Practice PE Chemical problems as decisions, not formulas: identify the governing balance, select a property model that matches the stated conditions, verify phase and units, then compute. Keep an assumption log for every problem so each simplification is written, justified, and stress-tested.
Name the Governing Balance Before Touching a Formula
Every chemical engineering practice problem reduces to one governing principle: conservation of mass, energy, or momentum. Identify which balance applies, list knowns and unknowns with units, and only then choose equations.
Classification is a skill you can drill. Read a problem and ask three questions: is anything entering or leaving (mass balance), is work, heat, or enthalpy changing (energy balance), and is a fluid moving through a resistance (momentum and pressure balance). A flash drum is a mass and VLE problem; a compressor is an energy problem; a pipeline is a momentum problem. Writing the balance name at the top of your work forces this classification in seconds.
Translation from scenario text to variables is where problems get hard. Phrases like 'operates adiabatically,' 'neglecting kinetics,' or 'at steady state' are instructions about which terms vanish from your balance. Build the habit of underlining these qualifiers and mapping each one to a term you delete or keep. A problem statement that mentions both a heat duty and an outlet temperature is telling you which unknown to solve for, so let the given-and-wanted list drive the equation choice.
Property Models: Ideal Gas, Raoult, Henry, or Activity Coefficients
Match the property model to pressure, temperature, and mixture behavior. Raoult's law, Henry's law, and activity-coefficient methods answer different questions, and the ideal gas law is a claim about Z, not a default setting.
The ideal gas law is valid only in the range where the compressibility factor Z is close to one, which generally means pressure well below the critical pressure and temperature well above the critical temperature. Saying 'the vapor is ideal' is therefore a claim you should be able to defend from the stated conditions. Compare the reduced pressure and temperature first; if the state is dense or near saturation, a compressibility factor or an equation of state is the defensible route, and the answer can differ materially.
Phase equilibrium models answer different questions, so choose by question type. Raoult's law describes vapor pressure over an ideal liquid mixture at modest pressure; Henry's law describes a sparingly soluble gas dissolved in a liquid; activity-coefficient methods describe liquid-phase nonideality such as polar pairs that deviate strongly from ideality. When a problem mentions azeotropes, immiscibility hints, or unusual component pairing, treat Raoult's law as a hypothesis to check rather than a starting point. Use this table as a first-pass filter before any calculation:
| Situation in the problem | Candidate model | Typical breakdown condition | Better check before computing |
|---|---|---|---|
| Low-pressure vapor, well above critical temperature | Ideal gas law (Z near 1) | High pressure or near-critical state | Estimate Z; if far from 1, use a compressibility factor or equation of state |
| Vapor-liquid equilibrium of a similar, nonpolar mixture | Raoult's law | Polar or associating component pairs | Consider an activity-coefficient model or system data |
| Sparingly soluble gas dissolved in a liquid | Henry's law | High solubility or reactive absorption | Confirm dilute conditions and use system-specific data |
| Dense gas or high-pressure vapor | Compressibility factor or EOS | Rapid property change near the two-phase region | Confirm the phase state before selecting the correlation |
Worked Scenario: Compressor Work and the Isothermal Trap
Compressor problems specify a machine and a path. An isentropic step adjusted by an efficiency fits an adiabatic compressor; isothermal work fits a perfectly intercooled multi-stage approximation, not a single machine.
Scenario: propane vapor enters a compressor at 1 bar and 300 K and leaves at 8 bar. Treating the vapor as an ideal gas with a heat-capacity ratio of about 1.13, isothermal work is RT ln(P2/P1), roughly 5.2 MJ per kmol. A candidate sees 'ideal gas' and computes exactly that, reporting 5.2 MJ/kmol and a modest outlet temperature. The stated machine, however, is a single adiabatic compressor with an isentropic efficiency of 0.75, and no intercooling is mentioned.
The better decision is to match the path to the machine: compute the isentropic outlet temperature, T2s = T1 (P2/P1)^((k-1)/k), about 381 K, convert the temperature rise to work with the heat capacity, about 5.9 MJ/kmol, and divide by the efficiency to get roughly 7.9 MJ/kmol and an actual outlet temperature near 408 K. The isothermal answer underpredicts both the required work and the outlet temperature, which would mislead any downstream equipment check. This is a simplified ideal-gas teaching example; a real machine analysis uses the property data your reference provides. Record two observations in your notes: 'ideal gas' governs the property model, not the process path, and an efficiency always multiplies the ideal work in the direction of reality for a compressor. Writing both sentences after each compressor drill makes the distinction automatic.
Worked Scenario: NPSH Available at Elevated Temperature
NPSH available is an absolute-pressure head balance at the pump suction. Use atmospheric pressure at an open surface, subtract the vapor-pressure head at the pumping temperature, and include suction-line friction.
Scenario: water at 60 degrees C, where the vapor pressure is about 19.9 kPa, is pumped from an open tank with the level 3 m above the pump centerline. Suction-line friction is 1.2 m of head. A candidate uses zero gauge pressure at the tank surface, forgets the vapor-pressure term, and computes 3 minus 1.2, about 1.8 m. On that number the pump selection fails, and the candidate rejects the layout.
