Hydrotreating, Desulfurization and Catalytic Reforming

[Book navigation](../index.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

Unit target

Quantify contaminant removal and identify the boundary between screening equations and actual treating-system design.

Engineering context

Sulfur compounds, acid gases, water and trace impurities affect corrosion, safety, emissions and catalyst life. Treating is often integrated with refinery fuel gas and sulfur recovery; the removal targets are typically product- and jurisdiction-specific. Simple exponential-removal equations are valuable for sensitivity but not guaranteed design performance. 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

State inlet composition, measurement basis, removal target, allowable residual, sampling method and disposal or regeneration route before selecting equipment. 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. [Hydrodesulfurization and sulfur balances](../lessons/unit-04-lesson-01.html) — [interactive lab 10](../labs/lab-10.html)
2. [Acid-gas removal and amine circulation](../lessons/unit-04-lesson-02.html) — [interactive lab 11](../labs/lab-11.html)
3. [Gas dehydration and water dew-point control](../lessons/unit-04-lesson-03.html) — [interactive lab 12](../labs/lab-12.html)
4. [Sulfur recovery and tail-gas treatment](../lessons/unit-04-lesson-04.html) — [interactive lab 12](../labs/lab-12.html)

Laboratory strategy

These three distinct models illuminate different physics or accounting relationships in the unit: Hydrodesulfurization residual sulfur, Amine contactor removal proxy, Gas dehydration approach. 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-04.html) to identify technical gaps. The [applied project](../projects/unit-04.html) then adds constraints from adjacent units so that a local process improvement can be evaluated for its plant-wide consequence.

Unit 04 · Lesson 01 — Hydrodesulfurization and sulfur balances

[Unit map](../units/unit-04.html) · [Open numerical laboratory](../labs/lab-10.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering problem

Hydrodesulfurization converts many organosulfur compounds toward hydrogen sulfide using hydrogen and catalyst. Different sulfur species show different kinetics; basic thiophenic compounds are not uniformly easy to remove. Hydrogen sulfide must be separated and managed downstream, creating an integrated treating and sulfur-recovery task.

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 hydrodesulfurization and sulfur balances indicates a specific decision lens within treating. 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 pseudo-first-order teaching relationship is C_S,out = C_S,in exp(−kτ). It is meaningful only if the measured sulfur basis and effective k remain consistent over the model conditions. Sulfur conversion is not the same as product mass yield.

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

A feed contains 12,000 ppmw sulfur; a toy model gives kτ = 3.5. Calculate the residual and removal fraction. State what additional data prove a real unit can reach that sulfur level.

Worked answer and interpretation

At kτ=3.5, the model outlet sulfur is 12,000 exp(−3.5)≈362.4 ppmw. The removal fraction is 1−exp(−3.5)≈0.9698, or 96.98%. This case illustrates why a large percentage removal need not satisfy a more stringent product target; species and catalyst data would be required for plant prediction.

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

Report sulfur as ppmw or mass percent, identify assay and outlet method, measure catalyst activity and hydrogen availability, and reconcile sulfur to products and acid-gas systems. Specific product regulations require current method and jurisdiction verification.

Place the result in a real flowsheet context. Treating routes move contaminants from one stream to another. Removal percentage alone is incomplete until residual stream composition, solvent or catalyst management and disposal or recovery paths are defined. For hydrogen sulfide in particular, an absorber can shift hazard inventory without eliminating it. 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

High fractional removal may still leave noncompliant residual sulfur if the inlet is elevated. Pseudo-first-order rates fail outside their calibration envelope.

