170
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Vacuum Steam Stripping of Volatile, Sparingly Soluble Organic Compounds from Water Streams Edgar A. Rasquln, Scott Lynn,' and Donald N. Hanson Department of Chemical Engineering, Unlversity of Cellfofnla, Berkeley, California 94 720
A mathematical model was used to study the effect of pressure, steam flow, and column length on the steam stripping of volatile organic solutes from water. It was found that, for a given inlet water temperature, there exists an optimum pressure of operation at which the steam flow required for effective stripping is a minimum. This pressure is the vapor pressure of water at feed temperature. In addition, the degree of stripping was found to depend almost completely on column length and to be insensitive to steam flow above the minimum amount required to achieve stable operation of the stripper. Saturated aqueous solutions of n-butyl acetate (6300 ppm) and diisopropyl ether (6900 ppm) at 30 OC were used as representative systems. At these concentrations of solute, the most economical method of operation is obtained by carrying out the process at a column pressure high enough to allow condensation of the effluent vapor with cooling water, using heat interchange between the entering and leaving water streams if necessary.
Introduction In chemical plants it is common to find water streams that contain small amounts of organic substances. These substances must usually be removed from the water for environmental or economic reasons. A frequent approach to this problem is extraction with a relatively volatile organic solvent, which, in turn, produces an effluent water saturated with the solvent. If its concentration is significant, this solvent must then be recovered from the aqueous stream. For example, phenolic compounds are extracted from the quench water in the Lurgi coal gasification process using diisopropyl ether (Phenosolvan process: Wurm, 1969; Beychok, 1974). Butyl acetate is an alternate solvent. Solvent recovery is accomplished through a three-step process. First, the solvent is stripped from the aqueous stream by an inert gas. Second, the solvent is absorbed from the gas by phenol, and the phenol-solvent mixture is sent to the main separator for phenol and the organic solvent. Third, the gas stream is scrubbed of phenol by the water stream entering the plant and is reused. A simpler process for recovery of the dissolved solvent from the water stream leaving the extraction unit is steam stripping (Earhart, 1975; Mulligan and Fox, 1976). However, in the previous work no particular consideration was given to optimizing the operation of the steam stripper; it was assumed to operate at 1 atm. In the analysis that follows it will be shown that operation at a lower pressure frequently offers attractive advantages over atmospheric pressure operation, and that design of such processes can be based successfully on simple procedures. The present work is thus a study of the removal of sparingly soluble, volatile organic liquids from solution in water by means of vacuum steam stripping in packed towers. The study deals with the two solvents named above, which are sometimes used for phenol extraction, but the conclusions derived apply to the stripping of other organic substances having comparable volatilities and solubilities in water. A similar investigation of processes for degassing such components as COz, 0 2 , and Nz from water was done by Rasquin et al. (1977). The same mathematical approach has been taken in this work. A model of the packed column has been utilized to study the effect of the different operating parameters: pressure, steam flow, and column length. 0019-7874/78/1017-0170$01.00/0
Modelling Procedure The packed tower was treated as a differential contactor whose operation could be expressed by the following equations: interphase flux for the dissolved organic component
gas-phase water concentration PW0
yw = -xw* P component mass balances d(Lxi) - d(Vyi) dz dz d(Lxw) - d(Vyw) dz dz
(3)
enthalpy balance d[L(HL,iXi + H ~ , w ~ w ) l d[V(Hv,iyi + Hv,w~w)I (4) dz dz interphase heat flux d[L(HL,iXi + H ~ , w ~ w = ) l -ha(TL - Tv) dz
(5)
pressure drop
+
-d=P
