Downstream Processing and Bioseparation Trains

Purpose. Relate harvesting, disruption, separation, concentration, and final product quality to recovery and economic tradeoffs.

Entry knowledge. Students should be able to balance mass and energy, work with differential equations, check dimensional consistency and interpret experimental uncertainty. Prior biological experience helps but is not assumed. The models are deliberately simplified; scientific claims require the limitations in each lesson to be stated.

Lesson pathway

1. [Biomass harvesting and mechanical separation](../lessons/unit-06-lesson-01.html) — [related numerical lab](../labs/lab-16.html)
2. [Cell disruption and extraction choices](../lessons/unit-06-lesson-02.html) — [related numerical lab](../labs/lab-17.html)
3. [Affinity and chromatographic separations](../lessons/unit-06-lesson-03.html) — [related numerical lab](../labs/lab-18.html)
4. [Membrane concentration, formulation and recovery](../lessons/unit-06-lesson-04.html) — [related numerical lab](../labs/lab-18.html)

Practise and demonstrate competence

• [Unit 06 assessment: 16 multi-part tasks](../assessments/unit-06.html) tests physical reasoning, calculation, falsification and design decision-making.
• [Unit 06 applied project](../projects/unit-06.html) requires an evidence ledger, assumption register, data table, quantitative check and defensible conclusion.
• [Laboratory manual](../LABORATORY-MANUAL.html) indexes the offline simulations and their modeling restrictions.

Outcomes and publication boundary

At the end of this unit, students should explain why the chosen equation is appropriate, reproduce at least one numerical prediction, describe a test that could disprove it, and articulate the information missing for a real process decision. No numerical curve in this resource is an industrial operating recommendation. All sample coefficients and operating points are fictional classroom inputs unless a source is specifically identified.

Unit 6 · Lesson 1 — Biomass harvesting and mechanical separation

[Unit 06 overview](../units/unit-06.html) · [Run numerical laboratory 16](../labs/lab-16.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering question

The harvest stage converts a dilute, complex broth into a cell-rich or cell-free stream, depending on product location. Centrifugation, filtration and flocculation have different recovery, throughput, shear and fouling risks. Sedimentation velocity is influenced by particle size and density contrast; a small shift in particle diameter can strongly alter ideal settling rates. At production scale, particle-size distributions and non-Newtonian broths make a single-size estimate unreliable. Recovery should be calculated on target product mass, not merely on total wet mass separated.

The larger aim of Downstream processing is to answer this question: Relate harvesting, disruption, separation, concentration, and final product quality to recovery and economic tradeoffs. A result must be interpreted as a statement about a specified physical boundary and observed quantities. Distinguish the underlying biological mechanism from the mathematical convenience that makes a calculation tractable. A model can be dimensionally consistent and still be badly chosen for the organism, medium or scale. Conversely, a complicated simulator is not superior unless its extra parameters can be identified and tested with observations.

A useful model and its assumptions

Working relation: For a small isolated sphere in creeping flow, Stokes settling speed is v=Δρ g d²/(18μ). Check particle Reynolds number and hindered settling before applying it to a dense cell slurry.

The displayed relationship is a starting point for reasoning. Before substituting numbers, name every term, give the unit and decide whether each quantity is a measured value, a fitted coefficient, or a controlled setting. Conservation laws are independent of constitutive assumptions, while kinetic and transfer coefficients depend on conditions. Make a sketch of the relevant system boundary and show what enters, accumulates and leaves. State whether the rate is per unit liquid volume, per unit catalyst or per unit cell mass; confusing these bases can lead to order-of-magnitude errors even when individual values seem realistic.

When a relationship contains an exponential, check which variable is integrated in the exponent and whether the exponent is dimensionless. When it contains a ratio, check what happens as the denominator approaches a limiting condition. When it describes an observable signal, identify the calibration that connects that signal to the claimed physical quantity. These checks are not substitutes for experiment, but they reject many wrong models before fitting begins.

Worked investigation with synthetic numbers

Assume d=8 µm, Δρ=80 kg/m³ and viscosity 1.5 mPa·s. Then v≈1.86×10⁻⁶ m/s. Halving diameter reduces predicted speed by a factor of four, even before considering aggregation and density variation.

Reconstruction task. Rewrite the stated computation as a ledger: input variable and unit, conversion used, intermediate result and final quantity. Show the same calculation with one input perturbed by 10% while retaining the others, and determine whether the output response is approximately proportional, nonlinear, or sensitive to a constraint. Then reverse the question: what input accuracy would be needed to distinguish the two predictions using a real instrument? Avoid claiming more significant figures than the chosen coefficients justify.

The example is intentionally synthetic. It should teach the direction and scale of a response, not imply that a specific organism or process will exhibit these numerical coefficients. If the result suggests substantial accumulation, ask where the required mass and energy originate. If it suggests extreme sensitivity, inspect whether the sensitivity arises from a genuine mechanistic feature or from mathematically approaching a singular assumption.

Measurement design and engineering judgment

Track target molecules across every stream. Close component and volume balances; measure both purity and recovery. Consider the location of the product before choosing a cell-harvest or disruption operation.

Use particle-size distributions and representative viscosity measurements to compare equipment trials. Record target recovery and purity in both outlet streams.

