Unit 9: Industrial Fuels, Petroleum Refining & Petrochemicals
Comprehensive refinery engineering and petrochemical process chemistry: crude oil assays and True Boiling Point (TBP) fractionation, atmospheric and vacuum pipestills, Fluid Catalytic Cracking (FCC) two-stage riser-regenerator dynamics, catalytic reforming aromatization, hydrodesulfurization (HDS), thermal steam cracking of naphtha, and syngas / C1 chemistry.
Β§9.1 Crude Oil Characterization: Assay, TBP Distillation & Watson Characterization Factor
Crude petroleum is an exceedingly complex multicomponent mixture containing hundreds of thousands of hydrocarbon isomers spanning molecular weights from $16\text{ g/mol}$ (methane) to $> 2,000\text{ g/mol}$ (asphaltenes), alongside heteroatoms (sulfur, nitrogen, oxygen, and trace metals $\text{V, Ni}$).
Fundamental Refinery Characterization Indices
1. API Gravity:
Inversely proportional to specific gravity at $60^\circ\text{F}$ ($15.56^\circ\text{C}$):
- Light crudes ($^\circ\text{API} > 31.1$, $\text{SG} < 0.87$) yield high fractions of premium gasoline and diesel.
- Heavy crudes ($^\circ\text{API} < 22.3$, $\text{SG} > 0.92$) contain massive vacuum residues requiring coking or hydrocracking.
2. Watson (UOP) Characterization Factor ($K_W$):
Quantifies the chemical paraffinicity vs aromaticity of a hydrocarbon fraction:
where $T_B$ is the Mean Average Boiling Point in degrees Rankine ($^\circ\text{R} = ^\circ\text{F} + 459.67$).
- Paraffinic hydrocarbons: $K_W = 12.5 - 13.0$.
- Naphthenic (cycloparaffinic): $K_W = 11.5 - 12.0$.
- Highly aromatic: $K_W = 10.0 - 11.0$.
True Boiling Point (TBP) Distillation Curve
Standard ASTM D2892 TBP distillation utilizes a 15-theoretical-plate packed column operating at a $5:1$ reflux ratio. It plots cumulative volume percentage distilled versus vapor temperature, defining standard refinery cut-points:
- Liquefied Petroleum Gas (LPG): $\text{C}_3 - \text{C}_4$ ($< 35^\circ\text{C}$).
- Light Naphtha: $\text{C}_5 - \text{C}_6$ ($35 - 90^\circ\text{C}$, petrochemical feed / isomerization).
- Heavy Naphtha: $\text{C}_7 - \text{C}_9$ ($90 - 180^\circ\text{C}$, catalytic reformer feed).
- Kerosene / Jet Fuel: $\text{C}_{10} - \text{C}_{14}$ ($180 - 240^\circ\text{C}$).
- Atmospheric Gas Oil (Diesel / AGO): $\text{C}_{14} - \text{C}_{20}$ ($240 - 360^\circ\text{C}$).
- Atmospheric Residue: $> 360^\circ\text{C}$ (feed to Vacuum Distillation Unit).
Β§9.2 Atmospheric & Vacuum Distillation: Pipestills, Side Strippers & Tower Hydrodynamics
The primary separation of crude oil is executed in a continuous sequence of two columns: the Atmospheric Distillation Unit (ADU) followed by the Vacuum Distillation Unit (VDU).
``` REFINERY CRUDE DISTILLATION CIRCUIT Desalted Crude (~250Β°C) β βΌ ββββββββββββββββ β FIRED HEATER β (Heats crude to 360-370Β°C; flashes into tower) ββββββββ¬ββββββββ βΌ ββββββββββββββββββββββββββββββββββββββββββββββββ β ATMOSPHERIC FRACTIONATING COLUMN (ADU) β ββ> Overhead: Off-gas & Light Naphtha β (30-50 Cross-flow Valve Trays, Pumparounds) β ββ> Side Draw 1: Heavy Naphtha (to Stripper) β β ββ> Side Draw 2: Kerosene / Jet A-1 β β ββ> Side Draw 3: Diesel / Light Gas Oil ββββββββββββββββββββββββ¬ββββββββββββββββββββββββ βΌ Atmospheric Residue (>360Β°C) ββββββββββββββββ β VACUUM HEATERβ (Heated to 400-415Β°C under deep vacuum) ββββββββ¬ββββββββ βΌ ββββββββββββββββββββββββββββββββββββββββββββββββ β VACUUM DISTILLATION UNIT (VDU) β ββ> Light Vacuum Gas Oil (LVGO) β (Structured Packing, 15-30 mbar deep vacuum) β ββ> Heavy Vacuum Gas Oil (HVGO to FCC) ββββββββββββββββββββββββ¬ββββββββββββββββββββββββ βΌ Vacuum Residue (>565Β°C to Coker / Bitumen) ```
1. Atmospheric Distillation Tower Dynamics
Crude oil is heated in a gas/oil-fired pipe furnace to $360 - 370^\circ\text{C}$ and flashes into the flash zone of a fractionator ($40 - 50$ valve trays).
