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1 Chemical Reaction Engineering - Musgrave Unsteady State Operations Lecture 14 - Page 1 Outline: Unsteady State Operations (Fogler 4.10) Next Time: (Fogler 5.1-5.2) 1. The Algorithm for Data Analysis (Fogler 5.1) 2. Batch Reactor Data (Fogler 5.2) Chemical Reaction Engineering - Musgrave Unsteady State Operation Lecture 14 - Page 2 When a CSTR is started, how long does it take to reach steady-State? Normally we avoid start-up and stopping of CSTR processes - so unsteady -state operation is unusual. However, we’ll analyze its start-up as follows: CRE Algorithm 1. Unsteady state mole balance 2. Rate law 3. Stoichiometry 4. Combine relationships 5. Evaluate expression Analytically ( if 0 th or 1 st order ) Numerically ( if higher than 1 st order or to check ) Graphically

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2 Chemical Reaction Engineering - Musgrave Unsteady State Operation Lecture 14 - Page 3 F j0 F j Mole Balance: 1. MBE encloses system 2. Assumptions/Conditions a. Not steady-state dr A dV = 0 3. Determine mole balance expression F A 0 F A + r A dV V = dN A dt In - Out + Generation = Accumulation Substitute in r j is constant: dN A dt 0 b. Perfect mixing - r j is the same throughout the reactor volume F A 0 F A + r A V = dN A dt And use: V i To obtain: F j = C j υ C A 0 C A t ( ) + r A τ = τ dC A dt τ V 0 υ 0 C A 0 C A + r A V υ 0 = V υ 0 d N A V dt And: Chemical Reaction Engineering - Musgrave Unsteady State Operation Lecture 14 - Page 4 F j0 F j 2. Rate Law: a. Zeroth order b. Or first order r A = kC A C A 0 C A + kC A τ = τ dC A dt r A = k 3. Stoichiometry: Not needed for 0 th and 1 st order rxns 4a. Combine: dC A dt + 1 + τ k τ C A = C A 0 τ C A 0 C A + k τ = τ dC A dt dC A dt + C A τ = C A 0 + τ k τ C A = C A 0 1 + τ k 1 exp 1 + τ k ( )
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