0.1775 0.2945 0 0.0008
-0.1000 1.6580 0 0
SO42-
~o ]31 ~2 C~
0.0196 1.1130 0 0.0050
0.0499 0.7793 0 0
0.2000 3.1973 -54.24 0
0.2210 3.3430 -37.23 0.0250
0.0217 0 0 0.0411
0 0 0 0
CO~-
~o ~i ~,2 C 4'
0.0362 1.5100 0 0.0052
0.1488 1.4330 0 -0.0015
0.2000 3.1973 -150 0
0.2210 3.3430 -150 0
0 0 0 0
0 0 0 0
HCO~"
B° ~1 ~2 C 4~
0.0280 0.0440 0 0
0.0296 -0.0130 0 -0.0080
0.4000 2.9770 0 0
0.3290 0.6072 0 0
0 0 0 0
0 0 0 0
OH-
13o ~I ~2 C¢
0.0864 0.2530 0 0.0044
0.1298 0.3200 0 0.0041
-0.1747 -0.2303 -5.72 0
0 0 0 0
0 0 0 0
0 0 0 0
*H3 SiO~"
~o ~i ~2 C¢
0.0454 0.3980 o o
-0.0003 0.1735 o o
0.2145 2.5300 o o
0.4746 1.7290 o o
0.2106 0.5320 o o
0 0 o o
*H2SiO~-
~o .GI ~2 C 4'
0.0196 1.1130 0 0.0050
0.0499 0.7793 0 0
0.2000 3.1973 -54.24 0
0.2210 3.3430 -37.23 0.0250
0.0217 0 0 0.0411
0 0 0 0
*AI(OH)~-
/~o /~1
0.0454 0.3980
-0.0003 0.1735
0.2145 2.5300
0.4746 1.7290
0.2106 0.5320
0 0
~2
o
o
o
o
o
o
C 4'
0
0
0
0
0
0
0.4746 1.7290 0 0
0.2106 0.5320 0 0
0 0 o 0
*Fe(OH)~-
13° ~I B2 C¢
0 . 0 4 5 4 -0.0003 0.3980 0.1735 o o 0 0
0.2145 2.5300 0 0
*Estimated values (See t e x t ) . P r i n c i p a l source of other data is from ref [3]. See description in text for details.
178
Vol. 20, No. 2 E.J. Reardon
either estimated or set to zero. The complete set of ion interaction parameter data that are required to solve the Pitzer relations are presented in Tables 2 through 6. Table 3: A parameter values at 25°C. Ion H2CO~ *H4SiO~
Ion H2CO~ *H4SiO~
Na +
K+
Ca ~+
Mg ~+
H+
MgOH +
0.1000 0.1000
0.0510 0.0510
0.1830 0.1830
0.1830 0.1830
0
0
0 0
CI-
SO~-
C O ~ - HCO~" OH-
°0.0050 -0.0050
0.0970 0.0970
*Values for H4SiO~
0 0
are estimated
0 0
H3SiO~- H2SiO~- AI(OH)~" Fe(OH)~"
0 0
using H 2 C O ~
0 0
0 0
0 0
0 0
a.s an analogy. !i2CO~ data is from ref [3].
The data in these tables are precisely as given by Harvie et al. [3] with the following exceptions: The parameter data for Na-HC03 and Na-C03 are only slightly different from that given in [3] and are based on a review of data by Monnin and Schott [4]. Parameter data for H-SO4 interaction are from Reardon and Beckie [5] and are not substantively different from those given in [3]. There are no published data governing the interaction of AI(OH);, Fe(OH);, H3SiO; or H2SiO~- with either Ca 2+, Mg 2+, Na +, K + or H +.. To estimate /5°, fl~j, fi~j and C~ parameters for each of the above cation/anion pairs, the HSO; ion was used as a model for Fe(OH);, AI(OH); and H3SiO; ions; and SO~- was used as a model for H2SiO~- ion. The parameter data for Me-HS04 or Me-SO, interactions are published [3] and were used to approximate the Me-Fe(OH)4, Me-AI(OH)4 and Me-H3Si04 ion Table 4 : 8 parameter values at 25°C. Ion
K+
Na+ K+ Ca~+
-0.0120
Ca 2+
Mg 2+
0.0700 0.0700 0.0360 0.0320 0 0.0050 0.0070 0.0920
Mg 2+ H+
0.1o{30
SO~-
C O ~ - HCO~
CISO.2 CO~-
0.0200
-0.0200 0.0200
*H3SiO~*H2SiO~*Al(OH)~"
MgOH +
0 0 0 0 0
Ion
HCO~ OH-
H+
0.0359 0.0100 -0.0400
OH-
*H3SiO~ *H2SiO~- *AI(OH)~- "Fe(OH)~-
-0.0500 -0.0130 0.1000
-0.006 0 0
0 0 0
-0.006 0 0
-0.0(16 0 0
0
0 0
o 0
0 0
0 o
0
0 0
0 0 0
* E s t i n ~ t e d values (See text). Principal source of other d a t a is from ref [3]. See description in text for details.
Voi. 20, No. 2
179 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
Table 5: Cation-anion-anion ¢ parameter values at 25°C. Na +
K+
Ion C[SO 2.CO~HCO~ OHHzSiO~" H2SiO~AI(OH)~"
Cl-
SO~-0.0014
CO~-0.0085 -0.0050
HCO[ -0.0143 -0.0050 O.OO2O
o
o.oo4o -o.oooo
o o
so?COb HCO~ OHH3SiO~ H2 S i O ( AI(OH)~-
OH-0.0060 -0.0090 -0.0170 0
"H3SiO[ -0.{X)60 -0.0094 0 0 0
-o.ooeo o -o.os00 -o.o677
"H~SiO~0.0014 0 -0.0050 -0.0050 -0.0090 -0.0094
*AI(OH)~" -0.0060 -0.0094 0 0 0 0 -0.0094
"Fe(OH)~" -0.0060 -0.0094 0 0 0 0 -0.0094 0
0 0 -0.0090 0 -0.0500 -0.0077
0 -0.0677 0 0 0 0 -0.0677
0 -0.0677 0 0 0 0 -0.0677 0
0.0120
-0.0100 0
0 0 0
0 O 0
-0.0250 O 0 0
0 O 0 0 0
-0.01S0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Ca 2+
ClSO.~CO~HCO~ OHHa SiO~ H~SiO(AI(OH)~-
-0.0180
0 O
Mg2+
elSO.2CO~HCO~ OHHaSiO~H2SiO~AI(OH)~-
-0.0040
0 0
-0.0960 -0.1610 0
0 0 0 0
0 -0.0425 0 0 0
-0.0040 0 0 -0.1610 0 -0.0425
0 -0.0425 0 0 0 0 -0.0425
0 -0.0425 0 0 0 0 -0.0425 0
H+
elSO~CO~HCO~OHH3SiO~ H2SiO4AI(OH)7
0
0 0
0 0 0
0 0 0 0
0.0130 0 0 0 0
0 0 0 0 0 0
0.013(:} 0 0 0 0 0 0
0.0130 0 0 0 0 0 0 0
MgOH+
C]SO~CO~HCOH OHH3SiO~" H2SiO~AI(OH)~-
0
0 0
0 0 0
0 0 0 0
0 0 0 0 o
0 0 0 0 0 O
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
v
*Estimated values (See text). Principal source of other data is from ref [3]. See description in text for details.
interaction parameters. An analogous approach was used to estimate 19, A and ¢ parameters for interactions involving these ions. • In the interaction model presented for natural waters by Harvie et al. [3], they accounted for the interaction of Mg 2+ with O H - through the formation of a MgOH + ion pair with a log dissociation constant of-2.19 at 25°C rather than than by reporting interaction parameters to describe the interaction. Although they point out that there may be problems with the approach and that more experimental d a t a are
180
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20, No. 2
Rea rdon
necessary to support the approach, we adopt this model in this study. In their model, they set all other anion interactions with MgOH +, except for CI-, to zero. We do the same in this study for the interaction of MgOH + with Al(OH)4 , Fe(OH)~, H3SiO; and H2SiO~-. One of the major advantages of the Pitzer interaction model approach is that the interaction between ions is described through a set of parameters rather than by the postulation Table 6: Anion-cation-cation ¢ parameter values at 25°C. Ion
K÷
C a ~+
M82+
H+
Na + K+ C a 2+ M g 2+ H+
-0.0018
-0.0070 -0.0250
-0.0120 -0.0220 -0.0120
-0.0040 -0.0110 -0.0150 -0.0110
so~-
Na + K+ Ca 2+ Mg2+ H+
-0.0100
-0.0550 0
-0.0150 -0.0480 0.0240
0 0.1970 0 0
0 0 0 0 0
co~-
Na + K+ C a 2+ Mg 2+ H+
0.0030
0 0
0 0 0
0 0 0 0
0 0 0 0 0
HCO{
Na + K+ C a 2+ M g 2+ H+
-0.0030
0 0
0 0 0
0 0 0 0
0 0 0 0 0
OH-
Na + K+ C a 2+ Mg 2+ H+
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
H3 SiO~
Na + K+ C a 2+ M g 2+ H+
0
0 0
0 0 0
-0.0129 -0.0265 0 -0.1780
0 0 0 0 0
"H2SiO~-
Na + K+ C a 2+ Mg2+ H+
-0.0100
-0.0550 0
-0.0150 -0.0840 0.0240
0 0.1970 0 0
0 0 0 0 o
"AI(OH)~"
Na+ K+ Ca2+ M g 2+ H+
0
0 0
0 0 0
-0.0129 -0.0265 0 -0.0178
0 0 0 0 0
°Fe(OH)7
Na+ K+ C a 2+ M g 2÷ H+
0
0 0
0 0 o
-0.0129 -0.O265 o -0.0178
0 0 o 0 0
CI-
*
* E s t i m a t e d values (See text).
MgOH +
0 0 0.0280 0
Principal source of other data is from ref [3].
See description in text for details.
