Activity Coefficients Predicted by the Local Composition Model for

18 Activity Coefficients Predicted by the Local Composition Model for Aqueous Solutions Used in Flue Gas Desulfurization

Fossil Fuels Utilization Downloaded from pubs.acs.org by CORNELL UNIV on 10/04/16. For personal use only.

Charles E. Taylor and Gary T. Rochelle Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate; SO2 vapor pressure over sulfite/ bisulfite solutions; and, CO2 vapor pressure over carbonate/bicarbonate solutions. The major objective of t h i s work is to extend the p r e d i c t a b i l i t y of solution e q u i l i b r i a models f o r flue gas d e s u l f u r i z a t i o n (FGD) processes by employing an a c t i v i t y c o e f f i c i e n t technique which is accurate over a wide concentration range. Current FGD equilibrium models use the Davies technique for a c t i v i t y c o e f f i c i e n t prediction. The Davies technique is useful only up to i o n i c strengths of 1 molal, thus l i m i t i n g the application of FGD equilibrium models to low i o n i c strength. In t h i s work a data base and methods have been developed to use the l o c a l composition model (LCM) (1,2,) for the prediction of a c t i v i t y c o e f f i c i e n t s in aqueous FGD solutions. The LCM was used to predict the s o l u b i l i t i e s in various multicomponent systems for gypsum, calcium s u l f i t e , magnesium s u l f i t e , calcium carbonate, and magnesium carbonate, SO vapor pressure over s u l f i t e / b i s u l f i t e solutions; and, CO vapor pressure over carbonate/bicarbonate solutions. Equilibrium calculations are useful in the design or operation of a flue gas d e s u l f u r i z a t i o n (FGD) f a c i l i t y and provide the necessary foundation f o r complex process simulation (e.g., absorber modeling) (3) · Since SO absorption into FGD s l u r r i e s is a mass transfer process which is primarily limited by l i q u i d phase r e s i s tance f o r most commercial applications, the solution composition, in terms of a l k a l i n e species, is very critical to the performance of the system. Accurate prediction of solution composition v i a equilibrium models is e s s e n t i a l to establishing driving forces for mass transfer, and ultimately in predicting system performance. 2

2

2

0097-6156/86/0319-0223S06.00/0 © 1986 American Chemical Society

FOSSIL FUELS UTILIZATION: ENVIRONMENTAL CONCERNS


224

By using the fundamental .principles of conservation of mass and charge, and chemical equilibrium expressions, the concentration of i n d i v i d u a l species in solution (sometimes c a l l e d the "species d i s t r i bution") can be calculated. The a v a i l a b l e equilibrium models for lime or limestone based FGD are the Bechtel-modified Radian e q u i l i brium program (BMREP) * C4) and the species 'distribution model (SDM) (_5). The SDM is the most current equilibrium model and has been improved considerably over e a r l i e r models to make it more general in nature. Some simple uses of equilibrium models include predicting the saturation or s o l u b i l i t y of gypsum to indicate scaling p o t e n t i a l , predicting SC^ vapor pressure to trouble-s|ioot problems with SC^ removal, and predicting dissolved a l k a l i n i t y or capacity of a solu t i o n . However, the BMREP and SDM have l i m i t a t i o n s which r e s t r i c t t h e i r use to low i o n i c strength processes. The p r a c t i c a l l i m i t for using the BMREP, SDM, or any equilibrium model for e l e c t r o l y t e solutions normally stems from the lack of correlations for e l e c t r o l y t e thermodynamics (e.g., a c t i v i t y c o e f f i cient techniques). Although lime or limestone processes inherently operate with low ionic strength because the dissolved s o l i d s are of low s o l u b i l i t y , there are a growing number of systems operating at higher ionic strength. Ionic strength of FGD systems is highly dependent on the type of process and c e r t a i n parameters such as chloride content of coal, amount of free water purged from the process, and the addition of soluble additives to the scrubbing liquid. The BMREP and SDM currently use the Davies technique for a c t i v i t y c o e f f i c i e n t p r e d i c t i o n . The Davies technique is a combi nation of the extended Debye-Huckel equation (6) and the Davies equation (7). The Davies technique (and hence both equilibrium models) is accurate up to i o n i c strengths of 0.2 molal and may be used for p r a c t i c a l c a l c u l a t i o n s up to i o n i c strengths of 1 molal (8). Ion-pair e q u i l i b r i a are incorporated for species that associate (e.g., 1-2 and 2-2 e l e c t r o l y t e s ) . The a c t i v i t y c o e f f i c i e n t s (y ) are calculated as a simple function of ionic strength (I) and are represented as: ±

logy

1

(1)

