Question 3 of 6: Characterization Factors, Visbreaking and an Ideal-Gas Tank Pressure

Question 3: Characterization Factors, Visbreaking and an Ideal-Gas Tank Pressure (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 (UOP) factor and the Bureau-of-Mines Correlation Index (4 marks)

Both are single numbers that summarise the paraffinic-versus-aromatic character of a crude or fraction from its (easily measured) boiling point and specific gravity.

• UOP / Watson characterization factor: $K_W = \dfrac{(T_B)^{1/3}}{SG}$, where $T_B$ is the mean average boiling point in degrees Rankine and $SG$ is the specific gravity at 60 °F. Interpretation: $K_W \approx 12.5{-}13$ → highly paraffinic; $\approx 11{-}12$ → naphthenic/mixed; $\approx 10{-}11$ → highly aromatic. It is used to classify crude type and to correlate physical properties.
• US Bureau of Mines Correlation Index: $CI = \dfrac{87\,552}{T_B} + 473.7\,SG - 456.8$, with $T_B$ the mean average boiling point in Rankine. Interpretation: $CI \approx 0$ → paraffinic (straight-chain); $CI \approx 100$ → aromatic; intermediate values → naphthenes or mixtures. Higher CI means more aromatic/naphthenic.

(b) Visbreaking (3 + 3 + 2 marks)

(i) What it is. Visbreaking (“viscosity breaking”) is a mild, once-through thermal cracking process applied to heavy residua (atmospheric or vacuum residue). Its purpose is to reduce the viscosity and pour point of the residue so that less valuable light cutter stock is needed to blend it to fuel-oil specification, while also making a modest yield of lighter distillate.

(ii) Typical operating conditions. Two configurations are used: coil (furnace) visbreaking at ~450–500 °C with a short residence time (~1–3 min) and ~5–20 bar; and soaker visbreaking at a lower ~430–450 °C with a soaking drum providing a longer residence time at similar pressure. Conversion is deliberately held low (a few per cent to the gasoline/gas-oil range) to stay short of the coke-formation and product-instability threshold.

(iii) Principal reactions. Free-radical thermal cracking: scission of long paraffinic side chains from naphthene/aromatic rings and cracking of large paraffins into smaller molecules (gas, naphtha, gas oil), which lowers the residue viscosity. Some dehydrogenation and condensation of aromatics also occurs; if pushed too far these lead to coke, which is why severity is limited.

(c) Pressure of SO₂ in a rigid tank

Given. A rigid tank holds sulphur dioxide, assumed ideal.

Find. The reading on the tank’s pressure gauge (gauge pressure).

Approach. Convert the mass to moles and the temperature to an absolute scale, apply $PV=nRT$ for the absolute pressure, then subtract atmospheric to obtain the gauge reading.

1. Moles of SO₂. $n = \dfrac{30\ \text{lb}}{64.07\ \text{lb/lbmol}} = 0.4682\ \text{lbmol}.$
2. Absolute temperature. $T = 18\,{}^\circ\text{C} \to (18\times\tfrac95+32)+459.67 = 524.07\ {}^\circ\text{R}.$
3. Absolute pressure (ideal gas). With $R = 10.731$ psia·ft³/(lbmol·°R):$$P_{\text{abs}} = \frac{nRT}{V} = \frac{(0.4682)(10.731)(524.07)}{40} = 65.8\ \text{psia}.$$
4. Gauge reading. The gauge reads absolute minus atmospheric ($\approx 14.7$ psia):$$P_{\text{gauge}} = 65.8 - 14.7 = \boxed{51.1\ \text{psig}}\;(\approx 3.5\ \text{bar g}).$$