2074
Ind. Eng. Chem. Res. 1990,29, 2074-2078
Simple Design of Monolith Reactor for Selective Catalytic Reduction of NO for Power Plant Emission Control Marek A. Buzanowski and Ralph T. Yang* Department of Chemical Engineering, State Uniuersity of New York at Buffalo,Buffalo, New York 14260
Theoretical and experimental results are presented for the selective catalytic reduction (SCR) of NO by NH, in the monolithic honeycomb reactor under power plant conditions. Both unpoisoned V20,/Ti02 and alkali poison-doped catalysts are used. A simple analytic solution is given that expresses the overall NO conversion as an explicit function of space velocity and other parameters. Explicit solutions are also given for the NO concentration profile within the honeycomb walls and for the effectiveness factor. A good agreement between experiment and theory is obtained. The theoretical solution also provides insight into the relative importance of the diffusion and reaction steps, as well as a guide for optimal monolith design for SCR. Introduction The use of monolithic honeycomb reactors has been dominated by automotive catalytic converters (Taylor, 1984). The unique advantages of the design methodologies for monolith reactors have been reviewed recently (Irandoust and Anderson, 1988). Monoliths have also found applications in catalytic oxidation and combustion (Prasad et al., 1984; Pfefferle and Pfefferle, 1988) as well as other applications (Irandoust and Anderson, 1988). Much work has been done on the design and modeling of monolith reactors for both automobile and nonautomobile applications (Bensalem and Ernst, 1982; Carberry and Kulkarni, 1973; Heck et al., 1974; Hegedus, 1975; Hlavacek and Votruba, 1976; Oh and Cavendish, 1985; Pereira et al., 1988; Senkan et al., 1979; Wei, 1975; Young and Finlayson, 1976; Zygourakis and Aris, 1983). Most of these models account for nonisothermality, and all models resort to numerical solution. Within the past decade, monolithic honeycomb reactors have found major application for power plant NO, control by the selective catalytic reduction (SCR) process. The process is already commercialized in Japan and a number of countries in Europe and is presently under consideration for use in the US. The stoichiometry of the reaction is 4NH3 + 4 N 0 + O2 4N2 + 6H20 (1) The commercial catalysts are Ti02-basedhoneycombs with supported V206/W03(Bosch and Janssen, 1988). A detailed model for the SCR reaction in monoliths has been developed by Beeckman and Hegedus (1988). An isothermal model was used to compare with experimental data by Stenger et al. (1988). These models, again, require numerical solutions. Because isothermality and other simplifying assumptions can be justified for the SCR reaction under power plant conditions, an analytic solution for the monolith reactor is possible. In this paper, we first derive a simple analytic solution that expresses NO conversion as an explicit function of the space velocity. Experimental results are then presented for honeycomb reactors with two different catalyst loadings, as well as for a poison-dopes catalyst, and are compared with model predictions. In addition, the NO concentration profile within the walls and effectiveness factor are also given in explicit forms by the solution, which provide insight into the relative importance of the individual transport and reaction steps to the overall conversion.
