Steam Cracking of Naphtha/Ethane to Light Olefins

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Unit target

Map major building-block pathways from hydrocarbon feed to olefins, aromatics and synthesis-gas intermediates.

Engineering context

Steam cracking, aromatic separation and syngas production are not interchangeable. Each pathway has a different feed envelope, conversion chemistry, heat profile and separation train. Species balances and selectivity distinguish desired product from co-products, while energy intensity and impurity management influence commercial feasibility. The modeler should decide what constitutes a material stream, what was measured directly, and which quantities follow from an equation. Whenever possible, start with an inlet-and-outlet balance in physical units rather than with an index or a normalized graph. An index can be useful for a classroom sensitivity exercise, but it can also conceal the absolute process magnitude needed to estimate utilities, storage or emissions.

Decision boundary

Compare feed routing with explicit yields and utilities; avoid claiming that an illustrative one-reaction model is an actual multi-furnace or equilibrium plant simulator. A good recommendation distinguishes what is established by conservation from what depends on kinetic, thermodynamic or operating assumptions. Record your data source and test method. Identify unknown parameters before asserting any performance. If two alternatives seem very close numerically, compute the range of results that plausible uncertainty could produce rather than picking the one with more decimals.

Technical study sequence

1. [Steam cracking and olefin selectivity](../lessons/unit-05-lesson-01.html) — [interactive lab 13](../labs/lab-13.html)
2. [Aromatics extraction and separations](../lessons/unit-05-lesson-02.html) — [interactive lab 14](../labs/lab-14.html)
3. [Synthesis gas and reforming routes](../lessons/unit-05-lesson-03.html) — [interactive lab 15](../labs/lab-15.html)
4. [Petrochemical intermediate supply chains](../lessons/unit-05-lesson-04.html) — [interactive lab 15](../labs/lab-15.html)

Laboratory strategy

These three distinct models illuminate different physics or accounting relationships in the unit: Steam cracking ethylene selectivity, Aromatics extraction recovery, Steam methane reformer stoichiometry. Take each model as a conditional hypothesis. For one model, reconstruct the default answer from the equation; for a second, find a limiting case; for the third, propose a measurement that could disprove it. A smooth trend is not an indicator of industrial accuracy, and sensitivity does not establish causality when the underlying variables are correlated.

Deliverable and independent scrutiny

Prepare a two-page engineering memo with a material and energy boundary, one calculation table, at least two uncertainty or failure scenarios, and a decision that names the data still needed. Use the [16 question assessment](../assessments/unit-05.html) to identify technical gaps. The [applied project](../projects/unit-05.html) then adds constraints from adjacent units so that a local process improvement can be evaluated for its plant-wide consequence.

Unit 05 · Lesson 01 — Steam cracking and olefin selectivity

[Unit map](../units/unit-05.html) · [Open numerical laboratory](../labs/lab-13.html) · [Assessment](../assessments/unit-05.html) · [Applied project](../projects/unit-05.html)

The engineering problem

Steam cracking of selected hydrocarbon feeds produces ethylene, propylene and by-products through a complex high-temperature reaction network. Feed quality, severity, residence time, steam dilution and quench time strongly affect selectivity and coke formation. The cracking furnace, rapid cooling and compression/fractionation train must be considered together.

The practical starting point is not the equation by itself; it is a description of the process boundary. Write down the feed, product, recovered co-product, waste and possible accumulation terms before choosing an indicator. In this lesson, the title steam cracking and olefin selectivity indicates a specific decision lens within petrochemicals. Its purpose is to connect a measured or assumed characteristic to an operational consequence with a statement of what would prove the link. Separate primary evidence, indirect proxy and calculated prediction; those three categories are not interchangeable.

Quantity definition and model reasoning

An illustrative primary conversion X=1−exp(−kτ) and declining ethylene selectivity S(X)=S0exp(−aX) produce Yethylene=X S(X). This deliberately introduces secondary loss at higher severity, but its coefficients are not commercial furnace kinetics.

To audit a model, begin with units. Write every mass flow on a common basis such as kg/h, every species flow on a consistent molar basis, and every energy rate as kW or MJ/h. Converting a component fraction from molar to mass basis requires component molar masses. A dimensionless index can be compared across scenarios only if the reference conditions and denominator have not changed. When the result is a percentage, specify percentage of what: total feed mass, converted feed, recovered product, sulfur atoms, or an observed time interval. The wrong denominator can change the interpretation even when the arithmetic is correct.

One useful way to check the numerical relationship is to inspect its limiting behavior. At zero conversion or removal, no product can appear or disappear through that mechanism; at complete removal, the tracked contaminant should be accounted for in another stream; at a cutpoint moved above or below the stated assay range, extrapolation should be rejected. A monotonic curve may be mathematically well behaved yet physically incomplete if secondary reactions, equilibrium or equipment capacity create a turning point outside the model.

Worked investigation: hypothetical data

For X = 0.70, S0 = 0.55 and a = 0.25, calculate the notional ethylene yield fraction. Check that yield is below conversion.

Worked answer and interpretation

The proposed ethylene-lump yield is 0.70×0.55×exp(−0.25×0.70)≈0.3232 of feed, or 32.32% of feed. The remaining converted material is not all propylene; it contains multiple possible co-product lumps. Higher single-pass conversion must be compared with furnace energy and product recovery.

Make a compact worksheet with four rows: starting assumptions, symbolic equation, numerical substitution and mass/energy/quality consistency check. Always place the units in the substitution row. An answer with four significant figures may be mathematically reproducible but should not be presented as a plant forecast when the assumed feed is only known roughly. Repeat the worksheet with one changed input, quantify the absolute and percentage change in the output, and ask which upstream measurement would be needed to defend that perturbation.

