Exercise set

Chemical Utility Steam, Cooling Water, and Condensate Exercises

Worked chemical utility exercises for cooling water, steam use, condensate capacity, cooling towers, heat recovery and utility release gates.

Branch: Chemical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises focus on chemical utility systems: cooling-water demand, steam use, utility headers, heat recovery, condensate removal, hot-weather capacity, cooling-loss hold time, thermal expansion, cooling tower approach and release gates.

Exchanger duty, LMTD, NTU, fouling and heat-balance closure are handled in the companion specialist exercise set.

Release Evidence Notes

Utility evidence should state the service boundary, simultaneous users, seasonal condition, supply and return limits, pressure basis, pump or header status, control-valve position, bypass state, maintenance state and release authority. A utility system can pass one exchanger duty while failing the simultaneous plant case.

Engineering Boundary Notes

These examples are simplified utility screens. Real plant utility release should also check pump curves, tower performance, steam pressure, condensate return, trap capacity, water treatment, pressure drop, water hammer, relief paths, control response, outage modes and environmental constraints.

Common Release Mistakes

sizing cooling water at normal weather but releasing summer operation;
counting header flow without checking far-user pressure;
ignoring condensate drainage and water-hammer risk;
treating heat recovery savings as available without schedule overlap;
accepting cooling-loss hold time without sensor and action evidence;
releasing a duty while a utility or interlock is degraded.

Scenario Map

Scenario	Exercises	Main calculation	Release decision
Cooling and steam demand	1, 2, 3, 4	Cooling-water flow, steam use, header margin and return temperature	Accept load, derate or upgrade utility capacity.
Heat recovery and efficiency	5, 13, 15	Annual fuel saving, pump power and exergy screen	Justify or reject recovery changes.
Condensate and abnormal service	6, 8, 9, 10, 14	Drainage, cooling-loss hold time, expansion, trap capacity and water hammer risk	Add protection, alarm, procedure or relief path.
Seasonal release	7, 11, 12, 16, 17, 18	Hot-weather cooling, tower approach, header pressure, uncertainty and release gate	Release only if seasonal utility evidence passes.

Validation Package Checklist

simultaneous utility users and seasonal case;
supply pressure, return limit, temperature and flow basis;
cooling tower, pump, header and remote-user margin;
steam, condensate, trap and drainage capacity;
heat recovery operating overlap and fuel basis;
release action for loss-of-utility, water hammer or margin failure.

Exercise 1: Cooling Water Flow

A condenser rejects $\dot{Q}=750\ \text{kW}$ to cooling water. Cooling water warms from $28^\circ\text{C}$ to $38^\circ\text{C}$ . Use $c_p=4.18\ \text{kJ/(kg K)}$ .

Solution

\dot{m}=\dfrac{750}{4.18(38-28)}=17.9\ \text{kg/s}

Engineering Comment

The demand should be checked against header pressure, tower capacity, treatment chemistry and hot-weather operation.

Plausibility Check

A ten-degree water rise for three quarters of a megawatt requires tens of kilograms per second.

Exercise 2: Steam Consumption for a Reboiler

A reboiler requires $1.8\ \text{MW}$ . Available steam latent heat is $2100\ \text{kJ/kg}$ . Estimate steam flow.

Solution

\dot{m}_s=\dfrac{1800}{2100}=0.857\ \text{kg/s}

Engineering Comment

Steam demand should include trap capacity, condensate drainage, pressure control and startup transients.

Plausibility Check

Roughly two megawatts divided by about two megajoules per kilogram gives about one kilogram per second.

Exercise 3: Cooling-Water Header Capacity

A cooling-water header can supply $70\ \text{kg/s}$ . Existing users require $46\ \text{kg/s}$ and a new exchanger requires $17.9\ \text{kg/s}$ . Compute margin.

Solution

M=70-46-17.9=6.1\ \text{kg/s}

Engineering Comment

Positive flow margin should still be checked at remote-user pressure and hot-weather tower return temperature.

Plausibility Check

The two demands use nearly sixty-four kilograms per second, leaving only a few kilograms per second.