- Heating above $375 - 380^\circ\text{C}$ is strictly prohibited to avoid thermal cracking (pyrolysis) and coke deposition inside furnace tubes.
- Side streams (heavy naphtha, kerosene, diesel) are withdrawn as liquids and passed through side-stream stripping columns with stripping steam to vaporize light ends and adjust flash points.
- Intermediate pumparounds withdraw hot liquid trays, cool them against cold crude feed, and return them higher up, redistributing reflux and reducing vapor volumetric loads.
2. Vacuum Distillation Engineering
Heavy hydrocarbons boiling above $360^\circ\text{C}$ cannot be separated at atmospheric pressure without thermal degradation.
- The atmospheric bottoms are piped into the VDU operating under deep vacuum ($15 - 30\text{ mbar}$ absolute, maintained by 3-stage steam ejectors and liquid ring vacuum pumps).
- At $20\text{ mbar}$, heavy hydrocarbons exhibit boiling point depressions of $150 - 200^\circ\text{C}$, allowing separation of Light Vacuum Gas Oil ($\text{LVGO}$) and Heavy Vacuum Gas Oil ($\text{HVGO}$, boiling up to $565^\circ\text{C}$ equivalent atmospheric cut point) without coking.
- Modern VDUs employ low-pressure-drop corrugated structured sheet packings (e.g., Mellapak) to maintain high liquid-vapor mass transfer efficiency while minimizing column pressure drop.
Β§9.3 Fluid Catalytic Cracking (FCC): Zeolite Y, Riser Kinetics & Regenerator Dynamics
Fluid Catalytic Cracking (FCC) is the primary conversion workhorse of the modern oil refinery, converting heavy vacuum gas oil ($\text{HVGO}$) and atmospheric residues into high-octane gasoline blendstock and light olefins ($\text{C}_3\text{-C}_4$).
1. Solid Acid Catalyst Architecture
Modern FCC catalyst particles ($60 - 80\,\mu\text{m}$ diameter, Geldart Group A fluidization powder) consist of ultra-stable Zeolite Y (Faujasite) embedded in an active amorphous alumina-silica matrix:
- Zeolite Y possesses a 3D cage structure with $7.4\text{ \AA}$ pore openings leading into supercages ($12\text{ \AA}$ diameter).
- Framework BrΓΈnsted acid sites ($\equiv \text{Si-O(H)-Al} \equiv$) donate protons to hydrocarbon molecules, initiating carbocation chemistry.
2. Carbocation Cleavage Mechanism
Unlike thermal cracking (which proceeds via neutral free-radical homolytic cleavage producing low-octane linear $\alpha$-olefins), catalytic cracking operates through ionic carbenium intermediates:
1. Initiation: An olefin is protonated by a BrΓΈnsted acid site, or an alkane loses hydride to a Lewis acid site, generating a carbenium ion:
2. Isomerization: Rapid hydride shifts and alkyl shifts rearrange linear chains into stable tertiary carbenium ions.
3. $\beta$-Scission: The carbenium ion cleaves at the covalent bond $\beta$ to the positively charged carbon, generating a smaller olefin and a new carbenium ion:
This mechanism selectively yields highly branched alkanes, iso-olefins, and aromatics, producing motor gasoline with a high Research Octane Number ($\text{RON } 92 - 95$).
3. Riser-Regenerator Heat Balance
Cracking is strongly endothermic ($\Delta H \approx +350 - 500\text{ kJ/kg}$) and occurs in a vertical pipe ("riser", $30 - 45\text{ m}$ height) in $1.5 - 3.0\text{ seconds}$ at $520 - 550^\circ\text{C}$:
- Cracking deposits $4 - 6\text{ wt}\%$ heavy carbonaceous coke on the catalyst particles, blocking micropores and deactivating acid sites.
- Spent coked catalyst is separated in ballistic cyclones and transferred to the fluidized-bed regenerator ($680 - 730^\circ\text{C}$).
- Air combustion burns off the coke:
- The intense heat of coke combustion raises catalyst temperature to $700^\circ\text{C}$. This red-hot regenerated catalyst circulates back to the riser bottom, supplying all the thermal energy required to vaporize and crack the fresh hydrocarbon feed in a completely self-sustaining energy balance.
FCC Zeolite Catalyst Deactivation & Vanadium/Nickel Metal Passivation
Cracking heavy residue feedstocks deposits heavy metals ($\text{Ni, V, Fe}$) onto the circulating zeolite catalyst particles:
- Nickel Poisoning: Deposited nickel acts as an aggressive dehydrogenation catalyst, increasing undesirable dry gas ($\text{H}_2, \text{CH}_4$) and coke yields at the expense of gasoline. Nickel is chemically passivated by injecting antimony or bismuth metallo-organic compounds into the feed:
- Vanadium Destruction: Under high-temperature oxidizing conditions in the regenerator ($700^\circ\text{C}$), vanadium oxidizes to volatile vanadic acid ($\text{H}_3\text{VO}_4$ or $\text{V}_2\text{O}_5$). Vanadic acid penetrates the zeolite pores, chemically attacking the framework $[\text{AlO}_4]^{5-}$ tetrahedra and collapsing the crystalline faujasite structure into amorphous silica-alumina. Vanadium is trapped by co-feeding magnesium/rare-earth titanate scavengers.