For numerical work, explicitly mark the inputs in this lesson as synthetic instructional values, including any yield factor, catalyst rate, representative boiling temperature or solvent efficiency. They must not be used as operating limits. If you wish to compare with published performance, define an independent, dated and source-specific dataset and evaluate whether its units and stream definitions match those of the exercise.

Plant integration and operating evidence

Compare ethylene and propylene output, fuel consumption, recycle, coke cleaning and fractionation requirements. Report each yield by a consistent mass basis and identify all co-products to preserve the carbon balance.

Place the result in a real flowsheet context. Petrochemical pathways depend on hydrocarbon molecular structure and on separation. Process integration can improve energy use, but the presence of valuable co-products does not eliminate the cost of obtaining on-spec feed and product. Document stoichiometric and yield bases separately. Ask where the upstream stream comes from, which downstream unit receives it, and how a change would shift at least one other required resource. A product-quality improvement might raise utility demand; more extensive contaminant removal might increase solvent regeneration; higher conversion may move load to gas compression or wastewater treatment. Draw the additional arrows on the block flow diagram, and do not claim that the local calculation has optimized the full plant.

For an evidence-based evaluation, design a measurement table with columns for variable, unit, sample or instrument location, time basis, quality method, expected repeatability and action on discrepancy. Include one direct process variable, one product property and one integration variable. A useful model-validation report should show residuals or errors for several cases, not only agreement at the nominal case used to choose parameters. Record potential confounding changes in feed, temperature, operator procedure and catalyst condition.

Assumption challenge and failure diagnosis

Increasing severity can increase conversion while lowering desired yield after secondary cracking. A one-variable yield curve cannot optimize furnace metallurgy or run length.

A critical reader should ask which implicit assumptions were required to write the equation: steady state or dynamic accumulation, ideal mixing or plug flow, fixed or changing properties, homogeneous or multiphase composition, constant versus variable selectivity, and independence versus coupling of disturbances. Pick the assumptions that matter here. If a model fails, identify whether the defect originates in incorrect units, an invalid physical assumption, unmeasured variability, or numerical implementation. Merely adding complexity does not fix poor calibration data.

In practical terms, define a stop condition for inference: a measurement outside the sampled composition range, evidence of a new phase, an unexpected hazard, a negative concentration, or an implausible material imbalance invalidates the shortcut. Escalate to a validated model or an expert review before making a design or safety claim. The appropriate corrective action can be to collect data, not to alter equipment.

Numerical laboratory and reproducible evidence

The linked [interactive laboratory, Steam cracking ethylene selectivity](../labs/lab-13.html), provides a separate numerical sensitivity exercise. Its governing relationship is X=1−exp(−kτ); S=0.55 exp(−0.25X); Yethylene=X S. The laboratory is connected to this lesson through its unit-level concepts, but it may explore a different variable from the preceding worked example. Check its JSON parameter definitions, alter one input at a time and export the sampled curve to CSV. Compare two cases by recomputing the equation manually; document the difference between software correctness and physical validity.

Before declaring completion, articulate these four results in your own words: the stream or specimen under study, the dimension and reporting basis of the output, the reason for the sign of its sensitivity, and a specific observation that could disconfirm the model. Relate the lesson to Sulfur recovery and tail-gas treatment as prior context and Aromatics extraction and separations as a subsequent design issue. This linkage should be causal, not merely a sequence of chapter names.

Independent checkpoints

1. Sketch the process boundary for steam cracking and olefin selectivity and label the stream or specimen basis that is actually measured.
2. Recreate the numerical reasoning from the worked investigation with all units and a limiting-case check.
3. Identify one operation, market specification or safety constraint that the formula does not contain.
4. Propose two measurements that would distinguish this model from a competing physical interpretation.
5. Describe why a correct plot of steam cracking ethylene selectivity does not establish plant-scale validity.

Editorial status: This is a provisional university-level teaching draft. Peer review, equipment-specific validation and current local requirements remain outside this instructional package.

Unit 05 · Lesson 02 — Aromatics extraction and separations

[Unit map](../units/unit-05.html) · [Open numerical laboratory](../labs/lab-14.html) · [Assessment](../assessments/unit-05.html) · [Applied project](../projects/unit-05.html)

The engineering problem

Benzene, toluene and xylenes require feed preparation, extraction or extractive distillation, and subsequent fractionation. Solvent selectivity is different from extraction capacity; high distribution ratios are not sufficient if solvent recovery is energy intensive. Impurity specifications can determine whether downstream petrochemical routes are feasible.

The practical starting point is not the equation by itself; it is a description of the process boundary. Write down the feed, product, recovered co-product, waste and possible accumulation terms before choosing an indicator. In this lesson, the title aromatics extraction and separations indicates a specific decision lens within petrochemicals. Its purpose is to connect a measured or assumed characteristic to an operational consequence with a statement of what would prove the link. Separate primary evidence, indirect proxy and calculated prediction; those three categories are not interchangeable.

Quantity definition and model reasoning

For a toy single equilibrium contact, recovery fraction R = KS/(F+KS) using distribution coefficient K and solvent/feed ratio S/F. It assumes constant K, complete phase disengagement and one transferred aromatic lump.

To audit a model, begin with units. Write every mass flow on a common basis such as kg/h, every species flow on a consistent molar basis, and every energy rate as kW or MJ/h. Converting a component fraction from molar to mass basis requires component molar masses. A dimensionless index can be compared across scenarios only if the reference conditions and denominator have not changed. When the result is a percentage, specify percentage of what: total feed mass, converted feed, recovered product, sulfur atoms, or an observed time interval. The wrong denominator can change the interpretation even when the arithmetic is correct.

