Design equations from GMBE: F_j0 − F_j + ∫r_j dV = dN_j/dt. Note: these equations must be derived — they are not given in exams.
Conditions
Rate Law: −rA = k · CA^n
Target
Levenspiel plot: FA₀/(−rA) vs X. CSTR volume = rectangle (height × width); PFR volume = area under curve. For positive-order reactions PFR always needs less volume than CSTR.
Feed & Rate Law
Reactors in Series / Parallel
Uses the same feed & rate law parameters above. Series analysis uses Levenspiel graphical stepping; parallel assumes equal feed split.
Rate laws are determined experimentally. For an elementary reaction the order equals the stoichiometric coefficient. −rA always has units mol/dm³·s (or mol/g_cat·s for heterogeneous).
Power Law Rate: −rA = k·CA^α·CB^β
Arrhenius: k(T) = A·exp(−E/RT)
Given k at reference T₀, find k at new T. Or find k from A and E directly.
Rate Constant Units
Reaction Order & Rate Constant Fitting
Enter CA₀, −rA₀ pairs — slope of log(−rA₀) vs log(CA₀) gives α, intercept gives ln k.
CA₀ = first CA value. Tests 0th (CA vs t), 1st (ln(CA/CA₀) vs t), 2nd (1/CA vs t) — best R² wins.
Estimates −rA = −dCA/dt via central differences, then fits log(−rA) vs log(CA) by regression.
Build the stoichiometric table for A + (b/a)B → (c/a)C + (d/a)D. Concentrations expressed as C_j = C_A0(Θ_j + ν̃_j X) for liquid; gas adds the (1+εX) denominator.
Reaction Stoichiometry (stoich coefficients)
Initial Conditions
yA₀ = mole fraction of A in feed. δ = (d+c−b−a)/a. ε = yA₀·δ
Full isothermal design algorithm: mole balance → rate law → stoichiometry → combine & evaluate. ODEs integrated numerically (RK4) where needed.
Rate Law: −rA = k · CA^n
Stoichiometry & Phase
Feed (Flow Reactors)
Solve
Pressure Drop (PBR only)
Selectivity and yield for parallel or series reactions. Reaction rates are power-law: r_j = k_j · CA^α_j.
Desired Reaction: A → D
Undesired Reaction: A → U
PFR Profile (liquid, isothermal)
A →(k₁) B →(k₂) C. Liquid phase, isothermal. Optimal τ maximises C_B.
Residence Time Distribution analysis. Inject inert tracer and measure C(t) in effluent. Pulse → compute E(t) directly. Step → differentiate F(t) = C_out/C_0 to get E(t).
C(t) Data — Pulse Experiment
Enter time values (s) and corresponding tracer concentration C(t) separated by commas. One pair per line or comma-separated pairs: t1,C1,t2,C2,...
Models for non-ideal reactors. RTD + Model + Kinetics = X_exit. Choose a model below.
Tanks-in-Series Parameters
σ²_θ = 1/n. Compute n from tracer data: n = t_m²/σ². For 1st order: X = 1 − 1/(1+τᵢk)ⁿ
Dispersion Model — Danckwerts (closed-closed)
1st order reaction. Pe_r = UL/D_a. Da₁ = kτ. X from analytical Danckwerts solution.
Segregation Model
X̄ = ∫X(t)·E(t)dt. Each globule acts as a batch reactor. Enter RTD data and rate law.
E(t) data — alternating t, E(t) values (must be normalised: ∫E dt = 1):
Maximum Mixedness Model
dX/dλ = r_A/C_A0 + [E(λ)/(1−F(λ))]·X. Integrate backwards from λ→∞ to λ=0. Enter E(t) data and rate law.
E(t) data — alternating t, E(t) values:
not solvedtap unit → add · tap port → connect
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Tap a reactor unit below to place it. Connect ports, configure via tap, then Solve.