ot10PLV2Tv(yiMWi ywMWw)
dz
P
auxiliary equations Xi
+ xw = 1
Yi+Yw=1
For analysis the column was divided into a number of differential elements, and at each point nine equations were used. The variables calculated a t each point were TL, Tv, P, L, V, and two mole fractions in each of the two phases. In writing the equations, the assumption was made that the mass transfer is controlled by liquid-phase diffusion. The further assumption was made that the heat-transfer resistance was entirely in the liquid phase because of the small heat capacity of the vapor stream. Thus the composition and temperature 0 1978 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Table I. Values of Less Common Parameters Used in Steam-Stripping Calculations nvstem
parameter
Kow ha AHv @ 30 O D @ 30 "C Po @ 30 O C
C
DIPE
BuAc
0.018 s-l 2.0 X lo6 J/s m3 K 35.4 X lo6 J/kg-mol 9.1 X m2/s 25.5 kN/m2
0.018 2.0 X lo6 J/s m3 K 28.6 X lo6 J/kg-mol 8.8 X mz/s 2.25 kN/m2
of the vapor at any point in the column were assumed to be the values for the vapor a t the interface, and the vapor phase was taken as saturated a t interface conditions. The pressure-drop equation used is the correlation developed by Leva (1954). The vapor temperature a t the bottom was set a t the saturation temperature of water and the vapor at that point was assumed to be pure water. The values of the less common parameters used in the calculations are listed in Table I. The equations were expressed in terms of the variables chosen, linearized, and approximated by their finite-difference forms. The resulting set of equations, together with the appropriate boundary conditions, was solved by the method of Newman (1968) for coupled ordinary differential equations. Details of the procedure are given by Rasquin (1977). During the present study, the liquid to be treated was assumed to enter the vacuum column at 30 "C. However, the conclusions reached are applicable across a wide range of feed temperatures. The superficial liquid mass velocity in the column was set a t 0.7535 kg-mol/m2-s (10 000 lb/ft2.h). The value of the mass-transfer coefficient for the dissolved component was obtained from the correlation by Sherwood and Holloway (1940). The mass-transfer coefficient was obtained for 2-in. Raschig rings but can be considered typical for the same size packing in other forms such as Pall rings. The heat-transfer coefficient was obtained from the ChiltonColburn analogy, using an exponent of 0.5 on the ratio of Schmidt number to Prandtl number. In all calculations, the concentration of solvent in the entering water was the saturation concentration at 30 "C. These values for butyl acetate (BuAc) and diisopropyl ether (DIPE) are 6300 and 6900 ppm, respectively. Activity coefficients for the dissolved components were obtained from mutual solubility data correlated with the van Laar equation. At 30 "C and saturation concentration the activity coefficient is 925 for BuAc and 809 for DIPE. Pressure drop calculations were based on data for 2-in. Pall rings (Eckert et al., 1958). The value for the desired concentration of solvent in the purified water was taken to be 50 ppm. Process Description The process under study is similar in many ways to other steam stripping operations. However, the concept of minimum steam requirement here is considerably different from that of a classic textbook stripper, and the normal interchangeability of column length and steam flow as means for accomplishing a desired degree of stripping is much reduced. How these characteristics of the process arise can best be seen by considering operation of the process, first with no steam flow and then with increasing amounts of steam. For the process to operate a t all with no steam admission, the column pressure must, of course, be below the saturation pressure of the liquid stream a t the temperature a t which it enters. At such a pressure, as the liquid flows through the column, the organic compound will transfer from the liquid phase to the vapor phase. Because the organic compounds being considered are reasonably volatile and because they exhibit very large activity coefficients a t their typical liquid concentrations, they resemble insoluble gases to a large extent.
