mates of the parameters with an iterative search for the parameters which yield the best fit of all frequency response data, treating them directly in the complex plane. The model used in this work, a single input-single output linear, second-order system with dead time, describes all of the tested processes adequately. This study, which describes an efficient technique of establishing and updating a dynamic model during predominantly normal operation of a process, can be extended to the on-line controlling of nonstationary processes, particularly those operating with corrupting noise.
Subscripts C = controller CL = closedloop D = derivative control action d = delay I = integral control action OL = openloop 0 = steady value Literature Cited First Symposium on Identification and System Parameter Estimation, IFAC
(1967). Second Symposium on Identification and System Parameter Identification, IFAC (1970). Third Symposium on Identification and System Parameter Identification. IFAC
(1973).
Nomenclature
A = input signal amplitude AR = amplituderatio E = amplitude of sinusoidal component C = amplitude of cosinusoidal component D = equivalent amplitude G = transfer function j = imaginary number k = process or controller gain PA = phase angle p = integer q = integer s = Laplace operator t = time u = ut x = process input signal y = process output signal
(m
Greek Letters 4 = phase shift or angle = time constant { = damping coefficient o = frequency
Astrom, K . J., Eykhoff, P., Automatica, 7, 123 (1971). Box, G. E. P., Chanmugam, J., hd. fng. Chem., Fundam.. 1, 2 (1962). Cusset, B. F., M. S. Thesis, University of California, Santa Barbara, 1972. Dreifke, G. E., Hougen, J. 0.. Mesmer, G., /SA Trans., 4, 353 (1962). Drelfke, G. E., Hougen, J. 0.. Proc. JACC, 608 (1963). Gallier, P. W. and R. E. Otto,Instr. Techn. 15, 65 (1968). Hougen, J. 0.. "Experiences and Experiments with Process Dynamics", AlChE Monograph Series, Vol. 60, 1964. Isermann, R., "Experimentelle Analyse der Dynamik von Regelsystemen", Bibliographisches lnstitut AG, Mannheim, Germany, 1971a. Isermann. R., Automatica, 7, 333 (1971b). Johnson, P. C., M. S. Thesis, University of California, Santa Barbara, 1970. Levin, M. J., "Estimation of Characteristics of Linear Systems in the Presence of Noise", Technical Report IBM2, Columbia University, New York. N.Y.. 1959. Levy, E. C.. I.R.E. Trans. Auto. Contr., 4, 37 (1959). Mellichamp, D. A., Coughanowr, D. R., Koppel, L. B., AlChf J., 12, 75 (1966). Nieman, R. E., Fisher, D. G., Seborg, D. E., lnt. J. Contrd, 13, 209 (1971). Sage, A. P., Melsa, J. L., "System Identification", Academic Press, New York, N.Y.. 1971. Van den Bos. A,, "First Symposium on Identification and System Parameter Estimation", Paper 4.6, IFAC, 1967. Van den Bos, A,, "Second Symposium on identification and System Parameter Estimation", Paper 7.2, IFAC, 1970. Vercammen, H., van Cauwenberghe, A. R., Conk fng., 17, 79 (1970). Wollaston, E. G., Swanson, B. S., "Systems and Process Control, l", AIChE. New York, N.Y., 1967.
7
Receiued for reuiew M a r c h 21, 1974 Accepted April 7,1975
Intraparticle Diffusion Effects in Residue Hydrodesulfurization Y. 1.Shah' Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 1526 I
J. A. Paraskos Gulf Research and Development Company, Pittsburgh, Pennsylvania 15230
Kinetic data for hydrodesulfurization and demetallization of 50% reduced Kuwait crude oil are obtained from a small scale, isothermal, bench scale reactor operating at about 76OoF and 2000 psia. Holdup effects are minimized by employing a high liquid hourly space velocity, a reasonably low conversion level, and proper distribution of liquid. Effectiveness factors are calculated for both hydrodesulfurization and demetallization by employing approximate analytical solutions for the effectiveness factor for the case involving an irreversible catalytic reaction involving two reactants.
