Kinetics of Heat Release in Petroleum Hydrogenation Stephen B. Jaffe Mobii Research and Development Corporafion, Paulsboro, New Jersey 08066
Net consumption of hydrogen in petroleum processing is accompanied by heat generation. A new method is described to predict heat release by following the hydrogen consumed by important classes of hydrocarbons. Typical petroleum reactions consuming hydrogen have been classified according to the quantity of heat released: olefin saturation 27-30 kcal/mol of H2, aromatic saturation 14.5-16.5 kcal/mol of H2, and saturate cracking 7-10 kcal/mol of H2. Carbon-carbon bond types, which react with hydrogen to liberate heat, are identified in the reaction classes. The bond types, olefin ir carboncarbon bonds, aromatic x carbon-carbon, and u carbon-carbon bonds are treated as pseudochemical species and arranged in a kinetic scheme which simulates petroleum hydrogenation reactions. Experimental determination of the concentration of bond types in petroleum mixtures is discussed and the method is applied to a commercial hydrogenation process. The fit to experimental data is shown.
Introduction Energy is always consumed when chemical bonds are broken and liberated when they are formed. Heat is generated in a chemical process when the energy liberated in bond formation exceeds t h a t consumed during bond breaking. When a hydrocarbon is cracked without a net consumption of hydrogen, a n olefin is usually one of the product molecules. The energy required to destroy one reactant u carbon-carbon (C-C) bond is greater t h a n the energy gained when t h e product olefin 7r carbon-carbon bond is formed and the overall process is endothermic. H H -C-C-C*H H
H
H
H
H
H
H
~~
-C-CH
i
H
H
H ._
+ C=CH
H
AH > 0
However, when hydrogen is consumed to create C-H bonds a t the expense of a C-C bond and a H-H bond, the result is the evolution of heat. H H -C-C-C-CH H
H
H
H
H
+ H-H G H -C-CH H H
+
H
H
H
H
+ HC-C-
AH < O
(2)
In any petroleum process where there is consumption of hydrogen, there is the potential for generation of large quantities of heat. In this work we concern ourselves exclusively with a method for mathematically modeling this heat release.
Heats of Reaction T h e general phenomenon of heat release in hydrogenation may be best understood with a brief review of thermochemistry. T h e quantity of heat evolved in a petroleum conversion process is related to the extent of hydrogen consumption. When hydrogen is consumed, H-H bonds are always broken and C-H bonds are always created. The energy content of C-H bond is reasonably constant and, therefore, variations in the heat release per mole of hydrogen consumed is related to variations in the energy required to break the C-C bond in the hydrocarbon. T h e C-C bond energy varies with the hybridization state of the carbon atoms and the strain of the configuration (Mortimer, 1962). A survey of typical reactions shows t h a t the heat released falls into several important classes depending upon the type of C-C bond cleaved. When hydrogen is consumed by a u C-C bond, there is either cracking or ring opening. Table I (Stull, e t al., 34
Ind. Eng. Chem., ProcessDes. Develop., Vol. 13,No. 1, 1974
1969) lists a number of these reactions. T h e heat released per mole of hydrogen consumed is virtually constant for paraffins at 10.4 kcal/mol of H2 (Table I, reactions a,g). There is a n exception if the scission involves a terminal C-C bond because the energy content of a C-H bond in methane is slightly different from a C-H in a methylene group. When methane is formed, there is deviation from the usual quantity of heat released to 15 kcal/mol of HP (reactions h,l). However, this is not a n important consideration in catalytic hydrogenation because the methane make is low. When hydrogen is consumed to open u C-C bonds in a naphthene ring, the heat released depends upon the strain in the system. The energy required to break a highly strained bond is less than a n unstrained. Therefore, the greater the strain, the greater the heat release per mole of hydrogen consumed. Cyclohexane which is unstrained yields 10.5 kcal/mol of HP similar to paraffins but cyclopentane which is strained yields more, 16.54 kcal/mol of H2 (reactions m , n ) . Cleaving decalin and hexahydroindane bear the same relation (reactions o,p,q). Isomerization involves no net change in hydrogen and the energy