Aromatics Extraction (BTX) and Polymer-Grade Monomers

[Book navigation](../index.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

Unit target

Analyze blending and finished-product quality with transparent approximations and validation requirements.

Engineering context

Product specifications define a feasible region, not just a marketing grade. Blending properties may be nonlinear; a calculated average can violate an actual standardized test. Crude-derived products also require storage stability, contaminants, emissions compliance, and safe custody transfer. 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

Use shortcut blend rules to rank candidate cases, then specify the laboratory or validated process correlation required before release decisions. 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. [Gasoline and oxygenate blending objectives](../lessons/unit-06-lesson-01.html) — [interactive lab 16](../labs/lab-16.html)
2. [Volatility, flash characteristics and phase behavior](../lessons/unit-06-lesson-02.html) — [interactive lab 17](../labs/lab-17.html)
3. [Diesel, jet and middle-distillate quality](../lessons/unit-06-lesson-03.html) — [interactive lab 18](../labs/lab-18.html)
4. [Lubricants, base stocks and viscosity blending](../lessons/unit-06-lesson-04.html) — [interactive lab 18](../labs/lab-18.html)

Laboratory strategy

These three distinct models illuminate different physics or accounting relationships in the unit: Linear gasoline octane screen, Ideal binary bubble pressure, Lubricant viscosity blending proxy. 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-06.html) to identify technical gaps. The [applied project](../projects/unit-06.html) then adds constraints from adjacent units so that a local process improvement can be evaluated for its plant-wide consequence.

Unit 06 · Lesson 01 — Gasoline and oxygenate blending objectives

[Unit map](../units/unit-06.html) · [Open numerical laboratory](../labs/lab-16.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering problem

Gasoline blending combines streams with different octane quality, volatility, sulfur and other properties. Optimizing one property alone can violate another. Octane indices and vapor pressure are not generally exactly linear in blend fraction; real blend values depend on components and standardized test methods.

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 gasoline and oxygenate blending objectives indicates a specific decision lens within product systems. 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

As a screening-only approximation, RONblend≈ΣviRONi for volume fractions vi at a stated condition. This is an interpolation, not a guarantee of test-engine performance. A mass-to-volume conversion needs stream densities.

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

Combine 30 volume units of model stream A with RON 92 and 70 units of B with RON 86. Estimate nominal RON and identify how nonlinearity could change the actual blend result.

Worked answer and interpretation

Linear volume-weighted RONscreen = 0.30(92)+0.70(86) = 87.8. The difference between 87.8 and a measured engine-test RON is not known without actual blend-response data. The arithmetic can rank simple scenarios, but the product must be assessed using the applicable formal test method.

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

Formulate blending as constrained optimization with measured stream availability, product demand, property limits and uncertainty margins. Clearly label linear property assumptions and require laboratory confirmation before product release.

Place the result in a real flowsheet context. Finished-product testing follows named methods and regulatory requirements that can change. Property approximations are screening tools; nonlinear interactions, measurement repeatability and storage conditions may alter observed values. Record the method, not merely the target number. 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 volume-weighted average of measured RON values can materially differ from actual blending octane. Therefore do not claim standards compliance from the approximation.

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, Linear gasoline octane screen](../labs/lab-16.html), provides a separate numerical sensitivity exercise. Its governing relationship is RONscreen=x RON_A+(1−x)RON_B. 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 Petrochemical intermediate supply chains as prior context and Volatility, flash characteristics and phase behavior 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 gasoline and oxygenate blending objectives 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 linear gasoline octane screen 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 06 · Lesson 02 — Volatility, flash characteristics and phase behavior

[Unit map](../units/unit-06.html) · [Open numerical laboratory](../labs/lab-17.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering problem

Volatility influences startup, emissions, vapor management and finished fuel quality. Reid vapor pressure is a standardized test property and is not simply the equilibrium bubble pressure at arbitrary temperature. A liquid-mixture pressure estimate can illustrate compositional effects while failing to predict actual standardized RVP.

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 volatility, flash characteristics and phase behavior indicates a specific decision lens within product systems. 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 an ideal binary liquid at fixed temperature, bubble pressure P = xA Psat,A + (1−xA)Psat,B by Raoult law. This requires genuine equilibrium vapor pressures at the same temperature, not arbitrary RVP numbers.

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

Two idealized constituents have vapor pressures 80 and 20 kPa at a shared temperature. Calculate bubble pressure at xA = 0.3 and xA = 0.7; explain the distinction from measured RVP.

Worked answer and interpretation

At xA=0.3, ideal bubble pressure is 0.3(80)+0.7(20)=38 kPa. At xA=0.7, pressure is 0.7(80)+0.3(20)=62 kPa. These values are equilibrium calculations for a hypothetical ideal binary at one temperature; neither number is Reid vapor pressure measured under its standard procedure.

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

Use calibrated thermodynamic methods and real test data to check vapor-liquid constraints. Separate process vessel pressure from test-method vapor pressure and from flash-point classification.

