95
Ind. Eng. Chem. Res. 1987,26,95-100
Eklund, H.; Svensson, 0.Ind. Eng. Chem. Process Des. Deu. 1983, 22,396-401. Ergun, S. J. Phys. Chem. 1956,60,480-485. Katta, S.; Keairns, D. L. Ind. Eng. Chem. Fundam. 1981,20,6-13. Ramachandran, P. A.; Doraiswamy, L. K. AIChE J . 1982, 28, 881-900.
Von Fredersdorff, C. G . Znst. Gas Technol., Chicago, Res. Bull. 1955, No. 19. Receiued for reuiew April 9, 1984 Revised manuscript received March 5 , 1986 Accepted May 10, 1986
Study of Char Gasification by Carbon Dioxide. 2. Continuous Gasification in Fluidized Bed Isao Matsui, Toshinori Kojima, Daizo Kunii, and Takehiko Furusawa* Department of Chemical Engineering, The University of Tokyo, Bunkyo-ku, Hongo, Tokyo, Japan
Coal char gasification with carbon dioxide was performed in a fludized bed. The continuous pyrolysis of the char was carried out in the nitrogen stream to evaluate the amount of gas produced by thermal decomposition. The gasification reaction was analyzed by assuming the reaction takes place independently after the pyrolysis is completed. The bubble size under the gasification condition was measured by use of the electroresistivity probe. The bubbling bed model and the thermogravimetrically obtained rate equation were used for the prediction of the conversions of both char and carbon dioxide, where the bubbling bed model was modified to give the stoichiometrically consistent material balance between the consumed char and carbon dioxide. The results of the fluidized bed gasification could be well explained by the modified bubbling bed model, where the effective bubble size was chosen as the bubble size observed at the middle height of the bed by the electroresistivity probe. The results in the previous paper in this issue indicated that the gasification rate of char changes with an increase in the extent of the reaction. Since the conversion of an individual solid particle depends on its length of stay within the bed, the outgoing particles from the gasifier with continuous feed and discharge of solids consist of particles of different ages, consequently different degrees of conversion. The outlet conversion of gas is influenced by the reaction rate, thus the conversion of solids. Therefore, the conversion of solids and gas is interdependent. Kunii and Levenspiel (1969) developed the calculation procedure of conversions of both solid and gas phases for a reaction, whose rate can be described as first order of the reactant gas. Caram and.Amundson (1979) analyzed the performance of the fluidized bed gasifier by use of the kinetic equation obtained by Johnson (1974) and Gibson and Euker (1975). The hydrodynamics of the bed used for the investigation were the complete mixing reactor model, the bubbling bed model (Kunii and Levenspiel, 1969), the simplified bubbling bed model, and the Davidson-Harrison model (1963). The effects of the model chosen and the bubble size on the bed performance including the conversions of both carbon and steam and the product gas compositions were examined. The data obtained by Tarman et al. (1974) were compared with the simulation results. It was stated that the total conversions of both carbon and steam could be satisfactorily predicted, and the gas compositions agreed fairly well with each other, except the hydrogen mole fraction. Sundaresan and Amundson (1979) analyzed the solid conversion by use of the population balance of solids, where complete mixing of the solids and plug flow of the gas were assumed. The effect of the combustion zone above the distributor on the total carbon conversion was also taken into consideration. Weimer and Clough (1981) presented a modified two-phase model taking into account both the jetting region and the homogeneous gas-phase reactions including oxidation of carbon monoxide and hydrogen and the water-gas shift reaction. The significant effects of the homogeneous re-
* Author to whom correspondence should be addressed. 0888-5885/87/2626-0095$01.50/0
actions on carbon conversion, bed temperature, and gaseous product distribution were observed. The mass and heat interchange between jet and emulsion had-a substantial effect on the overall bed performance. Yoshida and Kunii (1974) analyzed the composition of gas from the coal gasification system by assuming carbon-oxygen, carbon-carbon dioxide, and carbon-steam reactions to be irreversible first order to reactant gases and found that previously reported data were well explained by the Kunii-Levenspiel model (1969). All of the above studies were restricted to the numerical experiments based upon the rate data available in the literature. Haggerty and Pulsifer (1972) compared the results obtained