Process Representation, Flowsheets and Degrees of Freedom

Central engineering problem

A correctly drawn process boundary allows material and energy accounting while identifying what is measured and what is inferred.

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

• [Streams, boundaries and system diagrams](../lessons/unit-03-lesson-01.html)
• [Process flow diagrams and stream tables](../lessons/unit-03-lesson-02.html)
• [Batch, continuous and recycle systems](../lessons/unit-03-lesson-03.html)
• [Instruments and operational documentation](../lessons/unit-03-lesson-04.html)

Interactive laboratories

• [Lab 05: Tank inventory and material accumulation](../labs/lab-05.html)
• [Lab 06: Recycle loop circulation multiplier](../labs/lab-06.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 3.1: Streams, boundaries and system diagrams

Chemical Engineering Fundamentals · Unit 3: Process representation

Purpose and measurable learning outcomes

Choose the system boundary around the question. A mixer boundary encloses streams entering and leaving; a complete plant boundary may also capture recycle, storage, emission and utility exchanges. Track physical phase, component identities and direction. Crossed arrows are not junctions unless the diagram explicitly connects them. Material does not vanish when a vessel is temporarily filling.

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

Choosing a control volume is a modeling choice, not a fact dictated by a diagram border. A feed tank may be treated as one open control volume or as part of a plant-wide mass-balance boundary. Material carried by a recirculation line crosses the small boundary twice but may not cross the large plant boundary at all. The mathematical representation should match the measurement objective: inventory reconciliation, conversion measurement or environmental release accounting. For time-varying operation, integrate rates over the relevant interval instead of substituting one snapshot into a steady equation.

Governing quantitative relationship

Accumulation = input – output + generation – consumption; for conserved total mass generation and consumption are zero.

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 storage tank receives 11 kg/s and discharges 9 kg/s. Calculate 15-minute mass inventory change and state the needed assumption about discharge.

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: Applying steady state to a tank whose level is visibly changing.

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 storage tank receives 11 kg/s and discharges 9 kg/s. Calculate 15-minute mass inventory change and state the needed assumption about discharge. 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. Applying steady state to a tank whose level is visibly changing. 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 05](../labs/lab-05.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-03.html) · [Book contents](../index.html)

Unit 3.2: Process flow diagrams and stream tables

Chemical Engineering Fundamentals · Unit 3: Process representation

Purpose and measurable learning outcomes

A process flow diagram should show major equipment, numbered streams, phase identities and critical operating conditions. A stream table turns the drawing into an auditable quantitative model. The diagram does not replace a piping and instrumentation diagram. For multi-feed separators, enumerate all streams including vent, drain, waste, startup bypass and cleaning return when material accounting requires them.

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

The minimum stream table should state stream identifier, physical phase, total mass or molar rate, composition basis, temperature, pressure and information source. A blank entry can mean unknown, not zero. An estimated waste flow should be marked inferred, not measured. Use one index for species names, their molecular formulae and molar masses. PFDs are intentionally simplified, but they cannot hide environmentally relevant emissions or recovery outlets when the reported process boundary includes them. Revision control becomes especially important when streams are renumbered after a flowsheet change.

Governing quantitative relationship

For a nonreactive separator at steady state, F = P + W; if feed is 500 kg/h and product 430 kg/h, waste is 70 kg/h.

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

Create a stream table for a crystallizer with feed, mother liquor, wet crystals and recovered solvent. Identify measurements needed for closure.

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: Leaving a small vent off the flowsheet while claiming exact material-balance closure.

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. Create a stream table for a crystallizer with feed, mother liquor, wet crystals and recovered solvent. Identify measurements needed for closure. 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. Leaving a small vent off the flowsheet while claiming exact material-balance closure. 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 06](../labs/lab-06.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-03.html) · [Book contents](../index.html)

Unit 3.3: Batch, continuous and recycle systems

Chemical Engineering Fundamentals · Unit 3: Process representation

Purpose and measurable learning outcomes

Batch systems have charge, hold, transfer and cleaning times; continuous systems have rates and dynamics. A recycle stream may be large relative to fresh feed while overall saleable output is governed by fresh input and purge or losses. Distinguish a recycle ratio from recycle fraction, and state whether ratios use mass or molar rates. Never connect recycle without checking an outlet for inert buildup.

