Energy & Fuels 1994,8,1310-1315
1310
A Novel Laboratory Scale Reactor System for Studying Fuel Processes from the Initial Stages. 2. Detailed Energy and Momentum Balances He Huang, Dean M. Fake, William H. Calkins,*and Michael T. Klein Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received May 20, 1994@
The underlying basis for the exceptional performance of a heat exchanger preheater for a novel short contact time batch reactor (SCTBR) was investigated. Three levels of analysis, ranging from equilibrium calculations to a finite difference solution of the transient heat transfer problem, were used to solve the equations governing heat and momentum transfer. For a target reaction temperature of 400 "C, the tetralin exit temperature from the heat exchanger preheater was calculated to be 392 "C initially, down to 376 "C. This is in reasonable agreement with a measured 392-395 "C upon injection into the reactor. The small discrepancy is due, in part, to an unaccounted heat contribution from the reactor. This agreement confirms the utility of the preheater configuration and therefore the SCTBR as a tool to minimize heat-up effects in reaction analysis.
Introduction The study of complex, often macromolecular, hydrocarbon conversion reactions is enhanced by analysis at short reaction times. To this end, the design strategy and preliminary operation of a novel short contact time batch reactor (SCTBR) was described ear1ier.l The essential insight in the development of this system evolved from the realization that the long heat-up time involved in a "traditional" tubing bomb reactor experiment is usually due to the large heat capacity of the reaction vessel. The SCTBR system reduces the heatup time because the reactor is brought up to temperature before the introduction of the reactant(s1. The relevant heat-up time is then only the time required to heat up the reactant mixture. Ideally, this should occur quickly in preheater tubing that brings the reaction mixture up to temperature by the actual time of injection. This paper examines the performance of such a preheater, which is clearly an integral part of the effectiveness of the SCTBR concept. The full reactor system is described in detail in part 1 which presents a schematic of the SCTBR system. The reactor and preheater are immersed in a sand bath and brought to the target temperature before reaction. The cold reactant sample initially resides in a blowcase outside the sand bath and is blown through the preheater and into the reactor with high pressure nitrogen (or hydrogen). The preheater consists of about 21 ft of a coiled l/4 in. 0.d. stainless steel tubing with wall thickness of 0.035 in. Experiments discussed in part 1 indicate the reactant forms a plug about 5 ft long which traverses down the tube length in 0.3 s. The general analysis of this physical situation involves both heat and momentum transfer. This will be @Abstractpublished in Advance ACS Abstracts, October 1, 1994. (1)Huang, H.; Calkins, W. H.; Klein, M. T. A Novel Laboratory Scale Short Contact Time Batch Reactor System for Studying Fuel Processes 1. Apparatus and Preliminary Experiments. Energy Fuels, submitted for publication.
0887-0624/94/2508-1310$04.50/0
Table 1. Relevant Physical Properties of Tetralin and Stainless Steel2 density (e), g cm-3 tetralin stainless steel a
0.97 8.02
viscosity
heat capacity
(d,CP 1.810
(CD), J g-l "C-l
-
1.64 0.449
Estimated by t h e group contribution method.
accomplished using a standard run involving 30 g of injected tetralin, which has properties characteristic of a coal-tetralin slurry. Representative experimental conditions are nitrogen pressure 1000 psig, reaction temperature 400 "C, and ambient temperature 20 "C. The related physical properties of tetralin and stainless steel are listed in Table l.2-4Experimentally, the temperature of the tetralin stream reached 392 "C when measured by a thermocouple in the reactor.
Fluid Flow Calculation Transport of the tetralin stream into the reactor through the preheater is treated as an internal incompressible viscous flow. The flow rate of the tetralin stream through the preheater tubing is estimated by the energy balance equation5 of
In eq 1, positions 1 and 2 represent the fluid in the blow case and the preheater, respectively; hl, the head loss, (2) Lide, D. R. CRC Handbook of Chemistry and Physics, 72nd ed.; CRC Press, Inc.: Boca Raton, FL, 1991. (3)Perry, R. H.; Chilton, C. H. Chemical Engineer's Handbook, 5th ed.; McGraw-Hill Book Co.: New York, 1973. (4) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill Book Co.: New York, 1987. ( 5 ) Fox, R. W.; McDonald, A. T. Introduction to Fluid Mechanics, 4th ed.; John Wiley & Sons, Inc.: New York, 1993; Chapter 8.
