Multiple Reactions, Yield and Selectivity

Scope: Parallel reactions, series reactions, selectivity, yield.

Competencies

By the end of this unit, a reader should translate an operating observation into a defensible model, solve a numerical case using consistent units, identify the most influential assumption, and explain what evidence would invalidate the prediction. All calculations are teaching examples unless separately identified as standards-compliant design.

Unit learning sequence

• Lesson 1: Parallel reaction networks
• Lesson 2: Consecutive A-to-B-to-C reactions
• Lesson 3: Yield, selectivity and conversion
• Lesson 4: Feed policy for selectivity control

Applied design studio

Selectivity and production compromise. Analyze competing desired and side reactions with different concentration exponents. Develop concentration and addition policies; compare instantaneous selectivity against integrated product yield. Include disposal, temperature control and recovery costs rather than maximizing a dimensionless selectivity in isolation.

Measurement and reporting quality

A credible laboratory report separates raw data, corrected data, numerical predictions and observations. Preserve the original concentration basis and initial conditions. Label all time axes and distinguish a measured temperature from an assumed constant. Provide an uncertainty interval or at least a sensitivity range for the parameter controlling the decision. For safe desk exercises synthetic data are acceptable if labeled as such. Avoid suggesting unsupervised hazardous experiments or relying on classroom calculations for relief sizing.

Lesson 1: Parallel reaction networks

Read [full lesson](../lessons/unit-05-lesson-01.html). Core equation: S_{D/U} = r_D/r_U.

Lesson 2: Consecutive A-to-B-to-C reactions

Read [full lesson](../lessons/unit-05-lesson-02.html). Core equation: C_B/C_{A0} = k_1(e^{-k_1t}-e^{-k_2t})/(k_2-k_1).

Lesson 3: Yield, selectivity and conversion

Read [full lesson](../lessons/unit-05-lesson-03.html). Core equation: Y_{B/A0}=N_B,formed/N_{A0}; S_{B/U}=N_B/N_U.

Lesson 4: Feed policy for selectivity control

Read [full lesson](../lessons/unit-05-lesson-04.html). Core equation: r_D/r_U=(k_D/k_U) C_A^{m_D-m_U}.

Unit 5, Lesson 1 — Parallel reaction networks

Scope: Multiple reactions. Prerequisites: chemical material balances, algebra, introductory calculus and unit conversions.

Physical model and meaning

Desired and undesired products may compete for the same reactant; rates depend on concentrations and often temperature. In the present topic, parallel reaction networks is an engineering interpretation problem before it is an algebra problem. Write the species, the observable state, the system boundary, and the governing time or length scale. The underlying quantity should be measured or inferred on an explicit basis. A change in what is held constant—reactor volume, inlet molar flow, heat capacity or concentration basis—can change the correct equation even when the equipment looks similar.

Use the working relationship S_{D/U} = r_D/r_U. First identify the independent variable and the dependent response. State whether it represents a local rate, an integrated outcome, or a steady-state closure condition. Perform a dimensional check before substituting numbers. For a measured plant variable, distinguish an instrument reading from a property calculated by a constitutive expression. In particular, a model may be exact inside an idealization yet wrong when its boundary conditions fail.

Process context and a falsifiable claim

A desired first-order path competes with an undesired second-order path. Evaluate the effect of dilution on instantaneous selectivity and productivity together. A falsifiable statement predicts how the measured response changes under a controlled, safe perturbation. Select one operating variable and hold the competing causes approximately constant. Write down what should happen if the equation is valid, what opposite observation would reject the assumption, and what additional sensor or sampling measurement can separate the explanations. In kinetic work, a mismatch between prediction and measurement may reflect a bad rate law, nonuniform temperature, nonideal flow, unrecognized side reaction, or a sampling artefact. Check those mechanisms independently rather than adjusting one fitted parameter until the chart looks plausible.

The practical question is not simply whether a numerical answer can be calculated. It is whether the proposed intervention changes the relevant physical mechanism and whether the predicted magnitude is large relative to instrument uncertainty and normal process variation. A temperature variation, for example, may alter both kinetics and properties. A flow variation may change residence time, heat removal, and mixing simultaneously. A careful experiment identifies these confounders.

Worked engineering example

Given. Parallel routes A→D and A→U have r_D=k_D C_A and r_U=k_U C_A²; k_D=0.5 min⁻¹, k_U=0.1 L mol⁻¹ min⁻¹.

