Refinery Energy, Hydrogen Integration and Flare Networks

[Book navigation](../index.html) · [Assessment](../assessments/unit-07.html) · [Applied project](../projects/unit-07.html)

Unit target

Close resource balances across processing units, energy networks, utilities and emissions boundaries.

Engineering context

Refinery optimization crosses unit limits. A proposed yield increase changes the hydrogen, steam, cooling, wastewater, fuel-gas and carbon balances. The right system boundary makes waste heat and off-gas visible; the wrong one can move impacts from one accounting line to another. 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

Distinguish gross from net energy, mass from purity of hydrogen, and direct process emissions from downstream life-cycle emissions. 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. [Hydrogen generation, purification and allocation](../lessons/unit-07-lesson-01.html) — [interactive lab 19](../labs/lab-19.html)
2. [Heat recovery and exchanger networks](../lessons/unit-07-lesson-02.html) — [interactive lab 20](../labs/lab-20.html)
3. [Steam, water and power utility balances](../lessons/unit-07-lesson-03.html) — [interactive lab 21](../labs/lab-21.html)
4. [Direct emissions and carbon inventories](../lessons/unit-07-lesson-04.html) — [interactive lab 21](../labs/lab-21.html)

Laboratory strategy

These three distinct models illuminate different physics or accounting relationships in the unit: Hydrogen availability network, Heat exchanger effectiveness, Fuel-carbon direct emissions. 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-07.html) to identify technical gaps. The [applied project](../projects/unit-07.html) then adds constraints from adjacent units so that a local process improvement can be evaluated for its plant-wide consequence.

Unit 07 · Lesson 01 — Hydrogen generation, purification and allocation

[Unit map](../units/unit-07.html) · [Open numerical laboratory](../labs/lab-19.html) · [Assessment](../assessments/unit-07.html) · [Applied project](../projects/unit-07.html)

The engineering problem

Hydrogen is produced by reforming and purpose-built plants, then purified, compressed and distributed to consuming reactors. Different streams carry different purity, pressure and contaminant loads. The network optimization problem must account for both mass and quality, not only gross supply.

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 hydrogen generation, purification and allocation indicates a specific decision lens within plant integration. 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

Available hydrogen mass = Σ(Fi yi), where Fi is a total stream mass flow and yi is its hydrogen mass fraction. A simple demand deficit is max(0, D−available). Pressure compatibility and impurity requirements introduce additional constraints beyond this scalar arithmetic.

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 1000 kg/h stream is 80 mass% H₂ and a 500 kg/h stream is 50 mass% H₂. Compare the total contained H₂ with demand of 1200 kg/h, then state why direct connection may still be infeasible.

Worked answer and interpretation

Contained H₂ in stream 1 is 1000×0.80=800 kg/h, and in stream 2 it is 500×0.50=250 kg/h. Total contained H₂ is 1050 kg/h. Against demand 1200 kg/h, the scalar deficit is 150 kg/h. The purity and pressure requirements at individual sinks can prevent the apparent 1050 kg/h from being used directly.

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

Build a plant-wide table of sources, sinks, purges and compressor requirements; use conservative purity envelopes. Compare recovery upgrades with make-up production using utility and equipment constraints.

Place the result in a real flowsheet context. A network model needs flow, quality, pressure, temperature and availability. A nominal surplus of material or energy can be unusable because of incompatible state conditions. Audit gross and net flows and avoid double counting of an exchanged stream. 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

Treating all hydrogen in low-purity gas as immediately usable can be wrong. Compression and purification can reduce net benefit or make a nominal surplus unusable.

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, Hydrogen availability network](../labs/lab-19.html), provides a separate numerical sensitivity exercise. Its governing relationship is Havailable=F1y1+F2y2; deficit=max(0,D−Havailable). 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 Lubricants, base stocks and viscosity blending as prior context and Heat recovery and exchanger networks 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 hydrogen generation, purification and allocation 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 hydrogen availability network 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 07 · Lesson 02 — Heat recovery and exchanger networks

[Unit map](../units/unit-07.html) · [Open numerical laboratory](../labs/lab-20.html) · [Assessment](../assessments/unit-07.html) · [Applied project](../projects/unit-07.html)

The engineering problem

Heat integration reduces utility consumption by transferring heat between compatible process streams. Maximum heat recovery depends on supply and target temperatures, stream heat-capacity flow rates, minimum approach temperature, fouling and heat exchanger area. A larger exchanger does not remove all temperature-approach constraints.