-
Formulation of the Simplified Model Because the reactants in the SCR reaction are dilute in power plant combustion gases, e.g., NO < 1000 ppm, a OSSS-5885/90/2629-2074$02.50/0
number of simplifying assumptions can be justified. The first and foremost assumption is isothermality, which will be elaborated further. The multicomponent flux equations, i.e., the Stephan-Maxwell equations, can be approximated by Fick's law for the reactant NO. Since the SCR reaction is highly selective at temperatures below 400 "C, the ammonia oxidation reaction is neglected. The rate equation for the SCR reaction is (Bosch and Janssen, 1988) -dC,o/dt
= kChoChH,
(2)
for O2 concentration greater than 1% . The rate is firstorder with respect to NO and nearly independent of the concentrations of all other species-NH,, 02, N2, H20, SO2, etc. (SOzhas a small promoting effect but will be neglected here (Chen and Yang, 1990)J Consequently, we will treat the diffusion/reaction problem as a binary system: NO in an inert carrier. Furthermore, the width of each side of the honeycomb walls is assumed to be much greater than its thickness, so pore diffusion is assumed to be one dimensional. For automobile catalytic converters, the concentrations of CO and hydrocarbons (which are to be oxidized) are as high as several percent. Thus, large temperature excursions occur. Two aspects of temperature gradients are to be addressed for the SCR reactor: that inside the porous walls (in the radial direction) and that along the reactor (in the axial direction). The heat of reaction for SCR at 600 K is -97.2 kcal/mol of NO (exothermic). By using the Prater relation (Prater, 1958), the maximum temperature rise within the wall is 0.1 "C. The maximum temperature rise along the reactor can be calculated from a heat balance, assuming 100% conversion of NO along an adiabatic reactor. For 1000 ppm inlet NO, the maximum temperature rise is 12.8 "C, which is considerably less than that occurring in automobile catalytic converters, of nearly 150 "C (Hegedus, 1975). For typical power plant operations where NO is to be reduced from 500 to 100 ppm, the maximum temperature rise would be 5.1 "C. Consequently, we allow isothermality as a simplifying assumption. At a fixed location along the reactor, the flux equation for NO (denoted by A) in the porous wall is J A = -D,Ct dyA/dx (3) where De is the effective diffusivity of NO, Ct is the total concentration, yA is the mole fraction of NO, and x is the distance measured from the surface of the wall. The mass balance equation in the wall is dJA/dx = -kaCA (4) where k is the first-order rate constant given in eq 2 and 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2075 a is the surface area per volume of the porous material. Equations 3 and 4 may be combined and recast into dimensionless form: d2Y* -=dX*'
h2ka Y* De
(5)
where x* = x / h
Y* = YA/YAb are based on the half-thickness of the wall (h)and the bulk mole fraction in the cell (YAb). The Thiele modulus ( 4 ) is defined as 42 = h2ka n
u e
The boundary conditions are
Table I. Physical Characterizations of Titania Monolithic Honevcombsa and Pelleted S U D D O ~ ~ S honeycomb heat treatment temp 500 "C time of heat treatment 6h 44.4 m2/g BET surface area 325 A N2 desorption, PVD, m.p.s.* 280 A Hg porosity, m.p.s. 57.6% open porosity 1.6 g/cmS bulk density % Hg porosity 57.8% 0.038 cm wall thickness 31 no. of cells/cm2 pellets 450 O C heat treatment temp 4h time of heat treatment 30.6 m2/g BET surface area a Data for the titania monolithic honeycombs are taken from Lachman (1988). *Median pore size.
x*=O,
(7)
where Bi is the Biot modulus, Bi = k,h/D,, and k , is the gas film mass-transfer coefficient. Equation 7 is based on the continuity at the surface of the wall, where the flux is km(CAb - CAB)= -D,(dCA/dx)x=o (8) The other boundary condition is for symmetry at the center: x* = 1, dy*/dx* = 0 (9)
J1y* dx*
v=
(17)
Y:
The solution to eqs 5-9 is [e$(x*-2)+ e-4x8](y~ - 1) y* = $(e-2@- l ) / B i
or (10)