numerically by using the gas-phase plug flow model as well as the gas-phase complete mixing model with those obtained by the KatoWen model (1969) in the carbon-steam reaction, where the kinetic constants were assumed to be unaffected by the age and degree of conversion of the solid particles. It was stated that the three reactor models employed gave considerably different results. The significance of the experimental study of both the kinetic investigation under well-defined flow conditions and the fluidized bed gasification of sample of the same material with which the models could be compared was emphasized (Haggerty and Pulsifer, 1972). Furthermore parameters used for the model, such as bubble diameter, should be determined experimentally. As stated in the preceding paper in this issue, a limited number of investigations which justify the use of thermogravimetricallyobtained rates for the analysis and the design of the fluidized bed gasifier have been reported. In this study, the continuous gasification of the char with carbon dioxide, kinetically investigated in the preceding paper, is conducted in a small laboratory-scale fluidized bed. The experimentally obtained conversions of both the char and carbon dioxide are compared with the calculation results by use of the kinetic equation and the bubbling bed model proposed by Kunii and Levenspiel (1969). Thus, the applicabilities of the thermogravimetrically obtained rate and the fluidized bed model to the evaluation of the fluidized bed performance are tested. The bubbling bed 0 1987 American Chemical Society
96 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
I a WAY VALVE b CHAR FEEDER
w-'
r'f
c PREHEATEA d FLUIDIZED BED e ELECTRIC FURNACE f CATCH POT 9 CYCLONES
Figure 1. Flow sheet of the fluidized bed gasification system.
model assumes that all parameters, which describe the gas-solid contact, can be expressed by functions of a single parameter, the effective bubble size. A modification of the definition of bubble volume fraction within the bed is enlployed so that the conversions of gas and solid can be stoichiometrically consistent, and the justification of the modification is discussed. The bubble size determined experimentally under the gasification conditions is compared with the effective bubble diameter, which well explains the conversions of char and carbon dioxide.
Experimental Section Material. The proximate and ultimate analyses of the employed char were presented in the preceding paper. Research-grade carbon dioxide, which was diluted by nitrogen, was used as a gasifying agent. The concentration of carbon dioxide was chosen to be 47.4 kPa throughout the experiments. Apparatus. The fluidized bed gasification system used for this investigation is illustrated in Figure 1. The system was operated under atmospheric pressure. The main parts of the reactor are the fluidized bed, the solid feed system, the catch pot of overflowed char particles, and the cyclones. The reactor employed for these experiments is a 79 mm inner diameter stainless steel vessel. The effective bed height was maintained at 196 mm by removing the solids continuously through the overflow pipe. The lower part of the vessel is packed with ceramic balls (8 mm in diameter) and used for the gas preheating. A multiorifice plate used for the gas distributor was designed to obtain a sufficient pressure drop from 6.4 to 9.3 kPa to achieve homogeneous bubbling fluidization. The reactor was heated to the desired reaction temperature by means of an external electric furnace. The bed temperature was measured by a sheathed chromel-alumel thermocouple (6-mm outer diameter) located in the fluidized zone. The outside wall temperature was also detected by a sheathed chromel-alumel thermocouple (5-mm outer diameter) and controlled by a conventional on-off controller. The char was fed at 23 mm above the gas distributor, through a stainless tube (inner diameter 10 mm) from a hopper by use of a vibration feeder made by Shinko Electric Works Co. A continuous and stable feed of solids even at a small feed rate of 0.07 g/s or less could be realized. Nitrogen was fed to the hopper as a carrier gas during a run. Entrained particles from the reactor were seperated from the gas by two serial cyclones. Overflowed char was collected in a tight catch pot. Both of these particles were periodically sampled during a run. The weight decrease of the solids due to the gasification was measured by a conventional balance, and then the solids conversions were calculated. Product gases were also taken periodically in a sample vessel made of glass (300 cm3 in volume) and were analyzed by Shimazu gas chromatographs with thermal