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 heat recovery and exchanger networks indicates a specific decision lens within plant integration. 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 constant capacity rates and a countercurrent exchanger, Q = ε Cmin(Th,in−Tc,in), where ε is computed by NTU-effectiveness formulas; NTU = UA/Cmin. In a simplified classroom case Cmin≈Cmax, ε=NTU/(1+NTU).

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

With Cmin=Cmax=2 kW/K, inlet difference 100 K and UA=4 kW/K, compute NTU, ε and Q. Consider why increasing UA has diminishing marginal benefit.

Worked answer and interpretation

With equal heat-capacity rates C=2 kW/K and UA=4 kW/K, NTU=2 and ε=2/(1+2)=2/3. Predicted transfer is Q=(2/3)(2)(100)=133.33 kW, less than the maximum 200 kW. Extra area increases duty with diminishing marginal gain; this does not account for a complete pinch network.

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

Construct hot- and cold-stream tables and use pinch reasoning before placing individual exchangers. Compare energy targets with practical retrofit layout and materials. Distinguish heat duty from shaft work and steam utility demand.

Place the result in a real flowsheet context. A network model needs flow, quality, pressure, temperature and availability. A nominal surplus of material or energy can be unusable because of incompatible state conditions. Audit gross and net flows and avoid double counting of an exchanged stream. 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 calculated recoverable duty is not automatically economic once pressure drop, fouling, operability and capital are considered. The single exchanger model cannot optimize a whole HEN.

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, Heat exchanger effectiveness](../labs/lab-20.html), provides a separate numerical sensitivity exercise. Its governing relationship is NTU=UA/C; ε=NTU/(1+NTU); Q=ε C(Th−Tc). 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 Hydrogen generation, purification and allocation as prior context and Steam, water and power utility balances 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 heat recovery and exchanger networks 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 heat exchanger effectiveness 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 07 · Lesson 03 — Steam, water and power utility balances

[Unit map](../units/unit-07.html) · [Open numerical laboratory](../labs/lab-21.html) · [Assessment](../assessments/unit-07.html) · [Applied project](../projects/unit-07.html)

The engineering problem

Utility systems connect furnaces, boilers, cooling, water treatment, compressors and turbines. Fuel-gas balances depend on heating value, boiler efficiency and export or import. Steam network pressure levels matter because energy cannot be transferred without considering the quality or availability of that energy.

The practical starting point is not the equation by itself; it is a description of the process boundary. Write down the feed, product, recovered co-product, waste and possible accumulation terms before choosing an indicator. In this lesson, the title steam, water and power utility balances indicates a specific decision lens within plant integration. 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 simplified useful-boiler-energy balance is Quseful = η m_fuel LHV. For shaft work from an idealized turbine, W≈msteam(hin−hout)ηt; enthalpies must be evaluated for the states.

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 furnace burns 2 t/h of a notional fuel with LHV 40 MJ/kg and useful efficiency 82%. Calculate useful MW and list the combustion and heat-loss measurements needed for validation.

Worked answer and interpretation

Fuel mass flow 2 t/h is 2000 kg/h. Thermal input =2000×40=80,000 MJ/h. Useful heat at 82% is 65,600 MJ/h, or 65,600/3600≈18.22 MW. This excludes steam-side quality, exhaust conditions and distribution losses, and it is not sufficient for boiler or furnace sizing.

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

Map utility headers and account for condensate return, blowdown and make-up water. Include emissions, instrumentation and loss measurements in efficiency evaluation. Use matching energy and time units on all flows.

Place the result in a real flowsheet context. A network model needs flow, quality, pressure, temperature and availability. A nominal surplus of material or energy can be unusable because of incompatible state conditions. Audit gross and net flows and avoid double counting of an exchanged stream. 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 single efficiency is not enough for steam-system design. Heat loss, combustion excess air, turbine moisture and pressure drops require equipment-specific data.

