Process Concept and Route Screening

Design objective: Compare production paths using physically relevant evidence, not invented precision in a weighted score.

Common teaching scenario: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.

Unit-level engineering decision

The essential problem in this unit is not memorizing equations. It is forming a defensible decision from incomplete evidence. Compare production paths using physically relevant evidence, not invented precision in a weighted score. The case studies are synthetic; they provide a transparent set of inputs that can be checked without access to an operating facility. Before a numerical conclusion is adopted, identify the required physical evidence, constraints, and operating modes. Make clear whether the outcome is a conceptual screening result, a preliminary design basis, a vendor-specified rating, or a compliance decision. The four lessons examine distinct aspects of this decision.

Structured lesson sequence

1. [Reaction paths and conceptual chemistry](../lessons/unit-02-lesson-01.html)

Competing chemistry sets the theoretical ceiling on yield and waste before a flowsheet is drawn. Governing equation: selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths. Numerical benchmark: With k_P=0.6 h^-1 and k_W=0.2 h^-1, ideal parallel-path selectivity is 0.75; conversion is separate. Decision question: Route screening must distinguish a plausible lab reaction from an economically and operationally viable commercial process.

2. [Separation concepts and feasible recoveries](../lessons/unit-02-lesson-02.html)

Separation trains should be compared on achievable recovery, purity, energy and physical constraints. Governing equation: net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities. Numerical benchmark: For recovery fraction r=0.60 per ideal pass, three passes yield 93.6% recovery in this mathematical demonstration. Decision question: Before committing to a separation route, create a short experiment that could invalidate the estimated achievable recovery.

3. [Solvent, recycle and purge decisions](../lessons/unit-02-lesson-03.html)

A recycle reduces raw-material losses but can concentrate inerts and by-products. Governing equation: loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)]. Numerical benchmark: Fresh inert 1 t/h, recycle 0.8 and purge 0.1 imply a loop-equivalent inert flow of 3.571 t/h. Decision question: Choose the purge only after specifying which impurity sets the allowable concentration.

4. [Alternative ranking and decision gates](../lessons/unit-02-lesson-04.html)

A ranking should expose criteria and sensitivity; high scores must not mask fatal constraints. Governing equation: weighted benefit = Σ normalized criterion weight × evidence-supported score. Numerical benchmark: If two routes differ mainly in estimated utilities, test whether the preference survives a factor-of-two energy-cost change. Decision question: A route should advance only if its largest unresolved risk has a practical validation test.

Integrated design activity

Construct a compact design dossier for the following system: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. The dossier must contain a flowsheet or decision diagram, a variable and unit register, an assumption register, at least two checks based on first principles, a sensitivity chart from one of the interactive models, a documented failure case, and an explicit decision with a reversal condition. Begin with the minimum information needed to formulate the problem; do not assign invented precise values to unknown vendor or market inputs. When data is unavailable, use a marked synthetic scenario and report the evidence gap.

Evidence and model boundaries

Topic 1 — Reaction paths and conceptual chemistry. Keep mechanistic selectivity, product isolation recovery and saleable quality yield separate. The next evidence sources are bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance. Any screening estimate using selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 2 — Separation concepts and feasible recoveries. Do not claim purity improvement from a recovery-only equation. The next evidence sources are phase equilibrium, separation factors, product purity and pilot recovery data. Any screening estimate using net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 3 — Solvent, recycle and purge decisions. For a near-unity recycle fraction, small purge uncertainty dominates the loop inventory estimate. The next evidence sources are recycle composition analyses, impurity limits, filters and feed drift data. Any screening estimate using loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)] remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Topic 4 — Alternative ranking and decision gates. Treat safety disqualifiers and unverified intellectual-property restrictions as hard gates, not as low weighted points. The next evidence sources are expert review, route-test data, credible cost ranges and go/no-go thresholds. Any screening estimate using weighted benefit = Σ normalized criterion weight × evidence-supported score remains conditional until those inputs are independently confirmed. A graph can make sensitivity visible; it cannot supply absent physical evidence.

Unit laboratories

• [Lab 04: Parallel-route yield and selectivity](../labs/lab-04.html) — Screen a hypothetical A→P versus A→W first-order route.. Verification: P fraction must lie between 0 and 1 and is conversion times selectivity.