A defensible evidence plan identifies a process objective, measured signals, their frequency, instrument or assay uncertainty, and a comparison criterion selected before viewing the data. Include control conditions and independent replicates when the biological material varies across runs. Distinguish calibration measurements from hold-out verification data. If the main parameter is estimated from one narrow operating window, do not assume it will remain identifiable when oxygen, temperature, shear, pH or medium composition changes.

In a design review, explain the alternatives rather than selecting a model because it yields the highest projected titer or lowest cost. A common problem is conflating process capacity with process utilization: an available transfer rate is not automatically used, and biological demand can be low because the culture is inhibited. When a prediction is contradicted, investigate both the experiment and the model, and keep a record of the resulting revision.

Where the simple model fails

Stokes law fails when Reynolds number is not small or particles are nonspherical, deformable or concentrated. Centrifugal fields and flow residence-time distributions require more elaborate models.

A classroom model is especially fragile when extrapolated beyond its parameter-identification range. Carefully distinguish structural uncertainty (missing mechanism or wrong equation), parameter uncertainty (imprecisely estimated coefficient), and measurement uncertainty (sensor or assay error). Running many simulations with one incorrect equation does not resolve structural uncertainty. A useful sensitivity chart should therefore accompany a stated model boundary, not pretend to replace it.

For an independent verification, perform three checks: units and conservation; a limiting condition with a known qualitative answer; and a second calculation method or external measurement. Explain what each check can and cannot demonstrate. Automated agreement with an equation confirms the implementation, not necessarily the equation's suitability for a real reactor.

Guided laboratory and discussion

Open [Laboratory 16](../labs/lab-16.html). Record the default input values with units. Move the first slider to three equally spaced settings while leaving other controls unchanged; save the response to CSV and compare the graph with the governing relation in that laboratory. Then change a second independent parameter to test whether the original trend is stable. The laboratory describes its physical limits and reports an explicit warning where assumptions fail. The export is generated locally; no data leave the browser.

Investigative prompt: Calculate whether a change in particle diameter could justify flocculation, then identify additional experimental tests needed.

Interpretation prompt: Identify a response that the model cannot predict, and propose one targeted measurement needed to decide if the omission matters. Write a two-sentence decision: what is supported by the simulation and what remains unproven. A high-grade response distinguishes a mathematical identity, an observation and a contingent engineering inference.

Lesson check

1. State the modeled system boundary, the type of measurable quantity being predicted and the appropriate units.
2. Derive or reconstruct the stated relation from a rate law or conservation balance, and show a limiting case.
3. Reproduce the worked calculation, then vary one input and interpret sensitivity without generalizing outside the stated model.
4. Identify two independent measurements that could falsify the simplified hypothesis.
5. Present a recommendation that is explicitly conditional on the evidence rather than an unsupported production specification.

Continue: Cell disruption and extraction choices. Return to the [unit learning pathway](../units/unit-06.html) or attempt the [unit assessment](../assessments/unit-06.html).

Unit 6 · Lesson 2 — Cell disruption and extraction choices

[Unit 06 overview](../units/unit-06.html) · [Run numerical laboratory 17](../labs/lab-17.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering question

When the product is intracellular, disruption releases it but also releases nucleic acids, host proteins, lipids and proteases. Mechanical, chemical and enzymatic disruption differ in selectivity, cost and compatibility with the product. Applied mechanical energy per processed volume is a convenient bookkeeping metric, but is not a universal predictor of lysis: residence time, pressure pulses, cooling and cell morphology matter. Highly viscous lysates can compromise downstream filtration and chromatography, so a harvest decision cannot be made independently of purification.

The larger aim of Downstream processing is to answer this question: Relate harvesting, disruption, separation, concentration, and final product quality to recovery and economic tradeoffs. A result must be interpreted as a statement about a specified physical boundary and observed quantities. Distinguish the underlying biological mechanism from the mathematical convenience that makes a calculation tractable. A model can be dimensionally consistent and still be badly chosen for the organism, medium or scale. Conversely, a complicated simulator is not superior unless its extra parameters can be identified and tested with observations.

A useful model and its assumptions

Working relation: Specific volumetric energy is Ev=P/Q, where P is power in J/s and Q is volume flow in m³/s; Ev has units J/m³. This is an input, not a biological damage or disruption model.

The displayed relationship is a starting point for reasoning. Before substituting numbers, name every term, give the unit and decide whether each quantity is a measured value, a fitted coefficient, or a controlled setting. Conservation laws are independent of constitutive assumptions, while kinetic and transfer coefficients depend on conditions. Make a sketch of the relevant system boundary and show what enters, accumulates and leaves. State whether the rate is per unit liquid volume, per unit catalyst or per unit cell mass; confusing these bases can lead to order-of-magnitude errors even when individual values seem realistic.

When a relationship contains an exponential, check which variable is integrated in the exponent and whether the exponent is dimensionless. When it contains a ratio, check what happens as the denominator approaches a limiting condition. When it describes an observable signal, identify the calibration that connects that signal to the claimed physical quantity. These checks are not substitutes for experiment, but they reject many wrong models before fitting begins.

Worked investigation with synthetic numbers

If a device uses 1.2 kW and processes 60 L/h, Q=1.67×10⁻⁵ m³/s, so Ev≈72 MJ/m³. A different machine with equal Ev may still give different lysis and temperature rise.

