Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 593-598
593
Effect of Overdesign on the Operability of Distillation Columns Wayne R. Fisher, Michael F. Dohetty, and James M. Douglas’ Department of Chemical Engineering, Universi@ of Massachusetts, Amherst, Massachusetts 0 1003
Overdesign of the vapor capacity of a simple binary distillation column generally has a much greater effect on the range of operability of the column than overdesign of the number of trays. A universal graph is presented which provides an estimate of the overdesign factors required for columns with widely varying feed compositions. This graph can be used for all ideal columns with moderate to high purity splits. The only information required is the tlme-averaged and minimum anticipated feed compositions.
Introduction The final design of process equipment always includes a certain degree of overdesign to ensure feasible operation over a range of operating conditions. Also, overdesign factors are used to offset the effect of uncertainties in design model parameters, cost model parameters, and market estimates. The primary incentive to incur the additional capital costs associated with overdesign is to offset the very high operating costs resulting from anticipated process disturbances and possible errors in model parameters. The final degree of overdesign selected for each piece of equipment in a flowsheet can then have a profound effect on the profitability of a chemical process. Three systematic approaches to the selection of overdesign factors have been proposed in the recent literature. The most intuitively appealing approach is to select the overdesign factors which maximize the expected profit of a process operating at base-case conditions but using model parameters with known probability distribution, as suggested by Kittrell and Watson (1966). Malik and Hughes (1979) also consider the effect of economic model and process specification uncertainties. While pointing out that the proper solution may be computationally unfeasible, they suggest simplified limiting cases. An alternative procedure to ensure feasible operation is to optimize the flowsheet design while assuming “worst-case” conditions for all model parameters and process disturbances, as proposed by Nishida et al. (1972,1974). Finally, Swaney and Grossmann (1982) suggest that there is a trade-off between the (capital) cost of overdesign and the range of model parameters and process disturbances for which the process specifications can be satisfied. The procedure generally followed in industry, however, is to estimate the profitability of a process operating at some base-case conditions, using nominal values for all model parameters. Empirical overdesign factors are then applied to each piece of process equipment to ensure operability. If the process still appears to be profitable, more rigorous design and economic models are used. The effect of parameter uncertainty is not then considered until the most rigorous design models are developed and the process profitability is assured. The purpose of this article is to present a short-cut method to quantitatively assess the degree of overdesign appropriate for simple binary distillation columns at the preliminary design stage. Specifically, we would like to estimate the degree of overdesign required for a column whose feed composition varies significantly from base-case conditions. Column Classification The most convenient classification of binary distillation columns is the number of product streams exiting from the 0196-4305/85/1124-0593$01.50/0
column. A product stream is defined to be any stream whose minimum purity is determined from marketing or environmental considerations. Exceeding the purity specifications on these streams, however, generally results only in unnecessary operating costs. Non-product streams, on the other hand, are either used in the process (recycled or downstream) or purged as fuel and waste byproducta. Specification of the purity of each of these streams is a design decision and requires the solution of an optimization problem. Thus, a cost must be associated with the amount of impurity in the non-product stream and compared to the operating and capital costs required to increase this stream purity. For example, these costs may include the loss of valuable product in a waste stream or the incremental costs associated with recycle of an inert or byproduct with a reactant recycle stream. Design and Operating Considerations Two-Product Columns. The optimal design of a binary column with fixed feed composition and purity specifications on both product streams is discussed in detail by Peters and Timmerhaus (1980). The optimum reflux ratio that minimizes the sum of the capital and operating costs for the column is generally in the range of 1.1to 1.5 times the minimum reflux ratio for the separation. As the composition of the feed to the fixed column varies, the optimum reflux ratio is that which just satisfies the two product specifications. Under-refluxing results in one or both produch being unmarketable. Over-refluxing may guarantee product purities, but it results in unnecessarily large operating costs. One-Product Columns. Optimization of the design of a one-product column requires the selection of the column reflux ratio and the purity of the non-product stream. The cost associated with the loss of valuable product into the non-product stream must be estimated and is dependent upon the type of non-product stream considered. For waste streams, the full value of the product is lost. For reactant recycle streams, little product may actually be lost from the system, but the product acts as an inert and thus increases the capital and operating costs associated with other equipment (reactors, pre-heaters, etc.) in the flowsheet. As the feed composition to the column varies, the purity of the product stream must be maintained at its specified value. Again, however, we must select the non-product purity that minimizes the sum of the operating costs (heating, cooling, and product losses) associated with the column. Zero-Product Columns. Optimization of the design of zero-product columns requires the selection of the column reflux ratio and the purity of both non-product 0 1985 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