171
It is helpful to think of the vapor stream rising in the column as a light organic gas saturated with water at the local temperature. If no steam is admitted a t the bottom, the amount of solute that transfers into the vapor phase is primarily dependent on the energy balance. The energy to vaporize the solute, and to vaporize the water that accompanies it, must come from the liquid. As a result the liquid temperature falls rapidly as the liquid flows down through the column, even at the low organic concentrations being considered here. As the temperature drops, the vapor pressure of water drops, the local concentration of the organic component in the vapor phase rises, and the driving force for transfer of the solute from the liquid drops, in general effectively stopping the process a t levels of solute in the liquid that are unacceptably high. Adding energy by heating the incoming liquid is unavailing. Consideration shows that this energy is largely lost a t the top of the column in simple flashing of the liquid, and is thus not available further down in the column. On the other hand, if the process is operated so that the vapor and liquid flow concurrently, the vapor formed when the liquid flashes effects some stripping as the liquid flows down the column. However, the amount of vapor that must be generated in order to achieve a high degree of stripping of the solute is so large that the energy requirements are prohibitive. Rasquin et al. (1977) show that this process is economical for degassing COa and 0 2 from water; in that particular case the concentration of the dissolved light components is an order of magnitude or more smaller than the concentration of organic compounds being considered here. Returning to consideration of the countercurrent process, one may first assess the result of the addition of a small amount of steam at the bottom of the column. Since the liquid stream at this point is substantially subcooled relative to the column pressure, the steam immediately condenses, accomplishing nothing but an increase in the effluent liquid temperature commensurate with the amount of steam fed. As the amount of steam is increased this temperature rises, until finally it reaches the saturation temperature of water at column pressure. Any substantial increase in steam above this amount causes essentially the entire steam flow to propagate completely through the column, and the heating of the liquid stream takes place at the top of the column rather than a t the bottom. The amount of steam flow associated with this mode of operation is, in general, sufficient to accomplish any reasonable degree of stripping. The relative volatility of the solute is high, the driving force for mass transfer is therefore more than adequate, and hence any further increase in steam flow past this value is of only marginal usefulness in increasing the mass transfer. The degree of stripping achieved is then almost wholly dependent on the length of the column. Since the solutions under consideration are quite dilute, the source of the steam will make little difference to the behavior of the column; the steam may be sparged in directly or generated in a reboiler. Results a n d Discussion The anticipated variations in column performance with steam flow are shown in Figure 1 as calculated for stripping butyl acetate from water in a 4-m column operating a t 5.1 kN/m2 (38 Torr). At low steam flows the stripping achieved is almost the same as that obtained with no steam. As steam flow is increased past a critical amount the degree of stripping increases greatly, but then, at still higher steam flows, the stripping is again only slightly affected by changes in the amount of steam. Figure 2 shows the vapor flow profile through the column for four values of steam flow and illustrates how the profile is altered strikingly by small changes
172
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978 10,000
i
i
I.
Feed temp 3 0 T Feed
C O ~ C6300ppm
P
-
1000 -
\,/Equation
19)
-
I
-
?
.E
0.01
-
-
1
t
I c
-
-
1007
c
z
t
1 00
0.010 0.020 Steom flow imoies/mole feed!
0.030
Figure 1. Effect of inlet steam flow on column operation.
Outlet BuAc: 950 ppm
O
1 u 4.5
5.0 5.5 Column pressure i k N / m 2 )
6.0
Figure 4. Effect of pressure on the minimum steam flow. several column pressures are shown. The curves for 4.5 kN/m2 and 4.23 kN/m2 (the vapor pressure of water at 30 "C) coincide. It is apparent that column pressure has an effect on the value of the minimum steam flow. However, it is also apparent that column pressure has little effect on the degree of stripping obtained if the column is operated a t any steam flow reasonably greater than the minimum at a given pressure. This result stems from the fact that the partial pressure of BuAc in the vapor is low even at the highest column pressure considered, and further reduction through lowering column pressure has little effect since the diffusion is liquid-phase controlled. The minimum steam flow is determined almost entirely by the energy requirements. Calculations have shown that it can be closely estimated from the following simple energy balance. steam to heat entering (m.ii;:iinimum) = water from inlet temp
(
0.0080 '3305ppm
to saturation a t the bottom of the column
Vopor f l o w lmoles/rnole f e e d !
Figure 2. Effect of inlet steam flow on vapor-flow profile in column and on effluent concentration of butyl acetate.