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

A circulation loop can raise internal equipment duty without increasing final output. If fresh feed is 100 kg/h and the fraction returned is 0.4, then internal circulation for a no-reaction geometric loop is 100/(1−0.4)=166.7 kg/h. The exit of 66.7 kg/h is recycle and the 100 kg/h branch leaving the loop balances fresh input. Actual reactor loops rarely behave this simply because reaction alters flow, inert components accumulate and separators have different species recoveries. The model is best understood as a mathematical starting point for later material-and-energy-balance courses.

Governing quantitative relationship

For fresh rate F and returned fraction r in a simple nonreactive loop, circulating rate is F/(1-r) when the split model is valid.

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

Fresh flow is 100 kg/h and 40% of a well-mixed loop stream is returned. Compute circulation and the stream leaving the loop.

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: Interpreting a recycle ratio R/F as the same parameter as a recycle fraction R/(F+R).

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. Fresh flow is 100 kg/h and 40% of a well-mixed loop stream is returned. Compute circulation and the stream leaving the loop. 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. Interpreting a recycle ratio R/F as the same parameter as a recycle fraction R/(F+R). 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 05](../labs/lab-05.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-03.html) · [Book contents](../index.html)

Unit 3.4: Instruments and operational documentation

Chemical Engineering Fundamentals · Unit 3: Process representation

Purpose and measurable learning outcomes

P&IDs describe valves, lines, sensors, controllers, alarms and interlocks that a PFD intentionally omits. Identify instrument location, signal direction, fail-safe state, and the difference between a controller and an independent protective layer. Specifications should describe normal operating range as well as safe limits. Document revision, authorship and change history because operations rely on the current drawing.

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

A diagram that shows a pressure transmitter and a controller has not established the presence of a pressure-relief device or an independent shutdown. Process documentation must distinguish process control, alarm, operator intervention and independent safety function. One sensor may feed multiple screens but remain a single common failure point. The instrument range should be chosen based on credible operating and upset conditions; a transmitter that saturates during a hazard gives an operator false reassurance. Always record instrument calibration, alarm setpoints, bypass state and change approvals in the relevant system.

Governing quantitative relationship

For instrument span 0–200 kPa, a reading of 125 kPa represents 62.5% of span when the lower-range value is zero.

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

Sketch a tank level loop with transmitter, controller and outlet valve. Describe the effect of lost instrument air for two possible fail positions.

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: Assuming a controller display is an independent safeguard against the failure of that same controller.

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. Sketch a tank level loop with transmitter, controller and outlet valve. Describe the effect of lost instrument air for two possible fail positions. 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. Assuming a controller display is an independent safeguard against the failure of that same controller. 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 06](../labs/lab-06.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-03.html) · [Book contents](../index.html)

Unit 3 applied engineering project — A recycled-water preparation plant

Setting and purpose

A proposed pilot flowsheet includes a feed tank, mixer, filter, recycle branch and unknown discharge. 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

Draw PFD and stream table, label unknown values, test whether steady state is justified, and draft a measurement plan to close missing degrees of freedom. 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 3 assessment: Process representation

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 streams, boundaries and system diagrams

A storage tank receives 11 kg/s and discharges 9 kg/s. Calculate 15-minute mass inventory change and state the needed assumption about discharge.

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 3.1. 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

Applying steady state to a tank whose level is visibly changing. 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: Accumulation = input – output + generation – consumption; for conserved total mass generation and consumption are zero. 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 process flow diagrams and stream tables

Create a stream table for a crystallizer with feed, mother liquor, wet crystals and recovered solvent. Identify measurements needed for closure.

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 3.2. 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

Leaving a small vent off the flowsheet while claiming exact material-balance closure. 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: For a nonreactive separator at steady state, F = P + W; if feed is 500 kg/h and product 430 kg/h, waste is 70 kg/h. 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 batch, continuous and recycle systems

Fresh flow is 100 kg/h and 40% of a well-mixed loop stream is returned. Compute circulation and the stream leaving the loop.

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 3.3. 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

Interpreting a recycle ratio R/F as the same parameter as a recycle fraction R/(F+R). 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: For fresh rate F and returned fraction r in a simple nonreactive loop, circulating rate is F/(1-r) when the split model is valid. 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 instruments and operational documentation

Sketch a tank level loop with transmitter, controller and outlet valve. Describe the effect of lost instrument air for two possible fail positions.

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 3.4. 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

Assuming a controller display is an independent safeguard against the failure of that same controller. 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: For instrument span 0–200 kPa, a reading of 125 kPa represents 62.5% of span when the lower-range value is zero. 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.