Β§9.4 Catalytic Reforming & Hydroprocessing: Octane Upgrading & Hydrodesulfurization (HDS)
1. Catalytic Reforming (Octane Upgrading)
Catalytic Reforming converts low-octane heavy naphtha ($\text{RON } 40 - 50$) rich in linear paraffins into high-octane aromatic reformate ($\text{RON } 98 - 104$), generating massive surplus hydrogen.
- Bifunctional Catalyst: Platinum-Rhenium nanoparticles supported on chlorinated $\gamma$-alumina ($\text{Pt-Re}/\text{Al}_2\text{O}_3-\text{Cl}$):
- Platinum sites catalyze dehydrogenation and hydrogenation.
- Acidic chlorinated alumina sites catalyze skeletal isomerization and cyclization.
- Key Chemical Reactions:
- Dehydrogenation of cyclohexanes to aromatics (Fast, intensely endothermic):
- Dehydrocyclization of paraffins (Slower, endothermic):
- Isomerization of cyclopentanes to cyclohexanes.
- Multi-Bed Interheater Design: Because reforming reactions are intensely endothermic, reaction mixtures cool rapidly, stalling chemical equilibrium. Industrial units (e.g., UOP Platforming) arrange 3 or 4 adiabatic reactor beds in series with intermediate gas-fired heaters.
2. Hydrodesulfurization (HDS) Engineering
Environmental Euro VI / US Tier 3 fuel regulations cap sulfur in automotive gasoline and diesel at $< 10\text{ ppm}$ ($0.001\text{ wt}\%$). Hydrotreating exposes hydrocarbon streams to high-pressure hydrogen ($30 - 80\text{ bar}$) over sulfided Cobalt-Molybdenum or Nickel-Molybdenum catalysts on alumina ($\text{Co-Mo-S}/\text{Al}_2\text{O}_3$ at $320 - 380^\circ\text{C}$):
- Aliphatic thiols, sulfides, and disulfides hydrogenate easily:
- Refractory thiophenic heterocycles (dibenzothiophene and 4,6-dimethyldibenzothiophene) require hydrogenative ring saturation followed by $\text{C-S}$ bond hydrogenolysis:
The resulting hydrogen sulfide ($\text{H}_2\text{S}$) is absorbed in diethanolamine (DEA) scrubbers and converted to elemental sulfur in the Claus plant.
Β§9.5 Steam Cracking of Naphtha & Ethane: Olefin Production & Separation Train
Thermal steam cracking is the predominant industrial route for the manufacture of basic petrochemical building blocks: ethylene ($\text{C}_2\text{H}_4$), propylene ($\text{C}_3\text{H}_6$), and butadiene ($\text{C}_4\text{H}_6$).
1. Pyrolysis Kinetics & Rice-Herzfeld Mechanism
Hydrocarbon feedstocks (ethane, propane, light naphtha) mixed with dilution steam are passed through high-alloy nickel-chromium tubing coils inside radiant gas furnaces at $750 - 875^\circ\text{C}$:
- Role of Dilution Steam:
- Lowers hydrocarbon partial pressure, thermodynamically favoring low-molecular-weight olefins over high-molecular aromatics (Le Chatelier's principle).
- Supplies sensible heat and sweeps away coke precursors.
- Reacts endothermically with tube coke via the water-gas shift reaction.
- Reaction Mechanism: Proceeds via Rice-Herzfeld free-radical homolysis:
- Thermal cleavage of $\text{C-C}$ bonds into primary free radicals.
- Radical propagation via $\beta$-scission:
- Residence Time: Pyrolysis coils are engineered for ultra-short residence times ($0.1 - 0.5\text{ seconds}$) followed by instantaneous water/oil quenching in Transfer Line Exchangers (TLEs) to arrest secondary reactions that form tar and coke.
2. Low-Temperature Olefin Separation Train
The cracked effluent gas is compressed to $30 - 35\text{ bar}$, dried over molecular sieves (dew point $< -100^\circ\text{C}$ to prevent gas hydrate freezing), and separated in an intricate series of cryogenic distillation columns:
1. Demethanizer ($-100^\circ\text{C}$ to $-140^\circ\text{C}$): Rejects methane and hydrogen overhead.
2. Deethanizer: Separates $\text{C}_2$ fraction overhead from $\text{C}_3^+$ bottoms.
3. Acetylene Hydrogenation Reactor: Selectively hydrogenates trace acetylene ($\text{C}_2\text{H}_2 \to \text{C}_2\text{H}_4$).
