Nomenclature V = volume of filtrate collected A = filter cake surface area r = resistance of medium (all items except the filter cake) s = compressibility % = time AP = pressure drop across cake, precoat and support p = viscosity of filtrate o = mass of accumulated solids (dry cake basis) per unit volume of filtrate ct = average specific cake resistance cy' = particle size constant
L i t e r a t u r e Cited Electric Power Research Institute Report 206-0-0, Parts II & 111, "Evaluation of Coal Conversion Processes to Provide Clean Fuels", Palo Alto, California, Feb. 1974. Phinney, J . A., Chern. Eng. Prog., 71,65 (1975). Schmid. B. D.. Chem. Eng. Prog., 71,75 (1975). Scotti. L. J.. Jones, J. F., Ford, L., McMunn, B. D., Chem. Eng. Prog., 71, 61 ( 19 75).
Received for review October 17, 1975 Accepted January 26, 1976 This research was sponsored by the Research and Development Administration under contract with the Union Carbide Corporation.
Hot Spot Simulation in Commercial Hydrogenation Processes Stephen B. Jaffe Mobil Research and Development Corporation, Research Department, Paulsboro, New Jersey 08066
The occurrence of steady-state hot spots in a commercial hydrogenation process unit has been explained in terms of limited regions of low flow. A mathematical model has been developed which accounts for the temperature rise with rapid reaction of the fluid in the affected low flow region and for temperature drop with the eventual mixing of cooler fluid from the surrounding region. By matching the commercial profiles, an estimate can be made of the velocity of the low flow region and its lateral extent.
Introduction The axial temperature profiles shown in Figure 1 were observed in a commercial hydrogenation process unit. They represent steady-state profiles taken at the same time through parallel thermocouple wells. These hot spots can potentially cause damage to both the catalyst and reactor vessel as well as degradation of product quality. I t is of great importance to understand the nature and origin of these hot spots and estimate their size. Careful inspection of the profiles shows that the precipitous temperature rises and falls along the length of the reactor are independent of the positions of the interstage cooling. Temperature rises in such processes are not unusual; what is extraordinary are the temperature falls. Since the reactor is adiabatic and under commercial hydrogenation pressure, endothermic reactions are negligible, we are led to the conclusion that the profiles represent disturbances which are local. The marked differences in the two profiles support this conclusion. I t is proposed that limited regions of low flow may be responsible for the hot spots. Reactants entering the affected low flow region convert at a rate greater than those in the surrounding region. The heat liberated by the increased rate results in a higher temperature. As the reactants pass out of the low flow region, they eventually mix with the cooler reactants from the rest of the bed and the heat is dissipated. The cause of such a low flow region, such as catalyst fines or physical obstructions, has been the subject of much work a t our laboratory and will not be discussed here. Rather we recognize that a limited region of low flow can indeed account for the hot spot phenomena and describe the system mathematically with the aim of estimating the lateral extent of the disturbed region. 410
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
This paper provides a synthesis of the method of modeling heat release in petroleum hydrogen process of Jaffe (1974) and the method of modeling flow and mixing in packed beds of Deans and Lapidus (1960). The treatment, while obviously approximate, does serve to simulate the observed phenomena adequately. Heat Generation Heat is generated in petroleum hydrogenation processes by the net consumption of hydrogen (Jaffe, 1974). When hydrogen is consumed by a paraffin or naphthene through cracking or ring opening, a u C-C bond is broken and 7-10 kcal/mol of Hz is released. When hydrogen is consumed by saturating an aromatic, a TT C-C bond is broken and 14-16 kcal/mol of H2 is released. When an olefin saturates, a x C-C bond is destroyed and 27-30 kcal/mol is released. The heat released per mole of hydrogen consumed for these three types is remarkably constant over a wide range of hydrocarbon reactions with hydrogen. Conventionally, the petroleum hydrogenation reactions are modeled by identifying lumped species such as boiling point cuts in the petroleum mixture (Stangeland, 1974; Qader and Hill, 1969; Zhorov et al., 1971). A kinetic scheme is thereby devised accounting for the conversion of reactant lumped species into product lumped species. Rate constants for the kinetic scheme are determined by fitting experimental data. Once heats of reaction are assigned an adiabatic reactor simulation may be made. This approach, while generally useful at ordinary operating conditions for predicting conversion and selectivity, cannot be extrapolated to severe conditions present in the hot spot. What generally happens a t high temperatures to a model constructed in this way is that reactants become exhausted and the predicted reaction and
-5 I
i
I -1
!
