Nonreactive Process Networks, Recycle, Bypass and Purge

Mixers, splitters, bypasses, recycle and purge loops couple multiple individual units. Solve network equations systematically and verify every component at each boundary.

Core learning goals

• Explain and apply Mixing and dilution networks, including assumptions and independent verification.
• Explain and apply Separators, splitters and recovery, including assumptions and independent verification.
• Explain and apply Recycle and bypass calculations, including assumptions and independent verification.
• Explain and apply Purge design and inert accumulation, including assumptions and independent verification.

Lessons and reading order

• [Lesson 2.1: Mixing and dilution networks](../lessons/unit-02-lesson-01.html)
• [Lesson 2.2: Separators, splitters and recovery](../lessons/unit-02-lesson-02.html)
• [Lesson 2.3: Recycle and bypass calculations](../lessons/unit-02-lesson-03.html)
• [Lesson 2.4: Purge design and inert accumulation](../lessons/unit-02-lesson-04.html)

Unit synthesis: identify what is known

Mixers, splitters, bypasses, recycle and purge loops couple multiple individual units. Solve network equations systematically and verify every component at each boundary. A strong solution begins with a process sketch and a stream table. Write values to a stated basis, mark all missing data, and calculate degrees of freedom before attempting numerical iteration. A flow diagram is useful only if the stream symbols and assumptions can be traced into actual balance equations. If an unknown variable is introduced to close a balance, explain what physical instrument or property measurement would establish it.

Connecting the four lessons

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

Diagnostic exercise

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

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

Unit completion exercise

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

Unit 2.1: Mixing and dilution networks

Book 2: Material and Energy Balances — Nonreactive process networks

What you will be able to do

The output composition is a flow-weighted average, not an arithmetic average. Interpret x_out=(F_1x_1+F_2x_2)/(F_1+F_2) and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

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

Deriving the balance from the process boundary

Start from the observations implied by mixing and dilution networks. The output composition is a flow-weighted average, not an arithmetic average. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as x_out=(F_1x_1+F_2x_2)/(F_1+F_2). Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use unit consistency as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. Mix 300 kg/h at 0.08 solute with 200 kg/h at 0.30; the outlet has 84 kg/h solute in 500 kg/h, or 16.8 wt%. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. A concentration cannot exceed both feed concentrations for a nonreactive two-stream mixer. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

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

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

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in x_out=(F_1x_1+F_2x_2)/(F_1+F_2) scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

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

Verification and critical-thinking questions

1. State the system boundary and draw the streams for mixing and dilution networks; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: the output composition is a flow-weighted average, not an arithmetic average?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: A concentration cannot exceed both feed concentrations for a nonreactive two-stream mixer. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

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

Further study

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

Unit 2.2: Separators, splitters and recovery

Book 2: Material and Energy Balances — Nonreactive process networks

What you will be able to do

Overall split fractions and component recoveries are not interchangeable. Interpret recovery_A=(Px_PA)/(Fx_FA) and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

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

Deriving the balance from the process boundary

Start from the observations implied by separators, splitters and recovery. Overall split fractions and component recoveries are not interchangeable. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as recovery_A=(Px_PA)/(Fx_FA). Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use measurable stream composition as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. A 1000 kg/h feed at 20% valuable compound gives 170 kg/h of that compound in product; the component recovery is 85%. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. A product mass fraction alone is insufficient to calculate recovery without the product rate. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

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

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

Guided redesign exercise

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

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

Verification and critical-thinking questions

1. State the system boundary and draw the streams for separators, splitters and recovery; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: overall split fractions and component recoveries are not interchangeable?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: A product mass fraction alone is insufficient to calculate recovery without the product rate. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

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

Further study

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

Unit 2.3: Recycle and bypass calculations

Book 2: Material and Energy Balances — Nonreactive process networks

What you will be able to do

Internal streams can greatly exceed the net fresh feed without violating overall conservation. Interpret R/(F+R)=recycle_fraction; total mixer feed=F+R and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

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

Deriving the balance from the process boundary

Start from the observations implied by recycle and bypass calculations. Internal streams can greatly exceed the net fresh feed without violating overall conservation. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

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

A worked calculation and its interpretation

Illustrative case. For fresh feed 100 kg/h and recycle fraction 0.6 of combined mixer flow, the mixer handles 250 kg/h and recycle is 150 kg/h. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. Confusing R/F with R/(F+R) causes large recycle overestimates. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

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

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

Guided redesign exercise

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

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

Verification and critical-thinking questions

1. State the system boundary and draw the streams for recycle and bypass calculations; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: internal streams can greatly exceed the net fresh feed without violating overall conservation?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: Confusing R/F with R/(F+R) causes large recycle overestimates. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

