Chapter 6 Isothermal Reactor Design: Molar flow rate 반응공학 1.

Chapter 6 Isothermal Reactor Design: Molar flow rate 반응공학 1

Seoul National University
개요 지난 마지막 장에서 우리는 여러 단일 반응들을 위해 다양한 등온 반응기설계를 하기 위한 전화율을 사용했다. 전화율의 관점에서 볼 때 대개의 상황들에서 몰수지를 사용하는 것은 극도로 효과적인 전략이다. 그러나, 제 1장의 표 S-1에 나타낸 것처럼 몰농도 (NA, NB) 또는 몰유량 (FA, FB)의 항으로 표현된 몰수지를 이용하는 경우가 더욱 편리하거나, 어떤 경우에는 절대적으로 필요로 하게 된다. 이 장에서는, 이러한 경우들을 분석하기 위하여 CRE 알고리즘을 조금 변경한다. 변경된 알고리즘을 사용하여, 첫 번째로 각각 또는 모든 종류의 몰수지를 작성하고, 두 번째로 상대적인 반응속도를 사용하여 각각의 반응들을 다른 반응들과 연결시키는 작업을 한다. Seoul National University

다음 반응기들을 분석하기 위하여 (1) 몰유량(Fi) 으로 표현된 몰수지(mole balance)를 사용하는 경우: 마이크로반응기 (NOCl분해반응) 2NOCl  2NO + Cl2 멤브레인반응기 (에틸벤젠의 탈수소화) C6H5CH2CH3  C6H6CH=CH2 + H2 (2) 몰수 (Ni) 로 표현된 몰수지(mole balance)를 사용하는 경우: 반회분식 반응기 CNBr + CH3NH2  CH3Br + NCNH2 복합반응(8장)과 열효과(11~13장)를 고려하기 위해 이러한 변수들 (Ni , Fi)의 항으로 표현된 몰수지를 사용할 것이다. Seoul National University

Using CA (liquid) and FA (gas) in the mole balance and rate laws
6.1  There are many instances when it is much more convenient to work in terms of the number of moles (NA, NB) or molar flow rates (FA, FB, etc) rather than conversion.  Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates are preferred rather than conversion.  We now modify our algorithm by using concentration for liquids and molar flow rates for gases as our dependent variables.  The main difference between the conversion algorithm and the molar flow rate/concentration algorithm is that, in the conversion algorithm, we needed to write a mole balance on only one species, whereas in the molar flow rate and concentration algorithm, we must write a mole balance on each and every species. Seoul National University

Fig. 6-1 Isothermal reaction design algorithm for mole balances
A + 2B  C Stoichiometry (4) (a) Write the concentrations in terms of molar flow rates for isothermal gas-phase reaction Mole balance (1) Write mole balance on each species 각 성분에 대해서… ; ; (b) For liquid-phase reaction use concentration, CA, CB DP Rate law (2) Write rate law in terms of concentration (5) Write the gas-phase pressure drop in terms of molar flow rate Stoichiometry (3) Relate the rates of rxn of each species to one another combine (6) Use an ODE solver or a nonlinear equation solver to combine Steps (1) through (5) to solve for, for example, the profiles of molar flow rates, concentration and pressure. Seoul National University

Liquid phase  For constant-volume liquid-phase reaction  concentration is preferred variable  We have only to specify the parameter values for the system (CA0, v0, etc.) and for the rate law (kA, a, b) to solve the coupled ordinary differential equations for either PFR, PBR, or batch reactors or to solve the coupled algebraic equations for a CSTR. Table Mole balance for liquid-phase reactions Seoul National University

6.2 Mole balances on CSTRs, PFRs, PBRs, and Batch Reactors
Moles or molar flow rates concentration Batch CSTR PFR PBR Seoul National University

Gas phase  For gas phase reactions in a PFR:  need to be expressed in terms of the molar flow rates Mole balance: Rate law: Stoichiometry: Pressure drop: Total molar flow rate: (1-11) (3-3) y (4-17) (5-28) = FA + FB + FC + FD + FI We now combine all the preceding information as shown in Table 6-2. Seoul National University

Table 6-2 Algorithm for Gas phase reaction
1. Mole balances: CSTR PFR PBR Seoul National University