Vol. 20, No. 2
181 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
of the formation of ion pairs in solution. Some ion interactions are so strong, however, that the presence of ion pairs or additional species in solution must be recognized. Such a situation increases the complexity of the calculations required to obtain activity coefficient values, requires more assumptions as to the interaction parameters of the newly formed species with other ions in solution, requires more iterations of any numerical model used to determine the equilibrium state of a rock/water system and reduces the probability that a unique solution to the set of mass action and mass balance equations will be found. It is preferable if ion pair formation need not be invoked. Harvie et al. [3] found it necessary to invoke the formation of both CaCO~ and MgCO~ to account for the interaction of CO]with Ca 2+ and Mg 2+ ions. We have found that an equally good fit of the available solubility data can be obtained by using the/5 °, ~lj and C~ parameter data for Ca-SO4 and Mg-SO4 interaction as estimates for Ca-CO3 and Mg-CO3 interaction and with a value of -150 for the/5~- value of both ion pairs. We have adopted this more simplified approach to describe both Mg-COz and Ca-COB interactions in this study. It is emphasized that much of the parameter data recorded in Tables 2 through 6 have not been determined from an analysis of experimental data, but have been estimated. Consequently, this set of ion interaction parameter data is offered merely as a starting point for the quantitative analysis of chemical equilibria in cement/water systems rather than a definitive set of ion interaction parameters. Solution and Mineral Phase Reactions
There are a large number of potential solid phases that may control the chemical composition of water in contact with cementitious material. In order to appraise the influence of these solid phases on a water's chemical composition, a knowledge of the equilibrium constants describing the solid phase dissolution reactions is required. In addition, equilibrium constants for all reactions occurring strictly within the solution phase, such as ion hydrolysis and ion pairing or complexing reactions, must also be known. These equilibrium constants can be calculated from published standard chemical potential data for the substances involved in these reactions with the relation: P
log K = -(~'-~ 4=1
R
n,# ° -
~,
n,#°)/2.303
(1)
/=1
where P and R are the number of products and reactants involved in the reaction, respectively, and ni, is the stoichiometric coefficient of the i th product or reactant. A tabulation of chemical potential data at 25°C for the principal dissolved constituents and mineral phases in a cement/water system are recorded in Table 7. These data are derived from two principal sources - Harvie et al's compilation of chemical potentials [3] and Babushkin et al.'s text on silicate thermodynamics [7]. Equilibrium constants for a number of solution phase and solution/solid phase reactions have been calculated with the above relation and the data are recorded in Table 8. An equilibrium constant for the solubility reaction of CSH is not presented in this table but is given a special treatment in the following section.
182
Vol. 20, No. 2 E.J. Reardon
Table 7: S t a n d a r d chemical potentials ( # ° / R T ) at 25°C for various substances Substance
/~°/RT
Source
H20 CO2 H2CO~ H4SiO~ H+ Ca2+ Mg2+ MgOH+ Na+ K+ OHClHCO~ H3SiO~ AI(OH)~ Fe(OH)~ H2SiO~SO42CO~-
-95.663 -159.092 -251.340 -527.865 0.0 -223.300 -183.468 -251.940 -105.651 -113.957 -63.435 -52.955 -236.751 -505.364 -526.650 -339.622 -478.525 -300.386 -212.944
1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1
Substance Sepiolite Gypsum Brucite Arcanite Calcite Halite Nesquehonite Portlandite Gibbsite Ca-Aluminosilicate gel Ettringite Monoaluminosulfate K-Aluminosilicate gel Ca-Carboaluminate Silica (amorph) Syngenite C4AH13 C2AH8 C3AH6 Ca-oxychloride Mg-oxychloride
/z°/RT
Source
-3732.445 -725.560 -335.400 -532.390 -455.600 -154.990 -695.185 -362.120 -465.545 -1595.141 -6134.559 -3138.191 -1493.018 -2428.294 -342.626 -1164.800 -2964.380 -1943.777 -2022.875 -2658.450 -1029.600
3 1 1 1 1 1 4 1 2 2 2 2 2 6 5 1 2 2 2 1 1
1 ref [6] 2 ref [7] a ref [8] 4This study SAverage of values from 1 and 2 6 ref [9]
Treatment of CSH in the Chemical Model T h e CSH gel phase that is produced upon hydration of Portland cement presents special problems in accurately representing its solubility behaviour. This is because it cannot be considered as a pure phase with a unique solubility product. CSH exhibits pronounced variations in its C a / S i ratio depending on the C a / S i ratio of the solution in contact with the solid [10,11]. There is also evidence to show t h a t there are a number of distinct forms of CSH. One of these appears to occur only at early hydration times when C3S is still present within the hydrating cement particles [11,12]. Other, less soluble and more stable forms, occur at later times and are also observed to precipitate directly from supersaturated solutions. T h e solubility characteristic of these more stable forms are very similar and distinctly different from the early formed CSH. Both Suzuki et al. [13] and G a r t n e r and Jennings [11] presented t h e r m o d y n a m i c models to describe the solubility behaviour of the more stable CSH as a function of water chemistry. We have adopted the t r e a t m e n t of Gaxtner and Jennings [11] and used their compositional and solubility d a t a for CSH (cf. d a t a for Curve 2, Table III, ref [11]) in our analysis. We cannot, however, use their thermochemical d a t a directly in this study because they used a different activity coefficient and aqueous speciation model t h a n used in this study. Consequently, a re-evaluation of the thermochemical properties of CSH (specifically, its solubility products) are performed here.
Vol. 20, No. 2
183
CHEMICAL EQUILIBRIA, ION INTERACTION MODEL Table 8: Equilibrium constants for various reactions at 25°C. Mineral or Species
Reaction
log K s p
H4 SiO~ dissociation H3 SiO~- dissociation MgOH ÷ dissociation H 2 C O ~ dissociation H C O [ dissociation H20 dissociati~ CO2(0) dissolution Brucite Portlandite Ettrir~ite Silica (amorph) Ca- Carboalumlnate Sepiolite Gibbsite Calcite Gypsum Arcanite NesquehonJ te C4AH13 C2AH8 C3AH6 Ca-Muminosilieate gel Halite Ca-oxychloride Mg-oxychloride Syngenite Monoaluminosulfate K-Aluminosilicate gel
H4SiO~ --* H + + H3SiO~ H 3 S i O ~ ---* H + + H 2 S i O ~ M g O H + ---* M 9 2 + + O H H2CO~ ~ H + + HCO~ H C O ~ ---* H + + C O ~ H20 ~ H + + OHC02 + H20 ~ H2CO~ M g ( O H ) 2 ---* M g 2+ + 2 O H C a ( O H ) 2 ---* C a 2+ + 2 O H CasAI2Os(S04)3 . 32//20 - - - * 6 C a 2+ + 2AI(OH)~ + 3 S 0 2 - + 4 O H - + 2 6 H 2 0
-9.77 -11.66 -2.19 -6.34 -10.34 -14.00 -1.48 -10.89 -5.19
Si02 + 2H~O ---* H4SiO~
-2.64 -19.90 -54.95 -1.01 -8.41 -4.58 -1.78 -5.12 -27.49 -13.04 -19.95 -3.76 1.57 -15.25 -15.96 -7.45 -27.62 -2.15
-43.13
C a O . A1203 • C a C 0 3 • l l H 2 0 ~ 2Ca 2+ + 2 A I ( O H ) ~ + C O ~ - + 7 H 2 0 31120 + M g ( S i 6 O l s ( O H ) 2 . 6 H 2 0 ~ 4M92+ + 6H3SiO~ + 2OHAI(OH)3 + OH- ~ AI(OH)~ CaC03 ~ Ca 2+ + CO 2 C a S 0 4 • 2 H 2 0 "--* C a ~4 + S O T - + 2 H ~ O K~S04 ~ 2K+ + SO TM 9 C 0 3 • 3 H 2 0 --.* M 9 2 + + C02a - + 3 H 2 0 4CaO • AI203 • 13H20 ~ 4 C a 2+ + 2 A I ( O H ) ~ + 6 O H - + 6 H 2 0 2CaO. Al203 • 8H20 ~ 2Ca 2+ + 2 A I ( O H ) ~ + 2 O H - + 3 H 2 0 3 C a O • A1203 • 61120 .__, 3 C a 2+ + 2 A I ( O H ) ? + 4 0 H 7 H 2 0 + 2 O H - + C a O • A I ~ 0 3 • 2 S i 0 2 ----* ~ a 2+ + 2Al ( O H ) ~ + 2 H 3 S i O ~ NaCI ~ Na + + ClC a 4 C l 2 ( O H ) s • 13//20 ----, 4 C a ~+ + 2 C I - + 6 O H - + 13/-/20 Mg2CI(OH)3.4H20 ~ 2M92+ + C l - + 3 O H - + 4 H 2 0 K 2 C a ( S 0 4 ) 2 . H 2 0 - - ~ 2K + + C a 2+ + 2 S 0 ~ - + 1"120 Ca4 A I 2 0 6 S 0 4 . 12H20 ------*4 C a 2+ + 2 A I ( O H ) [ + S O ~ - + 4 O H - + 6 H ~ O 10H20 + 6 O H - + K 2 0 . A l 2 0 3 • 6 S i 0 2 ---* 2 K + + 2 A I ( O H ) ~ + 6 H s S i O ~
The Ca/Si ratios of the CSH referred to above are plotted as a function of the Ca/Si ratio of the equilibrated solutions in Figure 1. There is a fair degree of scatter in the data but a straight line relationship yields a reasonable representation of the compositional variation. This straight line relationship was used to calculate CaO and SiO2 concentrations for the solution phase in equilibrium with a specified solid composition. These compositions
o "
0 0
u} O
O
Figure 1 - Compositional data for CSH vs. SiO2 content of the solution from data for Curve 2, Table III, Gartner and Jennings [11]. ,
0
I
1
,
I 2
'
,
I
i
3
log SI02(/zmoles/L)
%1 4
184
Vol. 20, No. 2 E.J. Reardon
were used as input into a chemical speciation model that used the Pitzer Ion Interaction model to calculate ion activities coefficients. Solubility products were then calculated for each composition of CSH in equilibrium with each solution composition. The results of this analysis showed that both the solubility products and the solid phase compositions yielded nearly linear trends when plotted as a function of the Ca2+/H4SiO~ activity ratio
.15
,,p ¢0 0
v'
-10
o
-5
0
r
I
,
1
I
,
3
I
,
I
6
,
7
log a C a 2 + / a H 4 S i 0 4 °
2 neD
.o
¢D
O 1
0
,
-1
I
1
,
I
,
I
,
3 5 log a C a = + / a H 4 S l 0 4 °
I
7
,
9
Figure 2 - (a) Model calculated solubility product for CSH vs the activity ratio of Ca2+/H4SiO~ in solution. (b) Model calculated Ca/Si ratio of CSH vs the activity ratio of Ca~+/H4SiO,~ in solution.
