Model of Steady State Cyclohexane Oxidation for Ketone-Alcohol (K-A) Oil Production

Cylohexane oxidation is of great industrial importa nce in the production of intermediates for the manu f ct re of nylon6 and nylon-6,6. Most cyclohexane is commercially c onverted into a cyclohexanone–cyclohexanol mixture (known as K-A oil) by catalytic oxidation. K-A (Ketone-Alcoho l) oil is then used as a raw material for adipic ac id and caprolactam production. Practically, if the cyclohexanol conten t of KA oil is higher than that of cyclohexanone, i t is more profitable to convert it into adipic acid; otherwise caprolact am production is more likely. The steady state cycl ohexane oxidation reaction model in a stirred tank reactor for K-A oi l production is presented and solved in this paper. The model was derived based on the mass balance and mass transfer equations using the kinetic equation. The set of a lgebraic equations was solved using non linear programming. The advant age of this method is that the relationship among v ariables can be better understood and an appropriate solution to th e equation set can be obtained more quickly. Simula tion results are particularly useful for process design such as in d etermining reactor dimensions and operating conditi ons.


Introduction
Many organic chemicals are produced from the oxidation reaction of hydrocarbon.Most of the industrial interests are carried out at pressure of 10-30 bar and temperatures of 353-523 K [1].The liquid oxidation of cyclohexane is one example of the hydrocarbon oxidation reaction.This reaction is very important as it produces cyclohexanol and cyclohexanone as raw materials for the nylon-6 and nylon-6,6 industries.However the oxidation reaction of cyclohexane is very complex where cyclohexanol and cyclohexanone are intermediates of the reaction scheme.
Understanding this oxidation process is very important for economical plant operations and to ensure adequate safety procedures, which are necessary due to its high temperature and pressure characteristic.The Flixborough disaster [7] in a cyclohexane oxidation plant in the United Kingdom presents an excellent example for why this process should be designed and operated carefully.
The cyclohexane-oxidation-reaction scheme is illustrated in Fig. 1, based on the general hydrocarbon oxidation reaction.
The oxidation of cyclohexane is carried out at elevated temperatures and pressures and is usually catalyzed homogeneously under mild conditions using soluble catalysts, such as cobalt octoate/oleate/naphthenate.The conversion is limited to 4-15% to promote K-A yield in the range 85-90% [6].
There have been numerous studies on the reaction mechanisms of cyclohexane oxidation.In this work, the reaction scheme and kinetics of Alagy et al. [1] were adopted.The reaction scheme is described in Figure 2.
Figure 2 illustrates the great complexity of the reaction.The ratios of kinetic parameters (k 2 /k 1 , k 3 /k 1 and k 4 /k 1 ) were obtained by Alagy et al. [1].The ratios showed that the oxidation of cyclohexanol and cyclohexanone was faster than that of cyclohexane.Therefore, further cyclohexane conversion may lead to the formation of by-products.This scheme and its kinetic parameters (shown in Table 1) were specifically valid for boric acid promoted processes.
A mechanism proposed by Spielman [9] is shown in Figure 3, while Suresh et al. [2] presented the autocatalytic oxidation of cyclohexane which include initiation, propagation and termination steps as follows: Rao [10] proposed a reaction scheme (Figure 4) and kinetic model of cyclohexane oxidation for acetic acid and cobalt acetate as catalysts.
Significant industrial demand for K-A oil in recent years has stimulated various studies aiming to find milder, lower cost, and more environmentally friendly conditions; namely, to find greener and more efficient catalytic processes for the classic industrial method [11][12][13][14][15].
The aim of this research was to develop and solve the mathematical model of cyclohexane oxidation in single stirred tank reactor as a basis for further investigation in a series of reactors.The model was then simulated to study the effects of the gas-to-liquid molar-rate ratio (R G ), impeller speed (N p ), and space-time ( θ ) on the performance of the single reactor

Methods
Cyclohexane oxidation in a single reactor.The system studied in this paper is described in Figure 5. Cyclohexane in the form of liquid and air are introduced to the reactor which operate at 9.5 atm and 167 °C.The gas exiting the reactor is passed through condenser, where cyclohexane vapor condenses and is recycled back to the reactor.The other components such as CO, CO 2 , water vapor, oxygen, and nitrogen exit in the blow-down gas stream.
The operating conditions of the reactor are shown in ] ) where: A N = Ratio of cyclohexane molar rate in the product stream to that of cyclohexane in the feed stream.K and G are defined as follows: The mass transfer coefficient correlation used here is the Hickman equation [8]:  1) to (10) are brought to the left side, then there are 10 equations with zero values (f i = 0) and 10 variables that should be obtained (i.e. ).
This set of algebraic equations can be solved by considering equation ( 1) to (10) as the equalities constraints for the optimization problem with the following objective function: The above objective function was chosen because it contains all the variables that must be found.
The following inequalities constraints must be employed: Other inequalities constraints must be employed appropriately to obtain feasible solution (i.e.all the resulting variables are positive, real numerical values).