4. $\text{C}_2$ Splitter: A massive column ($100 - 120$ trays) separating ethylene from ethane. Ethane is recycled back to the cracking furnace.
5. Depropanizer & $\text{C}_3$ Splitter: Separates chemical- and polymer-grade propylene ($> 99.5\%$ purity).
Β§9.6 C1 Petrochemicals: Steam Methane Reforming (SMR) & Methanol Synthesis
C1 chemistry encompasses chemical transformations originating from single-carbon molecules: methane ($\text{CH}_4$), carbon monoxide ($\text{CO}$), and methanol ($\text{CH}_3\text{OH}$).
1. Steam Methane Reforming (SMR)
Synthesis gas (syngas: $\text{CO} + \text{H}_2$) is synthesized by reacting desulfurized natural gas with superheated steam over nickel catalysts supported on $\alpha$-alumina ($\text{Ni}/\alpha\text{-Al}_2\text{O}_3$) inside furnace reformer tubes at $800 - 900^\circ\text{C}$ and $20 - 35\text{ bar}$:
- Primary Reforming Reaction:
- Water-Gas Shift Reaction (WGSR):
The stoichiometric ratio of hydrogen to carbon monoxide is expressed by the Stoichiometric Number ($S_N$):
For ideal methanol synthesis, $S_N$ is targeted at $2.05$.
2. Modern Methanol Synthesis Technology
Synthesized from syngas over copper-zinc oxide-alumina catalysts ($\text{CuO-ZnO-Al}_2\text{O}_3$ / ICI or Lurgi process) at $220 - 275^\circ\text{C}$ and $50 - 100\text{ bar}$:
- Hydrogenation Reactions:
Isotopic tracing reveals that active surface $\text{CO}_2$ is the direct carbon source for methanol over $\text{Cu}^0/\text{Cu}^+$ sites. Because the reaction entails a reduction in moles ($3 \to 1$ or $4 \to 2$), Le Chatelier's principle demands elevated operating pressures ($50 - 80\text{ bar}$) and low temperatures to maximize equilibrium yield while recycling unreacted syngas.
Β§9.7 Industrial Fuels & Synfuels: Coal Gasification & Fischer-Tropsch Synthesis
Synfuels (synthetic liquid fuels) decouple liquid transport fuels from conventional crude petroleum reserves:
1. Coal Gasification (Entrained-Flow Gasifiers)
Finely pulverized coal or petroleum coke slurry is reacted with high-purity oxygen and steam in an entrained-flow gasifier (e.g., GE/Texaco or Shell) at $1300 - 1500^\circ\text{C}$ and $30 - 40\text{ bar}$:
Ash melts into liquid vitreous slag, while the discharged syngas is scrubbed of acid gases ($\text{H}_2\text{S}$ and $\text{CO}_2$) via the chilled methanol Rectisol process.
2. Fischer-Tropsch (FT) Synthesis
Syngas is converted into synthetic hydrocarbons over cobalt or iron catalysts:
- Anderson-Schulz-Flory (ASF) Polymerization Distribution:
Fischer-Tropsch chain growth follows an ideal polymerization probability distribution governed by the chain propagation probability $\alpha$:
where $W_n$ is the weight fraction of hydrocarbons with carbon number $n$.
- Low-temperature FT (LTFT, $200 - 240^\circ\text{C}$, cobalt catalyst, $\alpha \approx 0.90 - 0.95$): Yields ultra-clean synthetic waxes and high-cetane synthetic diesel ($> 70\text{ Cetane Index}$, zero sulfur, zero aromatics).
- High-temperature FT (HTFT, $320 - 350^\circ\text{C}$, iron catalyst, $\alpha \approx 0.70$): Yields motor gasoline and light chemical olefins.
Β§9.8 Sustainable Aviation Fuel (SAF), Biofuels & Circular Plastics Pyrolysis
Petroleum refineries are evolving into multi-feedstock processing hubs co-processing renewable fats, waste biomass, and post-consumer plastics:
1. Sustainable Aviation Fuel (SAF) via HEFA Processing
The dominant commercial pathway for aviation decarbonization is Hydroprocessed Esters and Fatty Acids (HEFA):
- Feedstocks: Used cooking oil (UCO), tallow, and carinata seed oil.
- Process Chemistry:
- Hydrodeoxygenation (HDO): High-pressure hydrotreating over $\text{Ni-Mo}/\text{Al}_2\text{O}_3$ at $350^\circ\text{C}$ ($60 - 80\text{ bar}$) eliminates oxygen from triglycerides as water, propane, and $\text{CO}_2$, yielding linear paraffinic waxes ($\text{C}_{16} - \text{C}_{18}$ alkanes).
- Hydroisomerization & Selective Hydrocracking: Paraffins pass over bifunctional noble metal / zeolite catalysts (e.g., $\text{Pt}/\text{SAPO-11}$) to selectively crack and branch straight chains into isoparaffins boiling in the jet fuel range ($\text{C}_9 - \text{C}_{15}$).