Solution. At C_A=2 mol L⁻¹, instantaneous S_D/U=0.5/(0.1×2)=2.5. At C_A=1 mol L⁻¹, S_D/U=5, but overall throughput and conversion must also be assessed.

Interpretation. This numerical example is valid only within its stated assumptions and unit system. Carry at least two plausible significant digits through intermediate steps, then round to the resolution of the input evidence. If experimental observations differ, report the difference before modifying the calculation. Check that all flows are on comparable molar bases and that any time units in a rate constant are consistent with the residence or observation time used.

Four checks before accepting the result

1. Relative rate exponents. Identify exactly which measurement or modeling choice controls this feature. Explain its physical role, record the correct units, and consider whether an independent observation could confirm it. A single agreement at one operating point does not demonstrate that the feature is represented correctly across the entire range.

2. Dilution and productivity. Ask what would change if this effect were twice as important as assumed. A meaningful sensitivity calculation changes one parameter while keeping the process basis fixed, then reports both the numerical response and any violated constraint. Include the consequence for experiment design.

3. Kinetic temperature sensitivity. Separate information actually measured from information embedded in a model. A fitted coefficient may compensate for an omitted physical mechanism. Check whether different candidate models predict measurably different responses over the available operating range.

4. Product recovery penalty. Revisit the design decision after accounting for uncertainty. Where a limit is approached, an apparently precise result must not justify operating beyond validated data. Keep a record of the parameter set and the approximation used to reach each conclusion.

Limits and engineering judgement

High selectivity can coincide with low conversion and large recovery costs. When this limitation is significant, do not conceal it in a footnote: label the specific prediction as a screening estimate and state what would be required for a validated design. A reactor choice depends on chemistry, phase behavior, heat exchange, material compatibility, sensor reliability and operator response. No single idealized expression can substitute for thermal-hazard testing, validated kinetic data or codes applicable to the actual facility.

Extension for the reader. Construct a two-case comparison: one case follows the stated ideal assumptions; the other changes the most credible violated assumption. Sketch the expected shape of the dependent variable versus the relevant input. If the shape is qualitatively different, propose an experiment that will tell the models apart. Document what new evidence would make you reverse the original recommendation.

Independent problems and answer guidance

Q1. For parallel reaction networks, explain the effect of relative rate exponents on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate relative rate exponents as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For parallel reaction networks, explain the effect of dilution and productivity on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate dilution and productivity as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For parallel reaction networks, explain the effect of kinetic temperature sensitivity on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate kinetic temperature sensitivity as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For parallel reaction networks, explain the effect of product recovery penalty on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate product recovery penalty as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Learning evidence

Submit a one-page assumptions register, unit-consistent calculation, sensitivity plot and model rejection test. The quality criterion is not a single memorized numerical answer: it is the ability to explain why the conclusion may change under an independently observable perturbation.

Unit 5, Lesson 2 — Consecutive A-to-B-to-C reactions

Scope: Multiple reactions. Prerequisites: chemical material balances, algebra, introductory calculus and unit conversions.

Physical model and meaning

An intermediate product rises and later declines because its formation and consumption operate on different time scales. In the present topic, consecutive a-to-b-to-c reactions is an engineering interpretation problem before it is an algebra problem. Write the species, the observable state, the system boundary, and the governing time or length scale. The underlying quantity should be measured or inferred on an explicit basis. A change in what is held constant—reactor volume, inlet molar flow, heat capacity or concentration basis—can change the correct equation even when the equipment looks similar.

Use the working relationship C_B/C_{A0} = k_1(e^{-k_1t}-e^{-k_2t})/(k_2-k_1). First identify the independent variable and the dependent response. State whether it represents a local rate, an integrated outcome, or a steady-state closure condition. Perform a dimensional check before substituting numbers. For a measured plant variable, distinguish an instrument reading from a property calculated by a constitutive expression. In particular, a model may be exact inside an idealization yet wrong when its boundary conditions fail.

Process context and a falsifiable claim

Select batch hold time to maximize B under constant-volume isothermal first-order kinetics; compare endpoint to shorter residence operation. A falsifiable statement predicts how the measured response changes under a controlled, safe perturbation. Select one operating variable and hold the competing causes approximately constant. Write down what should happen if the equation is valid, what opposite observation would reject the assumption, and what additional sensor or sampling measurement can separate the explanations. In kinetic work, a mismatch between prediction and measurement may reflect a bad rate law, nonuniform temperature, nonideal flow, unrecognized side reaction, or a sampling artefact. Check those mechanisms independently rather than adjusting one fitted parameter until the chart looks plausible.