One useful way to check the numerical relationship is to inspect its limiting behavior. At zero conversion or removal, no product can appear or disappear through that mechanism; at complete removal, the tracked contaminant should be accounted for in another stream; at a cutpoint moved above or below the stated assay range, extrapolation should be rejected. A monotonic curve may be mathematically well behaved yet physically incomplete if secondary reactions, equilibrium or equipment capacity create a turning point outside the model.

Worked investigation: hypothetical data

At S/F = 1.5 and K = 2, calculate single-contact recovery. Compare with half the solvent ratio and discuss diminishing returns.

Worked answer and interpretation

With K=2 and solvent/feed=1.5, the ideal one-contact recovery is (2×1.5)/(1+2×1.5)=0.75 or 75%. Halving the solvent/feed ratio gives 1.5/(1+1.5)=0.60 or 60%. Larger solvent flow improves this toy recovery while adding downstream solvent-regeneration duty that the equation omits.

Make a compact worksheet with four rows: starting assumptions, symbolic equation, numerical substitution and mass/energy/quality consistency check. Always place the units in the substitution row. An answer with four significant figures may be mathematically reproducible but should not be presented as a plant forecast when the assumed feed is only known roughly. Repeat the worksheet with one changed input, quantify the absolute and percentage change in the output, and ask which upstream measurement would be needed to defend that perturbation.

For numerical work, explicitly mark the inputs in this lesson as synthetic instructional values, including any yield factor, catalyst rate, representative boiling temperature or solvent efficiency. They must not be used as operating limits. If you wish to compare with published performance, define an independent, dated and source-specific dataset and evaluate whether its units and stream definitions match those of the exercise.

Plant integration and operating evidence

Calculate recovered-aromatic rate, raffinate losses, solvent circulation and recovery duty. Verify physical properties and phase equilibria for the actual solvent-system temperature and composition.

Place the result in a real flowsheet context. Petrochemical pathways depend on hydrocarbon molecular structure and on separation. Process integration can improve energy use, but the presence of valuable co-products does not eliminate the cost of obtaining on-spec feed and product. Document stoichiometric and yield bases separately. Ask where the upstream stream comes from, which downstream unit receives it, and how a change would shift at least one other required resource. A product-quality improvement might raise utility demand; more extensive contaminant removal might increase solvent regeneration; higher conversion may move load to gas compression or wastewater treatment. Draw the additional arrows on the block flow diagram, and do not claim that the local calculation has optimized the full plant.

For an evidence-based evaluation, design a measurement table with columns for variable, unit, sample or instrument location, time basis, quality method, expected repeatability and action on discrepancy. Include one direct process variable, one product property and one integration variable. A useful model-validation report should show residuals or errors for several cases, not only agreement at the nominal case used to choose parameters. Record potential confounding changes in feed, temperature, operator procedure and catalyst condition.

Assumption challenge and failure diagnosis

A high apparent extraction recovery says nothing about solvent contamination in the product or separation energy. Solvent toxicity, inventory and recycling must also be assessed.

A critical reader should ask which implicit assumptions were required to write the equation: steady state or dynamic accumulation, ideal mixing or plug flow, fixed or changing properties, homogeneous or multiphase composition, constant versus variable selectivity, and independence versus coupling of disturbances. Pick the assumptions that matter here. If a model fails, identify whether the defect originates in incorrect units, an invalid physical assumption, unmeasured variability, or numerical implementation. Merely adding complexity does not fix poor calibration data.

In practical terms, define a stop condition for inference: a measurement outside the sampled composition range, evidence of a new phase, an unexpected hazard, a negative concentration, or an implausible material imbalance invalidates the shortcut. Escalate to a validated model or an expert review before making a design or safety claim. The appropriate corrective action can be to collect data, not to alter equipment.

Numerical laboratory and reproducible evidence

The linked [interactive laboratory, Aromatics extraction recovery](../labs/lab-14.html), provides a separate numerical sensitivity exercise. Its governing relationship is R=K(S/F)/(1+K(S/F)). The laboratory is connected to this lesson through its unit-level concepts, but it may explore a different variable from the preceding worked example. Check its JSON parameter definitions, alter one input at a time and export the sampled curve to CSV. Compare two cases by recomputing the equation manually; document the difference between software correctness and physical validity.

Before declaring completion, articulate these four results in your own words: the stream or specimen under study, the dimension and reporting basis of the output, the reason for the sign of its sensitivity, and a specific observation that could disconfirm the model. Relate the lesson to Steam cracking and olefin selectivity as prior context and Synthesis gas and reforming routes as a subsequent design issue. This linkage should be causal, not merely a sequence of chapter names.

Independent checkpoints

1. Sketch the process boundary for aromatics extraction and separations and label the stream or specimen basis that is actually measured.
2. Recreate the numerical reasoning from the worked investigation with all units and a limiting-case check.
3. Identify one operation, market specification or safety constraint that the formula does not contain.
4. Propose two measurements that would distinguish this model from a competing physical interpretation.
5. Describe why a correct plot of aromatics extraction recovery does not establish plant-scale validity.

Editorial status: This is a provisional university-level teaching draft. Peer review, equipment-specific validation and current local requirements remain outside this instructional package.

Unit 05 · Lesson 03 — Synthesis gas and reforming routes

[Unit map](../units/unit-05.html) · [Open numerical laboratory](../labs/lab-15.html) · [Assessment](../assessments/unit-05.html) · [Applied project](../projects/unit-05.html)

The engineering problem

Steam methane reforming creates hydrogen-rich synthesis gas by an endothermic reaction. CO, CO₂, H₂ and residual methane depend on chemistry, temperature, steam/carbon ratio, pressure and downstream water-gas shift. Solid carbon risks, catalyst poisoning and heat management limit feasible conditions.

