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Exercise set

Chemical Process Balances and Reactors Exercises

Worked chemical engineering exercises for process balances and reactors covering total mass balance, component conversion, recycle purge, CSTR and PFR conversion, sensible heat duty, reaction heat removal, heat-exchanger area, Reynolds number, and reactor safety risk ranking.

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Chemical Engineering
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Exercise set
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v1.1.0 ยท reviewed

These exercises practise first-pass calculations used in chemical process balances and reactor design review. They connect total mass balance, component conversion, recycle purge, ideal CSTR and PFR behaviour, sensible heat duty, reaction heat removal, heat-exchanger sizing, pipe-flow regime, and safety risk ranking.

Assume simplified nominal values unless an exercise states otherwise. Real chemical-process decisions require verified physical properties, reaction kinetics, phase behaviour, heat-transfer data, relief and containment review, instrumentation design, operating procedures, commissioning evidence, and site-specific safety standards.

How to Use These Exercises

For each problem:

  1. define the system boundary and calculation basis before writing equations;
  2. state whether streams are mass, molar, or volumetric flows;
  3. keep composition, temperature, pressure, phase, and unit conversions explicit;
  4. separate steady-state balances from transient inventory or startup behaviour;
  5. identify which plant measurement would validate the result.

The most common mistake is closing a convenient arithmetic balance while ignoring an unmeasured vent, purge, recycle, side reaction, phase change, or inventory term. A balance is an engineering model, not only a spreadsheet total.

For each result, state the engineering decision it supports: material accounting, conversion screening, recycle control, heat-removal adequacy, exchanger sizing, hydraulic classification, or safety-barrier prioritisation. A numerical answer becomes useful only when the measurement basis, operating envelope, and acceptance criterion are explicit.

Exercise 1: Total Mass Balance with an Unknown Waste Stream

A process unit receives liquid feed at 2400\ \text{kg/h} and solvent at 1600\ \text{kg/h}. Measured outlet streams are product at 3650\ \text{kg/h} and vent at 75\ \text{kg/h}. The unit is at steady state.

Estimate the unknown waste stream.

Solution

At steady state:

\displaystyle \sum \dot{m}_{in}=\sum \dot{m}_{out}

Total inlet:

\dot{m}_{in}=2400+1600=4000\ \text{kg/h}

Known outlet:

\dot{m}_{known}=3650+75=3725\ \text{kg/h}

Waste stream:

\dot{m}_{waste}=4000-3725=275\ \text{kg/h}

Engineering Comment

The result assumes no accumulation and no other outlet. If the unit is warming up, filling, flashing, leaking, or producing unmeasured off-gas, the steady-state closure is not valid.

Exercise 2: Reactant Conversion and Product Formation

A reactor feed contains reactant A at F_{A0}=120\ \text{mol/min}. The outlet contains F_A=18\ \text{mol/min}. Of the consumed A, 92\% forms desired product P on a one-to-one molar basis.

Estimate conversion of A and desired product formation rate.

Solution

Conversion:

\displaystyle X_A=\frac{F_{A0}-F_A}{F_{A0}}
\displaystyle X_A=\frac{120-18}{120}=0.850=85.0\%

Reactant consumed:

F_{A,cons}=120-18=102\ \text{mol/min}

Desired product:

F_P=0.92(102)=93.8\ \text{mol/min}

Engineering Comment

High conversion does not prove good performance. The missing 8\% of consumed reactant may form side products, heavies, emissions, or fouling precursors that control safety, separation load, and product quality.

Exercise 3: Purge Flow for Inert Control

A recycle loop receives inert material with fresh feed at 2.0\ \text{mol/min}. The inert leaves only through a purge. The allowable inert mole fraction in the purge is 8.0\%.

Estimate the required purge flow.

Solution

At steady state, inert in equals inert out:

F_{I,in}=y_I F_{purge}

Solve for purge:

\displaystyle F_{purge}=\frac{F_{I,in}}{y_I}
\displaystyle F_{purge}=\frac{2.0}{0.080}=25.0\ \text{mol/min}

Engineering Comment

The purge protects the loop from inert buildup, but it may also remove reactant, solvent, or product. The design should include purge treatment, emissions control, composition measurement, and startup inventory behaviour.

Exercise 4: Nominal Residence Time and CSTR Conversion

A liquid CSTR has volume V=5.0\ \text{m}^3 and feed flow Q=1.2\ \text{m}^3/\text{h}. A first-order reaction has rate constant k=0.45\ \text{h}^{-1}.

Estimate residence time and ideal CSTR conversion.

