Process Operations, Unit Classifications and Equipment Sizing

Central engineering problem

A unit operation is a constrained physical model with measurable inputs, uncertain parameters and real operating limits.

The unit develops four tightly connected ideas. A process description should become a quantitative and testable claim: an explicit boundary, evidence for values, dimensional consistency, and a way to distinguish real physical behavior from model simplifications. The relevant measurements and operating envelopes must be named before making a process decision. In introductory chemical engineering, a plausible numerical result is necessary but not sufficient; it must also obey conservation, physical feasibility and operational safety.

Learning outcomes

After studying this unit, a student should be able to explain the physical role of the four topics, construct or interpret a simple numerical representation, identify a falsifying measurement, and document how the assumptions restrict the result. Numerical work should use explicit material or energy bases and show uncertainty or sensitivity whenever decisions depend on approximate data.

Lesson sequence

• [Chemical reactors and conversion](../lessons/unit-07-lesson-01.html)
• [Separations and selectivity](../lessons/unit-07-lesson-02.html)
• [Fluid transport and equipment performance](../lessons/unit-07-lesson-03.html)
• [Feedback control and dynamic behavior](../lessons/unit-07-lesson-04.html)

Interactive laboratories

• [Lab 14: First-order isothermal CSTR conversion](../labs/lab-14.html)
• [Lab 15: Darcy–Weisbach pipe pressure drop](../labs/lab-15.html)
• [Lab 16: Tank level feedback and controller gain](../labs/lab-16.html)

Synthesis activity

Build a one-page process evidence sheet that distinguishes four columns: directly observed quantities, derived quantities, estimated properties, and external constraints. For each lesson's primary equation, test whether a 10% change in its dominant input yields a proportionate response. Explain exceptions, including compositions bounded between zero and one and physical states requiring feasibility checks. Conclude with at least two measurements needed to confirm the result in a real laboratory or plant.

Assessment standard

Successful work must show a system boundary or process purpose, symbolic equations before values, units during substitution, an independent conservation or limiting-case check, and a concise explanation of where a more advanced treatment is required. Attach plots only when their input assumptions are documented. The purpose is transferable engineering reasoning rather than memorized formula application.

Unit 7.1: Chemical reactors and conversion

Chemical Engineering Fundamentals · Unit 7: Process operations

Purpose and measurable learning outcomes

The apparent kinetics observed in a reactor depend on chemical mechanism, temperature, catalysts and mixing or transport limitations. For a single first-order reaction in an ideal isothermal CSTR, X=kτ/(1+kτ). A real industrial reactor may require detailed heat and mass transfer models, pressure drop and safety analysis. Residence time is volume divided by relevant volumetric flow on a consistent basis.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

An ideal CSTR's conversion is a compromise between residence time and reaction rate. At rate constant 0.2 min⁻¹ and residence time 5 min, conversion is 50%; with 10 min it is 66.7%. This does not mean plant capacity can be increased by increasing reactor volume without consequences. Mixing power, heat removal, fluid dynamics, side reactions and residence-time distributions can control performance. For an exothermic reaction, energy balance and nonlinear thermal feedback may be more important than the simplified isothermal kinetic expression.

Governing quantitative relationship

With k=0.2 min⁻¹ and τ=5 min, ideal CSTR conversion X=0.5.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

Compare ideal CSTR conversion at 2 and 10 minutes for fixed k. Discuss diminishing returns and downstream separation demands.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Using a first-order liquid-phase ideal CSTR model for a high-temperature gas-phase runaway reaction.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. Compare ideal CSTR conversion at 2 and 10 minutes for fixed k. Discuss diminishing returns and downstream separation demands. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Using a first-order liquid-phase ideal CSTR model for a high-temperature gas-phase runaway reaction. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 14](../labs/lab-14.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-07.html) · [Book contents](../index.html)

Unit 7.2: Separations and selectivity

Chemical Engineering Fundamentals · Unit 7: Process operations

Purpose and measurable learning outcomes

Separation technology exploits differences in volatility, solubility, particle size, affinity or permeability. A separator often trades purity, recovery, energy and throughput. A product with higher purity may have lower recovery; specify both before comparing operating cases. Stage efficiency and equilibrium limits prevent perfect separation without cost. An illustrative split model is not a verified separation design.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Consider a separator that captures 90% of target A and carries over 8% of unwanted B. With feed rates 40 kg/h A and 60 kg/h B, the product contains 36 kg/h A and 4.8 kg/h B. Its A purity is 36/40.8≈88.24%, while its A recovery is 90%. A downstream customer demanding 95% purity might reject it even though recovery looks strong. Raising purity by tighter operating conditions could lower recovery; that tradeoff motivates multistage separation and economic evaluation.

