Styrene Design Problem

Prof. Wood

CHEG 464 Styrene Design Problem Background: Commercial development of styrene began during World War II with the introduction of synthetic rubber. Butadienestyrene copolymers later found extensive use in latex paints while various polystyrene plastics and foams are used in packaging, wall tile, household articles, and insulating material in refrigerators. Styrene can be produced via the catalytic dehydrogenation of ethylbenzene, which is derived from the alkylation of benzene with ethylene. Precursor feedstocks are commonly associated with petroleum refining and petrochemical processes. Although the present supply and economics dictate the use of petroleum derived feedstocks, a changing world situation could make coal-derived feedstocks acceptable alternatives. In either case, styrene is a valuable monomer in a variety of commercial products. Design Basis: The requested preliminary appraisal study should include all the process steps needed to manufacture 20 million pounds per year of styrene monomer from ethylbenzene. This plant will be considered as an addition to an existing petrochemicals complex. Wenner and Dybdal (1) provided information on the reaction kinetics of the dehydrogenation of ethylbenzene. The following reactions were proposed as being important: C6H5C2H5 ↔ C6H5C2H3 + H2

(Eq. 1)

C6H5C2H5 → C6H6 + C2H4

(Eq. 2)

C6H5C2H5 + H2 → C6H5CH3 + CH4

(Eq. 3)

Equilibrium information indicates that reaction 1 is the only one with an important reverse reaction. Reaction rate equations are given by Wenner and Dybdal (1) as follows (these pseudoelementary rate laws fit reaction kinetic data reasonably well): r1 = k1 (PE - PSPH2/K1)

(Eq. 4)

r2 = k2 PE

(Eq. 5)

r3 = k3PEPH2

(Eq. 6)

Effect of temperature on the reaction rate constants was interpreted from the experimental results as follows: log10k1 = (-11,370/4.575•ToK) + 0.883

(Eq. 7)

log10k2 = (-50,800/4.575•ToK) + 9.13

(Eq. 8)

log10k3 = (-21,800/4.575•ToK) + 2.78

(Eq. 9)

Reported experimental results were obtained with a packed-tube reactor, 0.75 in. i.d., 1.00 in. o.d. by 78 inches overall length. A preheat section of 1.5 ft. was packed with 6-mm porcelain Berl saddles followed by a 4-foot long catalyst section containing 348 cc of catalyst. Temperature was measured by a thermocouple in the catalyst bed 12 in. from the exit. Results of detailed calculations show that the effect of diffusion in the pores of the catalyst pellets was probably a significant factor in the rate mechanisms. However, given the same similitude of catalyst pellet size and pore structure, a reasonably accurate rate replication and scale-up can be obtained. Catalyst regeneration in the present project can be accomplished with a periodic superheated-steam treatment. A shell-and-tube heat-exchanger-type packed tube reactor should be used to provide the necessary large heat transfer area per unit catalyst volume. Ethylbenzene can be fed downward on the tube-side (tubes filled with platinum catalyst on a silica-alumina carrier) while hot flue gas is passed countercurrently and upward on the shell-side. Reactor design variables are too numerous unless some variables are fixed at reasonable or typical values. Variables include: tube length 1

