Ind. Eng. Chem. Res. 1992,31,69-75 Sundaram, K. M.; Froment, G. F. A Comparison of Simulation Models for Empty Tubular Reactors. Chem. Eng. Sci. 1979,34, 117-124. Trombetta, M. L.; Happel, J. Analysis and Design of Gas Flow Reactors with Applications to Hydrocarbon Pyrolysis. AZChE J. 1970,11, 1041-1050.
69
Velenyi, L. J.; Song, Y.; Fagley, J. C. Carbon Deposition in Ethane Pyrolsyis Reactors. Submitted for publication in Znd. Chem. Eng. Res., 1991. Received for review August 1, 1990 Accepted February 14,1991
KINETICS AND CATALYSIS Reaction Pathways in Lubricant Degradation. 3. Reaction Model for n -Hexadecane Autoxidation Steven Blaine and Phillip E. Savage* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
We have developed a reaction model that describes the autoxidation of n-hexadecane under severe conditions. The model rate equations were solved numerically concurrent with optimization of the reaction rate constants to yield the solution that provided the best correlation with experimental data. This numerical analysis showed that hydroperoxides were formed in the reaction step with the smallest reaction rate constants, and they decomposed in the steps with the largest rate constants. Thus, hydroperoxides were key reaction products. A comparison of the kinetics determined in this study with those reported in the literature showed that the rate constant for hydroperoxide formation during the initial stages of the autoxidation compared favorably with that determined by others. The reaction rate constants for the secondary reactions determined for the overall autoxidation under severe conditions, however, differed from those appearing in the literature for the initial stages of paraffin autoxidation. Thus, the kinetics of paraffin autoxidation appeared to depend on the extent of oxidation. An illustration of the implications of these findings to lubricant degradation is also presented.
Introduction The degradation of a liquid lubricant is frequently accompanied by deleterious changes in its physical and chemical properties that can adversely affect ita performance. Oxidation of the lubricant base oil has been identified as the primary agent of degradation (Fenske et al., 1941; Korcek et al., 1986; Gunsel et al., 1988; Naidu et al., 1984,1986), and this has motivated many investigations of base oil oxidation (Colclough, 1987; Jette and Shaffer, 1988; Tseregounis et al., 1987; Naidu et al., 1984, 1986; Korcek and Jensen, 1976; Dialmond et al., 1952; Spearot, 1974; Hsu et al., 1986). Petroleum base oils are complex mixtures of hydrocarbons, however, and heteroatom-containing compounds that can function as prooxidants or antioxidants are also often present. This complexity has frustrated resolution of the reaction fundamentals for the oxidation. One alternate approach for resolving the fundamentals of base oil oxidation is to study the oxidation of a simpler yet chemically relevant model reactant. Paraffinic hydrocarbons, which have C-C and C-H bonds that mimic those in petroleum base oils, are excellent model reactants. Many studies have focused on the oxidation of simple hydrocarbons to elucidate reaction pathways, kinetics, and mechanisms (e.g., Garcia-Ochoa et al., 1989; Lee et al., 1987; Brown and Fish, 1969; Van Sickle, 1972; Van Sickle et al., 1973; Suresh et al., 1988; Mill et al., 1972; Korcek et al., 1972; Jensen et al., 1979,1981;Hombek et al., 1989 W d y et al., 1988; Hazlett et al., 1977). Much of this work, 0888-5885/92/2631-0069$03.00/0