Governing quantitative relationship

Recovery of A = A in product / A in feed; purity of A = A in product / total product.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A feed contains 40 kg/h A and 60 kg/h B; product receives 36 kg/h A and 8 kg/h B. Find A recovery and purity.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Comparing two separation processes using purity alone while ignoring yield and energy.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A feed contains 40 kg/h A and 60 kg/h B; product receives 36 kg/h A and 8 kg/h B. Find A recovery and purity. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Comparing two separation processes using purity alone while ignoring yield and energy. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 15](../labs/lab-15.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-07.html) · [Book contents](../index.html)

Unit 7.3: Fluid transport and equipment performance

Chemical Engineering Fundamentals · Unit 7: Process operations

Purpose and measurable learning outcomes

Pumps and pipe networks transfer mechanical energy and experience losses related to friction, fittings, viscosity and geometry. Mass continuity fixes velocity from flow and area. Darcy–Weisbach provides a useful pressure-loss model when its friction factor is defined consistently. Laminar, transitional and turbulent regimes require different correlations; fixed f is only a sensitivity model.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

For 10 L/s through a circular 0.1 m pipe, the mean velocity is 4(0.01)/(π×0.1²)≈1.273 m/s. For Darcy f=0.02, length 50 m and density 1000 kg/m³, pressure drop is 0.02×(50/0.1)×1000×(1.273²)/2≈8.11 kPa, neglecting fittings. Pressure loss varies approximately with flow squared when f is held constant, and with diameter to the fifth power in this simplified fixed-flow expression. The latter sensitivity strongly motivates an explicit diameter assumption and velocity-range check.

Governing quantitative relationship

Velocity v=4Q/(πD²); ΔP=f(L/D)ρv²/2 for a straight pipe without minor losses.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

For a pipe with Q=0.01 m³/s, D=0.1 m, L=50 m, f=0.02, ρ=1000 kg/m³, estimate pressure drop.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Confusing Darcy friction factor with Fanning friction factor, which differs by a factor of four.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. For a pipe with Q=0.01 m³/s, D=0.1 m, L=50 m, f=0.02, ρ=1000 kg/m³, estimate pressure drop. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Confusing Darcy friction factor with Fanning friction factor, which differs by a factor of four. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 16](../labs/lab-16.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-07.html) · [Book contents](../index.html)

Unit 7.4: Feedback control and dynamic behavior

Chemical Engineering Fundamentals · Unit 7: Process operations

Purpose and measurable learning outcomes

A feedback loop observes an output, compares it with a setpoint and adjusts a manipulated variable. The dynamics of tanks, thermal masses and composition inventories introduce delay and lag. A higher controller gain can improve response but also cause oscillation or actuator saturation. An interactive first-order model teaches trends but cannot stand in for commissioning or a safety instrumented function.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Control dynamics are easiest to understand by comparing actuator demand with process response. A first-order plant approaches a constant commanded equilibrium rather than arriving instantaneously; after one time constant it completes roughly 63.2% of a step response. Proportional control with output limits may leave residual offset, while integral action can accumulate during saturation and cause overshoot. The simulation uses a normalized tank variable and an ideal controller, so it can illustrate relative trends but cannot determine safe tuning for an actual hazardous process or independent protective logic.

Governing quantitative relationship

First-order process: τ dy/dt + y = K u; for constant u, y approaches K u exponentially with time constant τ.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A tank level controller reacts to a sudden inlet disturbance. Explain why actuator limits and sensor delay could degrade an ideal simulated response.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Mistaking a normal feedback controller for a proven independent protection layer.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A tank level controller reacts to a sudden inlet disturbance. Explain why actuator limits and sensor delay could degrade an ideal simulated response. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Mistaking a normal feedback controller for a proven independent protection layer. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 14](../labs/lab-14.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-07.html) · [Book contents](../index.html)

Unit 7 applied engineering project — A mixing and pumping test rig

Setting and purpose

A nonhazardous aqueous stream passes through piping into an ideal stirred vessel and is monitored by a feedback loop. This is a synthetic teaching case, not a recommendation to operate a real process. Students must select reasonable illustrative numbers, label every invented number as an assumption, and keep all units, reference conditions and composition bases visible. The purpose is to assemble the unit's concepts into a consistent model that a reviewer can challenge.

