Optimization of Flow Design in Forced Flow Electrochemical Systems, with Special Application to Electrodialysis Ain A. Sonin* and M. S. lsaacson Department of Mechanical Engineering, Massachusetts institute of Technology, Cambridge, Massachusetts 02 139
The hydrodynamic performance characteristics of an electrochemical system influence the product cost by limiting the usable current density and controlling the power requirements for fluid transport and mixing. This paper presents a simple, rational method for determining how much hydrodynamic factors influence product cost in systems having various alternative flow conditions and channel geometries and for choosing the optimum channel geometry and flow conditions. The method incorporates the scaling laws for the mass transport and frictional characteristics and is thus independent of system scale. It is applied here to assess the state of the art in the design of electrodialysis systems used for demineralizing brackish waters. Empirical and theoretical data correlations of limiting current and pressure drop are presented for laminar and turbulent flow in unobstructed channels as well as for eddying flow induced by typical eddy promoters, and the possible effects of further hydrodynamic improvements on product cost are discussed.
1. Introduction
This paper deals with the optimization of the hydrodynamic design of electrochemical systems using forced flow. By hydrodynamic design we mean the choice of the geometry of the flow channels and the flow speed in them. The hydrodynamic design influences the product cost by limiting the usable current and controlling the power requirements for fluid transport and mixing. This paper presents a simple, rational method for determining how much hydrodynamic factors influence product cost and for choosing a hydrodynamic design which minimizes the product cost, given the state-of the art. The method incorporates the scaling laws for the mass transport and frictional characteristics and is thus independent of system scale. First, a somewhat simplified cost analysis is performed in order to show how the mass transfer and frictional characteristics of an electrochemical system influence the product cost. The mass transfer and frictional characteristics of a given type of system with a given type of flow path are most succinctly expressed in terms of the Sherwood number based on the limiting current and the friction factor based on the pressure drop across the flow channels. These two dimensionless quantities, when given as functions of the flow Reynolds number from either theoretical or empirical consideration, completely define the hydrodynamic performance of the given type of system, quite independent of system scale. It is shown in this paper that the interaction between the hydrodynamic performance characteristics and the product cost can easily be assessed on a plot of the Sherwood number Sh us. a modified friction factor f which is the product of the conventional friction factor to the one-third power and the Reynolds number. The hydrodynamic performance of a given type of system with a given type of flow channel is represented on this plot as a curve, tracing out all possible values of Sh and f for different Reynolds numbers. Different flow channel designs are represented by different performance curves. The cost analysis shows where the operating point must be on the (Sh, f ) plane in order to minimize the product cost. It is thus possible to choose, from the various channel designs suggested by the state of the art, the design which minimizes the product cost for the process under consideration, and to establish the optimum operating condition for that design. The method is applied in the second part of this paper
to assess the state of the art in the design of electrodialysis systems used for demineralizing brackish waters. 2. Criteria for Assessing Hydrodynamic Performance of an Electrochemical System Consider an electrochemical process, of which electrodialysis is an example, where an average current density j is carried over an area A as a result of a potential applied over a distance h (Figure 1).To maintain the process, a working fluid is passed through the system at a superficial flow speed V. Let 1 be the length of the current-carrying area in the flow direction, and let Ap be the pressure drop over this length. Beyond this the geometry is not defined: the interior of the system may, for example, contain eddy promoters, or corrugations of the surfaces, or other design features intended to improve the mass transfer rate. The cost of operating this system is assumed to arise from three contributions: (1) the cost of the electrical energy required to pass the current, (2) the cost of the mechanical energy required to pump the fluid past the current-carrying region, and (3) a “capital” or “ownership” cost, expressed as a cost per unit area A of the currentcarrying region. Following Ibl and Adam (1965), we assume that the ownership cost is independent of the two energy costs, a t least to a first approximation. We do not include in this analysis the cost of the working fluid itself (in the case of an electrodialysis system, this means that feed pretreatment costs are not included). With each contribution to the cost we associate a coefficient which is assumed to be independently known: k , is the cost of electrical energy delivered to the system ($/J); k , is the cost of the mechanical (pumping) energy delivered to the fluid in the system ($/J);and k , is the capital cost per unit operational time, per unit current-carrying area A($/m2 sec). The cost of operating the process, per unit time, can then be expressed as
The first term represents the capital cost per unit time, the second term represents the cost per unit time associated with the electrical resistive losses, and the third term represents the pumping cost per unit time, VhA/1 being the total fluid volume flow rate through the system. With regard to the third term, we have assumed that the priInd. Eng. Chem., Process Des. Develop., Vol. 13, No. 3,1974
241
/
MAXIMUM ALLOWABLE OPERATING CURR N T
F
6CURRENT-VOLTAGE
RELATION WITH NO POLARIZATION
‘ j D i m CONDlTlONSl (GOVERNED BY FLOW
@
Figure 2. Typical current-voltage relation. Figure 1. Model of flow channel of electrochemical system.