1 steam to provide\
1 steam
to saturate the \ desorbed solute a t
the latent heat \
of vaporization of the solute
'
)
\
the top of the column a t inlet temperature
'
(9)
401 0.010
'
0.014
I
I
0.018
'
0.022
'
0.026
Steom f l o w (moles/moie feed)
Figure 3. Effect of inlet steam flow on the stripping of n-butyl acetate from water.
in the amount of stripping steam supplied to the column. It is apparent that a minimum steam flow exists above which column operation is satisfactory, but that steam flows much greater than the minimum are not productive in increasing the stripping of the butyl acetate. Optimum operation of the column thus entails use of a steam flow near the minimum, and the determination of this quantity is important for design calculations. Figure 3 again shows the effluent concentration of BuAc for a 4-m column as a function of steam flow in the region of probable column operation. Curves for
The pressure at the bottom of the column is not known beforehand because of the unknown pressure drop in the column. Hence the amount of steam required to heat the entering water to saturation must be calculated by iteration. In practical column designs, however, the pressure drop is a small fraction of the total pressure. Figure 4 shows the relation between the true minimum steam flow, as determined from Figure 3, and column pressure. It also shows the minimum steam flow estimated from eq 9. Agreement is good throughout the region of higher pressure. However, the estimated minimum flow (eq 9) becomes much too high as column pressure nears the vapor pressure of water at inlet liquid feed temperature, approaching an infinite value there. This result stems from the approximation in eq 9 that the vapor phase leaving at the top of the column is saturated with water vapor at the inlet temperature. In the more exact calculations it is found that the vapor leaves the top of the column either slightly above or below the feed temperature, depending on column pressure and the amount of steam flow. At steam flows near minimum, however, the vapor leaves below feed temperature, and as a result, the sharp rise predicted by eq 9 does not occur. However, at column pressures a t or above the pressure at which eq 9 displays a minimum, the estimated minimum steam flow is only about 15%above
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978 173
\‘iq
DIPE
P r e s 5.1 kN/rnZ Inlet Concentrotion
i
C o l u m n Lenqlh ( m i
Figure 5. Effect of column length on the stripping of n-butyl acetate and diisopropyl ether. the true value. The difference is caused by assuming that all of the steam flows to the top of the column before any of it condenses. The value predicted by eq 9 is thus conservative, and can be used satisfactorily as a design value without the need for the complex column calculation. For the region of low pressures, in which the values predicted by eq 9 swing upward with decreasing pressure, a reasonable value can be obtained by simply taking the minimum in the curve. Determination of minimum steam flow for other column lengths shows only what would be expected from eq 9, a small increase with increasing length due to the increased pressure drop through the column. The degree of stripping of both BuAc and DIPE from water is shown in Figure 5 as a function of column length at a column pressure of 5.1 kN/m2 (38 Torr). The curves show that the concentration of either solvent in the effluent water decreases rapidly with increasing column length. However, Figure 5 again shows that, for a given column length, the degree of stripping obtained increases little with increasing steam flow; for diisopropyl ether, increased steam flow has essentially no effect. The lack of sensitivity of the degree of stripping to the steam flow is, in general, due to the high relative volatility of the dissolved solute. DIPE is substantially more volatile than BuAc. These results show dramatically the futility of trying to improve stripper performance for such systems by increasing steam flow. Operation should be conducted with the minimum amount of steam necessary to achieve stable stripper operation, and it is clear that the only way to achieve a particular degree of stripping is through a column of suitable length. Examination of Figure 5 shows that both lines for stripper performance are essentially straight and extrapolate to zero stripping a t zero column length, indicating that a relatively simple calculation of the degree of stripping for various column