- Freezing Point Adjustment: Isomerization depresses the freezing point below $-47^\circ\text{C}$ (meeting ASTM D7566 Jet A-1 standards), reducing lifecycle aviation carbon emissions by up to $80\%$.
2. Circular Chemical Recycling: Waste Plastics Pyrolysis
Mechanical recycling cannot process heavily contaminated or multi-layer packaging films. In Thermolytic Chemical Pyrolysis:
- Sorted waste polyolefins (polyethylene, polypropylene) are heated in an inert atmosphere ($450 - 550^\circ\text{C}$) in a fluidized bed or rotary kiln.
- Thermal homolytic scission cleaves synthetic carbon-carbon backbones into a synthetic liquid crude oil ("pyrolysis oil").
- After mild hydrotreating to remove chlorine (from trace PVC) and nitrogen contaminants, the pyrolysis oil is fed directly into refinery FCC risers or steam crackers, yielding virgin-quality circular polymer resins.
University Honors Industrial Case Study: Refractory Thiophenic Heterocycle Steric Hindrance in Ultra-Deep HDS
To achieve Euro VI / Tier 3 specifications ($< 10\text{ ppm sulfur}$), refineries must eliminate 4,6-dimethyldibenzothiophene (4,6-DMDBT):
- Steric Hindrance Barrier: The two bulky methyl groups ($\text{-CH}_3$) at positions 4 and 6 project directly adjacent to the heterocyclic sulfur atom, sterically shielding it from direct perpendicular coordination onto the active metallic Mo/W edge sites of the $\text{Co-Mo-S}$ catalyst crystallites.
- Alternative Hydrogenation Pathway:
Rather than direct desulfurization (DDS), 4,6-DMDBT must follow the much slower hydrogenation (HYD) pathway:
- Complete saturation of one adjacent benzene ring to form 4,6-dimethyl-tetrahydrodibenzothiophene.
- The non-planar, buckled cyclohexenyl ring pulls the methyl groups out of the plane, relieving steric strain.
- The sulfur atom coordinates to the catalyst site and undergoes $\text{C-S}$ cleavage.
- Industrial Response: Modern ultra-deep HDS catalysts utilize highly stacked $\text{Ni-Mo-W}$ clusters on wide-pore mesoporous supports operating at elevated hydrogen pressures ($60 - 80\text{ bar}$) with high hydrogen-to-oil treat gas ratios.
A petroleum laboratory analyzes a crude oil sample:
- Specific gravity at $60^\circ\text{F}/60^\circ\text{F}$ is $\text{SG} = 0.8498$.
- Mean Average Boiling Point is $T_B = 260.0^\circ\text{C}$ ($500.0^\circ\text{F}$).
- Calculate the API gravity ($^\circ\text{API}$) and classify the crude (Light, Medium, or Heavy).
- Determine the Watson Characterization Factor ($K_W$) and identify the predominant hydrocarbon paraffinic/naphthenic nature of this petroleum feedstock.
Step 1: API Gravity
Using the definition:
Since $^\circ\text{API} = 35.0 > 31.1$, the crude is classified as a Light Crude (e.g., Brent or West Texas Intermediate grade).
Step 2: Watson Characterization Factor ($K_W$)
Convert Mean Average Boiling Point to absolute degrees Rankine ($^\circ\text{R}$):
Calculate $K_W$:
With $K_W = 11.61$, the crude oil is classified as Naphthenic-Intermediate, containing substantial cyclic alkanes (cycloparaffins) and alkyl aromatics alongside linear paraffins.
An Atmospheric Distillation Unit (ADU) processes $100,000\text{ barrels/stream day}$ (BPSD) of light crude oil ($\rho = 135.0\text{ kg/barrel}$, total mass rate $\dot{m} = 13.50 \times 10^6\text{ kg/day} = 562,500\text{ kg/h}$). The TBP distillation yield breakdown is:
- Off-gas & LPG ($\text{C}_1-\text{C}_4$): $2.5\text{ wt}\%$
- Light Straight-Run Naphtha: $9.5\text{ wt}\%$
- Heavy Naphtha: $14.0\text{ wt}\%$
- Kerosene / Jet A-1: $12.0\text{ wt}\%$
- Atmospheric Gas Oil (Diesel): $24.0\text{ wt}\%$
- Atmospheric Residue ($> 360^\circ\text{C}$): $38.0\text{ wt}\%$
- Calculate the hourly mass production rates ($\text{metric tons/h}$) of each of the six fractionator streams.
- If the Atmospheric Residue is fed directly into a Vacuum Distillation Unit that recovers $65.0\text{ wt}\%$ as Vacuum Gas Oil ($\text{VGO}$) and $35.0\text{ wt}\%$ as Vacuum Residue (asphalt/pitch), calculate the hourly $\text{VGO}$ feed rate sent to the FCC cracking unit.