INTERSTAGE COOLING
INTERSTAGE
I‘1”/ +
INTERSTAGE COOLING
IO0
0
200 300 400 TEMPERATURE ABOVE N O R M A L REACTOR I N L E T , .F
Figure 1. Commercial temperature profile: -,well profile 1; - - _ _ _ _ -,well profile 2. ~
Figure 2. Idealized obstructed region.
the heat generation cease. In reality the reaction continues with the “product” reacting with hydrogen until there are no carbon-carbon bonds remaining. As an alternative the carbon-carbon bond method of Jaffe (1974) has been used. Here we follow the rate of heat generation by following the rate of hydrogen consumption by u carbon-carbon bonds [C-C], aromatic R bonds [C=C] and olefin x bonds [C=C]’. The bond types are treated as pseudochemical species which react with hydrogen and generate heat. They are arranged in a kinetic scheme:
[c=c]+ H2
ki
a
[c-c]
kz
(-AH1 = 14-16 kcal/mol of Hz) (1) [C=C]’
[C-C]
+ H2 - a
k3
[C-C] (-AH3 = 27-30 kcal/mol of H2)
+ H2 -+ kr
(2)
(-AH4 = 7-10 kcal/mol of H2) (3)
Aromatic x bonds saturate reversibly to form naphthenic (saturate) u bonds. Olefin P bonds saturate to form u bonds and u saturate bonds hydrogenate and crack. The constants Q and Q ’ are stoichiometric coefficients which account for the u [C-C] which become available for reaction when the T bond structure is saturated. Naphthene u [C-C] and paraffin u [C-C] are treated alike. We assume the rate of change of the C-C bond types is first order, that is, the rate of hydrogen consumption is proportional to the capacity to consume it. Thus, for hydrogen in great excess:
-d [C=C] dt
- -k,[C=C]
d --[C=C] dt d[C-C] -dt
’
kz +[C-C] a.
- -k3[C=C]’
- - ( k 4 + k 2 ) [C-C]
+ akl[C=C] + Q’ka[C=C]’
(6)
where t is the true residence time in the reactor. The rate of heat generation is, therefore, given by: d[C=C] d[C=C]‘ rate of heat generation = AH1 - AH3dt dt
+
and the rate of hydrogen consumption is the sum (1 +Q)-
d[C=C] d [C=C] +(l+a’)-+dt dt
’
d [C-C] dt
(8)
Figure 3. Stirred tank network.
In this way it is possible to follow the hydrogen consumption and thus the heat generation across the total range of conversion.