Table I. Column Design Specifications for Example 1 .XF = 0.50 q = 1.0 .XD = 0.99 R* = 1.2R,, x g = 0.01 a = 2.5 R,,, = 1.333 R* = 1.600 NR = 10.52 (use 11) Ns = 10.21 (use 10) For a 509” Increase in Reflux Ratio = 1.5 X 1.6 = 2.4 NR = 11 N s = 10
R,
XF,,,,,
-b;
ozr
For a 50% Increase in Number of Trays R,, = 1.6 NR = 1.5 X 11 =16 Ns = 1.5 X 10 = 15 X F , , ~ ~ 0.415
streams. Thus, the cost of poor separation for both streams
must be estiiaated. For example, a zero-product column may separate a reactant from a waste byproduct. The value of any reactant in the waste stream is lost and the recycle of (inert) byprodud with the reactant increases the costs associated with other equipment. Again, as feed composition to the fixed column varies, both stream purities must be selected to minimize the operating costs for the process.
Assessing Column Operability Modes of Column Overdesign. As the feed composition to a two-product binary column falls below its design value, the reflux ratio must increase to maintain the desired product purities. If the distillate rate remains constant &e., if the decrease in feed composition is a result of an increase in the heavy component flow rate), the vapor rate in the column must also increase. The maximum anticipated vapor rate for the column then corresponds to the lowest expected feed composition and the largest expected distillate flow rate. This vapor rate fixes the degree of overdesign required for the column’s reboiler, condenser, and tray diameter (to prevent flooding). Alternatively, we could increase the number of trays beyond that required at the base-case conditions so as to operate below the base-case reflux ratio for all anticipated feed compositions. That is, the base-case reflux ratio is achieved only a t the extreme disturbance in feed composition (xF&. The maximum anticipated vapor rate would then be calculated from the base-case reflux ratio and the largest expected distillate flow. In general, however, the degree of overdesign corresponding to this policy is much larger than that for increasing vapor rate only. We quantitatively compare these modes of overdesign in the example below. Example 1. The binary system benzenetoluene is used to compare the effect of the two policies of column overdesign on the range of operability of the column. The base-case operating conditions and design parameters are given in Table I. The base-case column design is demonstrated graphically in Figure 1using the McCabe-Thiele diagram method. If the feed composition falls below its base-case value (0.50),either the number of trays or the reflux ratio must be increased to maintain the product purities. If the number of trays is overdesigned,the feed line must always intersect the rectifying section operating line below the y-x equilibrium curve. From Figure 1, the minimum feed composition (even for infinite overdesign) for the base-case reflux ratio is 0.40. Figures 2 and 3 compare the effect of a 50% increase of the number of trays (at R* = 1.6) and a 50% increase
t p-l--m>04I
= 0.336 0
I’
I
oi
08
’ io
X
Figure 1. Base-case design using McCabe-Thiele method. __-~ -
lo-’-
m K ,
oat
‘
/
(feed Tray 16
06-
,y,v’
’041
I I
O
02
06
04
1
___L-
X
OB
10
Figure 2. Minimum operable feed composition for a 50% increase in number of trays. Feed tray is fixed at tray 16.
;&c---L 02
L 06 O BA 10
04
x
Figure 3. Minimum operable feed composition for a 50% increase in reflux ratio. Feed tray is fixed at tray 11.
of the reflux ratio (at NT* = 21). The minimum feed composition for each case is 0.42 and 0.33, respectively. It should also be noted that additional overdesign of the number of trays would result in little increase in the range of operability of the column, while increasing the reflux ratio can extend this range idefinitely. Estimate of Overdesign Factors. While overdesign of the number of trays is necessary to account for tray efficiencies, we have demonstrated that excessive overdesign has little effect on column operability. We will therefore emphasize here the effect of the overdesign of the maximum vapor capacity on column operability. The procedure presented below estimates the degree of overdesign of vapor rate required for simple binary columns given only the base-case (time-averaged) and the minimum anticipated feed compositions. The maximum reflux ratio corresponding to a fixed degree of overdesign for vapor rate can be calculated from Rm=
R*
+1 +
=:
(+)( $)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 505 Table 11. Column Design Specifications for Example 2 D = 273.0 mol/h q = 1.0 R*/R,i, = 1.2 XD = 0.9997 R,/R* = 1.1, 1.3, and 1.5 XB = 0.005 ff = 2.5 X F = 0.1 to 0.8
x; (design feed
composition)
Figure 5. Effect of design reflux ratio on the range of operable feed compositions for a fixed degree of overdesign.