Engineering question

Contrast friction losses, residence time, conversion approximation and controller behavior, including at least two limitations of the integrated model. State a single primary decision being supported, such as selecting a material-balance boundary, accepting a measurement, identifying a missing outlet or prioritizing an additional experiment. Do not use an unsupported plant-wide profit number or an unverified regulatory threshold to justify the decision.

Required evidence and calculation plan

1. Write a process statement that defines input materials, expected outputs and the relevant boundaries. Distinguish a batch inventory from a flow and give the measurement time basis.
2. Build an input data table with dimensions, source type, uncertainty estimate and acceptable bounds. Separate readings from engineering assumptions.
3. Derive at least three equations rather than relying only on a calculator. For each, show a dimensional check and a feasible limiting case. Include a separate component balance when a concentration or reaction is involved.
4. Carry out two contrasting cases: a nominal baseline and a plausible changed operating condition. If the changed condition violates the simplified model, stop and write that result as an important finding.
5. Use the unit laboratories as computational demonstrations; export plots, retain input settings, and compare with a direct hand calculation. Plots are evidence about a mathematical model, not proof about an operating plant.
6. Describe data or safety limitations. Include possible missing streams, property correlations, instrument bias, parameter dependence and common-cause uncertainty where they matter.
7. Communicate the result as a reproducible engineering note with an executive statement, flow diagram, equations, tables, a source list and an open list of unresolved questions.

Review checkpoints

• Conservation: material and energy accounting closure must be explicit; an unresolved residual is named, not silently forced to zero.
• Feasibility: compositions must be physically bounded and equipment temperatures and pressures checked against the model's assumptions.
• Traceability: a competent reader can identify exactly which values are assumed, measured or derived, and can reproduce the major quantities.
• Safety and ethics: no classroom calculation is presented as industrial relief sizing, pharmaceutical validation, field authorization or environmental compliance proof.

Deliverables

Submit one concise process diagram, one independently checkable calculation sheet, two simulation exports, a one-page uncertainty/sensitivity commentary and a 250-word statement on what evidence would change your conclusion. Defend the chosen model scope and openly identify a more advanced analysis needed before industrial deployment.

Unit 7 assessment: Process operations

These 12 problems combine quantitative reproduction, model validity, and audit methodology. Answers below are intended as diagnostic reasoning, not fabricated plant data.

Question 1: analysis of chemical reactors and conversion

Compare ideal CSTR conversion at 2 and 10 minutes for fixed k. Discuss diminishing returns and downstream separation demands.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 7.1. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 2: model validity

Using a first-order liquid-phase ideal CSTR model for a high-temperature gas-phase runaway reaction. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 3: quantitative audit

Use the lesson's worked equation: With k=0.2 min⁻¹ and τ=5 min, ideal CSTR conversion X=0.5. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 5: analysis of separations and selectivity

A feed contains 40 kg/h A and 60 kg/h B; product receives 36 kg/h A and 8 kg/h B. Find A recovery and purity.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 7.2. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 6: model validity

Comparing two separation processes using purity alone while ignoring yield and energy. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 7: quantitative audit

Use the lesson's worked equation: Recovery of A = A in product / A in feed; purity of A = A in product / total product. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 9: analysis of fluid transport and equipment performance

For a pipe with Q=0.01 m³/s, D=0.1 m, L=50 m, f=0.02, ρ=1000 kg/m³, estimate pressure drop.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 7.3. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 10: model validity

Confusing Darcy friction factor with Fanning friction factor, which differs by a factor of four. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 11: quantitative audit

Use the lesson's worked equation: Velocity v=4Q/(πD²); ΔP=f(L/D)ρv²/2 for a straight pipe without minor losses. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 13: analysis of feedback control and dynamic behavior

A tank level controller reacts to a sudden inlet disturbance. Explain why actuator limits and sensor delay could degrade an ideal simulated response.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 7.4. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 14: model validity

Mistaking a normal feedback controller for a proven independent protection layer. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 15: quantitative audit

Use the lesson's worked equation: First-order process: τ dy/dt + y = K u; for constant u, y approaches K u exponentially with time constant τ. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.