2. Rate law: Relative rate of reaction: y 3. Stoichiometry: Concentration: Total molar flow rate: Seoul National University

4. Combine: For an isothermal operation of a PFR with no DP 5. Evaluation:  Specify the parameter values: kA, CT0, a, b, T0, a, b, c, d  Specify the entering number: FA0, FB0, FC0, FD0, and final value: Vfinal 6. use an ODE solver: Seoul National University

6.3 Microreactors  Microreactors are emerging as a new technology in CRE.  Microreactors are characterized by high surface area-to volume ratio. A typical channel width might be 100 mm with a length of 20,000 mm. The resulting high surface area-to-volume ratio (ca. 10,000 m2/m3) reduces or even eliminates heat and mass transfer resistances often found in larger reactor.  Consequently, surface catalyzed reactions can be greatly facilitated, hot spots in highly exothermic reactions can be carried out isothermally. Seoul National University

6.3 Microreactors  These features provide the opportunity for microreactors to be used to study the intrinsic kinetics of reaction.  Another advantage of microreactor is their use in the production of toxic or explosive intermediates where a leak or microexplosion for a single unit will do minimal damage because of the small quantities of material involved.  Other advantages include shorter residence times and narrower residence time distribution.  Microreactors are also used for the production of special chemicals, combinatorial chemical screening, lab-on-a-chip, and chemical sensors. Seoul National University

Microreactor and Lab-on-Chip
Microreactor made of silicon anodically bonded with glass Lab-on-Chip made of glass and polymer for DNA amplification and detection Rutherford Appleton Laboratory (RAL) in the UK Seoul National University

Microreactor for DNA analysis
Seoul National University

Microreactor and Microplant
Microreactor with heat exchanger Microplant with reactor, valves, mixers Ehrfeld, Hessel, and Lowe, Microreactors: New Technology for Modern Chemistry (Wiley-VCH, 2000) Seoul National University

2g/s per a microreaction system
6.3 Microreactors  Production in microreactor systems can be increased simply by adding more units in parallel. For example, the catalyzed reaction R-CH2OH + ½O R-CHO + H2O Ag Required only 32 microreaction systems in parallel to produce 2000 tons/yr of acetate! 2g/s per a microreaction system Seoul National University

Example 6-1: Gas-Phase Reaction in a Microreactor
The gas phase reaction 2NOCl → 2NO + Cl2 is carried out at 425oC and 1641 kPa (16.2 atm). Pure NOCl is to be fed, and the reaction follows an elementary rate law. It is desired to produce 20 tons of NO per year in a microreactor system using a bank of ten microreactors in parallel. Each microreactor has 100 channels with each channel 0.2 mm square and 250 mm in length. Plot the molar flow rates as a function of volume down the length of the reactor. The volume of each channel is 10-5 dm3. What is the reactor volume necessary to achieve 85% conversion? Additional information: To produce 20 tons per year on NO at 85% conversion would require a feed rate of mol/s of NOCl or 2.26x10-5 mol/s per channel. Rate constant and activation energy (given): k = 0.29 dm3/mol-sec at 500K with E = 24 kcal/mol. J.B. Butt, Reaction Kinetics and Reactor Design, 2nd ed. New York, Marcel Dekker, 2001, p153 Seoul National University

Solution For one channel FAo = 22.6 mol/s FB = 19.2 mol/s, X=0.85, V=? = 22.6 x 0.85 2NOCl  2NO + Cl2 2A  2B + C A  B + ½C Although this particular problem could be solved using conversion, we shall illustrate how it can also be solved using molar flow rates as the variable in the mole balance. 1. Mole balances on species A, B, and C: 2. Rates: (a) Rate law: (b) Relative rates: Seoul National University

3. Stoichiometry: Gas phase with T=To and P=Po, then Concentration Gas Phase (4-17) Applying Equation (4-17) to species A, B, and C, for T=T0, P=P0, the concentrations are (E6-1.5) Equation (3-42) Seoul National University

4. Combine 5. Evaluate Use Polymath to solve three ODEs When using an ODE solver (Polymath), one does not have to actually combine the mole balances, rate laws, and stoichiometry as was done in the combine step in Chapter 5. The ODE solver will do that for you. Thanks, ODE solver! Seoul National University