Reconstruction task. Rewrite the stated computation as a ledger: input variable and unit, conversion used, intermediate result and final quantity. Show the same calculation with one input perturbed by 10% while retaining the others, and determine whether the output response is approximately proportional, nonlinear, or sensitive to a constraint. Then reverse the question: what input accuracy would be needed to distinguish the two predictions using a real instrument? Avoid claiming more significant figures than the chosen coefficients justify.

The example is intentionally synthetic. It should teach the direction and scale of a response, not imply that a specific organism or process will exhibit these numerical coefficients. If the result suggests substantial accumulation, ask where the required mass and energy originate. If it suggests extreme sensitivity, inspect whether the sensitivity arises from a genuine mechanistic feature or from mathematically approaching a singular assumption.

Measurement design and engineering judgment

Track target molecules across every stream. Close component and volume balances; measure both purity and recovery. Consider the location of the product before choosing a cell-harvest or disruption operation.

Measure target-product release and structural integrity across passes rather than ranking devices by energy alone. Include a heat balance and fouling assessment.

A defensible evidence plan identifies a process objective, measured signals, their frequency, instrument or assay uncertainty, and a comparison criterion selected before viewing the data. Include control conditions and independent replicates when the biological material varies across runs. Distinguish calibration measurements from hold-out verification data. If the main parameter is estimated from one narrow operating window, do not assume it will remain identifiable when oxygen, temperature, shear, pH or medium composition changes.

In a design review, explain the alternatives rather than selecting a model because it yields the highest projected titer or lowest cost. A common problem is conflating process capacity with process utilization: an available transfer rate is not automatically used, and biological demand can be low because the culture is inhibited. When a prediction is contradicted, investigate both the experiment and the model, and keep a record of the resulting revision.

Where the simple model fails

No simple energy proxy predicts retention of protein activity, capsid integrity or cell lysis. Local shear and pressure history differ between machines.

A classroom model is especially fragile when extrapolated beyond its parameter-identification range. Carefully distinguish structural uncertainty (missing mechanism or wrong equation), parameter uncertainty (imprecisely estimated coefficient), and measurement uncertainty (sensor or assay error). Running many simulations with one incorrect equation does not resolve structural uncertainty. A useful sensitivity chart should therefore accompany a stated model boundary, not pretend to replace it.

For an independent verification, perform three checks: units and conservation; a limiting condition with a known qualitative answer; and a second calculation method or external measurement. Explain what each check can and cannot demonstrate. Automated agreement with an equation confirms the implementation, not necessarily the equation's suitability for a real reactor.

Guided laboratory and discussion

Open [Laboratory 17](../labs/lab-17.html). Record the default input values with units. Move the first slider to three equally spaced settings while leaving other controls unchanged; save the response to CSV and compare the graph with the governing relation in that laboratory. Then change a second independent parameter to test whether the original trend is stable. The laboratory describes its physical limits and reports an explicit warning where assumptions fail. The export is generated locally; no data leave the browser.

Investigative prompt: Compare a secreted-product platform with an intracellular platform using an impurity and yield ledger for each stage.

Interpretation prompt: Identify a response that the model cannot predict, and propose one targeted measurement needed to decide if the omission matters. Write a two-sentence decision: what is supported by the simulation and what remains unproven. A high-grade response distinguishes a mathematical identity, an observation and a contingent engineering inference.

Lesson check

1. State the modeled system boundary, the type of measurable quantity being predicted and the appropriate units.
2. Derive or reconstruct the stated relation from a rate law or conservation balance, and show a limiting case.
3. Reproduce the worked calculation, then vary one input and interpret sensitivity without generalizing outside the stated model.
4. Identify two independent measurements that could falsify the simplified hypothesis.
5. Present a recommendation that is explicitly conditional on the evidence rather than an unsupported production specification.

Continue: Affinity and chromatographic separations. Return to the [unit learning pathway](../units/unit-06.html) or attempt the [unit assessment](../assessments/unit-06.html).

Unit 6 · Lesson 3 — Affinity and chromatographic separations

[Unit 06 overview](../units/unit-06.html) · [Run numerical laboratory 18](../labs/lab-18.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering question

Chromatography separates molecules by differential interactions with a stationary phase; the shape of elution peaks depends on mass transfer, binding kinetics, dispersion and column packing. Resolution can improve with column efficiency and selectivity, but these improvements can require longer cycle times, more pressure or expensive resin. A good laboratory resolution does not guarantee acceptable process economics. Dynamic binding capacity, cleaning compatibility and product stability matter alongside peak separation.

The larger aim of Downstream processing is to answer this question: Relate harvesting, disruption, separation, concentration, and final product quality to recovery and economic tradeoffs. A result must be interpreted as a statement about a specified physical boundary and observed quantities. Distinguish the underlying biological mechanism from the mathematical convenience that makes a calculation tractable. A model can be dimensionally consistent and still be badly chosen for the organism, medium or scale. Conversely, a complicated simulator is not superior unless its extra parameters can be identified and tested with observations.

A useful model and its assumptions

Working relation: A commonly used approximate expression is Rs≈(√N/4)[(α−1)/α][k/(1+k)], with plate count N, selectivity α>1 and retention factor k>0. It describes an idealized separation, not full binding chromatography.