Vol. 20, No. 2
185 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
3.5
÷
2.5 o)
_o
*
+
0
Figure 3 - Comparison of model calculated SiO2 and CaO contents of solutions saturated with respect to CSH and published solubility data reported in Ref. [10]. (See discussion in text)
E 1.8
+
+
+
u) o~ _o
•
+
+
4~
•
I
0.5
•
÷
+
-0.5 10
20
30
CaO (mmoles/L)
(R) of the equilibrating solution. These results are shown in Figure 2. The following two quadratic equations accurately represent these solubility relations:
(Ca) = 0.48548 + 0.11563R + 0.0104536R 2 logKsp= 4.507 + 1.3306R + 0.019172R 2
(2)
CSH
(3)
These two expressions can now be incorporated into an overall chemical equilibria model for cement/water systems to allow for a variable composition/variable chemical potential model for the CSH solid phase. Figure 3 demonstrates how accurately these expressions represent the available published solubility data for CSH. The upper curve represents the average of solubility data for the early-formed metastable CSH phase referred to by Jennings [10]. Individual data points for this phase are not shown on the diagram. The lower curvilinear trend of data points are solubility measurements of the more stable form(s) of CSH. The lower solid curve shown in the diagram is the predicted solubility of CSH with the chemical model in this study and equations 2 and 3.
Application of the Chemical Model Because a variable composition model has been adopted for CSH equilibria, any simulation of chemical equilibria between water and hydrated cement compounds, in which CSH is included, must consider as variables both the amounts of solid phases present and the concentrations of the various elemental species in solution. As an example application of the chemical model, the chemical changes that occur with the progressive addition of sulfuric acid to a kg of water containing one mole each of portlandite, CSH (Ca/Si = 2.12) and C4AH13 will be simulated. Such a simulation is relevant to understanding the mineralogic changes that occur in concrete as a result of attack by atmospheric sulfur dioxide.
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The variables in this simulation are the concentrations of the aqueous species, the amounts of the three solid phases mentioned above as well as the amounts of any new phases that m a y form as a result of the progressive addition of sulfuric acid. T h e amounts of the solid phases can be conveniently expressed in the same concentration units as the dissolved species - molalities, i.e. the number of moles of solid in contact with a kilogram of water. T h e relations that are to be solved are the pertinent solid phase equilibrium constant and ion dissociation constant expressions from Table 8, and mass balance expressions for Ca, Si, A1 and SO4. A Newton-Raphson technique was adopted to solve these relations [14,15]. This solving routine requires initial estimates for all the unknowns. T h e solution of the relations must therefore be performed a number of times before convergence is attained. T h e values of the various ion activity coefficients also change with each iteration and so the Pitzer relations must be included in the computational procedure. A copy of the c o m p u t e r p r o g r a m to calculate ion activity coefficients with the Pitzer relations is available upon request. T h e Newton-Raphson algorithm is described in detail by Crerar [14] and a reproduction of the computer p r o g r a m is given in Anderson and Crerar [15].
Table 9: Model results for sulfuric acid attack of CSH, C4AH13 and Ca(OH)2 Temperature pH aHuO Ca/Si of CSH H~SO4 added Species Ca 2+ H+ so
-
OHH3SiO~ H2SiO42AI(OH)~ H4SiO,] Amorph. Sil Gibbsite Gypsum Portlandite CSH C4A1H13 Phase Portlandite CSH Amorph. Silica Gibbsite Gypsum C4AIH13 Monoaluminosulfate Ettringite
Initial 25°C 12.48 1.00 2.12 0.0
Final 25°C 8.10 1.00 No CSH 0.73moles/kg H20
Concentration millimolality 20.1 4.253E-10
Concentration millimolality 14.9 9.963E-06
-
40.2 1.119E-04 0.0022 0.0152 1.865E-07 99.5 100.0 100.0 log SI 0.00 0.00 -7.09 -2.35 0.00
14.9
1.658E-03 5.813E-02 3.985E-05 1.461E-04 2.27 97.7 200. 717.
log SI -8.90 -0.64 0.00 0.00 0.00 -30.90 -21.27 -4.96
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187 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
The results of the simulation of the initial equilibration of the three solid phases with water (no sulfuric acid added) and final water chemistry (after addition of 0.73 moles of sulfuric acid) are shown in Table 9. The list of log SI values given at the bottom of the table are the model calculated saturation indices for the various mineral phases. Saturation indices are defined as: log S I = log I A P (4) Ksp where I A P is the ion activity product calculated from the the individual ion activities involved in the dissolution reaction for the mineral (Table 8) and Ksp is the solubility product for the mineral. A log SI value of zero indicates that the water is saturated with respect to a particular mineral and a value less than zero, undersaturated. Once the model is run to establish the equilibrium state of the grout/water system before addition of sulfuric acid, acid attack is simulated by rerunning the model successively, increasing the amount of SO4 present in the system each time. Phase changes are charted by monitoring the calculated saturation indices and mineral masses. Once the log S I value for a mineral phase reaches 0.0, it is designated to be present in the grout/water system. Similarly, once the mass of a mineral reaches zero, it is removed from the input list of mineral phases present. In this manner, the theoretical or thermodynamically-based reaction path can be delineated, revealing the progressive changes in solution composition and mineral masses, the appearance or disappearance of mineral phases as well as the locations of invariant points. By comparing the results for the initial and final conditions in Table 9, the effect of sulfuric acid addition is seen to transform the original mineral assemblage of CSH, C4AH13 and Ca(OH)2 into an assemblage of amorphous silica, gibbsite and gypsum. The results of the chemical changes that occur in the water phase with the progressive addition of sulfuric acid are graphically shown in Figure 4. The plateau regions in the diagram relate to invariant points, i.e. where the solution chemistry is buffered until one mineral phase transforms completely into another. The progressive effect of sulfuric acid addition on phase transformation is best illustrated by comparing the plots of mineral saturation indices with the mineral concentrations ol
OH
Ca ~
.=
-
.:
.......
/
O
/I
O c
Figure 4 - Results of the simulation of the change in water chemistry during the progressive attack of CSH, Ca(OH) 2 and C4AH13 by sulfuric acid.
8 -4 ........ +. ...... . / _o
A~
-. ..
/
. . . . . . . . . . . . -¢
i / ............................................................. i .....[
..
"'>":-t / / ..... i! ........s, ................/ i! , , ,t!
0.0
^,
/
0.2
, 0.4
Moles Of sulfuric
,,
,
0.@ acid a d d e d
,! \1 it.~ ! I ,~,. i 0.8
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plots in Figure 6. The pH is inversely proportional to the amount of sulfuric acid addition and is used as the X-axis in both diagrams. The top two p]ots in Figure 5 give the saturation indices and concentrations of the mineral phases that are initially present in the system. The bottom two plots give the same information for the mineral phases that appear during the simulation, i.e. as a consequence of the addition of sulfuric acid. These diagrams indicate the following order of phase changes: 1. pH 12.5 - Portlandite dissolves as Ettringite precipitates (invariant point) 2. p H 1 2 . 5 t o 1 2 . 0 -
C4AH13 dissolves
3. p H 1 1 . 6 t o 1 0 . 6 -
Gypsum precipitates
4. p H 1 0 . 6 5. p H 8 . 8 -
Gibbsite and Gypsum precipitate as Ettringite dissolves (invariant point) amorphous silica precipitates as CSH dissolves (invariant point)
The above modelled sequence of phase transformations is in agreement with that proposed by Babushkin et al. [7] based on visual observations and thermodynamic analysis of concretes affected by sulfur dioxide attack. The predicted variation in the composition of CSH with sulfuric acid addition is shown in Figure 6. There is an exponential decrease in the Ca/Si ratio with reaction progress.
o
CSH
CSH
.....,..~..
, .4
a
C4AH13
e -s
i C4AH13
" ..............,............
P' i
-4
,i
i 11
9
lS
.........,
•",
.
r
I
11
|
pH
.....
pH
4
o Ettr
GIl~slte
G,psufi
............................. ...-..---
I
J
J
Q
Am
iI- Gypsum ..°..o. . . . . . . . . . . . . . JAm SI,
Slll
!
"-.......
.,/
i 13
..,.
,,/,;
Ettr
-4
"
I
L
11
II
pH
i 13
11
9 pH
Figure 5 - Calculated mineral saturation indices and mineral masses vs pH for water chemistries given in Figure 4.
VoI.
189
20, No. CHEMI CAL EQUILIBRIA,
ION INTERACTION MODEL
2.5
Figure 6 - Calculated change in CSH composition with pH.