Solution

Residence time:

\displaystyle \tau=\frac{V}{Q}=\frac{5.0}{1.2}=4.17\ \text{h}

For a first-order ideal CSTR:

\displaystyle X=\frac{k\tau}{1+k\tau}
\displaystyle X=\frac{0.45(4.17)}{1+0.45(4.17)}=0.652
X=65.2\%

Engineering Comment

The CSTR equation assumes well-mixed behaviour and rate evaluated at outlet conditions. Dead zones, poor mixing, gas disengagement, catalyst settling, heat limits, or side reactions can make actual conversion lower.

Exercise 5: Ideal PFR Conversion with the Same Space Time

Use the same k=0.45\ \text{h}^{-1} and \tau=4.17\ \text{h} from Exercise 4. Estimate ideal first-order plug-flow conversion.

Solution

For a first-order ideal PFR:

X=1-e^{-k\tau}
X=1-e^{-0.45(4.17)}
X=1-e^{-1.876}=0.847
X=84.7\%

Engineering Comment

The ideal PFR gives higher conversion than the ideal CSTR for this first-order case. That comparison does not choose the reactor by itself; heat removal, pressure drop, fouling, control, catalyst handling, cleaning, and safety may dominate.

Exercise 6: Sensible Heat Duty

A liquid stream flows at \dot{m}=2500\ \text{kg/h} and is heated from 25^\circ\text{C} to 80^\circ\text{C}. Use C_p=3.8\ \text{kJ/(kg K)}.

Estimate heat duty.

Solution

Temperature change:

\Delta T=80-25=55\ \text{K}

Heat duty:

\dot{Q}=\dot{m}C_p\Delta T
\dot{Q}=2500(3.8)(55)=522{,}500\ \text{kJ/h}

Convert to kW:

\displaystyle \dot{Q}=\frac{522{,}500}{3600}=145\ \text{kW}

Engineering Comment

This calculation assumes constant heat capacity and no phase change. The design should check property variation, fouling, utility temperature, exchanger approach temperature, startup heating, and control-valve authority.

Exercise 7: Cooling Water for Reaction Heat Removal

An exothermic reaction consumes 90\ \text{mol/min} of reactant. Heat of reaction is \Delta H_{rxn}=-75\ \text{kJ/mol}, meaning heat is released. Cooling water is allowed to rise by 10\ \text{K}. Use C_p=4.18\ \text{kJ/(kg K)} for water.

Estimate heat release and required cooling-water mass flow.

Solution

Heat release:

\dot{Q}_{rxn}=90(75)=6750\ \text{kJ/min}

Convert to kW:

\displaystyle \dot{Q}_{rxn}=\frac{6750}{60}=112.5\ \text{kW}

Cooling-water mass flow:

\displaystyle \dot{m}_w=\frac{\dot{Q}}{C_p\Delta T}
\displaystyle \dot{m}_w=\frac{112.5}{4.18(10)}=2.69\ \text{kg/s}

Engineering Comment

The cooling flow is a normal-duty estimate. Reactor safety also requires response to cooling failure, feed mischarge, agitation loss, fouling, delayed heat release, relief load, and emergency shutdown logic.

Exercise 8: Heat-Exchanger Area

A process cooler must remove \dot{Q}=180\ \text{kW}. The estimated overall heat-transfer coefficient is U=650\ \text{W/(m}^2\text{K)} and log-mean temperature difference is \Delta T_{lm}=24\ \text{K}.

Estimate required heat-transfer area.

Solution

Heat-exchanger equation:

\dot{Q}=UA\Delta T_{lm}

Area:

\displaystyle A=\frac{\dot{Q}}{U\Delta T_{lm}}
\displaystyle A=\frac{180{,}000}{650(24)}=11.5\ \text{m}^2

Engineering Comment

The area estimate depends strongly on U and fouling. Detailed design should check stream properties, phase behaviour, pressure drop, cleanability, materials compatibility, corrosion allowance, and turndown operation.

Exercise 9: Pipe Velocity and Reynolds Number

A process liquid flows through a pipe with internal diameter D=0.050\ \text{m} at volumetric flow Q=2.4\ \text{m}^3/\text{h}. Use \rho=980\ \text{kg/m}^3 and \mu=0.002\ \text{Pa s}.

Estimate velocity and Reynolds number.

Solution

Convert flow:

\displaystyle Q=\frac{2.4}{3600}=6.67\times10^{-4}\ \text{m}^3/\text{s}

Area:

\displaystyle A=\frac{\pi D^2}{4}=\frac{\pi(0.050)^2}{4}=0.00196\ \text{m}^2

Velocity:

\displaystyle v=\frac{Q}{A}=\frac{6.67\times10^{-4}}{0.00196}=0.340\ \text{m/s}

Reynolds number:

\displaystyle Re=\frac{\rho vD}{\mu}
\displaystyle Re=\frac{980(0.340)(0.050)}{0.002}=8330

Engineering Comment

The flow is above the laminar range and should be treated as turbulent or transitional depending on roughness and disturbances. Pressure drop, fouling, heat transfer, and meter accuracy should be checked with the actual fluid properties.