The practical starting point is not the equation by itself; it is a description of the process boundary. Write down the feed, product, recovered co-product, waste and possible accumulation terms before choosing an indicator. In this lesson, the title synthesis gas and reforming routes indicates a specific decision lens within petrochemicals. Its purpose is to connect a measured or assumed characteristic to an operational consequence with a statement of what would prove the link. Separate primary evidence, indirect proxy and calculated prediction; those three categories are not interchangeable.

Quantity definition and model reasoning

The ideal primary reaction CH₄ + H₂O ⇌ CO + 3H₂ gives three H₂ moles per converted CH₄ mole before water-gas shift. A didactic approach-to-conversion factor is not an equilibrium solver.

To audit a model, begin with units. Write every mass flow on a common basis such as kg/h, every species flow on a consistent molar basis, and every energy rate as kW or MJ/h. Converting a component fraction from molar to mass basis requires component molar masses. A dimensionless index can be compared across scenarios only if the reference conditions and denominator have not changed. When the result is a percentage, specify percentage of what: total feed mass, converted feed, recovered product, sulfur atoms, or an observed time interval. The wrong denominator can change the interpretation even when the arithmetic is correct.

One useful way to check the numerical relationship is to inspect its limiting behavior. At zero conversion or removal, no product can appear or disappear through that mechanism; at complete removal, the tracked contaminant should be accounted for in another stream; at a cutpoint moved above or below the stated assay range, extrapolation should be rejected. A monotonic curve may be mathematically well behaved yet physically incomplete if secondary reactions, equilibrium or equipment capacity create a turning point outside the model.

Worked investigation: hypothetical data

For 100 kmol/h CH₄ feed and 70% conversion by the primary reaction only, compute CH₄ consumed, steam consumed, H₂ produced and CO produced.

Worked answer and interpretation

Using CH₄+H₂O→CO+3H₂ and 70% conversion of 100 kmol/h methane, 70 kmol/h CH₄ react. The primary reaction consumes 70 kmol/h water and produces 70 kmol/h CO and 210 kmol/h H₂. Remaining methane is 30 kmol/h. This excludes shift, side reactions, excess steam and separation.

Make a compact worksheet with four rows: starting assumptions, symbolic equation, numerical substitution and mass/energy/quality consistency check. Always place the units in the substitution row. An answer with four significant figures may be mathematically reproducible but should not be presented as a plant forecast when the assumed feed is only known roughly. Repeat the worksheet with one changed input, quantify the absolute and percentage change in the output, and ask which upstream measurement would be needed to defend that perturbation.

For numerical work, explicitly mark the inputs in this lesson as synthetic instructional values, including any yield factor, catalyst rate, representative boiling temperature or solvent efficiency. They must not be used as operating limits. If you wish to compare with published performance, define an independent, dated and source-specific dataset and evaluate whether its units and stream definitions match those of the exercise.

Plant integration and operating evidence

Complete species and energy balances around reformer, shift, cooling and purification units separately. Define whether hydrogen yield is measured before or after downstream purification, and report hydrogen purity as well as rate.

Place the result in a real flowsheet context. Petrochemical pathways depend on hydrocarbon molecular structure and on separation. Process integration can improve energy use, but the presence of valuable co-products does not eliminate the cost of obtaining on-spec feed and product. Document stoichiometric and yield bases separately. Ask where the upstream stream comes from, which downstream unit receives it, and how a change would shift at least one other required resource. A product-quality improvement might raise utility demand; more extensive contaminant removal might increase solvent regeneration; higher conversion may move load to gas compression or wastewater treatment. Draw the additional arrows on the block flow diagram, and do not claim that the local calculation has optimized the full plant.

For an evidence-based evaluation, design a measurement table with columns for variable, unit, sample or instrument location, time basis, quality method, expected repeatability and action on discrepancy. Include one direct process variable, one product property and one integration variable. A useful model-validation report should show residuals or errors for several cases, not only agreement at the nominal case used to choose parameters. Record potential confounding changes in feed, temperature, operator procedure and catalyst condition.

Assumption challenge and failure diagnosis

An equilibrium-free conversion formula can mislead at high pressure or limited steam. It is unacceptable for tube metal temperature, carbon activity or industrial reactor duty.

A critical reader should ask which implicit assumptions were required to write the equation: steady state or dynamic accumulation, ideal mixing or plug flow, fixed or changing properties, homogeneous or multiphase composition, constant versus variable selectivity, and independence versus coupling of disturbances. Pick the assumptions that matter here. If a model fails, identify whether the defect originates in incorrect units, an invalid physical assumption, unmeasured variability, or numerical implementation. Merely adding complexity does not fix poor calibration data.

In practical terms, define a stop condition for inference: a measurement outside the sampled composition range, evidence of a new phase, an unexpected hazard, a negative concentration, or an implausible material imbalance invalidates the shortcut. Escalate to a validated model or an expert review before making a design or safety claim. The appropriate corrective action can be to collect data, not to alter equipment.

Numerical laboratory and reproducible evidence

The linked [interactive laboratory, Steam methane reformer stoichiometry](../labs/lab-15.html), provides a separate numerical sensitivity exercise. Its governing relationship is CH4+H2O→CO+3H2; nH2=3 nCH4 X. The laboratory is connected to this lesson through its unit-level concepts, but it may explore a different variable from the preceding worked example. Check its JSON parameter definitions, alter one input at a time and export the sampled curve to CSV. Compare two cases by recomputing the equation manually; document the difference between software correctness and physical validity.

Before declaring completion, articulate these four results in your own words: the stream or specimen under study, the dimension and reporting basis of the output, the reason for the sign of its sensitivity, and a specific observation that could disconfirm the model. Relate the lesson to Aromatics extraction and separations as prior context and Petrochemical intermediate supply chains as a subsequent design issue. This linkage should be causal, not merely a sequence of chapter names.