however, was limited to the initial stages of the oxidation, where the hydrocarbon concentration remains essentially constant and hydroperoxides are the major oxidation product. These studies of the initial stages of hydrocarbon oxidation have led to the detailed resolution of reaction fundamentals for the formation of primary (Jensen et al., 1979; Emanuel, 1965; Brown and Fish, 1969; Benson, 1981; Denisov et aL, 1977; Van Sickle et al., 1973; Mill et al., 1972; Boss and Hazlett, 1975; Garcia-Ochoa et al., 1989) and some secondary (Jensen et al., 1981; Brown and Fish, 1969; Boss and Hazlett, 1975; Garcia-Ochoa et al., 1989) oxidation producta. Under more severe reaction conditions (i.e., longer reaction times and higher temperatures), however, the oxidation chemistry becomes more complex, as evidenced by the formation of a broader spectrum of oxidation products (Brown and Fish, 1969). Several researchers (Boss and Hazlett, 1969; Hazlett et al., 1977; Reddy et al., 1988) have investigated the oxidation of hydrocarbons under severe conditions, but much of this work involved only a qualitative or semiquantitative analysis of the reaction products. These studies provided some insight to the reaction pathways, but the lack of a unified protocol for the complete quantitative chemical analysis of hydrocarbon oxidation products may have prevented a more quantitative mathematical treatment of the reaction kinetics. In the first paper of this series (Blaine and Savage, 1991a),we presented an analytical protocol for quantifying the total concentrations of the different oxygen-containing 0 1992 American Chemical Society
70 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 k, k; I(; KETONES,
decomposition with respect to the hydroperoxide concentration. The value of n may be 1 or 2, depending on whether the hydroperoxide decomposition is first or second order, respectively (Garcia-Ochoa et al., 1989), and we will discuss this point more fully in the next section. The net rate of initiation may be expressed as the s u m of the constant (eq 2) and the first- and second-order initiation terms (eq 3 where n = 1and 2), as shown in eq 4.
k5
ALCOHOLS
Figure 1. Reaction pathways for paraffin autoxidation.
functional groups in a complex mixture of paraffin oxidation products. We then used this analytical protocol to analyze the products of n-hexadecane autoxidation (Blaine and Savage, 1991b) and resolve the reaction pathways that describe the chemical transformations between the different oxygen-containing functional groups. The present paper describes a mathematical model for n-hexadecane autoxidationthat is based on these reaction pathways. The purpose of this paper is threefold: (1)to describe the kinetic model for n-hexadecane autoxidation and show that it is consistent with experimental results, (2) to present quantitative values of the kinetics parameters for each step in the reaction pathway and compare these rate constants with others available in the paraffin oxidation literature, and (3) to explore the implications of this reaction model to lubricant degradation.
Reaction Kinetics Figure 1 displays the reaction pathways for paraffin autoxidation, which were resolved in the previous paper of this series (Blaine and Savage, 1991b). These pathways exclude polymerization reactions because we detected no high molecular weight polymers among the reaction products. In order to develop a mathematical model based on this network, it is necessary to obtain rate expressions for each of the reaction pathways. The hydrocarbon oxidation literature provided insight into the form of these rate expressions, and the kinetics of the oxidation for each of the individual species will now be discussed. n -Hexadecane. During the initial stages of hydrocarbon autoxidation, under conditions of high oxygen concentration, the disappearance of hydrocarbon can be described using the rate law shown in eq 1 (Van Sickle et al., 1973; Denisov et al., 1977; Boss and Hazlett, 1975). rRH
= k(Ri)o’5[RH]
(1)