Profiles of microreactor molar flow rates Flow rates in micro-mol/s
25 Flow rates in micro-mol/s FA 20 FB 15 Flow rates [mmol/s] FC 10 5 2.0e-6 4.0e-6 6.0e-6 8.0e-6 1.0e-5 V [dm3] Fig E6-1.1 Seoul National University

Example 6-1 Gas-Phase Reaction in a Microreactor

Example 6-1 Gas-Phase Reaction in a Microreactor
분석: PFR예제에서의 이 기상반응은 전화율을 사용하여 쉽게 풀 수 있다. 하지만, 멤브레인 반응기나 복합 반응들은 전화율을 이용하여 풀 수 없다. 표 6-2의 반응 알고리즘의 1단계에서 5단계에서 사용된 식들을 쓰고, ODE 풀이자인 폴리매스에 그 식들을 타자 쳐서 입력하면, 그림 E6-1.1에서 나타내어진 몰유량 프로파일을 얻을 수 있다는 것을 언급하고자 한다. 몰유량 프로파일은 반응기의 유입부에서 급격히 변화하고 부피가 6x10-6 dm3 이상인 하류에서는 매우 적게 변화 한다는 것을 주목해라. 실전 예제문제 파일로부터 이 프로그램을 사용하여 그래프를 그려보고 싶은 재미있는 변수들은 다음과 같다: 전체 몰유량 FT, 반응물들의 농도 CA, CB, CC (CB와 CC에 대해서는 2 개의 추가적인 방정식들을 타자 쳐야 한다) (3) 반응 속도 -rA, rB, rC.

4.9 Membrane reactors  Membrane reactors can be used to increase conversion when the reaction is thermodynamically limited as well as to increase the selectivity when multiple reactions are occurring.  Thermodynamically limited reactions are reactions where the equilibrium lie far to the left (i.e., reaction side) and there is little conversion.  If the reaction is exothermic, increasing the temperature will only drive the reaction further to the left, and decreasing the temperature will result in a reaction rate so slow that there is very little conversion.  If the reaction is endothermic, increasing the temperature will move the reaction to the right to favor a higher conversion; however, for many reactions these higher temperatures cause the catalyst to become deactivated.

4.9 Membrane reactors  The term membrane reactor describe a number of different types of reactor configurations that contain a membrane. The membrane can either provide a barrier to certain components while being permeable to others.  Like reactive distillation, the membrane reactor is another technique for driving reversible reactions to the right toward completion in order to achieve very high conversion.  These high conversion can achieve by having one of the reaction products diffuse out of a semipermeable membrane surrounding the reacting mixture.  As a result, the reversible reaction will not be able to take place, and the reaction will continue to proceed to the right toward completion.

Membrane Reactors

Membrane Reactors Palladium membrane reactor and its application to direct phenol synthesis

What kinds of membrane reactors are available?
Membrane reactors are most commonly used when a reaction involves some form of catalyst, and there are two main types of these membrane reactors: the inert membrance reactor and the catalytic membrane reactor.  The inert membrane reactor allows catalyst pellets to flow with the reactants on the feed side (usually the inside of the membrane). It is known as an IMRCF, which stands for Inert Membrane Reactor with Catalyst on the Feed side. In this kind of membrane reactor, the membrane does not participate in the reaction directly; it simply acts as a barrier to the reactants and some products.  A catalytic membrane reactor (CMR) has a membrane that has either been coated with or is made of a material that contains catalyst, which means that the membrane itself participates in the reaction. Some of the reaction products (those that are small enough) pass through the membrane and exit the reactor on the permeate side.

4.9 Membrane reactors C6H12  3H2 + C6H6 A  3B + C
 Inert membrane reactor with catalyst pellets on the feed side (IMRCF) C6H12  3H2 + C6H6 A  3B + C H2 molecule is small enough to diffuse through the small pore of the membrane while C6H12 and C6H6 cannot.

4.9 Membrane reactors C6H12  3H2 + C6H6 A  3B + C
 Catalytic membrane reactor (CMR) C6H12  3H2 + C6H6 A  3B + C Membrane reactors are commonly used in dehydrogenation reactions, where only one of the products (molecular hydrogen) is small enough to pass through the membrane. This raises the conversion for the reaction, making the process more economical.