a Probe
Figure 2. Electroresistivity probe and measuring circuit
conductivity detectors, Types 6A and 3BT, which have, respectively, column packings of Porapak QS and MS 5A. Ha, CO, CH,, and N2 were analyzed by MS 5A, and C02 was analyzed by Porapak QS. Procedure. Since the coal char employed for this experiment contains volatile matter, a certain amount of gas is produced by pyrolysis during a continuous run. The initial series of experiments was conducted in the nitrogen atmosphere for the evaluation of the amount of gas produced by pyrolysis. The reactor, initially packed with char, was heated up to the desired temperature at a rate of about 10 K/min in a nitrogen atmosphere. The superficial velocity of nitrogen through the gas distributor and solid feed tube was totally adjusted to be 187 mm/s at reaction temperature, which is the same as in the gasification condition. The gas velocity corresponds to 4.74-5.28 times the minimum fluidization velocity calculated by Wen and Yu's correlation (1966). When the desired temperature was attained, the feed of char was initiated. The outlet gas was sampled and analyzed by the gas chromatographs. Discharged solids were also taken in tight catch pots. Steady-state operation was assured by analyzing the product gas, and it was attained during 10 min after starting the feeding of char. In the gasification experiments, after the desired temperature was attained, the reactant gas mixture of carbon dioxide and nitrogen in place of nitrogen was introduced by switching the flow stream, and the feeding of char was initiated. The results of the gas analysis showed that about 3-4 h was required to achieve steady-state operation. The steady state was maintained for about 1 h, during which several sets of gas and solid samples were taken for the analyses. Measurement of Bubble Size. During a series of experiments, the bubble size in the bed was measured by use of an electroresistivity probe. The probe was designed to distinguish the nonconductive bubble phase from the conductive dense phase of char. The detail of the probe is described in Figure 2a, and the flow sheet of the measuring circuit is shown in Figure 2b. The probe consists of two Ni wires (1-mm diameter) double insulated by ceramic tubes (3 mm outer diameter tube and 6 mm outer diameter tube), except at the tips which were aligned vertically 6 mm apart. The probe was mounted through the top cover of the reactor, so that the tips could be moved vertically. The signal from the probe was recorded by an electromagnetic oscillograph made by Yokokawa Electric Works Co.
Experimental Results Pyrolysis in the Nitrogen Atmosphere. Figure 3 shows the gas yield by pyrolysis per unit amount of feed char in the nitrogen atmosphere. Carbon monoxide and
Ind. Eng. Chem. Res. Vol. 26,No. 1, 1987 97 10.0
Hz
01 AI
co
00
c
--
-A---
1Mo 1225 1250 BED TEMPERATME [ K I
-
"I.
._gob"" -
li00
1250 REO TEMPERATURE [ K ]
Figure 4. Conversions of solid and gas by continuous gasification in fluidized bed by carbon dioxide.
OS0
) (
m o u n t of CO obtained from
xco2 =
( 5
the gasiticntion experiments per unit time
-
widths, b and b', were defined as half-widths of the two signals from one identical bubble. Tone et al. (1974)studied the catalytic cracking of methylcyclohexane in a gas fluidized bed in the temperature range 303-923 K. The bubble frequency was measured by a capacitance probe, and the bubble diameter was evaluated by using the Kunii-Levenspiel correlation (1969) expressed as eq 3. The bubble height from eq 2 and the
(3)
m o u n t of CO obtained b p y r o l c e p e r unit
)
feed rate of C 0 2
Also the converison of char was defined as (%hzte)
-
(iEhEte)
-
X =
~ ?)~;dpy(
~
weight decrease
weight decrease
~
amount of total i ~
-
(
-
feed rate of ash (onta;;;in th.>
~
~
~
The variations of experimentally obtained gas and solid conversions with the bed temperature are shown in Figure 4. Bubble Size Measurement. A typical signal from the electroresistivity probe is given in Figure 5. Otake et al. (1975)proposed the evaluation method for the rise velocity of bubbles and the height of bubbles by analyzing similar signals observed in this study. The procedure was expressed by eq 1 and 2 by use of the time delay between rise velocity of bubbles bubble height
dh = ub(b
ub = l/a
+ b')/2
(1) (2)
two signals from one identical bubble and the widths of the signals where the value of the time delay between two signals, a, was evaluated by use of the distance between the two signal fronts in Figure 5 and the values of the
100 20.0 OISTANCE FROM OISTRIBUTOR [cml
Figure 6. Calculated bubble sizes based on the signals from electroresistivity probe.