Prof. Wood

and diameter, catalyst shape and size, feed temperature, heating medium temperature, mass velocity of the feed stream and others. Tables I and II contain lists of tentative fixed parameters and also variables to be investigated in this study. The experimental results of Wenner and Dybdal provide the basis and bench-mark values for those listed in the following tables. Assume that the pressure drop is given by the Ergun equation, (BSL-Eq. 6.4-14, p. 200 or p 696 Peters and Timmerhaus, or p 177 Folger). The styrene recovery and refining system may consist of one, two or three distillation columns in series to avoid exceeding the maximum-allowable temperature of 90oC; above this temperature styrene will polymerize (Faith et al.). In fact, even to reach 90oC, small quantities of a non-volatile inhibitor must be added to the top of the high-temperature column(s) to prevent styrene polymerization. Note no significant polymerization occurs in the reactor since the products are gases. With a maximum-allowable process stream temperature in this case, a vacuum distillation system will be necessary. The purity of all product distillation streams should be greater than 98%. Existing plant utilities include a vacuum system operating at 40 torr. A new sieve-tray design for use in vacuum operation provides overall column efficiencies above 50% and a pressure drop across each tray of 3 mm Hg or less in similar cases. The ethylbenzenestyrene system may be assumed to exhibit ideal solution behavior within 2% deviation for this case. Quick-method estimates may be based upon a reflux ratio of 1.4 x RD MIN and the Fenske-Underwood-Gilliland methods may be used. VLE may be considered ideal for SM-BZ. TABLE I: FIXED PARAMETERS FOR REACTOR DESIGN Catalyst: alumina, 1/8-inch spheres, ρc = 61 lb/ft3, ρp = 117 lb/ft3 Purchase cost = $4.20/lb (12/84) Overall heat transfer coefficient, h = 10 BTU/hr*ft2*oF Inlet flue gas temperature = 850oC Reactor tubes and tube-sheet: 316 stainless steel Reactor pressure range: 10 to 50 psig

TABLE II: REACTOR DESIGN VARIABLES FOR STUDY Tube length: 8, 12, 16 ft Tube diameter: 2, 4 inches o.d. Feed temperature: 450, 550, 6500C Superficial mass velocity of reactor feed: 3600, 4800, 6000 lb/hr*ft2

References: 1. 2. 3.

Wenner, R. R. and E. C. Dybdal, "Catalytic Dehydrogenation of Ethylbenzene, Chem. Eng. Progr., 44, 275 (1948). Peters, M. W. and K. D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", Fourth Edition, McGraw-Hill Book Company, New York, 1991. Faith, W. L., D. B. Keyes, and R. L. Clark, Industrial Chemicals, Wiley & Sons, NY (1950). NOMENCLATURE FOR CATALYTIC STYRENE MANUFACTURE

r1 k1 PE PS PH2

reaction rate, lb moles/(hr) (lb cat), for formation of styrene by eq. 1; r2 for eq. 2; r3 for eq. 3 rate constant, lb moles/(hr)(atm)(lb cat), for styrene formation; k2 for eq. 2; k3 for eq. 3 partial pressure, atm, ethylbenzene partial pressure, atm, styrene partial pressure, atm, hydrogen 2

Prof. Wood

K1 ToK T(z) To Tfg X Y Z Cpi(T) L F W di,do dc Fo FE(z) h ∆Hrl Po P(z) z ε ρc ρp ξ*

equilibrium constant for styrene formation, atm reaction temperature in Arrhenius equation, K reactor temperature as a function of position, oF reactor feed temperature, oF flue gas temperature, oF (assume constant.) fractional conversion to ethylbenzene, lb moles EB react/lb mole EB fed yield of styrene (S), lb moles S formed/lb mole EB reacted yield of toluene (T), lb moles T formed/lb mole EB reacted heat capacity of the ith component, BTU/(lb-mol oF) catalyst depth, feet feed to reactor, lb moles/hr catalyst weight, lb, dW differential catalyst element inner and outer tube diameter, inches mean catalyst particle diameter, inches feed rate of ethylbenzene, lb-mole/hr*tube molar flow rates of ethylbenzene, lb-mole/hr*tube FS(z), FH(z) for styrene and hydrogen overall heat transfer coefficient, Btu/hr*ft2*oF, based on do (assume constant) standard heat of reaction at 77oF for first reaction (Eq. 1), BTU/lb-mole, ∆Hr2, ∆Hr3 for the other two reactions total pressure at reactor inlet, psia pressure in reactor, psia axial distance from reactor inlet, ft void fraction in the tubes, ft3void/ft3 total volume catalyst density, lb catalyst/ft3reactor catalyst density, lb catalyst/ft3catalyst open-system extent of reaction, lb mol/hr

