Reactive Energy, Heats of Formation and Integrated Thermochemistry

Reaction heat, conversion, heat recovery and fuel use turn separate mass and energy calculations into a coupled process design problem.

Core learning goals

• Explain and apply Standard heats of reaction, including assumptions and independent verification.
• Explain and apply Adiabatic reactor temperature rise, including assumptions and independent verification.
• Explain and apply Fuel efficiency and utility accounting, including assumptions and independent verification.
• Explain and apply Balance reconciliation and uncertainty, including assumptions and independent verification.

Lessons and reading order

• [Lesson 7.1: Standard heats of reaction](../lessons/unit-07-lesson-01.html)
• [Lesson 7.2: Adiabatic reactor temperature rise](../lessons/unit-07-lesson-02.html)
• [Lesson 7.3: Fuel efficiency and utility accounting](../lessons/unit-07-lesson-03.html)
• [Lesson 7.4: Balance reconciliation and uncertainty](../lessons/unit-07-lesson-04.html)

Unit synthesis: identify what is known

Reaction heat, conversion, heat recovery and fuel use turn separate mass and energy calculations into a coupled process design problem. A strong solution begins with a process sketch and a stream table. Write values to a stated basis, mark all missing data, and calculate degrees of freedom before attempting numerical iteration. A flow diagram is useful only if the stream symbols and assumptions can be traced into actual balance equations. If an unknown variable is introduced to close a balance, explain what physical instrument or property measurement would establish it.

Connecting the four lessons

The first lesson establishes a local quantity or concept, while the later lessons expose how its interpretation changes with additional process complexity. For example, mass fractions remain valid for a blend but reacting compositions need generation terms; heat duties may be linear in temperature under constant heat capacity but nonlinear near a phase transition. Develop a single reference stream table and compare how each analytical step changes when more units are added.

Diagnostic exercise

Assume an otherwise plausible design produces an impossible negative outlet or a reported overall recovery of 105%. Instead of clipping the number, trace which equation or boundary was omitted or whose units were inconsistent. Check whether the solver was overdetermined by a redundant balance or underdetermined by a missing composition. Document the correction and rerun your limiting-case tests.

A second diagnostic asks you to separate measured and assumed quantities. Label uncertainties if known; do not attach precision to idealized coefficients. A balance audit should preserve the original measurements and record any reconciliation separately. This habit will become important in the integrated case studies and final project.

Unit completion exercise

Draw one example flowsheet for this unit and formulate an overall balance plus two meaningful independent additional equations, if the process contains enough components. State why each equation is independent. Determine what unknowns remain and choose the cheapest credible measurement to close the problem. Explain whether the modified process is still steady, and assess one alternative operating condition without assuming unchanged performance.

Unit 7.1: Standard heats of reaction

Book 2: Material and Energy Balances — Reactive energy and integrated process balances

What you will be able to do

Use stoichiometric coefficients to sum formation enthalpies at the same reference state. Interpret Delta_H_rxn=sum(nu_i*Delta_H_f,i) and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Thermal hazard screening for an exothermic conversion. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by standard heats of reaction. Use stoichiometric coefficients to sum formation enthalpies at the same reference state. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as Delta_H_rxn=sum(nu_i*Delta_H_f,i). Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use unit consistency as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. For CH4+2O2→CO2+2H2O(l), standard combustion enthalpy is approximately -890 kJ/mol methane under specified conditions. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. The sign and magnitude change if water exits as vapor rather than liquid. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Thermal hazard screening for an exothermic conversion. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in Delta_H_rxn=sum(nu_i*Delta_H_f,i) scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for standard heats of reaction; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: use stoichiometric coefficients to sum formation enthalpies at the same reference state?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: The sign and magnitude change if water exits as vapor rather than liquid. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 7.2: Adiabatic reactor temperature rise

Book 2: Material and Energy Balances — Reactive energy and integrated process balances