0
04 06 08 xf design feed compcnition) F(
02
10
Figure 4. Increase in reflux ratio required for separation, based upon the time-average and minimum anticipated feed composition.
where R* = base-case reflux ratio, V-/ V* = overdesign factor for vapor capacity, D* = design distillate flow rate, and D = operating distillate flow rate. The range of operability for a two-product column may then be thought of as the range of feed compositions and production rates for which the required reflux ratio is less than the maximum. If the reflux ratio required for an expected feed composition is greater than the maximum, the column can be made operable only a t the expense of decreased production rate. The example below demonstrates quantitatively the effect of overdesign of the maximum vapor rate in a distillation column using this definition of operability. Example 2. The binary system benzene-toluene illustrates the effect of overdesign on column operability. The column is assumed to be a two-product column and is designed by the method of Smoker (1938) using the data shown in Table 11. The base-case feed composition is expected to change as the overall process flowsheet is optimized. For each base-case design, we would like to assess the minimum operable feed composition corresponding to an assumed degree of overdesign of the column's vapor capacity. The results are summarized in Figure 4. Each point in Figure 4 corresponds to a solution of the problem represented graphically in example 1. For each base-case feed compositioh,the design reflux ratio is taken as 1.2 times the minimum reflux ratio. The maximum reflux ratio is then calculated from eq 1for each overdesign factor (assuming D = D*).If we use this reflux ratio and the nominal number of trays, the minimum feed composition is that which just allows the product specification to be met. For example, if the base-case feed composition is xF* = 0.50,then the minimum feed composition is xF,= 0.44 for a 10% increase in reflux ratio or xFmmin = 0.33 for a 50% increase. General Overdesign Factor Plots. Figure 4 is useful for detennining the degree of overdesign required to ensure operability for a specified base-case operation and range of feed compositions for the column described in Table 11. However, the effort reuired to develop such a plot for each column in a flow sheet is greater than can be justified at the preliminary design stage. Fortunately, Figure 4 provides a good estimate of the required overdesign for a wide range of columns that can be adequately modeled using Smoker's method. Figures 5,6, and 7 show that the range of operability for a fixed increase in reflux ratio (30%) is nearly independent of the design reflux ratio, relative
xD
8
:
0.9997
R' = I 2 R,
1
'0
02
04 06 08 x; (design feed cornposi!ion)
I 10
Figure 6. Effect of relative volatility on the range of operable feed compositions for a fixed degree of overdesign.
'0
02
04 ' 06 08 x* (design feed cmpoiition)
Figure 7. Effed of design separation factor on the range of operable feed compositions for a fixed degree of overdesign.
volatility, or separation factor. The recommended ranges of design specifications for which Figure 4 may be used to assess preliminary overdesign factors for simple binary columns are as follows: 0.1 < xF* < 0.8; R* < 2R,i,; CY < 10.0; S > lo6. Therefore, we see that Figure 4 is a universal curve for a wide range of ideal binary columns. Deviations from this curve occur when the number of ideal trays is less than about 10 in either the rectifying or stripping section of the column (i.e., when xF approaches unity, when cy is very high, and/or when the required purities are fairly low). Fortunately, small columns are less costly and we can afford to use large empirical overdesign factors without much economic penalty. The cost of overdesign is only important for larger columns and, for these, the universal curves shown in Figure 4 apply. Extension to One- and Zero-Product Columns. As discussed earlier, the desired reflux ratio for one- and
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Chem. Process Des. Dev., Vol.