Heat Dissipation The solution of the equations of change for multicomponent flow and reaction in a packed bed necessitated by a rigorous analysis is beyond the scope of this work. Rather a number of simplifications will be made which will greatly facilitate the estimation of the hot spot size. Instead of simulating the entire bed, we choose to consider only a region of low flow immersed in an infinite reacting medium. We imagine an obstruction to have caused a region characterized by some radius in which a low velocity profile is maintained. Beyond this radius, the bed is unaffected. Figure 2 shows a diagram of the system. A very convenient approach to handle this problem is the cell model of Deans and Lapidus (1960). They approximated a packed bed of spheres as a cylindrically symmetrical network of perfectly stirred stages. The network is shown in Figure 3. The reactants are envisioned to enter any given stage as a single phase from the two preceding stages, mix, and react. The equations are those of a single continuous stirred tank reactor. The effluent then feeds subsequent stages so that we treat an initial value problem which is computationally easy to handle. By suitably choosing the size of the stages any radial or axial Peclet number may be matched. Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 3, 1976
41 1
The analysis is a variation of that used by Deans and Lapidus (1960) using a varying velocity profile. Figure 4 is a small section of Figure 3 showing stages j - 2 and j in row i - 1and stage j - 1 in row i. From cylindrical symmetry the cross-sectional area of stage j - 1 may be derived A ( i ,j
'm'
- 1) = a d p 2 K , b2- 0' - 212] = r d p 2 K , [4j - 41
w ( i , j - 1) = tA(i,j - l ) u ( i , j - l ) p ( i , j - 1) = trdp2K,[4j - 4]u(i,j - l ) p ( i , j
- 1)
(10)
is the void fraction, u(i,j)is the linear fluid velocity, and p ( i , j ) is the average fluid density. A total mass balance may be used to relate the w ( i , j ) to the mass flow w ( i - 1,j - 2) and w ( i 1,j ) . The mass flow into stage j - 1from stage j - 2 through area a is t
w, = tndp2K,[2j - 3]u(i - 1, j - 2 ) p ( i - 1,j - 2) (11) similarly Wb
= trdp2K,[2j
- l ] u ( i - 1,j ) p ( i - 1,j )
(12)
Therefore, we may write
+ W b = tndp2K,([2j - 3 ] ~ (-i 1,j - 2) - 1,j - 2 ) + [2J - l ] u ( i - l , j ) p ( i - 1,j)) (13)
w ( i , j - 1) = wa p(i
I
(9)
where d p is the characteristic catalyst pellet diameter and K , is the number of pellets diameters per radial stage. The mass flow rate in stage i, j is then:
vL:j v
.
0
M-2 M M*2
Figure 5. Low flow velocity profile a t obstruction
' I
[E]
u ( i - l , j ) p ( i - 1,j) (14)
Equation 14 allows the calculation of the product u p (mass flux) in any row i from the knowledge of previous row i - 1. To treat the chemical conversion, we write a continuous stirred tank mass balance for each component in stage i, j 1. For the kinetic rate eq 4 and 6 (olefin contribution may be ignored)
j
j -2 Figure 4. Stirred tank network detail.
and combining with eq 10 we get
+
j+ I
j-l
j -3
I
M+I
I Figure 6. Stirred tank network detail a t boundary with unaffected region.
A similar equation may be written for 42(i - l,j - 1).K , is the number of characteristic pellet diameters per axial stage. The heat balance of a continuous stirred tank reactor is
+ k2a
= -klCI(i,j - 1) - C2(i,j - 1) (15) = f i I [ - k l C l ( i , j - 1)
+ kq)C2(i,j - 1) + aklCl(i,j - 1)
= -(k2
@l(i
+ f i 3 [ - k & d i , j - 1)l
(16)
Cl(i,j - 1)and Cz(i,j - 1)are concentrations of aromatic K bonds [C=C] and saturate u bonds [C-C], respectively, in moles per gram. &(i - 1,j - 1)and 42(i- 1,j - 1)represent the average feed compositions to stage j - 1from row i - 1 of [C=C] and [C-C].
k2 +C2(i,j - l)] a
where analogously to 4, $(i - 1,j - 1) is the average feed temperature to stage j - 1 from row i - 1
$(i - 1,j- 1)
wa C l ( i - 1,j- 2) - l j - 1) = ___ w a -k w b
&(i
412
- l j - 1) =
1
[ 2 j - 3]u(i - 1,j- 2 ) p ( i - 1,j - 2 ) C l ( i - 1,j - 2 ) [2j - 3]u(i - l j - 2)p(i - 1,j - 2 ) [2j - l]u(i - l , j ) p ( i - 1 , j )
Ind. Eng. Chem..
