Evaporation, Humidification and Industrial Drying

Scope: Humidity; drying curves; moisture diffusion; dryer design. Four lessons connect microscopic transport or process operating principles to practical calculations. Relevant laboratory models: 11, 12, 13.

Central engineering ideas

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

Four-lesson reading path

Lesson 1: Humid-air state and evaporation potential

Psychrometric humidity ratio differs from relative humidity; moisture pickup is constrained by both equilibrium and energy availability. The working equation Y=0.622 p_w/(P-p_w) makes a limited, testable claim about the dependence of transfer on specified properties. Hot gas with high relative humidity can be a poor dryer despite an apparently high temperature. The validity check is especially important here: Check saturated vapor-pressure data for the relevant temperature and pressure. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 1](../lessons/unit-05-lesson-01.html).

Lesson 2: Evaporators and vaporization duty

A single-effect evaporator needs sensible heating plus latent duty; boiling-point elevation and fouling affect real utility demand. The working equation Q=m_feed cp(T_b-T_in)+m_vap lambda makes a limited, testable claim about the dependence of transfer on specified properties. A concentrated liquor requires steam above the pure-solvent boiling point. The validity check is especially important here: Heat recovery, nonideal enthalpy and boiling-point elevation matter for real designs. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 2](../lessons/unit-05-lesson-02.html).

Lesson 3: Constant-rate drying and the critical moisture point

The constant-rate region is generally controlled by external heat and mass exchange while the product surface remains sufficiently wet. The working equation t_c=M_dry(X0-Xc)/(A N_c) makes a limited, testable claim about the dependence of transfer on specified properties. A wet granular product dries almost linearly in time until the critical moisture content. The validity check is especially important here: A measured critical moisture is material and equipment dependent. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 3](../lessons/unit-05-lesson-03.html).

Lesson 4: Falling-rate drying and internal diffusion

Once the surface dries, diffusion, capillarity and internal structure limit moisture removal, usually slowing the process. The working equation t_f=M_dry(Xc-Xe)/(A N_c) ln[(Xc-Xe)/(Xf-Xe)] makes a limited, testable claim about the dependence of transfer on specified properties. A food powder reaches a long drying tail that cannot be eliminated by increasing air speed alone. The validity check is especially important here: Empirical falling-rate laws must be checked against actual drying curves. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 4](../lessons/unit-05-lesson-04.html).

Analysis, synthesis and laboratory practice

First create a one-page property table: list fluid phase, bulk composition, surface or interface state, temperature, pressure, and the reference from which viscosity or diffusivity was obtained. Next sketch the principal control volume and write a component balance even when a transfer correlation is already known. Conservation closure should be computed using independent inventory data, not simply by substituting the computed flux back into the same equation.

Then use the simulation models to build a two-dimensional experiment: perform one sweep in the primary adjustable parameter and repeat at two distinct fixed values of a secondary parameter. Compare the resulting curves and explain whether the ranking changes. When model rankings do change, identify the competing effects. Where the equation predicts no change with a parameter that matters experimentally, the discrepancy is useful evidence of a missing mechanism rather than a reason to manipulate the fit.

For technical reporting, preserve the input CSV, baseline calculation, units and full list of assumptions. Include a short paragraph that distinguishes model sensitivity from actual process uncertainty, and identify one input that should be measured more precisely before design decisions. Link the interpretation to a measurable concentration, flow, pressure or inventory instead of treating the plotted output as a stand-alone achievement.

Suggested learning evidence: a control-volume sketch, two parameter sweeps, a worked balance, one falsification experiment and a paragraph about uncertainty.

Unit 5, Lesson 1: Humid-air state and evaporation potential

Unit: Evaporation and drying. Core model: Y=0.622 p_w/(P-p_w). Interactive laboratory: [Laboratory 11](../labs/lab-11.html).

What the phenomenon means

Psychrometric humidity ratio differs from relative humidity; moisture pickup is constrained by both equilibrium and energy availability. The governing relationship is Y=0.622 p_w/(P-p_w). In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

A process example and a defensible workflow

Hot gas with high relative humidity can be a poor dryer despite an apparently high temperature. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

Before a design estimate becomes a purchasing specification, attach a measurement plan: the temperature and composition range, the reference for transport properties, the proposed independent validation case and an acceptable error tolerance. If the coefficient comes from a chart, record the relevant fluid regime, dimensionless groups and length definition so that another engineer can reproduce it.

Interpretation and validity

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

Model assumptions should be tested against data rather than copied uncritically from a standard derivation. Vary one independent parameter at a time when possible; then vary a second parameter to reveal interaction. Report whether a discrepancy has the sign expected for fouling, film resistance, transient storage or a changed equilibrium. Use a simple residual plot instead of relying exclusively on R².