The practical question is not simply whether a numerical answer can be calculated. It is whether the proposed intervention changes the relevant physical mechanism and whether the predicted magnitude is large relative to instrument uncertainty and normal process variation. A temperature variation, for example, may alter both kinetics and properties. A flow variation may change residence time, heat removal, and mixing simultaneously. A careful experiment identifies these confounders.

Worked engineering example

Given. Consecutive first-order reactions have k₁=0.40 and k₂=0.10 min⁻¹; initial C_A=1 mol L⁻¹, t=4 min.

Solution. C_B=[0.40/(0.10−0.40)](exp(−1.6)−exp(−0.4))≈0.6246 mol L⁻¹. This is intermediate concentration, not final yield of B after unlimited reaction time.

Interpretation. This numerical example is valid only within its stated assumptions and unit system. Carry at least two plausible significant digits through intermediate steps, then round to the resolution of the input evidence. If experimental observations differ, report the difference before modifying the calculation. Check that all flows are on comparable molar bases and that any time units in a rate constant are consistent with the residence or observation time used.

Four checks before accepting the result

1. Intermediate hold time. Identify exactly which measurement or modeling choice controls this feature. Explain its physical role, record the correct units, and consider whether an independent observation could confirm it. A single agreement at one operating point does not demonstrate that the feature is represented correctly across the entire range.

2. Equal-rate numerical limit. Ask what would change if this effect were twice as important as assumed. A meaningful sensitivity calculation changes one parameter while keeping the process basis fixed, then reports both the numerical response and any violated constraint. Include the consequence for experiment design.

3. Temperature-program impact. Separate information actually measured from information embedded in a model. A fitted coefficient may compensate for an omitted physical mechanism. Check whether different candidate models predict measurably different responses over the available operating range.

4. Downstream quench. Revisit the design decision after accounting for uncertainty. Where a limit is approached, an apparently precise result must not justify operating beyond validated data. Keep a record of the parameter set and the approximation used to reach each conclusion.

Limits and engineering judgement

For nearly equal rate constants use the analytic equal-rate limit rather than numerically subtracting close exponentials. When this limitation is significant, do not conceal it in a footnote: label the specific prediction as a screening estimate and state what would be required for a validated design. A reactor choice depends on chemistry, phase behavior, heat exchange, material compatibility, sensor reliability and operator response. No single idealized expression can substitute for thermal-hazard testing, validated kinetic data or codes applicable to the actual facility.

Extension for the reader. Construct a two-case comparison: one case follows the stated ideal assumptions; the other changes the most credible violated assumption. Sketch the expected shape of the dependent variable versus the relevant input. If the shape is qualitatively different, propose an experiment that will tell the models apart. Document what new evidence would make you reverse the original recommendation.

Independent problems and answer guidance

Q1. For consecutive a-to-b-to-c reactions, explain the effect of intermediate hold time on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate intermediate hold time as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For consecutive a-to-b-to-c reactions, explain the effect of equal-rate numerical limit on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate equal-rate numerical limit as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For consecutive a-to-b-to-c reactions, explain the effect of temperature-program impact on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate temperature-program impact as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For consecutive a-to-b-to-c reactions, explain the effect of downstream quench on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate downstream quench as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Learning evidence

Submit a one-page assumptions register, unit-consistent calculation, sensitivity plot and model rejection test. The quality criterion is not a single memorized numerical answer: it is the ability to explain why the conclusion may change under an independently observable perturbation.

Unit 5, Lesson 3 — Yield, selectivity and conversion

Scope: Multiple reactions. Prerequisites: chemical material balances, algebra, introductory calculus and unit conversions.

Physical model and meaning

Conversion measures reactant consumption; yield and selectivity measure how efficiently that consumption makes a desired product. In the present topic, yield, selectivity and conversion is an engineering interpretation problem before it is an algebra problem. Write the species, the observable state, the system boundary, and the governing time or length scale. The underlying quantity should be measured or inferred on an explicit basis. A change in what is held constant—reactor volume, inlet molar flow, heat capacity or concentration basis—can change the correct equation even when the equipment looks similar.