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24-
8
0421
'9-
\
-50%
Overdesign
($=
1.5)
\
5 f
1 0.36, 12:
O+L&-LuA 10 12 14 16
REFLUX RATIO
Figure 8. Optimization of reflux ratio for a one-product column with a fixed column design. Table 111. Design Specifications for a One-Product Column q = 1.0 xF* = 0.70 a = 2.5 XD* = 0.9997 XB* = 0.005 R/R- = 1.2 D = 273 mol/h R* = 1.143 NR = 23.1 N s = 11.2 Operating Cost Model steam cost = $4/1000 lb cooling water cost = $0.15/1000 gal heat duty = 14400 X 273 X ( R + 1)Btu/h product losses = 0.10 X $16.5/mol X (q$)
zero-product columns represents the solution of an optimization problem. If the optimum reflux ratio exceeds the maximum calculated from eq 1, we could operate the column at its maximum reflux ratio and tolerate lower nonproduct purities. Figure 8 plots the annualized operating costa as a function of reflux ratio for the one-product column described in Table 111. For reflux ratios greater than the optimum, the operating costs are dominated by heating and cooling costs (which vary linearly with R) and product losses are negligible. As the reflux ratio falls below the optimum, the column pinches at the feed tray and the bottom composition rapidly approaches the feed composition (product losses become infinite). A reasonable definition for the range of operability for one- and zeroproduct columns may then be thought to be the range of feed compositions and production rates for which the optimum reflux ratio is less than the maximum. This approach is further simplified because the optimum nonproduct purities are generally quite close to their base-case design values, even for large variations in feed composition. These columns may then be treated as two-product columns and the overdesign factors obtained from Figure 4 and eq 1 are again adequate.
Economics of Overdesign If a process appears to be profitable for preliminary designs based on nominal values of uncertain parameters and while operating at base-case conditions, we would like to assess the effect of disturbances on the total annualized cost of the process. For distillation columns, the range of anticipated feed compositions and distillate flows determines the overdesign fador of the reboiler, condenser, and column diameter by fixing the maximum vapor rate. The capital cost associated with the column can then be expected to increase by a fador of (V-/V*)", where n varies from about 0.6 to 0.8 for most cost models. If similar overdesign factors were available for each piece of equip-
089F-dr-&+ FEED COMPOSITION
Figure 9. Required reflux ratio for a two-product column under widely varying feed compositions.
ment in the flowsheet, we could then begin to assess the effect of disturbances on the profitability of the process. The time-average operating cost associated with a distillation column can also be expected to exceed the operating cost calculated for base-case operating conditions. This is demonstrated in Figure 9, which plots the reflux ratio required for a two-product column (described in Table 11)as a function of feed composition. The operating costs associated with this column are directly proportional to the reflux ratio. If the variation of feed composition is small, then the variation of reflux ratio is quite linear. As the variation in feed composition increases, this relationship becomes increasingly nonlinear and the time-average operating cost is significantly larger than the basecase value. Thus, there may be some incentive to increase the number of trays in the column in order to offset the effect of low feed compositions. For the column represented by Figure 9, little incentive exists for increasing the number of trays if the variation of feed compositions requires less than 30% overdesign on the column vapor capacity. Two-product columns exhibit the greatest degree of nonlinearity of operating cost plots because both product composition specifications must be met. One- and zeroproduct columns vary somewhat more linearly with feed composition because the nonproduct stream purities are not rigid. The time-average operating costs for these columns are thus more likely to be close to the base-case value. Again, if the degree of overdesign of vapor rate is less than about 30%, little incentive should exist for increasing the number of trays.
Conclusions It has been demonstrated that while overdesign of the number of trays for a distillation column is important to account for tray efficiencies, excessive overdesign does not significantly increase the range of operability of the column. Overdesign of the column's maximum vapor capacity, however, allows operation over a wide range of feed compositions. A procedure to estimate the appropriate degree of overdesign for a column is presented, based only upon its time-average and minimum expected feed composition. Algorithm. On the basis of work presented, the following algorithm is recommended for preliminary design of binary distillation columns with time-dependent feed compositions. (1)Prepare a preliminary design using: (a) a simple column model, (b) best estimates for model parameters (relative volatility, tray efficiencies, etc.), (c) time-average or base-case value for feed composition, and
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
73F$
Product
Recycle
Figure 10. Simplified flowsheet for a deactivating catalytic reactor system.