The displayed relationship is a starting point for reasoning. Before substituting numbers, name every term, give the unit and decide whether each quantity is a measured value, a fitted coefficient, or a controlled setting. Conservation laws are independent of constitutive assumptions, while kinetic and transfer coefficients depend on conditions. Make a sketch of the relevant system boundary and show what enters, accumulates and leaves. State whether the rate is per unit liquid volume, per unit catalyst or per unit cell mass; confusing these bases can lead to order-of-magnitude errors even when individual values seem realistic.

When a relationship contains an exponential, check which variable is integrated in the exponent and whether the exponent is dimensionless. When it contains a ratio, check what happens as the denominator approaches a limiting condition. When it describes an observable signal, identify the calibration that connects that signal to the claimed physical quantity. These checks are not substitutes for experiment, but they reject many wrong models before fitting begins.

Worked investigation with synthetic numbers

With N=5000, α=1.2 and k=3, Rs≈2.21. Increasing N by fourfold doubles predicted resolution, at the expense of potential cycle time and pressure.

Reconstruction task. Rewrite the stated computation as a ledger: input variable and unit, conversion used, intermediate result and final quantity. Show the same calculation with one input perturbed by 10% while retaining the others, and determine whether the output response is approximately proportional, nonlinear, or sensitive to a constraint. Then reverse the question: what input accuracy would be needed to distinguish the two predictions using a real instrument? Avoid claiming more significant figures than the chosen coefficients justify.

The example is intentionally synthetic. It should teach the direction and scale of a response, not imply that a specific organism or process will exhibit these numerical coefficients. If the result suggests substantial accumulation, ask where the required mass and energy originate. If it suggests extreme sensitivity, inspect whether the sensitivity arises from a genuine mechanistic feature or from mathematically approaching a singular assumption.

Measurement design and engineering judgment

Track target molecules across every stream. Close component and volume balances; measure both purity and recovery. Consider the location of the product before choosing a cell-harvest or disruption operation.

Validate dynamic capacity and breakthrough, not just an ideal plate-count expression. Check that chromatogram integration properly handles overlapping peaks.

A defensible evidence plan identifies a process objective, measured signals, their frequency, instrument or assay uncertainty, and a comparison criterion selected before viewing the data. Include control conditions and independent replicates when the biological material varies across runs. Distinguish calibration measurements from hold-out verification data. If the main parameter is estimated from one narrow operating window, do not assume it will remain identifiable when oxygen, temperature, shear, pH or medium composition changes.

In a design review, explain the alternatives rather than selecting a model because it yields the highest projected titer or lowest cost. A common problem is conflating process capacity with process utilization: an available transfer rate is not automatically used, and biological demand can be low because the culture is inhibited. When a prediction is contradicted, investigate both the experiment and the model, and keep a record of the resulting revision.

Where the simple model fails

The approximate equation assumes chromatographic behavior not captured by nonlinear binding, gradients, large molecules or overloaded beds. No universal purity prediction follows.

A classroom model is especially fragile when extrapolated beyond its parameter-identification range. Carefully distinguish structural uncertainty (missing mechanism or wrong equation), parameter uncertainty (imprecisely estimated coefficient), and measurement uncertainty (sensor or assay error). Running many simulations with one incorrect equation does not resolve structural uncertainty. A useful sensitivity chart should therefore accompany a stated model boundary, not pretend to replace it.

For an independent verification, perform three checks: units and conservation; a limiting condition with a known qualitative answer; and a second calculation method or external measurement. Explain what each check can and cannot demonstrate. Automated agreement with an equation confirms the implementation, not necessarily the equation's suitability for a real reactor.

Guided laboratory and discussion

Open [Laboratory 18](../labs/lab-18.html). Record the default input values with units. Move the first slider to three equally spaced settings while leaving other controls unchanged; save the response to CSV and compare the graph with the governing relation in that laboratory. Then change a second independent parameter to test whether the original trend is stable. The laboratory describes its physical limits and reports an explicit warning where assumptions fail. The export is generated locally; no data leave the browser.

Investigative prompt: Prepare a stage-yield table for capture, intermediate and polishing operations, and distinguish analytical purity from process yield.

Interpretation prompt: Identify a response that the model cannot predict, and propose one targeted measurement needed to decide if the omission matters. Write a two-sentence decision: what is supported by the simulation and what remains unproven. A high-grade response distinguishes a mathematical identity, an observation and a contingent engineering inference.

Lesson check

1. State the modeled system boundary, the type of measurable quantity being predicted and the appropriate units.
2. Derive or reconstruct the stated relation from a rate law or conservation balance, and show a limiting case.
3. Reproduce the worked calculation, then vary one input and interpret sensitivity without generalizing outside the stated model.
4. Identify two independent measurements that could falsify the simplified hypothesis.
5. Present a recommendation that is explicitly conditional on the evidence rather than an unsupported production specification.

Continue: Membrane concentration, formulation and recovery. Return to the [unit learning pathway](../units/unit-06.html) or attempt the [unit assessment](../assessments/unit-06.html).

Unit 6 · Lesson 4 — Membrane concentration, formulation and recovery

[Unit 06 overview](../units/unit-06.html) · [Run numerical laboratory 18](../labs/lab-18.html) · [Assessment](../assessments/unit-06.html) · [Applied project](../projects/unit-06.html)

The engineering question

Ultrafiltration can retain macromolecules while allowing smaller solutes and water to pass, but real permeate flux falls with polarization, fouling and changing viscosity. Concentration factor measures reduction of retentate volume, not recovery of target product. Diafiltration can exchange buffer, while formulation must preserve quality attributes such as aggregation state, activity and chemical stability. Recoveries compound multiplicatively across stages, so small losses at each step can sharply reduce overall yield.