change is minimal. In general, heat is released with increasing branching. T h u s when methylcyclohexane cleaves to n-heptane, less heat is released t h a n to 2-methylhexane (reactions s,t). When the side chains of aromatics are broken away, heat is released. The u bond adjacent to the aromatic contains about 3 kcal/mol more than a u C-C bond in a paraffin. Hydrogenating t h a t bond produces less heat usually between 6.5 and 8.0 kcal/mol of Hz (reactions u,z). When it is the aromatic system itself that is attacked, the energetics are quite different. Destruction of the conjugate 7r bonds of a n aromatic structure requires less energy per mole of hydrogen t h a n does cleaving a u C-C bond. Consequently, the heat released during saturation is larger than the 10 kcal/mol of H2 associated with cleaving u C-C linkages. In Table II (Stull, e t al., 1969) a number of typical saturation reactions are listed. T h e heat release is remarkably constant u p to four rings. The resonance and strain considerations are similar since the configurations are limited to six-membered rings. If the K C-C bonds are not conjugated as in olefin saturation, the heat release is much larger because t h e energy held in t h e bond is less. Several olefin saturation reactions are listed in Table I11 (Stull, et al., 1969). Aliphatic olefins release a fixed quantity of heat upon saturation indicating the 7r bonds are uniform in energy (reactions a,d). The heat released from saturating side chains of cyclic compounds is only slightly less (reactions e,f) as is that from saturating cyclohexenes
Table I. Saturate Hydrogenation Reactions
Table 11. Aromatic Saturation Reactions AH, kcal’ mol of H,
AH,
kcal/ mol of Hz -10.4 -10.4 -10.4 -10.4 -.lo. 4 -9.7 -10.3 -13.0 -13.0 -13.0
n
Q-+ H, - ~ - C ~ H ~ ,
-16.4 -16.3 -15.9
-13.3
-15 5
-15.5 -10.5
-16.7
-16.5
-15.4
-7.4
-15.3
-14.4
-14.9
-9.1
-15.9
-8.7
-18.5
-7.9 -9.6
6.9
Table 111. Olefin Saturation Reactions AH, kcal mol of H?
-30.0 -30.0 -30.0 -32.8 - 2 8 .I
A
7.3
-29.5 -28.2
-7.0 .7.4 -23.8 -24.3
(reactions g j ) . Cycloolefins adjacent to aromatics are partially stabilized and the heat release is several calories less t h a n straight chain olefins (reactions j,k). In summary, the heat release from hydrogen consumption in hydrogenation falls into three important categories: saturates consume hydrogen with cracking or ring opening and yield 7-10 kcal/mol of H,; aromatics saturate yield 14-16 kcal/mol of Hz; and olefins saturate yield 27-30 kcal/mol of Hz.
Carbon-Carbon Bond Kinetics Heat release depends upon t h e distribution of hydrogen consumption between saturates, aromatics, and olefins. It
is desirable to follow the rates ot hydrogen consumed by these species. However. a single molecule can consume hydrogen as a n olefin, an aromatic, or a saturate so we focus instead on t h e C-C bonds in the molecule rather t h a n t h e molecule itself. One C-C bond must be broken for each mole of hydrogen consumed, therefore. we may treat C-C bonds stoichiometrically as pseudochemical species which have the capacity to react with hydrogen and generate heat. When hydrogen is consumed by a saturate, a u bond is broken. If [C-C] represents a concentration of u C-C bonds in moles/liter, we might write a simple reaction for cracking or ring openings Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 1 , 1974
35
+ HJ
[C-C]
- A H = 7-10 kcal/molH2
-+
(3)
We already know t h a t the heat release for this reaction is between 7 and 10 kcal/mol of H2, and we postulate t h a t all u C-C bonds consume hydrogen with a single rate constant. It must be remembered t h a t bonds disappear as hydrogen is consumed and, as eq 3 indicates, bonds are not conserved. For example, when n-hexadecane C16H34 reacts with hydrogen to form 2 mol of octane C8H18, the 15 bonds in the reactant decrease to 14 in the product. Similarly, when cyclohexane converts to hexane, six bonds decrease to five. When aromatics are saturated. H bonds are destroyed and u C-C bonds of the resultant naphthenes become available to consume hydrogen. If [C=C] represents in a simplistic sense a concentration of P bonds in moles/liter then for saturation [C=C] -t HL ?