Sources and References

Primary texts — Felder, R.M., Rousseau, R.W., and Bullard, L.G., Elementary Principles of Chemical Processes, 4th ed., Wiley, 2016; Himmelblau, D.M. and Riggs, J.B., Basic Principles and Calculations in Chemical Engineering, 9th ed., Prentice Hall, 2022.

Supplementary texts — Murphy, R., Introduction to Chemical Processes, McGraw-Hill, 2007; Reklaitis, G.V., Introduction to Material and Energy Balances, Wiley, 1983.

Online resources — MIT OCW 10.10 “Introduction to Chemical Engineering”; AIChE open-access concept videos; NIST WebBook for fluid properties; IUPAC “Green Book” on quantities and units.

---

Chapter 1: Units, Dimensions, and Engineering Calculations

1.1 The Role of Dimensional Analysis

Every chemical engineering quantity carries dimensions of mass, length, time, temperature, amount of substance, current, or luminous intensity. A dimensionally inconsistent equation is wrong regardless of its numerical agreement with data. The Buckingham pi theorem states that any physically meaningful equation among \( n \) dimensional variables reduces to a relation among \( n - k \) dimensionless groups, where \( k \) is the number of independent dimensions.

1.2 Unit Systems

Chemical engineers use the SI system (kg, m, s, K, mol) and, for legacy reasons in North America, the American engineering system (lb\(_m\), ft, s, °R, lbmol). The conversion factor \( g_c = 32.174 \) lb\(_m\)·ft/(lb\(_f\)·s\(^2\)) appears in US-customary force expressions and is set to unity in SI.

Temperature requires care: Celsius and Kelvin share the same interval size but different zeros; temperature differences are interval quantities (°C = K, °F = °R), while absolute temperatures are not interchangeable.

1.3 Engineering Quantities

Mass and moles are related by molecular weight \( M \): \( m = n M \). Density \( \rho \) and specific gravity \( SG = \rho/\rho_{ref} \) (reference typically water at 4 °C). Flow rates—mass (\( \dot m \)), molar (\( \dot n \)), and volumetric (\( \dot V \))—connect via \( \dot m = \rho \dot V = M \dot n \).

Pressure forms a cornerstone: absolute, gauge (\( P_{gauge} = P_{abs} - P_{atm} \)), and differential pressures are all used, often alternately without warning. Hydrostatic pressure in a column of fluid:

\[ P = P_0 + \rho g h. \]

1.4 Significant Figures and Error Propagation

Engineering answers carry uncertainty. For a function \( y = f(x_1, x_2, \ldots) \) of independent variables with uncertainties \( \sigma_i \),

\[ \sigma_y^2 = \sum_i \left(\frac{\partial f}{\partial x_i}\right)^2 \sigma_i^2. \]

Expressing a result to more digits than the input uncertainty justifies is both common and wrong.

Chapter 2: Process Variables and Process Streams

2.1 Composition of Mixtures

For a mixture of \( N \) components:

• Mass fraction \( w_i = m_i/m \), \( \sum w_i = 1 \).
• Mole fraction \( x_i = n_i/n \).
• Molarity \( c_i = n_i/V \).
• Parts per million (mass-based): \( w_i \times 10^6 \).

Conversions between mass and mole fractions use the average molecular weight \( \bar M = \sum x_i M_i = (\sum w_i/M_i)^{-1} \).

2.2 Ideal Gases

The ideal gas law \( PV = nRT \) holds when molecules are effectively non-interacting and point-like. For most gases at atmospheric pressure and ordinary temperatures, deviations are under 1%. The universal gas constant:

\[ R = 8.314 \text{ J/(mol K)} = 0.08206 \text{ L atm/(mol K)}. \]

Standard temperature and pressure definitions vary; a common engineering choice is 0 °C, 1 atm, giving 22.414 L/mol molar volume.

2.3 Real Gases and the Compressibility Factor

At high pressure or near the critical point, \( PV = ZnRT \) with compressibility \( Z = Z(T_r, P_r) \) where \( T_r = T/T_c \) and \( P_r = P/P_c \) are reduced coordinates. Generalized compressibility charts and equations of state (van der Waals, Peng-Robinson, Soave-Redlich-Kwong) correct ideal behavior.