Use the working relationship Y_{B/A0}=N_B,formed/N_{A0}; S_{B/U}=N_B/N_U. First identify the independent variable and the dependent response. State whether it represents a local rate, an integrated outcome, or a steady-state closure condition. Perform a dimensional check before substituting numbers. For a measured plant variable, distinguish an instrument reading from a property calculated by a constitutive expression. In particular, a model may be exact inside an idealization yet wrong when its boundary conditions fail.

Process context and a falsifiable claim

A pilot reports 95% A conversion while producing mostly undesired material. Build a full mole-balance table before communicating performance. A falsifiable statement predicts how the measured response changes under a controlled, safe perturbation. Select one operating variable and hold the competing causes approximately constant. Write down what should happen if the equation is valid, what opposite observation would reject the assumption, and what additional sensor or sampling measurement can separate the explanations. In kinetic work, a mismatch between prediction and measurement may reflect a bad rate law, nonuniform temperature, nonideal flow, unrecognized side reaction, or a sampling artefact. Check those mechanisms independently rather than adjusting one fitted parameter until the chart looks plausible.

The practical question is not simply whether a numerical answer can be calculated. It is whether the proposed intervention changes the relevant physical mechanism and whether the predicted magnitude is large relative to instrument uncertainty and normal process variation. A temperature variation, for example, may alter both kinetics and properties. A flow variation may change residence time, heat removal, and mixing simultaneously. A careful experiment identifies these confounders.

Worked engineering example

Given. A fed batch starts with 100 mol A; 80 mol A reacts, producing 60 mol desired B and 20 mol undesired U.

Solution. Conversion is 0.80; B yield on initial A is 0.60; B selectivity on consumed A is 60/80=0.75; B/U ratio is 60/20=3.

Interpretation. This numerical example is valid only within its stated assumptions and unit system. Carry at least two plausible significant digits through intermediate steps, then round to the resolution of the input evidence. If experimental observations differ, report the difference before modifying the calculation. Check that all flows are on comparable molar bases and that any time units in a rate constant are consistent with the residence or observation time used.

Four checks before accepting the result

1. Conversion versus yield. Identify exactly which measurement or modeling choice controls this feature. Explain its physical role, record the correct units, and consider whether an independent observation could confirm it. A single agreement at one operating point does not demonstrate that the feature is represented correctly across the entire range.

2. Product mole basis. Ask what would change if this effect were twice as important as assumed. A meaningful sensitivity calculation changes one parameter while keeping the process basis fixed, then reports both the numerical response and any violated constraint. Include the consequence for experiment design.

3. Selectivity denominator. Separate information actually measured from information embedded in a model. A fitted coefficient may compensate for an omitted physical mechanism. Check whether different candidate models predict measurably different responses over the available operating range.

4. Independent assay validation. Revisit the design decision after accounting for uncertainty. Where a limit is approached, an apparently precise result must not justify operating beyond validated data. Keep a record of the parameter set and the approximation used to reach each conclusion.

Limits and engineering judgement

A selectivity ratio may become undefined if the undesired byproduct rate is zero; state the limit. When this limitation is significant, do not conceal it in a footnote: label the specific prediction as a screening estimate and state what would be required for a validated design. A reactor choice depends on chemistry, phase behavior, heat exchange, material compatibility, sensor reliability and operator response. No single idealized expression can substitute for thermal-hazard testing, validated kinetic data or codes applicable to the actual facility.

Extension for the reader. Construct a two-case comparison: one case follows the stated ideal assumptions; the other changes the most credible violated assumption. Sketch the expected shape of the dependent variable versus the relevant input. If the shape is qualitatively different, propose an experiment that will tell the models apart. Document what new evidence would make you reverse the original recommendation.

Independent problems and answer guidance

Q1. For yield, selectivity and conversion, explain the effect of conversion versus yield on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate conversion versus yield as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For yield, selectivity and conversion, explain the effect of product mole basis on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate product mole basis as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For yield, selectivity and conversion, explain the effect of selectivity denominator on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate selectivity denominator as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For yield, selectivity and conversion, explain the effect of independent assay validation on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate independent assay validation as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Learning evidence

Submit a one-page assumptions register, unit-consistent calculation, sensitivity plot and model rejection test. The quality criterion is not a single memorized numerical answer: it is the ability to explain why the conclusion may change under an independently observable perturbation.

Unit 5, Lesson 4 — Feed policy for selectivity control

Scope: Multiple reactions. Prerequisites: chemical material balances, algebra, introductory calculus and unit conversions.