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, Fuel-carbon direct emissions](../labs/lab-21.html), provides a separate numerical sensitivity exercise. Its governing relationship is mCO₂=mFuel wC fox(44/12). 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 Heat recovery and exchanger networks as prior context and Direct emissions and carbon inventories as a subsequent design issue. This linkage should be causal, not merely a sequence of chapter names.

Independent checkpoints

1. Sketch the process boundary for steam, water and power utility 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 fuel-carbon direct emissions 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 07 · Lesson 04 — Direct emissions and carbon inventories

[Unit map](../units/unit-07.html) · [Open numerical laboratory](../labs/lab-21.html) · [Assessment](../assessments/unit-07.html) · [Applied project](../projects/unit-07.html)

The engineering problem

Fuels and process chemistry generate direct emissions; refinery inventories also include flares, vents, fugitive sources and imported energy depending on scope. A boundary declaration is essential before comparing plants or interventions. Carbon dioxide from full oxidation of fuel carbon is a stoichiometric calculation, not a total life-cycle analysis.

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 direct emissions and carbon inventories indicates a specific decision lens within plant integration. 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 fuel mass m, carbon mass fraction wC and oxidized fraction f, emitted CO₂ mass mCO2 = m wC f(44/12). The ratio converts carbon mass to CO₂ mass under the specified chemical assumption. Other greenhouse gases require separate species accounting.

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 10 t/h model fuel at 85% carbon with 99% complete carbon oxidation, calculate CO₂ t/h. Explain which additional sources a plant inventory would include.

Worked answer and interpretation

Fuel carbon flow =10×0.85=8.5 t C/h. Oxidized carbon =8.5×0.99=8.415 t C/h, giving 8.415×44/12≈30.86 t CO₂/h. This is direct stoichiometric fuel-carbon CO₂ under the given convention; it excludes purchased electricity, non-CO₂ combustion products and separate flare or process sources.

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 fuel by source, carbon content, oxidation and meters; reconcile annualized inventories with operating events. Report direct Scope 1 emissions separately from purchased-energy and downstream product emissions.

Place the result in a real flowsheet context. A network model needs flow, quality, pressure, temperature and availability. A nominal surplus of material or energy can be unusable because of incompatible state conditions. Audit gross and net flows and avoid double counting of an exchanged stream. 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 low direct-emissions number can be obtained by exporting a high-energy intermediate; this may relocate emissions beyond the chosen boundary rather than reduce total climate impact.

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, Fuel-carbon direct emissions](../labs/lab-21.html), provides a separate numerical sensitivity exercise. Its governing relationship is mCO₂=mFuel wC fox(44/12). The laboratory is connected to this lesson through its unit-level concepts, but it may explore a different variable from the preceding worked example. Check its JSON parameter definitions, alter one input at a time and export the sampled curve to CSV. Compare two cases by recomputing the equation manually; document the difference between software correctness and physical validity.

Before declaring completion, articulate these four results in your own words: the stream or specimen under study, the dimension and reporting basis of the output, the reason for the sign of its sensitivity, and a specific observation that could disconfirm the model. Relate the lesson to Steam, water and power utility balances as prior context and Catalyst activity and regeneration cycles 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 direct emissions and carbon inventories 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 fuel-carbon direct emissions 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 07 applied project — Plant integration

[Unit 07](../units/unit-07.html) · [Book projects](../index.html)

Commissioning question

A fictional integrated refinery-and-petrochemicals teaching facility is reviewing its plant integration 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: Close resource balances across processing units, energy networks, utilities and emissions boundaries.

Refinery optimization crosses unit limits. A proposed yield increase changes the hydrogen, steam, cooling, wastewater, fuel-gas and carbon balances. The right system boundary makes waste heat and off-gas visible; the wrong one can move impacts from one accounting line to another.

