Octane Numbers, Flash Point and a Butadiene Dehydrogenation with Recycle: 23-Chem-B6 Petroleum Refining and Petrochemicals, December 2015, Q2

Question 2: Octane Numbers, Flash Point and a Butadiene Dehydrogenation with Recycle (20 marks — equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Check — printed reaction

The source prints the reaction as “$C_4H_4 \rightarrow C_4H_6 + 2H_2$”, but both the surrounding text (“pure normal butane C₄H₁₀”) and hydrogen balance require the reactant to be n-butane, C₄H₁₀. The dehydrogenation is therefore taken as $C_4H_{10} \rightarrow C_4H_6 + 2H_2$, which is what makes the stoichiometry (2 mol H₂ per mol butane) consistent with the stream data.

(a)(i) Difference between the MON and RON methods (4 marks)

Both octane numbers are measured on the same standardized single-cylinder, variable-compression CFR (Cooperative Fuel Research) engine, by matching the test fuel’s knock to reference blends of iso-octane (2,2,4-trimethylpentane, ON = 100) and n-heptane (ON = 0). The methods differ only in severity of the test conditions:

RON (Research, ASTM D2699): mild — 600 rpm, ~52 °C intake-air temperature, fixed spark timing. Represents low-speed, part-throttle, city driving.
MON (Motor, ASTM D2700): severe — 900 rpm, pre-heated mixture (~149 °C), and spark advance varied with compression. Represents high-speed, high-load, sustained (highway) driving.

Because the MON conditions are more demanding, MON is always lower than RON for the same fuel; the gap (RON − MON) is the fuel’s sensitivity. North-American pump ratings quote the antiknock index AKI = (RON + MON)/2.

(a)(ii) What the octane numbers represent (4 marks)

An octane number is a measure of a gasoline’s antiknock quality — its resistance to knock, the spontaneous, uncontrolled autoignition of the unburned end-gas ahead of the spark-initiated flame front, which produces damaging pressure spikes. A fuel of octane number X knocks, under the test conditions, exactly like a blend of X vol% iso-octane with (100−X)% n-heptane. A higher octane number means greater knock resistance, which allows the engine to run at a higher compression ratio and more advanced spark timing — and hence deliver more power and efficiency — without knocking.

(b) Flash point (2 marks)

The flash point is the lowest temperature at which a fuel gives off vapour in sufficient concentration to form an ignitable mixture with air just above its surface, so that a momentary flash occurs when a small flame is applied (it need not sustain burning — that is the higher fire point). It is a volatility/flammability index used for safe handling, storage and classification, measured by closed-cup (Pensky–Martens/Abel) or open-cup (Cleveland) apparatus.

(c) Butadiene dehydrogenation with recycle

Given. Fresh feed is pure n-butane. The reactor–separator recycles part of the product back to a mixer.

Stream	Composition / rate
Reaction	C₄H₁₀ → C₄H₆ + 2 H₂
Product (leaving process)	65 mol/hr H₂, 15 mol/hr C₄H₁₀, n mol/hr C₄H₆
Recycle	20 mol/hr total: 20% C₄H₁₀ (4 mol/hr), 80% C₄H₆ (16 mol/hr)
Fresh feed	pure C₄H₁₀, rate F (unknown)

Find. (i) fresh-feed rate F; (ii) product C₄H₆ rate n; (iii) single-pass conversion of butane.

Figure 2 — Dehydrogenation flowsheet: fresh C₄H₁₀ and the recycle blend combine in the mixer, react in the catalytic reactor, and the separator splits the effluent into the product stream and the 20 mol/hr recycle.

Approach. Draw the envelope around the whole process (recycle is then internal): overall balances on hydrogen and on C₄ units give F and n; a balance across the reactor alone gives the single-pass conversion.

Overall hydrogen balance ⇒ feed rate. Every mole of butane that reacts (overall) releases 2 mol H₂, and all H₂ leaves in the product. With fresh feed F entering and 15 mol/hr butane leaving unreacted, butane reacted overall $= F-15$, so$$H_{2,\text{out}} = 2(F-15) \;\Rightarrow\; 65 = 2(F-15) \;\Rightarrow\; \boxed{F = 47.5\ \text{mol/hr}}.$$
Overall C₄ balance ⇒ product butadiene. Each butane converts to one butadiene, so all C₄ units are conserved: $F = (\text{C}_4\text{H}_{10}\ \text{out}) + (\text{C}_4\text{H}_6\ \text{out})$, giving$$n = F - 15 = 47.5 - 15 = \boxed{32.5\ \text{mol/hr C}_4\text{H}_6}.$$(Consistent with the H₂ balance, as it must be.)
Butane entering the reactor. The mixer combines fresh feed with the recycle butane: $47.5 + 4 = 51.5$ mol/hr into the reactor.
Butane leaving the reactor. The reactor effluent is split into product + recycle, so its butane equals the sum of the two: $15 + 4 = 19$ mol/hr. Butane converted in one pass $= 51.5 - 19 = 32.5$ mol/hr.
Single-pass conversion. Referenced to the butane fed to the reactor:$$X_{\text{single}} = \frac{51.5 - 19}{51.5} = \frac{32.5}{51.5} = \boxed{0.631\ (63.1\%)}.$$

Quantity	Result
(i) Fresh feed of pure C₄H₁₀	47.5 mol/hr
(ii) Product flow of C₄H₆	32.5 mol/hr
(iii) Single-pass conversion of butane	63.1%
Butane to reactor / converted per pass	51.5 / 32.5 mol/hr

Concept & Theory

Topic. Reactor with recycle: overall vs single-pass conversion.

Key relations. Overall balance uses only fresh feed and net product; single-pass conversion $=\dfrac{\text{reactant in} - \text{reactant out (reactor)}}{\text{reactant in (reactor)}}$, where the reactor inlet includes recycle.

Why this works. Placing the balance envelope around the whole process hides the recycle, so the fresh feed is fixed by the H₂ actually produced. Overall conversion (based on fresh feed) is high; single-pass conversion is lower because the recycle re-presents unconverted butane.

Common pitfall. Using the fresh feed (47.5) instead of the reactor inlet (51.5) as the single-pass denominator, or forgetting that recycle butane appears at both the reactor inlet and outlet.

Source. Felder, Rousseau & Bullard, Elementary Principles of Chemical Processes §4.7 (recycle and purge; overall vs single-pass conversion).