+
Process Des. Dev., Vol. 15, No. 3, 1976
(19)
Table I. Charge Stock Properties (API Gravity 36.4; Hydrogen Content 13.12%; Molecular W t 224) Aromatics Wt % by silica gel, 27.9; Mol wt, 201
Non-Aromatics Wt % by silica gel, 72.1; mol wt, 234
c=c/
c=c/ Alkylbenzenes Tetralins, indanes Alkyl naphthalenes Acenapbthenes, flourenes Phenanthrenes, anthracenes
mole
RA
RN
mol%
3 3
1 1
0 1
31.9 48.1
5
2
0
9.7
5-6
2
0
9.1
7
3
0
1.2
mole
Paraffins 1 Ring naphthenes 2 Ring naphthenes 3 Ring naphthenes 4 Ring naphthenes Mono-aromatics
When eq 11 and 12 are combined with eq 20, the result is similar t o eq 18. C,(i - l j )is the average heat capacity of the fluid a t the temperature found in stage i - 1,j.Equations 15 and 16 can be combined and solved implicitly for Cl(i,j - 1) 1)and Ca(i,j - 1).
Since the rate constants are Arrhenius functions of temperature, eq 19,21, and 22 form a set of coupled transcendental equations. These may be easily solved with eq 14,18, and 20 using a Newton-Raphson algorithm. Because of the initial value nature of the problem, each stage may be solved in turn stepping from one row to the next. An interesting parameter in systems which generate great amounts of heat in a small region is the adiabatic flame temperature. This may be calculated by the formula adiabatic flame temperature = (AH1 aAH3)4l(i - 1,j - 1) + AH342(i - 1,j C J i i - 1)
+
- 1)
U(1,m - 2) = urnin U ( l , m )=
(23)
0 0
0 1
58.7 15.0
0
2
12.1
0
3
10.3
0
4
3.4
1
0
0.5
At the boundary with the unobstructed region, the stages are arranged as shown in Figure 6. If row i - 1is thought of as the first row of the calculation, there is no problem to calculate the behavior of stage M 1 in row i in the ordinary way. Stage
+
-
+
M 2, on the other hand, is a t the edge of the infinite reacting medium and requires special treatment. The velocity here is kept constant at L'bulk. Fluid mass is thus continually supplied to the affected region. The feed compositions and temperatures are $1(i,MPP) = Cl(i,MPl) 4p(i,MP2) = Cz(i,MPl) (26)
These conditions keep the radial gradients of temperature and composition a t zero. At the center line the standard conditions for symmetry are used:
u(i
+ l , l ) p ( i + 1,l) = u ( i , l ) p ( i , l )
umin
+ -1 (ubulk - umin)
Experimental Section
3
2
Urnin
mol%
ri/(i,MP2) = T ( i , M P l )
Initial and Boundary Conditions The exact nature of the velocity variation between the minimum in the obstructed region and the bulk value in the unaffected bed cannot be determined. For simplicity the profile shown in Figure 5 was used as the inlet velocity profile. u(1,j) =
RN RA -
+ -3 (Ubulk - Urnin)
U(1,m -k 2) = Ubulk
(24)
The initial composition profile and temperature profile were flat Cl(i,j) = CIO C A i J = CZO T(i,j) = To
(25)
An experimental program was undertaken to obtain the rate constants defined by eq 4,5, and 6. A set of isothermal single pass runs were made with a 100-cm3bench scale laboratory reactor. The properties of a typical charge stock are listed in Table I. The space velocity was varied between 0.3 and 7 times the commercial rate while the Hz circulation rate and pressure were kept a t the commercial level. The isothermal temperature was varied over a 400 O F range above normal operating conditions. The product concentration of bond species was determined via mass spectrometer type analysis using the method described by Jaffe (1974). Ind. Eng.