0 1994 American Chemical Society
A Novel Laboratory Scale Reactor System
Energy &Fuels, Vol. 8, No. 6, 1994 1311
Table 2. S u m m a r y of Momentum Calculations to Determine Fluid Velocity no. of iterations 0 1 2 3 4
type of flow
Re 2.92 x 5.42 x 5.02 x 5.01 x
los lo4 lo4 lo4
f
-
0.0000
turbulent turbulent
0.0200 0.0235 0.0236 0.0236
turbulent turbulent
fi2
(m s-l) 119.3 22.1 20.5 20.4 20.4
represents the irreversible conversion of mechanical energy to thermal energy due t o the frictional flow; and a, the kinetic energy coefficient, is a function of the ratio of the centerline velocity to the average velocity. Rearrangement of eq 1 provides eq 2,
or, more compactly, eq 3.
(3) Since Aple >> gAy for this SCTBR system, gAy is negligible. For turbulent flow (as will be confirmed by 1. Substituting U1 = 0, eq 3 the Re number), a2 simplifies to
-
(4) For turbulent flow,
The friction factor, f , is a function of the Reynolds number ( R e )and relative roughness (chi). The generalized results are given in Moody's literature.6 Substituting eq 5 into eq 4 and rearranging gives g2 =
[!+;(e
+ l)]li2
Equation 6 shows that determination of the average velocity (52) of the tetralin flow in the preheater tubing requires evaluation of the friction factor, f . However, f is dependent upon R e , in turn dependent on U2 itself. Therefore, an iterative technique is required. An initial estimate for R e can be determined from the frictionless flow, i.e., UZ at f = 0. The subsequent iteration steps include the following: (1)calculating Reynolds number, R e , using the previously determined f i 2 ; (2) evaluating relative roughness, eldi, from the chart of relative roughness for pipes of common engineering materials;6 for stainless steel with di of 0.18 in., the relative roughness is 0.009; (3) reading the friction factor, f , from the curve with eldi of 0.009 in the chart of friction factor for fully developed flow in circular pipes;6 and finally (4)calculating bz using eq 6. The results are summarized in Table 2. The average velocity of the tetralin flow in the preheater is 20.4 d s , and the flow is turbulent. The average volumetric flow rate of the tetralin stream in the preheater, R,, is then calculated (6)Moody, L. F. Trans. ASME 1944,66 (8),671-684.
(7) where A,,t is the cross-sectional area of the tubing. The transport time of the tetralin stream going through the preheater tubing, t,, is estimated by
t, = VJR,
(8)
where Vt is the total space volume of the preheater tubing. Strictly, both density and viscosity are temperature dependent. The 20 "C values used in this calculation provide upper bounds and therefore conservative estimates of t,. As the tetralin streams through the preheater, its temperature will increase. This will lead to a decrease in both viscosity and density. At these conditions, the viscosity is more sensitive to temperature than density. Thus, the ratio of density to viscosity PIP increases as the temperature increases. For this reason, the estimated value of U2 in Table 2 is the low limiting value. Using this low limiting value and eq 8, the maximum transporting time, t,,", is 0.31 s. This value agrees very well with that (0.3 s) measured in experiments.