Failure mode to recognize: Check saturated vapor-pressure data for the relevant temperature and pressure. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for Y=0.622 p_w/(P-p_w). Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 5, Lesson 2: Evaporators and vaporization duty

Unit: Evaporation and drying. Core model: Q=m_feed cp(T_b-T_in)+m_vap lambda. Interactive laboratory: [Laboratory 11](../labs/lab-11.html).

What the phenomenon means

A single-effect evaporator needs sensible heating plus latent duty; boiling-point elevation and fouling affect real utility demand. The governing relationship is Q=m_feed cp(T_b-T_in)+m_vap lambda. In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

A process example and a defensible workflow

A concentrated liquor requires steam above the pure-solvent boiling point. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

Make a small mass-balance closure table with inflow, outflow, transfer rate and accumulation. Flux integrated over area must agree with the change in inventory after any time integration. When a calculation satisfies a local transfer law but violates total inventory, the likely issue is a basis conversion, interface area or hidden phase holdup.

Interpretation and validity

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

A reliable material balance begins by choosing a control surface and defining what passes through it. If the measured concentration belongs to the bulk while the governing law requires the interfacial value, the missing boundary condition must be solved or independently measured. Draw the transfer path before deciding which concentration difference is available. This small discipline prevents fitting a physically impossible flux to a convenient linear graph.

Failure mode to recognize: Heat recovery, nonideal enthalpy and boiling-point elevation matter for real designs. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for Q=m_feed cp(T_b-T_in)+m_vap lambda. Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 5, Lesson 3: Constant-rate drying and the critical moisture point

Unit: Evaporation and drying. Core model: t_c=M_dry(X0-Xc)/(A N_c). Interactive laboratory: [Laboratory 11](../labs/lab-11.html).

What the phenomenon means

The constant-rate region is generally controlled by external heat and mass exchange while the product surface remains sufficiently wet. The governing relationship is t_c=M_dry(X0-Xc)/(A N_c). In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

A process example and a defensible workflow

A wet granular product dries almost linearly in time until the critical moisture content. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

To check the engineering consequence, compute the predicted response at the nominal case, then repeat after increasing the principal resistance by 25%. For a truly inverse dependence on resistance, the answer should fall to 80% of its original value. If your result rises instead, revisit the boundary definitions and the sign convention. This is a sensitivity test, not a substitute for experimental validation.

Interpretation and validity

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

Practical measurements have time constants. A concentration electrode or humidity sensor may respond more slowly than the process, causing a fitted diffusion time or mass-transfer coefficient to absorb instrument delay. Record probe location and sampling interval, and compare apparent rates in the first, middle and final periods of the experiment. If the response changes with stirring intensity, external transfer may be important.

Failure mode to recognize: A measured critical moisture is material and equipment dependent. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for t_c=M_dry(X0-Xc)/(A N_c). Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 5, Lesson 4: Falling-rate drying and internal diffusion

Unit: Evaporation and drying. Core model: t_f=M_dry(Xc-Xe)/(A N_c) ln[(Xc-Xe)/(Xf-Xe)]. Interactive laboratory: [Laboratory 11](../labs/lab-11.html).

What the phenomenon means

Once the surface dries, diffusion, capillarity and internal structure limit moisture removal, usually slowing the process. The governing relationship is t_f=M_dry(Xc-Xe)/(A N_c) ln[(Xc-Xe)/(Xf-Xe)]. In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

A process example and a defensible workflow

A food powder reaches a long drying tail that cannot be eliminated by increasing air speed alone. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

An experiment should separately record an initial value, a late value and at least one intermediate point. Compare the rate inferred from each interval. Under a steady, linear, constant-property model the slopes should be similar after excluding instrument transients; a systematic change suggests the claimed steady regime was not reached or the physical properties are changing.

Interpretation and validity

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

A dimensionally plausible equation can still be wrong for the equipment. Confirm the area to which the flux refers, the concentration basis (mass, molar, dry or wet), and whether the flow is per total area or open pore area. In scaled equipment, area-to-volume ratio varies with size, so equal concentration gradients do not automatically imply equal total processing time.

Failure mode to recognize: Empirical falling-rate laws must be checked against actual drying curves. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for t_f=M_dry(Xc-Xe)/(A N_c) ln[(Xc-Xe)/(Xf-Xe)]. Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Applied project — Unit 5: Evaporation and drying

Engineering decision

Drying couples heat delivery, vapor removal, and internal moisture migration. A constant-rate interval reflects surface evaporation while enough liquid reaches the exposed surface; the later falling-rate interval may be controlled by capillary pathways, diffusion or moving evaporation fronts. Moisture content on dry basis differs from wet basis, and failure to state the convention creates large mistakes.

