Exercise set

Chemical Process Design and Scale-Up Exercises

Solved chemical process design exercises for batch scale factor, area-to-volume, conversion, reactor volume, residence time, heat duty, utilities and mixing.

Branch: Chemical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

These exercises focus on chemical process design and scale-up: batch scale factor, area-to-volume change, pilot conversion, reactor volume, residence time, heat duty, UA, utility flow, mixing power, viscosity, pressure drop, pump power and design-basis release. Commissioning, startup and performance testing are handled in a separate specialist exercise set.

Use the calculations as design-basis screens. Real scale-up requires representative pilot data, validated properties, process safety review, vendor data, utility confirmation, control strategy and documented approval.

How to use these exercises

Read the set as a scale-up review, not as a generic calculation sheet. Exercises 1 to 5 test whether the laboratory, pilot and plant bases are compatible before equipment is sized. Exercises 6 to 10 check heat removal and shared utilities, where scale-up often fails because surface area, peak heat release and header availability do not scale with production rate. Exercises 11 to 18 move into mixing, hydraulics, controllability and the final release decision.

For each exercise, write down the design basis before calculating: feed composition, batch or continuous mode, property source, temperature, pressure, residence time, utility condition and operating envelope. If any value is only a laboratory observation, mark it as an assumption until pilot, vendor or plant evidence closes it. The engineering comment below each exercise identifies the minimum review question that must be answered before the number can support a design decision.

Release Evidence Notes

Scale-up evidence should state laboratory basis, pilot basis, property source, equipment geometry, heat-transfer assumption, mixing criterion, residence-time basis, utility conditions, safety limits and the plant validation test that will close the design assumption. It should also identify whether the value comes from measured pilot data, a process simulator, a vendor guarantee, a conservative design rule or a placeholder awaiting confirmation.

The release file must keep normal operation, startup and upset states separate. A reactor may meet average heat duty in steady operation but still fail during addition, induction, fouling, viscosity increase or cooling-water header competition. A pump may meet clean hydraulic drop but fail after strainer loading, higher viscosity, lower suction head or control-valve throttling. These exercises show where those assumptions enter the first design screen.

Engineering Boundary Notes

The exercises use simplified sizing relationships. They do not replace rigorous process simulation, relief design, HAZOP, vendor guarantees, detailed hydraulics, control design or plant trials. Treat every pass result as permission to continue the design route, not as final plant approval. Treat every fail result as a hold point that needs a revised basis, additional pilot test, equipment change, operating limit or independent safety review.

Scale-up boundaries are especially strict for heat transfer, mixing and reaction kinetics. Constant batch mass, constant residence time, constant power per volume and constant Reynolds number are different criteria and cannot all be preserved at once. The chosen criterion must match the controlling failure mode: conversion, selectivity, hot spots, mass transfer, solids suspension, gas dispersion, fouling, pressure drop or operability.

Common Release Mistakes

Common mistakes include scaling by throughput alone, ignoring area-to-volume loss, using lab conversion without residence-time evidence, underestimating heat removal, and treating nominal utility capacity as available plant margin. Another recurring mistake is mixing batch and continuous assumptions, for example applying daily production targets to instantaneous heat release or sizing residence time with an average flow that cannot occur during startup.

Do not hide missing evidence inside design margin. A 20 percent volume margin does not validate kinetics, and a positive cooling-water margin does not prove heat removal if the peak duty, fouling allowance, valve authority and shared-header demand are unknown. Likewise, a low hydraulic power estimate is not a motor selection until pump efficiency, NPSH, startup viscosity, minimum flow and turndown limits are checked.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Scale basis	1, 2, 3, 4, 5	Batch size, geometry, conversion and residence time	Accept or revise design basis.
Heat and utilities	6, 7, 8, 9, 10	Heat duty, UA, cooling water, heat-up and header margin	Size equipment or derate target.
Mixing and hydraulics	11, 12, 13, 14, 15, 16, 17, 18	P/V, Reynolds number, pressure drop, pump power and risk	Confirm scale-up or mark validation hold.

Exercise 1: Batch Scale Factor

Lab batch is 2.0 kg. Plant target is 1500 kg/day with three batches per day. Find plant batch size and scale factor.