--, ajC-C] - A H = 14-16 kcal/mol H. (4) Here we postulate that all aromatics consume hydrogen reversibly a t the same rate and that the naphthene bonds produced consume hydrogen at the same rate as in eq 3. T h e heat release for this reaction has already been shown to be reasonably constant at 14-16 kcal/mol of H2. T h e stoichiometric coefficient, a, is the number of naphthenic bonds made available for each aromatic H bond saturated, a = - A[C-C]/A[C=C]. Saturation reactions have been described this way because it is unlikely t h a t the u C-C bonds in the resonant structure can consume hydrogen before t h e H bonds, therefore, we do not count them until t h e after saturation. T h e stoichiometric coefficient varies with t h e degree of condensation. For a single uncondensed aromatic ring (substantial ring) six u C-C bonds become available for each three T C-C bonds saturated, a = 6/3 = 2. For example
8 -0
Olefins can be treated in a manner analogous to aromatics with the stoichiometric coefficient set to one (the u C-C bond associated with the T bond becomes available). I t is not as necessary to preclude reaction a t u bonds adjacent to the x bond for olefins as for aromatics. However, if such attack were thought to be less likely, it could be reflected by adjusting the stoichiometric coefficient a ’ . If [C=C]’ is the concentration of olefinic x bonds in moles/ liter, then we may write
+ H2
[C=CY
-
a’[C-C]
- A H = 27-30 kcal/mol ( 5 )
T h e heat release for this reaction is between 27 and 30 kcal/mol of Hz and a’ = 1.0. Equations 3, 4, and 5 are representations of how various bond types must change when hydrogen is consumed. We now assume the rate of reaction is first order with bond concentration. In doing this, we take the rate of hydrogen consumption to be proportional to the capacity to consume it. Thus for the scheme
k
[C-C] + H J 9
We may write the following differential equations
d[C-Clldt
=
- k,[C-CI - k2[C-C] + ak,[C=C]
a’k,[C=C]’
+ 3H2
[C=Cl = 0 [C-C] = 6
[C=C] = 3 [C-CI = 0
A[C-C] - 3 - -~ A[C=C]
-
On the other hand, when one ring of a kata-condensed system saturates, five u C-C bonds become available for each two aromatic P bond, a = 5/2. Thus
a /
/
+ 2H2
[C=C],=
[C=Cl,,
[C=Cl’
=
rc=cl,’, [C-CI
= {[(A,
- k2
{[(As - k 2 - k,)[C=Cl,
a is either 2 or 5/2 over a wide range of compounds. S a t u -
=
[C-cl,
k,
- k,)[C=Cl,
-
[C=Cl = 5 [C-CI = 5
= 7 [C-CI = 0
-
; [C-Cl”
ak2 [C-CIO -
ration of the center ring of a polycondensed system might at first seem to violate these principles
a+.,-+ \
/
/
\
\
[C=C] = 6 [C=Cl = 7 A[C-C] 1C-Cl = 4 --A[c=c] [C-Cj = 0 = 4 However, a substantial ring is created and when it saturates the average is brought into line +4H?-+
[C=Cl = 7 [C-CI = 0
36
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1. 1974
(9)
These may be integrated subject to the initial conditions. Att=O
[C=Cl
-+
[ H I
+
LC-C]
=
{[(A,
- k,)[C-C], - a k ~ [ C = C l ~-
-
where
C=C
k,
-4
+ k , +k 4 ) 2
A I = (
(I4)
+
T h e kinetic scheme in eq 6 is stoichiometrically consistent with hydrogen and therefore the hydrogen consumed along a reaction p a t h may be calculated from a simple algebraic expression. The hydrogen consumed, HzCON, is the difference between the number of C-C bonds initially and those a t t h e time under consideration. T h u s H,CON = [[C=C],,’
- [C=C]’]
+ [[C=C],
- [C=C]]
-I-
[[[C-C],, - [C-C!]+
u[[C=Cl, - [C=Cll+ a’[[C=Clo’ - [C=Cl’ll (15) T h e third term contains the contribution to t h e u C-C bonds [C-C] from saturated aromatics a n d olefins. Rearranging eq 15
+
H&ON = (a’ 1) [[C=C]o’ - [C=CI’I -I( a 1) [[C=CI, - [C=CII [[CCIo - [C-C
+
+
(16)
Equations 11, 12, a n d 13 may then be substituted into eq 16 and the total hydrogen consumption evaluated as a function of time, the rate constants. and the initial concentrations of the bond species. We may relate C--C bond conversion to boiling point conversion which is traditionally used to follow hydrogenation reactions. When hydrogen is consumed in the saturation reaction. there is little difference in boiling point between reactants a n d products. There is never fragmentation. On the other hand. when hydrogen is consumed with cracking or ring opening, we usually get boiling point reduction. If we plot boiling point conversion against the true conversion of u C-C bonds l [ C - C ] calculated by the formula A[C-C]
=
[[C-CIO - [C-C]]
+ a[[C=Cl, a’[[C=Clo’
- [C=C]]
- [C=Cl’l
-I-
(17)
we should find a strong correlation. Determination of the bond species has not been dealt with previously and, therefore. will be discussed in t h e following section.