• [Lab 05: Recycle inert concentration](../labs/lab-05.html) — Investigate inert accumulation and purge sensitivity.. Verification: At zero recycle, loop inert must equal fresh inert; increasing purge reduces accumulation.

• [Lab 06: Successive ideal recovery](../labs/lab-06.html) — Idealized independent passes through a separation step.. Verification: Recovered target cannot exceed entering target and decreases when r decreases.

Unit review protocol

For each model, run default and altered cases. Check the governing relation algebraically for one point; verify dimensional consistency and domain validity; identify at least one limiting case; export a CSV and preserve the selected parameter settings in the report. A smooth graph can still be wrong, so treat independent calculations and physical evidence as separate gates. Before using the result outside a classroom, request suitable measured inputs, professional design reviews and applicable approvals.

[16-question assessment](../assessments/unit-02.html) · [Applied project](../projects/unit-02.html) · [Book contents](../index.html)

Unit 2 · Lesson 1: Reaction paths and conceptual chemistry

Learning pathway: [Process Concept and Route Screening](../units/unit-02.html) · [Simulation 04: Parallel-route yield and selectivity](../labs/lab-04.html) · [Assessment](../assessments/unit-02.html).

Engineering problem and conceptual boundary

Competing chemistry sets the theoretical ceiling on yield and waste before a flowsheet is drawn. The central design case for this part of the course is: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Route screening must distinguish a plausible lab reaction from an economically and operationally viable commercial process.

A rate-constant ratio is not generally constant across temperature, catalyst condition or concentration. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For reaction paths and conceptual chemistry, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: Keep mechanistic selectivity, product isolation recovery and saleable quality yield separate. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: With k_P=0.6 h^-1 and k_W=0.2 h^-1, ideal parallel-path selectivity is 0.75; conversion is separate. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for reaction paths and conceptual chemistry but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 04: Parallel-route yield and selectivity](../labs/lab-04.html). The implemented relation is Selectivity = kP/(kP+kW); conversion = 1 − exp[−(kP+kW)τ]. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: P fraction must lie between 0 and 1 and is conversion times selectivity. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Hold total k fixed while changing selectivity; which parameter changes process yield and which changes time to convert? The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Route screening must distinguish a plausible lab reaction from an economically and operationally viable commercial process. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: Keep mechanistic selectivity, product isolation recovery and saleable quality yield separate. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Only two parallel irreversible first-order routes, no heat effects, transport limits or changing catalyst activity. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for reaction paths and conceptual chemistry lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Reaction paths and conceptual chemistry.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: Keep mechanistic selectivity, product isolation recovery and saleable quality yield separate.
• I can run and explain the numerical limit test: P fraction must lie between 0 and 1 and is conversion times selectivity.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance

[Unit 2 overview](../units/unit-02.html) · [Lab 04](../labs/lab-04.html) · [Unit 2 assessment](../assessments/unit-02.html) · [Book contents](../index.html)

Unit 2 · Lesson 2: Separation concepts and feasible recoveries

Learning pathway: [Process Concept and Route Screening](../units/unit-02.html) · [Simulation 06: Successive ideal recovery](../labs/lab-06.html) · [Assessment](../assessments/unit-02.html).

Engineering problem and conceptual boundary

Separation trains should be compared on achievable recovery, purity, energy and physical constraints. The central design case for this part of the course is: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Before committing to a separation route, create a short experiment that could invalidate the estimated achievable recovery.

Sequential ideal recoveries assume identical separation opportunity at each pass, which real depleted streams usually violate. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For separation concepts and feasible recoveries, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: Do not claim purity improvement from a recovery-only equation. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: For recovery fraction r=0.60 per ideal pass, three passes yield 93.6% recovery in this mathematical demonstration. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for separation concepts and feasible recoveries but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 06: Successive ideal recovery](../labs/lab-06.html). The implemented relation is Recovery total = 1 − (1−r)^n. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: Recovered target cannot exceed entering target and decreases when r decreases. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Report both product recovery and unrecovered target at three versus six passes. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: phase equilibrium, separation factors, product purity and pilot recovery data. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Before committing to a separation route, create a short experiment that could invalidate the estimated achievable recovery. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: Do not claim purity improvement from a recovery-only equation. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: phase equilibrium, separation factors, product purity and pilot recovery data Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Assumes same independent fractional capture of what remains; purity and energy use are not predicted. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for separation concepts and feasible recoveries lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: phase equilibrium, separation factors, product purity and pilot recovery data. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Separation concepts and feasible recoveries.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: Do not claim purity improvement from a recovery-only equation.
• I can run and explain the numerical limit test: Recovered target cannot exceed entering target and decreases when r decreases.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: phase equilibrium, separation factors, product purity and pilot recovery data