Independent checkpoints

1. Sketch the process boundary for synthesis gas and reforming routes and label the stream or specimen basis that is actually measured.
2. Recreate the numerical reasoning from the worked investigation with all units and a limiting-case check.
3. Identify one operation, market specification or safety constraint that the formula does not contain.
4. Propose two measurements that would distinguish this model from a competing physical interpretation.
5. Describe why a correct plot of steam methane reformer stoichiometry does not establish plant-scale validity.

Editorial status: This is a provisional university-level teaching draft. Peer review, equipment-specific validation and current local requirements remain outside this instructional package.

Unit 05 · Lesson 04 — Petrochemical intermediate supply chains

[Unit map](../units/unit-05.html) · [Open numerical laboratory](../labs/lab-15.html) · [Assessment](../assessments/unit-05.html) · [Applied project](../projects/unit-05.html)

The engineering problem

Ethylene, propylene and aromatics are building blocks for polymers, fibers, solvents and many intermediates. A chain map distinguishes the chemical reaction yield from purification, transport, storage and the product-grade specification. Integrated facilities use co-products and utility sharing, but this coupling also creates operational dependencies.

The practical starting point is not the equation by itself; it is a description of the process boundary. Write down the feed, product, recovered co-product, waste and possible accumulation terms before choosing an indicator. In this lesson, the title petrochemical intermediate supply chains indicates a specific decision lens within petrochemicals. Its purpose is to connect a measured or assumed characteristic to an operational consequence with a statement of what would prove the link. Separate primary evidence, indirect proxy and calculated prediction; those three categories are not interchangeable.

Quantity definition and model reasoning

A polymerization mass balance may approximate polymer mass equal to monomer incorporated when chain addition creates no significant stoichiometric small-molecule by-product. Separate reactor conversion, recovered monomer and packaging losses explicitly.

To audit a model, begin with units. Write every mass flow on a common basis such as kg/h, every species flow on a consistent molar basis, and every energy rate as kW or MJ/h. Converting a component fraction from molar to mass basis requires component molar masses. A dimensionless index can be compared across scenarios only if the reference conditions and denominator have not changed. When the result is a percentage, specify percentage of what: total feed mass, converted feed, recovered product, sulfur atoms, or an observed time interval. The wrong denominator can change the interpretation even when the arithmetic is correct.

One useful way to check the numerical relationship is to inspect its limiting behavior. At zero conversion or removal, no product can appear or disappear through that mechanism; at complete removal, the tracked contaminant should be accounted for in another stream; at a cutpoint moved above or below the stated assay range, extrapolation should be rejected. A monotonic curve may be mathematically well behaved yet physically incomplete if secondary reactions, equilibrium or equipment capacity create a turning point outside the model.

Worked investigation: hypothetical data

Feed 100 t/d ethylene to a conceptual polymerization unit at 94% single-pass incorporation. If 80% of unconverted ethylene is recovered and recycled, compute initial polymer formed and the recovery stream. Explain why repeated-pass steady state requires another balance.

Worked answer and interpretation

From 100 t/d ethylene feed, immediate incorporation at 94% is 94 t/d polymer on the no-by-product mass assumption. Unconverted ethylene is 6 t/d; recovering 80% produces a 4.8 t/d recycle stream and 1.2 t/d unrecovered amount. Continuous recycle steady state requires re-solving feed and purge balances, not simply adding 4.8 to polymer output.

Make a compact worksheet with four rows: starting assumptions, symbolic equation, numerical substitution and mass/energy/quality consistency check. Always place the units in the substitution row. An answer with four significant figures may be mathematically reproducible but should not be presented as a plant forecast when the assumed feed is only known roughly. Repeat the worksheet with one changed input, quantify the absolute and percentage change in the output, and ask which upstream measurement would be needed to defend that perturbation.

For numerical work, explicitly mark the inputs in this lesson as synthetic instructional values, including any yield factor, catalyst rate, representative boiling temperature or solvent efficiency. They must not be used as operating limits. If you wish to compare with published performance, define an independent, dated and source-specific dataset and evaluate whether its units and stream definitions match those of the exercise.

Plant integration and operating evidence

Select routes according to feed supply reliability, product quality, utility availability, permitted emissions and downstream market demand. Estimate inventories and buffer capacity to handle decoupled production and logistics.

Place the result in a real flowsheet context. Petrochemical pathways depend on hydrocarbon molecular structure and on separation. Process integration can improve energy use, but the presence of valuable co-products does not eliminate the cost of obtaining on-spec feed and product. Document stoichiometric and yield bases separately. Ask where the upstream stream comes from, which downstream unit receives it, and how a change would shift at least one other required resource. A product-quality improvement might raise utility demand; more extensive contaminant removal might increase solvent regeneration; higher conversion may move load to gas compression or wastewater treatment. Draw the additional arrows on the block flow diagram, and do not claim that the local calculation has optimized the full plant.

For an evidence-based evaluation, design a measurement table with columns for variable, unit, sample or instrument location, time basis, quality method, expected repeatability and action on discrepancy. Include one direct process variable, one product property and one integration variable. A useful model-validation report should show residuals or errors for several cases, not only agreement at the nominal case used to choose parameters. Record potential confounding changes in feed, temperature, operator procedure and catalyst condition.

Assumption challenge and failure diagnosis

An impressive theoretical monomer yield is not equivalent to a commercially acceptable polymer-grade stream. Trace contaminants can poison catalysts despite minimal effect on bulk mass.

A critical reader should ask which implicit assumptions were required to write the equation: steady state or dynamic accumulation, ideal mixing or plug flow, fixed or changing properties, homogeneous or multiphase composition, constant versus variable selectivity, and independence versus coupling of disturbances. Pick the assumptions that matter here. If a model fails, identify whether the defect originates in incorrect units, an invalid physical assumption, unmeasured variability, or numerical implementation. Merely adding complexity does not fix poor calibration data.