T h e species in t h e kinetic description are defined by t h e bond type and not the molecular type. Analytical method must measure the quantity of bonds and not the quantity of molecules. The concentration of olefin bonds [C=C]’ may be measured with t h e bromine number. Each olefin bond will a b sorb one bromine molecule so the measurement in centigrams of bromine per gram is direct. However, some aromatics are also attacked and the test tends to overestimate. Since olefin saturation liberates t h e largest amount of heat per mole of hydrogen consumed, overestimates are preferred for design and safety purposes. If p is the oil density in g/cc [C=C]’
= p
bromine n u m b e r 15.98
moles liter
1 5Ca
(19)
T h e n-d-M (refractive index, density, molecular weight) correlations developed by Van Nes and Van Westen (1951) may be used to estimate Ca/C, the fraction of total carbon which is aromatic. [C=C] is then calculated from the weight fraction, H , and the density, p
C=C or Ca may be measured directly from a mass spectrometer type analysis by simply summing the contribution from each type. Each mole of alkylbenzenes, tetralins, and indanes contribute 3 mol of C-C, alkyl naphthalenes 5 mol of C=C. and alkyl anthracenes 7 mol of C=C and so on. T o calculate [C-C] by this method the average molecular weight is necessary.
(21) The available u C-C bonds per molecule is the total number of bonds ( u , x ) less those associated with aromatics and olefins. Since carbon always has four bonds, the total number of C-C bonds per molecule is the difference between four times the number of carbon atoms and the number of hydrogen atoms. However, each C-C bond is counted twice; therefore, we divide by 2 giving 1 H t o t a l C-C = 3 ( 4 C - H ) = 2C - (22) I
Equation 22 is true for all hydrocarbons but does not distinguish between bond types. In order to determine the available u C-C bonds, we must subtract from eq 22 those bonds which are not available. For each olefinic ir bond C=C’ we must deduct two bonds: one ir C=C’ and one associated u bond. However, for each aromatic A bond C=C there are two u C-C bonds unavailable: one associated with t h e A bond and one adjacent to it. In condensed aromatic systems there is one additional u C-C bond for each aromatic ring Ra in excess of the substantial ring Ras. Equation 22 is, therefore, modified t o available C-C = total C-C - 2C=C’ 3C=C - ( R a - R a s l
(23)
The general formula for a kata-condensed hydrocarbon (Van Nes and Van Westen, 1951) is H = 2C 2 - ( 2 R t 2Ras 4Ra Co) (’34) where R t is the total rings per molecule and Co is t h e number of olefinic carbon atoms. We solve eq 24 for Ras and substitute eq 19 and 22 into (23) noting by analogy with eq 19 C=C’ = YzCo to get
+
Determination of Carbon-Carbon Bond Species
=
+
+
+
available C-C = -H-(3Ra+Rt-1)
(255)
Equation 25 is valid for any kata-condensed hydrocarbon. We may check eq 23 and 25 for a hypothetical molecule
(18)
Determination of aromatic bonds [C=C] is also straightforward. T h e number of aromatic A C-C bonds per molecule C=C is always equal to half the number of carbon atoms in the aromatic (conjugated) portion of the molecule Ca.