Qualitative Heat-TransferAnalysis In advance of a general solution, two quick heattransfer calculations provide insight into the governing heat-transfer step. First, the preheater is considered a simple adiabatic vessel. This case provides a lower limit on the preheater exit temperature in the limit of thermal equilibrium. Second, an elemental approach is taken where preheater elements and tetralin elements are assumed to be in thermal equilibrium. This analysis is a limiting case where the preheater internal heat-transfer coefficient is infinite and heat transfer from the preheater to the tetralin instantaneously reaches equilibrium. Thermal Balance in the Preheater A thermal balance calculation within the preheater provides a first-order analysis of the heat transfer from the preheater. It assumes that only the sensible heat of the preheater tubing furnishes the heating of the tetralin stream. In this instance, the temperature rise of the tetralin sample would be proportional to the temperature drop of the stainless steel tubing, according to the energy balance of eq 9
m,C,B(T, - T,)= mtCpt(T,- Tt)
(9)
In eq 9, mt and m, are the masses of the tetralin stream and the preheater tubing, C,, and C,, the heat capacities of the tetralin stream and the preheater tubing, and Tt, T,,and T, the initial temperatures of the tetralin stream, the preheater tubing, and the adiabatic equilibrium temperature, respectively. For 30 g of tetralin, the adiabatic equilibrium temperature is 353 "C. This is 47 "C lower than the reaction temperature of 400 "C. This calculated temperature drop (47"C) is much higher than the 5-8 "C actually measured in experiments.
Heat Transfer from the Fluidized Sand to the Preheater during the Transport of the Tetralin Stream into the Reactor through the Preheater A possible reason for this difference between the experimental observation and the adiabatic thermal
Huang et al.
1312 Energy & Fuels, Vol. 8, No. 6,1994 equilibrium calculations is due to the heat transfer from the fluidized sand at the reaction temperature to the preheater tubing during the transport of the tetralin sample. Quantitatively, this transferred heat is proportional to the contact surface area, the temperature gradient, and the contact time interval. Mathematically,
The heat-transfer coefficient of the fluidized sand, Uf,, is 60-120 Btu/(h R2 OF) or 0.34-0.68 kW/(m2 "C), according to the sand bath manufacturer's tests.7 In this instance, Tb I 400 "c, and for a preliminary analysis, the previously calculated adiabatic equilibrium temperature 353 "C in section 2 was used as an average preheater tubing temperature. Substituting these values and tp," of 0.31 sec calculated in section 1into eq 10 gives Qfs 5 0.63-1.26 kJ, accounting for only 3-7% of total required heat for 30 g of tetralin from 20 to 392 "C. Furthermore, this amount of heat can increase the temperature of the 30 g of tetralin by a maximum of 13-25 "C. Thus, even if the contribution of the heat transfer from the fluidized sand during transport of tetralin sample were taken into account, there is still at least a 22-34 "C drop, much higher than the 5-8 "C drop determined in experiments.
Figure 1. Energy balance on a segment of length, dl, in the preheater tubing.
preheater tubing. According t o these assumptions, the differential form of energy balance within a differential length of the preheating tubing, dl (see Figure 11, becomes
Cp,(Te- TJ dmt,dl = Cps(T, - Te)dms,dl (11) where dmt,d and dm,,d are the masses of the tetralin sample and the preheater tubing in dl, respectively, and, 1 2 dmt,dz= zndi et dl
(12b) Substituting the values for corresponding variables and constants and calculating, eq 11becomes 0.26(Te - T,) dl = 0.537(Ts - T,) dl or
Thermal Balance along the Preheater In the previous thermal balance calculation, the preheater tubing was considered as a single unit. In other words, the heat was assumed to be extracted evenly along the preheater by the tetralin stream. Clearly, this is not the generally expected case. First, as the tetralin sample proceeds through the preheater tubing, the temperature of the tetralin stream rises from the ambient temperature (e.g., 20 "C) at the entrance and approaches the reaction temperature (e.g., 400 "C) at the exit. Thus, the temperature gradient, AT, at the entrance is much higher than that at the exit. More heat is therefore extracted from the entrance of the preheater. Second, each incremental amount of the tetralin experiences a different temperature gradient along the preheater. This is because the heat transferred t o the tetralin cannot be recovered by the heat transfer from the fluidized sand in the time of transport of the process stream through the preheater tubing. Thus, the temperature gradients along the preheater tubing are functions of both position along the preheater and sequence of tetralin increments going through the preheater. A semiquantitative thermal balance calculation along the preheater tubing provides a second-order analysis of the heat transfer in the preheater. As before, this analysis assumes that only the sensible heat of the preheater supplies the heating for the tetralin sample, ignoring the heat transfer from the fluidized sand to the preheater tubing in this 0.3 s time interval. More importantly, it also assumes that thermal equilibrium is instantaneously achieved a t each incremental position in the preheater tubing when each subsequent incremental amount of tetralin sample proceeds through the (7) Summers, P. H. Presented at the 48th Annual Convention of the Wire Association International, Inc., St. Louis, MO, Oct. 17, 1978.