The larger aim of Downstream processing is to answer this question: Relate harvesting, disruption, separation, concentration, and final product quality to recovery and economic tradeoffs. A result must be interpreted as a statement about a specified physical boundary and observed quantities. Distinguish the underlying biological mechanism from the mathematical convenience that makes a calculation tractable. A model can be dimensionally consistent and still be badly chosen for the organism, medium or scale. Conversely, a complicated simulator is not superior unless its extra parameters can be identified and tested with observations.

A useful model and its assumptions

Working relation: For an ideal retained solute with no mass loss, concentration factor CF=V0/Vr. Actual target recovery R=Mtarget,out/Mtarget,in must be measured separately.

The displayed relationship is a starting point for reasoning. Before substituting numbers, name every term, give the unit and decide whether each quantity is a measured value, a fitted coefficient, or a controlled setting. Conservation laws are independent of constitutive assumptions, while kinetic and transfer coefficients depend on conditions. Make a sketch of the relevant system boundary and show what enters, accumulates and leaves. State whether the rate is per unit liquid volume, per unit catalyst or per unit cell mass; confusing these bases can lead to order-of-magnitude errors even when individual values seem realistic.

When a relationship contains an exponential, check which variable is integrated in the exponent and whether the exponent is dimensionless. When it contains a ratio, check what happens as the denominator approaches a limiting condition. When it describes an observable signal, identify the calibration that connects that signal to the claimed physical quantity. These checks are not substitutes for experiment, but they reject many wrong models before fitting begins.

Worked investigation with synthetic numbers

If 100 L is concentrated to 20 L, CF=5, but if protein recovery is 90%, concentration increases only by 4.5-fold on a mass/volume basis. Using CF as a synonym for recovery would overstate product output.

Reconstruction task. Rewrite the stated computation as a ledger: input variable and unit, conversion used, intermediate result and final quantity. Show the same calculation with one input perturbed by 10% while retaining the others, and determine whether the output response is approximately proportional, nonlinear, or sensitive to a constraint. Then reverse the question: what input accuracy would be needed to distinguish the two predictions using a real instrument? Avoid claiming more significant figures than the chosen coefficients justify.

The example is intentionally synthetic. It should teach the direction and scale of a response, not imply that a specific organism or process will exhibit these numerical coefficients. If the result suggests substantial accumulation, ask where the required mass and energy originate. If it suggests extreme sensitivity, inspect whether the sensitivity arises from a genuine mechanistic feature or from mathematically approaching a singular assumption.

Measurement design and engineering judgment

Track target molecules across every stream. Close component and volume balances; measure both purity and recovery. Consider the location of the product before choosing a cell-harvest or disruption operation.

Measure feed, retentate and permeate concentrations, volumes and aggregate fraction. A mass balance can reveal apparent losses to adsorption or dead volume.

A defensible evidence plan identifies a process objective, measured signals, their frequency, instrument or assay uncertainty, and a comparison criterion selected before viewing the data. Include control conditions and independent replicates when the biological material varies across runs. Distinguish calibration measurements from hold-out verification data. If the main parameter is estimated from one narrow operating window, do not assume it will remain identifiable when oxygen, temperature, shear, pH or medium composition changes.

In a design review, explain the alternatives rather than selecting a model because it yields the highest projected titer or lowest cost. A common problem is conflating process capacity with process utilization: an available transfer rate is not automatically used, and biological demand can be low because the culture is inhibited. When a prediction is contradicted, investigate both the experiment and the model, and keep a record of the resulting revision.

Where the simple model fails

The volume-only model ignores osmotic pressure, variable flux and product adsorption. Formulation stability cannot be inferred from concentration factor.

A classroom model is especially fragile when extrapolated beyond its parameter-identification range. Carefully distinguish structural uncertainty (missing mechanism or wrong equation), parameter uncertainty (imprecisely estimated coefficient), and measurement uncertainty (sensor or assay error). Running many simulations with one incorrect equation does not resolve structural uncertainty. A useful sensitivity chart should therefore accompany a stated model boundary, not pretend to replace it.

For an independent verification, perform three checks: units and conservation; a limiting condition with a known qualitative answer; and a second calculation method or external measurement. Explain what each check can and cannot demonstrate. Automated agreement with an equation confirms the implementation, not necessarily the equation's suitability for a real reactor.

Guided laboratory and discussion

Open [Laboratory 18](../labs/lab-18.html). Record the default input values with units. Move the first slider to three equally spaced settings while leaving other controls unchanged; save the response to CSV and compare the graph with the governing relation in that laboratory. Then change a second independent parameter to test whether the original trend is stable. The laboratory describes its physical limits and reports an explicit warning where assumptions fail. The export is generated locally; no data leave the browser.

Investigative prompt: Contrast two concentration strategies by total recovery, time, buffer consumption and product-quality measurements.

Interpretation prompt: Identify a response that the model cannot predict, and propose one targeted measurement needed to decide if the omission matters. Write a two-sentence decision: what is supported by the simulation and what remains unproven. A high-grade response distinguishes a mathematical identity, an observation and a contingent engineering inference.