Introduction Worldwide concern about sulfur oxides emissions has prompted commercialization of processes for the removal of sulfur from residual fuels. The most successful of such 368 Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 4, 1975
processes react hydrogen and the raw fuel over a desulfurization catalyst at elevated temperatures and pressures. Desulfurization of residues constitutes the most difficult problem *in petroleum desulfurization, because contaminants which adversely affect the catalyst are concentrated
in the heaviest portion of the oil. In addition, steric factors tend to result in depressed desulfurization reaction rates for residues when compared with processing of the lighter, lower molecular weight feedstocks. One of the greatest problems associated with catalytic hydroprocessing of residual oils is the presence of trace quantities of soluble metal bearing organic molecules or molecular aggregates. The most abundant oil-soluble, organometallic species present in petroleum are nickel and vanadium. The bulk of the nickel and vanadium bearing molecules are present in the high molecular weight resin and asphaltene fraction. The high molecular weight portion of the residue being treated could be expected to display a larger mass transfer resistance in heterogeneous catalysis than the bulk or average material being treated. In the hydroprocessing of residuals, metals bearing compounds decompose to form metallic deposits on and in the catalyst structure resulting in what amounts to permanent deactivation. In an extended cycle process, a substantial portion of the on-stream catalyst volume is therefore employed merely as a storage zone for metals and other contaminants. Catalyst effectiveness factors and selectivity to both sulfur containing species, and metals bearing compounds, are of critical importance in the design of residue hydrodesulfurization (HDS) systems. In this paper, evaluation of effectiveness factors for sulfur and metals removal from a 50% reduced Kuwait crude are presented. Experimental data were obtained from a bench scale catalytic hydroprocessing unit a t 760°F and 2000 psia. Typical time dependence of the catalyst activity in the pilot scale reactor is illustrated. The paper also briefly outlines approximate analytical solutions, useful over the entire range of Thiele modulus, for the effectiveness factors for power law type kinetics involving two reactive species. Theory The gas-liquid-solid reaction system examined here can be visualized as one in which a gaseous reactant A (hydrogen) is dissolved in the liquid (residual oil) and which migrates to a solid catalyst where it reacts with another liquid reactant (sulfur or metallic compound), B, by a reaction of the type A(g)
-
+s
shown in Figure 1. As shown, the asymptotic solution differs significantly from the true one in the curved part of the 7 - A plot. A better approximate solution for 7 in the curved part of the v-& curve can be obtained by assuming solutions of the form
and (4)
The desired relations for T and T’ are obtained by suhstituting the assumed solutions for A and B into the governing differential equations. The final results are
+ and T’ tanh T’
dS2
2
=
- q tanh T’
+
T
A numerical solution for the catalyst effectiveness factor for the above rate expression is given by Satterfield (1970). The effectiveness factor 7 in this case would be functions of standard Thiele modulus
T’
( q 5 1) ( 6 )
The effectiveness factor is given by 9=-
(2)
1
(7 7 ) 2 cosh2 tanh
T
4S2
and T’ tanh T’
9=
rate = kAB
+I8
Figure 1. Comparison of the true solution for the effectiveness factor with the ones obtained by the present technique and from the normalization of the Thiele modulus ( 9 = 1).
+ B(1) catalyst product
Many rate expressions for the above reaction are reported in the literature. Here we assume that the rate is given by
0‘
4
( q 5 1)
(8)
$S2
The above solution should show maximum deviation from the exact solution for q = 1. For q = 1, 9 vs. dSobtained from the solution is shown by the crossed curve in Figure 1. These results indicate that the above approximate solution should be preferred over the asymptotic solution outlined earlier in the curved portion of the p$, plot.