Ri represents the rate of initiation for the oxidation (Le., the rate of production of free radicals), [RH] is the hydrocarbon concentration, and k is a global reaction rate constant. During the very initial stages of hydrocarbon autoxidation the key initiation reactions may occur by direct attack of oxygen at C-H bonds within the hydrocarbon (Emanuel, 1965). This process would be first order in hydrocarbon and in oxygen, but, during the incipient stages of the oxidation where this initiation mechanism is important, neither of these concentrations changes appreciably. Thus, the rate of this initiation step can be taken to be effectively constant. Ri = k’ (2) As the autoxidation progresses, however, the decomposition of hydroperoxides, which are primary oxidation products, serves as an additional initiation route. The rate of these initiation reactions is a function of the hydroperoxide concentration (Jensen et al., 1990),as shown in eq 3, Ri = k”[ROOH]” (3) where k” is a global rate constant and n is the order of
Ri = k ’ + k”[ROOH]
+ k”’[ROOHI2
(4)
Substituting eq 4 into eq 1 leads to the following as the form of the rate law for hydrocarbon disappearance under conditions of both incipient and autocatalytic oxidation. rRH
= k[RH](k’+ k”[ROOH]
+ k”’[ROOH]2]0.5( 5 )
The specific form of eq 5 used in the reaction model is TRH
= 14[RH](ko
+ kl[ROOH] + k1’[ROOH]2)0.5(6)
where ko, kl, and kl’ are the composite rate constants shown in Figure 1,and they are defined on a per methylene group basis. Using thisbasis for the rate constanta requires that the number 14 appear in eq 6 to account for the 14 methylene groups within the n-hexadecane molecule. This point will be discussed more fully in the next section. Hydroperoxides. As shown in Figure 1, the primary products resulting from hydrocarbon oxidation are alkylhydroperoxides. Thus, the rate of hydroperoxide formation is related to the rate of n-hexadecane disappearance. The two rates are not necessarily identical, however, because the ROO’ radicals that form hydroperoxides are free to abstract hydrogen not only from hexadecane, but also from any other molecule present within the reaction mixture that contains a CH, group. To account for this free radical attack at different CH2 groups on any given alkyl chain within the system, we modeled the kinetics of hydroperoxide formation using eq 7, which is essentially rROOHformn
= [CH,](k,
+ kl[ROOH] + k,’[ROOH]2)0.5 (7)
a more general form of eq 6. The change made in eq 6 to obtain eq 7 was replacing 14[RH] with [CH,]. This modification permits the rate of formation of hydroperoxides to depend on the total concentration of all unsubstituted methylene groups in the reaction mixture rather than solely on those in hexadecane. Having determined a rate law for hydroperoxide formation, we next sought an expression for hydroperoxide disappearance. Hydroperoxides formed from hydrocarbon oxidation decompose homolytically provided the hydrocarbon conversion is low. At higher conversions and higher hydroperoxide concentrations, where the concentration of paraffii autoxidation products is high, the decomposition can proceed via a different mechanism (Jensen et al., 1990). One potential mechanism for hydroperoxide disappearance in the presence of paraffin autoxidation products is decomposition to ketones assisted by some other product of the oxidation, as in reaction 8 (Jensen et al., 1990; Boss and Hazlett, 1975) RCH(O0H)R’ + M
-
R(C=O)R’
+ H20 +M
(8)
where M denotes a molecular species (e.g., carboxylic acids). One final route for hydroperoxide decomposition is the bimolecular reaction shown in reaction 9 (Denisov et al., 1977; Hiatt, 1980). The importance of this reaction will increase as the hydroperoxide concentration increases.