Step 1: ADU Product Stream Flow Rates
Total crude feed rate: $\dot{m}_{\text{crude}} = 562.5\text{ metric tons/h}$. Hourly production rates:
- Off-gas & LPG ($2.5\%$):
- Light Naphtha ($9.5\%$):
- Heavy Naphtha ($14.0\%$):
- Kerosene ($12.0\%$):
- Diesel / Gas Oil ($24.0\%$):
- Atmospheric Residue ($38.0\%$):
Sum check: $14.06 + 53.44 + 78.75 + 67.50 + 135.00 + 213.75 = 562.50\text{ metric tons/h}$.
Step 2: Vacuum Gas Oil ($\text{VGO}$) Yield
Atmospheric Residue feed rate to VDU:
VGO recovered ($65.0\%$):
Vacuum residue bottoms ($35.0\%$):
The refinery produces $138.9\text{ metric tons/h}$ of $\text{VGO}$ for fluid catalytic cracking.
A Fluid Catalytic Cracking (FCC) unit processes $\dot{m}_{\text{feed}} = 250\text{ metric tons/h}$ ($69.44\text{ kg/s}$) of heavy vacuum gas oil.
- Liquid feed enters the bottom of the riser at $200^\circ\text{C}$ and mixes with regenerated zeolite catalyst arriving from the regenerator at $T_{\text{regen}} = 700^\circ\text{C}$.
- The riser operates at an outlet temperature $T_{\text{riser}} = 530^\circ\text{C}$.
- Enthalpy required to preheat, vaporize, and endothermically crack the gas oil feed is $\Delta h_{\text{feed}} = 680\text{ kJ/kg feed}$.
- Specific heat of the zeolite catalyst is $c_{p, \text{cat}} = 1.15\text{ kJ/(kg}\cdot\text{K)}$.
- Heat losses from the riser shell are $3.0\%$ of the heat transferred.
- Calculate the total heat transfer required to vaporize and crack the feed per second ($\text{kW}$).
- Formulate the thermal balance to determine the required solid catalyst circulation rate ($\dot{m}_{\text{cat}}$) in metric tons per hour.
- Calculate the operational Catalyst-to-Oil mass ratio ($\text{C/O}$).
Step 1: Heat Duty Required by Hydrocarbon Feed
Hourly heat demand:
Including $3.0\%$ thermal loss ($1.03\times$):
In thermal kilowatts ($\text{kW}$):
Step 2: Catalyst Circulation Rate
As catalyst cools from $T_{\text{regen}} = 700^\circ\text{C}$ to $T_{\text{riser}} = 530^\circ\text{C}$, temperature drop is:
Enthalpy released per kilogram of circulating catalyst:
Required catalyst circulation rate:
In kilograms per second:
Step 3: Catalyst-to-Oil Ratio ($\text{C/O}$)
The unit operates at a $\text{C/O}$ ratio of $3.58$, circulating $895.7\text{ metric tons/h}$ of hot catalyst.
A hydrotreater treats $2,000\text{ metric tons/day}$ ($83.33\text{ t/h}$) of straight-run diesel containing $1.20\text{ wt}\%$ organosulfur (average $S = 32.06\text{ g/mol}$).
- Target product specification: ultra-low sulfur diesel containing $< 10\text{ ppm sulfur}$ ($0.001\text{ wt}\%$, $99.92\%$ desulfurization).
- In the complex diesel mixture, desulfurization of heterocyclic sulfur consumes an average of $3.50\text{ moles of H}_2$ ($2.016\text{ g/mol}$) per mole of sulfur eliminated.
- Concomitant olefin and partial aromatic saturation consumes an additional $0.40\text{ wt}\%\text{ H}_2$ on total diesel feed.
- Hydrogen is supplied with $95.0\text{ vol}\%$ purity (balance methane).
- Calculate the moles of sulfur eliminated per hour.
- Determine the hourly hydrogen consumption for desulfurization and for aromatic/olefin saturation in $\text{kg/h}$.
- Calculate the total volumetric flow rate of $95.0\%$ make-up hydrogen gas required at standard conditions ($\text{Nm}^3\text{/h}$, $22.414\text{ Nm}^3\text{/kmol}$).
Step 1: Sulfur Elimination Rate
Hourly diesel feed:
Initial sulfur entering:
Residual sulfur in product ($10\text{ ppm}$):
Sulfur eliminated:
Moles of sulfur eliminated:
Step 2: Hydrogen Consumption Breakdown
1. $\text{H}_2$ for desulfurization ($3.50\text{ mol H}_2/\text{mol S}$):
2. $\text{H}_2$ for aromatic/olefin saturation ($0.40\text{ wt}\%$ on feed):
Total pure $\text{H}_2$ consumed:
Step 3: Total Make-Up Hydrogen Gas Flow
Pure $\text{H}_2$ STP volume:
Since the make-up gas is $95.0\text{ vol}\%\text{ H}_2$:
The hydrotreater consumes $553.2\text{ kg/h}$ of pure $\text{H}_2$, requiring $6,475\text{ Nm}^3\text{/h}$ of $95\%$ make-up gas.