[Unit 2 overview](../units/unit-02.html) · [Lab 06](../labs/lab-06.html) · [Unit 2 assessment](../assessments/unit-02.html) · [Book contents](../index.html)

Unit 2 · Lesson 3: Solvent, recycle and purge decisions

Learning pathway: [Process Concept and Route Screening](../units/unit-02.html) · [Simulation 05: Recycle inert concentration](../labs/lab-05.html) · [Assessment](../assessments/unit-02.html).

Engineering problem and conceptual boundary

A recycle reduces raw-material losses but can concentrate inerts and by-products. The central design case for this part of the course is: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: Choose the purge only after specifying which impurity sets the allowable concentration.

An inert mass-balance model cannot predict solvent compatibility, viscosity, fouling or thermodynamic separation. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)]. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For solvent, recycle and purge decisions, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: For a near-unity recycle fraction, small purge uncertainty dominates the loop inventory estimate. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: Fresh inert 1 t/h, recycle 0.8 and purge 0.1 imply a loop-equivalent inert flow of 3.571 t/h. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for solvent, recycle and purge decisions but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 05: Recycle inert concentration](../labs/lab-05.html). The implemented relation is Loop inert = fresh inert/[1−r(1−p)]. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: At zero recycle, loop inert must equal fresh inert; increasing purge reduces accumulation. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Try high recycle and near-zero purge; explain why a modest purge change matters strongly near the denominator limit. The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: recycle composition analyses, impurity limits, filters and feed drift data. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: Choose the purge only after specifying which impurity sets the allowable concentration. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: For a near-unity recycle fraction, small purge uncertainty dominates the loop inventory estimate. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: recycle composition analyses, impurity limits, filters and feed drift data Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Steady ideal inert only; not a chemical mixture separator or impurity safety limit. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for solvent, recycle and purge decisions lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: recycle composition analyses, impurity limits, filters and feed drift data. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)] is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Solvent, recycle and purge decisions.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: For a near-unity recycle fraction, small purge uncertainty dominates the loop inventory estimate.
• I can run and explain the numerical limit test: At zero recycle, loop inert must equal fresh inert; increasing purge reduces accumulation.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: recycle composition analyses, impurity limits, filters and feed drift data

[Unit 2 overview](../units/unit-02.html) · [Lab 05](../labs/lab-05.html) · [Unit 2 assessment](../assessments/unit-02.html) · [Book contents](../index.html)

Unit 2 · Lesson 4: Alternative ranking and decision gates

Learning pathway: [Process Concept and Route Screening](../units/unit-02.html) · [Simulation 04: Parallel-route yield and selectivity](../labs/lab-04.html) · [Assessment](../assessments/unit-02.html).

Engineering problem and conceptual boundary

A ranking should expose criteria and sensitivity; high scores must not mask fatal constraints. The central design case for this part of the course is: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. Design work should begin by deciding what the process is required to accomplish, what physical behavior is known, what remains an assumption, and which constraints make a candidate concept unacceptable. A calculated number that is not connected to a defined engineering decision has little project value. For this lesson the decision is: A route should advance only if its largest unresolved risk has a practical validation test.

Numerical weights are judgments; the calculation does not prove safety, legality or feasibility. Interpret that physical observation as a condition on the model rather than as a measured result. A screening model can provide a reliable direction of sensitivity without providing a trustworthy absolute plant rating. Before applying a particular numerical result, identify its process boundary, time basis, component definition and operating mode. A rate evaluated under steady conditions cannot represent a transient upset unless accumulation and duration are modeled explicitly.