H2 diffuses through the membrane while C6H6 does not
Reactor shell Sweep Gas membrane H2 membrane membrane Reactants C6H12 H2 Products C6H6

Analyzing membrane reactors
 We shall choose the reactor volume rather than catalyst weight as our independent variable for this example. The catalyst weight, W, and reactor volume, V, are easily related through the bulk catalyst density, rb (i.e. W=rbV).  The mole balances on the chemical species that stay within the reactor, namely A and C, are shown in Fig and also in Table 4-6. (1-11)  The mole balances on C is carried out in an identical manner to A, (6-1)

 However, the mole balance on B (H2) must be modified because hydrogen leaves through both the side of the reactor and end of the reactor.  First, we shall perform mole balances on the volume DV shown in Fig. 6-3(d). The mole balances on hydrogen (B) is over a differential volume DV shown in Fig. 6-3(d) and it yields RB: Molar rate of B leaving through the sides the reactor per unit volume of reactor (mol/dm3·s) RB DV membrane FA FB FC FA FB FC membrane V V+DV Fig. 6-3(d) RB

RB RB: Molar rate of B leaving through the sides the reactor per unit volume of reactor (mol/dm3·s) membrane FA FB FC FA FB FC membrane V V+DV RB Mole balance on B in the catalytic bed: In by flow Out by flow Out by diffusion – – + Generation = Accumulation (6-2) Dividing by DV and taking the limit as DV → 0 gives (6-3)

CBS (6-4) B CB RB = Molar rate of B leaving through the sides the reactor per unit volume of reactor (mol/m3·s) WB =The molar flux of B (mol/m2·s) k’C= the overall mass transfer coefficient (m/s) a = the surface area per unit volume of reactor (m-1) kc = a transport coefficient (s-1) (6-5) (6-6)

Example 6-2 Membrane reactor for Dehydrogenation reactions
 According to The DOE, an energy saving of 10 trillion Btu/yr could result from the use of catalytic membrane reactors as replacements for conventional reactors for dehydrogenation reactions: such as the. A  B + C CH2CH3 CH=CH2 + H2 Dehydrogenation of ethylbenzene to styrene C4H10  C4H8 + H2 Dehydrogenation of butane to butylene C3H8  C3H6 + H2 Dehydrogenation of propane to propylene

The basic algorithm for solving reaction in the membrane reactor
RB=kcCB A  B + C FA FB DV FC membrane V+DV RB=kcCB A  B + C Equilibrium constant KC=0.05 P=8.2 atm T=227oC FA0=10mol/min 1. Mole balance: A, B & C for a differential mole balance on A in the catalytic bed at steady state for a differential mole balance on B in the catalytic bed at steady state for a differential mole balance on C in the catalytic bed at steady state

2. Rate law: 3. Transport out the sides of the reactor: CBS~0 kc is a transport coefficient. kc=f(membrane & fluid properties, tube diameter…)  constant 4. Stoichiometry: P & T = const

5. Combining and Summarizing: 6. Parameter evaluation: CT0=0.2 mol/L, k=0.7 min-1, KC=0.05 mol/L, kc=0.2 min-1 FA0=10 mol/min, FB0=FC0=0 7. Numerical solution: Solve with POLYMATH or MATLAB

POLMATH solution: kc=0.2 min-1 A  B + C FA0 =10 mol/min Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500 FA =4 mol/min

POLMATH solution: kc= min-1 A  B + C FA0 =10 mol/min Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500

POLMATH solution: kc=20 min-1 A  B + C FA0 =10 mol/min Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500

Effects of side stream, RB=kcCB
in a membrane reactor Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500 kc=0.20 min-1 A  B + C Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500 kc=20 min-1 Large side stream Reactor volume, V [L] FA FB FC 10 5 100 200 300 400 500 kc= min-1 Little side stream

분석 A의 몰유량은 반응이 평형에 가까워지는 지점인 약 100 dm3까지 급격히 떨어진다. 이 지점에서 반응은 그래프에서 보이는 비슷한 기울기를 지닌 FA와 FB에 의하여 B가 멤브레인을 통해서 제거되는 오른쪽 방향으로만 진행 할 것이다. 만약 B가 급격하게 제거되고 있다면 FB가 0에 가까워질 것이고 반응은 마치 비가역인 것처럼 진행될 것이다. 만약 B가 서서히 제거되고 있다면 FB는 반응을 통해 커질 것이고 반응 속도 -rA는 작아질 것이다. 문제 6-2B(b)에 이러한 현상을 다루었다.