Chem.. Process Des. Dev., Vol. 15,No. 3, 1976
413
At extreme conditions the product composition seemed to be approaching a mixture of light gases whose hydrogen to carbon ratio (H/C) corresponded to about a 1:l mixture of ethane and propane. The bond method assumes reaction ceases a t complete conversion to methane H/C = 4. In order to force the reaction end point carbon to hydrogen ratio B a t a lower value, we have modified the bond determination method. The analysis is given in Appendix I. The initial bond concentration was found to he
:: 20 2 ul
5
5 5
5
,on
[C=C] = 0.00482 mol/g of oil = 539 scf/bhl [C-C]
= 0.0378 mol/g of oil = 4217 scfhhl
Appendix I1 contains an example of how these compositions were calculated. Since the data were taken isothermally, the rateconstants could he fit to the integrated form of eq 4, 5, and 6. These equations are given by Jaffe (1974). The Rosenbrock method of rotating coordinates was used for the nonlinear parameter estimation. A compound objective function was used containing both the deviations from the observed C=C and ohserved hydrogen consumed. I
Choice of Model P a r a m e t e r s The density p ( i , j ) was estimated by the formula with an ideal gas temperature dependence = 0.036
[-T11084 (id
g/cm3
The average heat capacity Cp(i,j) used was estimated from enthalpy correlations a t
C,(i j) = 0.95
+ 0.0001613(T - 1100) kcal/g K
The heat of reaction for aromatic saturation was averaged a t 15.5 kcal/mol of Hz and for paraffin saturation a t 10 kcal/mol of HP.The effect of temperature on AHr was ignored. Wilhelm (1962) and others have found that, for sufficiently high Reynolds numbers, the Peclet numbers in both the axial and radial direction are constant; Per = 11.8 and Pe, = 2.0. Deans and Lapidus (1960) show that the stirred tank model will approximate these Peclet numbers when each stage is 0.845dp in width and LOdp in length; that is, K , = 0.845 and K, = 1.0. Results Once the model parameters are evaluated, specification of a low flow profile and radius of obstruction is sufficient to uniquely determine the spatial distribution of temperature. Numerous computer simulations were prepared varying the size and severity of the low flow region. The shape of the hot spots is similar to that shown in Figure 7 .The low flow in the affected region causes the temperature along the center line to rise rapidly to a maximum while off the center the changes are less severe. The cooler unaffected fluid continually mixes laterally in toward the center from the surrounding bed. Eventually, the center is reached and the profile crests. The temperature then drops, rapidly a t first, then more slowly until the heat is dissipated. The rise and fall are not symmetrical hecause the mechanism for one is different than for the other. We may characterize the simulated temperature distrihution by a "maximum temperature rise" (AT,.,) and a "heat dissipation length" (HDL).The maximum temperature rise is the greatest difference in the radial direction between the temperature inthe low flow region and the temperature in the unaffected region. The heat dissipation length is the distance from the onset of low flow to the point a t which the maximum 414
Ind. Eng. Chem.,
ProcessDes. Dev., Val. 15. No. 3. 1976
Figure 8. Graph for estimating hot spot size.
FLED
'r' Figure 9. Comparison of calculated and measured temperature profiles: -, well profile 1; - - - - .- - - - -,predicted profile;. .., "normal" profile.
.......
I
I
LeL'.pala'Ule
:--L..z.l,.-L.,,
'.*e "a3 'allecl
LO
:... . ,..- xr,L:,.&L--. . L . no LLb Yalue. " Y l l l l r L I I e a e C I I a r -
acterizations are somewhat arbitrary, they facilitate comparison between the model and the ohserved commercial hot spot profiles. We have determined ATm and HDL for a wide range of low flow velocities and hot spoit radii. The results are shown in Figure 8. The largest value of AT,,, is seen to be 675 O F which is the predicted adiabatic temperature rise and not far from the maximum observed value. This indica tes that whatever the ~
error in the individual parameters, their ratio given by eq 23 is not too far off. The calculations were not extended beyond 15 f t because that is the length of the reactor bed. The radius corresponding t o this H D L is 4 in. Obstructed regions larger than this generate too much heat to be cooled by the surrounding bed. Figure 8 allows us to estimate the size and severity of observed profiles. If we examine profile 1 in Figure 1, we may estimate for the hot spot in bed 4 AT,,, = 220 O F and H D L = 13.2 ft. From Figure 8 the velocity of low flow is 0.044 and the radius of the affected region is 3.3 in. The theoretical curve is matched to the observed in Figure 9. In summary, we have constructed a model of a hot spot caused by limited regions of low flow. I t may be used either to estimate the size and severity of the region based on measured temperature profiles or estimate that temperature profile given the size and severity of the region.