Here L)A,eff and DB,& are the effective diffusivities of A Experimental Section and B, within the catalyst, respectively, A, and B s are the concentrations of A and B a t the external surface of the A typical isothermal, fixed-bed hydroprocessing pilot catalyst, and L is the characteristic length for the catalyst plant was employed in the hydrodesulfurization of 50% Kuparticles (Reuther and Puri, 1973). An analytical asymptotwait reduced crude containing 4.09% sulfur. Feed inspecic solution has also been obtained by normalizing the tions are shown in Tables I and 11. Preheated hydrogen q) for q 5 1 and 45/ Thiele modulus 4s by 4: = &plus residual oil were passed concurrently and downflow over a fixed bed of catalyst. The reactor was charged with = &d3q/(3q - 1) for q 2 1. The effectiveness factor q = 50 g of an experimental HDS catalyst in two runs. In one tanh &/&’. For q = 1, a comparison between the true ~ - 4 ~ case, the reactor was charged with l/sz-in. diameter catalyst curve and the one obtained from this asymptotic solution is Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 4, 1975
369
Table I. Operating Conditions and Results of Fixed Bed Hydrodesulfurization of 50% Kuwait Reduced Crude Using Y32-in. Diameter Catalyst Extrudates Run conditions
Feed
Days on stream Average reactor temperature, OF Weight hourly space velocity
1
I
I
1
Products 1.8
3.8
760
4.9
759
9.97
6.9
762
10.02
761.5
9.86
li
f
10.14 04l
I
2
0
Product quality API Sulfur, wt% Nickel, ppm Vanadium, ppm
I
I
t
15.0 4.09 15 51
19.6 1.77 13 32
19.1 1.91 15 32
19.1 1.88 14 35
18.3 1.95 15 32
I
4 Time on stream, Daya
I
I
6
8
1
Figure 2. Product sulfur content from fixed-bed hydrodesulfurization.
Table 11. Operating Conditions and Results of Fixed Bed Hydrodesulfurization of 50% Kuwait Reduced Crude Using 500-595-p Catalyst Granules Run conditions
Feed
Products ~
Days on stream Average reactor temperature, "F Weight hourly space velocity
1.5 760.3
~~~~~
3.83 760
7.83 760 10
10.05
10.0
9.95
15.0 4.09 15 51
20.1 1.39 10 18
19.2 1.74 10 21
18.6 2.12 9.7 24
extrudates while the second run employed 500-595-w granules, crushed and sieved from the extrudates. The catalyst was sulfided with a 23.8 API gas oil containing 1.7% sulfur at 2000 psig and 650'F for 4 hr in each case. Residual oil feed was then introduced and the temperature brought to about 760'F with a WHSV of about 10 (LHSV of about 7.5). A high flow rate was used to minimize liquid holdup effects. In order to achieve proper distribution of liquid, the catalyst bed was preceeded by a 30 in. long prepacking zone containing quartz chips. Quartz chips in the 500-595I.L range we also interspersed with the catalyst granules to make the overall length occupied by the catalyst in both runs the same. Quartz chips are inert for all reactions of importance in this study. Once through gas, containing 95% hydrogen, at 5000 SCFharrel of oil feed was employed. A number of samples were taken during the course of both runs to observe catalyst aging effects a t constant operating conditions. Data on operating conditions and product quality are shown in Tables I and 11. Total liquid product was recovered and analyzed and in each case this represented about 97-99% by w t of the feed charged to the reactor. Thus, no corrections were made to account for the slight change in sulfur of metals contaminants removal due to the production of gases. 370
I
I
I
I
I
2
4
6
8
Is
Time on sfreom, Doyt
Figure 3. Product of vanadium and nickel contents from fixedbed hydrodesulfurization.
