Let's break down the solution **step-by-step** as requested: --- # **2. Absorption/Stripping Process Problem** ## **Given Data** - Feed gas: 30.0 mol% CO₂, 70.0 mol% CH₄ - Absorber solvent: 0.500 mol% dissolved CO₂ (balance is methanol) - Product gas from absorber: 1.00 mol% CO₂, essentially all CH₄ fed - Rich solvent (from absorber) to stripper - Nitrogen gas fed to stripper (same flow in/out) - 90% of CO₂ in liquid feed to stripper comes out in the column - Liquid leaving stripper: 0.500% CO₂ (recycled to absorber) --- ## **a) Flowchart of the Process** ### **Step 1: Draw and Label Streams** ```plaintext Feed Gas (F) Nitrogen (N2 in) | | v v +-------------+ +-------------+ | Absorber | | Stripper | +-------------+ +-------------+ | ^ | | ^ | | | | | | | | | | | | | Product Rich Solvent Stripped Recycled Gas (to Stripper) Gas Solvent (P) (S) (R) ``` #### **Labeling the streams:** - **F:** Feed gas (CO₂ + CH₄) - **S:** Solvent (methanol + CO₂) - **P:** Product gas (CH₄ + trace CO₂) - **L:** Rich solvent (methanol + CO₂, to stripper) - **N:** Nitrogen (to stripper) - **G:** Gas leaving stripper (N₂ + CO₂) - **R:** Recycled solvent (methanol + trace CO₂) --- ### **Flowchart (with composition):** ```plaintext [Feed Gas] 30% CO₂, 70% CH₄ | v +-------------+ | Absorber |<-------------------+ +-------------+ | | | | v v | [Product] [Rich Solvent] | 1% CO₂ ~CO₂ (to Stripper) | CH₄ (almost all) | | | v | +-------------+ | | Stripper |<------[N₂ in] | +-------------+ | | | | v v | [Gas: N₂+CO₂] [Lean solvent]---------+ (to atm) (to absorber) ``` --- ## **b) Degree of Freedom Analysis** ### **Species:** - CO₂ - CH₄ - Methanol - N₂ N₂ is only introduced in the stripper and leaves as well; it does not interact with other species. ### **Overall Process:** Let’s count: - **Unknowns:** Let’s assume 1 mol feed for simplicity. - Molar flow rates and compositions of each stream (to be calculated). - **Independent Species:** Yes, **N₂** is independent because it is not present in the absorber or in the feed; it only enters and leaves the stripper. Its only role is to strip CO₂. ### **Absorber:** N₂ is **not** an independent species in the absorber (not present). --- ## **c) Molar Flow Rates** Let: - \( F \) = total feed (basis: 100 mol for simplicity) - \( F_{CO_2} = 30 \) mol, \( F_{CH_4} = 70 \) mol - \( P \) = product gas leaving absorber **Product Gas:** - Contains 1.00 mol% CO₂, rest is CH₄ (assume negligible methanol and N₂) Let product gas flow = \( P \) - \( P_{CO_2} = 0.01P \) - \( P_{CH_4} = 0.99P \) Assume all CH₄ leaves in product gas: - \( P_{CH_4} = F_{CH_4} = 70 \) mol - \( 0.99P = 70 \implies P = 70.71 \) mol So, - \( P_{CO_2} = 0.01 \times 70.71 = 0.71 \) mol **CO₂ absorbed = CO₂ in feed - CO₂ in product** - \( = 30 - 0.71 = 29.29 \) mol CO₂ absorbed (per 100 mol feed) **Rich Solvent to Stripper:** - Contains 29.29 mol dissolved CO₂ **Stripping:** - 90% of CO₂ in feed to stripper is stripped out: - \( 0.9 \times 29.29 = 26.36 \) mol CO₂ stripped (leaves with N₂) - \( 0.1 \times 29.29 = 2.93 \) mol CO₂ remains (in recycled solvent) **Recycled Solvent:** - Contains 2.93 mol CO₂ in 100 mol methanol (assuming 100 mol solvent for basis). --- ### **Summary of Molar Flow Rates (per 100 mol feed):** - **Product gas leaving absorber:** \( \boxed{70.71 \text{ mol}} \) (contains 70 mol CH₄, 0.71 mol CO₂) - **CO₂ leaving stripper:** \( \boxed{26.36 \text{ mol}} \) --- ## **Summary Table** | Stream | Flow (mol) | CO₂ (mol) | CH₄ (mol) | N₂ (mol) | Methanol (mol) | |--------------------------|------------|-----------|-----------|----------|----------------| | Feed | 100 | 30 | 70 | 0 | 0 | | Product Gas (Absorber) | 70.71 | 0.71 | 70 | 0 | 0 | | Rich Solvent to Stripper | 29.29 | 29.29 | 0 | 0 | 100 | | CO₂+N₂ Gas (Stripper) | 26.36 | 26.36 | 0 | N₂ | 0 | | Recycled Solvent | 2.93 | 2.93 | 0 | 0 | 100 | --- ### **Final Answers** - **a) Flowchart:** See above. - **b) Degree of Freedom:** N₂ is independent in the overall process (only in stripper). - **c) Molar flow rates:** - Product gas leaving absorber: **70.71 mol** - CO₂ leaving stripper: **26.36 mol** --- If you need a **neatly drawn digital flowchart**, let me know!