Numerical Design Model of Furnace Reactor for Ethane Cracking

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

NUMERICAL DESIGN MODEL OF FURNACE REACTOR FOR ETHANE CRACKING

Wordu A. A1, Akinola B2 1Department of Chemical/Petrochemical Engineering, University of Science and Technology, Nkpolu, Porthacourt, Rivers State, Nigeria 2Department of Chemical/Petrochemical Engineering, University of Science and Technology, Nkpolu, Porthacourt, Rivers State, Nigeria

Abstract Appropriate design models for typical furnace reactor for cracking of 100% ethane feed has been developed. The research considers the radiation, convective, pressure drop effect and composite heat balance on the convective and radiation zones of the reactor operations. Principles of material and energy balances and pressure effects from the flow of feed material from the convective section to the radiation zone were incorporated into lumped-design model equations. The models were resolved applying numerical ode 45 to generate the profiles on conversion along the length of reactor, pressure drop effects and energy balance which were compared with plant data of Indorama Eleme petrochemicals complex to validate the dynamics in the reactor in figures 1,2,3, 4,5,6,7,and 8.The pressure effects profile of the reactor operation at steady states showed a quasi-flat shape at 30-45% conversion to constant pressure drop as depletion process progressed to 65% upwards.

Keywords: Furnace Reactor, Radiation-Convection Sections, Cracking, Heat Balance Radiation-Convection, Design Model, Numerical. ------***------

1. INTRODUCTION energy recovered from the cracked gas is used to make high pressure stream. This steam is in turn used to drive the In Petrochemical industry, furnace reactor is the turbines for compressing the cracked gas, propylene fundamental equipment for the cracking of ethane to yield refrigeration compressor and the ethylene refrigeration ethylene. Ethylene production is one of the largest sectors compressor [8]. and is the building blocks in manufacturing of petrochemicals. Notably among the olefins produced is ethylene whose worldwide production in 2012 (109 million tons in 2008) exceeds that of any other organic compound. Ethylene can also be synthesized by dehydrogenation of ethane. It is worthy to note that the dehydrogenation processes of ethane are expected to play a large role in the future production of ethylene since ethane is an abundant component in natural gas which is an alternate resource to traditional petroleum [3]. The furnace reactor consists of long coiled radiant tubes placed vertically inside a rectangular gas-fired furnace. The tubes are hung vertically to allow for expansion and to avoid sagging, consequently lengthening tube life. The furnace reactor system consists of the convection and radiation zones. The feedstock which is usually light hydrocarbons like ethane, ethane-propane mixtures or naphtha first enters the convection zone where it is pre-heated to about 500-8000c and any liquid vaporized before it enters the radiation zone where pyrolytic reactions takes place, inducing numerous free radical reactions. The products from the reactor are immediately quenched to stop Fig 1: Schematics of atypical ethane furnace reactor these reactions. First, pyrolysis of ethane gives rise to some carbon (coke) formation. This coke deposition increases 1.1 Process Concept of Furnace Reactor pressure drop and inhibits heat transfer up to a point where stops for mechanical cleaning are mandatory. The reactor is identified to comprise of two major sections of cracking reactions, radiation and convective zones. The Furthermore, the energy change associated with the process kinetics and convective forces of ethane cracking process is is endothermic and consequently, requires huge energy. essentially coupled in the numerical computer model for However, once started the energy efficiency is high as heat investigative study. Literature have shown that research ______Volume: 05 Issue: 07 | Jul-2016, Available @ http://ijret.esatjournals.org 204 IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 have been carried out on the radiation section [1], but did 2.2 Material Balance not consider convective section forces on the cracking process and the pressure drop along the reactor. The The furnace reactor is modeled as a plug flow reactor. The observed gap in the previous research forms the main frame- approach involves establishing the steady state material work of the present research. balance over a differential volume element (dVR) of reactor length (dz), as shown in figure (1) below. Basis is a mole of 2. MATERIALS AND METHOD ethane.

The furnace reactor is modeled as a tubular reactor. Design equations for predicting material and energy interchange in the reaction zone of the reactor as well as equation accounting for pressure drop along the reactor length were developed. Radiation and convective heat transfer equations Fig 2: Differential Element Of Tubular Reactor were established to account for temperature effects in the convective zone of the reactor and then coupled with the Taking a balance for 1 mole of fresh feed of ethane A over overall energy balance of the reactor system. the differential reactor volume (dvR); rate of inflow of feed into differential volume element FA equal to rate of outflow 2.1 Process Chemistry of feed from differential volume element FA  dFA minus Pyrolysis of ethane is represented essentially by the rate of depletion of feed due to chemical reaction within irreversible first order chemical reaction equation in the differential volume element  rA dvR and rate of temperature range of 900 to 1200K. accumulation of feed within volume element at steady state process gives equation (2), The stoichiometric balanced equation for ethane cracking process in furnace reactor is kinetically stated as [7] (2) FA  FA  dFA    r A dvR  0