mary resistance to the flow arises from the current-carrying region, rather than from any auxiliary plumbing. This assumption can be relaxed simply by interpreting Ap as the pressure loss in the system as a whole and carrying through the appropriate changes in the analysis. As is typical in electrochemical processes, we assume that the amount of product is directly related to the amount of electricity passed. It is convenient to work with the cost k of the product per coulomb of charge passed. This is obtained by dividing eq 1by the total currentjA
Now, the flow conditions in the system influence the product cost through Ap and V in the pumping cost term (the last one in eq 2), and also through j if concentration polarization occurs in the channels, since the effect of concentration polarization on the current-voltage relation is flow dependent. The cost can be reduced if the flow conditions can be improved so as to lower Ap and V and increase the current density for the given applied potential. However, it is clear that there is a limit to how much the product cost can be reduced in this manner. First, once Ap and V have been made so small that the pumping cost term is negligible, further reductions no longer reduce the product cost. Secondly, for a given potential, manipulation of the flow conditions cannot make the current density exceed the value it would have in the absence of concentration polarization. Once polarization is prevented, the local current density is governed essentially by Ohm’s law based on uniform conductivity and by electrode reactions and is no longer influenced by flow conditions (Figure 2). It follows, therefore, that once a system is developed to the extent that it can operate at its design point with negligible concentration polarization at a flow speed low enough that the pumping costs contribute negligibly to the total cost, further improvements in the flow conditions will be unnecessary, since they will not bring about any further significant reduction in the product cost. Such a system can then be said to have attained hydrodynamically ideal performance. As indicated schematically in Figure 3, hydrodynamically ideal performance can only be reached asymptotically, if at all, as flow conditions are improved. The two criteria for hydrodynamically ideal performance can be expressed as (3)
and (4) The first requires the optimum operating current under ideal conditions, jopt,ideal, to be a t least a factor a less than the limiting current jli, controlled by concentration 242
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3,1974
COSTS INFLUENCED BY CHOICE OF FLOW CONDITIONS AND FLOW CHANNEL DESIGN +HYDRODYNAMICALLY IDEAL PERFORMANCE
8
IMPROVEMENT I N FLOW CONDITIONS
-
Figure 3. Nature of product cost dependence on hydrodynamic design.
polarization. jopt,ideal is the current which minimizes the cost in eq 2 when the pumping cost term is negligible and there is no concentration polarization. The magnitude of a is chosen to be just sufficiently smaller than unity to ensure polarization-free operation (Figure 2). The appropriate value can be fairly accurately established, since current-voltage curves like the one sketched in Figure 2 are well known for a number of cases (see, for example, Levich (1962), or can be experimentally determined. The second equation requires the ratio of the pumping cost to the capital cost to be small compared with unity. The two criteria for hydrodynamically ideal performance can be put in more convenient form by expressing the limiting current and the pressure drop in dimensionless forms which condense the number of variables on which these quantities depend and also reflect their scaling laws. The limiting current density is expressed as a Sherwood number (5) where F is Faraday’s constant, D is the ion diffusion coefficient, for simplicity assumed equal for positive and negative ions, and c, is some appropriate reference value for the ionic concentration, in equivalents per unit volume. The pressure drop is expressed as a friction factor
where p is the density of the working fluid. We know from dimensional considerations that for a system of given geometry the Sherwood number depends only on the Reynolds and Schmidt numbers
(7) and
P sc 5 PD where is the fluid viscosity, while the friction factor is a function of Reynolds number alone. In what follows, it is convenient to introduce a modified fraction factor f f
A1’3Re
(9 )
which like the conventional friction factor X depends only on Re for any given system geometry. Inserting eq 5, 6 and 9 into eq 3 and 4, the two criteria for hydrodynamically ideal performance become