In practical terms, define a stop condition for inference: a measurement outside the sampled composition range, evidence of a new phase, an unexpected hazard, a negative concentration, or an implausible material imbalance invalidates the shortcut. Escalate to a validated model or an expert review before making a design or safety claim. The appropriate corrective action can be to collect data, not to alter equipment.

Numerical laboratory and reproducible evidence

The linked [interactive laboratory, Steam methane reformer stoichiometry](../labs/lab-15.html), provides a separate numerical sensitivity exercise. Its governing relationship is CH4+H2O→CO+3H2; nH2=3 nCH4 X. The laboratory is connected to this lesson through its unit-level concepts, but it may explore a different variable from the preceding worked example. Check its JSON parameter definitions, alter one input at a time and export the sampled curve to CSV. Compare two cases by recomputing the equation manually; document the difference between software correctness and physical validity.

Before declaring completion, articulate these four results in your own words: the stream or specimen under study, the dimension and reporting basis of the output, the reason for the sign of its sensitivity, and a specific observation that could disconfirm the model. Relate the lesson to Synthesis gas and reforming routes as prior context and Gasoline and oxygenate blending objectives as a subsequent design issue. This linkage should be causal, not merely a sequence of chapter names.

Independent checkpoints

1. Sketch the process boundary for petrochemical intermediate supply chains and label the stream or specimen basis that is actually measured.
2. Recreate the numerical reasoning from the worked investigation with all units and a limiting-case check.
3. Identify one operation, market specification or safety constraint that the formula does not contain.
4. Propose two measurements that would distinguish this model from a competing physical interpretation.
5. Describe why a correct plot of steam methane reformer stoichiometry does not establish plant-scale validity.

Editorial status: This is a provisional university-level teaching draft. Peer review, equipment-specific validation and current local requirements remain outside this instructional package.

Unit 05 applied project — Petrochemicals

[Unit 05](../units/unit-05.html) · [Book projects](../index.html)

Commissioning question

A fictional integrated refinery-and-petrochemicals teaching facility is reviewing its petrochemicals decisions after receiving evidence that the assumed nominal feed or operating condition is no longer reliable. Your task is to produce an engineering screening memo, not an equipment datasheet or operating instruction. The central problem is: Map major building-block pathways from hydrocarbon feed to olefins, aromatics and synthesis-gas intermediates.

Steam cracking, aromatic separation and syngas production are not interchangeable. Each pathway has a different feed envelope, conversion chemistry, heat profile and separation train. Species balances and selectivity distinguish desired product from co-products, while energy intensity and impurity management influence commercial feasibility.

Synthetic case boundary

Start from a nominal notional feed of 1,000 mass units per day for a single material balance; choose its actual chemical meaning and reporting basis before calculations. Allocate an assumed 10% uncertainty to the most sensitive unmeasured characteristic. Do not silently convert the same number into tonnes, cubic metres, kmol and standard gas volume. If a composition is needed, invent and label a test vector whose fractions sum exactly to unity. Keep the upstream and downstream units visible in a block flow diagram.

For this unit, the four required technical workstreams are Steam cracking and olefin selectivity, Aromatics extraction and separations, Synthesis gas and reforming routes, Petrochemical intermediate supply chains. Use the lesson descriptions to select what evidence exists and what has to be assumed. If your assumed inputs are internally inconsistent—for example, a product yield above converted material, more recovered hydrogen than contained hydrogen, or a heat exchanger duty exceeding its thermodynamic ceiling—correct the conceptual error rather than tuning an output.

Computational experiment

Run three independent unit laboratories: [lab 13: Steam cracking ethylene selectivity](../labs/lab-13.html), [lab 14: Aromatics extraction recovery](../labs/lab-14.html), [lab 15: Steam methane reformer stoichiometry](../labs/lab-15.html). For each lab, define a base case, one credible perturbation and a stress case near the end of the control range. Record the JSON model identifier, all parameter values, model output, units and qualitative interpretation. Export CSV. Reconstruct at least two displayed values with an independent worksheet or script, and plot both the baseline and a sensitivity trajectory.

Then write an uncertainty section: distinguish numerical precision, parameter uncertainty, structural model uncertainty and sampling uncertainty. An exact identity can be extremely precise but may be irrelevant to a poorly sampled feed. Conversely, a fitted kinetic coefficient can capture a short operating period and fail when catalyst activity changes. Explain which uncertainties could reverse the ranking of proposed alternatives.

Whole-plant coordination

Compare feed routing with explicit yields and utilities; avoid claiming that an illustrative one-reaction model is an actual multi-furnace or equilibrium plant simulator. Name at least one impact on a different department: sulfur or wastewater handling, hydrogen consumption, off-gas, steam and power, product specifications, instrumentation, emergency response or carbon accounting. A nominally favorable local change is not a positive overall result until its resource and product interactions are reconciled. Identify an affected stakeholder who owns the required measurement or approval.

Deliverables and scoring

1. Boundary diagram and data dictionary (20%): readable stream labels, units, basis, data provenance and calculation assumptions.

2. Calculation appendix (25%): auditable mass or energy balance, three lab experiments and independent numerical recomputation.

3. Validation design (20%): at least two measurements, instrument/assay location, measurement frequency and acceptance criteria.

4. Trade-off memorandum (20%): alternative scenarios, constraints, uncertainty range and a reasoned but conditional comparison.

5. Responsible practice (15%): safety and environmental exclusions, uncertainty about regulations, and an explicit statement that the work is not plant-commissioning advice.

Challenge extension

Suppose the feed characteristic that controls the main model suddenly moves beyond the laboratory range. Write a plan for collecting the minimum data that would permit responsible recalibration without risking an unsupported process change. Your memo should explain why extrapolation is not a substitute for evidence and should name a decision point where engineering review is mandatory. The strongest result may be a refusal to infer a safe or profitable configuration from insufficient information.