The better decision is a complete head balance in absolute terms: (101.3 minus 19.9) kPa converted to about 8.3 m of head, plus the 3 m of static elevation, minus the 1.2 m of friction, giving roughly 10.1 m NPSH available. At ambient-temperature water, atmosphere and vapor pressure nearly cancel, so the shortcut happens to work; at 60 degrees C the two terms differ by about 8.3 m, and the shortcut fails. That is why the discipline is to write the full balance every time, then compare against the pump's required NPSH with an appropriate margin. For a closed, pressurized vessel, the surface pressure is the vessel's absolute pressure, and the same balance structure applies unchanged.
Self-check: rewrite the calculation for a closed tank at 150 kPa absolute and confirm the available NPSH rises to roughly 16.3 m before friction adjustments, dropping to about 15.1 m after subtracting the 1.2 m of suction-line friction. If you cannot reconstruct that variant quickly, the balance is not yet solid.
Pressure-Drop Calculations: Regime, Convention, and Loss Accounting
Pressure-drop work has three gates: compute the Reynolds number to fix the regime, use one friction-factor convention throughout, and account every fitting with equivalent lengths or K-values, never a mixture of both.
The Reynolds number is not an intermediate result; it is the switch that selects your correlation. Laminar flow gives a friction factor inversely proportional to Reynolds number, while turbulent flow requires an explicit roughness-aware correlation. Computing Reynolds number first, and writing the regime beside it, prevents the common silent error of applying a turbulent correlation to a viscous, low-velocity line. In a teaching example, a flow rate misread by a factor of ten can flip the regime entirely, which is worth observing once deliberately so you never repeat it.
Convention discipline matters because two standard friction factors coexist, differing by a factor of four. Pick Darcy or Fanning at the start of the problem, label every f you write, and convert explicitly if a source table uses the other convention. For minor losses, choose either the equivalent-length method or the K-value method and stick with it; summing a fitting's K with another fitting's equivalent length double-counts nothing only if you convert both to the same head basis. Ending each pressure-drop problem with a one-line accounting list, pipe plus each fitting, makes omissions visible.
Sizing or Rating? Choosing LMTD versus Effectiveness-NTU
LMTD fits sizing problems where both outlet temperatures are known and area is sought. Effectiveness-NTU fits rating problems where the geometry is fixed and outlets are unknown. Naming the task type prevents circular calculations.
A sizing question gives you the duty and asks for area. A rating question gives you the exchanger and the flows and asks for outlet temperatures or duty. The LMTD method solves sizing cleanly when both terminal temperature differences are computable from known inlets and outlets; the effectiveness-NTU method solves rating cleanly because it needs no outlet temperatures as inputs. Deciding which question you are answering takes one sentence and eliminates the deadlock of needing an unknown outlet temperature to start an LMTD calculation.
Both methods rest on assumptions worth stating in your assumption log: a globally constant overall heat-transfer coefficient, constant heat capacities, and no phase change within a pass unless the problem handles condensation or boiling separately, as with a condenser following its own temperature profile. When a scenario specifies a crossflow or multipass geometry, the appropriate correction factor applies to LMTD, and skipping it is a modeling error, not an arithmetic one. After each exchanger drill, write which method you used and why; if the reason is habit rather than the task type, redo the classification. The same sizing-versus-rating distinction transfers to separations: a minimum-reflux calculation answers a different question than an operating-reflux column performance check. Naming the question before selecting the method is the transferable skill.
An Assumption-Log Exercise with a Self-Check Rubric
Build an assumption log for every practice problem: governing balance, property model, simplifications, and one sensitivity note. Score each log against a four-point rubric and track which decision types consistently slow you down.
The exercise: select three problems from different topic areas, such as one compression, one pump or NPSH, and one exchanger or column. Before any arithmetic, write four log lines: the governing balance with a one-line justification, the property model tied to the stated pressure, temperature, and mixture, every simplification with its source phrase from the problem, and a predicted direction of error if one assumption were dropped. Then solve. Finally, flip one assumption, for example replace ideal gas behavior with a compressibility factor, recompute the key result, and record how much it moved in your own example rather than assuming a universal threshold.
Expected observations: on low-pressure, moderate-temperature vapor problems you may see small changes from the property-model switch, while high-pressure or near-saturation states can move results noticeably. Regime flips in pressure-drop problems and missing vapor-pressure terms in NPSH problems can change conclusions, not just decimals. You should also observe which log line takes longest to write; that line is your next study target, because slow decisions, not slow arithmetic, are what timed practice exposes. Score each completed log with this rubric, one point per line:
- Governing balance named correctly with a one-line justification tied to the scenario.
- Property model chosen with explicit reference to the stated pressure, temperature, and components.
- Every value carries consistent units and the phase state is confirmed before correlations are applied.
- A sensitivity note states how the answer would move if one stated assumption were dropped.
| Phase | Focus | Concrete output |
|---|---|---|
| Phase 1 | Reference fluency | A one-page personal index of where key equations and property tools live in your reference material |
| Phase 2 | Unit and state drills | Short daily conversions plus phase-state checks until automatic |
| Phase 3 | Topic blocks | Fluids, thermodynamics, heat and mass transfer, separations, and process and safety decisions, each with assumption logs |
| Phase 4 | Mixed timed sets | Set a self-chosen time budget, then review by decision type rather than only right or wrong |
| Phase 5 | Full simulations | Complete runs under exam-style conditions, followed by assumption-log scoring and error-pattern notes |
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.