Mass Balance MATHEMATICAL MODEL FOR THERMAL CRACKING OF HYDROCARBONS ETHANE CRACKING

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1 MATHEMATICAL MODEL FOR THERMAL CRACKING OF HYDROCARBONS ETHANE CRACKING The simulation of a thermal cracking coil requires integration of a set of Mass balance Energy balance Momentum balance equations. Mass Balance df j πd t = - Σ(s ij r i ) (1) dz 4

2 Reaction Mechanism for Ethane Cracking C 2 H 6 CH 3 * + CH 3 * CH 3 * + C 2 H 6 CH 4 + C 2 H 5 * C 2 H 5 * C 2 H 4 + H * H * + C 2 H 6 H 2 + C 2 H 5 * H * + H * H 2 H * + CH 3 * H * + C 2 H 5 * CH 4 C 2 H 6 C 2 H 5 * + CH 3 * C 3 H 8 C 2 H 5 * + C 2 H 5 * C 4 H 10

3 Reaction scheme for ethane cracker model E (kcal/kmol) A C 2 H 6 C 2 H 4 + H E15 C 2 H 4 + 2H 2 2CH E08 C 2 H C 4 H C 4 H C 4 H H 2 C 2 H 4 1/3 C 6 H 6 + H E09 C 2 H 4 C 2 H 2 + H E08 C 2 H 4 2C + 2H E05 C 2 H 4 + C 2 H C 3 H C 3 H H E14

4 Reaction rates r 1 = A 1 exp(-e 1 /RT) (pp(c 2 H 6 ) - pp(c 2 H 4 )*pp(h 2 )/Kp 1 ) r 2 = A 2 exp(-e 2 /RT) pp(c 2 H 4 ) pp(c 2 H 6 )pp(h 2 ) - pp(ch 4 )/Kp 2 ) r 3 = r 1 P r 4 = A 4 exp(-e 4 /RT) pp(c 2 H 4 ) 2 r 5 = A 5 exp(-e 5 /RT) pp(c 2 H 4 ) 2 r 6 = A 6 exp(-e 6 /RT) pp(c 2 H 4 ) 2 r 7 = A 7 exp(-e 7 /RT) (pp(c 2 H 4 ) - pp(c 2 H 4 )*pp(h 2 )/Kp 1 )

5 Material balance equations d C2H6 /dz = Πd 2 /4 (-r 1 -r 7 ) d CH4 /dz = Πd 2 /4 (2 r 2 ) d C2H4 /dz = Πd 2 /4 (r 1 - r 2 - r 3 - r 4 - r 5 - r 6 - r 7 ) d C3H8 /dz = Πd 2 /4 (0.381r 7 ) d C3H6 /dz = Πd 2 /4 (0.952r 7 ) d C2H2 /dz = Πd 2 /4 (r 5 ) d H2 /dz = Πd 2 /4 (r 1-2r r 3 + r 4 + r 5 + 2r r 7 ) d C4H10 /dz = Πd 2 /4 (0.125r 3 ) d C4H8 /dz = Πd 2 /4 (0.125r 3 ) d C4H6 /dz = Πd 2 /4 (0.25r 3 ) d C6H6 /dz = Πd 2 /4 (0.333r 4 ) d C /dz = Πd 2 /4 (2r 6 )

6 Energy Balance dt 1 πd t 2 = [Q(z) πd t + r i (- H i )] dz F j Cp j 4 Cp = specific heat Q d t = heat flux = coil diameter r i = rate of reaction H = heat of reaction In order to avoid the complications of solving the above energy balance equation with the heat transfer coefficients, specific heats of each component, the heat flux profiles and heat of reaction, we have applied directly temperature profiles being used in industrial ethane cracker across the length of the reactor, in a polynomial form.

7 Momentum balance The pressure drop equation along the length of the cracking coil was derived by rapid estimates. In most empty tubular reactors kinetic energy changes are negligible and only the friction losses need be considered. The friction losses can be obtained from P f = ρ f z u 2 /2 g c In the Reynolds number ranges of steam cracking flow rates the friction factor for smooth tubes can be calculated using f = 0.184/N Re 0.2 where N Re = DG/µ m. Pressure drop was calculated by combining the above two Equations G 1.8 µ m 0.2 z P = D 1.2 ρ f y i µ i M i µ m = y i M i

8 The viscosity of individual component is calculated by 33.3 ( MT c ) [f(1.33t r )] µ i = V c f(1.33t r ) = T r (1.9T r ) 0.8log(1.9Tr) The above set of continuity equations for each species along with energy and pressure drop equations are numerically integrated using fourth order Runge-Kutta method to obtain the axial profiles of conversion, temperature, and pressure.