Lesson check

1. State the modeled system boundary, the type of measurable quantity being predicted and the appropriate units.
2. Derive or reconstruct the stated relation from a rate law or conservation balance, and show a limiting case.
3. Reproduce the worked calculation, then vary one input and interpret sensitivity without generalizing outside the stated model.
4. Identify two independent measurements that could falsify the simplified hypothesis.
5. Present a recommendation that is explicitly conditional on the evidence rather than an unsupported production specification.

Continue: Unit assessment. Return to the [unit learning pathway](../units/unit-06.html) or attempt the [unit assessment](../assessments/unit-06.html).

Unit 06 — Applied engineering project: Downstream processing

Status: fictional teaching case; all experimental measurements, process values and costs must be supplied or explicitly marked synthetic. This is not an authorization to conduct biological culture, run equipment, release a therapeutic or discharge wastewater.

Project brief

An intracellular enzyme is produced in a synthetic fermentation broth. Harvest, disruption, filtration and chromatographic capture each reduce product mass, and a processing shortcut may increase impurity burden even as target mass recovery improves.

The task is not to maximize a single simulated variable. It is to demonstrate that an engineering conclusion rests on a defensible boundary, conserved quantities, experimentally testable assumptions, and explicit uncertainty. Students must distinguish a model output from a measurement and a possible risk from an observed failure. A written recommendation must name the conditions that would reverse it.

Analytical scope

Write a stream-by-stream mass and target-product ledger. Compare a harvest-first train with an alternative train. Estimate Stokes settling limits, filtration-resistance trend and chromatography selectivity without converting the models into vendor guarantees.

Construct a process map with numbered stream or information flows. Give a name, unit, origin, expected uncertainty, and timing for every requested input. Show where the model has a fitted coefficient as opposed to a measured quantity. If a coefficient is not available, express results parametrically and give an illustrative sensitivity range; do not silently invent a best-estimate industrial value.

Evaluate at least two candidate decisions with one common denominator: product mass per time, target recovery, demand/supply margin, analytical comparability, or another defensible quantity aligned with the case objective. A design that seems superior only because different quantities are being compared should be rejected as unresolved. Use a conservation audit to check whether any claimed improvement moves beyond the available mass, substrate or energy.

Numerical investigations

1. Extract a first-principles relationship from one of the four unit lessons; identify dimensions and limiting cases.
2. Run [Lab 16](../labs/lab-16.html) and record the full model input vector. Export its parameter sweep and explain the default trend.
3. Run [Lab 17](../labs/lab-17.html); deliberately choose a second configuration with different assumptions. Give the independent reason to use the second model.
4. Run [Lab 18](../labs/lab-18.html). Identify any warnings, invalid domains, or model-regime boundaries and explain their physical significance.
5. Use a spreadsheet, pseudocode or a short program to independently verify one selected model output. Report discrepancy, units and rounding conventions. Test one zero-input, saturation, washout or conservation limit appropriate to the chosen model.

Measurement and evidence plan

To challenge your preferred conclusion, describe the specific experiment, sample or instrument measurement that would cause the most information gain. Plan a negative or reference control, repeat measurements where biological variability matters, and specify the comparison that would be judged before seeing the results. Report whether the experiment challenges parameter values, constitutive form or sensor calibration. Maintain separate pages for evidence actually collected, assumptions borrowed from literature and hypothetical inputs introduced for illustration.

Deliverables

Submit a unit-operation block diagram, mass/purity balance, stage-recovery waterfall, measurement plan for aggregation or activity, and a recovery-versus-quality trade-off with clear uncertainties.

The final package should contain a concise executive summary, a source-and-assumption register, dimensional and material balances, transparent calculations, a three-scenario sensitivity chart, and the source CSV files needed to reproduce every figure. Include two alternatives not selected and explain why they fail against the stated objective or evidence requirements.

Quality rubric (100 marks)

Reflection: Which additional observation, if obtained tomorrow, would have the highest chance of changing your recommendation? Explain why this information is more valuable than running another deterministic curve with the same uncertain assumptions.

Unit 06 — Assessment: Downstream processing

This assessment has 16 substantive multi-part problems: four for each lesson. The purpose is to test domain reasoning, consistent units, conserved quantities, uncertainty and evidence. Students may explicitly reject an ill-posed process claim. Model values and numeric scenarios in the questions are fictional, not real plant operating conditions.

Assessment rubric (10 marks per task): clear physical boundary and correct units (2); correct equation or causal mechanism (2); numerical reconstruction or falsifiable reasoning (2); explicit applicability limits and uncertainty (2); defensible experimental or process decision (2). A correct calculation that silently uses an unsupported model cannot earn full credit.

Lesson 1 — Biomass harvesting and mechanical separation

Q01 — Reproduce and perturb a calculation (10 marks)

A. Reconstruct the numbers. Begin with the following numerical evidence: Assume d=8 µm, Δρ=80 kg/m³ and viscosity 1.5 mPa·s. Then v≈1.86×10⁻⁶ m/s. Halving diameter reduces predicted speed by a factor of four, even before considering aggregation and density variation. Identify every supplied number, every resulting number and the unit basis for each. Recompute the result using your own calculator or code, not by copying the printed final value. Alter one input by 15%, while preserving all others, and quantify the absolute and percentage change in output. Is the local response linear, and would a 15% observation error have the same impact as a deliberate 15% process change? State one limiting case and judge whether the scenario remains physically possible under conserved mass, energy or material balances.

