Spring 2012 ENCH446 Project 2

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1 Spring 2012 ENCH446 Project 2 Raymond A. Adomaitis May 2, 2012 Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 1 / 36

2 Shale gas and the Marcellus formation oilshalegas.com dec.ny.gov Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 2 / 36

3 Shale gas pros and cons To start, several interesting NPR articles (also check the links within): Shell picks Pittsburgh area for major refinery Is US energy independence finally within reach? EPA concerns and a DOE sponsored shale-gas primer. Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 3 / 36

4 Shale gas reserves and gas composition Marcellus shale gas composition 1 (by mole fraction) Well C 1 C 2 C 3 CO 2 N From Composition Variety Complicates Processing Plans for US Shale Gas, a report by Bryan Research and Engineering, Inc. Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 4 / 36

5 Ethylene overview From Ethane from associated gas still the most economical, Oil & Gas Journal, 1998 Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 5 / 36

6 Ethylene overview Steam cracking of ethane to ethylene: 1 Dilute ethane stream with steam (e.g., 0.5 mole steam/mole ethane) 2 Heat to 850 o C 3 Millisecond residence time 4 Quench to stop the reaction process 5 Minimize coke formation Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 6 / 36

7 Ethane cracking reactions and kinetics C 2 H 6 C 2 H 4 + H 2 C 2 H 6 + C 2 H 4 C 3 H 6 + CH 4 C 3 H 6 C 2 H 2 + CH 4 C 2 H 4 + C 2 H 2 C 4 H 6 C 3 H 8 C 3 H 6 + H 2. Froment et al., I&EC Proc. Des. Devel (1976) Equilibrium and irreversible reactions Importance of propane and competing reactions Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 7 / 36

8 Individual report 2.1 A two page report on the shale gas background information How deep is the Marcellus formation? How big? What is its nominal thickness? The nature of the rock found above the formation? What are the environmental concerns related to the drilling and hydraulic fracturing operations? What are the environmental concerns associated with the subsequent gas production and downstream processing? A preliminary view of the gas processing operations with emphasis on existing commercial ethane cracking processes. Literature review on ethane cracking kinetics. Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 8 / 36

9 Ethane cracking reaction equilibrium and kinetics C 2 H 6 C 2 H 4 + H 2 (1) (2) (3) species H o f 298 G o f 298 A B C D J/mole J/mole K 1 K 2 K 2 (1) -83,820-31, e e-6 - (2) 52,510 68, e e-6 - (3) e e5 with R = J/(mol K) C ig p /R = A + BT + CT 2 + D/T 2 Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 9 / 36

10 Heat of reaction Reactions can be written in terms of their stoichiometric coefficients ν i : where ν 1 S ν M S M ν M+1 S M ν N S N (1) ν i < 0 for reactants ν i > 0 products Now consider a reaction A B taking place at constant pressure; the steady-state energy balance gives H = Q Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 10 / 36

11 Heat of reaction We define the standard state: P = 1 bar, T = 298 K and so the change in enthalpy associated with a reaction at standard conditions is written as H o 298 (< 0 for exothermic, > 0 for endothermic) H o 298 depends on how the reaction is written: 1 2 N H 2 NH 3 H298 o = 46kJ/(mol NH 3 ) N 2 + 3H 2 2NH 3 H298 o = 92kJ/(2mol NH 3 ) The standard heat of formation: standard heat of reaction producing 1 mole of a substance from its elemental compounds: C(s) + O 2 (g) CO 2 (g) H o f 298 = -393kJ/(mol CO 2) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 11 / 36

12 Heat of reaction Consider our forward reaction thus ν = ν 1 S 1 ν 2 S 2 + ν 3 S 3 C 2 H 6 (g) C 2 H 4 (g) + H and H o 298 = i ν i H o f 298 i so now looking up the heat of formation values of each component in our reaction component: C 2 H 6 (g) C 2 H 4 (g) H 2 (g) Hf o 298 : kj kj 0 H o 298 = 1( 83.82) + 1(52.51) + 1(0) = kj/mole ethane G o 298 = 1( 31.86) + 1(68.46) + 1(0) = Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 12 / 36

13 Dependence of H o on temperature For a constant pressure process dh = CpdT ; at standard state dh o = Cp o dt ν i dhi o = ν i Cpi o dt i i Using our notation for heat of reaction so at any T T 298 ν i dhi o = HT o Ho 298 i H o T = Ho R T 298 i ν i Cp o i R dt Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 13 / 36