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 71 ROOH
+ ROOH
+
RO2’
+ RO’ + H2O
(9)
For paraffin autoxidation under severe conditions, hydroperoxide decomposition may take place through several different mechanisms, and, hence, several different rate laws may be operative. Therefore, we have modeled the kinetics of hydroperoxide decomposition using a rate law that includes three different terms. In the early stages of autoxidation, where the hydrocarbon conversion and the hydroperoxide concentration are low, the decomposition is expected to be first order. At later stages, where the concentrations of hydroperoxides and secondary products are high, second-order reactions such as 8 and 9 are expected to become important. Carboxylic acids are a likely candidate for assisting the decomposition of hydroperoxides in reaction 8, and they are the most abundant products of the autoxidation at long reaction times. The rate law for hydroperoxide decomposition that results from these three pathways is shown in eq 10 = (k2 + k3 + k4)[ROOHI + (k2/+ k3’ + k,‘)[ROOHI2 + k/[ROOH][ACID] (10)
rROOH decomp
where k2 + k3 + k4 represents the overall first-order reaction rate constant, k2/ + k,’ + k,‘ represents the overall second-order reaction rate constant, and kc represents the second-order rate constant for product-assisted decomposition of hydroperoxides (reaction 8). The net rate of reaction of hydroperoxides can now be written as the difference of eq 7 for the rate of formation and eq 10 for the rate of decomposition. rRooH
+
+ k,’[ROOH]2)0.5+ (k2’ + k,’ + k4’)[ROOHI2+
= [CH2]{ko kl[ROOH]
{(k, + k3 + k,)[ROOH]
the rate laws for alcohols and esters, respectively. rALc
= k,[ROOH]
(14) &STER
rKET
= k,[ROOH]
+ k2’[ROOHI2 +
k2”[ROOH][ACID] - k,[KET] (12)
Figure 1includes two reaction pathways for carboxylic acid formation-the direct oxidation of ketones and the decompwition of hydroperoxides. This latter reaction may involve the formation of aldehydes (through j3-scission of alkoxy radicals) as intermediate products that are rapidly converted to carboxylic acids through direct oxidation (Boss and Hazlett, 1975; Jensen et al., 1981). In the reaction network of Figure 1,carboxylic acids are consumed only through esterification reactions, which also require the presence of alcohols. Using the rate expressions for hydroperoxide decomposition and ketone oxidation that we previously developed and assuming that the esterification is pseudo first order in both the carboxylic acid and alcohol concentrations lead to eq 13 as the net rate of reaction of carboxylic acids. rACID
= k,[ROOH]
+ k3’[ROOHI2 + k,[KET]
-
k,[ACID][ALC] (13) Using the reaction network in Figure 1and the previously developed rate expressions leads to eq 14 and 15 for
= k6[AC1Di [ALCl
(15)
Model Development The previous section detailed the rate expressions for the reactions of each functional group taking part in the oxidation. This section focuses on the development of a reaction model that uses these rate expressions and the pathways of Figure 1 to describe the reaction system. The oxidation experiments were conducted in a batch reactor that was described fully in the previous paper in this series (Blaine and Savage, 1991b). Because high oxygen flow rates were used in the experiments, some of the more volatile oxidation products were swept out of the reactor with the flowing gas stream. Therefore, the general mole balance for any species i in the reactor must include terms that account for the loss of material through both t h i s physical process and chemical reactions. Equation 16 provides this mole balance
where Ni is the number of moles of species i present in the reactor, FF is the molar flow rate of species i leaving the reactor, t is the reaction time, and V is the reactor volume. Writing Ni in eq 16 in terms of the species concentration (the measured variable), and keeping in mind that the reactor volume is not constant, we obtain eq 17.
k/[ROOH] [ACID]] (11)
Secondary Autoxidation Products. The reaction network in Figure 1shows that ketones are products of the hydroperoxide decomposition and that they can be directly oxidized to form carboxylic acids (Brown and Fish, 1969). Thus, the rate of ketone formation should be proportional to the rate of hydroperoxide decomposition, and, in the presence of excess oxygen, the ketone oxidation step can be treated as being pseudo first order in the ketone concentration. These assertions combine to give eq 12 as the reaction rate law for ketones.
+ k,‘[ROOHI2 - k,[ACID][&C]
{
:I($)
dCi = ri - FP + Ci dt
(17)
This equation describes the rate of change of the concentration of species i (Ci) within the reaction system for the autoxidation of n-hexadecane. The molar flow rate was calculated as the time derivative of NY, which is the number of moles of i that had been swept out of the reactor with the exiting gas stream. NF and V were both measured as functions of time, and these experimental data for v ( t ) and V(t) were then fit to polynomial functions. Differentiating these equations with res ect to time then provided analytical expressions for FiE? and dV/dt that could be substituted into eq 17. Rate laws for each species (eqs 6 and 11-15) were presented in the previous section, and substituting these into the general mole balance completea the model development. The rate constants (k&, k[-ki, and k/) serve as the model parameters. The full model for the autoxidation of n-hexadecane in our reactor system consists of the set of six simultaneous differential equations obtained when eq 17 is written for each reaction species i. Equations 18-23 constitute this complete model.
