Chemical Process Control and Plant Operations Exercises

These exercises practise first-pass calculations used in chemical process control and plant operations. They connect balance closure, measurement basis, residence time, process dynamics, alarm response, controller action, feedforward cooling, analyzer validation, protective-function availability, and operating-risk ranking.

Assume simplified nominal values unless an exercise states otherwise. Real plant operation requires validated instrumentation, operating envelopes, alarm rationalization, interlock proof testing, utility review, procedures, management of change, maintenance evidence, and trained operator response.

How to Use These Exercises

For each problem:

1. define the operating state and process boundary;
2. distinguish measurement, control action, alarm action, and interlock action;
3. keep mass flow, volumetric flow, time, temperature, and percentage units explicit;
4. state which plant record would validate the calculation;
5. identify whether the result affects safety, quality, throughput, energy, or environmental performance.

The most common mistake is treating a dashboard value as truth without checking sensor location, density basis, calibration, lag, bypass state, alarm priority, and whether the plant is actually at steady state.

For each result, identify the operational decision it can support: rate change, alarm response, controller review, analyzer release, bypass control, interlock proof testing, or shift-handover escalation. A useful operations calculation should leave an auditable trail from measurement to action.

Exercise 1: Operating Mass-Balance Closure

A process unit receives feed at 4200\ \text{kg/h} and solvent at 900\ \text{kg/h}. Measured outlet streams are product at 4600\ \text{kg/h}, purge at 320\ \text{kg/h}, and wastewater at 160\ \text{kg/h}. The unit is believed to be at steady state.

Estimate the mass-balance residual.

Solution

Total inlet:

Measured outlet:

Residual:

Residual as percentage of inlet:

Engineering Comment

The residual is small, but it should still be compared with flowmeter uncertainty and inventory change. If the residual trends upward, likely causes include meter bias, unmeasured venting, leaking, sampling mismatch, or non-steady operation.

Exercise 2: Volumetric Flow to Mass Flow

A feed flowmeter reports Q=1.8\ \text{m}^3/\text{h}. Laboratory density for the current batch is \rho=840\ \text{kg/m}^3.

Estimate mass flow. Then estimate the error if the control system still assumes \rho=800\ \text{kg/m}^3.

Solution

Actual mass flow:

Control-system mass flow estimate:

Error:

Percentage error:

Engineering Comment

A volumetric flow loop can be stable while the mass balance is wrong. Density compensation matters when composition, temperature, solvent ratio, or grade changes affect product quality or reaction stoichiometry.

Exercise 3: Residence Time After a Rate Increase

A liquid reactor has working volume V=8.0\ \text{m}^3. Normal feed flow is Q_1=1.6\ \text{m}^3/\text{h}. A production-rate increase raises feed flow to Q_2=2.0\ \text{m}^3/\text{h}.

Estimate residence time before and after the rate increase.

Solution

Normal residence time:

New residence time:

Residence-time reduction:

Engineering Comment

The rate increase reduces reaction time, mixing time, heat-removal margin, and disturbance response time. A production increase should not be released until conversion, quality, cooling, pressure drop, and downstream separation can tolerate the shorter residence time.

Exercise 4: First-Order Temperature Response

A process outlet temperature behaves approximately as a first-order response after a setpoint change. The initial temperature is 60^\circ\text{C}, final expected temperature is 80^\circ\text{C}, and time constant is \tau=6\ \text{min}.

Estimate temperature after 12\ \text{min}, ignoring dead time.

Solution

First-order response:

Substitute values:

Engineering Comment

After two time constants the process has not reached the final value. Slow thermal systems need alarm limits and operator actions that account for lag, stored heat, utility delay, and possible sensor dead time.

Exercise 5: Alarm Response Margin

A reactor high-temperature alarm is set at 88^\circ\text{C} and the shutdown trip is set at 96^\circ\text{C}. During a credible cooling-water upset, temperature can rise at 1.5\ \text{K/min}. The sensor has 2\ \text{min} of effective dead time.

Estimate the time from alarm to trip and the response time remaining after sensor dead time.

