Chemical Process Heat Transfer and Utility Systems Exercises

These exercises practise first-pass calculations used in chemical process heat-transfer and utility-system design. They connect heat duty, log-mean temperature difference, cooling-water demand, steam consumption, fouling resistance, heat flux, convective heat-transfer estimates, utility header capacity, heat recovery, and abnormal-condition risk ranking.

Assume simplified nominal values unless an exercise states otherwise. Real utility and heat-transfer decisions require verified properties, exchanger geometry, fouling data, pressure-drop limits, materials compatibility, relief review, utility reliability, control dynamics, operating procedures, and commissioning evidence.

How to Use These Exercises

For each problem:

1. define the thermal boundary and utility service;
2. keep heat, mass flow, temperature, pressure, area, and time units consistent;
3. separate normal duty, turndown, startup, fouled, and abnormal conditions;
4. identify which plant measurements validate the calculation;
5. state whether the result affects capacity, energy use, safety, quality, or emissions.

The most common mistake is sizing around a clean normal-duty case while ignoring fouling, seasonal utility temperature, pressure drop, control authority, condensate removal, and loss-of-utility scenarios.

For each result, state whether it supports exchanger sizing, utility-header capacity, operating limit definition, energy-recovery justification, cleaning strategy, or abnormal-condition protection. The same heat-duty number can imply different actions depending on fouling state, seasonal utility conditions, and safety consequence.

Exercise 1: Process Cooling Duty

A liquid process stream flows at \dot{m}=4500\ \text{kg/h} and must be cooled from 130^\circ\text{C} to 45^\circ\text{C}. Use C_p=2.9\ \text{kJ/(kg K)}.

Estimate cooling duty.

Solution

Temperature change:

Cooling duty:

Convert to kW:

Engineering Comment

The duty is a sensible-heat estimate. Check for phase change, nonideal heat capacity, fouling, exchanger approach temperature, seasonal utility limits, and whether the outlet temperature is safety-critical or only quality-critical.

Exercise 2: Log-Mean Temperature Difference and Area

A counterflow exchanger cools a hot stream from 150^\circ\text{C} to 90^\circ\text{C} while heating a cold stream from 30^\circ\text{C} to 70^\circ\text{C}. Required duty is 300\ \text{kW} and estimated U=500\ \text{W/(m}^2\text{K)}.

Estimate log-mean temperature difference and required area.

Solution

Terminal temperature differences:

Log-mean temperature difference:

Area:

Engineering Comment

This is a clean first-pass area. Detailed design should include correction factors for exchanger arrangement, fouling allowance, pressure drop, minimum approach, flow maldistribution, and whether either stream can change phase.

Exercise 3: Cooling Water Flow

A condenser rejects \dot{Q}=750\ \text{kW} to cooling water. Cooling water enters at 28^\circ\text{C} and leaves at 38^\circ\text{C}. Use C_p=4.18\ \text{kJ/(kg K)}.

Estimate required cooling-water mass flow.

Solution

Temperature rise:

Water mass flow:

Engineering Comment

The value must be checked against cooling-water header pressure, return temperature limit, tower capacity, treatment chemistry, fouling, and whether the condenser duty rises during startup or hot-weather operation.

Exercise 4: Steam Consumption for a Reboiler

A reboiler requires \dot{Q}=1.20\ \text{MW}. Available steam has useful latent heat of 2100\ \text{kJ/kg} at the operating pressure.

Estimate steam consumption in \text{kg/s} and \text{kg/h}.

Solution

Use \dot{Q}=1200\ \text{kJ/s}:

Convert to hourly rate:

Engineering Comment

Steam consumption is not only an energy number. The reboiler also needs correct condensate drainage, steam-trap capacity, control-valve authority, tube-wall temperature control, pressure relief review, and a response to steam-header disturbances.

Exercise 5: Fouling Impact on Overall Heat-Transfer Coefficient

A clean exchanger has inside film coefficient h_i=1200\ \text{W/(m}^2\text{K)}, outside film coefficient h_o=2200\ \text{W/(m}^2\text{K)}, and wall resistance R_w=0.00010\ \text{m}^2\text{K/W}. Fouling adds R_f=0.00025\ \text{m}^2\text{K/W}.

Estimate clean and fouled overall heat-transfer coefficients using:

Solution

Clean resistance:

Fouled resistance:

Relative reduction:

Engineering Comment

The fouling penalty is large enough to affect capacity and control. Fouling monitoring should use duty, flow, temperatures, pressure drop, and uncertainty bounds rather than relying only on calendar cleaning intervals.