= AZ*|

where A and Β are constants at a given temperature. Depending on the input values of a.^ and b ^ Equation 1 can represent either the ex tended Debye-Huckel or Davies equations, or an extension of the two. Both the BMREP and SDM approximate a c t i v i t y c o e f f i c i e n t s of uncharged species (e.g., ion-pairs, molecular species) by the follow ing expression: 1ο γ 8

±

= U I ±

(2)

where U. is an empirical constant. To improve the BMREP and SDM in equilibrium c a l c u l a t i o n s r e quires an a c t i v i t y c o e f f i c i e n t technique which is accurate over a wide concentration range. Rosenblatt (9,.10) i d e n t i f i e d the inherent


18. TAYLOR AND ROCHELLE

Activity Coefficients for Aqueous Solutions

225

l i m i t a t i o n s of the BMREP and SDM and investigated the use of the modified P i t z e r equation as an a c t i v i t y c o e f f i c i e n t technique f o r FGD solutions. The modified P i t z e r equation (11-13) was noted as the most elaborate and successful a c t i v i t y c o e f f i c i e n t technique in use (14). Rasenblatt concluded that Pitzer's equations offered a promising approach for thermodynamic modeling of FGD chemistry. Currently, Radian is incorporating the Bromley method (15) as a new a c t i v i t y c o e f f i c i e n t technique in the SDM (16). Recently, Chen and co-workers (1,_2, 17-19) developed the l o c a l composition model (LCM) for a c t i v i t y c o e f f i c i e n t prediction. The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified P i t z e r , and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. A d d i t i o n a l l y , the LCM does not require ion-pair e q u i l i b r i a to correct for a c t i v i t y c o e f f i c i e n t prediction at higher i o n i c strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair a c t i v i t y c o e f f i c i e n t s and e q u i l i brium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable a c t i v i t y c o e f f i c i e n t technique for aqueous solutions used in FGD; hence, a data base and methods to use the LCM were developed. The Local Composition Model The l o c a l composition model (LCM) is an excess Gibbs energy model for e l e c t r o l y t e systems from which a c t i v i t y c o e f f i c i e n t s can be derived. Chen and co-workers (17-19) presented the o r i g i n a l LCM a c t i v i t y c o e f f i c i e n t equations f o r binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with e l e c t r o l y t e s . The LCM a c t i v i t y c o e f f i c i e n t equations are e x p l i c i t functions, and require computational methods. Due to length and complexity, only the s a l i e n t features of the LCM equations w i l l be reviewed in t h i s paper. The "Aspen Plus E l e c t r o l y t e Manual" (1) and Taylor (21) present the f i n a l form of the LCM binary and multicomponent equations used in t h i s work. The approach taken by Chen and h i s co-workers in developing the LCM was to account for the excess Gibbs energy of e l e c t r o l y t e systems as the sum of long-range (ion-ion) interactions and short-range ( i o n ion, ion-molecule, and molecule-molecule) interactions. The extended Debye-Huckel equation proposed by P i t z e r (22) was used to account for the long-range interactions, and the l o c a l composition concept was used to account for the short-range interactions of a l l kinds. The excess Gibbs energy expression is therefore the sum of the unsymmetric l o c a l composition expression. The equation has the general form: ex RT

ex

*,pdh RT

ex

*,lc

RT

226

FOSSIL FUELS UTILIZATION: ENVIRONMENTAL CONCERNS

S i m i l a r l y , the a c t i v i t y c o e f f i c i e n t equations (which can be derived from the excess Gibbs energy expression) have the general form: Ιηγ* = l n P