Product quality API Sulfur, wt% Nickel, ppm Vanadium, ppm
i 0
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 4. 1975
Results and Discussion The experimental data needed for the calculations of integral rates of hydrodesulfurization and the demetallization reactions are outlined in Tables I and 11. The product concentrations of sulfur, nickel, and vanadium as functions of time, for both extrudate and granular catalysts, are also illustrated in Figures 2 and 3. The main purpose of these illustrations is to show the aging effect of the catalyst on the rates of both hydrodesulfurization and demetallization reactions. The aging could be caused by changes in both the intrinsic kinetic constants and the effectiveness factors of the catalysts. The latter may be caused by the possible deposition of metals resistance to hydrogen absorption. The highest absorption rate of hydrogen was found to be ap(g-mol Hz/sec-cm3 catalyst pellet). proximately 1.1 X The solubility of hydrogen a t 2000 psia and 760'F was estimated using the Chao Seader technique as modified by Grayson and Streed (1963) to be approximately gmol/cm3. In the absence of available data, the required mass transfer coefficient k L S was estimated from the relation suggested by Satterfield (1970) kLs = ~ D Hap/t ,
(9)
The bulk diffusivity D H was ~ estimated from the Wilke and Chang correlation (Reid and Sherwood, 1966) as approximately 2 X cm2/sec. u p , the external catalyst surface area per unit volume of the catalyst was 57.6 cm2/cm3. From the measured compacted bed density of 0.72 g/cm3 the void fraction for the catalyst bed t was estimated to be approximately 0.33. Using these data, H,/H* (ratio of sur-
face to bulk liquid concentration of hydrogen) was estimated to be 0.999, implying that the external mass transfer resistance for hydrogen in the present experiments was negligible. Assuming the same order of magnitude for k L s for other reactants and catalyst size, the external mass transfer resistances for these cases were also be concluded to be negligible. Effectiveness Factors If the parameters q for the present reactions are much less than unity then for all practical purposes hydrogen concentration can be assumed to be in excess and the reactions can be considered to be pseudo first order. We estimate the effective diffusivity of hydrogen to be approxicm2/sec (assuming tortuosity = 2). In a remately 4 x cent article, Newson (1975) estimates the minimum effective diffusivity for sulfur compounds in a 0.16-cm pellet to be 5 X cm2/sec. If we assume the same value for the effective diffusivity for a sulfur compound in the present experiments, the parameter q for the sulfur reaction can be estimated to be approximately 5 X This means that even if the estimates of effective diffusivities for the sulfur compound and the hydrogen and the solubility for hydrogen all are in error by an order of magnitude, q will still be much less than unity. Since the concentrations of nickel and vanadium compounds and their effective diffusivities (Newson, 1975) are much smaller than those for the sulfur compound, q’s for nickel and vanadium reactions should also be much less than unity. The effectiveness factors for the sulfur, nickel, and vanadium removal reactions at the onstream time of 1.8 days were calculated. The rates of reactions were obtained from the data shown in Tables I and I1 and Figures 2 and 3. For the sulfur removal reaction ve/vgwas calculated to be approximately 0.79 and the corresponding ratio of Thiele modulus was approximately 1.9. From these data and using the method outlined by Satterfield (1970),the effectiveness factors qe and vg were estimated to be 0.7 and 0.89, respectively. For nickel and vanadium removal reactions, unfortunately, the effectiveness factors for both granular and extrudate catalysts lie in the asymptotic region of the 7 - A curve. The calculations of the effectiveness factors, therefore, required independent estimates of the effective diffusivities of nickel and vanadium compounds. These estimates are not accurately available. The literature indicates (Newson, 1975) that the effective diffusivities of metal bearing compounds may range between and low7 cm2/sec. According to the present data, an effectiveness factor of approximately 0.4 for the granular catalyst means the effective diffusivity for the vanadium compound is apcm2/sec and that for the nickel comproximately 7 X cm2/sec, which are both pound is approximately 3 X reasonable numbers. It is clear that since qg lies in the asymptotic region of the q-& curve, it cannot be significantly greater than 0.4. Thus, effective diffusivities for the vanadium and nickel compounds cannot be significantly greater than the above mentioned values. Intrinsic Kinetics For the sulfur removal reaction a value for k,’ ( = k H , ) can be obtained in a straightforward manner as approximately 9 hr-l. Since the BET surface area as measured by N2 adsorption method was approximately 160.6 m2/g and the hydrogen solubility as mentioned earlier is estimated to be g-mol/cm3, the intrinsic rate constant for the sulfur (cm3 of fluid) removal reaction was approximately 2 x (cm3 of catalyst pellet)/(cm2 catalyst pellet) (g-mol of N2)