What you will be able to do

Sensible-heating capacity moderates exothermic reaction temperature rise. Interpret Delta_T≈-xiDelta_H_rxn/(sum_out n_iCp_i) for an adiabatic constant-Cp idealization and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Adiabatic stirred-reactor temperature screening. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by adiabatic reactor temperature rise. Sensible-heating capacity moderates exothermic reaction temperature rise. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as Delta_T≈-xiDelta_H_rxn/(sum_out n_iCp_i) for an adiabatic constant-Cp idealization. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use measurable stream composition as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. If 100 mol/s reacts with -50 kJ/mol and outlet heat capacity rate is 20 kJ/(s K), idealized temperature rise is 250 K. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. A constant-Cp prediction can become unreliable at large temperature rise or phase change. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Adiabatic stirred-reactor temperature screening. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in Delta_T≈-xiDelta_H_rxn/(sum_out n_iCp_i) for an adiabatic constant-Cp idealization scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for adiabatic reactor temperature rise; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: sensible-heating capacity moderates exothermic reaction temperature rise?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: A constant-Cp prediction can become unreliable at large temperature rise or phase change. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 7.3: Fuel efficiency and utility accounting

Book 2: Material and Energy Balances — Reactive energy and integrated process balances

What you will be able to do

Useful duty differs from fuel input because of stack and equipment losses. Interpret eta=Q_useful/Q_fuel; Q_fuel=Q_useful/eta and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Utility metering and boiler heat-loss diagnosis. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by fuel efficiency and utility accounting. Useful duty differs from fuel input because of stack and equipment losses. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as eta=Q_useful/Q_fuel; Q_fuel=Q_useful/eta. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use physical limit cases as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. A boiler delivering 8 MW steam duty at 80% efficiency requires 10 MW fuel heating-value input. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. Specify higher or lower heating value and whether condensation heat is recovered. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Utility metering and boiler heat-loss diagnosis. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in eta=Q_useful/Q_fuel; Q_fuel=Q_useful/eta scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for fuel efficiency and utility accounting; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: useful duty differs from fuel input because of stack and equipment losses?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: Specify higher or lower heating value and whether condensation heat is recovered. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 7.4: Balance reconciliation and uncertainty

Book 2: Material and Energy Balances — Reactive energy and integrated process balances

What you will be able to do

A numerically closed model can still be physically wrong if assumptions are untested. Interpret min sum_i((measured_i-estimated_i)/sigma_i)^2 subject to conservation constraints and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Cross-check feed metering, product weighing and inventory changes. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by balance reconciliation and uncertainty. A numerically closed model can still be physically wrong if assumptions are untested. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as min sum_i((measured_i-estimated_i)/sigma_i)^2 subject to conservation constraints. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use independent balance closure as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. If measured inlet is 100±2 kg/h and outlet is 97±3 kg/h, the 3 kg/h difference is not by itself proof of a leak. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. Never erase residuals by adjusting the least trusted instrument without investigating bias and boundary omissions. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Cross-check feed metering, product weighing and inventory changes. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in min sum_i((measured_i-estimated_i)/sigma_i)^2 subject to conservation constraints scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for balance reconciliation and uncertainty; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: a numerically closed model can still be physically wrong if assumptions are untested?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: Never erase residuals by adjusting the least trusted instrument without investigating bias and boundary omissions. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Applied project 7: Exothermic reactor: competing energy estimates

Scenario and process objective

A demonstration reactor accepts 2 kmol/h of reactive material. At nominal conversion 65%, the standard exothermic reaction heat is estimated as 65 MJ per kmol reacted. Product flow has an estimated sensible heat-capacity rate of 0.25 MJ/(h K). A junior designer predicts a negligible temperature rise by accidentally dividing kJ by MJ and does not consider latent heat or losses.

The project must be documented as a sequence of claims: identify what conservation enforces, which property data are assumed, which quantities are operator observations, and which decisions remain uncertain. Prepare a separate stream table for every external feed or outlet. Do not insert convenient values for missing streams and then present the case as uniquely solved. A correctly identified underdetermined model is more valuable than an unjustified numerical answer.

Calculation and reference result

Reacted material is 1.3 kmol/h, giving thermal release 84.5 MJ/h under the stated basis. If perfectly adiabatic and if the assumed outlet heat-capacity rate remains constant, the estimated temperature rise is 84.5/0.25=338 K. This is large enough to make a constant-property assumption questionable; it is not a safe operating prediction.

The figures above are idealized training values; they are not operational measurements. Repeat the calculation independently using base SI units and show at least one back-substitution into the original overall or species balance. Keep dimensional conversions visible, especially if a heat rate passes between kJ/h and kW or a composition passes between percent and fraction.