lengths is possible. Equation 1 can be integrated assuming all terms except x i and z to be constants and the appropriate average value of ( x i - x i * ) to be the log-mean average. For a system as volatile as DIPE, very accurate results are obtained by simply assuming that the interface concentration, x i * , of DIPE in the liquid is zero. For BuAc, use of a zero interface concentration shows a required length of 3.6 m to reach 50 ppm, whereas the detailed column calculations show 4.2 m. Use of a log-mean driving force in eq 1gives a required length of 4.6 m, which is conservative, and accurate enough for preliminary design. Finally, consideration must be given to the condensation of the overhead vapor from the column. For a feed a t a given temperature, the calculations done here show that the steam requirement is minimized by operation of the column at the
vapor pressure of water at feed temperature. Operation below the optimum pressure results in flashing of the feed and, in effect, operation at the vapor pressure of the feed at a new, lower temperature; the steam requirement remains essentially the same. On the other hand, operation above the optimum pressure requires additional steam; for an increase of about 20% the change is small, but a t higher pressures the steam requirement is increased significantly. However, if the column is operated with the feed near or above the temperature of the available cooling water, the overhead vapor cannot be condensed without compressing it. For the case of highly volatile dissolved compounds such as C02 or butane, compression of the overhead vapor or refrigeration is necessary in any event, and an economic balance between compression cost and increased steam cost must be used to determine the optimum column pressure. For dissolved solvents such as butyl acetate or diisopropyl ether the attractive alternative is operation of the column a t a higher pressure, specifically the pressure at which the overhead vapor can be condensed with the available coolant. For the two solvents considered here, and assuming condensation at 30 O C , the column pressure would have to be 6.4 kN/m2 (48 Torr) for BuAc and 30 kN/m2 (223 Torr) for DIPE. Steam requirements could be minimized by exchanging heat between the effluent liquid and the incoming feed to raise the feed temperature as close as economically feasible to the boiling point of water at column pressure. While this use of heat exchange would allow operation a t essentially any pressure, higher pressures would require a higher temperature excursion by the liquid feed and a higher duty in the exchanger. The column diameter is not affected significantly by the pressure of operation. I t is determined by L and the total liquid flow rate in the column since vapor velocities are small even a t the lowest pressures of interest. The optimum operating pressure will thus be determined by minimizing the sum of the costs of the condenser and the heat exchanger for heating the feed with the effluent water.
Acknowledgment One of the authors (E.A.R.) is grateful to the Hydrocarbon Research Fund of Venezuela (FONINVES) for their financial support. Nomenclature ha = liquid-phase heat-transfer coefficient, J/m3-s-K H = molal enthalpy, J/kg-mol KOLU = overall liquid phase mass-transfer coefficient, s-1 L = superficial liquid mass-velocity, kg-mol/m2.s MW = molecular weight P = column pressure, N/m2 Po = vapor pressure, N/m2 T L = liquid temperature, K Tv = vapor temperature, K V = superficial gas mass-velocity, kg-mol/m2.s x = liquid mole fraction x * = liquid mole fraction a t equilibrium with the vapor phase y = vapor mole fraction z = columnlength, m Greek Letters a,/3 = constants of pressure drop equation PM = molar liquid density, kg-mol/m3
Subscripts i = dissolved organic component w = water V = vapor phase L = liquid phase
174
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Literature Cited
Rasquin, E. A., Lynn, S., Hanson, D. N., Ind. Eng. Chem. Fundam., 16, 103
Beychok. M. R., "Coal Gasification and the Phenosolvan Process", presented at the 168th National Meeting of the American Chemical Society, Atlantic City, N.J., 1974. Earhart, J. P., Ph.D. Thesis, University of California, Berkeley, Calif., 1975. Leva. M., Chem. Eng. Prog. Symp. Ser., 50 (lo),51 (1954). Mulligan, T. J., Fox, R. D.,Chem. fng., 83 (22),49 (1976). Newman, J., Ind. Eng. Chem. Fundam., 7 , 314 (1968). Rasquin, E. A., M. S. Thesis, University of California, Berkeley, Calif., 1977.