Y

d h

* =

ln f Y

(4)

The long-range Pitzer-Debye-Huckel equation calculates a c t i v i t y c o e f f i c i e n t s as a function of ion strength, and no adjustable para meters are necessary. The short-range l o c a l composition equation calculates a c t i v i t y c o e f f i c i e n t s by accounting for a l l short-range interactions and requires a minimum of adjustable parameters. For binary systems, two adjustable binary parameters are necessary: salt-molecule and molecule-salt. For multicomponent systems three types of adjustable parameters are necessary: salt-molecule, mole c u l e - s a l t , and s a l t - s a l t . Therefore, the regressed parameters of the LCM data base are s p e c i f i c a l l y for the short-range contribution to the a c t i v i t y c o e f f i c i e n t equation. The approach to using the LCM for FGD applications involves some assumptions and s i m p l i f i c a t i o n s . Since the concentrations of a l l molecular species in solution are n e g l i g i b l e with respect to water, only salt-water and water-salt binary parameters are necessary. A l l salt-molecule and molecule-salt binary parameters for molecular species other than water are set equal to salt-water and water-salt binary parameters. A l l molecule-molecule interactions are assumed equivalent to water-water interactions and are set equal to zero. A d d i t i o n a l l y , a l l s a l t - s a l t parameters are set to zero. L a s t l y , the temperature dependence of a l l binary parameters is neglected. Results and Discussions The r e s u l t s of applying the LCM to t y p i c a l FGD solutions are summa r i z e d in Tables I and Table I I . Table I presents the f i n a l regressed LCM binary parameters for t y p i c a l FGD solutions. The implied forma t i o n reactions, and temperature dependent parameters for the e q u i l i brium constants are shown in Table I I . Regression of the necessary LCM binary parameters required various thermodynamic data. The Power method (23), an unconstrained nonlinear code, was used to minimize a nonlinear function f(x) = f(x,...,x ) of η v a r i a b l e s . The function f(x) normally represented the standard deviation of the thermodynamic property (e.g., a c t i v i t y c o e f f i c i e n t s , osmotic c o e f f i c i e n t s , s o l u b i l i t y products, or vapor pressure) being regressed using the LCM for a c t i v i t y c o e f f i c i e n t prediction. The η variables represent the f i n a l regressed binary parameters. Default values were used f o r binary parameters repre senting interactions of species present in low concentration, or when no thermodynamic data were a v a i l a b l e . Default values were determined by averaging binary prarmeters regressed by Chen and co workers (18) for each type of e l e c t r o l y t e (elg., 1-1, 1-2, 2-1, and 2-2). This approach should y i e l d a minimum error, since the binary parameters were well defined for each type of e l e c t r o l y t e . The LCM has proven to be useful in predicting data of molal i o n i c a c t i v i t y c o e f f i c i e n t s and vapor pressure depression of various single e l e c t r o l y t e , single solvent systems. The standard deviation of the natural logarithm of the mean a c t i v i t y c o e f f i c i e n t was 0.01 for uni-univalent aqueous s i n g l e e l e c t r o l y t e s (17). Similar r e s u l t s

18.

Activity Coefficients for Aqueous Solutions

TAYLOR AND ROCHELLE

cs

cs co ON

Ν

«1 ο

vo es r - oo Ν

CO 0 3

η

ON

CO f ) H

ON

r>

ON

ON ON

ON

r H CO r H r H r H r H

227

CO

ο vo ο oo co r - vo vo

ON

co vo r -

C O C O C O C S C O C O C O C O r H c S C O C O

>

>

>

ο

©

ο ο

> > > Q Q > Q Q Q Q


OH ^ • N N r-HOO H ^ O O Η » » 0\

Η

Α

Oy

Η

^-

ON

^

ON

ON

oo -«j- es es v© co t o ro ^ «n to t ^ a 00 H Ο H O O r H Ο τΗ r-i

vo » co I

© co o co M H t " Q O Q Q f t > Q

ON 0 0 rH rH 0 0 rH es 0 0 ON « « * "

Activity Coefficients Predicted by the Local Composition Model for

Recommend Documents