.I(/)
1.5
0
I0
1
0.5
0
i 13
I
~
11
I g
i ?
pH
The model predicts an overall decrease in the Ca/Si ratio from 2.12 at a pH of 12.5 to 0.5 at a pH just below 9.0 where the CSH-arnorphous silica phase transition occurs. Model Limitations There are a number of important limitations of the proposed chemical equilibria model for water in contact with cementitious material. The first concerns the relations adopted to describe CSH solubility. The solubility product and compositional expressions for CSH given in this study were determined using reported experimental data for CSH solubility in solution mixtures of CaO and Si02 [11]. These solubility data range from high pH, high Ca and low silica concentrations to high silica, low calcium and low pH conditions. The proposed model for CSH solubility behaviour in this paper accurately represents these experimental data. The highest pH of the solubility data, however, only corresponds to the limit of portlandite solubility (~ 12.5). In actual porewaters of cementitious material, there are usually considerable quantities of KOH and NaOH. The presence of these constituents imparts a porewater pH that is beyond the upper pH limit of the experimental data on which the solubility model for CSH has been based. At this time, there is insufficient experimental data to support the application of the proposed model for CSH under such high pH conditions. Another limitation of the model relates to the speciation model adopted for silica hydrolysis. In this study, only the species H4SiO~, H3SiO~- and H2SiO~- have been included in the speciation model. At pH's greater than 13, however, there is evidence that the species HSiO~- and SiO~- may also form. These species have not been included in the present model because there is some controversy as to whether these species actually occur in solution and, more importantly, because there is a paucity of ion interaction parameter data for trivalent and quadrivalent ions that could be used to estimate parameters for the interactions of these ions with other ions in solution. There is an additional limitation of the proposed model that relates to the description
190
Vol. 20, No. 2 E.J. Rea rdon
of chemical equilibria under the high pH conditions characteristic of porewaters in contact with high alkali cements. Such caustic solutions aggressively dissolve siliceous aggregate material, such as cherts, tufts, glasses, siliceous limestones and even felspathic minerals and quartz [16,17]. This addition of silica to the porewaters results in the precipitation of a variety of mineral phases, collectively referred to as alkali silica reaction products. These phases contain varying amounts of calcium, silicate, and sometimes aluminum [18,17] Invariably, potassium is associated with these reactions products, which may be gel-like or crystalline. Undoubtedly, some of this material is simply CSH with variable amounts of associated potassium ions [19], whereas other reaction products are discrete mineral phases with definite chemical compositions. The solubility model for CSH adopted in this study [11], does not allow for the incorporation of potassium in the gel structure. Similarly, there are no available thermodynamic data for any of the other alkali silica reaction products that would enable calculation and inclusion of their solubility products into the proposed chemical equilibria model. Consequently, a quantitative prediction of the behaviour of potassium ions in the porewater of cementitious material cannot be made at this time. Another important limitation of the proposed model is that it does not allow for protonation reactions or ion sorption at the surfaces of the crystalline and amorphous phases of hydrated cement. Such reactions could be of substantial importance at the high solid/water ratios typical of mixed concretes and grouts. Although surface protonation and ion sorption reactions do not affect the calculation of the chemical equilibrium composition of a water in contact with a designated set of hydrated cement compounds, they do influence the simulation of the transfer of elemental masses that are required to attain a particular equilibrium state. Although many models have been proposed to describe surface protonation and ion sorption reactions for oxide and silicate material, the application of these models to the specific compounds of hydrated cement has not received much attention. Finally, it is realized that with the presence of aggregate material of heterogeneous mineralogy in actual concretes and grouts, an attainment of chemical equilibria between porewater and all mineral phases present is not possible. Although chemical equilibria may exist between porewater and the hydrated compounds of the cement paste far from an aggregate particle, near such a particle the chemical composition must necessarily be different. Thus there is at all times not only heterogeneities in the chemical composition of the porewater of grouts and concretes, but concentration gradients that continuously effect compositional changes to all of this water. In this light, the application of any chemical equilibria model to describe reactions in such a chemically heterogeneous and dynamically evolving system must consequently be done with a considerable degree of caution. Acknowledgements The author would like to express his appreciation to Ontario Hydro, Ontario Ministry of the Environment and NSERC for the funding of this and related research. Appreciation is also extended to Marc-Andr~ Bdrub~ and his co-workers for the opportunity and inspiration to conduct this study while the author was a visiting professor with the Geological Engineering Research Group at Laval University.
Vol. 20, No. 2
191 CHEMICAL EQUILIBRIA,
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References
[1] Pitzer, K. S., 1979. Theory: Ion interaction approach. In Activity Coe~cients in Electrolyte Solutions., 1, (ed. R. M. Pytkowicz), 157-208 CRC press Inc. [2] Havvie, C. E. and Weave, J. H., 1980. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-C1-SO4-H20 system from zero to high concentration at 25 ° C. Geochim. Cosmochim. Acta, 44,981-988. [3] Havvie, C. E., Moller, N. and Weave, J. H., 1984. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-C1-SO4-OH-HCO3-CO3-CO2-H20 system to high ionic strengths at 25°C. Geochim. Cosmochim. Acta, 48, 723-751. [4] Monnin C. and Schott J., 1984. Determination of the solubility products of sodium carbonate minerals and an application to trona deposition in Lake Maadi (Kenya). GeocMm. Cosmochim. Acta, 48, 571-581. [5] Reavdon, E. J. and Beckie R. D., 1987. Modelling chemical equilibria of acid-mine drainage: The FeSO4-H2SO4-H20 system. Geochim. Cosmochim. Acta, 51, 23552368. [6] Robie R. A., Hemingway B. S. and Fisher J. R. (1979) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressure and at higher temperatures. U.S. Geol. Surv. Bull. 1452, 456pp. [7] Babushkin V. I., Matveyev G. M. and Mchedlov-Petrossyan O. P., 1985. Thermodynamics of Silicates. Springer-Verlag, Berlin, 459pp. [8] Drever J. I., 1988. The Geochemistry of Natural Waters (2nd ed) Prentice-Hall, New Jersey, 437pp. [9] Reavdon, E. J. and Dewaele P., 1989. Chemical Characteristics of the Carbonation of Grout Final Report to Ontario Hydro. [10] Jennings H. M., 1985. Aqueous solubility relationships for two types of calcium silicate hydrate. J. Amer. Ceram. Soc., 69, 614-618. [11] Gavtner E. M. and Jennings H. M., 1987. Thermodynamics of calcium silicate hydrates and their solutions. J. Amer. Ceram. Soc., 70, 743-749. [12] Ramachandran A. R. and Grutzeck M. W., 1987. Microstructural development during suspension hydration of tricalcium silicate under 'floating' and fixed pH conditions. Mater. Res. Soc. Syrup. Proc., 33-38. [13] Suzuki K., Nishikawa T., and Ito S., 1985. Formation and Carbonation of CSH in Water. Cement Concr. Res., 15, 213-224. [14] Crerav D. A., 1975. A method for computing multicomponent chemical equilibria based on equilibrium constants. Geochim. Cosmochim. Acta, 39, 1375-1384. [15] Anderson G. M. and Crerav D. A., 1989. Thermodynamics in Geochemistry. Monograph (in prep). [16] Diamond S., 1976. A review of alkali-silica reaction mechanisms 2. Reactive aggregates. Cement Concr. Res., 6, 549-560.
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Vol. 20, No. 2 E.J. Reardon
[17] B6rub~ M-A. and Fournier B., 1986. Les produits de la rgaction alcalis-silice dans le beton: Etude de cas de la region de Quebec. Canadian Mineralogist, 24, 271-288. [18] Knudsen T. and Thaulow N., 1975. Quantitative microanalyses of alkali-silica gel in concrete. Cement Concr. Res., 5,443-454. [19] Jawed I. and Skalny J., 1978. Alkalies in cement: A review II. Effect of alkalies on hydration and performance of Portland cement. Cement Concr. Res., 8, 37-52.
AN ION I N T E R A C T I O N M O D E L FOR T H E D E T E R M I N A T I O N OF C H E M I C A L E Q U I L I B R I A IN C E M E N T / W A T E R SYSTEMS
E.J. Reardon Department of Earth Sciences University fo Waterloo Waterloo, Ontario, Canada N2L 3G1 (Refereed) (Received March 31, 1989) ABSTRACT A chemical equilibria model is proposed for the simulation of reactions between porewater and the various amorphous and crystalline minerals of cementitious material at 25°C. The model utilizes the Pitzer Ion Interaction model as a basis for the calculation of ion activity coefficients. This allows the simulation of chemical equilibria between minerals and water to high solute concentrations. A variable compositional model for CSH based on the data of Gartner and Jennings is also incorporated into the solving relations. An example simulation of the effect of progressive additions of sulfuric acid on a cement paste are presented to illustrate the basic workings of the model.