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

Further study

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

Unit 2.4: Purge design and inert accumulation

Book 2: Material and Energy Balances — Nonreactive process networks

What you will be able to do

Nonreactive inerts entering a loop must ultimately leave it. Interpret F_inert=P*x_inert for a steady loop if purge is the only inert outlet and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Ammonia loop; construct inert balance before reactant balance. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by purge design and inert accumulation. Nonreactive inerts entering a loop must ultimately leave it. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as F_inert=P*x_inert for a steady loop if purge is the only inert outlet. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use independent balance closure as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. If 2 kmol/h inert enters and the purge contains 10 mol% inert, purge must be 20 kmol/h. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. A finite purge is essential when a recycled gas includes inerts and there is no other inert exit. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

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

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

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in F_inert=P*x_inert for a steady loop if purge is the only inert outlet scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

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

Verification and critical-thinking questions

1. State the system boundary and draw the streams for purge design and inert accumulation; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: nonreactive inerts entering a loop must ultimately leave it?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: A finite purge is essential when a recycled gas includes inerts and there is no other inert exit. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

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

Further study

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

Applied project 2: Fermentation broth dilution and trace inventory

Scenario and process objective

A batch formulation receives a concentrated aqueous nutrient solution and process water before inoculation. The nutrient stream is 600 kg at 18 wt% dissolved species; operators add 900 kg deionized water. A sampling record uses g/L without logging solution density. The process engineer must distinguish a mass fraction calculation from a volumetric concentration, and specify the additional property required for conversion.

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

Calculation and reference result

The initial nutrient mass is 108 kg and total charge becomes 1500 kg, giving 7.2 wt% nutrient if no loss or reaction occurs. The result is mass-based and does not require a density assumption. To express g/L one needs final solution density and a defined temperature; using 1.0 kg/L by convenience would give 72 g/L but that is an illustrative approximation, not a measurement.

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

Model criticism and operating context

If feed and water arrive at different temperatures, heat of mixing and sensible heat may change density. Once fermentation begins, the nutrient component is no longer conserved: reaction and gas loss terms must enter the balance. A transient sample should never be used to justify a steady-state interpretation.

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

Required investigation

Ask students to design three measurements that reveal whether the batch has been mixed uniformly. Prepare a simple mass-basis data reconciliation table and flag which entries are assumptions. Propose a credible microbial-growth model extension but do not fit it without time-series evidence.

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

Extension: implementation and quality assurance

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

Decision memo template

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

Questions for viva or peer discussion

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

Assessment — Unit 2: Nonreactive process networks

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

Topic 2.1: Mixing and dilution networks

1. Derivation. Build a balance for: Blending two wastewater streams before a neutralization stage. Derive the expression `x_out=(F_1*x_1+F_2*x_2)/(F_1+F_2)` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: Mix 300 kg/h at 0.08 solute with 200 kg/h at 0.30; the outlet has 84 kg/h solute in 500 kg/h, or 16.8 wt%. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: A concentration cannot exceed both feed concentrations for a nonreactive two-stream mixer. Identify the failed assumption and describe a corrective measurement.

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

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

Topic 2.2: Separators, splitters and recovery

1. Derivation. Build a balance for: Mineral processing; distinguish assay, grade and recovery. Derive the expression `recovery_A=(P*x_PA)/(F*x_FA)` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: A 1000 kg/h feed at 20% valuable compound gives 170 kg/h of that compound in product; the component recovery is 85%. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: A product mass fraction alone is insufficient to calculate recovery without the product rate. Identify the failed assumption and describe a corrective measurement.

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

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

Topic 2.3: Recycle and bypass calculations

1. Derivation. Build a balance for: Solvent recovery loop with a controlled side bypass. Derive the expression `R/(F+R)=recycle_fraction; total mixer feed=F+R` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: For fresh feed 100 kg/h and recycle fraction 0.6 of combined mixer flow, the mixer handles 250 kg/h and recycle is 150 kg/h. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: Confusing R/F with R/(F+R) causes large recycle overestimates. Identify the failed assumption and describe a corrective measurement.

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

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

Topic 2.4: Purge design and inert accumulation

1. Derivation. Build a balance for: Ammonia loop; construct inert balance before reactant balance. Derive the expression `F_inert=P*x_inert for a steady loop if purge is the only inert outlet` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: If 2 kmol/h inert enters and the purge contains 10 mol% inert, purge must be 20 kmol/h. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: A finite purge is essential when a recycled gas includes inerts and there is no other inert exit. Identify the failed assumption and describe a corrective measurement.

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

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

Grading rubric

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