Exercise 4: Return Temperature Limit

Cooling water enters at $30^\circ\text{C}$ and plant rules limit return to $42^\circ\text{C}$ . A duty causes a $13.5^\circ\text{C}$ rise. Does it pass?

Solution

T_{return}=30+13.5=43.5^\circ\text{C}

It fails the $42^\circ\text{C}$ return limit.

Engineering Comment

Return temperature can govern even when flow is available. The action may be derating, more flow, lower duty or tower review.

Plausibility Check

Adding more than twelve degrees to thirty degrees exceeds the low-forties limit.

Exercise 5: Annual Heat-Recovery Fuel Saving

A heat-recovery change saves $350\ \text{kW}$ for $5200\ \text{h/year}$ . Fuel cost is $0.045\ \text{USD/kWh}$ . Estimate annual saving.

Solution

E=350(5200)=1.82\times10^6\ \text{kWh/year}

S=1.82\times10^6(0.045)=81900\ \text{USD/year}

Engineering Comment

Savings require schedule overlap, controllability, fouling management and no downstream penalty.

Plausibility Check

Hundreds of kilowatts over thousands of hours produces millions of kilowatt-hours.

Exercise 6: Condensate Removal Risk Ranking

A steam heater has condensate drainage failure mode with severity $9$ , occurrence $4$ and detection $5$ . Compute RPN.

Solution

RPN=9(4)(5)=180

Engineering Comment

Condensate removal affects duty, water hammer and tube integrity. The risk control should be physical and procedural.

Plausibility Check

Nine times twenty gives one hundred eighty.

Exercise 7: Hot-Weather Cooling Capacity

At normal weather, tower supply is $28^\circ\text{C}$ . Hot weather raises it to $33^\circ\text{C}$ . The allowed return is $42^\circ\text{C}$ . What is the available temperature rise in hot weather?

Solution

\Delta T_{hot}=42-33=9^\circ\text{C}

Engineering Comment

Reduced temperature rise means the same duty requires more water or reduced throughput.

Plausibility Check

Hotter supply leaves less room before the fixed return limit.

Exercise 8: Cooling-Loss Thermal Hold Time

A reactor has thermal capacity $C=950\ \text{kJ/K}$ and net heat release after cooling loss is $38\ \text{kW}$ . Temperature margin to the alarm trip is $18^\circ\text{C}$ . Estimate hold time.

Solution

t=\dfrac{C\Delta T}{\dot{Q}}=\dfrac{950(18)}{38}=450\ \text{s}=7.5\ \text{min}

Engineering Comment

Hold time must exceed detection, diagnosis, field action and process response time with margin.

Plausibility Check

The heat capacity times margin is $17100\ \text{kJ}$ ; dividing by tens of kilowatts gives minutes.

Exercise 9: Blocked-In Liquid Expansion Volume

A blocked-in liquid volume is $3.0\ \text{m}^3$ . Volumetric expansion coefficient is $7.0\times10^{-4}\ \text{K}^{-1}$ and temperature rise is $22\ \text{K}$ . Estimate expansion volume.

Solution

\Delta V=V\beta\Delta T=3.0(7.0\times10^{-4})(22)=0.0462\ \text{m}^3

Engineering Comment

Blocked-in thermal expansion can create overpressure. Relief path and isolation procedures matter.

Plausibility Check

The fractional expansion is about one and a half percent of three cubic meters.

Exercise 10: Condensate Drainage Capacity

A steam heater generates condensate at $0.86\ \text{kg/s}$ . Trap capacity under current differential pressure is $0.72\ \text{kg/s}$ . Compute capacity shortfall.

Solution

S=0.86-0.72=0.14\ \text{kg/s}

Engineering Comment

Undersized condensate removal can flood the exchanger, reduce duty and create water hammer risk.

Plausibility Check

The trap capacity is slightly below demand.

Exercise 11: Cooling Tower Approach

Cooling tower cold-water temperature is $31^\circ\text{C}$ and wet-bulb temperature is $25^\circ\text{C}$ . Compute approach.

Solution

A=31-25=6^\circ\text{C}

Engineering Comment

Approach should be trended with fill condition, fan operation, water treatment and weather basis.