sh > I Sh* f3
> 1, which turns out to be the case of interest here. In empty channels without eddy promoters, the correlations depend on whether the flow is laminar (Re < 103) or turbulent (Re > 2 x lo3). The Sherwood number correlation given for laminar flow was derived analytically by Sonin and Probstein (1968, 1969) and confirmed experimentally by Grossman and Sonin (1972). It is essentially equivalent to Leveque’s law for heat transfer. The laminar flow friction factor is the familiar one from Poiseuille’s law for two-dimensional channels. The correlation for Sherwood number in the turbulent flow regime is also an analytical result, derived by Probstein, et al. (1972), for low salt removal per pass. As yet it has not been adequately confirmed by experiment, and some question remains about whether the particular exponents on Sc and Re are the best choices. For our present purposes, however, the equation serves as an adequate approximation, particularly since we shall see that turbulent flow in empty plane channels is not a very desirable flow condition for electrodialysis. The turbulent flow friction factor is the well-known one obtained by Blasius [see, for example, Schlichting (1968)l. When the flow channels contain eddy promoters, the Sherwood number and friction factor depend not only on Reynolds number but also on geometrical parameters which characterize the spacing, shape, and orientation of the promoters in the channels. In electrodialysis systems, strips may be inserted at regular intervals, as in Figures 8b and 8c, or a woven mesh or corrugated spacer may be inserted into the channel to create the necessary flow pattern. The widely marketed “tortuous path” systems made by Ionics, Inc., for example, employ strip type eddy promoters arranged as in Figure 8b, with h = 1 mm and Al = 10 mm and a total flow path length of several meters. It seems quite generally accepted that at the present state of the art the most promising flow conditions for practical systems are attained with eddy promoters, and considerable work has been done on mass transfer in such systems. See, for example, Rosenberg and Tirrell (1957), Mandersloot and Hicks (1965), Hicks and Mandersloot (1968), Process Research (1968), Kitamoto and Takashima (1971), Solan, et al. (1971), Belfort and Guter (1972), Winograd, et al. (1973). Nevertheless, relatively little work seems to have been done to systematically determine the forms of the Sherwood number and friction factor as functions of the Reynolds number and the geometrical parameters which characterize the eddy promoter design. The correlations shown in Table I are based on our own preliminary empirical studies on eddy promoters in the form of cylindrical rods transverse to the flow, having diameters equal to half the channel width h and placed at regular intervals Al (Figure 8c). These equations represent approximate correlations of data for Re > 300 and for A1 >> h. For Re < 250 the eddy promoters were found to be largely ineffectual, and the Sherwood number was only slightly larger than the value one would expect with the same channel without eddy promoters. Within the range 250 < Re < 300 the Sherwood number made the transition to the value given by the correlating equation in the table. We stress that the correlations given are as yet based on limited data (40 < Re < 2000, 16 < Al/h < 67, Sc N 500) and indeed the y3 power dependence on the Schmidt number has been assumed rather than empirically determined. However. the Sherwood number correlation is in reasonInd. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974
245
Table I. Limiting Current and Pressure Loss Correlations in Electrodialysis Systems
Flow conditions
Sh(Re)
X (Re)
300
Source
Plane, Smooth-Walled Channels
Laminar flow Re < 1000 Turbulent flow Re > 2000
Sh (f)
Sh = 3.30(?S~Re)“~
X =
Sh = 0.024Sc1’4Re7’8
X =
< Re < 2000 Sh
24Re-l
Sh
=
l.$-~(;Sc)”~p2
0.133Re-’I4
Sh = 0.046Sc1‘4ff11~22 Channels with Eddy Promoters Spaced at a Separation A1
= 1.9Sc1/J(:)o
5Re05
=
20(
):
06
Re-0
Sh
5
=
~
1.0Sc’ 3(
$y
38f0 6
Sonin and Probstein (1968) Probstein, et al. Present work
R4NGE OF f FOR ELEtTRODl4LYSIS
i IN
I
p4 (C)