Effects of changing the inlet flowrate, FA0
in a membrane reactor FAO=25 FAO=25 FAO=15 FAO=15 FAO=5 FAO=5 FAO=25 FAO=5 FAO=15 FAO=15 FAO=25 FAO=5 As expected, our flow rates increase as FA0 increases. Interestingly though, conversion actually decreases as FA0 increases. Why? Even though more of reactant A enters the reactor as the flow rate increases, it spends less time in the reactor, which causes the decrease in conversion.

Use of membrane reactors to enhance selectivity
 In addition to species leaving the membrane reactor, species can also be fed to the reactor through the membrane. For example, for the reaction A + B →C + D A could be fed only to the entrance, and B could be fed only through the membrane as shown here. FB0 FA0 Vt As we will see in Chapter 6, this arrangement is often used to improve selectivity when multiple reactions take place. (6-3’)

6.5 Unsteady-State Operation of Stirred Reactors
 Startup of a CSTR : Determine the time to reach steady-state operation  Semibatch reactor : Predict the concentration and conversion as a function of time A + B →C + D A, B C Reactive distillation Acetylation Esterification A B Semibatch reactor Ammonolysis Chlorination Hydrolysis M CA0 CA Startup of a CSTR

Utilizing the definitions of FA and NA, we have
Startup of a CSTR Time to Reach Steady State for a First-Order Reaction in a CSTR To determine the time to reach steady-state operation of a CSTR, we begin with the general mole balance equation applied to a well-mixed CSTR. (1) Utilizing the definitions of FA and NA, we have Conversion does not have any meaning in startup because one cannot separate moles reacted from moles accumulated. Consequently, we must use concentration rather than conversion as the variable in our balance equation. For liquid-phase reactions V =V0 and for a constant overflow, v =v0. After dividing by v0 and replacing V/v0 by the space time t, we find that (2)

Startup of a CSTR For a first-order reaction: Solution (3)
Letting ts be the time necessary to reach 99% of the steady state concentration, CAS: Rearranging (4-47) for CA=0.99CAS yields (4)

Startup of a CSTR Time to reach steady state in an isothermal CSTR
For most first-order system, steady state is achieved in three to four space times Time to reach steady state in an isothermal CSTR (5) For slow reactions with small k (1>>tk): For rapid reactions with large k (tk >>1): (6) (7)

6.6 Motivation of Semibatch Reactors
One of the best reasons to use semibatch reactors is to enhance selectivity in liquid-phase reactions. For example, consider two simultaneous reactions. On reaction produces the desired product D and the other produces an undesired product U. We want SDU as large as possible. kD A + B D kU A + B U

Maximizing SD/U for two reactants Rate selectivity parameter, S
D (Desired Product) A + B U (Undesired Product) The rate laws are Rate selectivity parameter=Instantaneous selectivity k1 k2

Different reactors and schemes for minimizing the unwanted product
B B A A B A B A B (a) CSTR (b) tubular reactor (c ) batch (d) semibatch 1 (e) semibatch 2 A B A B (f) Tubular reactor with side streams (g) Tubular reactor with side streams B A A B (h) Tubular reactor with recycle (i) Series of small CSTRs

6.6.2 Semibatch Reactors : Constant volumetric flow, vo
volume as a function of time (6-13) B B A (6-14) A Mole balance on A: [ in ] [ out ] [ gen. ] = [ acc. ] Mole balance on B: [ in ] [ out ] [ gen. ] = [ acc. ] (6-9) (6-10) (6-15) Overall mass balance of all species: [ in ] [ out ] [ gen. ] = [ acc. ] (6-11) (6-12) (6-16)