14 Reaction equilibrium We recall that the activity a i of chemical species i is a dimensionless effective concentration, for example a i = γ i C i where γ i is an activity coefficient and C i the concentration of that species. The activity of a pure species in a liquid or solid state is unity. For an ideal gas, the activity is the species partial pressure over the standard (not total!) pressure: a i = P i P o where P o = 1 bar for the discussion that follows. Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 14 / 36

15 Reaction equilibrium We state without proof that for the reaction (1) under constant-pressure conditions N i=1 a ν i i ( G o ) = exp T RT (2) If we assume the system behaves as an ideal gas and that the reaction takes place in a fixed reactor pressure P, the total pressure P is the sum of each species partial pressure P 1, P 2. Under these conditions we have the equilibrium relationship N i=1 y ν i i ( ) N P i=1 ν i 1bar = exp ( G o T RT ) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 15 / 36

16 Reaction equilibrium At temperature T, and because G o T = Ho T T S o T S R = T1 T 0 C p RT dt ln P 1 P 0 and P 0 = P 1 = P o G o T = Ho R T 298 RT i T ν i Cp i R dt T S o i ν i Cp i RT dt Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 16 / 36

17 Reaction equilibrium Therefore, because we can write T S o 298 = T 298 ( G o 298 H o 298) we now have something we can compute using the data in hand: with G o T = Ho T 298 ( G o 298 H o 298) +R y C2 H 4 y H2 y C2 H 6 T 298 i Cp i ν i dt RT R T 298 i ν i Cp i RT dt. ( ) ( P G o ) = exp T = K eq (T ) 1 bar RT Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 17 / 36

18 Reaction equilibrium - effects of T and P Define ξ [0, 1] as the reaction coordinate corresponding to the moles of ethane in the reaction mixture; therefore, n T = ξ + 2(1 ξ), y C2 H 6 = ξ 2 ξ, y C 2 H 4 = y H2 = 1 ξ 2 ξ ( ) y C2 H 4 y H2 (1 ξ)2 1 bar = y C2 H 6 ξ(2 ξ) = K eq(t ) P with κ(t, P) = K eq (1 bar/p) gives 0 = ξ 2 2ξ + 1/(1 + κ) ξ = 1 1 1/(1 + κ) so clearly κ is our goal. Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 18 / 36

19 Reaction kinetics C 2 H 6 r f r b C 2 H 4 + H 2 After Froment and Goossens (1976) r f = e 272,800/(RT ) [C 2 H 6 ] r b = k b (T )[C 2 H 4 ][H 2 ] mol/m 3 s At equilibrium, r f = r b so [C 2 H 4 ][H 2 ] [C 2 H 6 ] = y C 2 H 4 y H2 y C2 H 6 P RT = e 272,800/(RT ) k b (T ) = K eq 1 bar RT k b (T ) = e 272,800/(RT ) (RT ) K eq (T )(1 bar) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 19 / 36

20 Reactor material balance A" v" z" z"="l" T wall" Assume: steady state operation diffusion negligible flat velocity profile ṅ T (z = 0) = 2 ξ 0 mol/s Balance for C 2 H 6 : ṁ in ṁ out = A z(r f r b ) [ ṁ in = va Py ] [ C 2 H 6 ṁ out = va Py ] C 2 H 6 v = ṅt RT RT A z z+ z ( RT P ) d dz v Py c 2 H 6 RT = k f [C 2 H 6 ] k b [C 2 H 4 ][H 2 ] d ( ) ṅ T ξ P ξ dz A 2 ξ = k f RT 2 ξ k b ( P RT ) 1 ξ 2 2 ξ Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 20 / 36

21 Reactor material balance Therefore, ( ) 1 dξ P A dz = k 1 ξ 2 ( ) P ξ b k f RT 2 ξ RT 2 ξ subject to initial condition ξ(z = 0) = ξ 0 and with residence time τ determined by τ ( ) ṅ T RT dt = L A P 0 Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 21 / 36

22 Reactor energy balance Recall from basic thermo: ṁ out H out ṁ in H in = Q Given the reactor tube inner wall perimeter 2π A/π, [ Q = A z HT o (r f r b ) + U z 2π ] A/π (T wall T ) so with H = C ig p Av for T ref = 0. Thus ( ) P (T T ref ) = Cp ig RT AṅT A ( RT P ) P RT T d [ dz ṅt Cp ig T = A HT o (r b r f ) + U 2π ] A/π (T wall T ) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 22 / 36

23 Reactor energy balance The gas thermal conductivity k g and radial length scale A/π give a lower bound on the heat transfer coefficient so We note U = k g / A/π d ig (2 ξ)cp T = A HT o dz (r b r f ) + 2πk g (T wall T ). k g (C 2 H 6 ) 0.017, k g (C 2 H 4 ) 0.017, k g (H 2 ) 0.18 and so [ Cp ig T dξ + (2 ξ) T dz dc ig p dt + C ig p ] dt dz = A H o T (r b r f ) + 2πk g (T wall T ) W m K Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 23 / 36

