Question 5 of 6: Characterisation Factors, Visbreaking and an SO₂ Storage Tank

Question 5: Characterisation Factors, Visbreaking and an SO₂ Storage Tank (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.

(a) Watson K and the Bureau of Mines Correlation Index (4 marks)

Both are empirical indices of the chemical character (paraffinic vs. aromatic nature) of a petroleum fraction, derived from its boiling point and density.

UOP / Watson characterization factor $K$:

$$K = \frac{(T_B)^{1/3}}{SG},$$

where $T_B$ is the mean average boiling point in degrees Rankine and $SG$ is the specific gravity at 60 °F. Typical values: $K \approx 12.5\text{--}13$ for highly paraffinic stocks, $\approx 11.5$ for naphthenic, and $\approx 10\text{--}11$ for aromatic stocks. A higher $K$ means a more paraffinic (waxy, higher-hydrogen) crude, which cracks and reforms readily.

US Bureau of Mines Correlation Index (CI):

$$CI = \frac{48640}{T_B} + 473.7\,SG - 456.8,$$

with $T_B$ the volume-average boiling point in kelvin and $SG$ the specific gravity 60/60. The scale is anchored so that CI = 0 for a straight-chain paraffin and CI = 100 for benzene (aromatic): low CI indicates a paraffinic fraction, high CI a naphthenic or aromatic one. The two indices are complementary — Watson $K$ is high and CI low for paraffinic stocks, and vice-versa — and both let a refiner infer processing behaviour from two easily measured bulk properties.

(b) Visbreaking

(i) What it is. (3 marks) Visbreaking (“viscosity breaking”) is a mild, once-through thermal-cracking process applied to heavy vacuum or atmospheric residue. Its purpose is to lower the viscosity and pour point of the residue by cracking a small fraction of it, so that less valuable light cutter stock is needed to blend the residue down to fuel-oil specification, while also yielding some lighter gas-oil and naphtha.

(ii) Typical conditions. (3 marks) Coil (furnace) visbreaking operates at about 450–500 °C with a short residence time at 0.5–2 MPa; soaker visbreaking uses a slightly lower coil temperature (≈ 430–450 °C) with a longer residence time in a soaking drum. Conversion is deliberately held low (typically 5–15% to gas + naphtha) to stay short of coke formation and keep the product stable.

(iii) Principal reactions. (2 marks) The chemistry is free-radical thermal cracking: scission of long paraffinic side-chains from aromatic/naphthenic cores, C–C bond cleavage in paraffins to give smaller paraffins and olefins, and partial dehydrogenation. These reduce the average molecular weight (hence viscosity). Over-cracking must be avoided because continued condensation and polymerisation of the aromatic cores grows asphaltenes and forms coke.

(c) Pressure gauge reading on an SO₂ tank

Given. $m = 20$ lb SO₂ (M = 64.07 lb/lbmol) in $V = 40$ ft³ at $T = 26\ ^\circ$C. Treat SO₂ as an ideal gas; find the gauge pressure.

Find. The gauge pressure = absolute pressure − atmospheric (14.7 psia).

Approach. Convert mass to moles and temperature to Rankine, apply $PV=nRT$ in imperial units ($R = 10.731$ psia·ft³/lbmol·°R) for the absolute pressure, then subtract atmospheric.

1. Moles and temperature.$$n = \frac{20}{64.07} = 0.3122\ \text{lbmol},\qquad T = 26\ ^\circ\text{C} = 78.8\ ^\circ\text{F} = 538.5\ ^\circ\text{R}.$$
2. Absolute pressure (ideal gas).$$P_{abs} = \frac{nRT}{V} = \frac{0.3122(10.731)(538.5)}{40} = \boxed{45.1\ \text{psia}}.$$
3. Gauge reading.$$P_{gauge} = P_{abs} - P_{atm} = 45.1 - 14.7 = \boxed{30.4\ \text{psig}}.$$