From eqs 7 and 10, the NO mole fraction a t the wall surface is, for x* = 0,
I---
Bi e-24 + 1 From eqs 10 and 11, the concentration profile within the wall is e@(x*-2) + e-@x* y* = (12) We next consider the mass balance along the axial direction of the reactor, z:
where u is the linear gas velocity in the cell, which is assumed to be constant, u is the perimeter length of a cell in the honeycomb, and A is the cross-sectional area of a cell. The boundary condition is = O, YAb = YAO (14) The overall conversion of NO in the reactor is (15) X = (YAO- YAL) /YAO Thus, the conversion is given by 1
Equation 16 is an explicit expression for overall NO conversion. To calculate X, the values of k , and De need to be evaluated, and the rate constant, k , needs to be measured independently for the given catalyst. The other parameters can be obtained from the structural information of the honeycomb. The effectiveness factor of the monolithic porous material is defined based on the surface condition:
1
1
$4
- 1 Bi(e-24 + 1) -
v=-- 4 e-2@+ 1 Bi(e'4
- 1) + 1) + $(e2+ - 1)
(18)
It may be noted that previous definitions of r] based on the bulk conditions (Carberry and Kulkami, 1973; Senkan et al., 1979) would result in values lower than that calculated with eq 18. Experimental Section Catalyst Preparation. Two types of catalyst were prepared: pellets and honeycombs, both supported on TiO,. The Ti02 monolith support was Corning cellular ceramic catalytic substrate containing 100% TiOz, with square-shaped cells. The characterization of the substrate is given in Table I and in more detail by Lachman (1988). The pellets were prepared from powder T i 0 2 (Degussa, P25) using a densification procedure, fully described by Chen and Yang (1990). Its BET surface area was 30.2 m2/g. The procedures for Vz05 impregnation and the subsequent doping of the K20 poison were similar for both monolith and pellet catalysts. That for the pelleted catalysts was fully described by Chen and Yang (1990). The honeycomb support was impregnated with an oxalic acid solution of ammonium metavanadate followed by drying in air a t 120 "C for 3-4 h and calcination a t 420 "C for 4 h. The K 2 0 doping was obtained by a subsequent impregnation with potassium nitrate solution followed by decomposition at 420 "C in air. Catalysts (both honeycombs and pellets) of 3.45% Vz05/TiOz,1% V205/Ti02, and 0.85% K20/3.45% V205/Ti02(all % by weight) were prepared. The BET surface areas of the supported catalysts were slightly lower than that of the support (Chen and Yang, 1990). For example, the BET surface area of 5% VZO5/TiOzpellets was 26.2 m2/g (Chen and Yang, 1990). The pore structures of the 1% and 3.45% VzO5 catalysts were assured to be unchanged.
2076 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 Table 11. NO SCR Reaction over Pelleted Catalystsa catalyst 300 "C 200 "C 100 "C 3.45% V,05/Ti02 (a) 99.5 82.5 26.0 5.57 1.16 (b) 13.98 1.00% V205/Ti0, (a) 95.0 50.0 20.0 2.21 0.90 (b) 7.90 22.0 13.0 0.85% K,0/3.45% V2OS/TiO2 (a) 40.0 0.79 0.42 (b) 1.09 a (a) Overall NO conversion, %. (b) First-order rate constant, k (cm3/g/s). Reaction conditions: NO = 1000 ppm, NH, = 1000 ppm, 0, = 27'0, N2 = balance, GHSV = 15000 h-l.
Figure 1 . Schematic diagram of the experimental SCR reactor. A: Chemiluminescent NO/NO, analyzer. B NH, scrubber. C: Water vapor generator. D: Honeycomb catalyst. E: Programmable temperature controller.
Experimental Apparatus and Rate Measurement. The schematic diagram of the SCR apparatus is shown in Figure 1. The reactor was a quartz tube with a fritted support. The reactor was equipped with a thermocouple well and a gas preheating section. The reactant gas was a mixture simulating the flue gas. The flow rates were controlled by an FM 4575 (Linde Division) mass flow control blending system. The same gas mixture was used for all experiments with the following composition: 1000 ppm NO, 1000 ppm NH,, 2% 0 2 and , balance N2. The space velocity was varied between 5000 and 30000 h-' (based on room temperature