Q02 — Conservation and dimensional audit (10 marks)

B. Develop the relation, not just the answer. Take the stated working relationship: For a small isolated sphere in creeping flow, Stokes settling speed is v=Δρ g d²/(18μ). Check particle Reynolds number and hindered settling before applying it to a dense cell slurry. Begin from a species inventory, rate law or causal diagram appropriate to Biomass harvesting and mechanical separation. Show which terms would appear in the full statement, and identify each term removed in obtaining the simplified equation. Specify the units of two independent variables and of the predicted observable. Test at least two limiting conditions, including a zero rate, a dilute regime, a saturation boundary or a zero residence time where applicable. Explain how you would detect a wrong sign or a missing conversion factor without knowing the expected answer.

Q03 — Challenge the numerical model (10 marks)

C. Attempt to falsify the simulation. Open [Laboratory 16](../labs/lab-16.html) and record the exact default inputs with units. Save the full curve as CSV, choose three separated points, and calculate a finite-difference sensitivity from each adjacent pair. Repeat after changing a second parameter by a controlled amount. Use the model's stated restrictions—Stokes law fails when Reynolds number is not small or particles are nonspherical, deformable or concentrated. Centrifugal fields and flow residence-time distributions require more elaborate models.—to identify at least two reasons a real experiment could disagree. Propose an observable and an experimental control that would discriminate parameter error from a missing physical mechanism. Do not equate agreement with the software to biological validation.

Q04 — Design a discriminating experiment (10 marks)

D. Make an evidence-constrained decision. Consider this engineering action: Use particle-size distributions and representative viscosity measurements to compare equipment trials. Record target recovery and purity in both outlet streams. Develop two plausible alternatives and a comparison matrix with expected benefit, scientific risk, measurement effort and an uncertainty or scale-up limitation. Propose three measurements that could change your decision, including one that directly tests the simplified model and one that checks product quality or conservation. Explain what evidence would make you stop the trial. Write a clear recommendation conditional on that evidence; explicitly say why a purely synthetic numerical prediction does not permit an operational or regulatory claim. End with a one-paragraph communication suitable for a multidisciplinary design review.

Lesson 2 — Cell disruption and extraction choices

Q05 — Reproduce and perturb a calculation (10 marks)

A. Reconstruct the numbers. Begin with the following numerical evidence: If a device uses 1.2 kW and processes 60 L/h, Q=1.67×10⁻⁵ m³/s, so Ev≈72 MJ/m³. A different machine with equal Ev may still give different lysis and temperature rise. Identify every supplied number, every resulting number and the unit basis for each. Recompute the result using your own calculator or code, not by copying the printed final value. Alter one input by 15%, while preserving all others, and quantify the absolute and percentage change in output. Is the local response linear, and would a 15% observation error have the same impact as a deliberate 15% process change? State one limiting case and judge whether the scenario remains physically possible under conserved mass, energy or material balances.

Q06 — Conservation and dimensional audit (10 marks)

B. Develop the relation, not just the answer. Take the stated working relationship: Specific volumetric energy is Ev=P/Q, where P is power in J/s and Q is volume flow in m³/s; Ev has units J/m³. This is an input, not a biological damage or disruption model. Begin from a species inventory, rate law or causal diagram appropriate to Cell disruption and extraction choices. Show which terms would appear in the full statement, and identify each term removed in obtaining the simplified equation. Specify the units of two independent variables and of the predicted observable. Test at least two limiting conditions, including a zero rate, a dilute regime, a saturation boundary or a zero residence time where applicable. Explain how you would detect a wrong sign or a missing conversion factor without knowing the expected answer.

Q07 — Challenge the numerical model (10 marks)

C. Attempt to falsify the simulation. Open [Laboratory 17](../labs/lab-17.html) and record the exact default inputs with units. Save the full curve as CSV, choose three separated points, and calculate a finite-difference sensitivity from each adjacent pair. Repeat after changing a second parameter by a controlled amount. Use the model's stated restrictions—No simple energy proxy predicts retention of protein activity, capsid integrity or cell lysis. Local shear and pressure history differ between machines.—to identify at least two reasons a real experiment could disagree. Propose an observable and an experimental control that would discriminate parameter error from a missing physical mechanism. Do not equate agreement with the software to biological validation.

Q08 — Design a discriminating experiment (10 marks)

D. Make an evidence-constrained decision. Consider this engineering action: Measure target-product release and structural integrity across passes rather than ranking devices by energy alone. Include a heat balance and fouling assessment. Develop two plausible alternatives and a comparison matrix with expected benefit, scientific risk, measurement effort and an uncertainty or scale-up limitation. Propose three measurements that could change your decision, including one that directly tests the simplified model and one that checks product quality or conservation. Explain what evidence would make you stop the trial. Write a clear recommendation conditional on that evidence; explicitly say why a purely synthetic numerical prediction does not permit an operational or regulatory claim. End with a one-paragraph communication suitable for a multidisciplinary design review.

Lesson 3 — Affinity and chromatographic separations

Q09 — Reproduce and perturb a calculation (10 marks)

A. Reconstruct the numbers. Begin with the following numerical evidence: With N=5000, α=1.2 and k=3, Rs≈2.21. Increasing N by fourfold doubles predicted resolution, at the expense of potential cycle time and pressure. Identify every supplied number, every resulting number and the unit basis for each. Recompute the result using your own calculator or code, not by copying the printed final value. Alter one input by 15%, while preserving all others, and quantify the absolute and percentage change in output. Is the local response linear, and would a 15% observation error have the same impact as a deliberate 15% process change? State one limiting case and judge whether the scenario remains physically possible under conserved mass, energy or material balances.