9 COKING MODEL Thermal cracking of hydrocarbons is always accompanied with the formation of coke which deposited on the walls of the coil. Coke may be formed either directly from the feed stock and/or from the products. Many components from the feed and products are capable of yielding coke which are called the coke precursors. The coke deposited in the coil and in the TLX hampers heat transfer and thereby requiring higher tube skin temperature. The coke deposition also reduces coil diameter which in turn leads to higher inlet pressures which are detrimental to ethylene yield. The temperature increase of the tube wall and pressure drop necessitate shutdown of the plant for decoking. Rate of coke deposition depends on several factors such as feed stock, operating conditions, pyrolysis coil design, its material of

10 construction and pre treatments given to the inner walls of the coil. Coking kinetics and rate of coke deposition along the length of the cracking coil as a function of time have to be incorporated in the main pyrolysis model to able to simulate run length. This helps in predicting the coke thickness inside the coil which in turn predicts the run length of cracking coil for a given set of operating parameters and a desired yield pattern. The present model considers ethane, and ethylene as potential coke precursors for run length simulation of ethane cracking. Coking reaction scheme for ethane cracker model

11 E, Kcal/gmol A Reaction order (n) Ethane coke E15 1 Ethylene coke E10 1 The rate of coke formation can be expressed as m r c = r ci m is number of precursors i=1 r ci = A i exp(-e i / RT f ) c i ni where c i is the concentration of the coke precursor which can be expressed in terms of partial pressure and temperature. The initial gas temperature profile was maintained constant for the complete run length.

12 The concentrations of the precursors, C i, are generated by main reaction model along the length of coil. The average of concentrations at the entrance and exit of each pass is taken as the concentration of that particular pass. The continuity equation for coking is integrated by incrementing time in stepwise. We have taken 24 h as step length. The thickness of the coke deposited, b ck, is calculated using the following relation (Lichtenstein, 1964). d i α ck r c t s b ck = ( 1 - exp( )) 2 2ρ ck The pressure drop in coked tube is calculated using P ck = P(G ck /G) 1.8 (d/d ck ) 1.2 ( ρ ck /ρ) where P is clean tube pressure drop. The total increase in inlet pressure is calculated and checked with the limiting value. Once the increase in the inlet pressure

13 exceeds the limiting value the calculations are stopped and the corresponding time is reported as run length. Decoking is considered necessary when one of the following criteria is satisfied 1. Inlet pressure exceeding the limiting value 2. External tube skin temperature exceeding 1080 C External tube skin temperature The external tube skin temperature is calculated by using the following relations (Rase, 1977). T w = T + T f + T ck + T w Q 0 d o Q 0 d o Q 0 d o b w T f = ; T ck = ; T w =

14 h i d ck λ ck d ck λ w d where T is fluid temperature and T f is temperature drop across the film, T ck is temperature drop across the coke and T w is temperature drop across the tube wall. h i, inside heat transfer coefficient is calculated using Dittus Boelter relation λ f dck G 0.8 C p µ h i = ( ) ( ) d ck µ λ f 0.4 THE INPUT Molecular weights Critical properties Step size for calculations Temperature profile equations Coil geometry Kinetic parameters

15 Feed rate (Flow rate of ethane per coil, t/h) Dilution ratio Crossover temperature Coil outlet temperature Coil inlet pressure THE OUTPUT Concentration profile Temperature profile Pressure profile Product yields and Run length with varying feed stock quality and operating conditions External tube skin temperature

16 PROPANE CRACKING Reactions 1. C 3 H 8 C 2 H 4 + CH 4 2. C 3 H 8 C 3 H 6 + H 2 3. C 3 H 8 0.5C 4 H C 2 H 6 4. C 3 H 8 0.5CH C 3 H C 2 H 6 5. C 2 H 6 C 2 H 4 + H 2 6. C 2 H 6 CH C 2 H 4 7. C 2 H 6 0.5CH C 3 H 8 8. C 3 H 6 1.5C 2 H 4 9. C 3 H 6 + H 2 CH 4 + C 2 H C 3 H 6 C 2 H 2 + CH C 2 H 4 + H 2 C 2 H C 2 H 4 C 2 H 2 + H C 2 H C 3 H C 2 H 2 + H 2 C 4 H C 3 H 6 + C 2 H 2 C 5 s