A petrochemical pyrolysis furnace feeds $\dot{m}_{\text{naphtha}} = 40.0\text{ metric tons/h}$ of paraffinic light naphtha.
- Dilution steam is injected at a mass ratio of $0.50\text{ kg steam / kg naphtha}$.
- Single-pass chemical yields across the radiant coils:
- Ethylene ($\text{C}_2\text{H}_4$): $32.0\text{ wt}\%$
- Propylene ($\text{C}_3\text{H}_6$): $16.0\text{ wt}\%$
- 1,3-Butadiene ($\text{C}_4\text{H}_6$): $4.5\text{ wt}\%$
- Pyrolysis Gasoline (PyGas): $20.0\text{ wt}\%$
- Fuel Gas ($\text{H}_2 + \text{CH}_4$): $18.5\text{ wt}\%$
- Pyrolysis Fuel Oil (tar): $9.0\text{ wt}\%$
- Calculate the required mass feed rate of dilution steam in metric tons per hour.
- Determine the hourly production rates of polymer-grade ethylene, propylene, and butadiene in metric tons per hour.
- If the plant operates $8,000\text{ hours/year}$, calculate the annual ethylene production capacity in metric tons.
Step 1: Dilution Steam Feed Rate
Step 2: Hourly Chemical Olefin Yields
- Ethylene ($32.0\%$):
- Propylene ($16.0\%$):
- 1,3-Butadiene ($4.5\%$):
Step 3: Annual Ethylene Production Capacity
The furnace yields $12.80\text{ t/h}$ ethylene, $6.40\text{ t/h}$ propylene, and produces $102,400\text{ metric tons/year}$ of ethylene.
A steam methane reformer operates at $850^\circ\text{C}$ ($1123.15\text{ K}$) and $25.0\text{ bar}$. The overall net reforming stoichiometry is:
The plant feeds $10,000\text{ Nm}^3\text{/h}$ ($446.15\text{ kmol/h}$) of pure methane ($\text{CH}_4$, $16.04\text{ g/mol}$).
- Calculate the hourly generation rates of $\text{CO}$, $\text{CO}_2$, and $\text{H}_2$ in $\text{kmol/h}$ and STP $\text{Nm}^3\text{/h}$.
- Calculate the Stoichiometric Number ($S_N$) of the produced raw synthesis gas:
- Verify whether this syngas is suitable for direct methanol synthesis without hydrogen/carbon adjustment.
Step 1: Component Generation Rates
Methane feed rate:
From stoichiometry:
- Carbon Monoxide ($\text{CO}$):
- Carbon Dioxide ($\text{CO}_2$):
- Hydrogen ($\text{H}_2$):
Step 2: Stoichiometric Number ($S_N$)
Step 3: Suitability for Methanol Synthesis
For methanol synthesis ($\text{CO} + 2\text{H}_2 \to \text{CH}_3\text{OH}$), the stoichiometric requirement is $S_N = 2.05$. Because $S_N = 3.00 > 2.05$, the syngas contains a massive excess of hydrogen. To make it optimal for methanol synthesis, the plant must either:
- Co-feed external carbon dioxide ($\text{CO}_2$) to consume the excess hydrogen:
- Or separate the surplus hydrogen using Pressure Swing Adsorption (PSA) for hydrotreating units.
A Low-Temperature Fischer-Tropsch (LTFT) slurry-bubble column reactor operates over a cobalt catalyst. Product carbon number distribution follows the Anderson-Schulz-Flory (ASF) equation:
where $W_n$ is the weight fraction of hydrocarbons containing $n$ carbon atoms, and $\alpha$ is the chain growth probability.
- Show analytically that the carbon number $n_{\max}$ corresponding to the maximum weight fraction is given by:
- The operating conditions achieve $\alpha = 0.900$. Calculate the carbon number $n_{\max}$ of maximum production.
- Calculate the weight fraction of synthetic diesel fuel, defined as the cut from $n = 10$ to $n = 20$ ($\text{C}_{10}-\text{C}_{20}$):
Step 1: Analytical Derivation of $n_{\max}$
Express $W_n$ as a continuous function of $n$:
Differentiate with respect to $n$ and set to zero:
Since $(1 - \alpha)^2 \alpha^{n-1} \neq 0$:
Step 2: Maximum Weight Fraction Carbon Number for $\alpha = 0.900$
The peak production weight fraction occurs at $n = 9$ to $10$ ($\text{C}_9-\text{C}_{10}$).