Based on the styrene design project, I would like you to do the following: A. Derive the equations you would use to find the following quantities as a function of axial position in the reactor: Conversion of ethylbenzene:

X = moles E reacted/moles E fed

Yield of styrene:

Y = moles S produced/moles E reacted

Temperature of the reaction mixture:

T(oF)

Express your equations in terms of the parameters given in the design project description: Assume the overall heat coefficient h and flue gas temperature Tfg are constant. Assume the viscosity of the reaction mixture to be 0.02 cp, where 1 cp = 6.72 x 10-4 lbm/ft*s. Assume the pressure drop is given by the Ergun equation. Make it clear how you will determine X(z), Y(z), and T(z) from the dependent variables of your design equations. Then sketch the expected shapes of FE, FS, FH, X, Y, XY, and T vs. z (include results for large z). Calculate the initial value of Y. (Hint: it is not 0) B. Indicate how your set of equations would have to be modified if you could not assume a constant flue gas temperature, but were given the entering flue gas temperature (Tfg)o, the flow rate of the flue gas (qfg, lb/h-tube), and the flue gas heat capacity Cfg (Btu/lb-oF). 3

Prof. Wood

C. Solve the problem of Part A by stepping forward in position (with suitably small position increments). Have the program calculate and print out X, Y, XY (moles S produced/mole E fed), T, and P at incremental values of z up to a 30% conversion of ethylbenzene. (Build an upper limit of 20 ft into the program.) Also, print out the final molar flow rate of E and S, and the component mole fractions in the reactor effluent. D. Run the program using the following system parameters. di, do = 4.03 in., 4.50 in. ε = 0.48, dc = 1/8 in., ρp = 117.3 lb/ft3 catalyst Fo = 4 lb-moles/h-tube h = 9.7 Btu/h-ft2-oF (based on outside tube area) Po = 41 psig, To = 1000oF, Tfg = 1600oF print data with step size = 0.50 ft Suggestion: The first time you run the program, have it write the calculated values of the rate and equilibrium constants, heats of reaction, and the five derivatives at the initial conditions, and then STOP. Check these values. E. Calculate the number of tubes and their length required to produce 2.0 x 10 7 lb. styrene per year with a fractional conversion of ethylbenzene of roughly 30%. For your information, I am summarizing below the results of studies performed by Wenner and Dybdal [Chem. Eng. Progr., 44, 275 (1948)] and Bodman [The Industrial Practice of Chemical Process Engineering, MIT Press (1968)] on this reaction system, along with thermochemical data you will need. Thermochemical and Kinetic Data for Ethylbenzene-Styrene System (equations of Bodman corrected for mass transfer resistance in the catalyst particle) k1 = 650 exp (-19 100/l.987•T) log10k2 = -50 800/(4.575•T) + 9.13 log10k3 = -21 800/(4.575•T) + 2.78 T in Kelvin, k in lb-mole/(hr•lb catalyst•atm) or lb-mole/(hr•lb catalyst•atm2) K1 (500oC) = 2.8 x 10-2 atm K1 (600oC) = 2.4 x 10-1 atm

Assume the integrated (constant ∆H) form of vant Hoff's equation is valid

Substance

∆Hof @ 77oF, Btu/lb-mole

Ethylbenzene (g)

+12,816

26.18 + 0.0602T - 1.84 x 10-5T2

Styrene (g) Hydrogen (g) Benzene (g) Ethylene (g) Toluene (g) Methane (g)

+63,396 0 +35,676 +22,491 +21,510 -32,202

25.12 + 0.0542T - 1.71 x 10-5T2 6.89 + 3.94 x 10-5T + 2.11 x 10-7T2 16.29 + 0.043lT - 1.37 x 10-5T2 9.25 + 0.0155T - 5.08 x 10-6T2 20.86 + 0.0523T - 1.58 x 10-5T2 7.94 + 7.66 x 10-3T - 3.60 x 10-7T2

Cp[T(oF)], vapor-phase heat capacities BTU/(lb-mole oF)

4