Introduction T h e major elemental constituents of cement are the same as the aggregates that are used to produce grouts and concretes from cement - Ca, Mg, Na, K, Fe, A1, Si, S, C and C1. Upon interaction of H 2 0 with cement-based materials, these elements are partitioned between the solid and solution phases. The solid phases that form are an assemblage of h y d r a t e d compounds that may be crystalline or gel-like in character. T h e gel-like phases, most notably CSH, characteristically exhibit a wide range in chemical composition. For gel/water systems, a change in the composition of the solution phase effects a change in the composition of the solid. Variable composition solids are difficult to incorporate into chemical models. Another complicating factor to the chemical modelling of c e m e n t / w a t e r systems relates to the dissolved constituents which can attain very high concentrations. The Debye-Huckel and Davies equations, which are used to calculate ion activity coefficients, are stretched to the limit at such concentrations. Yet there is considerable interest in the cement research community to describe reactions in c e m e n t / w a t e r systems at exceedingly high solute concentrations, such as encountered in seawater or oil-field brines. The construction of a chemical equilibria model that can accurately describe the partitioning of elements between the solid and solution phases in cementitious systems is, quite accu175
176
Vol. 20, No. 2 E.J. Reardon
rately, a formidable challenge. In this paper, a preliminary step is made in this direction. The paper provides the necessary thermodynamic information and modelling strategy to enable the quantitative analysis of chemical equilibria in cement/water systems. The Chemical Model Solution Speciation
The aqueous species that are produced when water comes in contact with grouts, concrete or cement are a collection of hydrolysis products, ion pairs and complexes. To determine the equilibrium state of such solutions, the actual number of aqueous species that one need recognize may be considerably smaller than the actual number of species present. For example, although Fe3+ and A1a+ ions form a wide variety of hydrolysis products in water, only Fe(OH)7 and AI(OH)~ are important species at the pH conditions representative of porewaters in contact with cementitious material (pH > 8.0). In addition, if an ion interaction model is used to calculate individual ion activity coefficients, the effects of loosely associated ion pairs such as NaC03, CaSO~ and MgSO~ on solution equilibria can be accounted for by the inclusion of interaction parameters in the activity coefficient expressions. The use of an ion interaction model to calculate activity coefficients can thus considerably simplify the speeiation picture and consequently the calculation of chemical equilibrium states. In this study, we have adopted the Pitzer ion interaction model with which to perform the calculation of ion activity coefficients. The suite of aqueous species that are explicitly recognized with this model are shown in Table 1. In performing chemical equilibria calculations for a gas/water/solid system, all reactions between the solution and either the solid or the gas phase must be written in terms of, and only in terms of, these species. The pertinent activity coefficient expressions for the Pitzer ion interaction model have been published elsewhere [1,2,3]. and are not presented in thisreport. The reader is referred to Harvie et al. [3] for the particular formulation of the equations used in this study. The solution of the Pitzer equations to yield ion activity coefficient values requires ion interaction parameter data. For each cation/anion pair, up to four parameters are required - flo, fl~j,/3,% and C~, where i and j refer to cation and anion, respectively. For each cation/cation pair and anion/anion pair, such as Na+-Ca 2+ or CI--OH-, a single parameter is required (0~i or 0jj). For each cation/neutral species or anion/neutral species Table 1: Principal aqueous species in cement/water systems Cations
Anions
NeutralSpecies
Ca2+
CISO~HCO~ Fe(OH)7
H4SiO~
M g ~+ Na + K+
H+
AI(OH)7
MgOH +
H3SiO7
H~SiO~OH-
co~-
H~CO~
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177 CHEMICAL E Q U I L I B R I A ,
ION INTERACTION MODEL
a single p a r a m e t e r is required (Ain or Ajn). Finally, for each three ion interaction of either two cations and an anion or two anions and one cation, an additional parameter is required (¢iij or Cjjl). The strength of the Pitzer approach is its ability to accurately describe equilibria in multicomponent solutions based on data collected from binary and ternary salt systems. It is found that because the probability of interaction among three ions of the same charge or four or more ions is so low, additional interaction parameter data other than those cited above are not necessary to describe multicomponent solutions. Although much of the parameter data required to solve for the activity coefficients of the ions listed in Table 1 are available in the compilations provided by Pitzer [1] or Harvie et al. [3], some data are not available. This is the case for the interaction of iron, aluminum and silica species with other ions in solution. In this study, these missing data have been
Table 2: Values of single electrolyte interaction parameters at 25°C. Ion
Na +
K+
C a 2+
Mg2+
H+
MgOH +
CI-
~ ~ B2 C¢
0.0765 0.2664 0 0.0013
0.0483 0.2122 0 -0.0008
0.3159 1.6140 0 -0.0003
0.3523 1.6815 0 0.0052
0.1775 0.2945 0 0.0008
-0.1000 1.6580 0 0
SO42-
~o ]31 ~2 C~
0.0196 1.1130 0 0.0050
0.0499 0.7793 0 0
0.2000 3.1973 -54.24 0
0.2210 3.3430 -37.23 0.0250
0.0217 0 0 0.0411
0 0 0 0
CO~-
~o ~i ~,2 C 4'
0.0362 1.5100 0 0.0052
0.1488 1.4330 0 -0.0015
0.2000 3.1973 -150 0
0.2210 3.3430 -150 0
0 0 0 0
0 0 0 0
HCO~"
B° ~1 ~2 C 4~
0.0280 0.0440 0 0
0.0296 -0.0130 0 -0.0080
0.4000 2.9770 0 0
0.3290 0.6072 0 0
0 0 0 0
0 0 0 0
OH-
13o ~I ~2 C¢
0.0864 0.2530 0 0.0044
0.1298 0.3200 0 0.0041
-0.1747 -0.2303 -5.72 0
0 0 0 0
0 0 0 0
0 0 0 0
*H3 SiO~"
~o ~i ~2 C¢
0.0454 0.3980 o o
-0.0003 0.1735 o o
0.2145 2.5300 o o
0.4746 1.7290 o o
0.2106 0.5320 o o
0 0 o o
*H2SiO~-
~o .GI ~2 C 4'
0.0196 1.1130 0 0.0050
0.0499 0.7793 0 0
0.2000 3.1973 -54.24 0
0.2210 3.3430 -37.23 0.0250
0.0217 0 0 0.0411
0 0 0 0
*AI(OH)~-
/~o /~1
0.0454 0.3980
-0.0003 0.1735
0.2145 2.5300
0.4746 1.7290
0.2106 0.5320
0 0
~2
o
o
o
o
o
o
C 4'
0
0
0
0
0
0
0.4746 1.7290 0 0
0.2106 0.5320 0 0
0 0 o 0
*Fe(OH)~-
13° ~I B2 C¢
0 . 0 4 5 4 -0.0003 0.3980 0.1735 o o 0 0
0.2145 2.5300 0 0
*Estimated values (See t e x t ) . P r i n c i p a l source of other data is from ref [3]. See description in text for details.
178
Vol. 20, No. 2 E.J. Reardon
either estimated or set to zero. The complete set of ion interaction parameter data that are required to solve the Pitzer relations are presented in Tables 2 through 6. Table 3: A parameter values at 25°C. Ion H2CO~ *H4SiO~
Ion H2CO~ *H4SiO~
Na +
K+
Ca ~+
Mg ~+
H+
MgOH +
0.1000 0.1000
0.0510 0.0510
0.1830 0.1830
0.1830 0.1830
0
0
0 0
CI-
SO~-
C O ~ - HCO~" OH-
°0.0050 -0.0050
0.0970 0.0970
*Values for H4SiO~
0 0
are estimated
0 0
H3SiO~- H2SiO~- AI(OH)~" Fe(OH)~"
0 0
using H 2 C O ~
0 0
0 0
0 0
0 0
a.s an analogy. !i2CO~ data is from ref [3].
The data in these tables are precisely as given by Harvie et al. [3] with the following exceptions: The parameter data for Na-HC03 and Na-C03 are only slightly different from that given in [3] and are based on a review of data by Monnin and Schott [4]. Parameter data for H-SO4 interaction are from Reardon and Beckie [5] and are not substantively different from those given in [3]. There are no published data governing the interaction of AI(OH);, Fe(OH);, H3SiO; or H2SiO~- with either Ca 2+, Mg 2+, Na +, K + or H +.. To estimate /5°, fl~j, fi~j and C~ parameters for each of the above cation/anion pairs, the HSO; ion was used as a model for Fe(OH);, AI(OH); and H3SiO; ions; and SO~- was used as a model for H2SiO~- ion. The parameter data for Me-HS04 or Me-SO, interactions are published [3] and were used to approximate the Me-Fe(OH)4, Me-AI(OH)4 and Me-H3Si04 ion Table 4 : 8 parameter values at 25°C. Ion
K+
Na+ K+ Ca~+
-0.0120
Ca 2+
Mg 2+
0.0700 0.0700 0.0360 0.0320 0 0.0050 0.0070 0.0920
Mg 2+ H+
0.1o{30
SO~-
C O ~ - HCO~
CISO.2 CO~-
0.0200
-0.0200 0.0200
*H3SiO~*H2SiO~*Al(OH)~"
MgOH +
0 0 0 0 0
Ion
HCO~ OH-
H+
0.0359 0.0100 -0.0400
OH-
*H3SiO~ *H2SiO~- *AI(OH)~- "Fe(OH)~-
-0.0500 -0.0130 0.1000
-0.006 0 0
0 0 0
-0.006 0 0
-0.0(16 0 0
0
0 0
o 0
0 0
0 o
0
0 0
0 0 0
* E s t i n ~ t e d values (See text). Principal source of other d a t a is from ref [3]. See description in text for details.
Voi. 20, No. 2
179 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
Table 5: Cation-anion-anion ¢ parameter values at 25°C. Na +
K+
Ion C[SO 2.CO~HCO~ OHHzSiO~" H2SiO~AI(OH)~"
Cl-
SO~-0.0014
CO~-0.0085 -0.0050
HCO[ -0.0143 -0.0050 O.OO2O
o
o.oo4o -o.oooo
o o
so?COb HCO~ OHH3SiO~ H2 S i O ( AI(OH)~-
OH-0.0060 -0.0090 -0.0170 0
"H3SiO[ -0.{X)60 -0.0094 0 0 0
-o.ooeo o -o.os00 -o.o677
"H~SiO~0.0014 0 -0.0050 -0.0050 -0.0090 -0.0094
*AI(OH)~" -0.0060 -0.0094 0 0 0 0 -0.0094
"Fe(OH)~" -0.0060 -0.0094 0 0 0 0 -0.0094 0
0 0 -0.0090 0 -0.0500 -0.0077
0 -0.0677 0 0 0 0 -0.0677
0 -0.0677 0 0 0 0 -0.0677 0
0.0120
-0.0100 0
0 0 0
0 O 0
-0.0250 O 0 0
0 O 0 0 0
-0.01S0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Ca 2+
ClSO.~CO~HCO~ OHHa SiO~ H~SiO(AI(OH)~-
-0.0180
0 O
Mg2+
elSO.2CO~HCO~ OHHaSiO~H2SiO~AI(OH)~-
-0.0040
0 0
-0.0960 -0.1610 0
0 0 0 0
0 -0.0425 0 0 0
-0.0040 0 0 -0.1610 0 -0.0425
0 -0.0425 0 0 0 0 -0.0425
0 -0.0425 0 0 0 0 -0.0425 0
H+
elSO~CO~HCO~OHH3SiO~ H2SiO4AI(OH)7
0
0 0
0 0 0
0 0 0 0
0.0130 0 0 0 0
0 0 0 0 0 0
0.013(:} 0 0 0 0 0 0
0.0130 0 0 0 0 0 0 0
MgOH+
C]SO~CO~HCOH OHH3SiO~" H2SiO~AI(OH)~-
0
0 0
0 0 0
0 0 0 0
0 0 0 0 o
0 0 0 0 0 O
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
v
*Estimated values (See text). Principal source of other data is from ref [3]. See description in text for details.