C H  C H  H (1) 2 6g  2 4g  2(g)  F  r dv  F  dF A A R A A

A pure ethane is fed at known inlet temperature and pressure to a steel tube contained in an ethane pyrolysis furnace. Heat  r A dvR  dFA (3) is supplied by the furnace to the reactor. At temperatures of o about 980–1200 C, C-H bonds of ethane molecules The differential reactor volume element (dvR) is related to dissociates such that ethylene and hydrogen are produced as the differential reactor length by; major products. Conversion of ethane to ethylene can be as high as 65-70%. Thermodynamic properties such as dvR = Adz (4) 0 standard heat of formation ( H 298 ), Specific heat capacity (Cp) and related kinetic data for chemical species By substituting equation (4) into (3) and rearranging, we associated with the reaction equation (1) above is as shown obtain; in table (1) below [6] dF d F 1 A  AO  A  Table1. Physical Properties and data for ethane pyrolysis  r A   reaction dvR Adz

Component Cp (KJ/kgmolk) F (KJ/Kgmol) A0 (5)  r A   d A -2 Adz A = C2H6 - 83820 14.1504+7.549x10 T- 1.799 x 10-5 T2 For a first-order irreversible reaction, the kinetic rate -1 B = C2H4 52510 1.839 + 1.19167 x 10 equation is given mathematically; -5 2 T – 3.6515 x10 T - C = H2 0.00 27.012 + 3.5085 x 10 r A  K1CA (6) 3 4 -1 T + 6.9 x 10 T Reaction rate constant: At low pressure (P < 5 bar) of the reacting gas mixture, the 36354.6 gas law k  4.717 x 1014 Exp( T ) Atomic weights: C = 12, H = 1 PAVA  nARTR (7) Gas Constant (R): 3 n P 8.314Kpa.m A A (8)  CA  kgmol.K VR RTR ______Volume: 05 Issue: 07 | Jul-2016, Available @ http://ijret.esatjournals.org 205 IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

PA F d 1  P  C  (9) AO X  A  Tot. A r A     K   RTR A dz 1 A  RTR

From Daltons’ Law; d 1  P  A  K  A  Tot. (16) PA  yAPTOt. (10)   dz 1  A  FAO RTR

By substituting equation (9) into (8) we obtain; Hence the conversion XA as a function of reactor length z is defined by the solution of the first order ordinary differential yAPTot. equation (15). CA = (11) RT R From the Arrhenius Equation;

Substituting (10) into (6) we obtain the rate equation E K1 =A1 Exp ( ) (17) y P RTR r   K A Tot. (12) A RT R and by using data from table (1) we have;

Hence, determine the mole fraction of ethane (y ), mole A 363546 balance of the reacting species with respect to differential K  4.717 x 1014 Exp( ) (18) volume element figure 1 is shown in table 2 below; 1 T

Table 3. Mole balance for the reacting species Substituting equation (17) into (15) yields; Inlet molar Outlet molar flow rate Component flow rate at conversion x  36354.6  Exp( ) 14   d A 4.717 x 10 APTot.  TR 1   A  A = C2H6 FAO F (1- ) AO A        dZ  FAO R   TR  1   A 

B = C2H4 0 FAO    A   (19) C = H2 0 F AO For a given tube internal diameter, reactor pressure, and FT = FAO + FAO = TOTAL F = F 14 TO AO 4.717 x 10 APTot. FAO (1 + ) inlet ethane flow rate the term is FAO R

 36354.6  Hence, mole fraction of ethane (yA) is given by; Exp      TR  molar flow of ethane constant and the other term is yA  (13) TR Total molar flow of gas dependent on temperature.

1   A 3. ENERGY BALANCE y A  (14) 1   A The energy balance over the differential volume (dvR) element accounts for heat of reaction, heat transfer from By substituting equation (13) into (10), we have: furnace to the tube wall and sensible heat effects in the following gas stream.

 1  P r   K  A  Tot. (15) The overall energy balance with respect to the differential A   volume element of the reactor is given by the fundamental  1   A  RTR equation below [5], [2].

