I am happy to note I passed the PE exam, which I took on Pi day (3/14) this year (2018). I took some notes on the 2018 PE Chemical Practice Exam, the NCEES PE Chemical Reference Handbook (v 1.2) and on general ChE items I had forgotten, thought fundamental, or found interesting. I pasted them below, relatively unadulterated from notes I had maintained while studying, with the hope that they might be useful. Please comment or contact me (danielgputt@gmail.com) with anything I may have missed or gotten wrong. Note that I have posted no information with respect to the actual exam to avoid legal liability.

## PE Study

## General

- The ideal gas approximation is best at low pressures and high temperatures. Intermolecular potentials have less of an effect, and space between molecules is great.
- Fourier transform decomposes an arbitrary wave into a series of sines and cosines.
- Equations in the reference manual are often presented in rigorous and/or differential form, followed later in the text by integrated and/or special case forms. The latter are generally easier to use and should be sought.

## Material and Energy Balances

- Full mass balance: Input + Gen. – Consumption – Output = Accumulation
- Getting net heating value from combustion requires using combustion heat, and then a steam heater to condense.
- Positive heat of reaction: products have greater enthalpy. Reaction is endothermic.
- Breakdown of problems in practice test (number in the practice test is noted in parenthesis):
- 8 total
- 2 combustion (1, 6)
**1 solid/liquid phase diagram & Clausius/Clapeyron (2)**- Really the Clapeyron equation. Rearrange the equation into form y = mx to make the slope more quickly obvious. Phase change will have a positive enthalpy if solid to liquid. Delta V will determine slope. If delta V is negative, specific volume of the liquid is lower than the solid. Therefore, density of the liquid is higher, and density of the solid is lower. Last mile: careful in not fat fingering density and specific volume.

- 1 conversion of mole percent to mass percent (3)
- There is a quick formula for this on page 102 of the reference manual. Search Mole fraction.

- 1 basic process with recycle (4)
- 1 simple mass balance from a distillation tower (5)
- 2 reactions (know selectivity vs. yield) (7,8)

## Thermodynamics

- Reference manual considers work positive if it is outward. Makes sense, in a sense, as systems are generally created to perform work rather than to be worked upon.
- Q – W = dH
- Work/Heat are proportional to the natural log of pressure/volume in an isothermal process.
- Polytropic process equations can be directly derived from the ideal gas law. See the Wikipedia article.
- Entropy decreases with increasing pressure and increases with increasing temperature. Since temperature increases with increasing pressure and irreversibility, entropy will tend to increase.
- Compressibility factor is generally less than one. This means at a given pressure, a real gas generally takes up less volume than would an ideal gas. The real gas is thus naturally “compressed” by that factor.
- There is a formula in the reference manual to convert from wet basis to dry basis (page 102.)
- Dalton’s law was empirical and published in 1801. Pressure was probably the only thing accurately measurable. Dalton’s law does not hold for some real gases.
- Fugacity
- Units of pressure
- When liquid and vapor fugacities are equal, equilibrium is reached
- The fudge factor for a pure component is based on the equation of state (phi)
- The rigorous version is based on Gibbs free energy
- The fudge factor for mixtures (in addition) is based on an activity coefficient (gamma)
- The vapor phase does not have a gamma correction.
- “fudge-gacity” may be an appropriate moniker

- A minimum-boiling azeotrope boils at the lowest temperature of any composition. Like a eutectic point.
- Problems not present on practice exam:
- Detailed equilibrium calculations using non-ideal fluids (e.g. cubic EOS)
- Thermo problems using ideal gases (e.g. isothermal expansion)

- Breakdown of problems in practice test:
- 10 total (9-18)
- 2 reading phase diagrams (9, 11)
- 3 enthalpy balances (mCp * deltaT); one with reaction (10, 12, 14)
- In heat of reaction problems, watch if basis is based on reaction mixture, or on one component.

- 1 Clausius/Clapeyron (13)
- One heat of reaction via heat of formation (15)
- This was at standard conditions, may have to calculate at non-standard. Reference book has formula.

- One misc. phase equilibrium (conceptual, no calcs) (16)
- 2 steam turbines’ energy production (17, 18)