The reaction scheme then becomes
Appendix I Extension of Bond Analysis Reaction E n d Point. If B is the H/C ratio when hydrogen consumption ceases, then the total carbon-carbons are
0.319(3)
total C-C = 2C
B 4
- -H
(A-1)
Since B is less than 4, there are less total bonds because some must be reserved for the molecules which compose the inert product (e.g., ethane, propane). A reasonable approach is to adjust only the u C-C bonds because [C=C] and [C=C]’ can convert completely to C-C consuming the full measure of hydrogen. Thus, from Jaffe (1974) C-C
= total C-C
- 2[C=C]’ - 3[C=C] - (RA- RAS) (A-2)
and substituting Equation (A-1) and others from Jaffe, we get
(A-6) [C=C]’
(
[ c - c ] = Y [12 3(1-Ho) 12
(t- + -i)
2c
2C
12
+
k,i
[C-C]
a’
(2 - -3[C-C]
+ Hz
k4
(-4-8)
---*
By eq A-1 the hydrogen consumed by reaction A-8 becomes AHZISC - C = Bf4. The hydrogen consumed by reactions A-6 and A-7 is unchanged.
Appendix I1 Calculation of Initial Bond Compositions. Using the data in Table I, the moles of [C=C] per mole aromatic is:
+ 0.481(3) + 0.097(5) + 0.091(5.5) + 0.012(7) = 3.47 mol of [C=C]
mol of Arom
The moles of [C=C] per mole of nonaromatic (due to separation error) is 0.005(1) = 0.005 mol of [C=C]/mol of Arom. The total concentration of [C=C] is, therefore [C=C] = 0.279
0.005 (-)3.47 + 0.721 (x) 201 = 0.00483 mol/g of oil
Using the formula
we may calculate CA/C
C A-_ C
(0.00483) = 0.133 C on aromatic/total carbon 2(12) 1 - 0.1312
The concentration of [C-C] is calculated from eq A-4 which requires the calculation of RA and RT, the average numbers of aromatics rings per molecule and total rings per molecule, respectively. RAin the aromatic fraction is 0.319(1)
or
+ Hz
+ 0.481(1) + 0.097(2) + 0.091(2) + 0.012(3) = 1.212 R.k/mol of Arom
RAin the non-aromatic fraction is 0.005(1) = 0.005 RA/mol of non-Arom. Combining:
+
Ho - -( ~ R A RT - 1)] (A-4) MW
Because the aromatic and olefin saturation reactions remain unaffected by the end point H/C ratio but paraffin reactions are changed, the stoichiometric relations of Jaffe (1974) must be rederived. The stoichiometric coefficient a is the increase in [C-C] for every [C=C] or [C=C]’ saturated. The c C-C bonds produced by eq 1must be recalculated on the new end point in order to treat them the same as [C-C] in eq 3. These [C-C] are naphthenic bonds with H/C = 2 so by eq A-1
= 0.380 Arom ring/mol
Similarly for R N ,the average naphthenic rings per molecule, R N in the aromatic fraction = 0.481(1)-= 0.481 RN/mol of Arom. R N in the non-aromatic fraction is 0.15(1) + 0.121(2)
+ 0.103(3) + 0.034(4) = 0.837 RN/mOl of non-Arom
and combining:
-
2 2
- E (2) B 2
- - (2) 4
= 0.727 naphthenic rings/mol =2
- -4 (A-5) B
RT = RA
+ RN = 1.107 totaimolrings
For a reaction end point corresponding to a 1:1ratio mol of Ind. Eng. Chem., Process Des. Dev.. Vol. 15,No. 3, 1976
415
ethane to propane B = (6 eq A-4
[c-c]
[
1 = - 3(1
- 12
12
+ 8)/(2 + 3) = 2.8. Now, applying
- 0.1312)
(i- + 2’s)
(0.1312) - l2 (3 (0.380) 224
[c-c]
K , = number of pellet diameter per radial stage K , = number of pellet diameter per axial stage M W = average molecular weight Pe = Peclet number = V l / D = (velocity)(characteristic length)/diffusivity
1
+ 1.107 - 1)
= 0.0378 mol/g of oil
Nomenclature a = stoichiometric coefficient A(i,j) = area of stage j in row i B = hydrogen to carbon ratio a t complete conversion C = total carbon atoms per molecule C(i,j) = concentration of reactants in stage j in row i CA = aromatic carbon atoms per molecule CO = olefinic carbon atoms per molecule C,,(i,j) = heat capacity a t constant pressure at the temperature in stage i,j [C-C] = concentration of c carbon-carbon bonds, mol/g [C=C] = concentration of aromatic x carbon-carbon bonds, mol/g [C=C]’ = concentration of olefinic x carbon-carbon bonds, mol/g d p = catalyst pellet diameter H = hydrogen atoms per molecule H D L = heat dissipation length AH = heat of reaction i = index for stirred tank in axial direction j = index for stirred tank in radial direction k = first-order rate constant, (lh)