24 Reactor energy balance So finally dt dz = C ig p T dξ subject to initial condition dz + A Ho T (r [ b r f ) + 2πk ] g (T wall T ) (2 ξ) T + C p ig dc ig p dt T (z = 0) = T 0 Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 24 / 36

25 Subproject 2.2 Group report: Preliminary reactor design Outline of your (or my) kinetics scheme A plot of GT o as a function of temperature for 300 T 1200 K A plot of ξ as a function of 300 T 1200 K and 1 P 10 bar A list of the minimal set of reactor design parameters to be explored A numerical solution to the tubular reactor model with a discussion of its physical interpretation A first (quantitative) look at how the reactor system will be optimized... Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 25 / 36

26 Reaction equilibrium computations J/mol x H T o G T o Keq T (K) T (K) rate constants k f k b P=1 P=2 P=5 P=10 bar T (K) T (K) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 26 / 36

27 Representative isothermal reactor modeling results 1 Isothermal (1100 K, 2 bar) (C 2 H 6 mol/s) v (m/s) z (m) z (m) R tube = 5 cm, L = 2 m, T = 1100 K, P = 2 bar Single tube reactor with ṅ T = 2 ξ mol/s Note approach to correct equilibrium Residence time: τ = L 0 1 dz = 0.25 s v Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 27 / 36

28 Representative nonisothermal reactor modeling results 1 Nonisothermal 0.98 (mol/s z (m) R tube = 5 cm, L = 2 m, T wall = 1200 K, P = 2 bar Single tube reactor with ṅ T = 2 ξ mol/s T (K) % conversion 140 K temperature drop shutting down the reaction z (m) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 28 / 36

29 Reality check Consider the case where T (z = 0) = 1100 K and 10% ethane conversion: H o T = 144, 000 J/mol C p = 129 J/(mol K) T 0.1( 144, 000 J/mol)/(129 J/(mol K)) = 112 K Due to change in moles: dt dz = C pt dξ dz (2 ξ)c p Now assume ξ = 1 αz for z [0, L]: dt dz = T ( a) az = T (L) = T (0) 1 + al On the previous page, 0.9 = 1 αl so T (L) = 1100/1.1 = 1000 K Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 29 / 36

30 Reality check, continued For no reaction, constant C p dt dz = 2πk g (T wall T ) (1 mol/s)c p so 2π(0.017 W/m K)(100 K) (1 mol/s)(129 J/mol K) T (0.08 K/m)(2 m) = 0.2 K That s not very good heat transfer (U = k g /R tube = 0.34 W/m 2 K) Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 30 / 36

31 Subproject 2.3 Group report: Reactor design extensions Determine if our heat transfer coefficient is valid by computing a representative Reynold s number for the gas flowing through our system as a starting point Extend the nonisothermal reactor model to include steam as one of the feeds Present simulation results based on 1 mol/s C 2 H mol/s water as feed What is the role of steam in the feed stream? Develop a ChemCAD simulation of a process to separate the reactor effluent into water, H 2, ethane, and ethylene Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 31 / 36

32 Subproject 2.4 Group report: Closing the loop Modify material and energy balance equations to allow for an arbitrary reactor inlet concentration of steam, H 2, ethane, and ethylene Design a reactor effluent quench heat exchanger that promotes rapid effluent cooling to T < 373 K Connect the cooled reactor product stream to your ChemCAD simulation of a process to separate the reactor effluent into water, H 2, ethane, and ethylene Develop a representative design in which the ethane stream is recycled to the reactor Determine prices for ethane, ethylene, natural gas (to be used for the process furnace), and electricity Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 32 / 36

Ethane cracking furnace specifications 916 Ind. Eng. Chem. Res., Vol. 37, No. 3, 19985 linde.com Perfection.

Single furnace capacities up to 180,000 mta ethylene for liquid feeds and 260,000 mta for gas cracking are in operation or under construction, leaving still some room for a future increase.

Linde s PYROCRACK coils have been used successfully in commercial cracking furnaces for gas and liquid cracking. Long run lengths are achieved with conservative maximum heat flux Figure 1.

