PERTEMUAN 1

2. CONVERSION AND REACTOR SIZING

Objectives:After completing Chapter 2, you will be able to: Define conversion and space time. Write the mole balances in terms of conversion for a batch reactor, CSTR, and PFR. Size reactors either alone or in series once given the molar flow rate of A, and the rate of reaction, - rA, as a function of conversion, X.

Conversion:a measure of a reaction's progress toward completionConsider the general equationaA + bB cC + dD

The basis of calculation is always the limiting reactant. We will choose A as our basis of calculation and divide through by the stoichiometric coefficient to put everything on the basis of "per mole of A".

The conversion X of species A in a reaction is equal to the number of moles of A reacted per mole of A fed, ie

Batch Flow

What is the maximum value of conversion?For irreversible reactions, the maximum value of conversion, X, is that for complete conversion, i.e. X=1.0.For reversible reactions, the maximum value of conversion, X, is the equilibrium conversion, i.e. X=Xe.

Batch Reactor Design EquationsGeneral Mole Balance Equation for Batch Reactor:

For reactant A:

Thus:

For a constant volume batch reactor:

CSTR Design Equations General Mole Balance Equation for CSTR:

For reactant A:

Thus:

Because the reactor is perfectly mixed, the exit composition from the reactor is identical to the composition inside the reactor, and the rate of reaction is evaluated at the exit conditions.

PFR Design Equations General Mole Balance Equation for PFR:

For reactant A:

Thus:

Summary:

ReactorDesign Equations

Batch

CSTR

PFR

Reactor SizingBy sizing a chemical reactor we mean we're either detering the reactor volume to achieve a given conversion or determine the conversion that can be achieved in a given reactor type and size. Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either or as a function of X. For vs. X, the volume of a CSTR and the volume of a PFR can be represented as the shaded areas in the Levenspiel Plots shown below:

Numerical Evaluation of IntegralsSimpsons One-Third Rule.

Problem 2.1.Consider the liquid phase reaction

which is to take place in a PFR. The following data was obtained in a batch reactor. X00.40.8

-ra(mol/dm3.s)0.010.0080.002

If the molar feed of A to the PFR is 2 mol/s, what PFR volume is necessary to achieve 80% conversion under identical conditions as those under which the batch data was obtained? Problem 2.2.Repeat Problem 2.1. if the reaction takes place in a CSTR.Reactors in SeriesOnly valid if there are no side streams

Consider a PFR between two CSTRs

Problem 2.3.Reaksi fase gas: A B + C berlangsung pada suhu 422.2 K, tekanan total 10 atm (1013 kPa). Umpan terdiri atas A dan inert dengan perbandingan mol 1:1 (ekuimolar). Kecepatan volumetrik umpan, v0 = 6,0 L/s. CSTR beroperasi secara isotermal. Data percobaan:

X0.00.10.20.30.4

-rA (mol/L.s)0.00530.00520.00500.00450.0040

X0.50.60.70.80.85

-rA (mol/L.s)0.00330.00250.00180.001250.00100

Hitung VCSTR yang dibutuhkan untuk mencapai X = 80%.Jawab:V = 554,9 L

Problem 2.4.Hitung kembali soal di atas jika reaktor yang digunakan adalah sebuah PFR isotermal.Jawab:V = 225 L

Terlihat bahwa untuk mencapai konversi yang sama pada kasus ini, VPFR < VCSTR.

Problem 2.5. Hitung kembali soal di atas jika reaktor yang digunakan adalah 2 buah CSTR isothermal yang diseri. Konversi keluar reaktor yang pertama adalah 0,4.Jawab:V1 = 86,7 LV2 = 277,4 L

Total volum yang dibutuhkan = Jadi, untuk mencapai konversi yang sama, total volum 2 CSTR yang diseri < total volum 1 CSTR.

Bagaimana jika 2 atau lebih PFR diseri?Total volum yang dibutuhkan untuk mencapai konversi tertentu tidak tergantung pada jumlah PFR yang diseri. Bukti untuk 2 PFR yang diseri:

Semakin banyak CSTR yang diseri, total volum CSTR akan makin mendekati volum 1 buah PFR untuk mencapai konversi yang sama.

Problem 2.6.Hitung kembali soal di atas jika reaktor yang digunakan adalah 1 buah PFR isothermal dan 1 buah CSTR isothermal yang diseri. Konversi keluar reaktor yang pertama adalah 0,5.Jawab:a. Skema 1: PFR diikuti CSTRV1 = 97 LV2 = 208 L

Total volum yang dibutuhkan = b. Skema 2: CSTR diikuti PFRV1 = 131,4 LV2 = 128,5 LTotal volum yang dibutuhkan =

Beberapa definisi 1. Kecepatan reaksi relatif

Reaksi:

2. Space Time = holding time = mean residence time,

Definisi: Contoh: Untuk PFR:

Jika v = v0 (misal reaksi fase cair):

Space time is the time necessary to process one volume of reactor fluid at the entrance conditions. This is the time it takes for the amount of fluid that takes up the entire volume of the reactor to either completely enter or completely exit the reactor.Sample Industrial Space Times Reaction Reactor Temperature Pressure atm Space Time

(1)C2H6 C2H4 + H2PFR860C21 s

(2)CH3CH2OH + HCH3COOH CH3CH2COOCH3 + H2OCSTR100C12 h

(3)Catalytic crackingPBR490C201 s < < 400 s

(4)C6H5CH2CH3 C6H5CH = CH2 + H2PBR600C10.2 s

(5)CO + H2O CO2 + H2PBR300C264.5 s

(6)C6H6 + HNO3 C6H5NO2 + H2OCSTR50C120 min

3. Space Velocity, SV

Definisi: SV seringkali diukur juga pada kondisi operasi yang lain. Dua jenis SV yang umum dipakai di industri adalah:a. LHSV = Liquid Hourly Space Velocity: v0 diukur pada kondisi cairan bersuhu 60 atau 750F.b. GHSV = Gas Hourly Space Velocity: v0 diukur pada kondisi STP (suhu dan tekanan standar, 250C, 1 atm) .

Problem 2.7.

1. Which system is most efficient for a intermediate conversion of (0.3)? 2. Which system is most efficient for a intermediate conversion of (0.65)? 3. Which system makes the best use of the reactor volume (i.e., least wasted volume)?

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