Ca
= 12 co = 2
Ra = 2 Rt = 4 Ras = 2
C=C
=6
C=C’
1
t o t a l c - C = 34
Ind. Eng. Chem., Process Des. Develop.. Vol. 13, No. 1 , 1974
37
m
//L
U \ U (0
2+
3000
-
1500. 1
m m \
/ I
u
W E
v, U
2
+ i!
1000-
n W E
a
y
5001
0 H 2 CONSUMPTION OBSERVED
, "--
Figure 1. Fit to
H2 consumption
-
SCF/BBL
500
IO00 L
data.
1500
OBSERVED S C F / B B L
C=C
-
c--"aA-
2 , A-;:
Figure 2. Fit to saturation d a t a
By eq 23: available C-C = 34 - 2 - 18 = 14 bonds/molecule and by eq 25: available C-C = 3 2 4 ) - 38 - 18 - 9 - 3 = 14 bonds/molecule. The units of eq 25 are moles of bonds per molecule and must be changed to moles of bonds per liter. This is accomplished by introducing the density. p , the average molecular !\eight. MK'. and hydrogen content, H
12
t3Ra
+ Rt -1)
1
(266,
Ra. Rt. and as mentioned before. C a / C may be estimated from the n-d-M correlations or measured directly with a mass spectrometer type analysis. The above analysis is based on eq 20 which may be rearranged to add insight into the method
Carbon is not laid down as coke under ordinary conditions in a high hydrogen atmosphere so the amount of chemically combined carbon is invariant. T h e hydrogen-to-carbon ratio. H/C. is the reaction variable in eq 27 which can increase to a maximum value of four. This corresponds to conversion to methane and a zero rate of hydrogen consumption. Methane has np C-C bonds and is. therefore. "inert."
Comparison to Experimental Data The bond method was used to model heat release in a commercial hydrogenation process. In a n experimental program several charge stocks were processed over a wide range of conditions in pilot plant reactors. Complete mass spectrum type analyses were obtained for each charge stock and on selected products. From these. the bond concentrations were determined using the methods discussed above. Olefins were not present in the charge stocks so the analysis presented in eq 6-16 was used with the olefin concentration set to zero. The temperature effect on the rate constants is assumed to be Arrhenius. Since the activation energies of a reversible system are related by heat of reaction we have the constraint E? = E , A H 2 = E: 15.5 (28)
+
38
+
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 1, 1974
Figure 3. Relationship between boiling point conversion and C-C bond conversion.
Three frequency factors and two activation energies were then determined by fitting hydrogen consumption data to eq 16 and the A C-C bonds to eq 11 simultaneously by minimizing the objective function
4=
'
[HJON - H?CO?;]' -I-
[
pred
obsd
It' [C=C] pred
- [C=Cl
]y
(29)
obsd
The weighting factor. W, is necessary because the accuracy of the hydrogen consumption measurements is different from most of the C=C measurements. Since we fit the hydrogen consumed and the A C-C bonds we also fit the u C-C bonds by eq 13. The results of fitting are shown for three charge stocks in Figures 1 and 2. When the boiling point conversion is plotted against the conversion of u C-C bonds as calculated from eq 17, we find a strong correlation (Figure 3). This means that as we follow hydrogen consumption and bond conversion through the reactor. we can also follow the traditional conversion parameter.