R A = average number of aromatic rings per molecule RAS = average number of substantial rings per molecule RT = average total rings per molecule AT,,, = maximum temperature reached in the hot spot t = time, s T(i,j) = temperature of fluid in stage j or row i Ubulk = average fluid velocity in unobstructed region urnin = minimum velocity in obstructed region
u ( Q ) = fluid velocity in stage j or row i w ( r , j ) = mass flow rate of fluid in stage j of row i
Greek Letters t = void fraction p(i,j) = density of fluid in stage j or row i $(i - 1,j) = average concentration of fluid entering stage j in row i from row i - 1 $(i - 1j) = average temperature of fluid entering stage j in row i from row i - 1 Literature Cited Deans, H. A., Lapidus, L., AlChE J., 6 (4), 656 (1960). Jaffe, S. B., lnd. Eng. Chem., Process Des. Dev., 13, 34 (1974). Qader, S. A., Hill, G.R., lnd. Eng. Chem., Process Des. Dev., 8, 98 (1969). Stangeland, B. E., lnd. Eng. Chem., Process Des. Dev.. 13, 71 (1974). Wilhelm, R. H.. Pure Appl. Chem., 5 , 403 (1962). Zhorov, Yu. M., et al.. lnt. Chem. Eng., 11 (2), 256 (1971).
Received for review October 20, 1975 Accepted February 2,1976
The Oxidation of Bituminous Coal. 3. Effect on Caking Properties A. Y. Kam, A. N. Hixson, and D. D. Perlmutter’ Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 79 7 74
A quantitative study is reported of the effect of oxidation on the caking propensity of bituminous coal. An empirical caking index is found to correlate well with a defined semiempirical oxidation parameter. The preferred oxidation temperature for decaking treatment was found to be about 200 OC,since the higher oxygen utilization at higher temperatures does not appreciably contribute to the desired effect.
In two previous papers of this series (Kam et al., 1976a,b), a study was reported on the modelling and experimental kinetics of the oxidation of bituminous coal. This paper presents a quantitative study of the effects of oxidation on the caking properties of the coal samples used in the kinetic evaluations of Part 2. The samples, whose oxidation history is given in Table I, were tested to determine how changes in their caking properties could be related to the oxidation rate and extent parameters. In order to gain insight into the phenomenon of caking and the effect of oxidation of bituminous coal on its caking properties, it is desirable to establish a quantitative correlation between the extent of oxidation and the corresponding reduction in caking tendency. Such a correlation will also facilitate the practical application of the caking test data obtained here to the design of pretreatment processes. 416
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
The Plastic Properties of Coal When coal is heated, it undergoes two stages of change: the coal first softens and becomes “liquid-like,” and subsequently the particles cake and form a compact mass which swells and resolidifies into a coherent body with a porous structure, i.e., coke. At the same time the coal undergoes a chemical transformation, evolving gases and condensable vapors, and leaving a residue consisting almost exclusively of carbon and ash. The properties associated with these changes are generally referred to as the plastic properties of coal and have been studied extensively in researches on coke-making. Comprehensive reviews on the numerous papers published on this subject have been given by Howard (1963) and Loison et al. (1963). In general, the models proposed on the softening and caking phenomena of coal may be classified as physical or physico-