Governing relationship and dimensional basis

The principal starting relationship is weighted benefit = Σ normalized criterion weight × evidence-supported score. Write out the quantities in this equation and ask which are independently specified and which are inferred from other assumptions. Check that both sides have compatible units. When an output is expressed as a fraction it must not be treated as a mass or molar rate without multiplying by an appropriate total flow. When a cost or duty is given per year, make the operating-hour and utilization basis visible; a nameplate rate alone does not produce an annual total.

For alternative ranking and decision gates, the model is deliberately formulated as a minimal relation. A relation can be algebraically correct but physically incomplete, because it omits phenomena that do not appear in its chosen boundary. The specific concern here is: Treat safety disqualifiers and unverified intellectual-property restrictions as hard gates, not as low weighted points. In a design review, show the equation as an auditable expression and keep the evidence for its coefficients separate from the mathematical logic. If an assumed parameter later changes, the calculation may need to be revisited across the entire flowsheet rather than edited only in one table.

Worked engineering check

Illustrative case, not plant measurement: If two routes differ mainly in estimated utilities, test whether the preference survives a factor-of-two energy-cost change. Copy the stated inputs into a notebook, calculate the result independently using the governing expression and retain enough significant digits to detect a balance error. When you write the result, distinguish an exact identity within the model from a rounded numerical example. For example, an exact component balance can hold to floating-point tolerance, while an empirical estimate of reaction behavior may be uncertain by orders of magnitude if fitted kinetics are unavailable.

Explain why the chosen arithmetic is useful for alternative ranking and decision gates but not sufficient for a detailed design decision. The calculation provides a specific benchmark for checking the interactive lab, not a guarantee that the input values are representative. If an initial calculation produces a result that contradicts expected physical bounds—such as composition outside the feed range, negative absolute inventory, positive losses with a perfect collection assumption, or implausible unit conversions—do not tune inputs simply to improve the display. Revisit the boundary and the assumption that creates the inconsistency.

Laboratory investigation with a falsifiable prediction

Open [Simulation 04: Parallel-route yield and selectivity](../labs/lab-04.html). The implemented relation is Selectivity = kP/(kP+kW); conversion = 1 − exp[−(kP+kW)τ]. Before moving a control, predict what will happen to the output when the dominant parameter increases. Move that parameter to a value roughly halfway between the default and one end of its permitted interval. Record the previous and revised numerical outputs, the units, and a one-sentence explanation based on the equation. Then test a second parameter that changes the trend or limits the conclusion.

Specific falsification task: P fraction must lie between 0 and 1 and is conversion times selectivity. If the code violates this check, the appropriate result is a failing test and a documented defect, not an attractive screenshot. Investigation prompt: Hold total k fixed while changing selectivity; which parameter changes process yield and which changes time to convert? The numerical lab is intentionally small enough to trace by hand; it should stimulate a quantitative question about process behavior rather than replace a commercial flowsheet simulator.

A defensible design record

For this lesson, create a one-page calculation note with: a clearly stated objective, a simple process or equipment boundary, all specified inputs including source and units, the model equation, the worked numeric output, one independent check, at least two changes of a parameter, and a decision with a stated uncertainty. The immediate evidence package to acquire is: expert review, route-test data, credible cost ranges and go/no-go thresholds. Label synthetic data plainly. Do not call an illustrative scenario a site survey, a vendor quotation, a laboratory result or a market forecast.

The most important decision consequence is: A route should advance only if its largest unresolved risk has a practical validation test. A useful design note therefore contains a condition under which the recommendation would reverse. For example, the preferred concept may change if an availability assumption falls, an energy price rises, a flow composition moves beyond a separation range, or the estimated installed cost is outside the available budget. A reviewer needs the reversal threshold or at least a targeted experiment, not an unconditional claim that the concept is optimal.

Failure modes, omissions and escalation

Failure mode 1 — invalid physical simplification: Treat safety disqualifiers and unverified intellectual-property restrictions as hard gates, not as low weighted points. If a physical mechanism outside the model dominates the real process, numerical refinement cannot rescue the conclusion. Failure mode 2 — missing input provenance: expert review, route-test data, credible cost ranges and go/no-go thresholds Without that evidence, parameter values remain unverified. Failure mode 3 — misuse of precision: a software result displayed to four decimals may still originate in an order-of-magnitude engineering assumption. Accuracy is controlled by evidence, not the number of digits shown.