Project brief: Design a small experimental method to compare two candidate operating conditions related to humid-air state and evaporation potential; evaporators and vaporization duty; constant-rate drying and the critical moisture point; falling-rate drying and internal diffusion. The purpose is not to produce a procurement specification, but to identify which input most affects mass transfer and whether an economical operating change could plausibly meet the desired duty.

Data and deliverables

• Draw a process flow schematic showing flow paths, relevant interfacial area and material inventory.
• Specify the two parameter sets using the bounds in the interactive laboratories; preserve the original and modified CSV files.
• Derive the governing model and predict relative response without touching the controls. Then compare with calculated responses.
• Determine the physical property that would contribute most to uncertainty. Plan at least three replicate measurements at two operating points.
• Document material compatibility, potential exposure or emissions, hydraulic constraints and credible failure mechanisms.
• Write a one-page decision statement recommending either a pilot trial, a revised analytical model, or rejection of the proposed change.

Independent validation

In process calculations, separate the mass of dry solids from evaporating water. Estimate a heat duty from sensible heating plus latent vaporization; then check if the air stream can remove the vapor while satisfying outlet humidity and temperature limits. For heat-sensitive foods or pharmaceuticals, faster superficial evaporation can damage product quality. A drying curve should be supported by weighed samples and measured air conditions, not only by a fitted time law.

A strong answer explicitly separates a screening assumption from a measured process characteristic. If two mechanisms can lead to the same observed transfer rate, propose a controlled test that discriminates between them. Scale-up should retain the causal mechanism, not just the appearance of a laboratory curve.

Evaluation: method and assumptions 25%; balance closure and units 20%; experiment design 20%; quantitative interpretation 20%; candid limitations and safety 15%.

Laboratory 09: Absorber transfer units

Relevant unit: Absorption. Governing relationship: NTU = ln((y_in-y)/(y_out-y)); Z=HTU·NTU.

Physical question

What happens to the predicted absorber transfer units when its principal adjustable parameter changes, and how does that sensitivity relate to the mechanism described in this unit? The baseline parameter values are synthetic teaching inputs, not measurements from a named plant. This experiment is designed to expose a mathematical trend and make its units visible before real property data are substituted.

Experimental setup and protocol

Constant equilibrium mole fraction and HTU; not a detailed column design. List the assumptions on paper before changing inputs. Treat the first control as the independent variable; keep the remaining parameters fixed for the first sweep. Read the numerical output at the minimum, baseline and maximum setting, then export the 121-point curve. Repeat at a second value of the parameter most strongly coupled to the driving force. Use the on-screen schematic to identify the direction of transport and the conceptual location of the limiting resistance. It is not a scale drawing.

Parameters

• Gas outlet mole fraction: default 0.025 —, adjustable range 0.005–0.09 —. Check the measurement source and correlation domain before substitution.
• Gas inlet mole fraction: default 0.18 —, adjustable range 0.1–0.3 —. Check the measurement source and correlation domain before substitution.
• Equilibrium gas fraction: default 0.003 —, adjustable range 0–0.004 —. Check the measurement source and correlation domain before substitution.
• Height of transfer unit: default 0.9 m, adjustable range 0.2–2 m. Check the measurement source and correlation domain before substitution.

Interpretation and model boundaries

A countercurrent absorber simultaneously performs a mass balance and an equilibrium-limited separation. The operating line is constrained by inlet and outlet compositions and the solvent-to-gas molar rate ratio, while the equilibrium line expresses thermodynamic possibility. The gap between these lines is the local driving force. A pinch occurs when they touch, at which point a simple idealized finite-rate model predicts unbounded contact height.

The response curve is a local sensitivity plot in which other controls remain fixed. It does not automatically represent a physical trajectory through a reactor or a separation column. A reported ''outside model validity'' result indicates a mathematical or physical constraint such as an inverted concentration difference, invalid pinch, an incompatible moisture ordering, or a correlation beyond its specified regime. The laboratory deliberately leaves these cases visible so they can be diagnosed instead of silently clipped.

Investigation questions

1. Calculate the baseline result independently using NTU = ln((y_in-y)/(y_out-y)); Z=HTU·NTU. Convert all parameter units first. What is the largest source of numerical uncertainty?
2. Explain the curvature or straightness of the sweep. Does doubling the first parameter double, halve, or otherwise change the response?
3. Which plausible operating effect is excluded by the model: property variation, pressure drop, fouling, chemical reaction, unsteady accumulation, or imperfect contact? Describe a test for that effect.
4. If a customer specification required the output to improve by 15%, identify two possible changes and discuss an operational cost or safety implication of each.

Use restriction: Educational sensitivity model; it is not a substitute for verified correlations, material data, equipment design standards or engineering sign-off.

Laboratory 10: Minimum solvent ratio

Relevant unit: Absorption. Governing relationship: (L/G)_min=(y_in-y_out)/(x_out,max-x_in).