Figure 8. Flow channels with and without eddy promoters. able agreement with the correlation of Process Research (1968). Unfortunately, the dependence of X on h/Al has not been previously established. For our present purposes, we shall take the correlations given as indications of the performance of typical presently used eddy promoters. Although A1 is strictly speaking the distance between eddy-promoting strips (Figure 8), it can also be interpreted as the characteristic separation distance between mesh type promoters, as was done in the work of Process Research (1968). Note that our correlation equation cannot be extrapolated to values of A l / h which are not large compared with unity, since current shadowing by the strips would then be expected to decrease Sh and excessive channel blockage would increase A. Indeed, it is expected that the Sherwood number will begin to decrease again once A l / h is reduced beyond a certain critical value. Our own preliminary experiments, to be reported more fully in a separate paper (Isaacson and Sonin, 1974), indicate that this value is about 5 , and the recent work of Winograd, et al. (1973), confirms this conclusion. We shall therefore assume that our correlations apply down to A l / h N 5 and that further improvements in Sh cannot be achieved by reducing Al/h more. Also shown in Table I are the functional relationships between Sh and f, Sh(f), which correspond to the correlations for the Sherwood number and friction factor as a function of Reynolds number. These are the performance characteristics of the systems and flow conditions which they represent. Figure 9 shows plots of Sh us. f for empty channels as well as for channels with eddy promoters. The data are shown for Sc = 667, corresponding to the typical fluid properties listed in eq 30. With h = 1 mm, l / h = lo3 corresponds to a total flow channel length of 1 m (a typical convenient value) while l / h = 100 represents a path length of only 10 cm, about the minimum value practicable for a reasonable exploitation of the membrane area. A l / h = 10 represents the spacing of eddy promoters in the 246
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 3, 1974
I
101 IO2
,
,
1
I , , , , l
,
10’ f = Re j13,MODIFIED FRICTION FACTOR
1
1
1
,
lo4
Figure 9. Performance characteristics of electrodialysis flow channels with and without eddy promoters (Sc = 667). current Ionics tortuous path systems, while A l / h = 5 is an approximation to the closest promoter spacing feasible without significant current blockage. The optimum hydrodynamic design can now be determined by using the method outlined in section 2. First the value off* must be determined. We assume that the fluid viscosity and density are given by eq 30, so that eq 32 applies, and take k p / k e = 2, corresponding to a 50% pumping efficiency. The remaining quantity which must be specified is the ratio of capital or ownership cost to the electrical energy cost, k,/k,. Presently the electrical energy cost k, is about lc/kWh. The ownership cost coefficient k, includes the cost of the membranes, gaskets, electrodes, rectifiers, maintenance, etc.. and in present systems is estimated by McRae (1973) to be of the order of $60/m2 per channel pair per year. A typical value of h in present systems is 1 mm. On the basis of this, we assume conservatively that in systems typical of present technology, k,/ke should lie somewhere in the range $10-100/m2 year per e/kWh, and the value of h, which must be kept as small as practicable to minimize product cost, should lie between 0.5 and 1 mm. If follows that f * , as given by eq 32, should have a value between 200 and 800. Now, it is clear from Figure 9 that in this range of f, the highest value of Sherwood number is obtained with a system with eddy promoters spaced at A l / h N 5 , which represents the closest spacing that can be used without significant current blockage, as discussed earlier. It follows that such systems give the highest value of 0 = Sh(f*)/Sh* and therefore the lowest product cost at optimum conditions, at least among those being compared here. For an electrodialysis system, therefore, currently available data indicate that the best channel design is one using eddy promoters having the optimum spacing of about A l / h N 5 . From Table I, such channels have a per-
spacing of eddy promoters of the conventional type. Improvements in mass transfer and frictional characteristics beyond the present state of the art, for example by the development of eddy promoters which give a higher limiting current at a lower friction factor, can therefore bring about measurable cost reductions for these waters. For salt concentrations above about 6000-8000 ppm, however, virtually hydrodynamically ideal performance can be attained with the present state of the art, and further research on hydrodynamic design cannot bring about significant cost reductions. Cf
+
C p s ppm
Figure 10. Minimum product cost attainable in electrodialysis with the present state of the art, compared with cost which would be attained with hydrodynamically ideal performance.