Applicability boundary: Only two parallel irreversible first-order routes, no heat effects, transport limits or changing catalyst activity. This educational module does not size pressure vessels, specify safety instrumented functions, certify emissions compliance, supply construction documents or establish investment attractiveness. For an actual facility, relevant professional review, regulatory analysis, vendor thermal and mechanical design, and empirical validation are separate requirements that cannot be delegated to this one equation.

Independent study and examiner prompts

Conceptual: In what circumstances does the assumed relationship for alternative ranking and decision gates lose predictive value? Name one physical effect and one organizational or data-management effect. Quantitative: Reproduce the worked case with units and change one input by ten percent. State the sensitivity of the output, including whether a finite-difference result agrees with the local algebraic trend. Application: Relate the result to the unit case—A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.—and identify the critical tradeoff between an apparently favorable result and its implementation.

Critical appraisal: Draft the most persuasive argument against acting on this lesson’s estimate. Your argument must refer to evidence rather than taste. It should include at least one unavailable measurement from this list: expert review, route-test data, credible cost ranges and go/no-go thresholds. Then give the smallest practical study—vendor request, sample test, pilot run, site visit or model comparison—that could narrow the uncertainty. Communication: Write a two-sentence summary that separates a verified equation from a synthetic scenario assumption.

Short calculation audit for reviewers

Check that the supplied equation weighted benefit = Σ normalized criterion weight × evidence-supported score is the same one used in the laboratory, or state why the lab computes a related screening quantity rather than the entire model. Confirm that the active scenario does not violate stated slider ranges. Confirm that no unit conversion is silently required between mass flow, molar flow, volume, energy or currency. Separate conservation-law residuals from empirical-correlation fit errors. Keep the response to a failed check in the delivered report; an invalid baseline should not be silently replaced with a different input set.

Checklist for mastery

• I can define the process boundary and the measured or assumed quantities behind Alternative ranking and decision gates.
• I can reproduce the stated working example with units and without copying a displayed answer.
• I can name the main omitted mechanism: Treat safety disqualifiers and unverified intellectual-property restrictions as hard gates, not as low weighted points.
• I can run and explain the numerical limit test: P fraction must lie between 0 and 1 and is conversion times selectivity.
• I can distinguish a planning estimate from a mechanical, regulatory or safety approval.
• I can name the next evidence source: expert review, route-test data, credible cost ranges and go/no-go thresholds

[Unit 2 overview](../units/unit-02.html) · [Lab 04](../labs/lab-04.html) · [Unit 2 assessment](../assessments/unit-02.html) · [Book contents](../index.html)

Applied design project 2: Process Concept and Route Screening

Scenario: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.

Engineering goal: Compare production paths using physically relevant evidence, not invented precision in a weighted score.

Project brief and boundary

You are a junior design team preparing a conceptual recommendation for a supervised technical review. The project is not a request to produce construction-ready specifications. It asks whether a candidate concept merits a funded next study based on traceable evidence. Make one primary design decision linked to process concept and route screening and identify both how it could fail and what information is needed before capital is committed. Design responsibility, commercial feasibility, safety, permit requirements and site-specific code compliance remain independent gate reviews.

Task A — Form a reproducible design basis

A1. Reaction paths and conceptual chemistry: Competing chemistry sets the theoretical ceiling on yield and waste before a flowsheet is drawn. Start from selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths and reproduce the benchmark: With k_P=0.6 h^-1 and k_W=0.2 h^-1, ideal parallel-path selectivity is 0.75; conversion is separate. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance.

A2. Separation concepts and feasible recoveries: Separation trains should be compared on achievable recovery, purity, energy and physical constraints. Start from net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities and reproduce the benchmark: For recovery fraction r=0.60 per ideal pass, three passes yield 93.6% recovery in this mathematical demonstration. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: phase equilibrium, separation factors, product purity and pilot recovery data.

A3. Solvent, recycle and purge decisions: A recycle reduces raw-material losses but can concentrate inerts and by-products. Start from loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)] and reproduce the benchmark: Fresh inert 1 t/h, recycle 0.8 and purge 0.1 imply a loop-equivalent inert flow of 3.571 t/h. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: recycle composition analyses, impurity limits, filters and feed drift data.