Place the result in a real flowsheet context. Finished-product testing follows named methods and regulatory requirements that can change. Property approximations are screening tools; nonlinear interactions, measurement repeatability and storage conditions may alter observed values. Record the method, not merely the target number. 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

Real petroleum blends can be strongly nonideal and multicomponent. Do not use the ideal mixture bubble-pressure curve to issue specifications or size pressure-relief equipment.

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, Ideal binary bubble pressure](../labs/lab-17.html), provides a separate numerical sensitivity exercise. Its governing relationship is Pbubble=x PsatA+(1−x)PsatB. 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 Gasoline and oxygenate blending objectives as prior context and Diesel, jet and middle-distillate quality 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 volatility, flash characteristics and phase behavior 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 ideal binary bubble pressure 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 06 · Lesson 03 — Diesel, jet and middle-distillate quality

[Unit map](../units/unit-06.html) · [Open numerical laboratory](../labs/lab-18.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering problem

Middle distillates are evaluated through multiple characteristics including ignition quality, low-temperature behavior, boiling distribution, sulfur and stability. Jet fuel requires its own rigorous specifications and quality assurance. A change in crude cutpoint or treatment route affects several properties together and must not be assessed by one surrogate index.

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 diesel, jet and middle-distillate quality indicates a specific decision lens within product systems. 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 conservative component property such as sulfur concentration, blend concentration is mass weighted. A density blend may require volume correction; cetane number and cold-flow properties often require empirical or nonlinear blending relationships.

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

Consider 400 t of diesel blendstock at 10 ppmw sulfur and 600 t at 30 ppmw. Calculate blended ppmw. Explain why this result does not imply cetane or cloud-point compliance.

Worked answer and interpretation

Conservative sulfur is (400 t×10 ppmw+600 t×30 ppmw)/(400+600)t = 22 ppmw. No equation used here predicts cetane, distillation endpoint or cloud point. Those properties should be tested or predicted by separate validated correlations and then checked against the target grade specification.

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

Prepare a specification matrix with test method, sample point, target and uncertainty. Track interface material when transporting different grades and ensure blending plans are evaluated across temperatures and storage histories.

Place the result in a real flowsheet context. Finished-product testing follows named methods and regulatory requirements that can change. Property approximations are screening tools; nonlinear interactions, measurement repeatability and storage conditions may alter observed values. Record the method, not merely the target number. 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

Mixing two on-spec streams is not sufficient proof the blend meets every requirement, especially where nonlinear properties or contamination occur.

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, Lubricant viscosity blending proxy](../labs/lab-18.html), provides a separate numerical sensitivity exercise. Its governing relationship is ln μ=x ln μA+(1−x)ln μB. 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 Volatility, flash characteristics and phase behavior as prior context and Lubricants, base stocks and viscosity blending 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 diesel, jet and middle-distillate quality 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 lubricant viscosity blending proxy 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 06 · Lesson 04 — Lubricants, base stocks and viscosity blending

[Unit map](../units/unit-06.html) · [Open numerical laboratory](../labs/lab-18.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering problem

Lubricant formulation combines base-stock viscosity behavior with additives, temperature dependence and desired performance. Viscosity changes steeply with temperature, and different stocks may not obey a simple arithmetic mixing rule. Kinematic viscosity differs from dynamic viscosity through density.

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 lubricants, base stocks and viscosity blending indicates a specific decision lens within product systems. 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 screening approximation uses ln μmix = x ln μA + (1−x)ln μB for dynamic viscosity at one fixed temperature. This is an empirical-style log-mixing surrogate, not a universal certified lubricant formulation rule.

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

Blend 40% component A at 10 mPa·s with 60% component B at 100 mPa·s, on a stated ideal fraction basis. Calculate the logarithmic proxy and compare with a naïve arithmetic average.

Worked answer and interpretation

The logarithmic proxy is ln μ = 0.4 ln 10+0.6 ln 100, giving μ≈39.81 mPa·s. The arithmetic mean on the same fraction basis is 0.4(10)+0.6(100)=64 mPa·s. Neither value guarantees the measured mixture viscosity; calibration and consistent component mixing basis are still required.

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

Record the measurement temperature and whether viscosity is dynamic or kinematic. Evaluate low-temperature pumpability, oxidation stability, additive compatibility and shear behavior separately from a single-point mixture estimate.

Place the result in a real flowsheet context. Finished-product testing follows named methods and regulatory requirements that can change. Property approximations are screening tools; nonlinear interactions, measurement repeatability and storage conditions may alter observed values. Record the method, not merely the target number. 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 model at 40 °C cannot be extrapolated to an entire viscosity-temperature curve; a finished lubricant can behave non-Newtonian or change under aging.