interaction parameters. An analogous approach was used to estimate 19, A and ¢ parameters for interactions involving these ions. • In the interaction model presented for natural waters by Harvie et al. [3], they accounted for the interaction of Mg 2+ with O H - through the formation of a MgOH + ion pair with a log dissociation constant of-2.19 at 25°C rather than than by reporting interaction parameters to describe the interaction. Although they point out that there may be problems with the approach and that more experimental d a t a are
180
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necessary to support the approach, we adopt this model in this study. In their model, they set all other anion interactions with MgOH +, except for CI-, to zero. We do the same in this study for the interaction of MgOH + with Al(OH)4 , Fe(OH)~, H3SiO; and H2SiO~-. One of the major advantages of the Pitzer interaction model approach is that the interaction between ions is described through a set of parameters rather than by the postulation Table 6: Anion-cation-cation ¢ parameter values at 25°C. Ion
K÷
C a ~+
M82+
H+
Na + K+ C a 2+ M g 2+ H+
-0.0018
-0.0070 -0.0250
-0.0120 -0.0220 -0.0120
-0.0040 -0.0110 -0.0150 -0.0110
so~-
Na + K+ Ca 2+ Mg2+ H+
-0.0100
-0.0550 0
-0.0150 -0.0480 0.0240
0 0.1970 0 0
0 0 0 0 0
co~-
Na + K+ C a 2+ Mg 2+ H+
0.0030
0 0
0 0 0
0 0 0 0
0 0 0 0 0
HCO{
Na + K+ C a 2+ M g 2+ H+
-0.0030
0 0
0 0 0
0 0 0 0
0 0 0 0 0
OH-
Na + K+ C a 2+ Mg 2+ H+
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
H3 SiO~
Na + K+ C a 2+ M g 2+ H+
0
0 0
0 0 0
-0.0129 -0.0265 0 -0.1780
0 0 0 0 0
"H2SiO~-
Na + K+ C a 2+ Mg2+ H+
-0.0100
-0.0550 0
-0.0150 -0.0840 0.0240
0 0.1970 0 0
0 0 0 0 o
"AI(OH)~"
Na+ K+ Ca2+ M g 2+ H+
0
0 0
0 0 0
-0.0129 -0.0265 0 -0.0178
0 0 0 0 0
°Fe(OH)7
Na+ K+ C a 2+ M g 2÷ H+
0
0 0
0 0 o
-0.0129 -0.O265 o -0.0178
0 0 o 0 0
CI-
*
* E s t i m a t e d values (See text).
MgOH +
0 0 0.0280 0
Principal source of other data is from ref [3].
See description in text for details.
Vol. 20, No. 2
181 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
of the formation of ion pairs in solution. Some ion interactions are so strong, however, that the presence of ion pairs or additional species in solution must be recognized. Such a situation increases the complexity of the calculations required to obtain activity coefficient values, requires more assumptions as to the interaction parameters of the newly formed species with other ions in solution, requires more iterations of any numerical model used to determine the equilibrium state of a rock/water system and reduces the probability that a unique solution to the set of mass action and mass balance equations will be found. It is preferable if ion pair formation need not be invoked. Harvie et al. [3] found it necessary to invoke the formation of both CaCO~ and MgCO~ to account for the interaction of CO]with Ca 2+ and Mg 2+ ions. We have found that an equally good fit of the available solubility data can be obtained by using the/5 °, ~lj and C~ parameter data for Ca-SO4 and Mg-SO4 interaction as estimates for Ca-CO3 and Mg-CO3 interaction and with a value of -150 for the/5~- value of both ion pairs. We have adopted this more simplified approach to describe both Mg-COz and Ca-COB interactions in this study. It is emphasized that much of the parameter data recorded in Tables 2 through 6 have not been determined from an analysis of experimental data, but have been estimated. Consequently, this set of ion interaction parameter data is offered merely as a starting point for the quantitative analysis of chemical equilibria in cement/water systems rather than a definitive set of ion interaction parameters. Solution and Mineral Phase Reactions
There are a large number of potential solid phases that may control the chemical composition of water in contact with cementitious material. In order to appraise the influence of these solid phases on a water's chemical composition, a knowledge of the equilibrium constants describing the solid phase dissolution reactions is required. In addition, equilibrium constants for all reactions occurring strictly within the solution phase, such as ion hydrolysis and ion pairing or complexing reactions, must also be known. These equilibrium constants can be calculated from published standard chemical potential data for the substances involved in these reactions with the relation: P
log K = -(~'-~ 4=1
R
n,# ° -
~,
n,#°)/2.303
(1)
/=1
where P and R are the number of products and reactants involved in the reaction, respectively, and ni, is the stoichiometric coefficient of the i th product or reactant. A tabulation of chemical potential data at 25°C for the principal dissolved constituents and mineral phases in a cement/water system are recorded in Table 7. These data are derived from two principal sources - Harvie et al's compilation of chemical potentials [3] and Babushkin et al.'s text on silicate thermodynamics [7]. Equilibrium constants for a number of solution phase and solution/solid phase reactions have been calculated with the above relation and the data are recorded in Table 8. An equilibrium constant for the solubility reaction of CSH is not presented in this table but is given a special treatment in the following section.
182
Vol. 20, No. 2 E.J. Reardon
Table 7: S t a n d a r d chemical potentials ( # ° / R T ) at 25°C for various substances Substance
/~°/RT
Source
H20 CO2 H2CO~ H4SiO~ H+ Ca2+ Mg2+ MgOH+ Na+ K+ OHClHCO~ H3SiO~ AI(OH)~ Fe(OH)~ H2SiO~SO42CO~-
-95.663 -159.092 -251.340 -527.865 0.0 -223.300 -183.468 -251.940 -105.651 -113.957 -63.435 -52.955 -236.751 -505.364 -526.650 -339.622 -478.525 -300.386 -212.944
1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1
Substance Sepiolite Gypsum Brucite Arcanite Calcite Halite Nesquehonite Portlandite Gibbsite Ca-Aluminosilicate gel Ettringite Monoaluminosulfate K-Aluminosilicate gel Ca-Carboaluminate Silica (amorph) Syngenite C4AH13 C2AH8 C3AH6 Ca-oxychloride Mg-oxychloride
/z°/RT
Source
-3732.445 -725.560 -335.400 -532.390 -455.600 -154.990 -695.185 -362.120 -465.545 -1595.141 -6134.559 -3138.191 -1493.018 -2428.294 -342.626 -1164.800 -2964.380 -1943.777 -2022.875 -2658.450 -1029.600
3 1 1 1 1 1 4 1 2 2 2 2 2 6 5 1 2 2 2 1 1
1 ref [6] 2 ref [7] a ref [8] 4This study SAverage of values from 1 and 2 6 ref [9]
Treatment of CSH in the Chemical Model T h e CSH gel phase that is produced upon hydration of Portland cement presents special problems in accurately representing its solubility behaviour. This is because it cannot be considered as a pure phase with a unique solubility product. CSH exhibits pronounced variations in its C a / S i ratio depending on the C a / S i ratio of the solution in contact with the solid [10,11]. There is also evidence to show t h a t there are a number of distinct forms of CSH. One of these appears to occur only at early hydration times when C3S is still present within the hydrating cement particles [11,12]. Other, less soluble and more stable forms, occur at later times and are also observed to precipitate directly from supersaturated solutions. T h e solubility characteristic of these more stable forms are very similar and distinctly different from the early formed CSH. Both Suzuki et al. [13] and G a r t n e r and Jennings [11] presented t h e r m o d y n a m i c models to describe the solubility behaviour of the more stable CSH as a function of water chemistry. We have adopted the t r e a t m e n t of Gaxtner and Jennings [11] and used their compositional and solubility d a t a for CSH (cf. d a t a for Curve 2, Table III, ref [11]) in our analysis. We cannot, however, use their thermochemical d a t a directly in this study because they used a different activity coefficient and aqueous speciation model t h a n used in this study. Consequently, a re-evaluation of the thermochemical properties of CSH (specifically, its solubility products) are performed here.