## Heat Transfer

- Typical approach temp, countercurrent exchanger: T_hot_out – T_cold_in. As approach temperature approaches 0, exchanger area approaches infinity.
- Maximum heat transfer is the hot stream mass * Cp multiplied by the delta T between the hot inlet stream (max temp of system) by the cold inlet stream (min temp of the system.) If the hot outlet stream reached the temperature of the cold inlet stream, all heat of that stream would have been transferred, leaving no dT driving force, achieved by an infinitely large exchanger.
- Per manual, heat capacities vary over a factor of about 40 from 0.03 to 1.2 BTU/(lb*F), centered around 0.5, by mass.
- Thermal conductivity varies over 5 orders of magnitude from metals to gases.
- Overall heat transfer coefficient for exchangers varies over 3 orders of magnitude from 2 BTU/ft^2*F to 1300 BTU/ft^2*F. Condensing oil is 40-100 BTU/ft^2*F
- Prandtl number is diffusion of momentum/diffusion of heat.
- Oxidized steel has an emissivity of 0.85! The laser on the IR gun does not measure the temperature. It is just a guide, like a scope.
- When faced with an integral, solve for the end bound of integral, visualize at that constant value, then backtrack. Solve the simple problem first.
- For simple overall heat transfer (e.g. through a plate window or cylinder) use Q = UA*deltaT. For heat exchangers, use Q = UA* deltaT_log_mean. In special cases, when log-mean leads to 0/0, use the arithmetic mean.
- Problems not present on practice test but possible:
- LMTD calculation with heat exchanger (F) correction factor.
- More Nusselt/h correlations.
- Radiation problem using T^4 relation.
- Thermal resistance in parallel
- Fin heat transfer
- Heat exchanger NTUs

- Breakdown of problems in practice test:
- 13 total (19-31)
- 5 on Overall resistance through both cylinders and walls (combined heat transfer through different materials via conduction/convection) (19, 20, 22, 27, 30)
- In calculating area of pipe in heat transfer, watch that the surface area of a cylinder is used (pi*d*L) not the volume (pi*r^2*L)
- Watch for non-traditional sources of resistance (defined fouling factors, etc.)

**2 on heat exchange equipment Q = UA * LMDT (26, 28)**- (26) stated an azeotrope temperature at a different pressure than the problem conditions. That temperature had to be used for the problem. Azeotrope temperatures are sensitive to temperature, so this may be an error. LMTD was fairly straightforward.
- (28) if using the LMTD, 0/0 is obtained. Thus the equation Q = UA*DeltaT must be used. This is a common problem. Careful to use heat of vaporization when calculating steam use, not enthalpy of the vapor alone.

- 1 on radiation (23)
- 1 on correlations for convective heat transfer coefficient (h) (21)
- 2 conceptual (no calcs) (boiling and MW change) (24, 31)
- 2 Q = mCp * deltaT (25, 29)

## Kinetics

- Conversion is a measure of reaction completeness. A conversion of 1 (100%) signifies a remaining concentration of the initial reactant of 0.
- At equilibrium, forward and reverse rates of reaction are equal
- Rate is a reaction constant * concentration of reactants
- Therefore equilibrium constant is reaction constant of forward rate / reaction constant of reverse rate.
- Also equal to products over reactants, but the former makes more sense.

- A PFR is infinitely many differential CSTRs in series.
- Breakdown of problems in practice test:
- 9 total (32-40)
- 3 conceptual (no calcs) (32, 36, 40)
- Rate law given, state adsorption pattern
- Minimization of Gibbs Free Energy, what product obtained
- Relationship between rate/activation energy/temperature

- 1 rate law from elementary mechanisms (33)
- 1 conversion of rate constant to different units (34)
- May have gotten somewhat lucky here. Just used unit conversions, but solution used ideal gas laws.

- 1 Physical Chemistry equilibrium problem, using activity coefficients (35)
- 2 Spacetime calculations (PFR & CSTR) (37, 39)
- (37) is a reaction of shifting order. The spacetime calculations are in the reference manual for these already integrated, a potential time savings.
- (39) is straightforward

- 1 CSTR rate (38)

## Fluids

- Shear stress is proportional to the velocity difference between two layers of fluid. Like dragging a board over rough concrete. A better analogy would be two alike surfaces. Viscosity is the measure of roughness.
- Mass balance -> continuity equation. A1 v1 = A2 v2 is the simplified form. Rigorous is rho * A * v = rho * A * v
- When thinking of dividing or multiplying by S.G. in conversion h = 2.31 * psi/S.G., think of how much height liquid neutron star could be pumped to. Or think (h * S.G.) / 2.31 = psi.
- Reynold’s number is the ratio of inertial forces to viscous forces.
- Viscosity of motor oil (the most dramatic of the fluids listed) varies over 2 orders of magnitude for ~300 degrees F.
- Roughness factors vary over 3 orders of magnitude from PVC pipe to wood.
- Moody friction factor varies over about 1 order of magnitude.
- Fitting losses vary from L/D of 10 for a wide open gate valve to 830 for a “lift” check valve.
- Boats float because their average density is less than that of water.
- Terminal velocity is the settling velocity. If upward velocity is less than the settling velocity, the particles will settle.
- Head loss for a porous bed goes as (1 – porosity) / porosity^3. Curve knuckles upward around 0.4. Can be used to model pressure drop in plugging fixed bed reactor.
- In slug flow, slugs move faster than the bulk fluid. Presumably, this could impinge upon and shock equipment.
- Y – expansion factor – is charted on page 218.
- There is a simple equation for temperature rise of liquid across a pump on page 225.
- An equal percentage valve is called such as it is exponential – the flow increases by an equal percentage for each incremental valve position movement. E.G. from 10% to 20% valve position, flow increases by 50%. From 20% to 30% valve position, flow also increases by 50%. When combined with a centrifugal pump, whose pressure output decreases with increasing flow, a EP valve provides a more linear response to opening. Need to consider pump curve and Cv curve together in hydraulic calculations.
- Orifice plate flow equations on page 257. Fairly straightforward.
- Good graph of permanent pressure loss across an orifice on page 259.
- Problem types not present but possible:
- Conceptual questions on types of viscous fluids (Newtonian, shear thinning/thickening, etc.)
- Capillary rise
- Conservation of momentum
- Pressure drop through fittings
- Stokes flow