Physical model and meaning

Semibatch dosing, dilution, temperature programming and reactor staging alter concentrations and therefore competing reaction rates. In the present topic, feed policy for selectivity control is an engineering interpretation problem before it is an algebra problem. Write the species, the observable state, the system boundary, and the governing time or length scale. The underlying quantity should be measured or inferred on an explicit basis. A change in what is held constant—reactor volume, inlet molar flow, heat capacity or concentration basis—can change the correct equation even when the equipment looks similar.

Use the working relationship r_D/r_U=(k_D/k_U) C_A^{m_D-m_U}. First identify the independent variable and the dependent response. State whether it represents a local rate, an integrated outcome, or a steady-state closure condition. Perform a dimensional check before substituting numbers. For a measured plant variable, distinguish an instrument reading from a property calculated by a constitutive expression. In particular, a model may be exact inside an idealization yet wrong when its boundary conditions fail.

Process context and a falsifiable claim

A toxic reactive feed can be metered gradually into a vessel to suppress high-concentration side reactions. Include accumulation and temperature excursions in proposed policy. A falsifiable statement predicts how the measured response changes under a controlled, safe perturbation. Select one operating variable and hold the competing causes approximately constant. Write down what should happen if the equation is valid, what opposite observation would reject the assumption, and what additional sensor or sampling measurement can separate the explanations. In kinetic work, a mismatch between prediction and measurement may reflect a bad rate law, nonuniform temperature, nonideal flow, unrecognized side reaction, or a sampling artefact. Check those mechanisms independently rather than adjusting one fitted parameter until the chart looks plausible.

The practical question is not simply whether a numerical answer can be calculated. It is whether the proposed intervention changes the relevant physical mechanism and whether the predicted magnitude is large relative to instrument uncertainty and normal process variation. A temperature variation, for example, may alter both kinetics and properties. A flow variation may change residence time, heat removal, and mixing simultaneously. A careful experiment identifies these confounders.

Worked engineering example

Given. For r_D∝C_A and r_U∝C_A², the concentration is reduced by half through feed dilution.

Solution. Instantaneous desired-to-undesired selectivity doubles (all else fixed). Desired formation rate also halves at unchanged volume, showing the trade-off between selectivity and productivity.

Interpretation. This numerical example is valid only within its stated assumptions and unit system. Carry at least two plausible significant digits through intermediate steps, then round to the resolution of the input evidence. If experimental observations differ, report the difference before modifying the calculation. Check that all flows are on comparable molar bases and that any time units in a rate constant are consistent with the residence or observation time used.

Four checks before accepting the result

1. Addition policy. Identify exactly which measurement or modeling choice controls this feature. Explain its physical role, record the correct units, and consider whether an independent observation could confirm it. A single agreement at one operating point does not demonstrate that the feature is represented correctly across the entire range.

2. Local hot spots. Ask what would change if this effect were twice as important as assumed. A meaningful sensitivity calculation changes one parameter while keeping the process basis fixed, then reports both the numerical response and any violated constraint. Include the consequence for experiment design.

3. Semibatch accumulation. Separate information actually measured from information embedded in a model. A fitted coefficient may compensate for an omitted physical mechanism. Check whether different candidate models predict measurably different responses over the available operating range.

4. Metering failure. Revisit the design decision after accounting for uncertainty. Where a limit is approached, an apparently precise result must not justify operating beyond validated data. Keep a record of the parameter set and the approximation used to reach each conclusion.

Limits and engineering judgement

A recipe that maximizes model selectivity may create unsafe inventory or mixing conditions. When this limitation is significant, do not conceal it in a footnote: label the specific prediction as a screening estimate and state what would be required for a validated design. A reactor choice depends on chemistry, phase behavior, heat exchange, material compatibility, sensor reliability and operator response. No single idealized expression can substitute for thermal-hazard testing, validated kinetic data or codes applicable to the actual facility.

Extension for the reader. Construct a two-case comparison: one case follows the stated ideal assumptions; the other changes the most credible violated assumption. Sketch the expected shape of the dependent variable versus the relevant input. If the shape is qualitatively different, propose an experiment that will tell the models apart. Document what new evidence would make you reverse the original recommendation.