Plausibility Check

Cold water must be warmer than wet bulb, so the approach is positive.

Exercise 12: Cooling Tower Return-Temperature Limit

Tower return water is $41^\circ\text{C}$ and the plant high-return limit is $43^\circ\text{C}$ . Measurement uncertainty is $1.5^\circ\text{C}$ . Does it pass a guarded screen?

Solution

T_g=41+1.5=42.5^\circ\text{C}

Since:

42.5<43

it passes.

Engineering Comment

The margin is narrow. Summer operation, sensor drift or additional users can remove it.

Plausibility Check

The guarded value is only half a degree below the limit.

Exercise 13: Cooling-Water Pump Power

Cooling-water flow is $0.020\ \text{m}^3/\text{s}$ , pump head is $35\ \text{m}$ and efficiency is $0.72$ . Use $\rho=1000\ \text{kg/m}^3$ .

Solution

P=\dfrac{\rho gQH}{\eta}=\dfrac{1000(9.81)(0.020)(35)}{0.72}=9.54\ \text{kW}

Engineering Comment

Pump power is small compared with process heat duty but can matter for continuous utility cost and NPSH margin.

Plausibility Check

The hydraulic power is several kilowatts, and efficiency raises shaft power.

Exercise 14: Water-Hammer Risk from Fast Condensate Valve Closure

A condensate line velocity is $2.2\ \text{m/s}$ . A simplified surge estimate uses $\Delta P=\rho a\Delta v$ with $\rho=1000\ \text{kg/m}^3$ and wave speed $a=900\ \text{m/s}$ . Estimate surge pressure for full stop.

Solution

\Delta P=1000(900)(2.2)=1.98\times10^6\ \text{Pa}=19.8\ \text{bar}

Engineering Comment

Condensate and two-phase systems need drainage, venting, slow closure and support review. Surge can exceed normal operating pressure.

Plausibility Check

Stopping meters per second of liquid with high wave speed gives bar-scale pressure rise.

Exercise 15: Exergy Fraction of Recovered Heat

Recovered heat is available at $T_h=390\ \text{K}$ to an environment at $T_0=300\ \text{K}$ . Estimate ideal exergy fraction $1-T_0/T_h$ .

Solution

\psi=1-\dfrac{300}{390}=0.231

Engineering Comment

Low-temperature heat may save fuel but has limited work potential. The use should match the temperature level.

Plausibility Check

The source temperature is not far above ambient, so the fraction is well below one.

Exercise 16: Remote-User Pressure Margin

A remote cooler requires at least $180\ \text{kPa}$ supply pressure. Predicted pressure during simultaneous peak is $194\ \text{kPa}$ with uncertainty $10\ \text{kPa}$ . Does it pass guarded?

Solution

P_g=194-10=184\ \text{kPa}

Since:

184>180

it passes.

Engineering Comment

The pressure margin is small. Valve positions, strainer fouling and pump condition should be monitored.

Plausibility Check

Guarding the predicted pressure leaves only four kilopascals above the requirement.

Exercise 17: Utility Release Margin Count

A rate increase requires four utility gates: cooling flow, return temperature, steam pressure and condensate capacity. Three pass and condensate capacity fails. What is the release decision?

Solution

The release fails because one required gate fails:

1\ \text{failed gate}>0

Engineering Comment

Utility release should not average service gates. Condensate failure can remove heat duty and create mechanical risk.

Plausibility Check

Three pass results do not cancel one explicit release blocker.

Exercise 18: Utility System Release Gate

A utility release requires cooling-water margin above $5\ \text{kg/s}$ , guarded return temperature below limit, condensate capacity positive and no unresolved water-hammer concern. Results are $6.1\ \text{kg/s}$ , pass, $-0.14\ \text{kg/s}$ and no concern. Does it release?

Solution

The condensate capacity gate fails:

-0.14<0

The utility release fails.

Engineering Comment

A cooling-water pass does not prove steam-side readiness. Chemical utility release must cover all services used by the duty.

Plausibility Check

The failed condensate margin is explicit and negative.

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