By equating (5) and (14) we obtain;

______Volume: 05 Issue: 07 | Jul-2016, Available @ http://ijret.esatjournals.org 206 IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

Rateof Inflow of energy Rate of outflowof  Rate of generationof  Rate of accumulation' Into differential  energy from  energydueto chemical reaction of energy within             (20) volume element   differential volume   within differential  differential            element  Volume Element  Volume element 

Where; (i) Rate of inflow of energy into differential volume  H d  q  dT R A     1  C  (C C ) R element is given by; qdz dZ  F  A PA A PB PC dZ (ii). Rate of outflow of energy from differential volume  AO  (25) element is given by;

dTR HT  FACP A FB CPB  FC CPC dTR (21) Making subject of equation; R dZ

Where:

A C H  q   H R d A 2 6    dT F dZ B C2H4 R   AO  (26) dZ (1 )C   (C C ) C H2 A PA A PB PC

But, Where:

FA = FAO (1- A ) q = qc + qR (27) FB = FAO

FC = FAO The convective zone of the reactor preheats the feed to a

temperature TC. Heat from the flue gas of the furnace is Substituting into equation (21) gives transferred to the feed in two stages;

H  F 1 C  F  C  F  C dT (1) Conductive heat transfer of heat from flue gas to internal TR A0 A PA AO A PB AO A PC R surface of convective tube described by the equation;

HT  FA0 1A CPA  FAOA CPB  CPC dTR dq K R  T  T  (28) dA d FG i  H  F  1 C   C C dT TR AO A PA A PB PC R (2) Convective heat transfer of heat from internal surface of (22) tube to the feed gas described by the equation;

(iii) Rate of generation of energy due to chemical reaction within differential volume element is given by; dq  hi TC  Ti  (29) dA

FAO  H R d A (23) At steady state, heat transferred by conduction from flue gas

to convective tube wall equals convective heat transferred Substituting F , F , and F values into (19), we obtain; A B C from the tube wall to the flowing gas stream. Hence, by

equating equation (28) to (29) we obtain; FA0d A 1 HR   qdZ  FAO 1 A CPA  A CpB CPC dTR (24) dq K  T  T   hi T  T  (30) dA d FG i C i By dividing through equation (21) by dz and F then the AO, change in temperature as a function of length is described by From which we obtain; the first order ordinary differential equation. ______Volume: 05 Issue: 07 | Jul-2016, Available @ http://ijret.esatjournals.org 207 IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

Also, the heat capacity relationships in table 1 are applied

K directly in determining the heat of reaction  HR  in  TC  TFG  Ti   Ti (31) d equation (26) as shown in equation (35);

T But, convective heat flux can be expressed by the equation; 0 H R  H 298  CPB  CPC  CPA dTR (35) 298

qc  GCPA TC  Ti  (32) 0 The heat of reaction at 298k ( H 298 ) can be calculated Substituting equation (31) into (32), we obtain (33) as; from the heats of formation of Table 3.1 using the equation [6];

 K  q  GC   T  T  (33) = C0 C0  C0 (36) c PA   FG i PB PC PA  hid  = 52510 + 0.0 − −83820

= 52510 + 83820 For most applications, the heat flux (q ) to the tubes in the R radiant section ranges between 20 to 40 KW/M2. For this ∆퐻 0 = 136,330퐾퐽 푝푒푟 퐾푔푚표푙. 퐾 work, a literature value of 20 KW/M2 is used. Hence, the 298 total heat flux is given as; Introducing the heat capacity relationships of table 1 and the

calculated value for the heat of reaction at standard state  K  (298K) into equation (35) and integrating yields the heat of   (34) q  20  GCPA   TFG  Ti   hid  reaction HR at any reactor temperature TR (k) as shown;

4  2 3  6.9 x10  H  136,330  24.701 T  298  0.02384 T  298  6.177 x 105 T  2983     (37) R R R R  T  298   R 

3.1 Pressure Drop Table 1: Simulation Results For flow of fluids in pipes, the pressure drop along the Δp length of the pipe [5] X d(m) Z(m) T (k)  (S) A R (Kpa)

dp 2 fG2 0.30 0.0508 133.1250 1100.00 0.5990 4.6945 Tot.   (38) dZ 1000d 0.35 0.0635 136.8750 1185.00 0.6085 8.0480

0.40 0.0762 140.6250 1460.00 0.6011 10.7430 3.2 Solution Technique Equations (19) and (26) are nonlinear equations developed 0.45 0.0890 141.2500 1460.10 0.6000 12.4190 and are subjected to iterative simultaneous numerical 0.50 0.1016 145.0000 1460.50 0.5842 14.0950 process to obtain the profiles as in figures 1, 2 and 3 0.55 0.1270 148.7500 146.72 0.5789 15.7590 4. MODEL RESULTS 0.60 0.1400 153.1250 1460.80 0.5730 17.4540 Summary of simulation results obtained by linear 0.65 0.1524 155.000 1461.00 0.5700 19.1780 interpolation is as shown in table1 below;

The simulation results is obtained by using Runge-Kutta numerical method for solving simultaneous differential equation on computer program mat lab ODE 45 for the three lumped equations (19), (26) and (38) generated from the design model.

______Volume: 05 Issue: 07 | Jul-2016, Available @ http://ijret.esatjournals.org 208 IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

5. DISCUSSION

1500 Xa Tr

1000