hydrogen were the main products, and carbon dioxide was not detected. The solid residue from pyrolysis amounted approximately to the sum of the fixed carbon and ash content in the proximate analysis. Gasification Experiments. The production rate of carbon monoxide was evaluated by analyzing the outlet gas from the gasifier. The gasification process is considered to be comprised of two separable reaction steps: the pyrolysis and the gasification of in situ formed char. In this investigation, it was assumed that the former step was instantaneously completed and that the latter started after the pyrolysis. This assumption is supported by the experimental results concerning the continuous pyrolysis in the fluidized bed (Nagashima et al., 1977). The conversion of carbon dioxide was defined as 1
bed temperature 1277K distance from distributor 11 3cm
Figure 5. Typical signals detected by electroresistivity probe.
Figure 3. Amount of gas produced by continuous pyrolysis in fluidized bed.
o'ol!50
0 5 sec.
~
diameter calculated by eq 3 are shown in Figure 6. The bubble size increased linearly with the axial distance from the distributor, as observed by Tone et al. (1974). Ueyama and Miyauchi (1976)theoretically discussed the relationship between the bubble height detected by two vertically aligned probes and the equivalent bubble diameter. They concluded that under free bubbling conditions, the average value of the equivalent bubble diameter to sphere equals ll/ztimes the average of the detected bubble ~ ~ The ~ values $ height. of the diameter obtained by this manipulation are also shown in Figure 6. Some difference between the values calculated from the bubble frequency and the values obtained from the bubble rise velocity was observed. Rowe and Masson (1981)studied the effect of a probe on the bubble characteristics in the gas fluidized bed and found that the bubbles, especially large bubbles, tend to be elongated by the probe, as the bubbles approach a d pass the probe tip. The overestimation of the bubble size of the present study might be attributed to the elongation of the bubble along the probe. Therefore, the bubble diameter estimated from the bubble frequency measurement was employed for the analysis. The bubble size measurement under the gasification condition has not been well discussed in previous studies. Unfortunately, the results in this study could not be compared with those of the previous study. In general, the bubble size is thought to be affected by the bed temperature. The temperature dependency of the bubble size in the inert atmosphere is dependent of the particle size in the bed. The bubble size in the bed of the small particle
~
~
~
f
)
98 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 Table I. Basic Equations for the Hydrodynamic Parameters of the Bubbling Bed Model minimum fluidization velocity bubble rise velocity with respect to the emulsion phase bubble rise velocity bubble volume fraction volume fraction of solid in bubbles volume fraction of solid in cloud-wake weight fraction of solid in bubbles weight fraction of solid in cloud-wake
6Yc
mc =
(1 - 6)(1 - emf) me = 1 - mb - m, (1 - 6)(1 - "f) 'Ye = me
weight fraction of solid in emulsion volume fraction of solid in emulsion interchange coefficient between bubble and cloud-wake phases
interchange coefficient between cloud-wake and emulsion phases
(200-400 mm) decreases with the temperature rise (Mii et al., 1973). On the contrary, the bubble size in the bed with the large particle (3.2 mm) did not decrease under the elevated temperature condition (Sittiphong et al., 1981). Park et al. (1969) measured the bubble size in a 10 cm diameter fluidized bed of 70-450-pm coke particles at room temperature. The bubble height measured by electroresistivity probe signals was much larger than our results observed under the gasification condition. Therefore, it might be concluded that the bubble size in the bed of 500-590-pm coal char particles decreases as the bed temperature increases.
Evaluation of the Performance of the Fluidized Bed The conversions of carbon dioxide and char were evaluated by use of the thermogravimetricallyobtained kinetic equation and the bubbling bed model (Kunii and Levenspiel, 19691, where solids were assumed to be completely mixed within the bed. In this model, all the hydrodynamic properties of the bed are expressed as functions of a single parameter, the effective bubble size, db. Table I summarizes the equations required for the model. The calculation procedure which evaluates the conversions of both gas and solid for first-order reactions of the gas-phase component by the bubbling model was reported (Kunii and Levenspiel, 1969). Since the kinetic expression obtained in this series of the investigation was nonlinear and includes the effect of the reactant and the product inhibitions, the conversions were evaluated by numerical calculation. The kinetic study presented in the preceding paper gives the following rate equation for the carbon conversion.