Vol. 20, No. 2
183
CHEMICAL EQUILIBRIA, ION INTERACTION MODEL Table 8: Equilibrium constants for various reactions at 25°C. Mineral or Species
Reaction
log K s p
H4 SiO~ dissociation H3 SiO~- dissociation MgOH ÷ dissociation H 2 C O ~ dissociation H C O [ dissociation H20 dissociati~ CO2(0) dissolution Brucite Portlandite Ettrir~ite Silica (amorph) Ca- Carboalumlnate Sepiolite Gibbsite Calcite Gypsum Arcanite NesquehonJ te C4AH13 C2AH8 C3AH6 Ca-Muminosilieate gel Halite Ca-oxychloride Mg-oxychloride Syngenite Monoaluminosulfate K-Aluminosilicate gel
H4SiO~ --* H + + H3SiO~ H 3 S i O ~ ---* H + + H 2 S i O ~ M g O H + ---* M 9 2 + + O H H2CO~ ~ H + + HCO~ H C O ~ ---* H + + C O ~ H20 ~ H + + OHC02 + H20 ~ H2CO~ M g ( O H ) 2 ---* M g 2+ + 2 O H C a ( O H ) 2 ---* C a 2+ + 2 O H CasAI2Os(S04)3 . 32//20 - - - * 6 C a 2+ + 2AI(OH)~ + 3 S 0 2 - + 4 O H - + 2 6 H 2 0
-9.77 -11.66 -2.19 -6.34 -10.34 -14.00 -1.48 -10.89 -5.19
Si02 + 2H~O ---* H4SiO~
-2.64 -19.90 -54.95 -1.01 -8.41 -4.58 -1.78 -5.12 -27.49 -13.04 -19.95 -3.76 1.57 -15.25 -15.96 -7.45 -27.62 -2.15
-43.13
C a O . A1203 • C a C 0 3 • l l H 2 0 ~ 2Ca 2+ + 2 A I ( O H ) ~ + C O ~ - + 7 H 2 0 31120 + M g ( S i 6 O l s ( O H ) 2 . 6 H 2 0 ~ 4M92+ + 6H3SiO~ + 2OHAI(OH)3 + OH- ~ AI(OH)~ CaC03 ~ Ca 2+ + CO 2 C a S 0 4 • 2 H 2 0 "--* C a ~4 + S O T - + 2 H ~ O K~S04 ~ 2K+ + SO TM 9 C 0 3 • 3 H 2 0 --.* M 9 2 + + C02a - + 3 H 2 0 4CaO • AI203 • 13H20 ~ 4 C a 2+ + 2 A I ( O H ) ~ + 6 O H - + 6 H 2 0 2CaO. Al203 • 8H20 ~ 2Ca 2+ + 2 A I ( O H ) ~ + 2 O H - + 3 H 2 0 3 C a O • A1203 • 61120 .__, 3 C a 2+ + 2 A I ( O H ) ? + 4 0 H 7 H 2 0 + 2 O H - + C a O • A I ~ 0 3 • 2 S i 0 2 ----* ~ a 2+ + 2Al ( O H ) ~ + 2 H 3 S i O ~ NaCI ~ Na + + ClC a 4 C l 2 ( O H ) s • 13//20 ----, 4 C a ~+ + 2 C I - + 6 O H - + 13/-/20 Mg2CI(OH)3.4H20 ~ 2M92+ + C l - + 3 O H - + 4 H 2 0 K 2 C a ( S 0 4 ) 2 . H 2 0 - - ~ 2K + + C a 2+ + 2 S 0 ~ - + 1"120 Ca4 A I 2 0 6 S 0 4 . 12H20 ------*4 C a 2+ + 2 A I ( O H ) [ + S O ~ - + 4 O H - + 6 H ~ O 10H20 + 6 O H - + K 2 0 . A l 2 0 3 • 6 S i 0 2 ---* 2 K + + 2 A I ( O H ) ~ + 6 H s S i O ~
The Ca/Si ratios of the CSH referred to above are plotted as a function of the Ca/Si ratio of the equilibrated solutions in Figure 1. There is a fair degree of scatter in the data but a straight line relationship yields a reasonable representation of the compositional variation. This straight line relationship was used to calculate CaO and SiO2 concentrations for the solution phase in equilibrium with a specified solid composition. These compositions
o "
0 0
u} O
O
Figure 1 - Compositional data for CSH vs. SiO2 content of the solution from data for Curve 2, Table III, Gartner and Jennings [11]. ,
0
I
1
,
I 2
'
,
I
i
3
log SI02(/zmoles/L)
%1 4
184
Vol. 20, No. 2 E.J. Reardon
were used as input into a chemical speciation model that used the Pitzer Ion Interaction model to calculate ion activities coefficients. Solubility products were then calculated for each composition of CSH in equilibrium with each solution composition. The results of this analysis showed that both the solubility products and the solid phase compositions yielded nearly linear trends when plotted as a function of the Ca2+/H4SiO~ activity ratio
.15
,,p ¢0 0
v'
-10
o
-5
0
r
I
,
1
I
,
3
I
,
I
6
,
7
log a C a 2 + / a H 4 S i 0 4 °
2 neD
.o
¢D
O 1
0
,
-1
I
1
,
I
,
I
,
3 5 log a C a = + / a H 4 S l 0 4 °
I
7
,
9
Figure 2 - (a) Model calculated solubility product for CSH vs the activity ratio of Ca2+/H4SiO~ in solution. (b) Model calculated Ca/Si ratio of CSH vs the activity ratio of Ca~+/H4SiO,~ in solution.
Vol. 20, No. 2
185 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
3.5
÷
2.5 o)
_o
*
+
0
Figure 3 - Comparison of model calculated SiO2 and CaO contents of solutions saturated with respect to CSH and published solubility data reported in Ref. [10]. (See discussion in text)
E 1.8
+
+
+
u) o~ _o
•
+
+
4~
•
I
0.5
•
÷
+
-0.5 10
20
30
CaO (mmoles/L)
(R) of the equilibrating solution. These results are shown in Figure 2. The following two quadratic equations accurately represent these solubility relations:
(Ca) = 0.48548 + 0.11563R + 0.0104536R 2 logKsp= 4.507 + 1.3306R + 0.019172R 2
(2)
CSH
(3)
These two expressions can now be incorporated into an overall chemical equilibria model for cement/water systems to allow for a variable composition/variable chemical potential model for the CSH solid phase. Figure 3 demonstrates how accurately these expressions represent the available published solubility data for CSH. The upper curve represents the average of solubility data for the early-formed metastable CSH phase referred to by Jennings [10]. Individual data points for this phase are not shown on the diagram. The lower curvilinear trend of data points are solubility measurements of the more stable form(s) of CSH. The lower solid curve shown in the diagram is the predicted solubility of CSH with the chemical model in this study and equations 2 and 3.
Application of the Chemical Model Because a variable composition model has been adopted for CSH equilibria, any simulation of chemical equilibria between water and hydrated cement compounds, in which CSH is included, must consider as variables both the amounts of solid phases present and the concentrations of the various elemental species in solution. As an example application of the chemical model, the chemical changes that occur with the progressive addition of sulfuric acid to a kg of water containing one mole each of portlandite, CSH (Ca/Si = 2.12) and C4AH13 will be simulated. Such a simulation is relevant to understanding the mineralogic changes that occur in concrete as a result of attack by atmospheric sulfur dioxide.
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The variables in this simulation are the concentrations of the aqueous species, the amounts of the three solid phases mentioned above as well as the amounts of any new phases that m a y form as a result of the progressive addition of sulfuric acid. T h e amounts of the solid phases can be conveniently expressed in the same concentration units as the dissolved species - molalities, i.e. the number of moles of solid in contact with a kilogram of water. T h e relations that are to be solved are the pertinent solid phase equilibrium constant and ion dissociation constant expressions from Table 8, and mass balance expressions for Ca, Si, A1 and SO4. A Newton-Raphson technique was adopted to solve these relations [14,15]. This solving routine requires initial estimates for all the unknowns. T h e solution of the relations must therefore be performed a number of times before convergence is attained. T h e values of the various ion activity coefficients also change with each iteration and so the Pitzer relations must be included in the computational procedure. A copy of the c o m p u t e r p r o g r a m to calculate ion activity coefficients with the Pitzer relations is available upon request. T h e Newton-Raphson algorithm is described in detail by Crerar [14] and a reproduction of the computer p r o g r a m is given in Anderson and Crerar [15].
Table 9: Model results for sulfuric acid attack of CSH, C4AH13 and Ca(OH)2 Temperature pH aHuO Ca/Si of CSH H~SO4 added Species Ca 2+ H+ so
-
OHH3SiO~ H2SiO42AI(OH)~ H4SiO,] Amorph. Sil Gibbsite Gypsum Portlandite CSH C4A1H13 Phase Portlandite CSH Amorph. Silica Gibbsite Gypsum C4AIH13 Monoaluminosulfate Ettringite
Initial 25°C 12.48 1.00 2.12 0.0
Final 25°C 8.10 1.00 No CSH 0.73moles/kg H20
Concentration millimolality 20.1 4.253E-10
Concentration millimolality 14.9 9.963E-06
-
40.2 1.119E-04 0.0022 0.0152 1.865E-07 99.5 100.0 100.0 log SI 0.00 0.00 -7.09 -2.35 0.00
14.9
1.658E-03 5.813E-02 3.985E-05 1.461E-04 2.27 97.7 200. 717.
log SI -8.90 -0.64 0.00 0.00 0.00 -30.90 -21.27 -4.96
Vol.
20,
No. 2
187 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
The results of the simulation of the initial equilibration of the three solid phases with water (no sulfuric acid added) and final water chemistry (after addition of 0.73 moles of sulfuric acid) are shown in Table 9. The list of log SI values given at the bottom of the table are the model calculated saturation indices for the various mineral phases. Saturation indices are defined as: log S I = log I A P (4) Ksp where I A P is the ion activity product calculated from the the individual ion activities involved in the dissolution reaction for the mineral (Table 8) and Ksp is the solubility product for the mineral. A log SI value of zero indicates that the water is saturated with respect to a particular mineral and a value less than zero, undersaturated. Once the model is run to establish the equilibrium state of the grout/water system before addition of sulfuric acid, acid attack is simulated by rerunning the model successively, increasing the amount of SO4 present in the system each time. Phase changes are charted by monitoring the calculated saturation indices and mineral masses. Once the log S I value for a mineral phase reaches 0.0, it is designated to be present in the grout/water system. Similarly, once the mass of a mineral reaches zero, it is removed from the input list of mineral phases present. In this manner, the theoretical or thermodynamically-based reaction path can be delineated, revealing the progressive changes in solution composition and mineral masses, the appearance or disappearance of mineral phases as well as the locations of invariant points. By comparing the results for the initial and final conditions in Table 9, the effect of sulfuric acid addition is seen to transform the original mineral assemblage of CSH, C4AH13 and Ca(OH)2 into an assemblage of amorphous silica, gibbsite and gypsum. The results of the chemical changes that occur in the water phase with the progressive addition of sulfuric acid are graphically shown in Figure 4. The plateau regions in the diagram relate to invariant points, i.e. where the solution chemistry is buffered until one mineral phase transforms completely into another. The progressive effect of sulfuric acid addition on phase transformation is best illustrated by comparing the plots of mineral saturation indices with the mineral concentrations ol
OH
Ca ~
.=
-
.:
.......
/
O
/I
O c
Figure 4 - Results of the simulation of the change in water chemistry during the progressive attack of CSH, Ca(OH) 2 and C4AH13 by sulfuric acid.
8 -4 ........ +. ...... . / _o
A~
-. ..
/
. . . . . . . . . . . . -¢
i / ............................................................. i .....[
..
"'>":-t / / ..... i! ........s, ................/ i! , , ,t!
0.0
^,
/
0.2
, 0.4
Moles Of sulfuric
,,
,
0.@ acid a d d e d
,! \1 it.~ ! I ,~,. i 0.8
188
Vol. E.J.
