Let's solve each part **step by step**. This is a classic heat exchanger design problem. We'll proceed as follows: --- ## **Given Data** - **Amyl acetate (n-pentyl acetate, C₇H₁₄O₂)** - Mass flowrate: 85,000 lb/h - Inlet temperature: 175°F - Outlet temperature: 125°F - Inlet pressure: 45 psia - Specific gravity: 0.83 - Max pressure drop: 7 psi - **Amyl alcohol (1-pentanol)** - Inlet temperature: 75°F - Outlet temperature: 120°F - Inlet pressure: 50 psia - Specific gravity: 0.81 - Max pressure drop: 7 psi --- # **Part (a): Initial Configuration for Shell-and-Tube Heat Exchanger** ### **Step 1: Assign Streams** - **Hot fluid:** Amyl acetate (cooling from 175°F to 125°F) - **Cold fluid:** Amyl alcohol (heating from 75°F to 120°F) ### **Step 2: Shell/Tube Assignment** - **Viscosity, fouling, and pressure drop considerations:** - Typically, the fluid with the higher fouling tendency, higher viscosity, or higher allowable pressure drop goes through the tubes. - Given similar properties, it's often convenient to put the hot fluid (amyl acetate) through the **shell side** and the cold fluid (amyl alcohol) through the **tube side**. - Here, both pressure drops are the same, so either arrangement is possible. - **Recommendation:** Place the amyl alcohol (cold stream) in the tubes (easier cleaning if fouling) and amyl acetate in the shell. ### **Step 3: Initial Exchanger Type and Size** - **Type:** 1-shell pass, 2-tube pass (1-2 exchanger), floating head or U-tube type recommended for ease of cleaning. - **Tube size:** 3/4-inch OD, 16 BWG (standard) - **Tube length:** 12 ft (standard) - **Pitch:** 1 inch (square or triangular) - **Number of tubes:** To be determined - **Baffles:** Single segmental, 20-25% baffle cut --- # **Part (b): Rating Calculations** ## **Step 1: Energy Balance** **Heat lost by amyl acetate = Heat gained by amyl alcohol** Let’s calculate the duty and required flowrate of amyl alcohol. --- ### **1. Calculate Heat Duty (\( Q \))** #### **For Amyl Acetate (C₇H₁₄O₂):** - **Mass flowrate:** \( \dot{m}_A = 85,000 \) lb/h - **Inlet temp:** \( T_{A,in} = 175^\circ F \) - **Outlet temp:** \( T_{A,out} = 125^\circ F \) - **Specific heat (\( c_{pA} \))**: Let's estimate \( c_p \approx 0.5 \) Btu/lb·°F (typical for organics). \[ Q = \dot{m}_A \times c_{pA} \times (T_{A,in} - T_{A,out}) \] \[ Q = 85,000 \times 0.5 \times (175 - 125) = 85,000 \times 0.5 \times 50 = 85,000 \times 25 = 2,125,000 \text{ Btu/h} \] --- ### **2. Calculate Required Mass Flowrate of Amyl Alcohol** Let \(\dot{m}_B\) = mass flowrate of amyl alcohol - **Inlet:** 75°F - **Outlet:** 120°F - **\( c_{pB} \)**: Assume \( 0.6 \) Btu/lb·°F (alcohols are higher than esters). \[ Q = \dot{m}_B \times c_{pB} \times (T_{B,out} - T_{B,in}) \] \[ 2,125,000 = \dot{m}_B \times 0.6 \times (120-75) = \dot{m}_B \times 0.6 \times 45 = \dot{m}_B \times 27 \] \[ \dot{m}_B = \frac{2,125,000}{27} \approx 78,704 \text{ lb/h} \] --- ### **3. Flowrates in GPM** #### **Amyl Acetate:** - SG = 0.83 - Density (\( \rho \)) = 0.83 × 62.4 = **51.79 lb/ft³** - \( \dot{V}_A = \frac{85,000}{51.79 \times 60} = \frac{85,000}{3,107.4} \approx 27.36 \) ft³/h = \( \frac{27.36}{60} = 0.456 \) ft³/min ≈ **3.41 GPM** #### **Amyl Alcohol:** - SG = 0.81 - Density = 0.81 × 62.4 = **50.54 lb/ft³** - \( \dot{V}_B = \frac{78,704}{50.54 \times 60} = \frac{78,704}{3,032.4} \approx 25.95 \) ft³/h = \( \frac{25.95}{60} = 0.432 \) ft³/min ≈ **3.23 GPM** --- ### **4. LMTD Calculation (Counterflow)** \[ \Delta T_1 = T_{A,in} - T_{B,out} = 175 - 120 = 55^\circ F \] \[ \Delta T_2 = T_{A,out} - T_{B,in} = 125 - 75 = 50^\circ F \] \[ \Delta T_m = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)} \] \[ \Delta T_m = \frac{55 - 50}{\ln(55/50)} = \frac{5}{\ln(1.1)} = \frac{5}{0.0953} \approx 52.45^\circ F \] **For a 1-shell, 2-tube pass (approximate F correction factor = 0.95):** \[ \text{Corrected LMTD} = 0.95 \times 52.45 \approx 49.83^\circ F \] --- ### **5. Required Heat Transfer Area** Assume overall heat transfer coefficient (\( U \)): - For organics, shell-and-tube: \( U = 100 \) Btu/h·ft²·°F (conservative) \[ Q = U \times A \times \Delta T_m \] \[ A = \frac{Q}{U \times \Delta T_m} = \frac{2,125,000}{100 \times 49.83} = \frac{2,125,000}{4,983} \approx 426.7 \text{ ft}^2 \] --- ### **6. Tube Side Calculations** - **Standard tube:** 3/4" OD, 0.710" ID, 12 ft length **Surface area per tube** \( = \pi \times d_{o} \times L \) \[ A_{tube} = \pi \times 0.75 \text{ ft} \times 12 \text{ ft} = \pi \times 0.0625 \text{ ft} \times 12 = \pi \times 0.75 = 2.36 \text{ ft}^2 \text{ per tube} \] \[ N_{tubes} = \frac{426.7}{2.36} \approx 181 \text{ tubes} \] --- ### **7. Tube Passes** - For a compact exchanger, 2 tube passes are typical. - Number of tubes per pass = 181 / 2 = 90.5 ≈ 90 tubes per pass. --- ### **8. Tube Side Velocity** Check if velocity is reasonable (2–6 ft/s is typical). - **Tube flow area:** \( A_{flow} = N_{tubes/pass} \times \frac{\pi}{4} d_{i}^2 \) - \( d_{i} = 0.710 \) in = 0.0592 ft \[ A_{flow} = 90 \times \frac{\pi}{4} \times (0.0592)^2 \approx 90 \times 0.00275 = 0.247 \text{ ft}^2 \] - **Volumetric flowrate:** 3.23 GPM = 0.431 ft³/min = 0.00718 ft³/s \[ v = \frac{Q}{A_{flow}} = \frac{0.00718}{0.247} = 0.029 \text{ ft/s} \] This is **very low**. For good heat transfer, tube velocity should be at least 2 ft/s. --- ### **9. Adjust Tube Count** - The tube count is far too high for the flowrate. - Try using **fewer, shorter tubes** (e.g., 1 pass, 30 tubes, 6 ft length). - Recalculate area and tube velocity accordingly. --- ## **Summary of Initial Configuration** - **Type:** 1-2 Shell-and-Tube Heat Exchanger - **Shell Side (amyl acetate):** Inlet 175°F, Outlet 125°F, 85,000 lb/h, SG = 0.83, Max ΔP = 7 psi - **Tube Side (amyl alcohol):** Inlet 75°F, Outlet 120°F, 78,700 lb/h, SG = 0.81, Max ΔP = 7 psi - **Tubes:** 3/4" OD, 12 ft length, 2 passes, 181 tubes (initially, but needs adjustment) - **Area required:** 427 ft² - **U (est.):** 100 Btu/h·ft²·°F --- # **Part (c): Recommendations** - **Tube velocity is too low** (0.03 ft/s vs. 2 ft/s desired). - Therefore, use **fewer tubes** and/or **shorter tubes** to increase velocity. - **Possible actions:** - Reduce tube length to 6 ft. - Reduce tube count to ~30–40 tubes. - Increase number of passes to further increase velocity. - **Recalculate heat transfer area and pressure drop** for the new configuration. --- ## **Final Answers (Summary Table)** | Parameter | Initial Value | Comments / Recommendations | |--------------------------|-------------------|------------------------------------------| | Type | 1-2 S&T | Reasonable for this service | | Area required | 427 ft² | Based on energy balance | | No. of tubes | 181 | Too many for low flowrate | | Tube velocity | 0.03 ft/s | Too low; must increase | | Recommendation | Fewer tubes, | Use 1-pass, shorter tubes, or more passes| | | shorter tubes | | --- ## **Summary of Steps** 1. **Estimate heat duty and required area.** 2. **Select exchanger configuration and estimate tube count.** 3. **Check tube velocity.** 4. **If velocity too low, reduce tube count/length or increase passes.** 5. **Recalculate area and pressure drop.** 6. **Iterate until area, velocity, and pressure drop are all acceptable.** --- ## **Final Answers** ### **(a) Initial Configuration** - **1-shell, 2-tube pass shell-and-tube heat exchanger** - **Hot fluid (amyl acetate) in shell, cold fluid (amyl alcohol) in tubes** - **3/4" OD, 12 ft tubes, 181 tubes (initially)** - **427 ft² heat transfer area** ### **(b) Rating Calculations** - **Duty:** 2,125,000 Btu/hr - **LMTD:** 49.8°F (corrected) - **Area required:** 427 ft² - **Tube velocity:** 0.03 ft/s (too low) ### **(c) Recommendations** - **Reduce number of tubes (to ~30–40) or tube length (to 6 ft) to increase velocity.** - **Consider 1-pass or 4-pass configuration.** - **Recalculate area, tube velocity, and pressure drops for new configuration.** --- ### **If you want more detailed calculations for the revised configuration, please specify!**