various flows, or vice versa, by more exact column calculations. The final location of the optimum feed plate should be determined by a search of the neighboring plates. Nomenclature A, B, C, D = specific components b(x,)h = flow of component i in the bottom product, mol/unit time d ( x , ) d = flow of component i in the top product, mol/unit time F L J= @ I / ( ~ I - @RS,]) GI j = f f , / ( a , @SS,,) TZRS = number of stages in the rectifying section nhs = number of stages in the stripping section
VR,
= flow of vapor in the rectifying section, mol/unit
time = flow of vapor in the stripping section, mol/unit time x, = mole fraction of component I in the liquid leaving the feed stage Vbh
dss,] = root of eq 3 lying numerically just above a, Z = summation over all components
Subscripts A,B,C,D = refer to corresponding specific components i = refers to any component j = refers to any component other than the light key component in the rectifying section, any component other than the heavy key component in the stripping section hd = refers to any heavy diluent component hk = refers to the heavy key component Id = refers to any light diluent component lk = refers to the light key component Literature Cited Alder, B. J., Hanson, D. N., Chem. Eng. Prog., 46, 48 (1950). Erbar. J. H., Maddox, R. N., Pet. Refiner, 40 (5), 183 (1961). Gilliland, E. R., lnd. Eng. Chem., 32, 1220 (1940). Klein, Gerhard, Hanson, D.N., Chem. Eng. Sci.. 4, 229 (1955) Underwood, A. J. V., J, Inst. Pet., 31, 111 (1945). Underwood, A . J. V., J. Inst. Pet., 32, 598 (1946). Underwood, A. J. V., Chem. Eng. Prog.. 44, 603 (1948).
Greek Symbols = relative volatility of component i @RS, = root of eq 1 lying numerically just below a,
Received for reuieu. May 14. 1976 A c c e p t e d October 4,1976
Application of a Diffusion Limiting Model to a Tube-Wall Methanation Reactor Richard R. Schehl,' James K. Weber, Mark J. Kuchta, and William P. Haynes Process Engineering Division, Pittsburgh Energy Research Center, U.S. Energy Research and Development Administration, Pittsburgh, Pennsylvania 15213
The applicability of a diffusion limited model in predicting the performance of a large scale annular tube-wall methanation reactor is examined. The model, developed by Senkan et al. (1976) in a recent article is adapted to the reactor geometry used in our study and tested against experimental data. It is demonstrated that, for the geometry and catalyst used in this study, the reactor is not diffusion limited and that kinetic resistance must be included in any realistic model.
Introduction The Pittsburgh Energy Research Center has been investigating, for a number of years, the feasibility of a tube-wall reactor in the catalytic methanation step for upgrading raw synthesis gas to high-Btu pipeline quality substitute natural gas (SNG) (Demeter e t al., 1967; Forney, 1972; Haynes et al., 1973; Ralston et al., 1974; Strakey e t al., 1975). This type of system has been investigated in units ranging from benchscale (8.5 scfh) to pilot plant scale (1800 scfh) and a multi-tube reactor designed for a 13 000 scfh feed has been incorporated into the Synthane prototype plant. The tube-wall methanator has the advantage of being able to accommodate feeds containing as much as 25% CO and yet operate under near isothermal conditions. In a recent article, Senkam et al. (1976) presented a diffusion limiting model for the tube-wall reactor. Film theory was used to arrive a t an expression for mass transfer rates and the model was generalized to include nonisothermal systems. The model was developed for a surface reaction of arbitrary stoichiometry and then applied to the specific case of a hypothetical tube-wall methanation reactor. The purpose of this communication is to appropriately modify the model so as to
describe turbulent flow through an annulus with the reaction catalyzed on the outer wall and test the applicability of the model by comparing model predictions with experimentally measured values. Reactor Description Studies of the annular tube-wall methanation reactor were carried out in a pilot-plant scale unit depicted in Figure 1.The reactor is constructed of 304 stainless steel 2-in. schedule 40 pipe, 14 ft in length. Surrounding the 2-in. reactor tube was a 4-in. diameter pipe jacket containing boiling Dowtherm in the annular space to remove the heat of reaction. A 1.5-in. inch tube coaxially located in the reactor confines the reacting gas to the annular region defined by the 2-in. pipe and 1.5-in. tube. The temperature of the coolant, and hence, the catalyst temperature is regulated by controlling the pressure in the cooling system. Nucleate boiling is assumed to take place on the outer surface of the reactor tube, thereby providing a natural convective circulation of the Dowtherm. Dowtherm vapor is condensed via cooling water and returned to the reservoir. The inside surface of the 2-in. reactor tube was coated with Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
227
Neglecting axial dispersion, the material balance for the reactant CO across an element of length, dz, takes the form T C wells
where D1 and D:! are the 0.d. of the inner tube and i.d. of the outer tube, respectively. Following the derivation of Senkan et al. (1976), local gas velocity, molal density, mole fraction, and molal flux may be expressed in terms of local conversion and fractional change in volume due to reaction. Considering the more general feed stream composition described above, local conversion, (, refers to the local conversion of the limiting reactant, CO, and 6.4, the fractional change in volume, is defined according to Levenspiel (1962) as
I'
t~ accounts for both the reaction stoichiometry and the presence of inerts. The fractional change in volume may be expressed as a function of the inlet mole fraction of the deficient reactant as
3 u Figure 1. Pilot plant tube-wall methanation reactor.