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, Hydrodesulfurization residual sulfur](../labs/lab-10.html), provides a separate numerical sensitivity exercise. Its governing relationship is Sout=Sin exp(−kτ). 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 Thermal conversion, coking and residue routing as prior context and Acid-gas removal and amine circulation 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 hydrodesulfurization and sulfur balances 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 hydrodesulfurization residual sulfur 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 04 · Lesson 02 — Acid-gas removal and amine circulation

[Unit map](../units/unit-04.html) · [Open numerical laboratory](../labs/lab-11.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering problem

Amine treating absorbs H₂S and often CO₂ from gas or liquid streams. Solvent type, loading, circulation, temperature, reaction kinetics, foaming and regeneration determine performance. A process diagram must include contactor, flash, heat exchange, regenerator and acid-gas disposal or sulfur-recovery route.

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 acid-gas removal and amine circulation indicates a specific decision lens within treating. 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 simple gas-phase transfer surrogate is yout = yin exp(−NTU), with NTU modeled as a monotonic function of solvent-to-gas ratio. A rigorous absorber requires equilibria, packing or tray performance, heat effects and solvent speciation.

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 inlet acid gas of 4 mol% and teaching NTU = 2, estimate outlet mole fraction; then describe why acid-gas composition and lean loading must be measured.

Worked answer and interpretation

At a dimensionless NTU of 2, outlet acid gas is 0.04 exp(−2)=0.005413 mole fraction, or approximately 0.541 mol%. No corresponding solvent circulation can be inferred without actual transfer coefficient and rich/lean loading information; capture is not equivalent to sulfur destruction.

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

Track inlet acid-gas molar flows, lean and rich solvent loading, reboiler energy, corrosion control and waste. Check the practical distinction between acid-gas capture and ultimate disposal; captured sulfur is not eliminated.

Place the result in a real flowsheet context. Treating routes move contaminants from one stream to another. Removal percentage alone is incomplete until residual stream composition, solvent or catalyst management and disposal or recovery paths are defined. For hydrogen sulfide in particular, an absorber can shift hazard inventory without eliminating it. 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 solvent-flow curve is not a licensed amine design and does not produce a safe H₂S exposure assessment. Breakthrough or foaming may cause sudden deterioration not captured by smooth equations.

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, Amine contactor removal proxy](../labs/lab-11.html), provides a separate numerical sensitivity exercise. Its governing relationship is yout=yin exp(−kL/G). 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 Hydrodesulfurization and sulfur balances as prior context and Gas dehydration and water dew-point control 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 acid-gas removal and amine circulation 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 amine contactor removal 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 04 · Lesson 03 — Gas dehydration and water dew-point control

[Unit map](../units/unit-04.html) · [Open numerical laboratory](../labs/lab-12.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering problem

Gas dehydration protects cold processing, pipelines and downstream equipment from water condensation and hydrate risks. Glycol absorption and solid desiccants have distinct regeneration, contamination and turndown behavior. Reporting only water removal percentage can be misleading: downstream dew point depends on pressure, temperature and composition.

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 gas dehydration and water dew-point control indicates a specific decision lens within treating. 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 approach-to-equilibrium proxy uses Wout = Weq + (Win−Weq)exp(−kN), where N represents notional contact stages. The equation predicts an asymptotic residual water concentration and is not a true vapor-liquid equilibrium model.

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 800 mg per reference m³ inlet water, model equilibrium floor 20 mg/m³ and two effective contacts with k = 0.8. Calculate outlet and explain which physical performance parameters are missing.

Worked answer and interpretation

The instructional contact equation gives Wout=20+(800−20)exp(−0.8×2)≈177.5 mg/reference m³. This is a concentration under a declared reference-volume convention, not a water dew point. The thermodynamic equilibrium and the actual regeneration performance must be known to assess hydrate management.

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

Specify water content with unambiguous units, reference conditions, operating pressure and test method. Compare outlet moisture to dew-point and hydrate management requirements using credible equilibrium data before process decisions.

Place the result in a real flowsheet context. Treating routes move contaminants from one stream to another. Removal percentage alone is incomplete until residual stream composition, solvent or catalyst management and disposal or recovery paths are defined. For hydrogen sulfide in particular, an absorber can shift hazard inventory without eliminating it. 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 arbitrarily low asymptotic Weq hides solvent and equipment limits. Water concentration in mg/m³ without a temperature/pressure reference can be ambiguous.