Sherwood, T, K,, ~
(1977). ~ , A,
L,, T l
~
i ~lnst, Chem, ~~ ~
,~36,39-7~ ~
(1940). Wurm, H.J., Gluckauf, 104 (12),517 (1968).
Received f o r review April 11,1977 Accepted April 20,1978
Modeling of Thermal Cracking Kinetics. 3. Radical Mechanisms for the Pyrolysis of Simple Paraffins, Olefins, and Their Mixtures K. Meenakshi Sundaram and Gllbert F. Froment' Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium
Radical reaction schemes for the cracking of ethane, propane, normal and isobutane, ethylene, and propylene were set up. The kinetic parameters of these schemes were determined by fitting experimental data obtained under nonisothermal and nonisobaric conditions in a pilot plant. The set of continuity equations for both molecular and radical species was integrated using Gear's algorithm for stiff differential equations. The reliability of the parameters was tested by simulating the cracking of binary and ternary paraffinic mixtures. A satisfactory fit of the results of mixtures cracking was obtained with a reaction scheme derived from the superposition of the schemes for single-component cracking.
Introduction Thermal cracking reactions mainly proceed via free radical mechanisms (Laidler, 1965). Many specific mechanisms have been proposed to explain the cracking of simple molecules. The majority of the mechanisms have been deduced from data obtained at subatmospheric pressures, low temperatures, and low conversions. Moreover, they were derived through the pseudo-steady-state concept which assumes the radical concentrations to be constant. This condition is not fulfilled in reality, neither in an industrial reactor nor even in an isothermal bench scale reactor (Edelson and Allara, 1973). For these reasons, at elevated temperatures the uncertainties in the parameters are high and sometimes attain orders of magnitude. In the present paper radical schemes for the cracking of normal and isoparaffins, olefins, and their mixtures are developed. The determination of their kinetic parameters is based upon experiments conducted in a pilot reactor under conditions as close as possible to those used in industry (Van Damme et al., 1975; Froment et al., 1976a,b, 1977). Continuity Equations Free radical reactions involve initiation, propagation or H-abstraction, and termination steps. The continuity equation for t h e j t h species in an isothermal reactor with plug flow may be written d F, dz
= -0Rj = -0
N
,E (sijri) 1-1
For nonisothermal and nonisobaric conditions the reaction rate ri has to be computed for the experimentally measured 0019-7874/78/1017-0174$01.00/0
gas temperature and total pressure profiles. It is assumed that the reactions are elementary and therefore the order corresponds to the molecularity. Also, the rate coefficients obey the Arrhenius relationship within the temperature range covered. The first-order differential equations represented by eq 1 are usually nonlinear and coupled, and hence analytical solutions are not possible. The concentrations of the radicals are much lower than those of the molecular species (e.g., vs. 10-2 M) so that the eigenvalues of the differential equations differ by orders of magnitude. With classical integration methods, an extremely small step size has to be used to ensure the stability of the numerical integration. To overcome the mathematical difficulties, pseudo-steady state for radical concentration has been assumed. This assumption allows the differential equations for the radicals to be replaced by algebraic equations (Snow, 1966; Pacey and Purnell, 1972b; Blakemore and Corcoran, 1969). In a recent communication the present authors (to be published) have quantified the errors induced by this assumption and shown that for reliable parameter estimates, the complete integration for the continuity equations for both molecular and radical species for the entire conversion range is essential, because the radicals vary significantly and continuously with conversion. Of the many currently available methods for integration of stiff differential equations (see Aiken and Lapidus, 1974, 1975a,b; Seinfeld et al., 1970; Sena and Kershenbaum, 1975a1, the one proposed by Gear (1971) seems to emerge. It is also adopted in this work. Gear's method can be applied to any degree of stiffness and allows for any degree of accuracy of integration with moderate computer time. It essentially uses the Adams-Moulten predictor-corrector method, which is an implicit technique. 0 1978 American Chemical Society
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