Results and Discussion
Figure 6 shows the effect of the gas-to-liquid molar-rate ratio (R G ) on the oxidation performance (conversion, selectivity, and alcohol-ketone ratio).The conversion and alcohol-ketone ratio increased with the gas-to-liquid molar-rate ratio, while the selectivity decreased.
According to equations ( 13) and ( 14) the increase in the gas molar rate ( Q ) will increase the value of the liquid mass transfer coefficient, which will then enhance the dissolved oxygen concentration in the liquid phase.
The cyclohexanol-to-cyclohexanone ratio could also increase with higher dissolved oxygen concentration because of the faster by-product formation rate compared to that of cyclohexanone (k 4 >k 2 ) and (k 4 >k 3 ).This means that the oxidation of cyclohexanone is faster than its formation from cyclohexanol and cyclohexane.Despite that, the oxidation of cyclohexane into cyclo-hexanol was faster than into cyclohexanone (k 1 >k 2 ) and the equlibrium esterification with boric acid could shift the esterification toward the right when the cyclohexanol formed.The selectivity decreased because the higher oxygen concentration in the liquid phase favored the oxidation reaction of cyclohexanol into cyclohexanone and cyclohexanone into by-products.It also favored the CO and CO 2 formation in the oxidation reaction.
Figure 7 shows that the impeller speed increased the cyclohexane conversion but decreased the selectivity of cyclohexanol and cyclohexanol.The impeller speed could   could also increase the mass transfer coefficient, and the effects of this increase were the same as increasing the gas molar flow rate.
Figure 8 shows the effect of space-time on the conversion, selectivity and alcohol-to-ketone ratio.The conversion of cyclohexane increased as the space-time increased due to longer reaction time.However, this higher conversion could decrease the selectivity.The alcohol-to-ketone ratio was relatively constant with the increase of space-time.

Conclusions
The mathematical model of cyclohexane oxidation in a single stirred tank reactor has been developed and solved using constrained non-linear programming.This model allows further investigation of the effect of process operating condition on the performance of the reactor.The effect of the gas-to-liquid molar-rate ratio (R G ), impeller speed (N p ) and space-time (θ ) on the performance of the reactor (conversion, selectivity and alcohol-ketone ratio) are presented.The resulting model and solution procedure, which was derived for single reactor, can be readily extended for reactor train in series arrangement.

P 2 =
cyclohexanol molar rate in the product stream to that of cyclohexane in the feed stream.C N = Ratio of cyclohexanone molar rate in the product stream to that of cyclohexane in the feed stream.O H Water partial pressure in the gas exiting the reactor.A P = Cyclohexane vapor pressure at the reactor temperature.ϕ = Oxygen mole fraction in the blow down gas stream.η = CO and CO 2 mole fraction in the blow down gas stream.D N = Ratio of byproducts molar rate in the product stream to that of cyclohexane in the feed stream.E N = Ratio of cyclohexanone molar rate in the product stream to that of cyclohexane in the feed stream

3 T
Liquid side mass transfer coefficient, sec -1 g P = Gassed power, Watt p N = Impeller speed, rps Q = Volumetric gas flowrate, m 3 /sec Da = Impeller diameter, m D = Tank diameter, m V = Liquid volume, m 3 s V = Gas superfisial velocity, m/s The data needed to solve the equations above are: He = Henry's constant for oxygen in cyclohexane G ρ = Gas density, mol/cm = Temperature, °C The overall performance of the oxidation such as conversion, selectivity and the alcohol-ketone ratio are calculated according to the following equations: If the right sides of equations (

Figure 6 .
Figure 6.The Effect of R G on the Oxidation Performance at Impeller Speed = 70 rpm, and θ =3600 sec

Figure 8 .
Figure 8.Effect of Space-Time at R G = 5, and Impeller Speed =100 rpm