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Process engineering, explained one unit op at a time

The physics, the governing equations, and the common pitfalls behind every unit operation MaximaLabs simulates — with an example you can open and run.

1

Level 1 — The Basics: Stream Controls & Stage Ops

Mixer

Combine several streams into one; outlet state comes from the combined material and energy balance.

Fout=∑kFkF_{out} = \sum_k F_k
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Splitter

Divide one stream into several with the same composition but split flows.

Fj=ϕj Fin,∑jϕj=1F_j = \phi_j\, F_{in},\qquad \sum_j \phi_j = 1
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Flash drum

A single equilibrium stage: split a feed into vapor and liquid at a given temperature and pressure.

Ki=yixi=γi Pisat(T)PK_i = \frac{y_i}{x_i} = \gamma_i\,\frac{P_i^{sat}(T)}{P}
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2

Level 2 — Energy & Pressure Dynamics

Heat exchanger

Transfer heat between a hot and a cold stream; duty is set by the energy balance, area by the LMTD/U rating.

Q=Fhot(hhot,in−hhot,out)=Fcold(hcold,out−hcold,in)Q = F_{hot}(h_{hot,in}-h_{hot,out}) = F_{cold}(h_{cold,out}-h_{cold,in})
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Pump

Raise the pressure of a liquid; work depends on the head and pump efficiency.

W=F (Pout−Pin)ρ ηW = \frac{F\,(P_{out}-P_{in})}{\rho\,\eta}
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Compressor

Raise the pressure of a gas; temperature rises with the compression ratio.

S(T2s,P2)=S(T1,P1)(real-gas isentropic, solved for T2s)S(T_{2s}, P_2) = S(T_1, P_1) \quad(\text{real-gas isentropic, solved for } T_{2s})
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3

Level 3 — Multi-Stage & Equilibrium Separations

Distillation column

Separate a mixture by repeated boiling and condensation across equilibrium stages, solved with the MESH equations.

Mi,j:  li,j−1+vi,j+1+fi,j−li,j−vi,j=0M_{i,j}:\; l_{i,j-1} + v_{i,j+1} + f_{i,j} - l_{i,j} - v_{i,j} = 0
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Adsorption column

Selectively capture components on a solid adsorbent via a competitive Langmuir isotherm.

qi=qmax,i bi pi1+∑jbjpj,n˙i,ads=qi Wq_i = \frac{q_{max,i}\,b_i\,p_i}{1+\sum_j b_j p_j},\qquad \dot n_{i,ads} = q_i\,W
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4

Level 4 — Reaction Engineering & Energy Transition

Kinetic reactor

A CSTR or PFR whose conversion is set by a rate law and residence time, not by equilibrium.

r=kf ⁣∏react ⁣Cn−kr ⁣∏prod ⁣Cn    (reversible),k=k0e−Ea/RTr = k_f\!\prod_{react}\! C^{n} - k_r\!\prod_{prod}\! C^{n}\;\;(\text{reversible}),\quad k=k_0 e^{-E_a/RT}
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Equilibrium reactor

Reaction extent set by chemical equilibrium (Keq), with a van't Hoff temperature correction.

∏iaiνi=Keq(T)\prod_i a_i^{\nu_i} = K_{eq}(T)
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Bioreactor

Microbial growth on a substrate following Monod kinetics in a chemostat.

μ=μmax SKs+S\mu = \mu_{max}\,\frac{S}{K_s + S}
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Electrolyzer

Split water into hydrogen and oxygen with electrical power (green hydrogen).

H2O→H2+12O2\mathrm{H_2O} \rightarrow \mathrm{H_2} + \tfrac{1}{2}\mathrm{O_2}
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