(sec). This number can be in error by as much as f 2 5 % due to the inaccuracy involved in the estimation of hydrogen solubility. The surface area measurement should be accurate within a few percent. From a consideration of the stereochemistry of nickel and vanadium bearing structures, one would expect the rate of vanadium removal to be greater than for the nickel removal under the same reaction conditions. The data shown in Tables I and I1 indicate this to be the case. Although both nickel and vanadium atoms have been found to be imbedded in the plane of porphyrins, it is believed that the vanadium atoms are linked to an oxygen atom which is perpendicular to the plane of prophyrins. This is not the case in nickel prophyrins, however. It is suspected that the oxygen atom in the vanadium bearing structure forms a stronger link with the catalyst surface than can occur with the nickel bearing compounds, which results in the vanadium rate being higher than that of nickel. Concluding Remarks In an industrially important residue, HDS process, effectiveness factors for removal of those contaminants which significantly decrease catalyst activity were found to be significantly higher for the smaller catalyst than the larger catalyst. On the other hand, the desired reaction, namely the removal of sulfur, was found not to change very significantly with the catalyst size over the range studied. As process time increases, the higher metals removal is believed to cause the activity of the granular catalyst for the desired sulfur reaction to decline for the extrudates. Thus, in the HDS process, a catalyst which performs best initially is not necessarily best for the long term. Furthermore, since the intrinsic kinetics of the demetallization reactions aear to be more favorable than that for the desired sulfur removal reaction, the optimum reactor performance could be obtained by selecting a catalyst size which will give the best average effectiveness factor for the sulfur removal reaction over the period of operation. In industry, the decline in the effectiveness factor with time is often compensated by an increase in the reaction temperature. Nomenclature A = concentration of the gaseous reactant u = dimensionless concentration of A u p = specific liquid-solid interfacial area B = concentration of the liquid reactant B b = dimensionless concentration of the liquid reactant Di = bulk diffusivity of the species i in the liquid Deff = effective diffusivity of the species in the pores of the catalyst (Die/?) H = concentration of hydrogen k ~ s liquid side mass transfer coefficient k = kinetic constant for the reaction as defined by eq 1 ( k = ksSA k s = intrinsic surface reaction rate constant L = characteristic length of the catalyst (volume of the catalyst/total effective externa surface area of the catalyst) S = sulfur concentration S, = catalyst surface area per unit volume x = axial distance within the catalyst in the direction of its finite dimension; x = 0 at the catalyst outer surface V = vanadium concentration Greek Letters & = Thiele modulus as defined by eq 2 { = dimensionless axial distance within the catalyst T , # = constants defined by eq 8 and 9 qi = effectiveness factor for species as defined by eq 7 { = void fraction of the catalyst bed i = tortuosity factor for the catalyst 8 = porosity of the catalyst Ind. Eng. Chem.. Process Des. Dev., Vol. 14, No. 4, 1975
371
Subscripts L = liquid phase s = conditions a t the catalyst external surface g = granular catalyst e = extrudate catalyst S,N,V = conditions pertaining to the sulfur, nickel, and vanadium compounds
Sixth World Petroleum Congress, Frankfurt, June 1963. Newson, E. J., Ind. Eng. Chem., Process Des. Dev., 14, 27 (1975). Reid, R. C., Sherwood, T. K., “The Properties of Gases and Liquids,” 2nd ed, McGraw-Hill, New York, N.Y., 1966. Ruether, J. A,. Puri. P. S., Can. J. Chem. Eng., 51, 345 (1973). SatterfieM, C. N., “Mass Transfer in Heterogeneous Catalysis,” M.I.T. Press, Cambrldge. Mass., 1970. Thiele, E. W., I d . Eng. Chem., 31 (7), 916 (1939).