Exercise 6: Heat Flux Check

A reactor jacket removes 180\ \text{kW} through effective area A=12\ \text{m}^2. The operating heat-flux guideline is 20\ \text{kW/m}^2.

Check heat flux and margin.

Solution

Heat flux:

Margin to guideline:

Engineering Comment

The nominal heat flux is below the guideline. The review should still check local hot spots, agitator performance, fouling, viscosity changes, batch addition rate, emergency cooling, and whether the full area is actually wetted.

Exercise 7: Tube-Side Reynolds and Nusselt Number

Water flows through a tube with inside diameter D=0.025\ \text{m} at Q=1.8\ \text{m}^3/\text{h}. Use \rho=1000\ \text{kg/m}^3, \mu=0.001\ \text{Pa s}, Pr=5.0, and thermal conductivity k=0.60\ \text{W/(m K)}.

Estimate velocity, Reynolds number, Nusselt number using Nu=0.023Re^{0.8}Pr^{0.4}, and convective coefficient h=Nu\,k/D.

Solution

Flow conversion:

Area:

Velocity:

Reynolds number:

Nusselt number:

Convective coefficient:

Engineering Comment

The correlation is a screening estimate. Detailed use requires checking the correlation range, entrance effects, wall temperature, property variation, roughness, fouling, and whether the flow is fully developed and single phase.

Exercise 8: Cooling-Water Header Capacity

A cooling-water header can supply 120\ \text{kg/s}. Existing users require 85\ \text{kg/s}. A new exchanger requires 650\ \text{kW} of cooling with an allowed water temperature rise of 8\ \text{K}. Use C_p=4.18\ \text{kJ/(kg K)}.

Check total header load and remaining margin.

Solution

New exchanger flow:

Total header load:

Remaining margin:

Engineering Comment

The header has nominal flow margin. The design should still check pressure at the far users, simultaneous peak cases, tower return temperature, pump curve, isolation valves, fouling, and whether maintenance or hot weather removes the margin.

Exercise 9: Annual Heat-Recovery Fuel Saving

A heat-recovery exchanger recovers 400\ \text{kW} for 6000\ \text{h/year}. The displaced boiler has efficiency \eta=0.82.

Estimate annual useful heat recovered and avoided fuel energy.

Solution

Useful heat recovered:

Avoided fuel energy:

Convert to GJ:

Engineering Comment

The energy saving is meaningful only if the exchanger is available when the heat source and sink overlap. Fouling, bypassing, product contamination risk, pressure drop, startup mismatch, and maintenance downtime can reduce realized savings.

Exercise 10: Condensate Removal Risk Ranking

A steam heater can lose duty and create water hammer if condensate removal fails. A failure-mode review assigns severity S=9, occurrence O=4, and detection D=5.

After trap monitoring, correct line slope, startup drain checks, and operator alarm response are added, occurrence is estimated at O=2 and detection at D=3. Compare traditional risk priority numbers.

Solution

Initial risk priority number:

Revised risk priority number:

Reduction:

Engineering Comment

The revised ranking is lower, but the control must be validated in the installed system. Condensate drainage depends on piping slope, trap sizing, noncondensable venting, startup procedure, differential pressure, maintenance access, and alarm response.

Heat-Transfer and Utility Review Checklist

Before using these calculations for design, debottlenecking, or operations support, check:

• Are physical properties taken at representative bulk and wall temperatures?
• Are clean, fouled, startup, turndown, seasonal, and loss-of-utility cases separated?
• Are exchanger area, pressure drop, flow distribution, phase behaviour, corrosion, and cleanability reviewed together?
• Are utility headers checked for simultaneous users, pump curves, return temperature, maintenance outages, and remote-user pressure?
• Are heat-flux limits connected to wetting, agitation, viscosity, local hot spots, and emergency cooling?
• Are empirical correlations used only inside their valid Reynolds, Prandtl, geometry, and phase ranges?
• Are energy-recovery estimates adjusted for availability, bypass operation, contamination risk, and operating schedule?
• Are abnormal-condition controls supported by installed equipment checks, proof testing, procedures, alarms, and maintenance access?

Strong utility engineering treats heat-transfer calculations as operating evidence, not only sizing arithmetic. Each result should show which margin is available, when it disappears, and what plant record confirms it.