Interactive laboratory 09: Reformer aromatics production

[Open lab in the browser](lab-09.html) · [Unit 03](../units/unit-03.html)

Engineering purpose

Apply an Arrhenius severity proxy to conversion and a fixed aromatic-lump selectivity. The selected input is intentionally a one-variable exploratory slice. Move one setting at a time, check whether the displayed rate or fraction remains physically meaningful, and compare the curve against the conservation requirements of the process. The exercise is designed to show sensitivity and falsifiability, not to choose equipment sizes or plant operating conditions.

Equations and units

k=kref exp(Ea/R(1/Tref−1/T)); Y=X S

The result is reported as % of feed. Entered quantities are documented in the associated JSON and visible controls. Distinguish this calculated quantity from plant measurements and from a standardized certificate-of-analysis property. Whenever the formula contains a fitted coefficient or lumped index, describe what experimental dataset would be needed for calibration.

Procedure and recorded evidence

1. Start from the displayed nominal controls and record the output with all units.
2. Change the primary parameter to one end of its range. Use the plot to identify the sign and approximate local slope; record both the input and output.
3. Return to nominal settings, vary the second parameter when available, and explain why the primary trend changes—or why the one-dimensional model prevents a conclusion.
4. Export the 81-point dataset. Plot it independently in a spreadsheet or numerical notebook; check the endpoint values by hand using the equation.
5. Test a limiting or boundary case. State what would make the equation physically inappropriate or numerically invalid, even when the software shows a smooth graph.

Investigation

Compare temperature sensitivity at low and high conversion. Compare your result with an independent arithmetic calculation. Report a mass-, species-, or energy-balance audit appropriate to the process rather than relying on numerical agreement alone.

Scientific boundary

Surrogate kinetics; no equilibrium, benzene speciation or catalyst life. The graph is not evidence of a measured plant result. The model omits material characteristics, uncertainty sources and coupled constraints that would be required in a licensed process simulation. A useful lab report has separate sections for model prediction, measurement requirements, likely failure modes and decisions that must be deferred until validation.

Interactive laboratory 10: Hydrodesulfurization residual sulfur

[Open lab in the browser](lab-10.html) · [Unit 04](../units/unit-04.html)

Engineering purpose

Explore an effective first-order sulfur concentration decline with increasing contact index. The selected input is intentionally a one-variable exploratory slice. Move one setting at a time, check whether the displayed rate or fraction remains physically meaningful, and compare the curve against the conservation requirements of the process. The exercise is designed to show sensitivity and falsifiability, not to choose equipment sizes or plant operating conditions.

Equations and units

Sout=Sin exp(−kτ)

The result is reported as ppmw. Entered quantities are documented in the associated JSON and visible controls. Distinguish this calculated quantity from plant measurements and from a standardized certificate-of-analysis property. Whenever the formula contains a fitted coefficient or lumped index, describe what experimental dataset would be needed for calibration.

Procedure and recorded evidence

1. Start from the displayed nominal controls and record the output with all units.
2. Change the primary parameter to one end of its range. Use the plot to identify the sign and approximate local slope; record both the input and output.
3. Return to nominal settings, vary the second parameter when available, and explain why the primary trend changes—or why the one-dimensional model prevents a conclusion.
4. Export the 81-point dataset. Plot it independently in a spreadsheet or numerical notebook; check the endpoint values by hand using the equation.
5. Test a limiting or boundary case. State what would make the equation physically inappropriate or numerically invalid, even when the software shows a smooth graph.

Investigation

Find contact index needed for 99% nominal removal at k=1/h. Compare your result with an independent arithmetic calculation. Report a mass-, species-, or energy-balance audit appropriate to the process rather than relying on numerical agreement alone.

Scientific boundary

Ignores sulfur species, inhibition, deactivation and hydrodynamics. The graph is not evidence of a measured plant result. The model omits material characteristics, uncertainty sources and coupled constraints that would be required in a licensed process simulation. A useful lab report has separate sections for model prediction, measurement requirements, likely failure modes and decisions that must be deferred until validation.

Unit 05 assessment — Petrochemicals

[Return to unit](../units/unit-05.html) · [Solutions rubric](../ASSESSMENT-RUBRIC.html)

Instructions. Answer all sixteen tasks. Use hand calculations or exported simulator data where appropriate. State your assumptions, units and the difference between data and hypothetical values. Results are not checked by automated grading.

Steam cracking and olefin selectivity

Question 01 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — For X = 0.70, S0 = 0.55 and a = 0.25, calculate the notional ethylene yield fraction. Check that yield is below conversion. — write the defining equation from first principles or its stated empirical assumptions, substitute the quantities with explicit units, and compute a result and reasonable significant figures. Explain what precise physical quantity the answer represents. Then change one input by 10% and determine the approximate sensitivity, specifying whether a percentage or a percentage-point change is being discussed.

Question 02 — Test the conservation boundary

Draw an inlet–outlet boundary around the relevant operation for steam cracking and olefin selectivity. Include feed, saleable product, recycle, off-gas, waste, accumulation and energy transfer where applicable. State a component or elemental balance that must be satisfied. Create a simple inconsistent dataset, quantify its imbalance and propose two concrete measurements that would help identify the error.

Question 03 — Challenge the physical model

Consider the assumption in the lesson that Increasing severity can increase conversion while lowering desired yield after secondary cracking. A one-variable yield curve cannot optimize furnace metallurgy or run length. Construct a plausible case in which its limitation becomes important. Predict the direction of model bias if defensible, identify any sign that cannot be inferred, and design a laboratory or process-data check to distinguish an inadequate equation from a sensor or sampling error.