tA
Raney nickel (42% Ni-58% Al). The wall was prepared by sand-blasting the stainless steel surface with an iron free grit and then flame spraying .a light coat of bonding material consisting of 80% Ni and 20% A1 to a thickness of about 0.007 in. Subsequent to the bond coat, Raney nickel alloy powder (80-200 mesh) was flame sprayed onto the bond surface until the desired thickness of 0.023 in. was achieved. An oxy-hydrogen flame was used in the flame spraying procedure. The catalyst was activated by passing a 2 wt % solution of NaOH through the reactor until 70% of the aluminum in the Raney alloy had reacted. The extent of leaching was determined by measuring the amount of hydrogen evolved. After rinsing the residual caustic from the system the reactor was flushed with hydrogen and brought to reaction temperature and pressure under a hydrogen atmosphere. The reactor was operated for a total of 650 h a t a pressure of 300 psig and temperature of 385 "C. Feed to the system consisted of a 3:l ratio of Hz to CO a t a flow rate of 450 scfh. The synthesis gas was blended with three parts by volume recycled (water free) product gas before being introduced to the reactor. Initial CO conversion for the system was 99%. Conversion declined throughout the run to a value of 95% upon shutdown.
Mathematical Model Let us consider the annular tube-wall reactor described in the previous section. The reacting gas, flowing through the annulus under turbulent conditions, is assumed to be thoroughly mixed in the radial direction; i.e., there are no thermal or concentration gradients across the turbulent core. The reactants diffuse through the laminar sublayer, adsorb, react to form the products which then diffuse back into the bulk phase. The methanation reaction CO
+ 3H2
+
CH4
+ H20
(1)
is assumed to go to completion a t the catalyst surface, viz., a diffusion limiting condition. The feed, in general, to the reactor is considered to be a mixture of CO, H?, COi, CH4, and H20 although in this application CO:! and H20 are only present in minor amounts. Temperature effects on gas density and transport properties of the gas may be neglected. Thermocouple wells located in the annular space recorded only small variations in temperature through the reactor, ca. 5-10 "C. 228
Ind. Eng. Chem., Process Des. Dev., Vol. 16,No. 2, 1977
= -2yo
(4)
An expression for the mass transfer film thickness is obtained by applying a Colburn form of relationship for the friction factor of the wall.
Rothfus et al. (1955)have reported that the friction factor for the outer wall bears the same relation to the Reynolds number for the outer portion of the annular stream, 2(r2:! - X2)pu/r2F, as the friction factor for circular tubes does to the Reynolds number for circular tubes. X is the position of maximum velocity in the annulus and is estimated from
The film thickness for mass transfer may then be approximated by
Due to the feed composition used in our experiments, the Schmidt number for CO changes by less than 1%from the inlet to the exit of the reactor. Hence the Schmidt number may be considered constant over the length of the reactor. Using these relations peculiar to our annular tube-wall methanation reactor, the expression for the rate of conversion becomes
(9) Equation 8 is analogous to eq 12 in Senkan's article. Application The data shown in Table I are used in the application of the diffusion limited model described above to the annular tube-wall methanation reactor. The particle size used in flame spraying the catalyst onto the inside surface of the outer tube was 80 through 200 mesh. Assuming a mean particle size of 0.005 in., the fanning friction factor may be estimated using Perry and Chilton (1973) with a relative roughness of 0.01. For the calculated Reynolds number of 5400, the friction factor is estimated to be 0.012. With an inlet CO concentration of 7.1 mol %, 6.4 assumes the value -0.142. The experimental data
Table I. Tube-Wall Reactor Operating Conditions
Inlet, mol %
co H2 COL H20 CHI Flow
I
I
-
1
300 psig
System pressure System temperature Outside diameter of inner tube Inside diameter of outer tube Reynolds number Schmidt number
:'t
3E5 O C 1.5 in. 2.02 in.