Solution

m_b=\dfrac{1500}{3}=500\ \text{kg},\qquad SF=\dfrac{500}{2.0}=250

Engineering Comment

A 250x scale-up changes mixing, heat removal, charging and abnormal inventory.

Plausibility Check

Three equal plant batches split 1500 kg/day into 500 kg each.

Exercise 2: Area-to-Volume Ratio

Pilot area is 0.10 m2 and volume is 0.010 m3. Plant area is 8.0 m2 and volume is 5.0 m3. Compare ratios.

Solution

(A/V)_p=10.0\ \text{m}^{-1},\qquad (A/V)_f=1.6\ \text{m}^{-1}

\text{reduction}=\dfrac{10.0-1.6}{10.0}=84\%

Engineering Comment

Heat removal and wall effects may not scale with mass throughput.

Plausibility Check

The plant vessel is much larger, so lower area intensity is expected.

Exercise 3: Pilot Conversion Product Rate

Feed is 1200 kg/day, reactant fraction is 0.40 and conversion is 82 percent. Estimate reacted mass per day.

Solution

m_r=1200(0.40)(0.82)=394\ \text{kg/day}

Engineering Comment

Pilot conversion should be tied to residence time, mixing and temperature profile.

Plausibility Check

Reacted mass must be less than the 480 kg/day reactant feed.

Exercise 4: Reactor Working Volume

Required liquid flow is 2.4 m3/h and residence time is 1.5 h. Add 20 percent design margin. Find working volume.

Solution

V=2.4(1.5)(1.20)=4.32\ \text{m}^3

Engineering Comment

Margin should not hide poor kinetic or mixing evidence.

Plausibility Check

Without margin the volume is 3.6 m3, so 4.32 m3 is correct.

Exercise 5: Residence Time at Higher Flow

If the installed reactor is 4.32 m3 and startup flow rises to 3.0 m3/h, find residence time.

Solution

\tau=\dfrac{4.32}{3.0}=1.44\ \text{h}

Engineering Comment

Higher throughput can erode conversion margin even when equipment volume is unchanged.

Plausibility Check

Flow above 2.4 m3/h lowers residence time below 1.8 h.

Exercise 6: Heat Duty Scale-Up

Reaction heat is 220 kJ/kg product and product rate is 500 kg/batch over 2 h. Find average heat duty.

Solution

Q=\dfrac{220(500)}{2(3600)}=15.3\ \text{kW}

Engineering Comment

Peak heat release may exceed the average during addition or reaction acceleration.

Plausibility Check

110,000 kJ over 7200 s gives about 15 kW.

Exercise 7: Required UA

Heat duty is 15.3 kW and mean driving temperature difference is 18 C. Find required UA.

Solution

UA=\dfrac{15300}{18}=850\ \text{W/K}

Engineering Comment

UA should be validated with fouling and agitation state.

Plausibility Check

Tens of kW over tens of degrees gives hundreds of W/K.

Exercise 8: Cooling Water Flow

Remove 15.3 kW with cooling water temperature rise of 8 C. Use $c_p=4.18$ kJ/(kg K). Find water flow.

Solution

\dot{m}=\dfrac{15.3}{4.18(8)}=0.458\ \text{kg/s}

Engineering Comment

Header pressure and control-valve authority still need checking.

Plausibility Check

Less than 1 kg/s is plausible for a 15 kW duty.

Exercise 9: Utility Header Margin

Available cooling water is 2.2 kg/s. Existing users need 1.5 kg/s and the new process needs 0.458 kg/s. Find remaining margin.

Solution

M=2.2-1.5-0.458=0.242\ \text{kg/s}

Engineering Comment

Small header margin may disappear during startup when multiple users peak together.

Plausibility Check

Total demand is just under 2.0 kg/s, leaving about 0.24 kg/s.

Exercise 10: Heat-Up Energy

Heat 3500 kg of liquid from 25 C to 80 C with $c_p=3.6$ kJ/(kg K). Find energy.

Solution

E=3500(3.6)(80-25)=693000\ \text{kJ}

Engineering Comment

Heat-up energy should be connected to available utility duty and startup time.

Plausibility Check

Large mass and 55 C rise give hundreds of megajoules.