(13)
T, =
T,
+ O.484Tt 1.484
(14)
When 1 g of tetralin, equivalent to a 6.28 cm length of the preheater tubing, was taken as an incremental unit, the temperatures of each subsequent gram of tetralin sample along the preheater tubing and the temperatures of each incremental length (6.28 cm) of the preheater tubing for each gram of tetralin sample through it were calculated using eq 14. According to this equation and the first assumption, the following iterative equations applied: T,(ij) =
+
Ts(i - lj) 0.484Tt(Zj - 1) 1.484
(15)
T,(ij) = Te(Zj- 1)
(16)
T,(ij) = T,(i - lj)
(17)
with the initial conditions of
T,(Z,O) = 400 "C
(184
T,(Oj)= 20 "C
(1%)
In these equations, i represents the ith unit length of 6.28 cm (correspondingto 1g of tetralin in the tubing) from the entrance of the preheater tubing, and j the j t h gram of tetralin sample proceeding through the preheater. The calculated adiabatic equilibrium temperatures for the lst, 2nd, ..., and 30th grams of tetralin increments along the preheater and tubing temperatures at 6.28, 12.56, ..., 200.96 cm for the lst, 2nd, ..., 30th grams of tetralin sample through the preheater tubing using eqs 15, 16, and 17 are tabulated in Table 3. To illustrate these data, the temperature profiles for
A Novel Laboratory Scale Reactor System
Energy &Fuels, Vol. 8, No. 6, 1994 1313 t=O
t
= t,
I
////////// // / Y /
z=L,
z==
=L,
2 4
lpl
t>tp
Figure 2. Temperature profiles for each incremental gram of the tetralin and of the corresponding length of preheater tubing as the tetralin proceeds down the preheater. Table 3. Calculated Adiabatic Equilibrium Temperatures (T,)for the lst, 2nd, and 30th grams of Tetralin along the Preheater Tubing and Tubing Temperatures at 6.28, 12.66, 200.96 cm for Each Tetralin Increment through It
...,
...,
6.28 cm 12.56cm 18.84cm
lstg 276°C 360°C 387°C
2ndg 193°C 305 "C 360°C
3rdg 136°C 250°C 324°C
200.96cm
400°C
400°C
400°C
-
-
-
-
... ... ... ... ... ...
30thg 20.0% 20.0 "C 20.2"C 400°C
each gram of the tetralin increment along the preheater as it proceeds down to the exit are plotted in Figure 2. These temperature profiles also represent the tubing temperatures corresponding to each subsequent gram of tetralin through the preheater tubing. Clearly, this differential instantaneous heating provides for essentially complete heat up to the reaction temperature. This suggested that a general analysis would reveal the modest effect of transient heat transfer.
General Analysis The general analysis models the transient convection heat transfer without a priori assumption of the limiting heat-transfer step. The system consists of a preheater tube 21 ft in length, initially at the target reaction temperature (in this case 400 "C). Cold tetralin enters the tube and forms a plug approximately 5 ft in length. The time taken for the tetralin to exit the blow case and form this plug is 0.08 s. The plug then moves through the tube in 0.3 s. Figure 3 illustrates the transient operation of the preheater with respect to a reference frame moving with the tetralin. A few approximations were invoked to facilitate a tractable solution. These approximations are as follows: 1. The sand bath is perfectly mixed; there are no fluctuations from the bulk temperature, Tb. The cooling of an industrial scale sand bath through the addition of 30 g of cold tetralin can be considered negligible. 2. There are no radial temperature gradients in the tube wall since the wall tube is thin.
Figure 3. Reference frame for finite difference analysis.