5400 0.78
Outlet, mol %
7.1 26.5 0.6 0.1 65.7 1773 scfh
0.7 9.4
, 0
0.7 7.3 81.9 1555 scfh
,L ,
CIMENSIONLESS
PCSITION
Discussion As a result of the foregoing calculations, it must be concluded that a diffusion limited model is not applicable to tube-wall methanators utilizing a Raney nickel catalyst. For the accurate description of this type of reactor, it is evident that kinetic resistance a t the catalyst surface must be taken into account. Indeed, Senkan et al. (1976) point out in their paper that a reactor with a finite reaction rate will necessarily be longer than the value obtained using a diffusion limited model. A model for methanation reactors with thermally sprayed catalyst has been developed which included both diffusion and kinetic resistance. Ralston et al. (1974) and Wei and Chen (1974) first applied this type of analysis to tube-wall methanators using a kinetic rate expression developed by Wen et al. (1968). Later Schehl e t al. (1975) and Haynes et al. (1975) appropriately modified the model for application to adiabatic hot-gas-recycle methanation reactors. In this more recent analysis, the kinetic expression of Lee and Feldkirchner (1970) and Lee (1973) (10)
along with an empirical catalyst deactivation rate equation was used. The mass transfer rates to the catalyst surface were given by:
-rco = k ,o(C~o - Cco) (11)
where the transfer coefficients are estimated from the standard j-factor correlation (Treybal, 1955). At steady state conditions (10) and (11)are evaluated simultaneously in order to evaluate the total rate of conversion according t o da
,
i
,
,
Kz /D*
10 DISTANCE
dJtZco -- rco
, ,
Figure 2. Comparison of experimentally measured CO mole fraction profile (A) with profile calculated from diffusion limiting model (-1.
in Table I show the CO conversion was 91% for the mixed fresh feed and recycle stream. By integrating eq 9, the value of Kz/D* required for 91% CO conversion is found to be 2.12. Evaluating K and D* from the given data yields a value of z of only 5.6 ft, while experimentally it was found that a reactor length of 14 ft was required to accomplish the same conversion. Gas samples were taken a t Y j and yj of the distance through the reactor as well as the inlet and exit of the reactor. The experimentally measured mole fractions are compared with those calculated from the model in Figure 2 . Once again, the discrepancy between experimental findings and model predictions may be noted.
-3rro = k ( H L ( C ~ ICHJ
1
(12)
THROUGH R E A C T O R
,f t
Figure 3. Comparison of experimentally measured CO mole fraction profile ( A )with profile calculated from combined kinetic and diffusion resistance model (-1.
The above model, consisting of eq 10,11, and 12, has been applied to the annular tube-wall methanation reactor. The values suggested by Lee (1973) for E, h l , and k ? were used along with a value of 4.3 X 10") for the preexponential factor. The preexponential factor was evaluated by a nonlinear least-squares fit of the model to temperature data from an adiabatic hot-gas-recycle methanator employing the same catalyst. Agreement with experimental data was remarkably good. The model predicted a CO conversion of 93.7% compared to the measured 91.3%. The profile of CO mole fraction measured experimentally is compared with calculated values in Figure 3. In order to compare the relative importance of kinetic resistance and diffusion resistance, it is convenient to calculate the ratio of reactant concentration a t the catalyst surface to reactant concentration in the bulk phase. A value of 1would infer a reaction limited case. Under the conditions which the annular tube-wall reactor was operated CcolCco assumed a value of about 0.2. This, of course, indicates an intermediate condition between two extremes but, nevertheless, points to the fact that kinetic resistance is significant and cannot be neglected. Nomenclature A = preexponential factor a = superficial surface area of catalyst, ft' C = local molar concentration in bulk phase, lb-mol/ft C = local molar concentrations a t catalyst surface, lb-mol/ ft D1 = o.d. of inner tube, ft Dr = i.d. of outer tube, f t D* = (DL' - D i 2 ) / D p ,f t
'
Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 2, 1977
229
E = activation energy, 1.25 X lo4 Btullb-mol f = friction factor K = dimensionless coefficient, 2 f N ~ ~ ~ - ~ / ~ k l = constant, 1270 ( l b - r n ~ l / f t ~ ) - ~ 122 = constant, 635 ( l b - m ~ l / f t ~ ) - ~ h , = mass transfer coefficient, lb-mol/h-ft2-concentration difference J22 = molar flow rate, lb-mollh N = molar flux, lb-mol/h-ft2 N s = ~ Sherwood number N R = ~ Reynolds number Nsc = Schmidt number R = gas constant, 1.987 Btu/lb mol O R r l = D112,ft r2 = 0212, ft rco = rate if CO conversion, lb-mol/h - superficial ft2 catalyst T = catalyst temperature, OR V = local volumetric flow rate, scfh u = local gas velocity, ftlh yo = inlet CO mole fraction z = axial distance through reactor, f t Greek Letters 6 = laminar film thickness, ft t~ = fractional change in volume X = defined i n e q 6 , ft y = gas viscosity, Iblft-h 6 = local CO conversion p = gas density, lb/ft3