597
Table IV. Design Data for Deactivating Catalytic Reactor System reaction rate = r = kaCA deactivation rate = da/dt = -kDa k~ = 104/h %SOR = 0.70 cycle length = 6 months (4200 h) a = 2.0 R* = 1.2R,, ZD XB
0.999 = 0.008
tray efficiency = 0.5 latent heat of B = 15000 Btu/lb-mol
0 55 0
1000
3000 TIME (hours)
Figure 11. Time-dependentfeed compositkn for deactivating catalytic reactor example.
055
060
065
om
FEED COMPOSITION
Figure 12. Effect of feed composition on operating cost for the product/recycle column in Figure 10.
(d) heuristics for optimum reflux ratio (e.g., R*/R- = L2), fractional recoveries, etc. (2) If the process looks profitable, estimate a reasonable range for anticipated operating conditions (i.e,, X F and D).(3) Ensure column operability by estimating the appropriate overdesign for vapor rate from Figure 4 and e4 1. (4) Replace heuristics used in preliminary design with optimizations and reassess profitability. ( 5 ) Assess nonlinearity of operating cost with respect to feed composition if wide variations are expected (probably not necessary if required vapor rate overdesign is less than 30%). If operating costs become very large at low feed compositions, overdesign number of trays to reduce this effect. (6) If the process still appears profitable, develop more rigorous design models. Optimization of the process a t base-case conditions is still appropriate if the above overdesign factors are included to ensure operability. (7)Using the best design models available, w e 9 8 the effect of parameter uncertainty on operability and profitability. The method outlined above is demonstrated for a simplified reactor/separation system in the Appendix for a process with a deactivating catalytic reactor.
Acknowledgment This work was supported by the National Science Foundation under Grant CPE-8105500. Appendix Illustrative Example-Deactivating Catalytic Reactor System. The utility of the above approach is demonstrated with the following example. We would like to specify the appropriate overdesign factor for the distillation column shown in the simplified flowsheet (Figure 10). Assume that loo0 lb-mol/h of B are to be produced from a feedstock of pure A by an irreversible, first-order reaction. The initial design conversion is 70%. As the catalyst in the reactor deactivates, conversion decreases and the recycle flow increases. The feed composition to the column thus decreases with time until the process is shut down and the catalyst is regenerated. The base-case feed composition can be taken as the time-average feed composition for the cycle. The design data and base-case operating conditions are given in Table IV. Using the CSTR approximation for the reactor model and the rate expression from Table IV, we can express the reactor conversion as a function of time. ka8~ X = (-41) (1 + k d F ) where a = exp(-kDt), t = time, and eF = reactor volume/reactor feed flow rate. We can relate the reactor residence time, eF, to conversion by noting (A2) x = Qo/QF = O F / ~ O hence (Ita80 - 1) x = (A3) ka8o Also, by noting that X F = x , we can express feed composition to the column as a function of time. (ka8o - 1) xF=x= 644) ka80 The feed composition is plotted in Figure 11using the data in Table IV. The feed composition at the end of the cycle has fallen to XF = 0.543 (a = 0.657) and the time-average feed composition is XF = 0.622. Our preliminary (base-case) design should be based on xF* = 0.622 and X D = 0.999. For the one-product column, the optimum base-case bottoms composition minimizes the sum of the capital costs, heating and cooling costs, and incremental recycle costs associated with the product recovery. Using the heuristic of 99.5% recovery, we calculate xB* = 0.008 at xF* = 0.622. As the feed composition falls from xF = 0.70 to xF = 0.543, the bottoms composition should be selected to minimize the sum of the operating costs for the fixed equipment. Even when the column is treated as a twoproduct column, however, Figure 12 shows that the op-
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 590-607
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erating cost curve is quite linear. Thus, the time-average operating costs for this column should be nearly equal to the operating cost calculated at the time-average feed compition. For this case, little overdesign on the number of trays would be warranted. From Figure 4, the increase in reflux ratio needed to accommodate the full range of feed compositions (xFm = 0.543 and XF* = 0.622) is about 10%. The required overdesign factor for vapor capacity can then be calculated from eq 1.