and 1 atm) for all experiments. The N2was oxygen-free grade (C0.5 ppm 02).The NH, was anhydrous grade (99.9%) and O2was ultrahighpurity grade, 99.99% minimum. A chemiluminescent NO/NO, analyzer (Therm0 Electron Corporation, Model 10) was employed to measure the reaction product. The SCR reactor effluent was scrubbed with an ammonia trap by a concentrated aqueous solution of phosphorous acid, prior to entering the NO, analyzer. By this measure, possible errors caused by NH, oxidation in the chemiluminescent analyzer were avoided (Chen and Yang, 1990). The SCR activity was measured by the NO, conversion expressed by NO, conversion = X = ([NO,lin - [NO,],,,)/[NO,]in
The experimental procedure and conditions for the pelleted catalysts were fully described by Chen and Yang (1990). A series of experiments were conducted to ensure that the effects of the mass-transfer steps (both film diffusion and pore diffusion) were absent under the flow/ pellet size Conditions. Thus, the intrinsic rate constant, k, could be obtained from the data using the pellets. The rate constant was calculated from the integral reactor with a first-order reaction (Chen and Yang, 1990). Results and Discussion Evaluation of the Effective Diffusivity ( D e ) .Since the pore structure of the monolith material was essentially monodisperse, the following equation was employed to evaluate D,: tD De = 7
where 7 is the tortuosity factor, assumed to be 6 from values for similar materials (Satterfield, 1970). D is the transition diffusivity, evaluated by using the Bosanquet formula from molecular and Knudsen diffusivities. The diffusion was approximated as binary: NO in N2. The values of I), are 4.64 x 10-~ cmz/s at 100 O C , 5.45 x io-,
Table 111. Overall Conversion ( W )of NO over 3.45% V205/Ti02 (by Weight) Honeycomb Catalysto 300 "C 200 "C 100 "C modelb exptlb modelb exptlb modelb exptlb 99.8 99.3 59.5 58.1 99.9 99.5 5000 35.1 89.9 36.4 10000 99.0 99.2 89.1 96.2 77.2 78.0 26.0 25.0 15000 95.6 20.3 21.1 20000 90.4 90.8 67.0 67.5 14.0 11.1 79.2 52.5 53.0 30000 79.1 OReaction conditions: NO = 1000 ppm, NH, = 1000 ppm, O2= 2'70,N2 = balance. Model: eq 16. bGHSV,h-l. Table IV. Overall Conversion (70) of NO over 170 V2OS/TiO2(by Weight) Honeycomb Catalysto 300 "C 200 "C 100 O C modelb exptlb modelb exptlb modelb exptlb 53.9 49.5 5000 99.9 99.1 89.6 87.5 10000 97.6 97.2 67.8 68.5 32.1 33.0 19.8 50.0 22.7 15000 91.6 90.6 53.0 15.5 43.5 17.6 20000 84.5 83.5 43.3 71.5 31.5 23.5 12.1 10.0 30000 71.1 Reaction conditions: NO = 1000 ppm, NH, = 1000 ppm, O2 = 270, N, = balance. Model: eq 16. bGHSV, h-l. Table V. Overall Conversion (% ) of NO over Poisoned 0.85% K20/3.45 % V,0,/Ti02 Honeycomb Catalyst" 300 "C 200 "C 100 "C modelb exptlb modelb exptlb modelb exptl; 33.7 31.2 77.3 59.3 58.8 5000 78.6 36.2 18.6 18.0 53.7 54.5 34.0 10000 39.6 25.9 22.5 12.8 12.9 15000 40.2 20.1 9.8 10.2 32.0 32.5 20.2 20000 22.4 13.9 15.9 6.6 8.1 30000 22.6 Reaction conditions: NO = 1000 ppm, NH, = 1000 ppm, O2 = 2 % , N, = balance. Model: eq 16.
cm2/s at 200 "C, and 6.15 X cm2/s at 300 OC. Measurement of the Rate Constant (k).The firstorder rate constants were measured by using pelleted catalysts under conditions where diffusion effects were minimized (Chen and Yang, 1990). The rate constants were calculated from the conversions by assuming plug flow in an integral reactor. The results are given in Table I1 for three catalysts at three different temperatures. Monolith Model Predictions and Experimental Results. Equation 16 is the analytic solution for the monolithic honeycomb reactor, expressing NO conversion (X) as a function of linear velocity ( u ) and other parameters. Equation 12 can be used to calculate the concentration profile within the walls. Equation 18 yields values of the effectiveness factor. The experiments involved three different catalysts, 3.45% V206/Ti02,1% V2O5/TiO2,and 0.85% K20/3.45% V2O5/TiO2,and three temperatures, 100,200, and 300 OC, and the space velocity (GHSV) was varied between 5000 and 30000 h-l.