Literature Cited Grayson. H. G., Streed, C. W., “Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrogen-Hydrocarbon Systems,” a paper presented at
Received for review July 29, 1974 Accepted May 12, 1975
Chemical and Physical Processes of Hydrocarbon Combustion: Physical Processes Rodney A. Geisbrecht and Thomas E. Daubert’ Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
Firmly establishing the interrelation of vapor-phase partial oxidation processes to associated process parameters has been studied using ethane as a model feedstock and a raining solids type reactor. The systems have been shown to be comprised of coupled chemical and physical transport processes. Geisbrecht and Daubert (1975) described the chemical processes of ethane partial oxidation by developing a mechanism which quantitatively correlates and predicts experimental behavior over substantial ranges of process conditions. This paper deals with the physical processes occurring in such systems and quantitatively accounts for the temperature distribution within the reactor, couples the chemical kinetics and physical transport processes, and shows the influences which must be taken into account in design of reactors. Extension of the method to the combustion of propane, butanes, and n-hexane validates the recommended method. The method discussed should be easily extrapolated to other types of chemical reactors.
Introduction Perhaps the single most important factor leading to the development of the raining solids type of reactors is the fact that the extreme exothermicity of partial oxidation processes prevents reliable and efficient temperature control through conventional procedures. A fluidized bed reactor would be ideal for these processes except that a suitable particulate solid is not available. Since most surfaces are known to inhibit the conversion process, the high surface to volume ratio within a fluidized bed reactor completely inhibits the reactions. The use of a fluidized bed reactor, then, awaits the development of a suitable solid which does not inhibit the conversion processes. Such a development would represent a significant “break-through” in hydrocarbon partial oxidations and perhaps in many free radical processes such as chlorination. A transported bed reactor does not offer much flexibility but is being utilized for these processes. A conventional open tube reactor is plagued by localized hot spots which may develop, especially near oxidant injection points, and result in their undesirable complete combustion effects. I t has already been shown that the addition of a “rain” of particulate solids does indeed shift the product distribution in favor of the low-temperature products a t the expense of the high-temperature products. However, there is no drastic reduction in the complete combustion products-carbon monoxide and carbon dioxide. In fact their formation is actually enhanced and the carbon dioxide to carbon monoxide ratio 372
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 4, 1975
continually increases within the total oxide product. Since carbon monoxide could at least be utilized in synthesis-gas and/or Fischer-Tropsch production processes, the carbon dioxide generation is undoubtedly a disadvantage of particulate solids in most situations. One could argue, therefore, that unless it is desired to produce low-temperature products (oxidation products as opposed to oxidative-cracking products) in preference to the high-temperature products there is no advantage in a raining solids system. However, the partial oxidation processes of this study were carried out in a 1.5-in. i.d. prototype. In the scaled-up reactor the temperature control via the reactor wall would be severely hampered compared to the pilot reactor. This will rest in very severe hot spots and the advantages of a raining solids operation will then become much more apparent. It should be noted that even with the pilot reactor, temperature control in the sense of stabilization is very difficult to achieve in the absence of a particulate solids rain. To maintain any given temperature level the reactor heat controls must be cycled about the average temperature level which would otherwise continuously rise to undesirable levels. With a raining solids operation only an occasional and minor adjustment of heat controls is required to maintain a desired temperature level. Results and Discussion Temperature Distributions with the Raining Solids Reactor. Because of the strong exothermicity of combus-