2.4 Vapor Pressure and Humidity

Vapor pressure of a pure liquid is correlated by the Antoine equation:

\[ \log_{10} P^{sat} = A - \frac{B}{T + C}. \]

For humid air, relative humidity is \( RH = P_{H_2O}/P^{sat}_{H_2O} \) and absolute humidity \( H = m_{H_2O}/m_{dry\ air} \).

Chapter 3: Fluid Statics and Flow

3.1 Hydrostatics

In a static fluid, pressure varies only with depth: \( dP/dz = -\rho g \). For incompressible fluids this integrates immediately; for compressible atmospheres one uses the ideal gas law and obtains the barometric formula

\[ P(z) = P_0 \exp\!\left(-\frac{Mgz}{RT}\right). \]

Manometers (U-tube, inclined, differential) measure pressure differences via hydrostatic balance, foundational to flow and level measurement.

3.2 Flow Regimes and the Reynolds Number

The Reynolds number

\[ Re = \frac{\rho v D}{\mu} \]

classifies pipe flow as laminar (\( Re < 2100 \)), transitional (2100 < \( Re \) < 4000), or turbulent (\( Re > 4000 \)). Viscosity \( \mu \) [Pa·s] measures momentum diffusivity; water at 20 °C has \( \mu \approx 10^{-3} \) Pa·s.

3.3 Mechanical Energy Balance

For steady flow of an incompressible fluid between sections 1 and 2:

\[ \frac{v_2^2 - v_1^2}{2} + g(z_2 - z_1) + \frac{P_2 - P_1}{\rho} + F - W_s = 0, \]

where \( F \) is friction loss and \( W_s \) is shaft work. Bernoulli’s equation recovers when \( F = W_s = 0 \). Friction factor correlations (Fanning or Darcy) and loss coefficients for fittings close the model.

Chapter 4: Material Balances

4.1 The General Balance Equation

For any conserved quantity (total mass, component mass, moles of a non-reacting species) in a control volume:

\[ \text{accumulation} = \text{input} - \text{output} + \text{generation} - \text{consumption}. \]

At steady state the accumulation vanishes. Without reaction, generation and consumption are zero for each species.

4.2 Degree-of-Freedom Analysis

Count unknowns, equations, and specifications. A problem is well-posed when DOF = 0, underspecified when DOF > 0, and overspecified when DOF < 0. Unknowns include unknown flow rates and compositions; equations include material balances (one per independent species), equilibrium relations, and auxiliary specifications (ratios, splits).

4.3 Recycle, Bypass, and Purge

Industrial processes rarely work single-pass. Recycle improves conversion or solvent utilization; bypass allows process control without altering main throughput; purge prevents accumulation of inerts or byproducts. For each, careful choice of balance envelope—overall versus single-pass—simplifies or complicates algebra dramatically. Overall balances treat the whole unit as a black box, giving the simplest relations between fresh feeds and net products.

4.4 Multi-Unit Flowsheets

Real processes involve several connected units. Material balances on each unit and on the overall system are together overdetermined; pick the smallest independent set. Sequential modular solution walks unit by unit, solving each with the outputs of upstream units as inputs. Simultaneous equation-based solution assembles a large sparse system and solves with Newton-type methods.

Chapter 5: Reacting Systems

5.1 Stoichiometry

For a reaction \( \sum_i \nu_i A_i = 0 \), species change by \( \Delta n_i = \nu_i \xi \) where \( \xi \) is the extent of reaction. Extent-based balances eliminate coupling between species, reducing dimensionality: an \( N \)-species, \( R \)-reaction system has \( N - R \) conserved atomic elements.

5.2 Conversion, Yield, Selectivity

• Fractional conversion of limiting reactant: \( X = (n_{A,0} - n_A)/n_{A,0} \).
• Yield of product \( P \): moles of \( P \) produced per mole of limiting reactant fed, often normalized by stoichiometric maximum.
• Selectivity: moles of desired product per mole of undesired byproduct.

High conversion does not imply high yield when parallel or series reactions consume reactant unproductively; process design often targets intermediate conversion with recycle to maximize yield.

5.3 Combustion Stoichiometry

Complete combustion of hydrocarbon \( C_xH_y \) requires \( (x + y/4) \) moles of O\(_2\) per mole of fuel. Air-fuel ratio, percent excess air, and Orsat dry-basis flue-gas analysis are routine calculations. Partial combustion producing CO appears when air is insufficient or mixing is poor.