-d[RH1 -. dt
-14[RH](ko + kl[ROOH] +k,’[ROOH]2)0.5-
d[ROOH] = [CH2](ko+ kl[ROOH] + k1’[ROOH12)0.5dt ( k 2 + k3 + k,)[ROOH] - (124 + k,’ + k,‘)[ROOHI2 k,”[ROOH][ACID] - {FROOH + [ROOHI dV 1
t)( v)
4r
72 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
d[KET] - k,[ROOH] + k;[ROOHl2 + kc[ROOH] X --
N-HEXADECANE
.-It
s3 d[ACID] dt
= k,[ROOH]
+ k,'[ROOHI2 + k,[KET] -
8
I2 8 1
d[ALC]
= k,[ROOH] .-I*
+ k:[ROOH]'
n 0
d[ESTER] dt
-
10
5
15
20
:
REACTION TIME (HOURS)
k,[ACIDl[ALCl - {@STER
+ [ESTER]
TI(
dV
1
y ) (23)
The concentration of methylene groups, [CH,], appearing in eq 19 can be estimated by writing a balance for the number of moles of methylene groups (NCH2)present in the reactor at any point in time, as given in eq 24. The
3
NCH2 = N# - VCCi - C C j N $ - ~ ~ N R H (24)
e
'
i
i l
term m C i represents the number of moles of carbon atoms bearing oxygen-containing functional groups. These carbon atoms are no longer CH, groups and hence are unavailable for the production of hydroperoxides. The term C C j N t accounts for the moles of CH2groups swept out of the reador, where i is the species index (i = ROOH, KET, ACID, ALC, ESTER) and j is an index equal to the number of CH2groups in the molecule leaving the reactor. Our chemical analysis protocol did not permit us to identify and quantify each individual molecular product (Blaine and Savage, 1991a), but rather it provided the concentrations of the different functional groups. Thus, we did not have enough information to determine j and N;. Therefore, we approximated the summation over the carbon number index by assuming that the average number of CH2groups attached to a molecule swept out of the reactor was 4 (Le., j = constant = 4). The precise numerical value selected for this average had a negligible effect on the model results because the number of CH, groups swept out of the reactor was small compared to the number initially present in the reactor. Furthermore, the choice of 4 as an average value is reasonable because most products volatile enough to be swept out of the reactor contained between 1 and 8 carbon atoms (Jensen, 1989). With this approximation, the material balance of eq 24 simplifies to NCH2 = NE$, - E C i - 4xNF - 1 4 N 8 ~
(25)
Because the values of Ci, N:, and NEHwere measured, we were able to estimate NcH, at any reaction time. Finally, dividing eq 25 by the reactor volume yields an expression for the methylene group concentration, [CH,], which can be substituted into eq 19. The model represented by eqs 18-23 and 25 can be combined with experimental concentration versus time data and an optimizationalgorithm to determine optimized values of the model parameters (k,,-k6, kl'-k4/, and k,"). The equations can then be numerically integrated to calculate the species concentrations as functions of reaction
t8 ' HYDROPEROXIDES 0 0
2
4
6
8
10
CARBOXnlC ACIDS
2
REACTION TIME (HOURS)
Figure 2. Temporal variations of reaction product concentrations: model calculations and experimental data. (a, top) n-Hexadecane at 140 and 180 "C. (b, middle) Hydroperoxides and ketones at 180 "C. (c, bottom) Carboxylic acids, alcohols, and esters at 180 "C.
time. The details of this numerical analysis are discussed in the following section.
Estimation of the Kinetics Parameters The numerical values of the 12 parameters in eqs 18-23 (Le,, k&6, k