This equation is rewritten for the gas concentration, d[COzl --dt
~l[COZl PYC -(l 1 + k2[C02] k,[CO] MB
+
-
X)
(16)
The conversions of each solid depend on the age spent within the fluidized bed. The reaction rate of each solid is thus a function of the age. Since the reaction rate obtained in the preceding paper was approximated by a linear
Table 11. Mass Balance Equation for the Bubbling Bed Model reactant gas rate esuation
reactant gas mass balance
solid conversion rate
kl[cozle (1 - X) (20) m e l kZ[COzlc ks[COIe
+
+
Table 111. Values of Parameters for the Bubbling Bed Model 3.0, 4.0,5.0 bubble diameter, cm 0.5 void fraction of bed a t minimum fluidization condition ratio of wake volume to bubble volume 0.25
function of solid conversion and the solid in the bed was assumed to be completely mixed, the reaction rate of the solids could be expressed by use of the average conversion. Table I1 summarizes the basic kinetic equations and the mass balance equations for the evaluation of the bed performance. Values of the parameters used were given in Table 111.
Comparison of Calculation Results with Experimental Results Several fluidized bed models have been proposed. Among these models, the Kunii-Levenspiel model is simple and easy to be applied to the fluidized bed simulation
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 99 and analysis. However, some special care was taken in this study. Although the original Kunii-Levenspiel model (1969) assumes that the introduced gas into the bed flows through the bed as bubbles and that the gas in the emulsion phase is stagnant, the bubble volume fraction is calculated by eq 7 where the gas flow was divided into two streams: bubble gas and incipient gas flowing through the emulsion. The calculated volume fraction of the bubble is used for eq 9-12. The underestimated bubble fraction of eq 7 will result in the overestimation of the fraction of solid in the emulsion phase and subsequently the underestimation of the left side of eq 20. As an example, when uo= 6ud, the amount of gas consumed was about 1.2 times as large as that of solid conversion, since the underestimation of the solid conversion increased the conversion of gas. In such reaction systems as above, where the solid in the bed is consumed, the fluidized bed model should give the stoichiometrically consistent material balance between the consumptions of both solid and gas. To achieve this consistency, a modification was made for the bubble volume fraction in the Kunii-Levenspiel model. The gas was assumed to flow through the bed only as bubbles and the volume fraction of the bubble, 6, was evaluated by modifying eq 7 as
This modification led to consistent reaction amounts between the gas and solid phases. The calculation was conducted by varying the bubble diameter as an adjustable parameter. The effects of the bubble size on the conversions of the solid and gas are shown in Figure 4. The bubble size, which well explains both solid and gas conversions, is equivalent to the observed bubble size at the middle height of the bed. Chavarie and Grace (1975a,b) analyzed the experimental results by the bubbling bed model (Kunii and Levenspiel, 1969) and reported that the experimental data could be well explained by using the bubble size measured at the middle height of the bed. As pointed out in the preceding paper, the gasification rate equation was not entirely expressed as first order to solid conversion. Rate equations derived from the slopes at the different solid conversion levels were also used for the simulation. The rate equation derived from the slope at X = 0.35 could well express the experimental results of the laboratory-size fluidized bed gasifier, and the value of the solid conversion, X = 0.35, corresponds to the experimentally obtained solid conversion in the fluidized bed gasifier. The rate equation from the slope at X = 0.15 and 0.50 resulted in about 20% and 30% lower conversions of both solid and gas, respectively. Therefore, the rate constants were required to be evaluated by selecting the conversion level of carbon. Squires (1961) analyzed the gasification data obtained by May et al. (1958) and discussed the difference between the gasification rate observed in the fixed bed and that in the fluidized bed. He stated that the intensive solid circulation between the oxidizing and the reducing zones in the fluidized bed gasifier might increase the reactivity of the surface of the carbon particles, and this effect might be more clearly observed as the reaction temperature increases. The further investigation concerning this effect under a higher temperature condition than that in this investigation will be presented in a later paper by Matsui et al. As described above, the gasification rate equation was thermogravimetrically obtained from the conversion-time