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2077 i
h 1.0
c
0 IC
$
0.8
k
J
h"
x
cu
6o
0
c:
50
0.6
0
0 40
t-
30
L
20
t-
Ul Ul
0.4
6
r(
c
0 0.2
.3
Ul
c 0
I 0
100
I
I
I
200
300
400
T, OC Figure 2. Overall NO conversion from the monolithic honeycomb reactor containing 3.45% VzO5/TiO2(solid curves), 1% V205/Ti02 (dashed curves), and 0.85% K20/3.45 V2O5/TiO2 dotted curves). The upper curves are for 10000 h-' and lowers ones 20000 h-l (GHSV). [NO] = [NH,] = 1000 ppm, LO2] = 2%. Table VI. Values of Thiele Moduli, Biot Numbers, and Effectiveness Factors for the SCR Reaction over Monolithic Catalvstsa monolithic catalyst 1% 0.85% V2O5/ K20/3.45% temp, 3.45% V205/Ti02 Ti02 V20S/Ti02 "C 33.7 Bi 33.7 33.7 100 4+ 0.690 0.605 0.428 7 0.867 0.894 0.943 200 Bi 42.9 42.9 42.9 9 1.431 0.901 0.530 7 0.623 0.795 0.916 300 Bi 43.7 43.7 43.7 @ 2.130 1.605 0.597 7 0.456 0.575 0.896 ~
OConditions: NO = 1000 ppm, NH3 = 1000 ppm, 02 = 290, Nz = balance, GHSV = 10000 h-l.
u
!,
cI
0.0
0.2
0.4
0.6
0.8
1 .o
D i m e n s i o n l e s s d i s t a n c e , X* Figure 3. NO concentration profile within the monolith wall for unpoisoned and poison-doped catalysts. The three curves are for 100 "C (upper), 200 O C (middle), and 300 O C (lower) for each catalyst. GHSV = IOOOO h-l, NO = NH3 = IO00 ppm, O2 = 2%, N2 = balance. (.
1.0
c 0 .C
2
0.8
k
4
c: QI 0
c
0.6
0 0 Ul
0.4
(fl
a r(
c
0 .I4
Typical results a t 10000 and 20 000 h-' space velocities are shown in Figure 2. The complete results are given in Tables 111-V. The model predictions calculated directly from eq 16 are also given in Tables 111-V and compare favorably with the experimental data. This comparison assures the usefulness of the simple model. Table V lists the results for 0.85% K20-doped catalyst. K 2 0 is among the strongest poisons (Chen and Yang, 1990) that are also abundant in coals. From these results, it is clearly seen that small amounts of K 2 0 (and other alkali metals (Chen and Yang, 1990)) can significantly lower than the overall conversion of NO. The effectiveness factors ( q ) ,calculated from eq 18, are given in Table VI, along with values of Biot numbers (Bi) and Thiele moduli (4).As may be intuitively expected, the effectiveness factor increased as the intrinsic activity of the catalyst decreased (from 3.45% Vz05loading without poison to that with KzO poison). The effectiveness factor decreased with increasing temperature, because the temperature dependence of the surface reaction was stronger than that of the diffusion steps. The concentration profile of NO within the porous wall provides useful information on the interplay between film mass transfer, pore diffusion, and surface reaction. The
0.0
i
0.2
I
I
I
2078 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
The simple model also provides an u n d e r s t a n d i n g of the relative importance of the film diffusion, pore diffusion, and surface reaction steps. In addition, the effectiveness factor calculated from the model can be used as a useful tool for optimum catalyst design. Acknowledgment
This research was supported by the Electric Power Institute ( E P R I ) . Discussions with J. Edward Cichanowicz of the EPRI were most helpful. We are also grateful to Irwin M. Lachman of Corning for supplying the honeycomb supports. Research
Nomenclature a = surface area per volume of the material in the walls, cm2/cm3
A = cross-sectional area of t h e cell in t h e honeycomb, cm2 Bi = Biot modulus, = hk,/De