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, Lubricant viscosity blending proxy](../labs/lab-18.html), provides a separate numerical sensitivity exercise. Its governing relationship is ln μ=x ln μA+(1−x)ln μB. 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 Diesel, jet and middle-distillate quality as prior context and Hydrogen generation, purification and allocation 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 lubricants, base stocks and viscosity blending 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 lubricant viscosity blending proxy 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 06 applied project — Product systems

[Unit 06](../units/unit-06.html) · [Book projects](../index.html)

Commissioning question

A fictional integrated refinery-and-petrochemicals teaching facility is reviewing its product systems 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: Analyze blending and finished-product quality with transparent approximations and validation requirements.

Product specifications define a feasible region, not just a marketing grade. Blending properties may be nonlinear; a calculated average can violate an actual standardized test. Crude-derived products also require storage stability, contaminants, emissions compliance, and safe custody transfer.

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 Gasoline and oxygenate blending objectives, Volatility, flash characteristics and phase behavior, Diesel, jet and middle-distillate quality, Lubricants, base stocks and viscosity blending. 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 16: Linear gasoline octane screen](../labs/lab-16.html), [lab 17: Ideal binary bubble pressure](../labs/lab-17.html), [lab 18: Lubricant viscosity blending proxy](../labs/lab-18.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

Use shortcut blend rules to rank candidate cases, then specify the laboratory or validated process correlation required before release decisions. 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 11: Amine contactor removal proxy

[Open lab in the browser](lab-11.html) · [Unit 04](../units/unit-04.html)

Engineering purpose

Show acid-gas decrease with a dimensionless number of transfer units tied to solvent-to-gas ratio. 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

yout=yin exp(−kL/G)

The result is reported as % mol. 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

How much extra solvent index is needed to halve residual acid gas? 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

No solvent speciation, reaction equilibria, loading limit or thermal balance. 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 12: Gas dehydration approach

[Open lab in the browser](lab-12.html) · [Unit 04](../units/unit-04.html)

Engineering purpose

Use a declining approach-to-floor relationship for nominal gas moisture versus contact effectiveness. 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

Wout=Weq+(Win−Weq)exp(−kN)

The result is reported as mg/ref m³. 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

Why does removal effectiveness flatten as the floor is approached? 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

Not a dew-point/hydrate equilibrium or validated contactor rating. 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 06 assessment — Product systems

[Return to unit](../units/unit-06.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.

Gasoline and oxygenate blending objectives

Question 01 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — Combine 30 volume units of model stream A with RON 92 and 70 units of B with RON 86. Estimate nominal RON and identify how nonlinearity could change the actual blend result. — 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 gasoline and oxygenate blending objectives. 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 A volume-weighted average of measured RON values can materially differ from actual blending octane. Therefore do not claim standards compliance from the approximation. 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 gasoline and oxygenate blending objectives. Use this practice context: Formulate blending as constrained optimization with measured stream availability, product demand, property limits and uncertainty margins. Clearly label linear property assumptions and require laboratory confirmation before product release. 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.

Volatility, flash characteristics and phase behavior

Question 05 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — Two idealized constituents have vapor pressures 80 and 20 kPa at a shared temperature. Calculate bubble pressure at xA = 0.3 and xA = 0.7; explain the distinction from measured RVP. — 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 volatility, flash characteristics and phase behavior. 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 Real petroleum blends can be strongly nonideal and multicomponent. Do not use the ideal mixture bubble-pressure curve to issue specifications or size pressure-relief equipment. 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 volatility, flash characteristics and phase behavior. Use this practice context: Use calibrated thermodynamic methods and real test data to check vapor-liquid constraints. Separate process vessel pressure from test-method vapor pressure and from flash-point classification. 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.

Diesel, jet and middle-distillate quality

Question 09 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — Consider 400 t of diesel blendstock at 10 ppmw sulfur and 600 t at 30 ppmw. Calculate blended ppmw. Explain why this result does not imply cetane or cloud-point compliance. — 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 diesel, jet and middle-distillate quality. 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 Mixing two on-spec streams is not sufficient proof the blend meets every requirement, especially where nonlinear properties or contamination occur. 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 diesel, jet and middle-distillate quality. Use this practice context: Prepare a specification matrix with test method, sample point, target and uncertainty. Track interface material when transporting different grades and ensure blending plans are evaluated across temperatures and storage histories. 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.

Lubricants, base stocks and viscosity blending

Question 13 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — Blend 40% component A at 10 mPa·s with 60% component B at 100 mPa·s, on a stated ideal fraction basis. Calculate the logarithmic proxy and compare with a naïve arithmetic average. — 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 lubricants, base stocks and viscosity blending. 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 A model at 40 °C cannot be extrapolated to an entire viscosity-temperature curve; a finished lubricant can behave non-Newtonian or change under aging. 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 lubricants, base stocks and viscosity blending. Use this practice context: Record the measurement temperature and whether viscosity is dynamic or kinematic. Evaluate low-temperature pumpability, oxidation stability, additive compatibility and shear behavior separately from a single-point mixture estimate. 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.