- Breakdown of problems in practice test:
- 13 total (41-53)
- 3 conceptual (no calcs)
- 2 Laminar vs turbulent flow profiles, friction factor (41, 43)
- 1 flowmeter dP (52)

- 1 dP vs. flow amenable to industrial calculations (42)
- 2 miscellaneous, odd geometry calculation heavy (packed bed, bob viscometer) (44, 53)
- 1 v * A = Volumetric flow rate (45)
**2 Bernoulli equations (46, 49) (watch out for velocity head)**- (46) is strange. Do not understand why the higher density at the outlet leads to lower hp in total.
- (49) Page 229 lays out pump head calculations in common units. Use this to take velocity head into account. Read the question carefully. Looks for head imparted into fluid. Efficiency of the pump does not have to be considered.

- 2 Darcy pressure drop (47,
**50**)- In (50) exchanger passes are doubled (from 2 to 4.) Velocity doubles, but so does length. Doubling of length doubles the pressure drop, doubling of velocity quadruples the pressure drop. Total increase is 8x.

- 1 pump curve (48)
- 1 manometer/orifice plate (51)

## Mass Transfer

- Sum of liquid fractions (xis) have to equal one when calculating dew pressure or dew temperature. The vapor fractions are already known. Creating a drop of liquid will not change the vapor fractions significantly. Pressure and temperature will affect the proportions of liquid, which will have to sum to equal one, by varying P and T.
- Conversely, in bubble point calculations, liquid fractions are known, and the composition of the first bubble has to be calculated with compositions which to sum to one.
- Diffusion is four orders of magnitude faster in gases than in liquids. On the order of the density difference between water (1000 kg/m^3) and atmospheric steam (0.6 kg/m^3)
- Diffusion is proportional to a constant and the concentration gradient.
- Colburn analogy: Eddies transfer heat, momentum and mass in a similar manner.
- Reactions can be controlled by kinetics, diffusion, or both.
- Start at the top right of a tower.
- V1 and Lo are related by mass balance. (Must be a line.)
- Lo and V1 mix intimately
- Lo becomes L1 by mass transfer. Moves to equilibrium line, with composition of V1.
- L1 returns to the mass balance line with crossing stream V2.
- Repeat as needed. Mass balance, equilibrium, mass balance, equilibrium, etc…

- Refluxing more for a given number of trays (operating scenario) must increase purity. Think of total reflux when the operating line is 45 degrees.
- Page 355 has an equation to estimate drop diameter in a dispersed phase of a liquid-liquid separator. Might be useful in Stokes’ Law calculations.
- Drying is faster with airflow perpendicular to the surface than with airflow parallel to the surface.
- Problem 62 uses a log-mean equation on page 299. The (Yin) and (Xin) values should be subscripts. As written, it appears these should be multiplied this is not correct.
- Breakdown of problems in practice test:
- 11 total (54-64)
- 1 Henry’s law (similar problem: Raoult’s law?) (54)
- 1 Saturation pressure and activity coefficient (55)
- 1 ternary phase diagram (56)
- 2 conceptual
- 1 dew point/composition (57)
- 1 tray hardware (60)

- 1 column bottom mass balance (58)
**1 absorber traditional (59)**- Able to solve quickly with one key assumption: the carrier gas is not absorbed. After that, simple mass balance.

- 1 McCabe Thiele (61)
- 2 packed towers (62, 63)
**1 adsorption (64)**- Key: adsorption is increased by increasing concentration. Le Chatlier’s principle.

## Plant Design and Operation

- Breakdown of problems in practice test:
- 16 total (65-80)
- 1 financial (NPV) (65)
- 1 P&ID (66)
- 2 distillation high level (could be classified as mass transfer) (67, 68)
- 3 safety (RV, confined space, reactor) (69, 70)
- 1 instrumentation (bubble tube, ideal gas law) (71)
- 1 Process control (what variable to manipulate) (72)
- 2 inspection/corrosion/metallurgy (73,74)
- 1 pump curve (could be in fluids) (75)
**1 misc. re: optimal changeout frequency of filters (required integrating exp. Fcn.) (76)**- Calculator can perform integrals. Integral of exp(ax) is number 22 on page 57 of the manual.

- 1 tank dike sizing (77)
- 1 volitalization of substance into a room (78)
- 1 Environmental regulation (80)