Solution

Temperature margin between alarm and trip:

Time from alarm value to trip value:

Remaining response time after dead time:

Engineering Comment

The operator has only about three minutes after measurement lag. The alarm action must be simple, trained, and effective; otherwise the protective function should rely on automatic interlock action rather than manual response.

Exercise 6: Proportional Controller Output

A temperature controller has setpoint 80^\circ\text{C} and measured value 76^\circ\text{C}. Controller bias is 40\% output and proportional gain is K_c=3\%\ /\ ^\circ\text{C}. Use proportional-only action:

where e=r-y.

Estimate controller output.

Solution

Error:

Controller output:

Engineering Comment

The output change is understandable, but proportional-only control usually leaves offset. Integral action, actuator limits, valve fail position, loop direction, process gain, and dead time must be reviewed before tuning is changed in the plant.

Exercise 7: Feedforward Cooling Adjustment

A reactor normally requires cooling-water flow of 12\ \text{kg/s} at a given temperature rise. Feedforward logic assumes heat release is proportional to feed rate. Feed rate increases by 25\%.

Estimate required cooling-water flow if the allowed water temperature rise is unchanged.

Solution

Feedforward scaling:

Additional cooling-water flow:

Engineering Comment

Feedforward can reduce temperature excursions only if feed-rate measurement is reliable and cooling-water capacity is available. Feedback control is still needed because reaction heat, fouling, concentration, and utility temperature may not scale perfectly with feed rate.

Exercise 8: Analyzer Validation Against Laboratory Result

An online analyzer reports product impurity at 2.55\%. A validated laboratory sample from the same time window reports 2.48\%. The analyzer validation tolerance is \pm0.10 percentage points.

Check the analyzer difference and validation status.

Solution

Analyzer difference:

Since:

the analyzer is within the stated validation tolerance.

Engineering Comment

The analyzer is acceptable for this check, but validation should also consider sampling time alignment, stream lag, calibration range, drift, maintenance status, and whether the analyzer is used for release, control, or alarm action.

Exercise 9: Simplified Interlock Availability

A feed-shutdown safety function requires temperature sensor, logic solver, final isolation valve, and instrument air to be available. Estimated availabilities for the operating window are:

Estimate simplified series availability.

Solution

Series availability:

Engineering Comment

The simplified result shows why diagnostics, proof testing, bypass control, valve maintenance, and utility reliability matter. A safety function is not validated by control logic alone; the full chain must work.

Exercise 10: Bypassed Analyzer Risk Ranking

A product-quality analyzer can be bypassed during maintenance, allowing off-spec material to pass to storage. Initial rankings are severity S=7, occurrence O=5, and detection D=5.

After bypass permits, timed bypass alarms, laboratory hold-point sampling, and shift-handover logging are introduced, occurrence is estimated at O=3 and detection at D=2. Compare traditional risk priority numbers.

Solution

Initial risk priority number:

Revised risk priority number:

Reduction:

Engineering Comment

The revised ranking is lower, but it depends on disciplined operations. The bypass record, laboratory sample, tank routing, alarm response, quality release, and shift handover must all be auditable.

Plant Operations Review Checklist

Before using these exercises as templates for a real operating decision, check:

• Is the operating state normal, startup, shutdown, upset recovery, grade transition, or maintenance?
• Is each measurement corrected for density, calibration, sensor location, sampling lag, and valid range?
• Are alarm margins compared with operator response time, process dead time, and trip setpoints?
• Are manual responses simple enough to execute under credible upset conditions?
• Are controller calculations checked against actuator limits, valve fail position, loop direction, and process gain?
• Are feedforward assumptions backed by utility capacity, reaction heat data, and feedback correction?
• Are analyzer results tied to sampling alignment, quality release rules, bypass status, and laboratory confirmation?
• Are interlock and bypass controls supported by proof-test records, permits, handover notes, and management-of-change evidence?

Strong plant operations engineering turns small calculations into controlled actions. The result should clarify what must be measured, who must respond, and which evidence proves that the response remains valid.