curves at the different levels of carbon conversion, and successfully the equation could explain the performance of the fluidized bed gasifier. It might be concluded that the basic kinetic equation from the conversion-time curves by the thermogravimetric analysis is useful to predict the carbon and carbon dioxide conversions by selecting the carbon conversion level to be used for the derivation of the rate equation. The C-H20 gasification system might be discussed on the same context as the C-C02 system, since the C-H20 system is in many respects analogous to the C-C02 system. Therefore, the results of this study show that it is useful for the design basis of the fluidized bed gasifier to use the thermogravimetrically obtained data taken for the identical coal char with that gasified in the fluidized bed. Conclusion The char gasification by carbon dioxide was conducted in the continuous fluidized bed reactor. The continuous pyrolysis of the same sample was also carried out in the nitrogen stream to evaluate the amount and the composition of the gas produced by the pyrolysis. The bubbling bed model was modified to give the stoichiometrically consistent material balance between the gas and solid consumptions. The measured conversions of both carbon and carbon dioxide by the gasification reaction could be well explained by the calculation results obtained by using the bubbling bed model and the thermogravimetrically obtained kinetics. The best calculation results were obtained by using the bubble size observed at the middle height of the bed. Acknowledgment
D. K. thanks the Ministry of Education, Science and Culture, Japan, for Grants in Aid for Energy Research (56040005, 57040006, and 58040009). Nomenclature a = time delay between two identical bubble signals, s b, b’= width of the signal from the electroresistivity probe, S
[CO,]b, [CO,],, [CO,], = concentrations of carbon dioxide in the bubble, cloud-wake, and emulsion phases, respectively, mol/cm3 [colt,, [co],, [co],= concentrations of carbon monoxide in the bubble, cloud-wake, emulsion phases, respectively, mol/cm3 D = diffusion coefficient, cm2/s db = bubble diameter, cm d h = bubble height, cm d = particle diameter, cm = weight fraction of carbon g = acceleration of gravity, cm/s2 h = height, cm k , = rate constant in the Langmuir-Hinshelwood-type rate equation, l / s k,, k3 = constants in the Langmuir-Hinshelwood-type rate equation, cm3/mol (&,c)b, (Kce)b= gas interchange coefficient between bubble and cloud-wake and cloud-wake and emulsion, respectively,
8
1 = distance between two aligned tips, cm MB = molecular weight of carbon, g/mol mb, m,, me = fraction of bed solid present in bubble, cloudwake, emulsion phases, respectively n = bubble frequency, l / s uo = superficial gas velocity, cm/s umf= minimum fluidization velocity, cm/s v b = volume of bubble, cm3
I n d . Eng. Chem. Res. 1987, 26, 100-104
100
V , = volume of wake, cm3 X = carbon conversion Xcop = conversion of carbon dioxide Greek Letters
Yb,.yo ye = volume fraction of solids in bubbles, in cloud-wake,
in emulsion phases, respectively 6 = volume fraction of bubble cmf = void fraction at minimum fluidization condition
= viscosity of gas, g/cm/s pg, p s =
density of gas and solid, respectively, g/cm3
Registry No. COz, 124-38-9.
Literature Cited Caram, H. S.; Amundson, N. R. Ind. Eng. Chem. Process Des. Deu. 1979,18, 80-96. Chavarie, C.; Grace, J. R. Ind. Eng. Chem. Fundam. 1975a, 14, 75-79. Chavarie, C.; Grace, J. R. Ind. Eng. Chem. Fundam. 197513, 14, 79-86. Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: London, 1963. Haggerty, J. F.; Pulsifer, A. H. Fuel 1972,51, 304. Gibson, M. A,; Euker, C . A,, Jr. Paper presented a t the 68th AIChE Annual Meeting, Los Angeles, CA, 1975. Johnson, J. L. Adv. Chem. Ser. 1974,131,145. Kato, K.;Wen, C. Y. Chem. Eng. Sci. 1969,24,1351-1369.
Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969. May, W. G.; Mueller, R. H.; Sweetser, S. B. Ind. Eng. Chem. 1958, 50, 1289. Mii, T.; Yoshida, K.; Kunii, D. J . Chem. Eng. Jpn. 1973, 6, 100. Nagashima, I.; Yamamoto, N.; Fujikawa, T.; Furusawa, T.; Kunii, D. Kagaku Kogaku Ronbunshu 1977,3,236-242. Otake, T.; Tone, S.; Kawashima, M.; Shibata, T. J . Chem. Eng. Jpn. 1975,5, 388-392. Park, W. H.; Kang, W. K.; Capes, C. E.; Osberg, 0. L. Chem. Eng. Sci. 1969,24,851-865. Rowe, P. N.; Masson, H. Trans. Inst. Chem. Eng. 1981,59,177-185. Sitthiphong, N.; George, A. H.; Bushnell, D. Chem. Eng. Sci. 1981, 36, 1259. Squires, A. M. Trans. Inst. Chem. Eng. 1961,39,3. Sunderesan, S.;Amundson, N. R. Chem. Eng. Sci. 1979,34,345-354. Tarman, P.; Puwani, D.; Bush, M.; Talwalker, A. R&D Report 95, Interim Report 1 to the Office of Coal Research, Period of Operation May 1973-June 1974. Tone, S.; Seko, H.; Maruyama, H.; Otake, T. J . Chem. Eng. Jpn. 1974,7,44-51. Ueyama, K.; Miyauchi, T. Kagaku Kogaku Ronbunshu 1976, 2, 430-431. Weimer, A. W.; Clough, D. E. Chem. Eng. Sci. 1981,36, 549-567. Wen, C. Y.; Yu, Y. H. AIChE J . 1966, 12,610. Yoshida, K.; Kunii, D. J. Chem. Eng. Jpn. 1974,7,34-39. Received for review April 9,1984 Revised manuscript received March 5, 1986 Accepted May 10: 1986
Design Calculations for Multiple-Effect Evaporators. 1. Linear Method Richard N. Lambert and Donald D. Joye* Department of Chemical Engineering, Villanova University, Villanova, Pennsylvania 19085
Frank W.Koko Department of Chemical Engineering, Bucknell University, Lewisburg, Pennsylvania 17837
A calculational procedure useful in the design of multiple-effect evaporator systems is presented in this work. This algorithm reduces the series of nonlinear algebraic equations that govern the evaporator system to a linear form and solves them iteratively by a linear technique, e.g., Gaussian elimination. The algorithm is simple, easy to program, inherently stable, and virtually guarantees convergence, thereby eliminating the biggest problems with general nonlinear methods. Boiling point rise and nonlinear enthalpy relationships are included and require only a knowledge of their functions in temperature and composition. These relationships are obtained by curve fitting or interpolation. For a given number of stages, the calculational procedure computes design variables such as area (or area ratios between effects), externally supplied steam rate, stage temperatures and flows, etc. Such results are directly useful in design analysis and economic optimization programs. Evaporators are widely used in the chemical industry to concentrate solutions and recover solvents. By multiple staging of evaporator units, the amount, and therefore the cost, of externally supplied steam can be reduced. Depending upon the evaporator capital cost (determined primarily by size or heat-transfer area), the number of units in the series, and the steam cost, a minimum cost design can be determined. The economic analysis depends on a mathematical model of the evaporator train which is solved for specified design variables. The mathematical model involves nonlinear algebraic equations, which have proven both hard to teach and difficult to solve. In this work we present a calculational procedure to compute *Author t o whom correspondence should be addressed.
0888-5885/87/2626-0100$01.50/0
evaporator size given inlet and outlet conditions. The calculational procedure is simple enough to be useful in the classroom, yet stable and accurate enough to be useful as a design tool. The classical approach for the solution of the evaporator series is the trial-and-error method discussed in many textbooks and handbooks (Foust et al., 1980;Geankoplis, 1983; Perry et al., 1984; McCabe et al, 1985). In this technique, the temperature driving force, which is the temperature difference between steam chest and boiling liquid in the evaporator, is first estimated; then the evaporator heat exchange area of each stage is calculated. Iterations are then performed changing the estimated temperature difference of the previous trial until some restriction on the design parameters is met, usually that 0 1987 American Chemical Society