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, Gas dehydration approach](../labs/lab-12.html), provides a separate numerical sensitivity exercise. Its governing relationship is Wout=Weq+(Win−Weq)exp(−kN). 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 Acid-gas removal and amine circulation as prior context and Sulfur recovery and tail-gas treatment 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 gas dehydration and water dew-point control 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 gas dehydration approach 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 04 · Lesson 04 — Sulfur recovery and tail-gas treatment

[Unit map](../units/unit-04.html) · [Open numerical laboratory](../labs/lab-12.html) · [Assessment](../assessments/unit-04.html) · [Applied project](../projects/unit-04.html)

The engineering problem

Claus sulfur recovery reacts H₂S in an oxidizing and catalytic sequence to form elemental sulfur. The process includes combustion, heat recovery, condensation and catalytic conversion, often followed by tail-gas treatment. Sulfur recovery is fundamentally an element balance, and emission accounting must include the unrecovered sulfur species.

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 sulfur recovery and tail-gas treatment indicates a specific decision lens within treating. 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 pedagogical multistage approximation gives residual fraction (1−η)^N for identical independent fractional-removal stages. Real Claus reactions approach equilibrium and stages are neither identical nor perfectly independent.

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

If 100 kmol/h of H₂S enters a conceptual recovery block with 95% sulfur atom recovery, estimate sulfur mass in t/h and sulfur remaining in other streams. Do not claim all unrecovered sulfur becomes SO₂.

Worked answer and interpretation

The feed carries 100 kmol H₂S/h, hence 100 kmol sulfur atoms per hour. At 95% conceptual recovery, 95 kmol S/h are recovered; using 32.065 kg/kmol gives about 3.046 t sulfur/h. Five kmol sulfur atoms per hour remain in other streams, equivalent to 0.160 t S/h. Their chemical forms are not specified.

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

Convert inlet H₂S molar flow to moles of sulfur and mass of product using atomic molecular mass; include sulfur condensers, tail-gas, recycle and flare pathways. Monitor compliance at the actual stack boundary.

Place the result in a real flowsheet context. Treating routes move contaminants from one stream to another. Removal percentage alone is incomplete until residual stream composition, solvent or catalyst management and disposal or recovery paths are defined. For hydrogen sulfide in particular, an absorber can shift hazard inventory without eliminating it. 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

Multiplying independent stage efficiencies exaggerates recovery when thermodynamics, catalyst poisoning or carryover constrain later stages. The proxy is not a sulfur-plant capacity calculation.

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, Gas dehydration approach](../labs/lab-12.html), provides a separate numerical sensitivity exercise. Its governing relationship is Wout=Weq+(Win−Weq)exp(−kN). 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 Gas dehydration and water dew-point control as prior context and Steam cracking and olefin selectivity 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 sulfur recovery and tail-gas treatment 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 gas dehydration approach 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 04 applied project — Treating

[Unit 04](../units/unit-04.html) · [Book projects](../index.html)

Commissioning question

A fictional integrated refinery-and-petrochemicals teaching facility is reviewing its treating 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: Quantify contaminant removal and identify the boundary between screening equations and actual treating-system design.

Sulfur compounds, acid gases, water and trace impurities affect corrosion, safety, emissions and catalyst life. Treating is often integrated with refinery fuel gas and sulfur recovery; the removal targets are typically product- and jurisdiction-specific. Simple exponential-removal equations are valuable for sensitivity but not guaranteed design performance.