Exercise 10: Cooling-Failure Risk Ranking

A reactor safety review identifies loss of cooling during feed addition as a failure mode. Initial rankings are severity S=10, occurrence O=3, and detection D=5.

After independent high-temperature interlock, cooling-flow proof, and feed-shutdown testing are added, occurrence is estimated at O=2 and detection at D=2. Compare traditional risk priority numbers.

Solution

Initial risk priority number:

RPN_1=SOD=10(3)(5)=150

Revised risk priority number:

RPN_2=10(2)(2)=40

Reduction:

\Delta RPN=150-40=110

Engineering Comment

The lower RPN is not a complete safety case. The interlock, valve fail position, sensor independence, proof-test interval, relief system, operating procedure, bypass control, and commissioning evidence must all be validated.

Engineering Review Checklist

Before using these calculations in a design review, commissioning package, or plant troubleshooting note, check:

  • Is the calculation basis stated clearly enough that another engineer can reproduce it?
  • Are all streams classified by phase, composition, temperature, pressure, and measurement method?
  • Are recycle, purge, vent, drain, side-product, and accumulation terms explicitly considered?
  • Are kinetic expressions being used inside their validated temperature, concentration, catalyst, and mixing ranges?
  • Are heat duties checked against utility availability, fouling allowance, control authority, and abnormal operation?
  • Are hydraulic classifications connected to pressure drop, metering accuracy, erosion, fouling, and heat-transfer consequences?
  • Are safety improvements supported by independent safeguards, proof testing, bypass control, and documented commissioning evidence?
  • Are numerical margins converted into actionable limits, alarms, operating procedures, or design changes?

Strong chemical-process calculations do not stop at balanced equations. They define what must be measured, what assumptions must remain true, and which plant decision is justified by the result.

REF

See also

  1. Chemical Process Balances and Reactors Chemical Engineering
  2. Chemical Process Calculations Formula Sheet Chemical Engineering
  3. Chemical Process Design, Scale-Up, and Commissioning Chemical Engineering
  4. Chemical Process Design, Scale-Up, and Commissioning Exercises Chemical Engineering
  5. Chemical Process Heat Transfer and Utility Systems Chemical Engineering
  6. Chemical Process Heat Transfer and Utility Systems Exercises Chemical Engineering
  7. Chemical Process Control and Plant Operations Chemical Engineering
  8. Chemical Process Control and Plant Operations Exercises Chemical Engineering
  9. Chemical Process Safety and Hazard Control Chemical Engineering
  10. Chemical Process Safety and Hazard Control Exercises Chemical Engineering
  11. Separation Processes and Distillation Engineering Chemical Engineering
  12. Separation Processes and Distillation Engineering Exercises Chemical Engineering
  13. Thermal Energy Systems and Heat Exchangers Energy Engineering
  14. Mechanical Fluid Flow and Piping Systems Mechanical Engineering
  15. Mechanical Fluid Flow and Piping Systems Exercises Mechanical Engineering
  16. Environmental Water and Wastewater Systems Environmental Engineering
  17. Contaminated Site Remediation and Groundwater Protection Environmental Engineering
  18. Mineral Processing and Ore Handling Systems Mining and Georesources Engineering
  19. Mineral Processing and Ore Handling Systems Exercises Mining and Georesources Engineering
  20. Mass Balance Chemical Engineering model
  21. Chemical Reactor Chemical Engineering device
  22. Reaction Rate Chemical Engineering quantity
  23. Heat Duty Chemical Engineering quantity
  24. Flow Rate Mechanical Engineering quantity
  25. Density Materials Engineering quantity
  26. Continuity Equation Mechanical Engineering model
  27. Heat Exchanger Energy Engineering device
  28. Heat Flux Energy Engineering quantity
  29. Vapor Pressure Chemical Engineering quantity
  30. Valve Coefficient Chemical Engineering metric
  31. Viscosity Mechanical Engineering quantity
  32. Reynolds Number Mechanical Engineering quantity
  33. Nusselt Number Energy Engineering quantity
  34. Laminar Flow Mechanical Engineering phenomenon
  35. Turbulence Mechanical Engineering phenomenon
  36. Thermal Efficiency Energy Engineering metric
  37. Efficiency Energy Engineering metric
  38. Oxidation Chemical Engineering process
  39. Interlock Industrial and Management Engineering device
  40. Failure Mode Industrial and Management Engineering concept
  41. Risk Priority Number Industrial and Management Engineering metric
  42. Validation Industrial and Management Engineering method
  43. Uncertainty Analysis Mathematical Engineering method
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