formance characteristic of the form of eq 20, with
n = 0.6; a
= 0.54s~"~
(33)
The optimum operating point depends on the hydrodynamic performance parameter 0. Substituting eq 27, 28, and 33 into eq 22a, we find for our best channel design
Once 8 is established for the particular conditions of interest, the optimum Sherwood number is obtained from eq 21 graphically or by iteration. Alternatively, since it appears from Figure 5 that the result is quite insensitive to the specific values of n, one can to a good approximation use the analytic solution of eq 2 1 which is easily obtained for the specific case n = 3/4
The optimum flow speed and current density can now be obtained following the method of section 2. For a typical case the flow speed corresponds to a Reynolds number in the range 102-103, depending on feed properties and the precise values of the cost coefficients. The product cost corresponding to optimum operating conditions is given by eq 23, which for the case at hand can be written
where
is the product cost (per unit volume) which would be attained if the system could be optimized a t ideal conditions. From eq 35 and 36 we obtain the optimum product cost for our best system design, expressed in terms of the parameter 8. The relation is shown in Figure 10, where we have assumed for illustration that the fluid properties are given by eq 30, and taken k p / k e = 2 and h = 1 mm (t? is in any case not very sensitive to the precise magnitudes of the latter two quantities). The cost ratio is then a function only of k , / k , and cf cp, as shown in the figure. It is clear from Figure 10 that with the capital cost typical of present systems ($50-100/m2 year) and with electrical energy costs of the order of l$/kWh, as much as 30% or more of the product cost is traceable to hydrodynamic factors when the feed concentration is low (a few thousand ppm or less), even when the system has the optimum
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4. Concluding Remarks A general method has been formulated for assessing how much the hydrodynamic design affects the product cost in an electrochemical system and for determining the optimum design and flow conditions for product cost minimization. The method is based on some simplifying assumptions. For example, we have assumed that the cost coefficients are independent of current density and flow speed and that the pressure drop occurs primarily across the flow channel rather than the inlet or outlet ports or auxiliary plumbing. These assumptions can be relaxed, if necessary, by modifying the present analysis in a fairly straightforward manner. A first-order correction for variable cost coefficients can be made by simply using the results of the present analysis and regarding the cost coefficients as the appropriate functions of operating conditions. The pressure loss outside the flow channel can be accounted for, if it is significant, by replacing the friction kh/l where k here represents the presfactor X with X sure loss, in units of the dynamic pressure 1h p v Z , in the system apart from the flow channel itself. Applying our method to the electrodialysis system used for brackish water demineralization, it is shown that the best performance from an economic viewpoint is attained with channels containing closely spaced eddy promoters. If we accept our preliminary empirical results for the hydrodynamic performance of such channels as being indicative of the present state of the art, mass transfer and frictional limitations are shown to be important when the feed water has a salt concentration less than about 60008000 ppm. The development of better eddy promoters than the ones characteristic of the present state of the art could in principle bring about a reduction in the product water cost by 30% or more for brackish feed waters of low concentration (a few thousand ppm). At higher salt concentrations (over 6000-8000 ppm), the presently available eddy promoters are adequate, in the sense that further improvements in the hydrodynamic design cannot bring about a further significant reduction in the total product cost when the operating conditions are optimized. These conclusions are not new to those who have been closely involved with the development of commercial electrodialysis systems. However, to our knowledge they have not been previously articulated quantitatively in general terms. Acknowledgment This research was sponsored by the Office of Saline Water, U. S. Department of the Interior, under Grant N o . 14-30-2749.
+
Nomenclature Coherent units are indicated below. In the text, other units are used only where specifically stated. a = dimensionless coefficient in performance characteristic, eq 20 A = area of current-carrying region, m2 cf = concentration of saline feed in electrodialysis, equiv/ m3 Ind. Eng. Chem., Process
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247