Q10 — Conservation and dimensional audit (10 marks)

B. Develop the relation, not just the answer. Take the stated working relationship: A commonly used approximate expression is Rs≈(√N/4)[(α−1)/α][k/(1+k)], with plate count N, selectivity α>1 and retention factor k>0. It describes an idealized separation, not full binding chromatography. Begin from a species inventory, rate law or causal diagram appropriate to Affinity and chromatographic separations. Show which terms would appear in the full statement, and identify each term removed in obtaining the simplified equation. Specify the units of two independent variables and of the predicted observable. Test at least two limiting conditions, including a zero rate, a dilute regime, a saturation boundary or a zero residence time where applicable. Explain how you would detect a wrong sign or a missing conversion factor without knowing the expected answer.

Q11 — Challenge the numerical model (10 marks)

C. Attempt to falsify the simulation. Open [Laboratory 18](../labs/lab-18.html) and record the exact default inputs with units. Save the full curve as CSV, choose three separated points, and calculate a finite-difference sensitivity from each adjacent pair. Repeat after changing a second parameter by a controlled amount. Use the model's stated restrictions—The approximate equation assumes chromatographic behavior not captured by nonlinear binding, gradients, large molecules or overloaded beds. No universal purity prediction follows.—to identify at least two reasons a real experiment could disagree. Propose an observable and an experimental control that would discriminate parameter error from a missing physical mechanism. Do not equate agreement with the software to biological validation.

Q12 — Design a discriminating experiment (10 marks)

D. Make an evidence-constrained decision. Consider this engineering action: Validate dynamic capacity and breakthrough, not just an ideal plate-count expression. Check that chromatogram integration properly handles overlapping peaks. Develop two plausible alternatives and a comparison matrix with expected benefit, scientific risk, measurement effort and an uncertainty or scale-up limitation. Propose three measurements that could change your decision, including one that directly tests the simplified model and one that checks product quality or conservation. Explain what evidence would make you stop the trial. Write a clear recommendation conditional on that evidence; explicitly say why a purely synthetic numerical prediction does not permit an operational or regulatory claim. End with a one-paragraph communication suitable for a multidisciplinary design review.

Lesson 4 — Membrane concentration, formulation and recovery

Q13 — Reproduce and perturb a calculation (10 marks)

A. Reconstruct the numbers. Begin with the following numerical evidence: If 100 L is concentrated to 20 L, CF=5, but if protein recovery is 90%, concentration increases only by 4.5-fold on a mass/volume basis. Using CF as a synonym for recovery would overstate product output. Identify every supplied number, every resulting number and the unit basis for each. Recompute the result using your own calculator or code, not by copying the printed final value. Alter one input by 15%, while preserving all others, and quantify the absolute and percentage change in output. Is the local response linear, and would a 15% observation error have the same impact as a deliberate 15% process change? State one limiting case and judge whether the scenario remains physically possible under conserved mass, energy or material balances.

Q14 — Conservation and dimensional audit (10 marks)

B. Develop the relation, not just the answer. Take the stated working relationship: For an ideal retained solute with no mass loss, concentration factor CF=V0/Vr. Actual target recovery R=Mtarget,out/Mtarget,in must be measured separately. Begin from a species inventory, rate law or causal diagram appropriate to Membrane concentration, formulation and recovery. Show which terms would appear in the full statement, and identify each term removed in obtaining the simplified equation. Specify the units of two independent variables and of the predicted observable. Test at least two limiting conditions, including a zero rate, a dilute regime, a saturation boundary or a zero residence time where applicable. Explain how you would detect a wrong sign or a missing conversion factor without knowing the expected answer.

Q15 — Challenge the numerical model (10 marks)

C. Attempt to falsify the simulation. Open [Laboratory 18](../labs/lab-18.html) and record the exact default inputs with units. Save the full curve as CSV, choose three separated points, and calculate a finite-difference sensitivity from each adjacent pair. Repeat after changing a second parameter by a controlled amount. Use the model's stated restrictions—The volume-only model ignores osmotic pressure, variable flux and product adsorption. Formulation stability cannot be inferred from concentration factor.—to identify at least two reasons a real experiment could disagree. Propose an observable and an experimental control that would discriminate parameter error from a missing physical mechanism. Do not equate agreement with the software to biological validation.

Q16 — Design a discriminating experiment (10 marks)

D. Make an evidence-constrained decision. Consider this engineering action: Measure feed, retentate and permeate concentrations, volumes and aggregate fraction. A mass balance can reveal apparent losses to adsorption or dead volume. Develop two plausible alternatives and a comparison matrix with expected benefit, scientific risk, measurement effort and an uncertainty or scale-up limitation. Propose three measurements that could change your decision, including one that directly tests the simplified model and one that checks product quality or conservation. Explain what evidence would make you stop the trial. Write a clear recommendation conditional on that evidence; explicitly say why a purely synthetic numerical prediction does not permit an operational or regulatory claim. End with a one-paragraph communication suitable for a multidisciplinary design review.

Practice task linked to this lesson: Contrast two concentration strategies by total recovery, time, buffer consumption and product-quality measurements.