R,, = reflux ratio at maximum vapor rate (see eq 1) Rmin= minimum reflux ratio ROE= optimum operating reflux ratio S - separation factor = [ x D ( I - x B ) ] / [ x B ( l - X D ) ] V* = design vapor rate = (R* + 1)D* V,, = maximum vapor rate n = reactor conversion X B = bottom composition XD = distillate composition XF = feed composition X F , = ~ minimum ~ ~ operable feed composition XSOR = start of run conversion Greek Letters
or
cy
Vm,/V*
= 1.07
Nomenclature catalyst activity B = bottom flowrate C, = concentration of reactant A D = distillate flow rate k = reaction rate constant kD = catalyst deactivation rate constant NR = number of theoretical trays in the rectifying section Ns = number of theoretical trays in the stripping reaction NT = number of theoretical trays n = capital cost factor exponent q = feed quality R* = design reflux ratio a =
= relative volatility
0~ = reactor residence time 80 = constant = reactor volume/fresh feed flow rate
Literature Cited Klttrell, J. R.; Watson, C. C. Chem. Eng. Prog. 1966, 62, 79. Mallk, R. K.; Huges R. R. Comput. Chem. Eng. 1979, 3 , 473. Nishida, N.; Ichikawa, A.; Tazaki, E. Ind. Eng. Chem. Process Des. D e v . 1974, 13, 209. Nlshida, N.; Ichikawa, A,; Tazaki, E. AIChEJ. 1974, 18, 561. Peters, M. S.; Tlmmerhaus, K. D. "Process Design and Economics for Chemical Englneers"; McOraw-Hill: New York, 1980. Smoker, E. H. Trans. AIChE 1938, 3 4 , 165. Swaney, R. E.; Grossmann, I . E. "A Metrlc for Operational Flexiblllty in Chemical Process D d g n " , paper presented at the AIChE Annual Meeting, Los Angeles, Nov 1982.
Received f o r review August 26, 1983 Accepted August 13, 1984
Effect of Phase Behavior on Hydrotreater Performance: Simulation and Experimental VerOf ication Ramakrlshna V. Nailiham, James A. Guln;
Arthur R. Tarrer, and Chrlstlne W. Curtls
Auburn Coal Conversion Laboratory, DepaHment of Chemical Engineering, Auburn Unhersity, Auburn University, Alabama 36849
The effect of vaporization of the liquid feed components on reactor performance for hydrogenation of naphthalene, dissolved in a diluting solvent, is studied. The vapor-liquid equilibrium constant of the vehicle solvent, hydrogen flow rate, temperature, pressure, and feed concentration are shown to affect the naphthalene conversion in several diverse ways. The role of vapor-liquid equilibrium in evaluating hydrotreating kinetics is examined through a simulation model. Experimental results are obtained with a continuous stirred tank reactor for the catalytic hydrogenation of naphthalene in the presence of two vehicle solvents, having considerably different volatilities. The experimental data are in general agreement with the simulation predictions.
Introduction Interest in the catalytic hydrotreatment of Solvent Refined Cod (SRC) and coal-derived liquids has recently increased for two main reasons. First, SRC is a solid fuel and must, therefore, be further processed for use as a transportation fuel. This can be achieved by hydrotreating SRC selectively for maximum production of middle distillates. Second, the deteriorated recycle solvent must be upgraded in order to maintain solvent quality and sufficiency in the process. Thermal hydrogenation of the deteriorated solvent results in only a marginal improvement in solvent quality (Moniz et al., 1983). Catalytic hydrotreatment is, then, an attractive route for selectively upgrading of the recycle solvent. Solvent hydrotreatment can be performed either in a separate reactor or in the same reactor in which SRC is upgraded. The Exxon Donor Solvent process employed the former route while the In0796-4305/05/7 724-0590$07.50/0
tegrated Two-State Liquefaction (ITSL) process at Wils o n d e , AL,employs the latter route. Interest in catalytic hydrotreatment of heavy petroleum resid fractions and heavy crudes has also intensified in recent years due to the decreased availability of lighter crudes and more stringent environmental regulations. Hydrotreating reactions generally occur at higher temperatures (700 to 850 O F ) . In addition, high hydrogen flow rates are used to provide good mixing in the reactor as well as to suppress coke formation on the catalyst through an increase in hydrogen paxtial pressure in the reactor. These operating conditiqns provide a significant opportunity for the components'in the reactor to distribute between the vapor and liquid phases. The extent of vaporization can be as high as 40% under the normal operating conditions in a typical coal liquefaction process (Brunson, 1979). As shown in this paper, the relative distribution of the feed 0 1985 American Chemical Society