Model criticism and operating context

Actual reaction rate depends on temperature and feed, and high heat release may cause thermal runaway where kinetics and heat removal interact. Such hazards need formal process safety analysis, validated kinetics, appropriate design standards and qualified engineering review. This book deliberately does not specify safe reactor sizing.

A design report needs a statement of operating range and expected effects that the simplified equations leave out. For example, thermodynamic equilibrium may be inappropriate during a rapid transient; a nominal heat-transfer coefficient may depend on fouling or regime; a flow meter may give an average that is misaligned with an inventory sampling time. Identify which omitted effect could reverse the preferred operating decision.

Required investigation

Compare the model temperature rise for conversion 20% through 80% and propose measurements required for a rigorous nonisothermal reactor model. Explain why adding a heat-removal term without measuring its dependence on temperature does not close a safety analysis.

Provide a graphical sensitivity study with clearly labeled axes and units. Use at least two independent checks on the reported values. One check must be a conservation identity and the other a dimensional, physical-bounds, or alternative-method check. If the case is not fully determined, specify the least expensive measurement that would make the next calculation defensible, and quantify how measurement uncertainty could influence the decision.

Extension: implementation and quality assurance

Design a two-stage implementation plan: first, a low-cost experiment or audit, and second, a revised model calibrated with those observations. Decide how you would document instrumentation, calibration, sampling and data provenance. Provide a concise statement of operational risks that would prevent deployment of the model without expert supervision.

Decision memo template

• What is known: state the measured feed and product values, date range, units and calculation basis.
• What is calculated: identify conserved totals, composition conversions and any heat duty.
• What is assumed: list ideal-gas behavior, perfect mixing, constant heat capacity, reaction completion or transfer efficiency only if used.
• What remains uncertain: name unmeasured streams, material properties or error correlations.
• What to do next: propose a specific measurement and the change in decision it could permit.

Questions for viva or peer discussion

1. Which equation would become invalid if inventory changed over the measurement window?
2. Can a numerically closed overall mass balance conceal a large component imbalance? Construct an example.
3. What is the most dangerous units mistake for this case, and what magnitude would it introduce?
4. Explain the effect of a 10% feed increase on both production and utility rates, including capacity limits.
5. What evidence would allow a simplified teaching model to support a plant engineering decision?

Assessment — Unit 7: Reactive energy and integrated process balances

These questions demand a calculation or a defended explanation. State units and assumptions for every numerical answer.

Topic 7.1: Standard heats of reaction

1. Derivation. Build a balance for: Thermal hazard screening for an exothermic conversion. Derive the expression `Delta_H_rxn=sum(nu_i*Delta_H_f,i)` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: For CH4+2O2→CO2+2H2O(l), standard combustion enthalpy is approximately -890 kJ/mol methane under specified conditions. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: The sign and magnitude change if water exits as vapor rather than liquid. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 7.2: Adiabatic reactor temperature rise

1. Derivation. Build a balance for: Adiabatic stirred-reactor temperature screening. Derive the expression `Delta_T≈-xi*Delta_H_rxn/(sum_out n_i*Cp_i) for an adiabatic constant-Cp idealization` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: If 100 mol/s reacts with -50 kJ/mol and outlet heat capacity rate is 20 kJ/(s K), idealized temperature rise is 250 K. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: A constant-Cp prediction can become unreliable at large temperature rise or phase change. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 7.3: Fuel efficiency and utility accounting

1. Derivation. Build a balance for: Utility metering and boiler heat-loss diagnosis. Derive the expression `eta=Q_useful/Q_fuel; Q_fuel=Q_useful/eta` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: A boiler delivering 8 MW steam duty at 80% efficiency requires 10 MW fuel heating-value input. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: Specify higher or lower heating value and whether condensation heat is recovered. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 7.4: Balance reconciliation and uncertainty

1. Derivation. Build a balance for: Cross-check feed metering, product weighing and inventory changes. Derive the expression `min sum_i((measured_i-estimated_i)/sigma_i)^2 subject to conservation constraints` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: If measured inlet is 100±2 kg/h and outlet is 97±3 kg/h, the 3 kg/h difference is not by itself proof of a leak. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: Never erase residuals by adjusting the least trusted instrument without investigating bias and boundary omissions. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Grading rubric

Award credit for a correctly defined boundary and flow basis (25%), an equation with independent unknowns (25%), numerical units and magnitude checks (20%), critical assumptions and uncertainty (20%), and readable presentation (10%). More digits are not a substitute for property data.