A4. Alternative ranking and decision gates: A ranking should expose criteria and sensitivity; high scores must not mask fatal constraints. Start from weighted benefit = Σ normalized criterion weight × evidence-supported score and reproduce the benchmark: If two routes differ mainly in estimated utilities, test whether the preference survives a factor-of-two energy-cost change. Label numbers as synthetic, experimental, quoted or specified. Identify the actual evidence source required: expert review, route-test data, credible cost ranges and go/no-go thresholds.

Task B — Build a traceable numerical investigation

[Lab 04 — Parallel-route yield and selectivity](../labs/lab-04.html): Hold total k fixed while changing selectivity; which parameter changes process yield and which changes time to convert? Validate the bound: P fraction must lie between 0 and 1 and is conversion times selectivity. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

[Lab 05 — Recycle inert concentration](../labs/lab-05.html): Try high recycle and near-zero purge; explain why a modest purge change matters strongly near the denominator limit. Validate the bound: At zero recycle, loop inert must equal fresh inert; increasing purge reduces accumulation. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

[Lab 06 — Successive ideal recovery](../labs/lab-06.html): Report both product recovery and unrecovered target at three versus six passes. Validate the bound: Recovered target cannot exceed entering target and decreases when r decreases. Export the CSV and annotate which equation limits the model. Do not claim that an illustrative spreadsheet predicts a real plant.

Task C — Challenge the concept

Construct a short failure-first register with at least one physical failure, one commercial or cost failure, one operational difficulty and one missing-data risk. For process concept and route screening, list the observable sign of each problem, the assumption it challenges and the cheapest credible test that could expose it. A risk register without an assigned next action or a stop/go criterion is not a useful project deliverable. Distinguish a design variation from an independent protection measure and seek qualified safety review where warranted.

Task D — Submit an engineering decision pack

The pack contains: (1) design-basis sheet; (2) flowsheet or concept comparison; (3) numbered stream and parameter tables with units; (4) independent hand checks; (5) controlled simulation figures and exported CSV; (6) constraints and exclusions; (7) cost or utility sensitivity where relevant; (8) failure and uncertainty register; (9) recommendation with what evidence would reverse it; (10) references and revision log. Document whether assumptions are invented for pedagogy, grounded in a published reference, requested from a supplier, or measured. A professionally reviewed design would need additional engineering discipline sign-offs.

Acceptance test

A reviewer unfamiliar with your work should be able to reproduce a benchmark from the unit, locate the 3 related labs, see why the governing equations are dimensionally consistent, find at least one intentionally adverse case, and identify an unresolved assumption that could invalidate the proposed decision. The case is: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery. All evidence obtained and not obtained should be distinguishable. Do not present an unresolved conceptual model as an approved site or plant design.

[Unit notes](../units/unit-02.html) · [Unit assessment](../assessments/unit-02.html)

Unit 2 assessment — Process Concept and Route Screening

Context: A hypothetical A-to-P route competes with an unwanted A-to-W route, followed by product recovery.

Answer all sixteen multi-part problems. All illustrative figures are synthetic. Include units, inputs, methods, checking and limitations. Each problem should use a different numerical or investigative test; do not replace a requested calculation with a qualitative assertion.

Multi-part questions

Lesson 1: Reaction paths and conceptual chemistry

Q1 — First-principles reconstruction. Starting with the physical boundary discussed in Reaction paths and conceptual chemistry, derive or justify selectivity to P = k_P/(k_P+k_W) for two independent first-order parallel paths in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: With k_P=0.6 h^-1 and k_W=0.2 h^-1, ideal parallel-path selectivity is 0.75; conversion is separate. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q2 — Perturbation study. In [Lab 04](../labs/lab-04.html), take the baseline parameter set, vary Desired-path k through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q3 — Independent falsification. Test the assertion: P fraction must lie between 0 and 1 and is conversion times selectivity. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q4 — Evidence and decision memo. Write a 200–300-word decision note addressing: Route screening must distinguish a plausible lab reaction from an economically and operationally viable commercial process. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: bench reaction kinetics, impurity profiles and calorimetry appropriate to the substance. Discuss this known limitation: Keep mechanistic selectivity, product isolation recovery and saleable quality yield separate. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 2: Separation concepts and feasible recoveries