20, No. 2
Reardon
plots in Figure 6. The pH is inversely proportional to the amount of sulfuric acid addition and is used as the X-axis in both diagrams. The top two p]ots in Figure 5 give the saturation indices and concentrations of the mineral phases that are initially present in the system. The bottom two plots give the same information for the mineral phases that appear during the simulation, i.e. as a consequence of the addition of sulfuric acid. These diagrams indicate the following order of phase changes: 1. pH 12.5 - Portlandite dissolves as Ettringite precipitates (invariant point) 2. p H 1 2 . 5 t o 1 2 . 0 -
C4AH13 dissolves
3. p H 1 1 . 6 t o 1 0 . 6 -
Gypsum precipitates
4. p H 1 0 . 6 5. p H 8 . 8 -
Gibbsite and Gypsum precipitate as Ettringite dissolves (invariant point) amorphous silica precipitates as CSH dissolves (invariant point)
The above modelled sequence of phase transformations is in agreement with that proposed by Babushkin et al. [7] based on visual observations and thermodynamic analysis of concretes affected by sulfur dioxide attack. The predicted variation in the composition of CSH with sulfuric acid addition is shown in Figure 6. There is an exponential decrease in the Ca/Si ratio with reaction progress.
o
CSH
CSH
.....,..~..
, .4
a
C4AH13
e -s
i C4AH13
" ..............,............
P' i
-4
,i
i 11
9
lS
.........,
•",
.
r
I
11
|
pH
.....
pH
4
o Ettr
GIl~slte
G,psufi
............................. ...-..---
I
J
J
Q
Am
iI- Gypsum ..°..o. . . . . . . . . . . . . . JAm SI,
Slll
!
"-.......
.,/
i 13
..,.
,,/,;
Ettr
-4
"
I
L
11
II
pH
i 13
11
9 pH
Figure 5 - Calculated mineral saturation indices and mineral masses vs pH for water chemistries given in Figure 4.
VoI.
189
20, No. CHEMI CAL EQUILIBRIA,
ION INTERACTION MODEL
2.5
Figure 6 - Calculated change in CSH composition with pH.
.I(/)
1.5
0
I0
1
0.5
0
i 13
I
~
11
I g
i ?
pH
The model predicts an overall decrease in the Ca/Si ratio from 2.12 at a pH of 12.5 to 0.5 at a pH just below 9.0 where the CSH-arnorphous silica phase transition occurs. Model Limitations There are a number of important limitations of the proposed chemical equilibria model for water in contact with cementitious material. The first concerns the relations adopted to describe CSH solubility. The solubility product and compositional expressions for CSH given in this study were determined using reported experimental data for CSH solubility in solution mixtures of CaO and Si02 [11]. These solubility data range from high pH, high Ca and low silica concentrations to high silica, low calcium and low pH conditions. The proposed model for CSH solubility behaviour in this paper accurately represents these experimental data. The highest pH of the solubility data, however, only corresponds to the limit of portlandite solubility (~ 12.5). In actual porewaters of cementitious material, there are usually considerable quantities of KOH and NaOH. The presence of these constituents imparts a porewater pH that is beyond the upper pH limit of the experimental data on which the solubility model for CSH has been based. At this time, there is insufficient experimental data to support the application of the proposed model for CSH under such high pH conditions. Another limitation of the model relates to the speciation model adopted for silica hydrolysis. In this study, only the species H4SiO~, H3SiO~- and H2SiO~- have been included in the speciation model. At pH's greater than 13, however, there is evidence that the species HSiO~- and SiO~- may also form. These species have not been included in the present model because there is some controversy as to whether these species actually occur in solution and, more importantly, because there is a paucity of ion interaction parameter data for trivalent and quadrivalent ions that could be used to estimate parameters for the interactions of these ions with other ions in solution. There is an additional limitation of the proposed model that relates to the description
190
Vol. 20, No. 2 E.J. Rea rdon
of chemical equilibria under the high pH conditions characteristic of porewaters in contact with high alkali cements. Such caustic solutions aggressively dissolve siliceous aggregate material, such as cherts, tufts, glasses, siliceous limestones and even felspathic minerals and quartz [16,17]. This addition of silica to the porewaters results in the precipitation of a variety of mineral phases, collectively referred to as alkali silica reaction products. These phases contain varying amounts of calcium, silicate, and sometimes aluminum [18,17] Invariably, potassium is associated with these reactions products, which may be gel-like or crystalline. Undoubtedly, some of this material is simply CSH with variable amounts of associated potassium ions [19], whereas other reaction products are discrete mineral phases with definite chemical compositions. The solubility model for CSH adopted in this study [11], does not allow for the incorporation of potassium in the gel structure. Similarly, there are no available thermodynamic data for any of the other alkali silica reaction products that would enable calculation and inclusion of their solubility products into the proposed chemical equilibria model. Consequently, a quantitative prediction of the behaviour of potassium ions in the porewater of cementitious material cannot be made at this time. Another important limitation of the proposed model is that it does not allow for protonation reactions or ion sorption at the surfaces of the crystalline and amorphous phases of hydrated cement. Such reactions could be of substantial importance at the high solid/water ratios typical of mixed concretes and grouts. Although surface protonation and ion sorption reactions do not affect the calculation of the chemical equilibrium composition of a water in contact with a designated set of hydrated cement compounds, they do influence the simulation of the transfer of elemental masses that are required to attain a particular equilibrium state. Although many models have been proposed to describe surface protonation and ion sorption reactions for oxide and silicate material, the application of these models to the specific compounds of hydrated cement has not received much attention. Finally, it is realized that with the presence of aggregate material of heterogeneous mineralogy in actual concretes and grouts, an attainment of chemical equilibria between porewater and all mineral phases present is not possible. Although chemical equilibria may exist between porewater and the hydrated compounds of the cement paste far from an aggregate particle, near such a particle the chemical composition must necessarily be different. Thus there is at all times not only heterogeneities in the chemical composition of the porewater of grouts and concretes, but concentration gradients that continuously effect compositional changes to all of this water. In this light, the application of any chemical equilibria model to describe reactions in such a chemically heterogeneous and dynamically evolving system must consequently be done with a considerable degree of caution. Acknowledgements The author would like to express his appreciation to Ontario Hydro, Ontario Ministry of the Environment and NSERC for the funding of this and related research. Appreciation is also extended to Marc-Andr~ Bdrub~ and his co-workers for the opportunity and inspiration to conduct this study while the author was a visiting professor with the Geological Engineering Research Group at Laval University.
Vol. 20, No. 2
191 CHEMICAL EQUILIBRIA,
ION INTERACTION MODEL
References
[1] Pitzer, K. S., 1979. Theory: Ion interaction approach. In Activity Coe~cients in Electrolyte Solutions., 1, (ed. R. M. Pytkowicz), 157-208 CRC press Inc. [2] Havvie, C. E. and Weave, J. H., 1980. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-C1-SO4-H20 system from zero to high concentration at 25 ° C. Geochim. Cosmochim. Acta, 44,981-988. [3] Havvie, C. E., Moller, N. and Weave, J. H., 1984. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-C1-SO4-OH-HCO3-CO3-CO2-H20 system to high ionic strengths at 25°C. Geochim. Cosmochim. Acta, 48, 723-751. [4] Monnin C. and Schott J., 1984. Determination of the solubility products of sodium carbonate minerals and an application to trona deposition in Lake Maadi (Kenya). GeocMm. Cosmochim. Acta, 48, 571-581. [5] Reavdon, E. J. and Beckie R. D., 1987. Modelling chemical equilibria of acid-mine drainage: The FeSO4-H2SO4-H20 system. Geochim. Cosmochim. Acta, 51, 23552368. [6] Robie R. A., Hemingway B. S. and Fisher J. R. (1979) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressure and at higher temperatures. U.S. Geol. Surv. Bull. 1452, 456pp. [7] Babushkin V. I., Matveyev G. M. and Mchedlov-Petrossyan O. P., 1985. Thermodynamics of Silicates. Springer-Verlag, Berlin, 459pp. [8] Drever J. I., 1988. The Geochemistry of Natural Waters (2nd ed) Prentice-Hall, New Jersey, 437pp. [9] Reavdon, E. J. and Dewaele P., 1989. Chemical Characteristics of the Carbonation of Grout Final Report to Ontario Hydro. [10] Jennings H. M., 1985. Aqueous solubility relationships for two types of calcium silicate hydrate. J. Amer. Ceram. Soc., 69, 614-618. [11] Gavtner E. M. and Jennings H. M., 1987. Thermodynamics of calcium silicate hydrates and their solutions. J. Amer. Ceram. Soc., 70, 743-749. [12] Ramachandran A. R. and Grutzeck M. W., 1987. Microstructural development during suspension hydration of tricalcium silicate under 'floating' and fixed pH conditions. Mater. Res. Soc. Syrup. Proc., 33-38. [13] Suzuki K., Nishikawa T., and Ito S., 1985. Formation and Carbonation of CSH in Water. Cement Concr. Res., 15, 213-224. [14] Crerav D. A., 1975. A method for computing multicomponent chemical equilibria based on equilibrium constants. Geochim. Cosmochim. Acta, 39, 1375-1384. [15] Anderson G. M. and Crerav D. A., 1989. Thermodynamics in Geochemistry. Monograph (in prep). [16] Diamond S., 1976. A review of alkali-silica reaction mechanisms 2. Reactive aggregates. Cement Concr. Res., 6, 549-560.
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[17] B6rub~ M-A. and Fournier B., 1986. Les produits de la rgaction alcalis-silice dans le beton: Etude de cas de la region de Quebec. Canadian Mineralogist, 24, 271-288. [18] Knudsen T. and Thaulow N., 1975. Quantitative microanalyses of alkali-silica gel in concrete. Cement Concr. Res., 5,443-454. [19] Jawed I. and Skalny J., 1978. Alkalies in cement: A review II. Effect of alkalies on hydration and performance of Portland cement. Cement Concr. Res., 8, 37-52.