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 Hydrogen generation, purification and allocation, Heat recovery and exchanger networks, Steam, water and power utility balances, Direct emissions and carbon inventories. 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 19: Hydrogen availability network](../labs/lab-19.html), [lab 20: Heat exchanger effectiveness](../labs/lab-20.html), [lab 21: Fuel-carbon direct emissions](../labs/lab-21.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

Distinguish gross from net energy, mass from purity of hydrogen, and direct process emissions from downstream life-cycle emissions. 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 13: Steam cracking ethylene selectivity

[Open lab in the browser](lab-13.html) · [Unit 05](../units/unit-05.html)

Engineering purpose

Reveal the competition between increased feed conversion and declining desired selectivity. The selected input is intentionally a one-variable exploratory slice. Move one setting at a time, check whether the displayed rate or fraction remains physically meaningful, and compare the curve against the conservation requirements of the process. The exercise is designed to show sensitivity and falsifiability, not to choose equipment sizes or plant operating conditions.

Equations and units

X=1−exp(−kτ); S=0.55 exp(−0.25X); Yethylene=X S

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

Procedure and recorded evidence

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

Investigation

Scan residence and explain why recovered ethylene differs from the reactor yield. 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 detailed radical mechanism, furnace heat transfer or coke. 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 14: Aromatics extraction recovery

[Open lab in the browser](lab-14.html) · [Unit 05](../units/unit-05.html)

Engineering purpose

Apply one-stage ideal distribution between raffinate and solvent-rich phases. 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

R=K(S/F)/(1+K(S/F))

The result is reported as % recovery. 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

Calculate the solvent increase required to exceed 80% single-stage recovery. 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

Fixed distribution coefficient; does not assess selectivity or solvent regeneration. 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 07 assessment — Plant integration

[Return to unit](../units/unit-07.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.

Hydrogen generation, purification and allocation

Question 01 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — A 1000 kg/h stream is 80 mass% H₂ and a 500 kg/h stream is 50 mass% H₂. Compare the total contained H₂ with demand of 1200 kg/h, then state why direct connection may still be infeasible. — 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 hydrogen generation, purification and allocation. 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 Treating all hydrogen in low-purity gas as immediately usable can be wrong. Compression and purification can reduce net benefit or make a nominal surplus unusable. 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 hydrogen generation, purification and allocation. Use this practice context: Build a plant-wide table of sources, sinks, purges and compressor requirements; use conservative purity envelopes. Compare recovery upgrades with make-up production using utility and equipment constraints. 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.

Heat recovery and exchanger networks

Question 05 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — With Cmin=Cmax=2 kW/K, inlet difference 100 K and UA=4 kW/K, compute NTU, ε and Q. Consider why increasing UA has diminishing marginal benefit. — 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 heat recovery and exchanger networks. 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 calculated recoverable duty is not automatically economic once pressure drop, fouling, operability and capital are considered. The single exchanger model cannot optimize a whole HEN. 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 heat recovery and exchanger networks. Use this practice context: Construct hot- and cold-stream tables and use pinch reasoning before placing individual exchangers. Compare energy targets with practical retrofit layout and materials. Distinguish heat duty from shaft work and steam utility demand. 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.

Steam, water and power utility balances

Question 09 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — A furnace burns 2 t/h of a notional fuel with LHV 40 MJ/kg and useful efficiency 82%. Calculate useful MW and list the combustion and heat-loss measurements needed for validation. — 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 steam, water and power utility 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 11 — Challenge the physical model

Consider the assumption in the lesson that A single efficiency is not enough for steam-system design. Heat loss, combustion excess air, turbine moisture and pressure drops require equipment-specific data. 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 steam, water and power utility balances. Use this practice context: Map utility headers and account for condensate return, blowdown and make-up water. Include emissions, instrumentation and loss measurements in efficiency evaluation. Use matching energy and time units on all flows. 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.

Direct emissions and carbon inventories

Question 13 — Reconstruct the quantitative link

Given the synthetic case posed in the lesson — For 10 t/h model fuel at 85% carbon with 99% complete carbon oxidation, calculate CO₂ t/h. Explain which additional sources a plant inventory would include. — 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 direct emissions and carbon inventories. 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 low direct-emissions number can be obtained by exporting a high-energy intermediate; this may relocate emissions beyond the chosen boundary rather than reduce total climate impact. 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 direct emissions and carbon inventories. Use this practice context: Track fuel by source, carbon content, oxidation and meters; reconcile annualized inventories with operating events. Report direct Scope 1 emissions separately from purchased-energy and downstream product emissions. 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.