Nomenclature a = stoichiometric coefficient C = total carbon atoms per molecule
C a = aromatic carbon atoms per molecule Co = olefinic carbon atoms per molecule C-C = g carbon-carbon bonds per molecule [C-C] = concentration of u carbon-carbon bonds, moles/ liter C=C = aromatic T carbon-carbon bonds per molecule [C=C] = concentration of aromatic T carbon-carbon bonds, moles/liter C=C' = olefinic H carbon-carbon bonds per molecule [C=C]' = concentration of olefinic B carbon-carbon bonds, moles/liter E , = activation energy for reaction i H = hydrogen atoms per molecule A H = heat ofreaction, kcal/mole H2CON = chemical hydrogen consumption k , = first-order rate constant for reaction i, l./sec M W = average molecular weight R = gasconstant Ra = average number of aromatic rings per molecule Ras = average number of substantial rings per molecule
R t = average total rings per molecule t = time, sec W = weightingfactor
Greek Letters A, = eigenvalues of differential equations describing rate
of hydrogen consumption density, g/cc 4 = s u m of squares of deviation
p =
L i t e r a t u r e Cited Mortimer, C. T., "Reaction Heats and Bond Strengths," Pergamon Press, New York, N. Y.. 1962. Stull, D.R., Westrum, E. F., J r . , Sinke, G . C , "The Chemical Thermodynamics of Organic Compounds," Wiley, New York, N . Y . . 1969. Van Nes, K., Van Westen, H. A , "Aspects of the Constitution of Mineral Oils," Elsevier, New Y o f k , N.-Y., 1951
Receiced for rerieu February 20, 1973 Accepted July 30, 1973 Presented at the S e w Orleans AIChE Meeting, March 14, 1973
Dynamic Simulation of the Main Extraction Batteries of the Israel Mining Industries Phosphoric Acid Process Menahem Libhaber, Paul Blumberg, and Ephraim Kehat* Chernicai Engineering Department Technion-/sraei
institute of Technoiogy Haifa. lsraei
A dynamic simulation model was developed for the extraction and the purification batteries of the Israel Mining Industries ( I . M . I . ) phosphoric acid process. An equilibrium model was used to represent the equilibrium relationships, the solubility of water in the solvent, and the changes of volumes and densities of the two phases. The validity of the model was confirmed by simulating experimental runs of a small scale system. The effect of step changes of the concentration of the important variables is discussed. The dominant parameter is the calcium concentration of the acidulate stream. Changes of calcium concentration in this stream can be compensated for by changing the solvent flow rate or the flow rate of the hydrochloric acid stream.
T h e object of this study was to simulate the dynamics of the extraction and purification batteries of t h e I.M.I. phosphoric acid process. These are interconnected mixersettler batteries, involving a large number of components, complicated by the varying solubility of water in the solvent. the varying density of the two phases, a n d the very complex equilibrium relationships. In particular it was desired to maximize the extraction of uranium and phosphoric acid from the feed solution and to determine how to compensate for variations in the feed conditions.
The I.M.I. Phosphoric Acid Process ( B a n i e l a n d B l u m b e r g , 1967; I.M.I. Staff, 1971) Crushed phosphate rock is dissolved in hydrochloric acid. T h e acidulate contains large quantities of P043-, C1-, H-, and CaT and small quantities of SiF6, F - , Fe3-, Fe2-. C6-, and a few other metallic ions. .4 series of four extraction batteries is used to separate the phosphoric and hydrochloric acids from the acidulate. The acids are then separated by distillation. Finally, the phosphoric acid is concentrated by evaporation. T h e solvents used in this extraction battery are various mixtures of n-butyl alcohol and isoamyl alcohol. ( A 50% mass concentration of each solvent was used in this study.) T h e
four extraction batteries are (1) the extraction battery to which the acidulate is fed, and in which most of the phosphoric acid is extracted by the solvent; ( 2 ) the purification battery which back-extracts the small amounts of calcium in the solvent leaving the extraction battery; (3) the washing battery in which t h e acids are transferred to a n aqueous phase; ( 4 ) the stripping battery, in which the remaining acids in the raffinate from the extraction battery are recovered. T h e flowsheet of the extraction batteries is shown in Figure 1. T h e important batteries are the extraction and the purification batteries, and these were simulated in this study. T h e solvent to aqueous phase flow rate ratios are 2 to 5 for the extraction battery and 20 to 50 for the purification battery. The uranium is present in the same streams as the phosphoric acid in this process. Hurst, et ai. ( 1 9 T 2 ) , have discussed the problem of recovery of uranium from wet process phosphoric acid. The relevant streams for uraniu m recovery are shown in Figure 2 . The highest uranium concentration is obtained in the raffinate of the purification battery, from which it may be recovered (Ketzinel. er al., 1972). Figures 3-6 show typical steady-state concentration profiles of P205, HC1, Ca: and U in t h e two batteries Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
39