C = concentration, mol/cm3 CA = concentration of NO, mol/cm3 C, = total concentration, mol/cm3 = bulk concentration of CA, mol/cm3 CAS= CA a t t h e surface of t h e wall, mol/cm3 D = diffusivity, cm2/s De = effective diffusivity, cm2/s GHSV = gas hourly space velocity, at room temperature, h-' h = half thickness of t h e wall, cm J = molar flux, mol/cm2/s k = first-order rate constant, c m / s k , = film mass-transfer coefficient, c m / s L = total length of honeycomb reactor, cm r = pore radius, cm t = time, s T = temperaure, K u = linear velocity, c m / s CAb
x = distance coordinate, from t h e surface into t h e wall, cm x* = x / h
X = overall NO conversion y = mole fraction Y* = CA/CAb Y*s = C A s / C A b
yAO= mole fraction of A at the inlet of t h e monolith YAL = mole fraction of A at t h e outlet of t h e monolith z = distance along t h e reactor, cm
Greek Symbols = void fraction in porous walls @ = Thiele modulus, (h2ka/De)*/2 c
u = perimeter length of a cell in honeycomb, cm/cell T = tortuosity 7 = effectiveness factor
Literature Cited Beeckman, J. W.; Hegedus, L. L. Design of Monolith Catalyst for Power Plant NO, Emission Control, Presented at the AIChE Annual Meeting, Washington, DC; American Institute of Chemical Engineering: New York, 1988; Paper 72e. Bensalem, 0.; Ernst, W. R. Mathematical Modeling of Homogeneous-Heterogeneous Reactions in Monolithic Catalysts. Comb. Sci. Technol. 1982, 29, 1-13. Bosch, H.; Janssen, F. Catalytic Reduction of Nitrogen Oxides. Catal. Reu. 1988,2, 369-531. Carberry, J. J.; Kulkarni, A. A. The Non-isothermal Effectiveness Factor for Monolith Supported Catalysts. J . Catal. 1973, 31, 41-51. Chen, J. P.; Yang, R. T. Mechanism of Poisoning of the V206/Ti02 Catalyst for Reduction of NO by NH,. J. Catal. 1990, in press. Heck, R. H.; Wei, J.; Katzer, J. R. The Transient Response of a Monolithic Catalyst Support. Ado. Chem. Ser. 1974, 133, 34. Hegedus, L. L. Temperature Excursions in Catalytic Monoliths. AIChE J. 1975,21, 849-853. Hlavacek, V.; Votruba, J. Steady-State Operation of Fixed-Bed Reactors and Monolithic structures. In Chemical Reactor Theory-A Reuiew; Lapidus, L., Amundson, N. R., Eds.; Prentice-Hall: Englewood Cliffs, NJ, 1976; pp 314-404. Irandoust, S.; Anderson, B. Monolithic Catalysts for Nonautomobile Applications. Catal. Reu.-Sci. Eng. 1988, 30, 341-392. Lachman, I. M. Porosity and Pore Size Distribution in High Surface Area Monolithic Cellular Ceramic Catalytic Substrates. Catalysis 1987; Ward, J. W., Ed.; Elsevier, Amsterdam, 1988; pp 531-539. Oh, S. H.; Cavendish, J. C. Mathematical Modeling of Catalytic of Catalytic Converter Lightoff. AIChE J. 1985, 31, 943-949. Pereira, C. J.; Kubsh, J. E.; Hegedus, L. L. Computer-Aided Design of Catalytic Monoliths for Automobile Emission Control. Chem. Eng. Sci. 1988,43, 2087-2094. Pfefferle, L. D.; Pfefferle, W. C. Catalysis in Combustion. Catal. Reu.-Sci. Eng. 1988,29, 219-264. Prasad, R.; Kennedy, L. A,; Ruckenstein, E. Catalytic Combustion. Catal. Rev.-Sci. Eng. 1984,26, 1-57. Prater, C. D. The Temperature Produced by Heat of Reaction in the Interior of Porous Particles. Chem. Eng. Sci. 1958, 8, 284-286. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. Senkan, S. M.; Evans, L. B.; Howard, J. B. An Analysis of WallSupported Catalyst Structures. Ind. Eng. Chem. Process Des. Deu. 1979,18, 125-130. Stenger, H. G., Jr.; Meyer, E. C.; Hepburn, J. S.;Lyman, C. E. Nitric Oxide Reduction Using Co-impregnated Rhodium on an Alumina Celcor Honeycomb. Chem. Eng. Sci. 1988,43, 2067-2072. Taylor, K. C. Automobile Catalytic Conuerters; Springer-Verlag: Berlin-New York, 1984. Wei, J. The Catalytic Muffler. Ado. Chem. Ser. 1975, 148, 1-25. Young, L. C.; Finlayson, B. A. Mathematical Modeb of the Monolith Catalytic Converter. AIChE J . 1976,22, 331-343, 343-353. Zygourakis, K.; Aris, R. Multiple Oxidation Reactions and Diffusion in the Catalytic Layer of Monolith Reactors. Chem. Eng. Sci. 1983, 38, 733-744.
Received for review February 5, 1990 Accepted June 29, 1990