Q5 — First-principles reconstruction. Starting with the physical boundary discussed in Separation concepts and feasible recoveries, derive or justify net recovered P = P_in × (1 − (1−r)^n) for n ideal independent recovery opportunities in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: For recovery fraction r=0.60 per ideal pass, three passes yield 93.6% recovery in this mathematical demonstration. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q6 — Perturbation study. In [Lab 06](../labs/lab-06.html), take the baseline parameter set, vary Recovery per pass through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q7 — Independent falsification. Test the assertion: Recovered target cannot exceed entering target and decreases when r decreases. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q8 — Evidence and decision memo. Write a 200–300-word decision note addressing: Before committing to a separation route, create a short experiment that could invalidate the estimated achievable recovery. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: phase equilibrium, separation factors, product purity and pilot recovery data. Discuss this known limitation: Do not claim purity improvement from a recovery-only equation. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 3: Solvent, recycle and purge decisions

Q9 — First-principles reconstruction. Starting with the physical boundary discussed in Solvent, recycle and purge decisions, derive or justify loop inert input = fresh inert / [1 − recycle fraction × (1−purge fraction)] in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: Fresh inert 1 t/h, recycle 0.8 and purge 0.1 imply a loop-equivalent inert flow of 3.571 t/h. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q10 — Perturbation study. In [Lab 05](../labs/lab-05.html), take the baseline parameter set, vary Purge fraction through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q11 — Independent falsification. Test the assertion: At zero recycle, loop inert must equal fresh inert; increasing purge reduces accumulation. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q12 — Evidence and decision memo. Write a 200–300-word decision note addressing: Choose the purge only after specifying which impurity sets the allowable concentration. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: recycle composition analyses, impurity limits, filters and feed drift data. Discuss this known limitation: For a near-unity recycle fraction, small purge uncertainty dominates the loop inventory estimate. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Lesson 4: Alternative ranking and decision gates

Q13 — First-principles reconstruction. Starting with the physical boundary discussed in Alternative ranking and decision gates, derive or justify weighted benefit = Σ normalized criterion weight × evidence-supported score in the declared setting. Give every variable and its dimension. Reproduce the supplied check case: If two routes differ mainly in estimated utilities, test whether the preference survives a factor-of-two energy-cost change. Identify whether your result is a material balance, mathematical correlation, operating target or economic scenario. Explain why this classification controls how the result can be used.

Q14 — Perturbation study. In [Lab 04](../labs/lab-04.html), take the baseline parameter set, vary Desired-path k through at least five values, and export the resulting CSV. Compute one finite-difference sensitivity from the tabulated points. Predict and explain the direction of change from the model equation before looking at the plotted curve. State when the apparent trend may cease to apply to actual equipment.

Q15 — Independent falsification. Test the assertion: P fraction must lie between 0 and 1 and is conversion times selectivity. Choose one deliberately extreme combination permitted by the controls and report the result to at least three useful significant figures where meaningful. Explain whether a surprising output is a code defect, a breakdown of assumptions, or a valid mathematical limit. Do not ignore invalid or nonfinite outputs when an infeasible physical state is intentionally selected.

Q16 — Evidence and decision memo. Write a 200–300-word decision note addressing: A route should advance only if its largest unresolved risk has a practical validation test. Contrast the synthetic lesson calculation with the following evidence still required for an operational claim: expert review, route-test data, credible cost ranges and go/no-go thresholds. Discuss this known limitation: Treat safety disqualifiers and unverified intellectual-property restrictions as hard gates, not as low weighted points. Name a realistic first validation experiment or vendor request and explain which unfavorable result would change the decision.

Marking and evidence standards

Allocate 25% to correct model and dimensions, 25% to worked numeric results and residual checks, 25% to parameter investigation and plots, and 25% to evidence quality, limitations and communication. Submit calculations, CSV exports, a one-page design note and a clearly labeled outstanding-information list. Material that implies these synthetic results certify an industrial design should not receive full credit.

[Unit notes](../units/unit-02.html) · [Applied project](../projects/unit-02.html)