Physical question

What happens to the predicted minimum solvent ratio when its principal adjustable parameter changes, and how does that sensitivity relate to the mechanism described in this unit? The baseline parameter values are synthetic teaching inputs, not measurements from a named plant. This experiment is designed to expose a mathematical trend and make its units visible before real property data are substituted.

Experimental setup and protocol

Dilute balance; rich-liquid loading is assumed feasible. List the assumptions on paper before changing inputs. Treat the first control as the independent variable; keep the remaining parameters fixed for the first sweep. Read the numerical output at the minimum, baseline and maximum setting, then export the 121-point curve. Repeat at a second value of the parameter most strongly coupled to the driving force. Use the on-screen schematic to identify the direction of transport and the conceptual location of the limiting resistance. It is not a scale drawing.

Parameters

• Maximum liquid exit loading: default 0.12 —, adjustable range 0.04–0.3 —. Check the measurement source and correlation domain before substitution.
• Lean liquid inlet loading: default 0.01 —, adjustable range 0–0.03 —. Check the measurement source and correlation domain before substitution.
• Gas inlet: default 0.22 —, adjustable range 0.08–0.4 —. Check the measurement source and correlation domain before substitution.
• Gas outlet: default 0.025 —, adjustable range 0.005–0.06 —. Check the measurement source and correlation domain before substitution.

Interpretation and model boundaries

A countercurrent absorber simultaneously performs a mass balance and an equilibrium-limited separation. The operating line is constrained by inlet and outlet compositions and the solvent-to-gas molar rate ratio, while the equilibrium line expresses thermodynamic possibility. The gap between these lines is the local driving force. A pinch occurs when they touch, at which point a simple idealized finite-rate model predicts unbounded contact height.

The response curve is a local sensitivity plot in which other controls remain fixed. It does not automatically represent a physical trajectory through a reactor or a separation column. A reported ''outside model validity'' result indicates a mathematical or physical constraint such as an inverted concentration difference, invalid pinch, an incompatible moisture ordering, or a correlation beyond its specified regime. The laboratory deliberately leaves these cases visible so they can be diagnosed instead of silently clipped.

Investigation questions

1. Calculate the baseline result independently using (L/G)_min=(y_in-y_out)/(x_out,max-x_in). Convert all parameter units first. What is the largest source of numerical uncertainty?
2. Explain the curvature or straightness of the sweep. Does doubling the first parameter double, halve, or otherwise change the response?
3. Which plausible operating effect is excluded by the model: property variation, pressure drop, fouling, chemical reaction, unsteady accumulation, or imperfect contact? Describe a test for that effect.
4. If a customer specification required the output to improve by 15%, identify two possible changes and discuss an operational cost or safety implication of each.

Use restriction: Educational sensitivity model; it is not a substitute for verified correlations, material data, equipment design standards or engineering sign-off.

Unit 5 assessment — Evaporation and drying

The assessment distinguishes memorization, calculation, interpretation and model criticism. Use SI conversions explicitly, give dimensional units for computed transfer rates and justify equilibrium assumptions.

Problem 1: Humid-air state and evaporation potential

Hot gas with high relative humidity can be a poor dryer despite an apparently high temperature. Write a component balance and model the transfer using Y=0.622 p_w/(P-p_w). Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Check saturated vapor-pressure data for the relevant temperature and pressure.

Problem 2: Evaporators and vaporization duty

A concentrated liquor requires steam above the pure-solvent boiling point. Write a component balance and model the transfer using Q=m_feed cp(T_b-T_in)+m_vap lambda. Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Heat recovery, nonideal enthalpy and boiling-point elevation matter for real designs.

Problem 3: Constant-rate drying and the critical moisture point

A wet granular product dries almost linearly in time until the critical moisture content. Write a component balance and model the transfer using t_c=M_dry(X0-Xc)/(A N_c). Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: A measured critical moisture is material and equipment dependent.

Problem 4: Falling-rate drying and internal diffusion

A food powder reaches a long drying tail that cannot be eliminated by increasing air speed alone. Write a component balance and model the transfer using t_f=M_dry(Xc-Xe)/(A N_c) ln[(Xc-Xe)/(Xf-Xe)]. Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Empirical falling-rate laws must be checked against actual drying curves.

Problem 5: Laboratory analysis

Select Laboratory 11 from the unit and export a sensitivity CSV. Report the largest and smallest finite result, calculate a percentage sensitivity at the baseline using two nearby points, and explain whether you expect the same sensitivity when the temperature or composition changes. Give at least two plausible sources of nonrepeatability in a physical test.

Rubric (100 points): physical model and assumptions 25; calculations and dimensional checks 25; clear diagrams and evidence 15; data interpretation 20; limitations and safety 15. Numbers produced by the simulation are not independent evidence that its selected correlation applies to a real installation.