Literature Cited Derneter, J. J., Youngblood, A. J., Field, J. H., Bienstock, D., U.S. Bur. Mines Rep. Invest., 7033 (1967). Forney, A. J., published in bound proceedings of Fourth Synthetic Pipeline Gas Symposium, Chicago, Hi., Oct 30-31, 1972. Haynes, W. P., Elliott, J. J., Forney, A. J., published in bound Vol. 16, No. 2. pp 47-63, of Preprints of Papers presented at 163rd National Meeting of the American Chemical Society, Boston, Mass., Apr 10-14, 1972. Haynes, W. P., Schehl, R. R.. Weber, J. K.. Forney A. J., presented at 69th Annual AlChE Meeting, Los Angeles, Calif., 1975. Lee, A. L., Clean Fuel for Coal Symposium, Chicago, IO., Sept 1973. Lee, A. L., Feidkirchner, H. L., Tajbl, D. J., Symposium on Hydrogen Processing of Solid and Liquid Fuels, American Chemical Society, Chicago, Illinois, 14 (4), Part 1, 126 (1970). Levenspiel, O., "Chemical Reaction Engineering", Wiley, New York, N.Y., 1962. Perry, R. H., Chiiton. C. H.. "Chemical Engineers' Handbook", McGraw-Hill, New York, N.Y., 1973. Ralston, T. D., Haynes, W. P., Forney, A. J., Schehl, R. R., U.S. Bur. Mines, Rep. Invest., 7941 (1974). Rothfus, R. R., Monrad C. C., Sikchi K. G., Heideyer W. J., Ind. Eng. Chem., 47, 913 (1955). Schehl, R. R.. Haynes, W. P., Forney, A. J., ERDA PERC/Ri-75/3, (1975). Senkan, S. M., Evans, L. B., Howard, J. B.. Ind. Eng. Chem., Process Des. Dev., 15, 184-187 (1976). Strakey, J. P., Forney, A. J., Haynes, W. P., ERDA PERC IC-75/1, (1975). Treybal, R. E., "Mass Transfer Operations", McGraw-Hill. New York, N.Y., 1955. Wei, V. T., Chen J., Chem. Eng. Frog., 58 (1974). Wen, C. Y., Chen, P. W., Kato, K., Galli, A. F., Prep., Div. Fuel Chemistry, Am. Chem. Soc., 12 (3), 104 (1968).
Received f a r recieu: May 26, 1976 Accepted October 22, 1976
Regeneration of Sulfated Dolomite from a Coal-Fired FBC Process by Reductive Decomposition of Calcium Sulfate in a Fluidized Bed John C. Montagna,* John F. Lenc, Gerhard J. Vogel, and Albert A. Jonke Chemical Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439
Dolomite or limestone is sulfated when used as a sulfur-sorbent in the fluidized bed combustion of high sulfur coal. Dolomite that was sulfated by this process was regenerated for subsequent reuse as a sorbent to CaO-MgO by reductive decomposition in a fluidized bed. Regeneration was accomplished by the incomplete combustion of methane in a fluidized bed of sulfated dolomite to generate the heat and the required reducing gases for the reactions at 1010-1 100 "C.Experimental results indicate that at the conditions studied, the use of shallower fluidized beds, lower fluidizing-gas velocities, and higher reaction temperatures increased both the extent of regeneration and the SO1 concentration in the effluent gas. Dolomite losses due to attrition ranged from 5 to 15%. When regenerated dolomite was resulfated, it was found that the dolomite that had been regenerated in the hightemperature (1100 "C)experiments was less reactive as a sulfur acceptor than was dolomite that had been regenerated at a lower temperature (1040 "C). Nevertheless, the reactivity of dolomite samples regenerated at all temperatures compared favorably with that of virgin dolomite.
Introduction Combustion of high sulfur coal in a fluidized bed of sulfur-accepting material is a promising method of generating electric power and/or steam while easily meeting emission standards for oxides of sulfur and nitrogen. In fluidized bed combustion (FBC) the temperature of the fluidized bed is -900 OC. Natural stones such as limestones and dolomites are presently receiving the greatest consideration as sulfur-accepting materials (sorbents) because of their high calcium content (sulfur reacts with calcium to form CaS04) and because these materials are abundant. 230
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
It is estimated, based on experimental results (Vogel et al., 1975),that about one tonne of natural stone will be sulfated for each four tonnes of coal (-3 wt % S)combusted. In terms of electric power, for a 1000-MW plant (70% capacity factor), -2000 tonnes of stone per day will be sulfated. If the stone is used only once, large amounts of sulfated stones will be produced, creating a waste disposal problem. Multicyclic utilization of the stones by regenerating the CaO is a potentially attractive alternative which would greatly reduce the quantity of solid waste that must be disposed of. Based on present sorbent cost, the utilization of a sorbent regeneration process