6.6.2 Semibatch Reactors : Constant volumetric flow, vo
Mole balance on C: [ in ] [ out ] [ gen. ] = [ acc. ] (6-19)

Isothermal semibatch reactor with 2nd–order reaction
Concentration of CNBr (A) and CH3Br (C) with time Example 6-3 CNBr + CH3NH2  CH3Br + NCNH2 A B  C D Irreversible liquid phase Isothermal elementary reaction in a semi-batch reactor t=0, CA0=0.05 gmol/ℓ, CB0=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ Bromine cyanide Methyl amine Methyl bromide

Concentration of CNBr (A) and CH3Br (C) with time Example 6-3 Mole balances of A, B, C, and D: A (6-14) B (6-16) C (6-18) (6-19) D

Concentration of CNBr (A) and CH3Br (C) with time Example 6-3 Rates:

Concentration of CNBr (A) and CH3Br (C) with time Example 6-3 Liquid volume with time : Conversion, X : t=0, CA0=0.05 gmol/, Feeding B: CB0=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ

Concentration-time trajectories
in Semibatch Reactor 0.05 CNBr + CH3NH2  CH3Br + NCNH2 (A) (B) (C) (D) t=0, CA0=0.05 gmol/, Feeding B: CB0=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ 0.04 0.03 CA Concentration [mol/dm3] 0.02 CC =CD 0.01 CB 0.00 100 200 300 400 500 Time [s] C의 농도가 최고점을 통과한다는 것을 주목할 필요가 있다. 최고점이 생기는 것은 A가 모두 소비되고 C가 더 이상 생성되지 않으며 C의 몰농도를 희석시킬 B가 연속적으로 반응기 안으로 유입되기 때문이다.

Reaction rate-time trajectories
in Semibatch Reactor 0.0025 CNBr + CH3NH2  CH3Br + NCNH2 (A) (B) (C) (D) t=0, CA=0.05 gmol/, CB=0.025 gmol/ℓ, v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ 0.0020 0.0015 Reaction rate [mole/s•L) 0.00 50 100 150 200 250 Time [s]

Reaction rate-time trajectories
in Semibatch Reactor 분석: 경향을 살펴보자. 반응속도에 따라 A는 약 250초 만에 0에 가깝게 떨어진다. 결과적으로 이 시간 후에 매우 적은 C가 생성되고 생성된 것은 반응기로 유입되는 B에 의해 희석되기 시작하고 B가 넘치기 전에 멈추게 된다. 이 반응을 수행한 시간을 어떻게 생각하는가? 약 5분 걸렸다. 이 시간은 심지어 밸브를 닫고 여는데도 매우 부족한 시간이다. 교훈을 얻자: 이 예제는 반회분식 반응기를 분석하는 방법은 보여주고 있지만 반응시간에 매우 짧으므로 이 온도에서는 반회분식 반응기를 이용하여 반응은 할 수 없다. 대신에 측면을 통해 B가 유입되는 관형 반응기나 또는 A가 첫 번째 반응기로만 유입되는 연속 연결된 CSTR들의 각각 반응기에 적은 양의 B를 유입할 수 있도록 한 반응기를 사용할 수 있다. 이것에 대하여는 제 8장에서 더 토의하자.

마무리 이 장은 등온반응기에 대한 화학반응공학의 핵심을 제공하고 있다. 이 장을 완성한 후에 독자들은 이 장에서 논의된 모든 반응기들, 즉 회분식반응기, CSTR, PFR, PBF, 멤브레인반응기 및 반회분식 반응기에 대하여 다음과 같은 알고리즘 블록 쌓기(algorithm building block)를 적용할 수 있게 된다. Evaluation Combine Stoichiometry Rate Law Mole Balance 독자들은 압력강하를 계산할 수 있게 되며, 시스템 변수들이 미치는 영향을 기술할 수 있게 된다. 독자들은 전화율 (제 5장)을 사용하거나 또는 농도와 몰유량(제 6장)을 사용하여 화학반응공학문제들을 풀 수 있게 된다.

Chapter 6 Isothermal Reactor Design: Molar flow rate 반응공학 1.

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Chapter 6 Isothermal Reactor Design: Molar flow rate 반응공학 1.

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Presentation on theme: "Chapter 6 Isothermal Reactor Design: Molar flow rate 반응공학 1."— Presentation transcript:

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