3. There is no axial thermal conduction in the tube. The characteristic time for conduction is on the order of minutes and is much larger than the 0.3 s residence time of the plug in the preheater. 4. The tetralin is in turbulent plug flow with no axial conduction. The modeling of the preheater can be considered from two equivalent frames of reference. On the one hand, a coordinate frame can be fixed to the preheater wall and tetralin moves in the axial (2') direction with velocity v . Alternatively, the frame of reference can be fixed to the tetralin plug and the preheater tubing can be considered to be moving with a superficial velocity v , as in Figure 3. This reference frame maximizes the CPU memory allocated to the tetralin plug, the part of interest. Under these conditions, we need only keep track of the temperature of the section of tube in direct contact with the plug. The part of the tube wall upstream must be a t 400 "C since the tetralin has not reached there yet. The part downstream does not further influence the plug temperature and may be ignored. With a reference frame fxed to the tetralin plug, and the approximations listed above, the relevant heat balances for an element of preheater and tetralin are eqs 19 and 20.
(energy stored in tube) = (heat gained by tube convection) (heat from bath) - (heat lost to tetralin) (19)
+
(energy stored in tetralin) = (heat from tube) (20) The peculiar convection term arises from the fact that the wall is moving with respect to the reference frame; hot tube is replacing colder tube in the preheater element. The governing differential equations (eqs 21 and 22) for the temperature of the wall, T,,and the temperature of the tetralin, Tt,are
Huang et al.
1314 Energy & Fuels, Vol. 8, No. 6, 1994 400 395
nd,' ---&IC 4 s
p[
di 2 %",(z,t) 1--u (d)) az
Es! 390
+
2 2
8 E r-"
$
0
385
380 375
370 365
360
These partial differential equations (pdes) are accompanied by the following boundary and initial conditions as shown in Figure 3: At t = 0: Tt(z,O)= 20 "C and Ts(O,O)= 400 "C. If t e is the entry time, or the time it takes for the plug to completely enter the tube, then for t < te and z > u t , Tt(z,t)= 20 "C and T,(O,t)= 20 "C and Ts(O,t)= 400 "C. That is, the part of the plug still in the blow case is at 20 "C. If t, is the penetration time for the leading edge of the plug to exit the heat exchanger tube then for t > t, and z < u(t - tp), Tt(z,t) = Tt(z,tp f (zlu)). The part of the fluid that has left the preheater maintains its exit temperature. In finite difference form the pdes are eqs 23 and 24:
T,(ij
0
0.2
0.4 0.6 0.8 Tetralin Plug Fraction
1
Figure 4. Tetralin outlet temperature.
At + 1) = T & j ) - 3+Ts(ij) - T,(i - 1 , j ) ) A2 (D+ E)Ts(Zj)At+ ET,(ij)At + Cht (23) Tt(ij + 1)= Tt(Zj)+ AAt(T,(ij)- Tt(ij)) (24)
where the coefficients A, B , C , D and E are given in Table 4. The plug was divided into 100 segments, Az. /3 was defined as the fraction of each segment that passes into the next segment for the next time interval, according to eq 25.
At p=-v
-
A2
Table 4. Parameters in Difference Eq 23 and 24 (25)
For small /3 (/3 0) the calculated temperatures were stable. Thus, /3 = 0.1 was used for this analysis. However, as /3 1the temperatures fluctuated significantly. The internal heat transfer coefficient was calculated via the Colburn Nu number correlation for turbulent flow in pipess as in eq 26.
Nu = 0.023Re4/5Pr1'3
Figure 5. Temporal variation in temperature profile of the tetralin plug. A=-
vi
@p$i
B=v
n=
4u0
(26)
The results are shown in Figures 4, 5, 6, and 7. The outlet temperature of the tetralin (Figure 4) is the temperature at which the fluid leaves the preheater. This is insensitive t o the outside heat-transfer coefficient, U,, when it is varied within the manufacturer's specifications. The tetralin initially exits the preheater at 392 "C and, over time, drops slightly to 376 "C. The average temperature the tetralin enters the reactor is around 385 "C, in reasonable agreement with the measured 5-8 "C temperature drop. Figure 5 shows the temperature of the plug as it passes through the preheater. This indicates that the last of the tetralin nears the reaction temperature ('370 "C) near the end of the heat exchanger. Therefore, the (8) Incropera, Frank, P.; De Witt, David, P. Fundamentals of Heat and Mass Transfer,2nd ed.; John Wiley & Sons, Inc.: New York,1985; Chapter 8.