Exercise 11: Mixing Power per Volume

Pilot mixing power is 0.08 kW in 0.010 m3. Match P/V in a 5.0 m3 vessel. Find power.

Solution

\dfrac{P}{V}=8.0\ \text{kW/m}^3,\qquad P_f=8.0(5.0)=40\ \text{kW}

Engineering Comment

Constant P/V may not preserve blend time, gas dispersion or solids suspension.

Plausibility Check

Scaling volume by 500 at constant P/V scales power by 500.

Exercise 12: Reynolds Number

Liquid density is 980 kg/m3, impeller diameter is 0.75 m, speed is 2 s^-1 and viscosity is 0.18 Pa s. Find mixing Reynolds number.

Solution

Re=\dfrac{\rho ND^2}{\mu}=\dfrac{980(2)(0.75^2)}{0.18}=6125

Engineering Comment

Viscosity changes during reaction can move the mixing regime.

Plausibility Check

The result is above laminar but not extremely high.

Exercise 13: Pipe Velocity

Flow is 18 m3/h through a 65 mm internal diameter pipe. Find velocity.

Solution

v=\dfrac{18/3600}{\pi(0.065)^2/4}=1.51\ \text{m/s}

Engineering Comment

Velocity affects pressure drop, erosion, settling and control-valve range.

Plausibility Check

Small pipe and several cubic metres per hour give metre-per-second velocity.

Exercise 14: Pressure Drop Margin

Calculated line pressure drop is 1.8 bar and available pump differential is 2.4 bar. Find margin.

Solution

M=2.4-1.8=0.6\ \text{bar}

Engineering Comment

Margin should include fouling, viscosity, static head and control valve losses.

Plausibility Check

Available differential exceeds calculated drop, so margin is positive.

Exercise 15: Pump Hydraulic Power

Flow is 18 m3/h and pressure rise is 2.4 bar. Estimate hydraulic power.

Solution

P=\Delta p Q=(2.4\times10^5)(18/3600)=1.20\ \text{kW}

Engineering Comment

Motor power must include pump efficiency and startup conditions.

Plausibility Check

Moderate flow and a few bar require only a few kilowatts hydraulic power.

Exercise 16: Turndown Design Flow

Design flow is 18 m3/h and required turndown is 4:1. Find minimum controllable flow.

Solution

Q_{min}=\dfrac{18}{4}=4.5\ \text{m}^3/\text{h}

Engineering Comment

Equipment, meters and control valves must all support the same turndown.

Plausibility Check

Four-to-one turndown means minimum is one quarter of design.

Exercise 17: Scale-Up RPN

Heat-removal scale-up has severity 9, occurrence 4 and detection 5. Compute RPN.

Solution

RPN=9(4)(5)=180

Engineering Comment

High severity should create validation hold points even if occurrence is moderate.

Plausibility Check

The product of three mid-high scores is near 200.

Exercise 18: Design-Basis Release Gate

Release requires utility margin positive, residence time at least 1.4 h and heat-removal RPN below 150. Results are 0.242 kg/s, 1.44 h and 180. Decide.

Solution

M>0,\qquad 1.44>1.4,\qquad 180>150

The design-basis release fails because scale-up heat-removal risk remains too high.

Engineering Comment

Passing sizing arithmetic is not enough when a high-risk scale-up item is unresolved.

Plausibility Check

Two criteria pass and one mandatory risk criterion fails, so the release is held.

Validation Package Checklist

laboratory, pilot, vendor and design assumptions are separated;
heat, mass, mixing and residence-time bases are explicit;
property values match expected composition and temperature;
utility and hydraulic margins include shared-system constraints;
scale-up risks have validation hold points;
control, relief and operability assumptions are not inferred from sizing alone;
vendor guarantees state duty, fluids, fouling, materials, turndown and battery limits;
plant trial criteria define conversion, heat removal, pressure drop, utility stability and product quality;
release decision states accept, revise, pilot again, derate or hold.

A complete validation package should let another engineer trace each plant value back to its source. If the laboratory basis, pilot basis, vendor basis and installed plant basis disagree, the design is not released; it is an unresolved scale-up assumption with a documented owner and closure test.

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