33 Ethane cracking furnace specifications 916 Ind. Eng. Chem. Res., Vol. 37, No. 3, linde.com Perfection. Large single furnace capacities are designed with the Linde twin-cell firebox concept combined with a common convection section. Single furnace capacities up to 180,000 mta ethylene for liquid feeds and 260,000 mta for gas cracking are in operation or under construction, leaving still some room for a future increase. Modern twin-cell furnaces can be designed for individual cell decoking, an operation in which one cell remains in normal operation where as the other radiant cell is decoked. Linde s PYROCRACK coils have been used successfully in commercial cracking furnaces for gas and liquid cracking. Long run lengths are achieved with conservative maximum heat flux Figure 1. Flow diagram of the calculations. Figure 2. Top view of the ethane furnace. Furnaces in an ethylene plant in Saudi Arabia steady state. A total of time steps were taken Table 1. Furnace Dimensions and Operating Conditions for each of the three run length simulations that have been performed. The three run length simulations elliptical reported here each required around 8 h of CPU time on circular long short Turn-key perfection an IBM/RS6000/375 computer. Furnace With its long experience as turn-key For contractor of petrochemical mega projects, perature Linde can of thepetitive process turn-key gasor was convertible keptcontracts constant to its at a value height (mm) each runtoday length Linde is simulation, in a position to offer the most crossover com- tem- length (mm) offer the experience of a technology supplier clients, either alone or in very strong regional of 600 C. However, the process gas inlet temperature width (mm) and a first class worldwide EPC contractor alliances with first class EPC contractors. is determined by the heat transfer in the convection thickness of refactory (mm) one hand, which translates into a single point However, besides turn-key responsibility, Linde thickness of insulation (mm) section of the furnace, and thus by the flue gas outlet responsibility in execution of projects. can offer all kinds of services to the industry, no. of side wall burners temperature in the radiation section of the furnace. The including studies, front-end engineering, detail flue gas outlet temperature differs for both coil types Firing Conditions Global alliances engineering, procurement and construction. initial total heat input (MW) and rises with time. Accounting for these variations in In order to strengthen its position worldwide, final total heat input (MW) Linde has entered into regional crossover cooperations temperature Based on the requires experience from the a mega calculation project of the with engineering partners, known convection to be absolute leaders in certain areas of an the additional world. iteration tremendous loop experience in the in modularization calculations. of Simula- feedstock 100% ethane section of a gas ofterminal the furnace in Norway, Linde andhas would gained introduce Operating Conditions hydrocarbon feed rate 3500 kg/h/coil A very successful cooperation tion is in place time with wouldplant becomponents augmented and in by project a factor execution of 2, without steam dilution kg/kg Samsung Engineering of Korea adding for the Asian/ meaningful under extreme precision environmental to theconditions. calculation This results. coil inlet temperature 600 C Pacific market, which has led to contracts for experience allows Linde to offer plants in all Raymond A. Adomaitis Spring 2012, ENCH446, coil outlet Project pressure atm 33 / 36 5 world-scale ethylene plants in China, Thailand, parts of the world, including areas with poor After Heynderickx and Froment, I&EC Res (1998): Furnace tube inside diameter: 0.15 m; tube length: 100 m 3500 kg/hr fresh ethane feed/tube; 0.35 kg H 2 O/kg ethane

34 Subproject 2.5 Group report: Energy integration Furnace energy requirements based on a cracking furnace operating with 50% excess air and flue gas temperature of 200 o C Assume ethane feed to unit is available at 2 bar and 300 K Account for all heating/cooling/electricity expenses (e.g., no direct purchasing of steam, liquid nitrogen, etc.) Shortened class meeting schedule next week - will discuss final reports and presentations at that time, will complete grading of Subproject 2.4 this week Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 34 / 36

35 Subproject 2 final report Page limit: 10, including title page; not including references and appendices. 1 Title page, including title, team number, members, member contributions, date, project profitability statement, honor pledge Project assumptions and basis Reactor modeling equations Reactor system description Separation process flow diagram Separation process stream and equipment summaries Safety and environmental issues Energy integration strategy Capital equipment summary Utilities, including on-site steam generation, cooling water, refrigeration demands Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 35 / 36

36 Subproject 1 group presentation Time limit: 5 minutes with 3 minutes for questions and transitions 1 Use readable text and figures 2 Do not spend time on motivation: concentrate on your process flow diagram, specific design choices and novel aspects of your design 3 Reactor preheater, reactor, and quench exchanger design 4 Separation system design with emphasis on cryogenic operations 5 Discuss safety and environmental aspects 6 Energy integration 7 Summarize costs and profitability analysis on a single slide Raymond A. Adomaitis Spring 2012, ENCH446, Project 2 36 / 36

Mass Balance MATHEMATICAL MODEL FOR THERMAL CRACKING OF HYDROCARBONS ETHANE CRACKING

Mass Balance MATHEMATICAL MODEL FOR THERMAL CRACKING OF HYDROCARBONS ETHANE CRACKING 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.