preheater tubing is maximized and loss due to wetting is minimized. The region Tt = 20 "C represents tetralin still in the blow case. Figure 6 presents the temperature of the preheater wall in contact with the tetralin plug at any given time. Initially the wall is at 20 "C since the plug is in the blow case (see Figure 3 for t = 0 and the wall is the cold blow case wall. Figure 6 shows that the end of the preheater is cooled negligibly on exit of the final element of tetralin (t = 0.41, z = 1). In effect, the temporal variation of the temperature of the wall at z = 1 provides the final spatial temperature profile of the whole preheater
A Novel Laboratory Scale Reactor System
Energy & Fuels, Vol. 8, No. 6, 1994 1315 These analyses confirm that the SCTBR drastically reduces the heat-up time effect on kinetic analysis.
400 @ I
Acknowledgment. The support of various portions of this work by the Department of Energy under DEFG22-93PC93205 and by CONSOL Inc. under DOE subcontract DE-AC22-89PC898893 is gratefully acknowledged.
0
Notation
Figure 6. Temporal variation in temperature profile for the preheater wall in contact with the tetralin. 400 350
50 0
LzItxLa
0
5
10
15
20
Preheater Length (ft)
Figure 7. Final preheater temperature profile. assuming that the sand bath does not provide any significant heat in this time frame. Figure 7 presents the final preheater axial temperature profile, where time has been converted to length through the velocity v.
Conclusions Fluid flow analysis of the SCTBR preheater system shows that a process stream is transferred under pressure into the reactor in 0.31 s, in agreement with experimental results (0.3 SI. Finite difference analysis of heat transfer in the SCTBR preheater predicts an average preheater exit temperature of 385 "C compared to the measured 392395 "C for a desired reaction temperature of 400 "C. This heat-transfer analysis shows that more of the sensible heat is extracted from the preheater in the short time interval of transfer of the process stream through it than would be expected from the total sensible heat content of the preheater. The reason for the high efficiency is that more heat is extracted from the inlet portion of the preheater where the temperature gradient is high than from the end of the preheater where the temperature gradient is low.
cross-sectional area of the preheat tubing wall specific heat tetralin specific heat inside tube diameter differential length of the preheater tubing outside tube diameter roughness relative roughness friction factor f gravitational acceleration constant g,l-ds2 head loss hl, m2/s2 0.1295 - 5.4 x 106(Tr- 293) kt L, 21 ft preheater length tetralin plug length Lt mass of a process stream ms,g mass of the preheater tubing mt, g 0.023Reu6Pr1'3,nusselt number Nu pressure P, Pa Pr C&Jkt, Prandtl number heat transferred from the fluidized sand to Qfsy kJ the preheater tubing etvdi/pt, Reynolds number Re average volumetric flow rate R,, m3/s outside surface area of the preheater tubSot,m2 ing time time step transport time for a the tetralin plug t o completely enter the preheater transport time for a process stream from the blow case into the reactor through the preheater sand bath temperature adiabatic equilibrium temperature reference temperature wall temperature at position z and time t tetralin temperature at position z and time t inside heat-transfer coefficient Ui, NU kJdi Uf,, kW/(m2*K) heat-transfer coefficient of the fluidized sand U,, 340 W/(m2.K) outside heat-transfer coefficient superficial tube velocity ii, u , 20.4 m/s total space volume of the preheater tubing Vt, m3 height Y ?m plug segment length h,m axial position 2, m kinetic energy coefficient a dimensionless time step B 0.0206T,-0~s797 exp(424.83/(Tr- 140)) Pa.s Pt es, 8238 kg/m3 wall density 973 kg/m3 tetralin density A,t, cm2 C ,, 576 J/(kgK) C ,, 1645 J/(kgK) di, 0.18 in. dl, cm do,0.25 in. e, m eldi