Independent problems and answer guidance

Q1. For feed policy for selectivity control, explain the effect of addition policy on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate addition policy as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For feed policy for selectivity control, explain the effect of local hot spots on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate local hot spots as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For feed policy for selectivity control, explain the effect of semibatch accumulation on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate semibatch accumulation as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For feed policy for selectivity control, explain the effect of metering failure on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate metering failure as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Learning evidence

Submit a one-page assumptions register, unit-consistent calculation, sensitivity plot and model rejection test. The quality criterion is not a single memorized numerical answer: it is the ability to explain why the conclusion may change under an independently observable perturbation.

Unit 5 project — Selectivity and production compromise

Decision brief

Analyze competing desired and side reactions with different concentration exponents. Develop concentration and addition policies; compare instantaneous selectivity against integrated product yield. Include disposal, temperature control and recovery costs rather than maximizing a dimensionless selectivity in isolation.

Inputs and provenance

Use clearly labeled synthetic data or independently verified measurements. For kinetic data, provide temperature and concentration units and a method for estimating variability. For operating studies, identify volumetric flow reference states and a clearly bounded control volume. Each property value needs its source, temperature and composition. Do not use reaction safety screening as a substitute for a required hazard study.

Deliverables

1. A process flow schematic with each boundary, measured variable and manipulated control.
2. A transparent mathematical model: species balances, an energy balance where relevant, parameters and numerical solver tolerances.
3. At least two physically feasible alternatives evaluated on identical input and output bases.
4. Four numerical checks: conservation, dimensional consistency, a limiting case, and sensitivity to the most uncertain parameter.
5. A testable prediction about operation under a realistic perturbation, with a criterion that would reject the model.
6. A limitations register identifying missing kinetics, transport, physical-property and safeguards evidence.

Review questions

Explain why the selected architecture is robust to its dominant uncertainty. Identify an apparently attractive but misleading performance metric and calculate the consequence of improving it at the expense of another. Explain how a tracer experiment, thermal test, feed assay or controlled startup could resolve a key uncertainty. Finally, state why the desk-study result must not authorize equipment operation or process-safety decisions.

Suggested evaluation rubric

Mass/energy accounting 25%; model assumptions and evidence 20%; correct calculations 20%; exploration of alternatives 15%; uncertainty and limitations 15%; readable reports and reproducibility 5%.

Unit 5 — Assessment: Multiple reactions

All 16 questions require an explanation of the physical premise, not only a final number. Provide units and state where a calculation is valid.

Lesson 1 — Parallel reaction networks

Q1. For parallel reaction networks, explain the effect of relative rate exponents on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate relative rate exponents as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For parallel reaction networks, explain the effect of dilution and productivity on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate dilution and productivity as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For parallel reaction networks, explain the effect of kinetic temperature sensitivity on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate kinetic temperature sensitivity as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For parallel reaction networks, explain the effect of product recovery penalty on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate product recovery penalty as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Lesson 2 — Consecutive A-to-B-to-C reactions

Q1. For consecutive a-to-b-to-c reactions, explain the effect of intermediate hold time on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate intermediate hold time as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For consecutive a-to-b-to-c reactions, explain the effect of equal-rate numerical limit on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate equal-rate numerical limit as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For consecutive a-to-b-to-c reactions, explain the effect of temperature-program impact on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate temperature-program impact as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For consecutive a-to-b-to-c reactions, explain the effect of downstream quench on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate downstream quench as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Lesson 3 — Yield, selectivity and conversion

Q1. For yield, selectivity and conversion, explain the effect of conversion versus yield on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate conversion versus yield as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For yield, selectivity and conversion, explain the effect of product mole basis on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate product mole basis as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For yield, selectivity and conversion, explain the effect of selectivity denominator on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate selectivity denominator as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For yield, selectivity and conversion, explain the effect of independent assay validation on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate independent assay validation as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.

Lesson 4 — Feed policy for selectivity control

Q1. For feed policy for selectivity control, explain the effect of addition policy on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate addition policy as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q2. For feed policy for selectivity control, explain the effect of local hot spots on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate local hot spots as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q3. For feed policy for selectivity control, explain the effect of semibatch accumulation on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate semibatch accumulation as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof. Q4. For feed policy for selectivity control, explain the effect of metering failure on the interpretation or validity of the calculated result. State an observable diagnostic, a limiting assumption and one safe engineering response.

Answer guide. Begin from the governing model and its units; isolate metering failure as an explicit hypothesis. Compare a controlled model prediction against a measured trend. Reject the hypothesis if the discrepancy is systematic and larger than credible uncertainty; otherwise collect additional evidence rather than treating a point estimate as proof.