cp = product concentration in electrodialysis, equiv/m3 c, = reference concentration, equiv/m3; for electrodialysis, c, ( c f c p ) / 2 D = salt diffusion coefficient, m2/sec f = E X1I3 Re, modified friction factor f* = defined in eq 13; for electrodialysis, in eq 28 F = Faraday's constant, 9.649 x IO4 C/equiv h = system width as in Figure 1, m; in electrodialysis system, width of dialysate channel as in Figure 7 j = average current density over current-carrying area, A/m2 j l l m = limiting value of j k = product cost per coulomb of charge passed through the system, $ / C k , = capital (or ownership) cost coefficient, $/m2 of current-carrying area per sec of operation k , = electrical energy cost, $ / J k , = cost of pumping energy delivered to fluid, $ / J K , = cost per unit volume of product water in electrodialysis $/m3 1 = length, in flow direction, of current-carrying section, m A1 = separation between successive eddy promoters (Figure 8) n = index in performance characteristic, eq 20 A p = pressure drop, in flow direction, along currentcarrying section, N/m2 R = universal gas constant, 8.31J/"K mol Re = p V h l p , Reynolds number p / p D , Schmidt number Sc = Sh = Sherwood number, defined in eq 5 Sh* = defined in eq 12 or 16; for electrodialysis, eq 27 T = absolute temperature of fluid, "K V = superficial flow speed of fluid, m/sec 2 = ion charge number, assumed same for positive and negative ions in electrodialysis
+
Greek Letters cy = a safety factor, defined with regard to eq 3 0 = a dimensionless hydrodynamic performance parameter defined in eq 22
X = conventional friction factor, defined by eq 6
= fluid viscosity coefficient, kg/m sec = fluid density, kg/m3 = average electrical conductivity of working fluid, ohm-1 m - l 9 = potential drop across channel pair in electrodialysis, V 90 = an electrode activation potential, eq 14
p p u
Subscripts opt = optimum value, that is, value which minimizes product cost opt,ideal = optimum value which would be attained under hydrodynamically ideal conditions Literature Cited Belfort, G., Guter, G. A., DesaIination, 10, 221 (1972). Grossman, G., Sonin, A. A,, Desalination, 10, 157 (1972). Hicks, R. E., Mandersloot, W. G. B., Chem. €ng. Sci.. 23, 1201 (1968). Ibl, N . , Adam, E., Chem. Ing. Tech.. 37, 573 (1965). Isaacson, M.. Sonin, A. A,, in preparation, 1974. Kitamoto, A,, Takashima, Y . , Desalinafion, 9, 51 (1971). Levich, V . G . , "Physiocochemical Hydrodynamics," Prentice-Hall, Englewood Cliffs, N. J. 1962. Lynch, M. A,, Jr., Mintz. M . S., J . Amer. Water Works Ass., 64, 711 (1972). Mandersloot. W. G. B., Hicks, R. E., Ind. Eng. Chem., Process Des. Develop.. 4, 304 (1965). McRae, W., lonics Inc., Watertown. Mass., private communication. 1973. Probstein, R. F., Sonin, A . A,, Gur-Arie, E.. Desaiinafion, 11, 165 (1972). (In this reference there is a slight numerical error: the coefficient 0.013 in eq 7.1 and 7.2 should be replaced by 0.011.) Process Research, Inc., Office of Saline Water Research and Development Progress Report No. 325 (1968). Rosenberg, N. W., Tirrell, C. E., lnd. Eng. Chem.. 49,,780 (1957). Schlichting, H., "Boundary-Layer Theory," 6th ed, McGraw-Hill, New York, N. Y., 1968. Solan, A,, Winograd, Y . , Katz, U., Desalination, 9, 89 (1971). Sonin. A . A,, Probstein, R . F . , Desalination, 5 , 293 (1968). Sonin. A . A,, Probstein, R. F . , Desalination. 6, 270 (1969). Spiegler, K. S., Ed., "Principlesof Desalination;" pp 200-289, Academic Press, New York, N . Y.. 1966. Winograd, Y., Solan, A,, Toren. M . , Desalination. 13, 171 (1973).
Received for review July 13, 1973 Accepted J a n u a r y 31, 1974
Reaction of Sulfur Dioxide with Limestone and the Influence of Pore Structure Miloslav Hartman and Robert W. Coughlin*' Institute of Chemical Process Fundamentals. Czechoslovak Academy of Science. 165 02 Prague, Czechoslovakia
A simple structural model has been developed and used to correlate experimental results for the reaction of porous particles of limestone with SOn and oxygen in flue gas at high temperature. The model incorporates parameters such as the porosity of the natural rock, its true theoretical density, the content of calcium carbonate, and its conversion to sulfate. The agreement between the model and the experiments implies that the reaction is strongly influenced by reduction in porosity caused by the sulfation reaction, with both the reaction rate and the porosity becoming very small at conversions of about 50%. The pore-size distributions of unsulfated calcines and sulfated samples are remarkably different. The pores with radius larger than 3980 A are probably responsible for the high capacity of limestone to react with Son. Incomplete conversion of calcium oxide results from the strong diffusional resistance developed in the interior of the particles owing to reduction in porosity as the reaction proceeds.
Introduction The widespread availability and low cost of limestone and dolomite underlie their consideration as sorbents in
'
Address correspondence to this author at the Department of Chemical Engineering, Lehigh University, Bethlehem, Pa. 18015.
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processes for SO2 removal from flue gas (Hartman, e t al., 1969). There has been considerable interest in dry hightemperature processes, such as the reaction between limestone and sulfur dioxide in combustion gas at high temperature and in the presence of excess oxygen as follows CaC03(s) + SOp(g) ' / 2 0 2 ( gf ) CaSO,(s) + C02(g) (I)
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