Question 04 — Prepare an operating evidence decision

Prepare a one-page decision memo linked to steam cracking and olefin selectivity. Use this practice context: Compare ethylene and propylene output, fuel consumption, recycle, coke cleaning and fractionation requirements. Report each yield by a consistent mass basis and identify all co-products to preserve the carbon balance. State one measurable target, two competing operational or design choices, one external constraint, and three data sources or instruments. Recommend only the next evidence-collection step; do not convert the classroom model into a real plant setpoint.

Aromatics extraction and separations

Question 05 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — At S/F = 1.5 and K = 2, calculate single-contact recovery. Compare with half the solvent ratio and discuss diminishing returns. — write the defining equation from first principles or its stated empirical assumptions, substitute the quantities with explicit units, and compute a result and reasonable significant figures. Explain what precise physical quantity the answer represents. Then change one input by 10% and determine the approximate sensitivity, specifying whether a percentage or a percentage-point change is being discussed.

Question 06 — Test the conservation boundary

Draw an inlet–outlet boundary around the relevant operation for aromatics extraction and separations. Include feed, saleable product, recycle, off-gas, waste, accumulation and energy transfer where applicable. State a component or elemental balance that must be satisfied. Create a simple inconsistent dataset, quantify its imbalance and propose two concrete measurements that would help identify the error.

Question 07 — Challenge the physical model

Consider the assumption in the lesson that A high apparent extraction recovery says nothing about solvent contamination in the product or separation energy. Solvent toxicity, inventory and recycling must also be assessed. Construct a plausible case in which its limitation becomes important. Predict the direction of model bias if defensible, identify any sign that cannot be inferred, and design a laboratory or process-data check to distinguish an inadequate equation from a sensor or sampling error.

Question 08 — Prepare an operating evidence decision

Prepare a one-page decision memo linked to aromatics extraction and separations. Use this practice context: Calculate recovered-aromatic rate, raffinate losses, solvent circulation and recovery duty. Verify physical properties and phase equilibria for the actual solvent-system temperature and composition. State one measurable target, two competing operational or design choices, one external constraint, and three data sources or instruments. Recommend only the next evidence-collection step; do not convert the classroom model into a real plant setpoint.

Synthesis gas and reforming routes

Question 09 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — For 100 kmol/h CH₄ feed and 70% conversion by the primary reaction only, compute CH₄ consumed, steam consumed, H₂ produced and CO produced. — write the defining equation from first principles or its stated empirical assumptions, substitute the quantities with explicit units, and compute a result and reasonable significant figures. Explain what precise physical quantity the answer represents. Then change one input by 10% and determine the approximate sensitivity, specifying whether a percentage or a percentage-point change is being discussed.

Question 10 — Test the conservation boundary

Draw an inlet–outlet boundary around the relevant operation for synthesis gas and reforming routes. Include feed, saleable product, recycle, off-gas, waste, accumulation and energy transfer where applicable. State a component or elemental balance that must be satisfied. Create a simple inconsistent dataset, quantify its imbalance and propose two concrete measurements that would help identify the error.

Question 11 — Challenge the physical model

Consider the assumption in the lesson that An equilibrium-free conversion formula can mislead at high pressure or limited steam. It is unacceptable for tube metal temperature, carbon activity or industrial reactor duty. Construct a plausible case in which its limitation becomes important. Predict the direction of model bias if defensible, identify any sign that cannot be inferred, and design a laboratory or process-data check to distinguish an inadequate equation from a sensor or sampling error.

Question 12 — Prepare an operating evidence decision

Prepare a one-page decision memo linked to synthesis gas and reforming routes. Use this practice context: Complete species and energy balances around reformer, shift, cooling and purification units separately. Define whether hydrogen yield is measured before or after downstream purification, and report hydrogen purity as well as rate. State one measurable target, two competing operational or design choices, one external constraint, and three data sources or instruments. Recommend only the next evidence-collection step; do not convert the classroom model into a real plant setpoint.

Petrochemical intermediate supply chains

Question 13 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — Feed 100 t/d ethylene to a conceptual polymerization unit at 94% single-pass incorporation. If 80% of unconverted ethylene is recovered and recycled, compute initial polymer formed and the recovery stream. Explain why repeated-pass steady state requires another balance. — write the defining equation from first principles or its stated empirical assumptions, substitute the quantities with explicit units, and compute a result and reasonable significant figures. Explain what precise physical quantity the answer represents. Then change one input by 10% and determine the approximate sensitivity, specifying whether a percentage or a percentage-point change is being discussed.

Question 14 — Test the conservation boundary

Draw an inlet–outlet boundary around the relevant operation for petrochemical intermediate supply chains. Include feed, saleable product, recycle, off-gas, waste, accumulation and energy transfer where applicable. State a component or elemental balance that must be satisfied. Create a simple inconsistent dataset, quantify its imbalance and propose two concrete measurements that would help identify the error.

Question 15 — Challenge the physical model

Consider the assumption in the lesson that An impressive theoretical monomer yield is not equivalent to a commercially acceptable polymer-grade stream. Trace contaminants can poison catalysts despite minimal effect on bulk mass. Construct a plausible case in which its limitation becomes important. Predict the direction of model bias if defensible, identify any sign that cannot be inferred, and design a laboratory or process-data check to distinguish an inadequate equation from a sensor or sampling error.

Question 16 — Prepare an operating evidence decision

Prepare a one-page decision memo linked to petrochemical intermediate supply chains. Use this practice context: Select routes according to feed supply reliability, product quality, utility availability, permitted emissions and downstream market demand. Estimate inventories and buffer capacity to handle decoupled production and logistics. State one measurable target, two competing operational or design choices, one external constraint, and three data sources or instruments. Recommend only the next evidence-collection step; do not convert the classroom model into a real plant setpoint.