17 Reaction rates A(sec-1) E (kmol/m3 sec) or * (m3/kmol s) (kcal/kmol) r 1 = kp 1 pp(c 3 H 8 ) 2.62E r 2 = kp 2 pp(c 3 H 8 ) 2.00E r 3 = kp 3 pp(c 3 H 8 ) 2.20E r 4 = kp 4 pp(c 3 H 8 ) 1.10E r 5 = kp 5 pp(c 2 H 6 ) 0.34E r 6 = kp 6 pp(c 2 H 6 ) 3.90E r 7 = kp 7 pp(c 2 H 6 ) 0.20E r 8 = kp 8 pp(c 3 H 6 ) 0.99E r 9 = kp 9 pp(c 3 H 6 )pp(h 2 )* 1.00E r 10 = kp 10 pp(c 3 H 6 ) 1.40E r 11 = kp 11 pp(c 2 H 4 )pp(h 2 )* 0.68E r 12 = kp 12 pp(c 2 H 4 ) 7.70E r 13 = kp 13 pp(c 2 H 4 ) 1.40E r 14 = kp 14 pp(c 2 H 2 )pp(h 2 )* 9.90E r 15 = kp 15 pp(c 2 H 2 )pp(c 3 H 6 )* 9.00E

18 Material Balance d(ch 4 )/dz = r r 4 + r r 7 + r 9 + r 10 d(c 2 H 4 )/dz = r 1 + r r r 8 + r 9 - r 11 - r 12 - r 13 d(c 2 H 6 )/dz = 0.5r r 4 - r 5 - r 6 - r 7 + r 11 d(c 3 H 8 )/dz = -r 1 - r 2 - r 3 - r r 7 d(c 3 H 6 )/dz = r r 4 - r 8 - r 9 - r r 13 - r 15 d(c 2 H 2 )/dz = r 10 + r 12-2r 14 - r 15 d(h 2 )/dz = r 2 + r 5 + r 12 - r 9 - r 11 - r 14 d(c 4 H 10 )/dz = 0.5r 3 d(c 4 H 6 )/dz = r 14 d(c 5 s)/dz = r 15

19 REACTION SCHEME FOR LPG CRACKING No. Reaction A E, Kcal/gmol Source 1. C 2 H 6 C 2 H 4 + H E E 2. 2C 2 H 6 C 3 H 8 + CH E E 3. C 2 H 4 + C 2 H 6 C 3 H 6 + CH E E 4. C 3 H 8 C 2 H 4 + CH E P 5. C 3 H 8 C 3 H 6 + H E P 6. C 3 H 8 + C 2 H 4 C 2 H 6 + C 3 H E P 7. C 3 H 6 C 2 H 2 + CH E P 8. C 2 H 6 C 2 H 4 + H E P 9. 2C 3 H 6 3C 2 H E P 10. C 2 H 2 + C 2 H 4 C 4 H E P 11. C 3 H 6 + C 2 H 6 1-C 4 H 8 + CH E P 12. 2C 3 H C 6 + 3CH E P

20 13. n-c 4 H 10 C 3 H 6 + CH E NB 14. n-c 4 H 10 2C 2 H 4 + H E NB 15. n-c 4 H 10 C 2 H 4 + C 2 H E NB 16. n-c 4 H 10 1-C 4 H 8 + H E NB 17. C 3 H 6 + H 2 C 2 H 4 + CH E NB 18. C 2 H 2 + C 2 H 4 C 4 H E NB 19. i-c 4 H 10 i-c 4 H 8 + H E IB 20. i-c 4 H 10 C 3 H 6 + CH E IB 21. i-c 4 H 10 + C 2 H 4 2-C 4 H 8 + C 2 H E IB 22. i-c 4 H 10 C 3 H 4 + CH E IB 23. C 3 H 4 C E IB 24. C 2 H 2 + C 2 H 4 C 4 H E IB

21 THERMAL CRACKING OF ETHANE-PROPANE MIXTURES Reaction Scheme for the Cracking of Mixtures of Ethane and Propane The combination of both ethane and propane cracking models enabled a molecular reaction scheme for the cracking of mixtures of both the components.

Modeling of a Fluid Catalytic Cracking (FCC) Riser Reactor

Modeling of a Fluid Catalytic Cracking (FCC) Riser Reactor Dr. Riyad Ageli Mahfud Department of Chemical Engineering- Sabrattah Zawia University Abstract: Fluid catalytic cracking (FCC) is used in petroleum