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 Hydrodesulfurization and sulfur balances, Acid-gas removal and amine circulation, Gas dehydration and water dew-point control, Sulfur recovery and tail-gas treatment. 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 10: Hydrodesulfurization residual sulfur](../labs/lab-10.html), [lab 11: Amine contactor removal proxy](../labs/lab-11.html), [lab 12: Gas dehydration approach](../labs/lab-12.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

State inlet composition, measurement basis, removal target, allowable residual, sampling method and disposal or regeneration route before selecting equipment. 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 07: FCC conversion and yield

[Open lab in the browser](lab-07.html) · [Unit 03](../units/unit-03.html)

Engineering purpose

Follow a nominal FCC conversion toward a gasoline-range product with a conversion-dependent selectivity penalty. 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

X=1−exp(−kτ); Ygasoline=X·0.62exp(−0.20X)

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

Find whether conversion and gasoline yield increase at the same fractional rate. 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

Single-lump conceptual network with invented parameters, not FCC kinetics. 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 08: Hydrocracker hydrogen consumption

[Open lab in the browser](lab-08.html) · [Unit 03](../units/unit-03.html)

Engineering purpose

Compute converted feed and a proportional net hydrogen demand from a severity-controlled conversion proxy. 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

X=1−exp(−kτ), H2=F X α /1000

The result is reported as t H₂/h. 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

Test how feed throughput affects H₂ demand at constant 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

Consumption factor is illustrative; not a stoichiometric or process design result. 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 04 assessment — Treating

[Return to unit](../units/unit-04.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.

Hydrodesulfurization and sulfur balances

Question 01 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — A feed contains 12,000 ppmw sulfur; a toy model gives kτ = 3.5. Calculate the residual and removal fraction. State what additional data prove a real unit can reach that sulfur level. — 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 hydrodesulfurization and sulfur balances. 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 High fractional removal may still leave noncompliant residual sulfur if the inlet is elevated. Pseudo-first-order rates fail outside their calibration envelope. 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 hydrodesulfurization and sulfur balances. Use this practice context: Report sulfur as ppmw or mass percent, identify assay and outlet method, measure catalyst activity and hydrogen availability, and reconcile sulfur to products and acid-gas systems. Specific product regulations require current method and jurisdiction verification. 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.

Acid-gas removal and amine circulation

Question 05 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — For inlet acid gas of 4 mol% and teaching NTU = 2, estimate outlet mole fraction; then describe why acid-gas composition and lean loading must be measured. — 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 acid-gas removal and amine circulation. 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 solvent-flow curve is not a licensed amine design and does not produce a safe H₂S exposure assessment. Breakthrough or foaming may cause sudden deterioration not captured by smooth equations. 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 acid-gas removal and amine circulation. Use this practice context: Track inlet acid-gas molar flows, lean and rich solvent loading, reboiler energy, corrosion control and waste. Check the practical distinction between acid-gas capture and ultimate disposal; captured sulfur is not eliminated. 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.

Gas dehydration and water dew-point control

Question 09 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — For 800 mg per reference m³ inlet water, model equilibrium floor 20 mg/m³ and two effective contacts with k = 0.8. Calculate outlet and explain which physical performance parameters are missing. — 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 gas dehydration and water dew-point control. 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 arbitrarily low asymptotic Weq hides solvent and equipment limits. Water concentration in mg/m³ without a temperature/pressure reference can be ambiguous. 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 gas dehydration and water dew-point control. Use this practice context: Specify water content with unambiguous units, reference conditions, operating pressure and test method. Compare outlet moisture to dew-point and hydrate management requirements using credible equilibrium data before process decisions. 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.

Sulfur recovery and tail-gas treatment

Question 13 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — If 100 kmol/h of H₂S enters a conceptual recovery block with 95% sulfur atom recovery, estimate sulfur mass in t/h and sulfur remaining in other streams. Do not claim all unrecovered sulfur becomes SO₂. — 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 sulfur recovery and tail-gas treatment. 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 Multiplying independent stage efficiencies exaggerates recovery when thermodynamics, catalyst poisoning or carryover constrain later stages. The proxy is not a sulfur-plant capacity calculation. 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 sulfur recovery and tail-gas treatment. Use this practice context: Convert inlet H₂S molar flow to moles of sulfur and mass of product using atomic molecular mass; include sulfur condensers, tail-gas, recycle and flare pathways. Monitor compliance at the actual stack boundary. 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.