Step 3: Synthetic Diesel Cut Fraction ($\text{C}_{10}-\text{C}_{20}$)
Using the closed-form summation formula for $W_{\ge k} = (1 - \alpha + k \alpha) \alpha^{k-1}$:
- Cumulative fraction for $n \ge 10$:
Let us compute rigorously:
Therefore:
- For $k = 10$:
- For $k = 21$ (fractions above $\text{C}_{20}$):
Weight fraction in the diesel range ($\text{C}_{10}-\text{C}_{20}$):
The synthetic diesel cut represents $37.1\text{ wt}\%$ of the total Fischer-Tropsch hydrocarbon product.
A bio-refinery converts Used Cooking Oil (UCO, pure triglyceride of oleic acid, triolein $\text{C}_{57}\text{H}_{104}\text{O}_6$, $M = 885.4\text{ g/mol}$) into Sustainable Aviation Fuel (SAF) via the HEFA process.
- Plant throughput: $\dot{m}_{\text{feed}} = 50.0\text{ metric tons/h}$ of triolein ($56.47\text{ kmol/h}$).
- Complete Hydrodeoxygenation (HDO) reaction:
Molar masses: $\text{H}_2 = 2.016$, $n\text{-octadecane C}_{18}\text{H}_{38} = 254.5\text{ g/mol}$, propane $\text{C}_3\text{H}_8 = 44.1\text{ g/mol}$, $\text{H}_2\text{O} = 18.02\text{ g/mol}$.
- In the subsequent hydroisomerization and cracking stage, $n$-octadecane yields:
- $65.0\text{ wt}\%\text{ SAF (kerosene cut)}$
- $20.0\text{ wt}\%\text{ renewable diesel}$
- $15.0\text{ wt}\%\text{ renewable naphtha / LPG}$
consuming an additional $0.50\text{ wt}\%\text{ H}_2$ on octadecane.
- Calculate the mass of pure hydrogen consumed by the HDO stage per hour in $\text{kg/h}$.
- Determine the hourly production rate of $n$-octadecane paraffin intermediate in metric tons per hour.
- Calculate the hourly production rate of finished Sustainable Aviation Fuel (SAF) in metric tons per hour and the overall process mass yield on raw oil.
Step 1: Hydrogen Consumed in HDO
Moles of triolein fed per hour:
Stoichiometric $\text{H}_2$ consumed ($15\text{ mol H}_2\text{ / mol triolein}$):
Mass of $\text{H}_2$:
Step 2: Production of $n$-Octadecane
From stoichiometry, $1\text{ mol triolein} \to 3\text{ mol C}_{18}\text{H}_{38}$:
Mass of $n$-octadecane:
(Theoretical mass yield of paraffin intermediate $= 43.12 / 50.0 = 86.23\%$).
Step 3: Finished SAF Production Rate
SAF yield from octadecane is $65.0\text{ wt}\%$:
Overall mass yield of SAF on raw cooking oil:
The plant consumes $1.71\text{ t/h}$ of $\text{H}_2$ in HDO to yield $28.0\text{ metric tons/h}$ of finished Sustainable Aviation Fuel ($56.1\text{ wt}\%$ overall yield).
A circular plastics chemical recycling plant pyrolyzes $\dot{m}_{\text{plastic}} = 10.0\text{ metric tons/h}$ ($10,000\text{ kg/h}$) of sorted post-consumer polyolefins ($60\text{ wt}\%\text{ polyethylene}$, $40\text{ wt}\%\text{ polypropylene}$) in a fluidized bed reactor at $500^\circ\text{C}$.
- Endothermic heat of depolymerization/cracking is $\Delta h_{\text{pyro}} = 1,850\text{ kJ/kg plastic}$.
- Continuous product mass yields:
- Synthetic Pyrolysis Oil ($\text{C}_5-\text{C}_{22}$ liquid): $78.0\text{ wt}\%$
- Pyrolysis Non-Condensable Fuel Gas ($\text{C}_1-\text{C}_4$): $16.0\text{ wt}\%$ ($\text{LHV} = 44,000\text{ kJ/kg}$)
- Carbonaceous Char/Coke: $6.0\text{ wt}\%$
- Calculate the hourly production rate of liquid synthetic crude oil in metric tons per hour.
- Determine the total thermal power required by the pyrolysis reactor in thermal megawatts ($\text{MW}$).
- Calculate the thermal energy content of the byproduct fuel gas per hour and verify whether burning the fuel gas makes the plant completely thermally self-sustaining.
Step 1: Synthetic Pyrolysis Oil Production
The plant yields $7.80\text{ metric tons/h}$ of circular liquid naphtha/wax feed.
Step 2: Pyrolysis Thermal Power Requirement
Hourly heat duty:
In thermal megawatts ($\text{MW}$):
Step 3: Energy Self-Sufficiency Verification
Byproduct fuel gas produced:
Thermal energy released by gas combustion:
Comparison:
The combustion of byproduct fuel gas generates $3.8\times$ the total heat required for pyrolysis, rendering the recycling process completely thermally self-sustaining with a huge exportable energy surplus.
Solved Honors Problems & Derivations
Step-by-step rigorous solutions with full physical, thermodynamic, and process engineering validation.